Abandoning Equality

A Dissertation on the Primacy of Inequality in Results of Making Comparisons, Including Those About Social Justice and Fairness.



Author: Dr.9 Mattanaw, Christopher Matthew Cavanaugh, Retired

Interdisciplinarian with Immeasurable Intelligence. Lifetime Member of the High Intelligence Community.6

Former Chief Architect, Adobe Systems

Current President/Advisor, Social Architects and Economists International.



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This paper was originally planned for publication in 2016, but misgivings in the method of expression of various points which plainly contradict the common social worldview lead to my repeatedly wanting to verify my own perspective and think of alternative ways to make my same arguments more persuasively, or less provocatively. In my initial drafts however, I was also aware that people have very ambivalent views concerning their received views on equality, one moment thinking in a style that denies equality, while in another mode of thinking, taking it to be undeniable, and unquestionable. Very few people seemed to have a subtle perspective akin to my own, and I had the feeling that my audience was somewhat uniformly going to be against me. My desire to wait in order to write my opinions on the matter is unusual too. My website is much against self-restraint on sharing ideas, because my view is that quick sharing without much concern for editing and manner of expression tells more about how one really thinks. It also permits a thinker to share more in a lifetime and not less. My website plainly exemplifies this point of view as many of my postings do not have spell check, and have ideas that are very far from being completely worked out. However, for this article I wanted it to be much more carefully considered, to have a better chance that my audience would receive the message more favorably.

If there is anything I wish to convey to the reader it is this: The thesis of this paper is very well tested. I ask that the reader be as patient as possibl regardin the development of this topic, since later portions of the essay provide answers to questions that readers will have along the way. I expect the reader will disagree with certain early points, but will find that later clarifications will satisfy their concerns. A concern of mine while writing was that ordinary experience would reveal examples that could not be thought of on demand while sitting and writing. I did have many moments when sudden ideas came to mind that caused me some stress at thinking my thesis needed revision. However, careful reflection revealed that this was due to indoctrination, and initial inability to see how my thesis might relate more than superficially. Again and again, I thought about it carefully, and recovered my more careful and rational method of thought which did prove to show that the thesis really is solid, and apparently does not have exceptions.

Knowing that yet more potential objections in imagined counterexamples will arise in readers, I do welcome additional tests of the view. What I am wanting to convey to the reader, is that many tests have been conducted, and it will not be an easy task, to instantly contradict this position. It is much stronger position than might immediately be recognized. Particularly who one is in the traditional mindset that is accepting somewhat unreflectively of equality, and not those other mindsets where you would deny them. I’m not sure there are many people in the United States or in Western Democracies who do not have incompatible strongly held convictions about equality that go for and against received traditions.

This paper intends to clarify it by denying that the form of equality that is desired can exist, and that our mindset that shifts away from equality is the one that is closer to the truth of the matter.

The style of this paper is partly academic, and partly conversational. More conversational discussion will lead the reader into the topic, in a style more akin to what exists in popular works. Readers may be persuaded before the work proceeds to more technical discussion, in a more academic format, which provides increasing substantiation of what is stated earlier in the essay.

Some comments regarding literature review are desirable. This is a topic I’ve thought about and studied in a variety of contexts, some of which are abstruse and extremely complex. I am well aware, for example, of studies in mathematical logic which are intended to provide foundations for the concept of equality, in trying to define natural numbers, and basic arithmetic, using logic. I do not rely on these studies for direct reference, but have been informed by my experience regarding them. Logical Atomism and Number Theory are interesting subjects that illustrate that even equality as a concept in mathematics can be contended, and requires demonstration or proof. Work on this topic is slow and torturous, since very few are sufficiently technically able to develop upon earlier progressions. It includes the work of authors like Gottlob Frege, Alfred North Whitehead, Bertrand Russell, Guiseppe Peano, Kurt Gödel, Terence Tao and myself. I have other writings in progress which touch on this work more directly.

Definitions are especially important in this paper, and more than 15 scientific reference books for physics and mathematics were checked regarding definitions of equality. The finding was that each reference book assumed and did not define what equality was mathematically, trusting that the mathematical usage of equality was sufficient to convey what it was. If the reader searches among handbooks and encyclopedias of physics, chemistry, science, and mathematics, this observation will be confirmed; that equality is not defined for those who want to look it up in available books of reference. It seems this assumption is not unjustifiable, as equality is defined in a somewhat obscure area of mathematics and logic, and is not the main subject matter of the reference materials themselves, although one must wonder why entire fields would be uninterested on what justifies the concept, for their own knowledge if not for work related utility. The word equality in mathematics is so trusted that reference materials in the sciences and physics, and chemistry, do not define what it is. For this paper, we also do not need to define what equality is in mathematics and I will trust that all readers have been adequately exposed to the concept in their early educations. This will be sufficient to illustrate to the reader how political and social ideas about Equality7 really differ from the mathematical usage all have been exposed to, but also how it relies upon that mathematical usage to gain our unreflective confidence.


This paper discusses the thesis that the clearest treatment of human similarities and differences assumes propositions10 that are contrary to what has been assumed in equalitarian culture.4 These propositions include that people taken individually are unequal on almost any individual measure that is of interest regarding their traits, at high precision especially, but also often or usually even at low precision5. Taking people to be complex objects that are the complete combination of their measurable biology, they are clearly unequal as wholes, which are aggregates of individual measurable characteristics, causing doctors to provide separate and individual treatment to patients. Diversity is an expression of specific inequalities of traits, that are detectable by our sensory systems, upon comparison of one complex animal and another. Desire and concern for spreading welfare, and improving social justice, must use true propositions and not utilize false assumptions, in order to grow and develop, when that method of development is not contrary to knowledge, or is not manipulative. Phrases like “human equality” are too simplistic and do not state what is under comparison or what has been measured. It appears this is due to our history of advocacy using political slogans, and our marketing needs related to spreading social advocacy messages. It appears due to promotion of a political perspective using principles of advertising and marketing, which do not use complete statements, and does not rely on truth, but persuasion and repetition. Obstacles to clarity of knowledge on humans and their welfare needs, and social-justice systems, requires accurate and true knowledge; and growth is hoped to be scientific, on learning principles, and not principles of advertising for attention or simplistic political messaging. What is true in ideas relating to the desire for social welfare to be distributed more extensively and in better relation to real needs and diversity of traits need to be identified. One such truth is that all people were babies who were unable to control their nature and origins, and that this truth really does extend to all people universally. This idea was used, with a pretended application of mathematics, to claim that humans initially were not only babies, but were globally equal. To clarify how mathematics would be applied correctly using the truth that we were all babies, the author prepares the reader first, regarding what may and may not be considered equal on the basis of measurements, coming from mathematics. It is discussed that the authority that slogans had on human similarities were related to a borrowing of authority from mathematics. This borrowing is not justified where math is not applied. When applied correctly, it clarifies and does not diminish desire for spreading welfare among diverse people and situations. It is clarified when equality is found on earth. Pointers to additional reading from the present author are given for other developments on the same topic, where it is too involved or loosely related from the present article. It is found that inequality is an easy and expected thing to find, whereas, natural equality is not, particularly where complex objects are becoming understood in total.


Equality as a social and political movement, has borrowed the word “equal” from mathematics, in order to seem precise and true without reflection, but has not retained the clarity required to justify that borrowing. Because of this, our thinking about the social project for creating greater fairness and welfare has become vague and ambiguous, and mostly traditional, and not that innovative. “Human Equality” or “Equality” in capitalized form have both become a sort of collective assumption4. Everyone has some awareness in which they superficially agree concerning “Equality” but none can say with good specificity what it is. This can be contrasted with general education on elementary mathematics, in which the word “equality” is used with good clarity. There are historical relationships between Equality, in uppercase, which is how I’ll designate the socio-political movement towards fairness, and equality, in the lowercase, which I’ll designate as the word we are all familiar with from mathematics and the sciences. The capitalized version of the word equality really does use the word “equal” with certain purposes we will discuss, and really does within it have some commitment to something that is more approximately related to the mathematical meaning of the word, or a roughly mathematical meaning, which includes sameness, identity, equivalence, and even alternative usages which are quickly taken to be synonymous, like egalitarian, equitable, fair, and similar words, which really are not synonymous.

There are a variety of words which have similar meanings that are used in substitution for one another when one word feels like it has been overused in conversation, or when one used often is not quite fitting–but they don’t really mean quite the same things. For example, if “equal” is used too repetitively, or seems too strong, one may use instead equitable, or equivalent, and so on. Using equitable, one has used a word that is not quite synonymous, and sometimes it is an admission that there isn’t actually an equality but something close to equality. It is used as a substitute, but is also used to indicate less commitment to sameness in what is being communicated. Using words as a synonym for equal that mean instead “approximately equal” implies that there is some understanding that exacting equality in what is compared doesn’t really exist. There are other words often used similarly, like “balanced”, “proportional”, “congruous”, and many other words that the reader is likely able to think of, and remembers using.

Each of these terms that are used in alternation when talking about Equality7 as a socio-political project, except “just”, or “fair” really do have a usage which is stemming from mathematics or the sciences.6 In math class, we know that congruent, equivalence, equality, have similar meanings that are precise only in mathematics, but within math, the words fair and just are more seldom used.6 Within mathematics they are not substitutes for one another.5 The employment of these terms from mathematics is not accidental. There is an idea that fairness would have a balance of sorts and that a balance would have a mathematical computation which would reveal something close to equality. The “balance of justice” is a symbol which shows equal distribution of moneys which on a balance or scale would show parity (another word which roughly means equality. I will add them as more come to mind throughout the remainder of this article). Justness symbolically to us is illustrated in fair allocation of money, which does seem to have an expectation of mathematical equality. A fair two sided balancing scale will not be level if one side does not equal the other in measure of weight, if calculations are made at a level that is not too precise for the scale. If we wanted to go further than the precision of a scale, we would start to say that sufficient parity exists or sufficient equitability exists, if parties who are seeking a justness in financial allocation are not concerned about any additional level of precision, or they are willing to overlook more precision for being reasonable with each other as to the methods used.

There are many interactions in which this type of Equitability or Equality really is considered and felt to be just and fair. If one engages in a sales transaction with a business and purchases what is really wanted and desired at a price that feels fair given knowledge of the market, and methods employed at negotiation or arriving at a price, which may be fixed or predetermined, then both parties may really feel that a fair and even happy result was arrived at. There can be great pleasantness at arriving at an equitable deal.

However, in our social customs in conversation and discourse in the media and with one another on very many other topics which are much more ambiguous, we still employ those same concepts that are better used in areas where some precision is possible. In these areas, we become much more inexact in our language, and somewhat ambiguous, and sometimes unfortunately, even largely meaningless, as I will later show. This more poor usage relates to our use to the capitalized Equality, or phrase “human equality”, with specific things missing which would otherwise give clarity to the conversation, which exist in other experiences which really do make such words more accurately usable.

When we say Equality, and I was guilty of this error for a long time, because I was conforming to popular usage, we do not really state what it is that is under consideration. If I say this to someone in public, I would anticipate though, a quick response: “Well, you are supposed to already know what that means and what is under consideration.” I know that though, and that is why here I have taken the step to capitalize it. Conversation cannot go further to show what is really erroneous in this way of thinking, if I cannot take steps though, to show that certain omissions need to be revealed to provide a more clear understanding that this is not a way of speaking that provides the same confidence and clarity as the symbol of the balance and finding of equality in transactions which really do allow for accuracy. If this Equality is challenged, what people will begin to want to react with are assumptions about your worldview which are false. They will want to say that you don’t believe in fairness, or justness. That you don’t believe that an improved equitability of sorts in human comparisons is not beneficial. But they would say this while missing that you really do, and you are thinking about this, perhaps like me, because you want to fix something that would block us from going further in that direction. The conversation has to go further than these obstacles in order to clearly communicate what must be improved and what errors might exist, and these initial objections are really hard to get past, because people really do begin to think that you might be somehow aggressively against them, while fascinatingly, knowing what is wrong with Equality really might mean that you are more for them than they would realize, thinking the way they are thinking. It is really unfortunate that conversations might end on this type of objection.

I wish to get into this topic faster to get to the details, but one more obstacle to a more complete analysis must be shared. And that’s that early thinkers, and originators of political documents, and now debunked political philosophies, have been sloppy with their usage of their marketing slogans on social fairness and justness, and that is one reason why we are in a predicament around capitalized Equality. We have treated certain documents as authorities on this, and have been raised on equality being axiomatic and self-evident, and the like. In the Declaration of Independence of the United States we hear things like “we take these truths to be self-evident” which again relates social justice to mathematics. The non-mathematician may not be aware that using the word “self-evident” is really another way to borrow precision from mathematics. Some statements in mathematical proofs are taken to be intuitively axiomatic or self-evident, in that they are logically irrefutable or simple in their veracity. It’s another way of saying “No mathematician would seriously challenge these logical transitions, or these simple statements.” However, social theorists like Thomas Jefferson have utilized these same words and constructions in settings where they are not admissible. The purpose of this usage is to give the reader the impression that such statements cannot be contradicted. And in a statement to an adversary saying “we hold these truths to be self-evident” is like saying “there really is no conversation to be had any longer on this topic.” For the present conversation, some have really been raised to believe vague and ambiguous ideas about Equality outside any context which permits of high accuracy are still, nevertheless, to be accepted as self-evident or axiomatic, forgetting that with decreased clarity of situation and applicability of terms, the meaningfulness of the statements and the concepts begin to erode. This is very opposite to the intention of self-evidence and axiomaticity in mathematics, and in these situations, the mathematical certainty cannot be borrowed. There really is a point in which Equality is something that should be separated in one’s mind, from precision and math, and trust. Equality really can be used in a way that is not trustworthy.

Here we come to an uncomfortable conclusion though:

“But we have the word equal within Equality.”

Which is very uncomfortable. It implies that as we use the word Equality outside of an area where there is precision, we are still using a word that is very closely connected with mathematics, and trust, and we are at risk of being deceived. We are at risk of thinking that wherever the word equal is used, something has been proven. However, mathematicians are aware that work must be shown to be accurate to demonstrate that equality has been arrived at, using the correct mathematical methods and rules of logic.

I would like to be able to convey to the reader that our predicament on this is not yet worse.

Equality in math is taken as an axiom in math, which really does mean that of anything that can be tainted in math, this is what ought not be blemished.

We will in this paper explore the mathematical concept of equality, and we will arise at the conclusion, that people have not striven to define it. It is precisely one of those areas where self-evidence is employed. It may even be one of the few areas where we can understand what an axiom and self-evidence really is.

In this paper I will strive to clarify what is happening here, and how we can move forward. I will uncover some points which I think will reveal that we will be in social discomforts for a long time, to recover from an erroneous way of thinking, an to eventually stumble and arrive at a more clear way of thinking and talking on this topic. But more importantly I will provide what is also a satisfying and contenting answer, which should allow us to more precisely create fairness and social justness, on a way of thinking that gets past some obstacles like these which I pointed out earlier.

Babies, Zygotes and Equality

There was a period in American and British thinking, certainly not exclusive in ingenuity to what others have done in human history, but seemingly new and somewhat unprecedented in political formation and legal recordings, which focused on what was called “tabula rasa” psychology, or the psychology that people become what they are based on experience and begin roughly as unlearned things ready to absorb experience.

Part of this perspective is one that is instrumental to conveying why it is important to provide welfare to those who were born without any experience, like yourself, and myself, but did not receive much opportunity for experience, or certain physiological advantages. There is another part of this view, that is unhelpful and works against the objectives to establish welfare, even when there may be positive intent. This idea that we were all inexperienced babies, placed on earth in a strage time and place, each of us in differing places, with differing bodies, and growth pathways, is useful for conveying what has been in our control and not, but the idea has been overextended by political thinkers to imply more than it does, namely that Equality exists. We can clarify our views on morality and politics by separating what is useful in this perspective from what is not; what has been beneficial to us in this idea, from what has not been beneficial.

Here let’s focus on some propositions which appear to be true regarding this idea that people were all babies initially without certain important types of life-controls:

  • Everyone was a baby.
  • All learning animals were babies.
  • A baby animal will absorb information from its environment, including biases and cultural information.
  • Babies are interchangeable regarding relevant types of powerlessness and non-control.
  • Who we are is largely not in our control.12
  • A zygote and infant’s ability to self-modify it’s own physiology is measurable, and appears to be negligible, even without performing measurements.
  • A person’s ability to self-modify during its lifetime appears measurable, and appears to be greater than those of a zygote or baby’s, but just as negligible regarding control of preconditions.
  • All animals die, and have a clear beginning and end to their life-cycles.

Taking each one at a time, let’s see some details about each proposition.

All people really do have a baby-beginning, which means that we have one really interesting universal piece of information applicable to all people. This may be one of the most significant and underutilized fact about life, which does support much that is desired in sharing welfare amongst all or most people, and animals. The idea is that no person has any creation related credit for their own bodies and minds, and position in life, and initial trajectory for learning. Who you start out as, and who you become, is mostly out of your control. It is mostly outside of anyone’s control. Moreover, babies really do have capacities to learn similarly, having similar brains, and similar ways of interacting with the world; particularly if they are of the same species. We learn the same languages, and successfully communicate. We really do have a similar readiness to receive knowledge, and this is shown by the results and assumptions of our education systems. Knowing that people are similar in this way, and that there is little merit in original receiving of genetics, and of placement in a particular region, and of early upbringing, and trajectory of life, if one is in a really good position in life, one begins to wonder, if one is caring, how to care for others who did not have any demerit, which would make them have less. Everyone was a baby, so why would we not want to provide care and concern, to others who have really terrible situations at the least. Personally, I think we should be willing to care for more than those in the most terrible situations, but observing the world, it appears we have not done much for the people who are worst off.

Any baby can be made to conform to any nationalism. We anticipate, and expect, that if a baby is born in a specific region, that they will acquire the views of the nation that claims ownership that land-region. An implication is that you are of your own nation, because you were born in a particular region. If a baby is transported to another nation at birth, they will receive the knowledge, customs, and assumptions and biases of that nation, and not another. However, it is understood, that by moving any new baby to any new country, that baby will absorb that nation, and the primary cause of that would be their being transported to a region and left there to grow.

People are interchangeable with respect to their original life controls. I could be someone else instead" is a thought that relates to this observation. Combined with the prior point, if your identical twin is placed in another nation, they will really become someone different from you (babies have no knowledge and absorb what is in their environment), and they will have potentially much less resources and potential happiness, if that nation is not well developed. The idea here is that this person really has nearly identical genetic code to you, but not living beside you where it would appear in time that they were really as similar to you as something could be, they were transported to a place, where maybe they age and die early. Knowing this person was just like you, it is odd to not be concerned about welfare, if one claims also to be working on welfare. Other people, being only more dissimilar to you by matter of degree, still were babies, and still also did not choose or merit living in any one nation or another. Living in that nation, they may age and die early, and in similar ways, perhaps to your identical twin!

Who we are is largely predetermined.12First you were a baby of a certain genetic heritage, located in a particular region, where there were certain customs, and a dominant language, and you were steered by adults to certain information. You were present to absorb from your parents, and from messages in your surroundings. Your comforts were gradually related to your nation, in the type of foods, the appearances of surroundings, and in your understanding of verbal speech. You could not understand the languages of other nations. Growing older, you acquired the mental abilities, formed in this setting, with properties related to the setting, combined with your genetics, to make periodic decisions. Throughout your days, you did many behaviors automatically. You walked along to classes, looked around without reflecting how to manage your neck, and you became attracted to objects according to your animal nature. Within this way of behaving, sometimes you would make selections, between what you could imagine were options, and what options may have been put in front of you. It already must be admitted, you do this only periodically. You sit and sleep and act mostly without actively deciding; when you do decide, you decide on options and mind that was already prepared for you. This means even when you are being you, deciding things for which you’d like credit, and some praise, you are still already relying greatly, mostly, on what was already there, and this traces back to when you were a baby, when you could take no credit at all, for your surroundings and your body and head. Reflecting now, that this is the case for everyone else who exists, it seems that welfare is not something people could make for themselves, or deprive themselves of; minds already formed, periodically making decisions, that create or decrease welfare, are still doing what they do, based on what was provided before, and what exists in their thinking abilities, and manner of thinking related to language and region. The implication is even people who seem to harm themselves are not really to be thought of as being in control of harming themselves as much as people imagine makes it something they deserve. Likewise, making good decisions on the basis of mind and situation generated from history, does not mean that one merits good things, as much as they might want to think they do. There is room for merit and demerit but this is not the location to discuss that point. That will be discussed elsewhere in another article.

A zygote and infant’s ability to self-modify it’s own physiology is measurable, but we do not expect that they would have much control even if we measured it. It is uninteresting to measure an infants ability to self control. We can measure our abilities to control our physiological compositions at conception, and up through birth, and we would find that we have very minimal abilities to self-define. We measurably have no ability to control what has preceded our lives too. Our abilities to self-define our physiological compositions includes our instructional information for growth and our compositions later in life. At time of birth, and in utero, humans really have what can be summarized as nearly zero influence on their own physiology, excluding what a baby in utero changes on its decisions regarding its own behavior, which result in differences even in utero. However, we consider that to be negligible or due to physiological conditions which already preexisted or due to an interaction between predecided growth rules and the environment. The observation that we were all babies, and that we had very little influence on our environments, has lead us to mutually conclude that really it seems we had no influence. If measured it appears our influence is nearly zero, although work on this will reveal it is not exactly zero, for the many various ways we can self-influence even in utero. The following propositions seem truthful. All humans had zero, on all measurements of influence and power, to control events before birth that were relevant to creation of physiology, including growth instructions within physiology, that would control growth and composition that they would later have.

A person’s ability to self-modify during its lifetime appears measurable, and appears to be greater than those of a zygote or baby’s, but just as negligible regarding control of preconditions. Simply by getting older, one does not incdrease the influence one did not have when one was a zygote or baby, for those periods of time before, and during, that time of being a baby or zygote. This is equivalent to stating that there is an inability to alter one’s past, and conditions before one was born. Humans seem to have a tendency to observe the controls they presently have (which also appear to be not that powerful), back in time to earlier dates in their lives. In other words, a successful business man will come to believe that certain decisions or acts somehow increase power of self-alteration before those powers existed. Since zygotes and babies appear to have little influence on their conditions and preconditions, one can notice then that growth and development along life would seem to increase powers in a way that appears predictable. This means the growth of powers from greater powerlessness to more power in life appear measurable. If a baby has negligible power, then shortly after being a baby, it would appear that power would be negligible or nearly negligible. It is a task of science to eventually arive at a clear description of when it becomes less negligible in anyone’s life, and for some lives certainly it remains negligible on certain measures.13. These considerations provide us reasons for having similar thoughts about the conditions of life that people have when they are older, and not only when they were babies. We can see, for example, that even though people appear to have various powers of self influence, we know that environments and history will influence people in such a way that they will seem to be harmed even if it appears that they may have certain powers to control their situations. Viewed in retrospect, alcoholics and drug abusers often had conditions and physiologies that trended them towards their life situations, such that we start to think that there are interchangeabilities of adults with respect to controls. To give another example, if one is born into an aboriginal family in poverty, and becomes an alcoholic later, one might observe, that a baby put into an aboriginal family in poverty, from elsewhere, would likely have similar conditions and potentially may also be alcoholic later. This means there are interchangeabilities in the babies, but also interchangabilities in the adults relating to those other interchangeabilities of babies. Adoption studies seem to confirm that babies will make people like others in their environments as adults and not only as babies, in that if a person from one culture is moved to another, they will resemble people in that culture later, even as adults, and not only as children.14.

  • All humans, had negligible influence, that cause us to want to say zero influence, at conception up to the time of birth, regarding their physiology, including growth instructions within physiology, that would control growth and composition later in life, including traits of brain size, and various properties of the brain that are not under influence of decisions by the brain.

These specific measures, used for all people, imply that there are some equalities of interest that are very narrow, but universal among human animals. In this discussion, it is important to notice these equalities are specific to what is measured, and not what has not been measured. An additional proposition may be added:

  • None of the properties of babies themselves, or resulting people, along their life cycles, have been yet measured.
  • No other measurements have been taken regarding the properties of the people themselves, including millions and billions of physical properties about their compositions.

From this we can infer (and we could use formal logic to do so, but here will proceed informally):

  • We have not aggregated individual measurements sufficient to consider equality of babies as complex objects.

This simply means we have insufficient measures to make an inference about babies compared in total, or people compared in total along their life cycles. However, we this does not mean we do not have something important. Namely, we have found that people seem to have zero power to control their own compositions, including brain compositions and growth instructions, before birth (we can’t influence earlier in timelater, and, nearly zero influence during development in utero.

If we were each measured on our abilities to control our initial creation, it would be that we have no control at all. We would all be measured to be powerless on our origin stories. We cannot influence how our parents met and who are parents would be, and where they would be on Earth. This does not mean that we are equal on all measures, but just that very important measure. That very important measure is one that is truthful and honest, and applies to everyone, and has great implications for our lives, and for who is really deserving of what, since it appears people can deserve very little, that harms or benefits them.

Democratic nations have utilized a more vague version of this more accurate and detailed fact, that we were all babies with measurably zero influence about our composition early at life, and our early life situations, to incorrectly further infer that we are totally equal in value. In historical documents, like the Declaration of Independence, we see “…we were all created equal…” which appears close to what we accept as true above. When many of us reflect on this idea, that we were all babies initially, powerless to define our physiological compositions, and who we are, and where we were, and what time we were born, and period of hisotry, we come to want to alleviate some problems in some lives that were especially difficult. Since none conrolled the starting point, and many suffered because of their starts, we think things like “what if my start was as difficult as theirs?” There can be no merit or demerit in any starts that anyone had because we did not control the events. People do not deserve to be harmed, we think, if they had no control at all. Likewise, we see that we did not deserve to have special benefits, if we did not have any measurable control of our situations. However, we know the reality is that situations and initial conditions, including initial physiological compositions and growth instructions, really do result in either really good benefits, or some serious detriments, or in many situations, basic or mundane conditions. Some will starve, some will be fed, and some will live in opulent luxury, and all without any control over initial conditions and many important conditions which determine later conditions (physiological composition and physiological growth instructions).

and measurably and equally had no control over our initial starts, an inaccurate view, very vague, that we somehow each of us are totally equal, on all measures. We have started to talk of equalities without doing any comparisons at all, and have started to think that mature adults are equal irrespective of traits and resulting outcomes. Simplicity of expression in marketing, saying things like “Human equality” without stating what that equality is about, has resulted in various successful projects for expanding welfare. There were side effects to this simplicity of thinking and marketing, and of growing from a germ idea that was true, to other ideas that were untrue.

Marketing and advertising, including catchy slogans, and attractive short messages that are easy to remember, are vital for spreading social and political projects. Nowadays, if we want to spread a social message, we might convey it briefly using social networks, including some that only allow a very small number of characters to say things (one requires 255 characters or less). In capitalistic countries, advertising is a form of entertainment, and punchy, provocative, and fun expressions are more likely to create successful efforts. Methods of advertising trace back to propaganda, and other early methods of gaining attention and sales, through the history of our nations, back to early times. It relates to persuasion with limited time and attention of an audience. It relates to creating attention quickly where there isn’t any. In order to convince others that a movement of Equality is needed, and that equalitarian culture is desirable, marketing methods are necessary. This means we can anticipate consequences to these methods of marketing. Primarily, they are short and unclear, and do not rely on rationality and good quality of logical thinking to convince. Instead, what is mostly desired is that people will attend, hear the message, and remember it. They hope that it will influence minds and perhaps result in gossip, and conversation. If marketing results in conversation it is often very successful, because not only was a message attended to, more were created. Equality and equalitarian culture were slowly popularized using short messages, in news, and other sources of messages. News is a form of advertisement although that is not readily recognized. Short headlines and short news messages convey quickly in a similar methodology to plain advertisements, which also are found in news sources. News influences what gets advertised, and it is hoped that what gets advertised becomes real news. Any way to copy messages to create more is important in the toolkit of the message spreader, whatever their medium happens to be. What is important to convey here, is that the Equality project7 has been in the news, has been advocated by politicians briefly using propaganda, marketing and advertising techniques, and so on, and has utilized short messages, that were intended above other considerations to be persuasive, and result in proliferation of new messages by others for free. The goal is to use less effort to get others to repeat messages. If everyone is talking about Equality and the benefits of equalitarian culture, then success is more likely. If no one is talking about it, then even if the initial messages were costly, and rational, then there is likely not going to be success. It means minds have not been thinking about it.

The Equality movement7 in our history has been detrimented by the methods of marketing it has relied upon for its own success. This means that its tools that it needed to become a success has aresulted in side effects that are not beneficial. This was likely known to some original figures important for early spread. People tend to like to use true statements to persuade and not merely persuasive statements. However, companies and politicians know they have to be catchy and inevitably utilize what will be persuasive for ensuring their success, because their efforts are costly. This means it is known there will be side effects to the same work that results in progress. Some may use the phrase “collateral damage” to explain this kind of phenomena. If I want an Equality movement to succeed, because I know it means some people will be living much better lives, I will be willing, perhaps, to sacrifice that some persuasion was not due to rational thinking, or that short messages may result in less detailed worldviews. My main mission is to make people feel better, perhaps for the very long distant future, and for now, I’m willing to persuade with messages, that I am not entirely satisfied with, because of how short those messages are, or what happens to be catchy to the audience.

There have been many side effects to these efforts which resulted in a style of thinking that is too simplistic. This style of simplistic thinking, having a long history, is now traditional, and certain old pieces of propaganda still surface during holdiays, or voting events, or times when people are narrowly thinking about what has been beneficial in equalitarian culture. While thinking about civil rights movements, I will be less in thought about competition, and more about shared welfare, and objectives about making sure people have their basic needs addressed. Instead people are in a celbratory mode of thinking. The marketing and propaganda, and way of popularizing a larger equality has resulted in a lack of clarity of what is really true in human similarities and differences, and unfortunately because this was a method of popularization with slogans, it truly became popular. What is popular is the simplicity and vagueness of expression, but not the clarity on the key facts which are useful to making welfare something we can improve on. Development on this idea requires increasing precision, and by getting our details right, we will have a better chance of a more mature and developed social justice and distribution of welfare that was closer to the intentions of people who were focusing on “tabula rasa” and a morality taking our origins as babies unable to influence our own being as an important fact.

Vagueness and Equality

Words like equality, in mathematics, have a special place regarding expectation of precision, which comes from a long history of interdisciplinary accomplishments, using methods of proof which appear among the best that humans have been able to arrive at. If trust we have in mathematics is to be borrowed for alternative usage, for political purposes, by politicians and others advancing politics, it must explain why the trust should be extended to their purposes, and the usage must be clear and unvague, carrying over precision which existed in mathematics. Political conversation is not mathematics. Globally humans have arrived at an appreciation for math, and many groups of people have made contributions to what is now the total works that comprise mathematics as a whole. Equality, the movement coming from equalitarian culture, borrows this word that has special precision, but does not itself utilize the same mathematical methods which have been trusted; instead, it borrows the word to create a feeling of trust that exists in mathematics, for other purposes related to development of justice, wherever it has been honest in its intentions. In my thinking, if the word equality is utilized, its employment must be mathematical, or else it’s borrowing must be justified. Particularly if it is going to inherit special status that has been created in mathematics, but not where it will be employed. Equalitarian culture, if pressed to explain the relationship of Equality with equality, has difficulty making the coneection; it is unable to explain what is mathematical about the Equality which is a vision of sorts, regarding social justice. If people are asked to explain Equality, they begin to speak with vagueness. Explanations become ambiguous. Ambiguity is not something that is allowed in mathematics regarding equality, and for this reason there must be a very good explanation for borrowing the word, otherwise damage to mathematics itself is being done. There is an erosion on an understanding of what makes equality special, and mostly trustworthy without criticism. In my own thinking I will not permit a concept to have a special status, like Equality, if I cannot very precisely explain its meaning, without vagueness. I will show various reasons why Equality is too vague, and this will explain why I cannot give it a special status.

For the purposes of this article I will go along with our trust in mathematics and assume that the concept of equality is really as trustworthy as other mathematicians have assumed. I will not here be questioning word equality as it is used in mathematics, although I do and will elsewhere, in other writings onmathematics. Because the trust in equality is so strong in mathematics, people will overlook that although equality has been extremely useful, there are issues with its definition, and manner of usage, even within math. I do not consider the concept of equality to be one that is sacrosanct even within mathematics and the sciences, and in my other writings on mathematics, and works in progress, I challenge even our very basic idea of mathematical equality, so even this concept is not something that one cannot strive to understand in greater detail, and make criticisms and find issues regarding. However, for now I will share that the mathematical idea of equality really does, to me, have a level of precision that is the cause for our wanting to utilize it elsewhere. We have inherited an error, however, in that it cannot be borrowed as frequently and in as many ways as we have borrowed it, wherever we have been outside of mathematics and in discussions that are imprecise.

Now recognizing that equality really is considered special because of our usage within the disciplines of mathematics and the sciences, and in everyday uses which seem confirmed again and again, we can now turn our attention to its usage in social life. Especially in politics, and the advancement of political agendas, like Equality. One might ask:

“Outside of math, in our use of Equality, in social life, how have we been vague and ambiguous?”

For this let us recognize that people are not uniformly in agreement regarding politics, and in our own conversations regarding equality, we should be able to recall differences of opinion. Notice that in social life, and in politics, we are in a party system in which one group typically opposes another regarding political views. We can expect, that people really will have differing views about what Equality is and what implications about it are. In practice we do expect and anticipate that what people may think about equality will vary, and we cannot expect that people will be in agreement about what Equality is in particular and what its details are. Also, I want to revisit that I mentioned that the reader in many contexts really does disagree about certain social uses of the word “equal”. I bring this up to prepare the reader not to be too disagreeable concerning areas in which we’ve come to assume that Equality is clear and not vague, by mentioning that, really there are many occasions in which we don’t agree on social equality, and in many ways we don’t even want it.

Sometimes people are forgetful about other parts of life in which equality is not something that is assumed, but rather, inequality is what is assumed and expected, like in competitive situations, like sports, education, and work. In competition, we want to see and experience the very best examples of human ability. In our rewards of other people, and in our expectation on receiving rewards, we have an idea that there can be very large differences between people, that call for very different rewards. We celebrate certain great successes in business and are often unconcerned about how business people are rewarded. We celebrate athleticism and amazing productions of art and entertainment, and seem to want to praise and provide better lives to those who seem to enrich our lives by their excellences. Here it is very clear that what we don’t want is human equality. We want to experience something different, unique traits that are awesome and powerful and surprising. We want to be entertained by uniqueness. We celebrate the greatnesses that are only possible with diversities. We want to see all the differences that people have in all their traits. We are aware that many really do have weaknesses and traits that we do not desire by comparison, and that contrasts can be very large. We celebrate the special olympics through examples of highest physical achievement, pairing olympic gold medalists in regular olympic games with those of the special olympics. We want to see great traits expressed even in people who have other traits we do not find desirable, and even consider, in private moments, to be really unfortunate or even disastrous. We want to see our children born with beauties exceeding the beauties of others. We do not want to see that they are malformed, or that they will have serious deficiencies, which may affect their minds, and quality of life in the key traits which we use to demarcate human life from the lives of our other non-human animal relatives. We prefer being humans over what other life nature shows us.

If we consider that we really do see diversity in life, and that we value excellences, and disklike greatly certain unexcellences, we really can see we want certain kinds of inequalities. We want to experience the beauties of excellences and notice differences from unexcellences. Also, we want to reward those who are virtuous and display good characteristics and actions, but we want to punish or not reward those who exhibit traits we dislike and abhor. We even want to ignore or overlook things which are more plain and mundane in our environments as “nothing special” or as undeserving of praise or lingering attention. In many ways I think it is irrefutable that we really do often see that people are unequal, if we are to do real comparisons, and not only that, we don’t want to be equal on those comparisons. This is why I think sometimes we are really uncomfortable on the topic of equality. I think some may be like me, feeling unable to share, that really there is something not quite right in our socially received view of Equality, and that this is because on one side we really do want people to have enjoyable and rewarding lives, whatever their differences happen to be, and that we really do like people who are different from us, and want to allocate our care and concern for others somewhat apart from our knowing everyone is different, while simultaneously wanting to reward certain excellences greatly. What has not yet been considered here, is that we also want to take away and punish people, and not reward, traits which we happen to dislike, which may nevertheless be natural, and part the full diverse expression of human traits.

People do not appear to want to maintain in all situations their belief in Equality. Rather, there are times in which they want to repeat traditional ways of thinking, and maybe celebrate cultural attainments which relate. However, there are numerous situations in which they will transition to another way of thinking which values diversity and inequalities. I don’t think people can on all occasions in which social justice comes up, always utilize the same ideas that exist in Equality. People will alternate positions depending on the context. If it is about sports, people will suddenly forget equalitarian culture. If it is about national competitions, including conversation about warfare, they will forget equalitarian cutlure and will side typically with advancing their own cultures survival or dominance. If people are talking at work about who gets promoted and who does not, they will not want to focus on the Equalities which might result in a drive to keep people at the same level of pay and title. Instead, they will move to a more competitive mindset, and think it unfair if one cannot advance, or does not advance according the interpersonal differences, which means diversities, and inequalities.

There is also a very strong belief that people ought to self improve. People enjoy learning, and making themselves feel stronger, smarter, more moral, and more viruous. It has been overlooked, I have found in my conversations since I was a teen, that self improvement implies that one has become better than one was. Some are so satisfied with their results of their work on themselves over years, that they would even complain about who they once were, thinking themselves much less than what they’ve become. This is greatly at odds with the views of Equality, since one already believes that one can be quite dissimilar in value to oneself over time. If one is better after making self improvements, then anyone who was similar to the former self, than the later self, will be considered someone who is not as high in value. One makes social comparisons to verify that one’s self-improvements seem to mean that one has improved. “Before, I was like these other people, in these various ways. But now, I’m much better than I was, and much better than they are also.”

Social comparisons imply that one is seeking to find differences that relate to relative value differences. In competitions relating to sexuality, and appearance, and ability approval and disapproval in others, one can see again that people do not really want Equality. Again, they want attractive mates, mates that are powerful and strong (if women), and want people who are not average, or below average, as much as those who are excellent and display many virtues, and good traits. Furthermore, this is not something people are showing a trend that they do not want it; instead, there is, and has been in all history, a trend that people really want this to remain. Changing sexuality and inclinations regarding attractiveness to be more harmonious with Equality does not seem a goal people have. Instead, people are seeking out what appears special, more beautiful, more compatible with their aesthetic preferences. They are highly interested in somethings while they exclude all others. They must choose a single partner, and not have many, and they really do wish their partner is one that is perhaps, better than they can even have for themselves. This does cause people to recognize that the traits they have may not be as valuable as the traits others really do have, that they may really want for themselves, and choose if they had the ability to. In life they did not have such a choice at the outset. In the future, it may really become possible for people to choose their traits to a greater extent, and given easy options, they will make those choices indicating they do not think what they could be is equal with what they are before making a choice. People really do have the ability to select some traits but with difficulty if it is something durable. For example, men will want to be more athletic, stonger, and show better musculature. If it seems reasonably within reach, people will work hard to have it. However, there are examples in which it was attained even with very laborious efforts, particularly in bodybuilding, by people who looked and behaved very differently earlier than later. Bodybuilders would not agree that their fomer selves are as valuable as their later selves. The many fans, followers, and learners that give them attention indicate that they do not value themselves as much as the bodybuilders, in many ways, and that if they attained similar appearances, they would be much better than they are.

Returning to work life, we can see also that we value those who have advanced very far, and if we are women we include that in our appraisal of them as good candidates for mating and for relationships. While at work, we want to be rewarded if we show certain traits and progressions ourselves, which seem akin to those already existing in others who have advanced, and are supposedly successful on their merits. Those who are successful on their merits are greatly interested in creating an appearance that it really was from their merits, to exhibit their attainment of greater value in a way that is agreeable to workers. It seems really clear that in work life, we think people merit advancement on their self improvements. When someone learns, and performs well, and increases knowledge and productivity, and succcess, they are better and not equal to their earlier selves, in ways that are plainly measurable. When you finish your education, and your career, you really are measurably an improvement from your earlier self. On these areas where you have merits and excellences that are rewarded, you also think you have benefits, and advantages, and measurable qualities, that since they are better than they were, for you, are certainly better than everyone else, where they are in the same position you were. A doctor will consider themselves to be an advancement on when they weren’t doctors and measurably better in various ways, than those starting out in the same level of ignorance, and readiness for improvement. There isn’t any reason to pretend that finishing is equal to starting, on all those points where finishing was suppose to be a development goal.

Earlier I have stated that my perspective regarding the present topic is one that is well tested. I really have thought about what might challenge this point of view in real life, where we often find counterexamples to views we thought were global. Our views are tested by the diversity of experience in real life which cannot be tested in any other way. In our minds, we try to survey all scenarios, but in practice do occasionally recognize contradictions and incompatibilities, sometimes in views we think are good, and are solid. I have taken special effort to ensure that years of life experience tested this view because I know it is one that is considered, on tradition, one that is sufficiently compared to the variety of experiences we all have. For this reason I have been careful to compare it with other parts of life that do not really usually bring to mind equalitarian culture, like sporting events, nationalistic pride and celebrations of military victory, work life which appears less democratic, our love of good entertainment and entertainers, our sexuality and values concerning attractiveness and desirability of mates, and competition more generally. Surveying life, and my own experiences, I have found that we are largely ambivalent in our views about Equality, and we really do value inequalities in one type of context, which is competitive, and switch to another type of view, when the context involves political agendas, and involves celebrations about what has been achieved by certain political movements. One is in favor of diversity and the other is in favor of Equality.

These two types of thinking explain why people alternate in worldview in different situations, and why they may occasionally become annoyed about the topic. I think the reader may begin to alternate in mind between thinking that people are Equal in some way that is more vague and ambiguous, but social, relating to justice, but will also think, in a work and competitive context, that they are better in various ways. I would like the reader to reflect that truly, in the area that is competitive, there truly is something to this view, that the reader has adopted a position, that will arise in mind over and over again, that is against human equality and more in favor of diversity. I hope the reader can admit, that when they are feeling advantages they have, in a competitive context, they are thinking they have a betterness, which is measured by the competition, that relates to diverse allocation of traits. In other words, reflect on how you can win and perhaps become a winner, without having some trait allocation which others have not benefited from. You are an expression of diversity and you have a benefit of an inequality which favors you in competitive measures.

Winning, over time, implies having special skills or traits that resulted in frequent victories. You cannot win in chess over and over, or wrestling, or in beauty competitions, without having something others didn’t have, which are measured to be unequal when one has become a winner, or champion. Also notice, that for any champions which exist in the world, there are many who you could never be like, because you have forever not been given those traits and advantages, and results of work, which they have gotten. You are measurably and in many ways less, on specific measures, on specific activities, in which others excel. This should be an easy admission. I have many advantages but I am not at all endowed to compete as a pro basketball player in the position of center.

There is clarity about a desirableness of inequality when thinking about competitions like sports, and thinking more carefully about our experiences enjoying sports as spectators, and as athletes, we can come to a more subtle understanding about what we value about inequality, and about how that contrasts with Equality. Stats and performance and a simple view of athletes shows us clearly where measurable difference exist. Our view about diversity is not challenged by sports, and we feel nice reflecting on humans strengths which others do not have, and we are willing to reward some more than others, and think it just, within tolerances. In sports some are quite enthusiastic about measurement. The very best athletes are compared on their metrics and their data which we call stats. We use the measures of these players, which might be pretty exacting, to try to compare them to see who is really ultimately and totally best at their particular sport. We want to “total” the measures, and complete the measurement as to who might be finally considered the most unequal of all, or that which is most excellent and greatest. This is something we enjoy and don’t consider to be greatly at odds with our worldview.

The personal life of an athlete, however, is treated more in the politial sphere than it is within sporting discussion regarding measurable skills and accomplishments. As soon as the personal lives of athletes comes into view, and touches on moral discussion, we do become more sensitive about wanting to allocate cares in ways that do not simply relate to their rewards as being measurably better athletes. Think of athletes who have been accused of crimes, or even athletes who have been accused of infidelity. This is where vagueness creeps into the topic, which seems to come from uppercase Equality, and it happens in many different ways, which are not easy to anticipate, but are routinely in areas where clarity of measure does not exist in a way which resembles the clarity of comparison within the sporting context. Clarity is more obvious when thinkin about measurable differences in sports, and what is seen in their performances in sporting competitions, and there is less clarity, when this is intermixed with personal lives, and moral or political ways of thinking.

Let us consider an example in which an athelete is accused of an actual legal or moral transgression. We will invent an example so we are not dwelling on common examples involving real athletes which we certainly have heard of many times2 Suppose an athlete is accused of transgressing some social rule and perhaps a family member of that athlete has been harmed. In that situation we begin to think that the other person is unfortunate, and we would like their fortune to be better, and we would like to give them care and concern which might bring their situation to one that feels just, so they are doing well again. Their wellness, and our wellness, thinking ourselves harmed by witnessing injustice, might also be improved, we thinking, by removing care and concern to the athlete, who is a specimen of excellence in sporting, but now perhaps seemingly a specimen in unexcellence in private family life. In this social setting, outside of the sport, however, we really do lose sense of proportions and become confused as to what is fair and equitable, not having the measures and information and stats, and means of comparison, and clear ways of comparing which exist within the sport. In social life we are much more confused about how justice is to be allocated, particularly because we cannot measure.

On the largest scale of human conversation between nations and within nations when we talk of Human Equality and Equality we have trouble unfocusing from one topic in isolation, like about sports competitions, to combining all topics in which they relate to life in general globally. Nationalistic competition confuses the idea that people have regarding Equality within their nations. We have already seen, that in a highly specific scenario of one athlete’s family, we have vagueness. If we grow that situation to include all people, and all the harms they have suffered, and benefits they have gotten, and try to allocate cares and concerns, we are suddenly in the confusion we really are in. Socio-political life is not one of clarity and science when it is having discussions about topics like this. It is much more an example of disorder and confusion, with socially accepted methods of conversing over the topic. This means that people can have very different ideas about what the situations are, who should be cared about and when, and how cares are allocated, and have no measurements at all. We know that people vary this way in our everyday experience with the news and media, and in what we hear from others, and what is clear is that there is huge variety and lack of clarity, and very little data and measurement, and agreement as to method of comparison. But what is common to all, is that outside the sporting context where they agree on inequality, they really do switch to a social agreement about vague rules which require statements about Equality. One has to state that one believes in a more general diffuse equality that did not ever do any measurements. In this vagueness, still however, one is expected to have strong affirmative beliefs about it. That even with all the diversity we really enjoy, there is some kind of similarity, or sameness, that we are confusingly supposed to use, to ensure that cares are allocated in a way that does not include measurement. In other words it is an odd Equality that is anti-measurement.

A Brief Statement on Improving Justice and Well-being

The primary objective of this paper is to overcome an obstacle that will result in more social justice and not less. I feel I need to articulate that I am on the side of furthering human welfare, and not taking away from it. I am strongly opposed to decreasing human welfare, and feel it somewhat strange that I would need to much a statement. However, many think that changing views regarding Equality would somehow result in decresing human well being, or somehow imply that the writer is someone of a deplorable character, not wanting progress on feeling good generally, but an actual desire to make humans feel worse, globally. I am wanting to improve the condition of people who have not received good allocation of care, and resources which would make their lives better, which would be in keeping with, and prove to an extent, the reality of the allocation of care. In other words, I don’t want to say that care should be allocated better. I want their conditions to be really improved, so that you can say you did care to begin with.

To me commitment to words and terms is greatly unimportant to improving well-being. I have stated earlier, that part of my thesis is that we have to get rid of Equality in order to overcome obstacles that exist, preventing our more clear thinking about social justice. It is my view, that the vagueness that exists in Equality is something that blocks our realization of objectives of fairness and justice, which should not be identified with it. Fairness and justice are not the same thing as vague Equality. They would be the same as precise forms of allocations of goods and cares which related to measures which are mathematical, and being mathematical, employ the type of equality which we really trust. This is akin to saying we would get scientific about it. It would also include those things we enjoy in human diversity which includes things we want to be unequal, on measures similar to those in competitive sports. This means that our improved view of justice and fairness would incorporate what we want that implies inequalities which are desirable. Diversity is a result of inequalities on traits and this needs to be included and not excluded from thinking about social justice.

Social justice and general fairness is something I would not succeed completely describing here. That is not the purpose of this article. The purpose of this article is to take steps necessary to make it possible to better articulate what better fairness and justice would consist of. However, wanting to point in the direction that I most minds rightly point, when thinking about what is not incorrect or too vague about social justice, I want to say that repulsive harm to people who simply have not been given natural benefits in life, or are victims to repulsive forms of irrelevant prejudices, and nationalities, should have a better distribution of resources. I personally would go further, to say that plain victims of cruelty are protected, including human and non-human animals. To be transparent, I do include animals. I am greatly in favor of making sure that people who are not getting cared or are distribute resources in such a way as they would imagine that they were more completely cared for, and not ignored.

This is somewhat like pointing out that a certain composite imbalance still exists that is vague, but definitely exists. Some may confusingly and vaguely state that this is what Equality is. What is happening in such a claim though is an attempt to preserve that which is creating an obstacle by saying “look, you are saying that there is a kind of master general balance that could exist that doesn’t.” I’m merely wanting to point out, however, that there is something that can be agreed upon regarding social justice which admits gross inequitabilities, involving starving children, and extreme wealth differences which appear unjustified. Such an admission would forget, that one’s mind quickly switches over to the other side, that sees value in rewarding professional athletes on merits in a way greatly different from others, and there isn’t much objection to that. This point here illustrates the problem. Really the Equality view needs to go away, and more comprehensive perspective using measures and details which admits that diversity is inequality is required. Nevertheless, I wanted to remind the reader, that the objective here is to improve social justice and not detract from it, even if there are some difficulties changing the way of speaking about it.

Moving from Vagueness to Clarity

The word “equality” is not one that is right in all usages, and arguably it is not easy to use correctly, unless in very simplistic matters. A regular person can create simple equations, saying perhaps that 3 times 4 is equal to 12. But when it is very complex, they will not be able to tell whether two formulas are equal or not. This implies that everything that is not simple is something in which equality may be unknown, when comparing two things.

Switching to the political context, one would not expect more precision, and a greater ability to find equalities, than if one is in a scientific context. Politicians are not mathematicians. That someone utilizes it in a political context, does not indicate that their usage is correct, or immune from criticism. Somehow, people forget that equalities are not easy to confirm, from their struggles in math class. Instead, they switch to a political context, and believe quickly that various Equalities exist, without doing any math. Being non-mathematical, this kind of usage is especially open to criticism, not closed. In math, work is frequently criticized until it is really believed that equations are correct and reflect equalities, and not mistakes. If one does not get an equation correct in math, one gets it wrong, or completely wrong, in a school context. Teachers may not give any credit at all for an incorrect answer, indicating that an equality exists when it is really not equal.

Just learning in mathematics, we made mistakes, and the best mathematicians are making mistakes until they finally get their work right; implying, that one must know how to get it right even in the social-political sphere, in order to confirm Equality in an particular argument. Politicians and lay-people would not be better at finding precision, and would not be more immune from utilizing the word incorrectly than mathematicians. Instead, they would be more likely to get it wrong, perhaps not really understanding what the word means, or by using it in a traditional way that is defective due to how it was introduced and practiced in daily experience. The trust we have in equality is not from anyone in the public, other than mathematicians who have found ways to use it correctly!

Equality is a tool that is used. If it is not used like a tool there is an indication it isn’t being used at all. It has rules of utility. We can recall rules of mathematics that allows us to make changes to equations while preserving equal comparisons. We did not at any time not use it as a tool to indicate values or formulas on one side and the other aren’t identical. In the political sphere, there have not been rules set up for usage, and transformations, and comparisons, the same way that it has been done in mathematics. Again, this is because it is not mathematical, and instead has borrowed the word from math to create credibility, to futher a political movement.

Mathematicians provide us with good examples of the utilization of equality, which can assist us in knowing when it has not been used well, but instead resembles Equality. When intelligent mathematicians have employed equality well, it was in the comparison of values which were the results of precise measurements, or in the comparison of numbers. We can recall in math making equalities like 2n = 8, where n is 4, or in phyics, 3cm*n = 9cm, where n is 3. The mathematical trust and precision that we have given to the word is for it implies that there has been an evaluation anytime it is used, which is a valuation in numbers, or a valuation in numbers with concrete measurements, or a combination of the two. When one first takes Physics, one learns that there is a difference between their studies on math, and science, in that math often omits the use of measurements entirely, whereas, it is of paramount importance in science that measurements are used. It is somewhat tricky to learn how measurements are to be manipulated in conjunction with numbers.

Good examples of the usage of equality require that values are available for making comparisons, to confirm equality. Mathematics and science both expect that there is an evaluation which results in a comparison of equality. It is not possible to write an equality formula without their being an evaluation. We always expect that there is a number on one side, or forumula which includes expressions involving numbers, that will be identical, equivalent, or equal to what is on the other. Anything placed on one side of an equation already has a value related expression. Both in science, and in mathematics, the reader is trained to do this, from school, and would not object to this idea, that equality expects a comparison of values. One cannot truthfully write an equals sign, an “=” between two numbers, or mathematical formulae, or expression, unless the values that are involved are equal to each other. One cannot put an equal sign until one has recognized that values really are equal. Otherwise the symbols used would be what we know as inequalities and not equalities. We have the symbols for greater than “>”, or less than “<”, to denote when valuations are different on each side. If it is conditional on formula reduction or evaluation, we use greater-than-or-equal-to “>=” and less-than-or-equal-to “<=”. In programming, we have unequal, which is “!=”. If an equality is written down on paper, and what is on the left side is not the same value as what is on the right side, we have written it incorrectly. What would correct it would be to write “!=” not equal to, instead of “=” for equal to. These symbols are not used when values have not been compared. If there are no values, then one has left math using equality, and has proceeded to do something else. You don’t use equality when a measurement has not happened or is not expected to happen, or if you don’t have a number or formula that results in values on one side, and the other6.

Let’s start looking at some examples, beginning with an empty equality comparison, with blanks that would be filled in with values, measurements, for formulae which can be evaluated using various inputs. Our examples will primarily be simple ones to make sure there is good clarity. The findings from these simple examples also apply to those that are increasingly complicated, so we do not need to provide really complex examples.

__________ = __________

Looking at simple math in which we are all familiar, we can see something is expected on the left, and on the right, and those things would often be plain numbers, which would come from measurements in the world, which are compared. Now let’s make the example real, thinking about what we might really want to compare from everyday experience. Using sports again, let’s compare two athletes on traits they might have. This is something routinely done in boxing, to compare athletes who are supposedly of similar enough characteristics to have what might be called a “fair fight”. Let’s say we have one athlete who is 165 centimeters tall, and the other is 166 centimeters tall. Now we have two values that allow for a real comparison, which then permits us to ask whether there is equality or not. Filling out the above equality with the values, we have:

165 = 166

But this is incorrect, and in school we would be corrected by our math instructor who would tell us that 165 is not equal to 166. Instead, we would have to rewrite this in order to get it right, as an inequality:

165 != 166

This would be correct. Notice that for any value that is not 166, if we filled that value in on the left hand side, it would be unequal also. Only for 166 would it be equal. This means that it would very seldom be an equality that is found when comparing heights with any specific individual. For someone who is 166cm tall, they are only equal in height with another who has 166cm in height. For all other comparisons it would be unequal, and therefore we expect and anticipate inequality and not equality.

But if each athlete were measured to be 166 centimeters tall, then our equation below would be correct:

166 = 166

What we have done above is something required if we want to inherit the authority and trust created by mathematics in claiming that two things are equal to one another. If we really make comparisons between values and measurements, and we find them to be really equal, we can really place an equality between them, and say they are mathematically equal, at some level of precision. Here that level of precision is centimeters. By doing it right, we are getting much closer to being able to say that things are equal, and doing it this way, we can build up comparisons between objects to see just how equal or unequal they are, in a way that a scientist would do it. Later we will see, that doing this type of comparison results in better quality comparisons of complex objects, including athletes, and people, which allow us to decide how to provide social justice and distribution of rewards and resoruces. Doing it this way, instead of assuming people are equal in total, without noticing differences or doing any math, we will feel more honest. Again, usually when things are compared this way, inequalities are found and not equalities. But these inequalities, like inequality in height, indicates that we have diversity in heights. Presently in equalitarian cultures diversity is much celebrated, particularly in athletics, with the result there is confusion about Equality, because when we compare for real we keep seeing and finding inequalities instead.

Talking more mathematically and scientifically, we might say that there are two objects in the world, two people, who are athletes, who are equal in height at the time of this measurement, to a measure of one centimeter. That is an example of a rough equality which is clear and really does exist to our satisfaction in nature, between two athletes. There is no need to talk about some vague social Equality on this point. We really can rely on mathematical equality which itself has that trust which we really can borrow from a long history of math, the discipline which itself depends on it, as self-evident. Outside of math, in a vague social territory, where much argumentation and disagreement is expected, it is not self evident, that Equality exists. It is only when we are doing something such as this, that we are permitted to say such a thing. Otherwise, we really are tainting math, and are pretending to have the rigor, and discipline, and clarity, that only math has.

Above it was mentioned that we can build up to see how more complex objects compare in a scientific way, and focusing on athletes, we notice that this is what we really do in sports. In boxing we need more information than height to see if two athletes are compatible enough to have a contest. We could not on height alone infer that these two athletes are compatible, and if we did not measure more, sports enthusiasts would complain that there is unfairness in the fight. Typically we’ll also measure athletes on weight as well. Suppose we measure the athletes on weight, and find that they are both 68 kilograms. We can say on that they are roughly equal regarding weight too, to a precision of 68 kilograms. Using these two metrics we can begin to make a table similar to those that show how athletes compare before a fight.

There are rules in mathematics concerning what is irrefutable, self-evident, proven, or axiomatic, and these rules do not carry over into social and political discussions, they way they are presently conducted. Notice outside of math, and science, and chemistry, and physics, we are not really permitted to say things are self-evident, in the same way as has been attempted in historical political documents. You can’t be a witness to something and claim it is self-evident. Rather, you may have witness evidence that something has happened. Likewise, you cannot look at two people, and simply exclaim that it is self-evident somehow, that they are equal in value. You certainly cannot claim it is self-evident, that any two people who are compared are equal to each other. At most you can produce evidence that the equalities exist. Self-evidence and irrefutability relats to extremely precise work being done or has been done that is mathematical, or scientific, and not political. There are some exceptions, like in mutual perceptions of events, in with two people perceiving the same thing, can mutually admit as a datum, that that thing was perceived or happened, without interpretation. For example, “My friend and I both saw a tornado, and also videotaped it. Between the two of us, it is evident we saw a tornado.” Something similar to this relates to confirmation of measurements. Above the two athletes were said to each have a height of 166cm. More than one measurer mutually confirm that it was true that these were the measurements. Between the two of them, if they each really did measure it correctly, it appears evident the measure is 166 (between them, but others would need additional confirmation potentially). However, for now let us not focus on this. Trust that the author really did consider this and many other factors in the arriving of the conclusion that we really do need to rely on the more mathematical style of thinking separate from the vague Equality style of thinking, and this will be more clear as we make our way through this article. This article will get technical.

Here are our first two values which will start our table comparing the athletes, on different relevant measures:

68 kilograms weight 166 centimeters height

Here we will complete our table comparing these athletes with details that are common for comparing boxers. We will also compare their “reach”, which related to how long their arms are. Let us also add their body fat percentages, and lean mass. For these values I’m simply coming up with numbers. Using these values we will find impossible metrics potentially (combined with weight and height). Let’s say they are all found equal:

68 kilograms weight = 68 68 kilograms weight 166 centimeters height = 166 centimeters height 170 centimeters reach = 170 centimeters reach 12 percent body fat = 12 percent body fat 60 percent lean mass - 60 percent lean mass

As we add values to our table we get a better view of relevant details of these two people, which allows us to better estimate their compatibility to have a fair fight; and for the purposes of the present article, what should be evident to the reader is that only by doing this can we begin to see how simmilar or dissimilar two complex objects might be, including people. At this point, if these two athletes are still having the same measurements for each measure, would have very similar traits if viewed visually. This would mean one could expect that if they were both seen, they would have many visual things in common versus if hey were compared with others. This would mostly be concerning their dimensions, and if we think about it we are measuring spatial aspects. If we were to draw pictures of each person using only geometrical figures like an artist might, when beginning a sketch, those figures might look much alike, compared with if the same were done for others. What this implies is that their aggregate measures are beginning to come to a comparison of complex objects that are starting to seem more spatially equal. They are approaching more total equality, as one moves from a single measure to what could later be a huge number of measurements.

We really do not think that as we add values to this table that we would repeatedly find equalities like this, even at low precisions for each measure; by this the reader should notice that adding more measures to compare complex objects we increasingly expect to find differences on some measures, and certainly don’t expect them to be equal on all measures. A reader might find it annoying or irritating that even five measures were provided in the example showing equality. But why would that be? The reason for that is that in the real world taking two complex objects for comparison, like people, who are different and diverse, even if similar, we would immediately notice differences, and we know that if we measured these differences, inequalities would be found for those metrics. Looking above, it is clear that these two athletes wouldn’t really exist for comparison, or it would be really rare, even for just these five measures. We would even start to disbelieve reports if they showed too much similary, because we know in practice such similarities for even a few measures is unlikely, even if we are comparing things we expect to be similar already, or compatible, like these two boxers. Boxers wouldn’t be compared if they were not already seen to be similar by people who can quickly make visual comparisons.

We tend to disbelieve that equality exists even on single measures, however, and this is because at high precision, we know we will typically find inequalities.8 The very first measure on height was already not believable; and this is because of two reasons With these simple measures, we are still concealing details that would reveal differences between these athletes, because so far we have only used low precision numbers, which make it appear like the athletes are more similar than they really are; by this what the author should notice is that we are only stating as a convenience that these athletes are equal, to a level of precision, knowing that if we compare more exactly, we suspect we will find small differences. This suspicion about the unreality of finding them equality, for me, was earlier though. It was at the very first measurement. If I am prepared to hear about the measurements of height of two different people, I am instantly ready to hear different values. Two people, who are close in height, who are boxers, really might get the same value, but that still doesn’t resolve my concern, because my expectation is that if they are measured more precisely than centimeters and inches, a difference would be found. What this means is

On just one common measure at a high level of precision the expectation is that people are unequal and not equal.

This brings us to an important finding that we will assume for the remainder of this article, and it is that:

No two people are equal in total, and we expect this, even if we are measuring only one thing, and if we go one measure at a time, we expect them to be unequal on all things.

Measuring any two people on any measure at high precision we would not anticipate that they would have an equal result. When we do find an equality, it is because, we have not measured precisely. We have found a rough equality, which has permitted us to ignore differences which still existed in the precision.

That doesn’t mean we weren’t doing a good job measuring, especially if one compares with not measuring. We also saw, that if we kept measuring, we get to a picture of what the person really is. If we measured all the traits of the one athlete, and the other, and drew out both people, we would have pictures of what both people really look like. But, it would not be perfect. We would have created what is like a video game likeness for the athletes, and not the athletes.

Two people therefore can be roughly equal on measures for specific traits, but not in total, but more precisely, not at all, excepting for very specific scenarios, which really are not related, but will be considered later in this article.

Vague Equality is wanting to ignore variations in people to claim that they are Equal, but it was found that they cannot be mathematically equal even on one measure, and certainly not when all of them are totaled together. This means that Equality is to be greatly distrusted, once gain, because it borrows a mathematical concept that would provide precise results that opposes a political agenda, Equality. The opposing viewpoint is the one that creates clarity, and not vague Equality.

Since we suspect that on a single measure of a single trait, that we would not find equality at high precision, and since visual comparisons of people have created expectations that for any two people compared, differences will be seen, that will result in different metrics, when measured, we have the proposition9:

Inequality is self-evident

I have said earlier that equality is a rare area in math, where there is an exclusive ability to say things are self-evident. If you compare two heights, and each are 66 cm, then when you put 66 on both sides of the equation, it is found to be true. In math without measurements it is taken to be self evident, instant knowledge, that if 66 is on one side, and 66 is on the other, there is an identity, or a true equality. Seeing both on each side, one does not fight at all against it. All mathematicians agree that

66 = 66

Likewise, if you do a good rough measure two athletes, and they are

66 cm = 66 cm

Two physicist-mathematicians would agree they are equal height, to a precision of 66cm.

However, physicists would agree, that measuring with more precision, for almost any measure, would for each measure, result in an inequality. These two athletes, measured more closely, would be each perhaps:

66.047 cm != 66.214 cm

Which means that the physicist-mathematician, or just mathematician, and really anyone who thinks about it, would know in advance, that two people are going to be unequal on height. I am tempted to conclude that this point is self-evident, however, it really is confirmed in the data. We happen to have histories of knowledge that makes us really expect, on statistical grounds which are natural in our minds, that if we compare two people who are close in height, they will be unequal. You don’t want to fight me on this conclusion, and you really do think that would be the outcome.

Now, that was for one measure. Consider that for a highly complex object like an athlete we use many measures. On all measures we expect the same situation, even just for sporting measurements, that are normal for athletes to get measured on. If we get really good at measuring athletes, we have hundreds of measures. But if we go into biology, and medicine, we have millions. This is why I have concluded above that inequality is self-evident. You will not fight me regarding this because you agree. But better for us both:

Inequality is self-evident implies Diversity in total is self-evident.

This means that we expect uniqueness for every person. So while we have this vague idea of Equality, capitalized, which we are finding doesn’t quite make sense, we do have what seems to be on the same side as that idea we were wanting to retain, Diversity. Diversity really appears to be a clear concept, that does not have the defects of vagueness of Equality capitalized. It depends also on the automatic perception of inequality which makes it really obvious. Both concepts depend, on our proof of their existence, which supports the obviousness of them both, of mathematical measures which utilize comparisons using equality. We just find again and again that things are not actually equal when measured in precision. Look around any room with people in it, and you already know this though.

It appears unreasonable to fight complaints against Equality as a social norm

This is why this article seemed necessary for me to write, but also spend extra time considering. I know that if I go against a social norm like Equality that I’m going to have people want to dispute me. However, I also know, that going the other long path at explanation, going in the details, that people would not want to dispute me. Awkwardly though, they are left in contradiction, if I don’t do more work to make them feel comfortable, that they really were aright to want social betterment, while they were not correct in persisting in joining everyone on vague Equality. Notice that even if the reader agrees, they would face also the issue I face, of trying to explain and articulate that to others. This was my issue finally completing this paper:

“How am I going to tell people that Equality is unreal but they’ll get what they were wanting be accepting Inequality is self-evident.”

Saying inequality is self-evident feels similar to calling everyone in my culture a liar, or at least, very confused. I think it is the case that all were confused due to the way that our nations taught us topics relating to democratic ideals, which have characteristics of marketing and propaganda. Going with “Equality” as a slogan did have force too, which indicates it has potential as a tool of propaganda and marketing. However, it has terribly confused itself for a mathematical worldview; in reality, it doesn’t compare anything doesn’t take measurements.

I think the cause of this related to our wanting to overlook that people are different in wanting to allocate care and concern for well-being. Both the reader, and myself, would persist in thinking “regardless of what the person’s traits are, we want the to have minimum care and freedom from cruelty.” The details of what the fairness consists of here is something people greatly disagree on. But going into the details the way we are now doing it, will get us to a better idea of clarity about how to allocate resources amidst inequalities. Remember, in sports, people are not expecting to pay all athletes the same way. But almost everyone would be confused to explain why.

This is because where there is competition, and merits and excellences, and weaknesses and unexcellences, people expect to be rewarded differently. This means we really want inequalities in treatment relating to inequalities in people. Someone who is doing well frequently, might get an unequal amount of praise. But we do think that is fitting too.

But what does that mean about making sure people are cared for at a minimum amount, or at an amount we find pleasing, regardless of differences. Is that what fairness and justice are? To be clear, this is emphatically not what equality is, and notice we haven’t measured anything. This is an area where I anticipated a reader may think like I do, and state that this is the equal treatment that was had in mind. But this is due to vagueness and lack of detail, and the reason is because a system that strives at this has to account for interpersonal differences, regional differences, and the like, in trying to give what seems like it might be fair. Consider human resources tries to pay people for the same work in different markets a rate fair for that market, without thinking about the person. This seems fair because it is doing it regardless of the person, but it is unable to do it well regarding the markets, and should take into consideration personal preferences. This is what happens when a worker applies for a job, and gets it in one market that is not the other, and is expected, to have preferences that align with the region. The distribution of care and concern at a basic level is also undefined, which means that what is given in one region can never be measured equal to another region, even if in each region those calculations correspond to a separate measure which corresponds to the basic measure.

Here is where I want the reader to be cautious. There is a strong desire for people to say “That’s the equality I was talking about, therefore no more thinking is needed.” But that is entirely incorrect. It ignores that many confusions about different meanings of the vague Equality were combined, and did include for some, this one. That doesn’t save the errors. Furthermore, it doesn’t protect it against our alternative strategy, which really does lead to clarity. Suppose we gave everyone a dollar value of money equal per capita, even if that amount sent out was equal, it turns out that it doesn’t actually result in Equality that is social justice and fairness, and in measure isn’t equal either, in the precision (i.e. Families with children versus single households was not considered, which means even choice is ignored). Everything outside of this fund of money which does send out checks with the same value written on them, is inequality and competition-like. That’s everything in our natural world we live in, except the check! And the result would not be what people would want. Because what people want is clarity on what the situation is, and unequal distribution of goods to achieve more balanced well-being, and not equal distribution.

Truly Equal Things

Moving towards a greater precision in understanding the entire topic, including all of nature with humans within it, let’s take some time to talk about what really can be equal. Earlier we arrived at the proposition that inequality is largely self-evident, while equality is not. Equality is more difficult to demonstrate, and one expects that on precise examination, inequality will be discovered instead. Nevertheless, here are things which appear to seem more likely candidates for truly equal things, and an example was given above regarding checks from the government with the same numbers or amounts of money writtenon them (money objects). We will resume this example to show how and why money instruments are still unequal, but before returning to that topic, let’s first consider other real world object which apparently have true equality comparisons at high precision, or absolutely. Notice that for the statement

These two objects or people are equal in mass.

means they are equal absolutely, unless one agrees to calling them equal at a lower precision, which conceals differences which might exist at a higher precision. This means when we use the word equality in mathematics, we are really looking for absolute equality. When we use precision in architecture and construcution, we are looking at rough equality, not absolute equality in equal building parts and components.

Finding and equality requires work, whereas inequalities require less. An interesting consideration supporting the current thesis is that equality is not the simplest thing to find, even if one searches carefully. Examining the topic more closely one arrives at strange realizations that things thought to be definitely equal, still are not on greater consideration.

One can safely assume inequalities of comparisons on statistical grounds. Simple measurements at high precision that still result in the same values might be said to be approaching equality, but are not really exactly or absolutely equal. If comparisons of precise measurements are made over and over again, data is collected indicating that inequalities are often or always found. Taken frequently enough, for most things we encounter, the data becomes so uniformly on the side of inequality, that we become justifiedin expecting and later assuming inequalities. With enough data it would reveal why it appears self-evident that inequalities would arise, without taking measurements. Statistical information can be used to justify assuming nearly absolutely that inequalities would exist, and therefore:

We can use statistics to define what we have thought to be self-evident.

Statistical methods are used in manufacture quality assurance to determine the expected frequency of defects resulting from inequalities in parts. Parts have various aspects which can be measured, which is more apparent when one thinks of engineering diagrams, or technical drawings, or part specifications, and so on. If any particular dimension is too different from another on a measure, too unequal, they may no longer be interchangeable. Interchangeability implies that there are “close-enough functional equalities”, but this is still a form of suitable equality, or “congruent inequality”. Congruent inequality could be taken to mean congruence or concordance of measures despite absolute inequality, which brings us to:

Equality is definable in terms of inequality.

This appears true, but also appears a contradiction, and a paradox, until one distinguishes what is meant by equality from inequality, which contains the same word. Put without paradox:

Things which are different on close inspection can be treated as interchangeable within certain conditions.

These conditions would provide the rules in which people typically arrive at their inclination to say any two things are equal. This means we can discard the word equal, or redefine it as an acceptable similarity arriving in an interchangeability or identity.

Interchangeability results from a build up of similarity on all relevant measurements of an object, related to a functional equivalence, which simply means those two objects can be used to perform really similar work, or be utilized to fulfill some really similar goal. A mathematician, can also, comparing two values, without any units specified, might be lead to believe, falsely, that an equality exists, corresponding to the equation. 15 Here we will use an argument scaling from single measurements of specific dimensions, to larger objects on an aggregate of measures. Measuring two things, and finding them to have equal length, at extreme precision, it might enable mutual interchangeability in manufacture, might be considered suitably equal. However, such a measure is still imperfect, and quality control in manufacture would still estimate some likelihood of failure or defect. On that one measure, going ever more precise, one would find that they still are not equal down to the elemental level. Nowadays in manufacture of metal parts, some are creating cuts which are invisible to the eye, but nevertheless, resulting parts are known to be unequal. Expressed in an equation, the two values, at that level of precision, would be considered “good enough equal” to a physicist and mathematician, but not purely equal.

Mathematics is not the same as physics in omission of specific measurements and units. A physicist would say that certainly these two things are not equal in an ultimate way, because precision of measurement can be increased in various ways. Mathematicians, on paper, can make symbols match, and somehow think purity has been attained, and true equalities “found”, never looking away from the paper, or never thinking and only using the hands.16 An example would help. Suppose two computer chips are measured each to be 2.475895732 centimeters in width. Without units, presented to a mathematician, 2.475895732 = 2.475895732, might lead to an inference that this is true. However this is not about the objects, but about the mathematical statement on paper. Certainly, the right is equivalent to the left, and there is an identity, and these values are the same. However, there is no corresponding natural thing which has this equality. We say roughly they are equal, or that they are very precisely but not ultimately equal, once we are talking about chips, on that measure with that unit. Perhaps our instrument for measuring that length does not go to a greater accuracy. Either way the physicist would immediately assume that still they are not equal.

Using this example of a computer chip, we can see how greater level of similarity is achieved between two complex objects.. Chips produced in a manufacturing center really are mostly interchangeable, not only in the width of the chip, but in the total function along relating to all relevant measures of the chip. Clearly many similarities would have to be present in order for the chips to be interchangeable, which means they also look quite complex when you view them. Your view of them would start to result in increasing inability to notice differences. As a consumer, you would not see the chip, but you would experience similarities between models. You buy a computer and it works, and someone else buys the same model, and it works for them also, very likely, if they do similar tasks. This means measuring that chip like we measure athletes, along all the relevant areas of interest for the business, we find that they are very nearly equal on all areas of comparison. If we had only those measurements, and we were to draw out the chip from no other information, we would draw what appears to be the same chip. The blueprint would be a drawing which would be very similar in various respects to the drawing we might make without reference to it. This would indicate in a wide number of ways we have two objects, which are complex, that are interchangeable, that are approaching what might be considered absolute equality, or equality, and not “congruent inequality”.

However, again the physicist will say that they still are not ultimately equal, and we actually really do expect and anticipate the same. Viewed under powerful microscopes, the edge of one chip would have strange surface characteristics unlike the other chip. However, similar differences would exists on many of the other measures which would relate to the functionality of the device. Working on these chips, comparing the results of manufacturing, specialists would be utilizing tools to aid the eye. Looking at chips using such tools, definite differences would be noticeable. Along with those differences would be measurable inequalities.

Is functional equality something that produces absolute equality? One might say, there are aspects of the two devices which are equal in ways that are more resistant to this type of difference finding. This might be the design of the device which might relate to paper-based, formal mathematical equivalences. There is more that can be said about this later, but for now, it will be noted the devices in total are truly different, and even with really exacting similarities, there is an expectation that some devices would fail, indicating industry knowledge about non-equivalence of the chips. Failure is a definite indication that even functional equality has not been attained. Although it is to be considered if any two functional pieces produced are funtionally equal, although the answer to this appears “No” also.

Non-diversity in interchangeability is expected, meaning that chips should appear non-diverse products on completion. Chips are complex, but they are highly controlled. Their designs are not intended to have any diversity. People, however, have considerable diversity. Comparing people with chips, again, we find that the expectation of inequality is universal. The expectation of differences that make diversity possible is universal. Chips are unequal at high precision, even when they are not diverse! Here we can return to our primary subject matter briefly, seeing what this might imply about other complex objects, namely animals, and humans. Humans could never have the similarity and interchangeability as chips, and since those are unequal already, even when there is no diversity, we know there can be no equality in total among humans.

When is there no diversity in humans? There is only one type of non-diversity that applies to humans, and that is identical twins.17 This would be a limited non-diversity like those of the computer chips resulting from manufacture. They are copies although the copying process in human zygotes via meiosis differs from the copying process from blueprint designs in a factory. In both cases, there are great enough similarities that we can comment that they are low diversity collections. Cloning is another example of creation of identical twins, as meiosis of zygotes is simply natural cloning. If we were able to fill a city with only one person’s clones, it would be what we think of low diversity. Notice we already think there is low diversity, if a particular city is not cosmopolitan, and includes mostly people of the same race and ethnicity (appearance and behavior). Focusing on the example that currently exists, of identical twins, we know that there are still differences between copies, even if it is the lowest diversity example that we have for humans. From this we can form the proposition:

Some diversity exists in any comparison of two humans.

An implication of this is again, our earlier proposition:

Inequality in aggregate is always present for animal complex objects.

A statistical or soundness argument, with an inductively true premise18., would lead us to:

“People’s perceptual systems always notice differences and inequalities for any two animal complex objects when examined closely.”

Which is a kind of definition of:

“Inequality is self-evident.”

Because self-evidence is a conclusion regarding how people react to observations they make.18

Now let’s consider manufactured objects down to an even greater level of precision to see if we can find an equality If we think of simpler things that are designed that are manufactured to high precision, that are interchangeable in function, we find that we have things that seem really more equal. This is because we’ve reduced the complexity of the complex objects, so there are less aspects which might be compared, which would reveal to us noticeable differences. With these simpler complex objects, though, we still have a similar issue that we discussed before on single measures. At higher precision we simply expect to find differences. In manufacture there is a recurring issue about inequalities that would be found at the elemental level, particularly for chips that are supposed to be designed to smaller and smaller scale. If we are comparing two electrical wires that have a similar purity in the metal, like gold bullion, in a space related application, where the technology of fabricating the wire comes from a manufacturing process that already has a 99.99999999999% expectation of functioning19, and consistency of dimensions, we would still find that they do not have the same elemental configurations. Calculating variety on elemental configurations of gold in gold wires, or gold lithographs, imprints, and so on, using what a professional physicist might know, we would still find, I thin, a near zero probability of equality. Notice this is in an interchangeable part at maximum purity and consistency, for only one desired element.

Now at the elemental level, let’s shift away from the manufacture of objects, to what nature provides as simple building blocks, including molecules and atoms. In school we were taught that there is chemical elemental and molecular interchangeability, with natural rules provided in chemical and physical equations. Here we have the appearance of two major efforts relating to two key parts of the conversation obove: work on identifying what is interchangeable, resulting in a periodic table and references on molecules, and creation of transformation rules which are akin to what is found in math, or is physico-mathematical. Here we are not yet in the domain of the very smallest building blocks of physical things, as atoms are constituted of smaller parts, some of which have not yet been identified. It is not clear when they all would be identified, or if they could be identified. Nevertheless, we are at a place in our discussion where we are at very small objects which have been named “atomic” for being perhaps the smallest which were thought to be interchangeable, building up mostly everything we see that has mass. We accept or have assumed that one atom of gold will be the same as another atom of gold. They are extremely interchangeable, within nature and not only in our designs about how to utilize it. However, there are still differences that physicists would notice. Firstly, one molecule of one atom might not have the same number of electrons. Additionally,they cannot occupy the same position at the same time. It is not clear that location of an object is truly a differentiating property of an object. That’s not something I’ll be able to decide here. But if there are two identical twin people, and they occupy different space, they can be influenced differently at the same time, and would have different lifetimes. Similarly, one atom of gold will have a different lifetime than another atom. Already we assume that the Earth is composite, made of atoms that had different historiestracing far back before the its origin: Earth was formed of a larger of atoms having different life histories (coming from different events involving sub-atomic particles too).

Considering the success of chemistry and physics, that has depended on assumptions of interchangeability of atoms and molecules, and the assumptions of transformation rules of molecules, we can see that we have found something really close to what we originally thought equality might be. More stable atoms, or subatomic particles, or other fundamental things in nature, like light photons, might be even less subject to differences that might be considered lifetime differences. They might have fewer things that can be different about them, and have greater interchangeability. I do not know if it is known that there is anything in nature that cannot be inspected more closely, however, or does not have spatial differences at any given time. I don’t know that a Physicist would be willing to claim, that because we have limitations on measuring and instrumentation, that there is not a very deep level of structure within seemingly identical things that would show differences, if they could be shown. If what is to be compared is not observable, or not each measure of interest is measurable, then it appears we have another solid proposition:

Proposition 9: Equality in nature cannot be confirmed for any two things compared.

This strengthens our argument, because now not only have we stated that absolute equality, or equality, would be rare, such that inequality is self-evident, we now understand that we cannot confirm any equality. Not even a single example:

Proposition 10: Equality is not detectable in anything

There is a disparity between what are mathematics says about nature and our ability to confirm its predictions, which implies certain equalites on measures are unverifiable. Considering motion of objects, which includes any movement of elements composing objects, there is an assumption of infinitesimal divion. Equations regarding paths of objects in motion which imply infinitesimal predictions about objects under comparison, require increasingly difficult verifications which are impossible for our instrumentation. This means that properties of objects composing larger objects cannot be confirmed in their equalities of measures at highest precision. This method of representation may include commitments to non-confirmation and non-confirmability of equalities. Again, this would serve to confirm using another line of argument the above proposition, that equality is not confirmable in anything, and only using limitations on one measure that applies universally or nearly univarsally to all objects observed. Some will say, on this basis, that it appears that nature is following what can be found on paper very elegantly. For example, perhaps an object in space is traveling along a curve which is represented very nicely mathematically, such that, there is some expectation that the formula used can show more precision than any instrument would verify. In other words, you can predict its position over and over, and measure that position, but you can also use the formula, to predict interstitial positions for which verification with instruments is not possible. Such a thing might indicate that in the physical-mathematical formulas we can see equalities which cannot be seen to really exist in nature, but appear to correspond predictably with nature.

From this, however, is nothing satisfactory to me to confirm that equality truly does exist in nature, and there are other considerations, which are in my current interest outside this paper, that I will share at a later time, that relate to conclusions we might draw here. This is not something that is confirmed by anyone at present, though. What we might say about this, is that we are inconclusive as to whether there are genuine equalities anywhere at all, and that there is no authority which can claim “yes” or “no” about this at present. I would expect this to be an area of hot contention, and dispute potentially between physicists, mathematicians, and chemists, those who blend the discipline into philosophy, like I do.

Expectations about what equality is in objects of nature is something that I don’t believe is defined. I think in science the working position is similar to that in manufacture. We encounter things that behave very similarly, and in some ways apparently exactly alike, but nevertheless, are separate. Interchangeability may be what we would use to determine whether objects are exact. Chemical equations function like other mathematical equations in the expectations of consistency of results and utilizes the same symbol, and similar mathematical operations. Specific elements are entered into manufacturing processes which use chemical formulas, assuming extreme homogeneity, if approaching perfect homogeneity in results. The best assembly line, and manufacture, appears to be of atoms, which are then used very consistently. This type of thing in nature appears to be where we do find something we can somewhat agree is equal, even if we have some concerns about the ultimate precision of that equality.

In my work outside of this paper, I’m inquiring as to the fundamentals of mathematics in its workings and applications. This means that a resulting mathematics I would use might not be quite the same as the mathematics someone else would use, using base10 arithmetic and various conventionally accepted operations on numbers. This might mean that the math I arrive at would not be the same as the math used by someone else, and yet might have similar results, that are non-identical. This would imply that even mathematical systems cannot be considered equal. Yet what I am striving for is one that is more natural and less arbitrary. So it could turn out that one candidate mathematical system applied to nature would have a non-arbitrariness, that would allow us to claim that certain equalities really do exist, which are not yet identifiable.

This paper does not have a final statement about this topic, but rater reiterates, that this way of thinking leads to greater precision, leads to better understanding of complex objects, which in total are always, at a level of animal complexity, unequal. It confirms that diversity is also always to be expected, at animal complexity. Diversity is confirmed by measurements which show equalities we can see often very easily.

Vague Equality in the social sphere should be abandoned. It combines too many vague ideas that are not really mathematical in origin, while trying to pretend self-evidence that is hardly achievable in science or in math. Self-evidence and precision do exist, but that’s due to gradual work in the sciences and using measurement and mathematics, which is why we trust it so much. But we can’t simply claim people are Equal, and then say that it is self-evident, because we are pretending we are using math, by using borrowed words.

People are not equal to one another. They are not equal to one another even if one focuses on really narrow measures we commonly employ. We do contain chemicals that go down to the elemental level, that allow for us to function. However, knowing that you contain carbon does not make you in total equal to me. Lifeless matter contains carbon. Non-human animals contain carbon. And there is no single ingredient we can point out, that would lead us to conclude, that on its basis we are equal. And that is because to do that, we would be considering a very small part of us, and not us in total. Considering each person in total, using all of their measurements, we said would allow us to draw them out, such that we would have something that looks quite a lot like them. We can only get to that, from all those measures and all that data. You cannot take any individual piece, and come close at all to knowing the whole.

Humanity and Equality

Using humanity to select any two organisms at random, one would not end up with two people, who are anywhere near what we would have considered equal, using our measures in sports. This would be a way to have two people who are the most dissimilar people and not the most similar. Meaning, maximally different organisms on earth, that can mate, are taken to be equal. But that’s the same thing as saying two people who are the most different are the same, on the basis of belonging to the same category.

This paper is nearly complete, but there is one error which again comes up which must be considered, so that readers will be able to adjust in ordinary life to changes that are implied. One will either make this error about to be discussed, and have to self-correct over time, or else notice other people making the error, and having to tolerate it or help them realize the changes that need to be made.

This is thinking that a particular word, which seems to apply to everyone, or categorize everyone, makes them “the same”, and therefore is the source of equality. The example I think that most definitely will take time to eradicate, is of thinking that because people are human, they are all equal. That they are all members of the same species, means they are all the same.

Notice based on the preceding conversation, that one has to overlook all the diversity, all the differences in measure, all the things we think makes one having strengths which should be rewarded, to get somewhat foggy, thinking there is some property we can see that is ‘being a human’ which makes everyone the same. Consider that you cannot see this trait either. You can more or less point out similarities, but you will struggle to draw out a blueprint of what a human is, working alone, trying to determine what is really similar between everyone.

Fortunately for us though, the term human is already a scientific one. The term human does not imply equality even in science, but a compatibility of sorts. A sexual interchangeability is part of what has been used to define what a human is. This definition appears somewhat related to what is used also, of overlapping genetic similarity. One person is said to be more than 99% similar in DNA code to another, but still not quite equal. Trying to define human by pointing out specific DNA is not possible, which also indicates that DNA variation exists across all humans, and that there is no fundamental blueprint which is common to all humans and their DNA. In other words, there is no set which would be the center of a Venn diagram, using all DNA sets, which can then be pointed out as a prototype human.

Species membership is well understood, however. Species membership really is due to sexual reproduction. One species cannot mate with another and have a very good expectation of viable offspring, which means that humans really are separable and classifiably distinct from other primates. Humans themselves are roughly interchangeable sexually, although perfect interchangeability has not been confirmed. It is not clear that there are divergences within human populations which make one person sexually incompatible with another. Nevertheless, take one person and mate them with another, one can expect that they will have viable offspring. For any two people who fall into the set of primates we vaguely visually distinguish as human, we can rightly call them human, if they can sexually reproduce. There are many off cases to this, but I think we will get through the purpose of this conversation without covering those.

Now take two people at random on earth, let’s say females who are interchangeable sexually with a male (notice we did not consider equality between sexes at all. Being human does not appear enough to make a male human equal to a female, although we already recognized in the earlier conversation, that we wouldn’t expect equality anyway). Now we have, say, two women, who are both definitely of the class and category “human”. What about putting them in the same class, makes them totally equal? That is the issue, that some will persist in saying that one can ignore all traits, and simply say that if we have two humans, they are equal to one another. Well, we have two confirmed humans, both women, potentially from very different places on earth, and having a million features dissimilar. We consider these people as expressing diversity. The male would not consider them interchangeable, although sexually he could reproduce with either. He already is thinking they are not the same, and are not equal. But some will persist and think that by classifying them using the same word, by having a category in which they both fall, they are totally equal.

But why not simply give a full description of each person, and all these details including the sexuality related details, and classify them as humans, and avoid talking about how they might be equal?

This is where I think the fundamental flaw exists. Categorization is, just like a specific measurement, a very narrow way of looking at a complex object. Finding two humans who really are human doesn’t lead us to want to infer they are identical. Particularly if that categorization is not about something in total that equates them, but something narrow like sexuality, and ability to reproduce. A much better way to compare objects to search for ways they are similar is to simply look at all the details one can have, and not one detail, or category, even if that category also has implications about various similarities that can be expected.

If you were to take two people by their DNA and draw them up, would you anticipate, that what you would draw up, would be two of the same people? Definitely not, because the expectation is that there would be diverse results of reproduction, and that drawing up a person is somewhat like, their natural growth from their DNA.

Now let’s say you took the complete description of one person, and all their measurements, and their DNA, and anything else you have, and you draw them up. Would you expect, that if they have the very precisely similar measurements, similar DNA, similar data, etc.. and draw them up, which is like growing them, that they would be the same.

Well, in this case, you would have identical twins.

But notice people take humanity to be that category that would make people equal to each other somehow on category alone, without any other details.

Hearing that someone is a human has some implications as to expectations about appearance, but these vary greatly.

The thing which results in the better estimation as to what a person would appear like, and be, would be the complete description, with all the measurements and DNA, and not the category of human, which would lead one to have only a very rough idea of what a person would.


In this paper we have arrived at a number of propositions which appear more trustworthy than others, considering the topic of human variety and similarity. These appear to be:

  • Inequality is expected for any comparison of any two complex animal objects, including people.
  • Diversity is expected for any comparison of any two complex animal objects, including people, excepting only somewhat for identical twins.
  • Diversity is the result of differences which are measurably unequal.

These propositions are so trustworthy that there are several conclusions that we can make that are very reliable:

  • Humans as a rule are unequal.
  • Humans as a rule exhibit inequality.
  • Humans as a rule exhibit diversity.

We have also seen, that the program of understanding people, with assumptions about equality are erroneous given these propositions. The program of understanding people with assumptions about equality like those discussed is one that results in vagueness, and is a cause of obstacles to our development and progress for social justice and fairness. Whereas, a program of understanding people, with details and measurements, is not incompatible with the above propositions. Instead, it is compatible with the above propositions. Programs using such an approach lead to greater clarity, and less vagueness, as they get more detailed. One should not expect that we are near the terminus of justice, and being far from this terminus, we should anticipate increasing detail as we increase our knowledge about it. In traditional culture, there is a resistance to developing additional details in our knowledge about it which indicates that equality marketing is partly interested in increasing or preserving ignorance over increasing knowledge. The above propositions are not incompatible with increasing knowledge concerning justice and moving closer to a future terminus on its application.

We’ve achieved equality.

The above is not a statement which is about growing knowledge. Rather, it is decisive at a time when no decision about the topic would be wise. It also does not indicate what has been compared and what the values are; so again, it continues the marketing error of using a short phrase as shorthand, for something people are not clear about. “Equality” is not a standalone expression for a meaningful comparison or result of meaningful zoological comparisons.

Imagine if people were to state that Equality between people and crocodiles existed. You’d wonder what that equality was, if you didn’t immediately recognize that specific inequalities and diversity would be more obvious.

It is the position of the author, and a thesis of this paper, that we ought to abandon the idea of human equality as we have inherited it in tradition. Keeping it would be akin to continuing and promoting a program of vague Equality, which is contrary to the above propositions which really are self-evident, and support diversity. It is better instead, to speak more about variety and to utilize measurements, if we really believe ourselves scientific, and to assume the above propositions, which are antithetical to current and prior assumptions that people are equal (in the short-sentence format). If the above propositions are accepted, and they are self-evident so you really do need to accept them, then the equality movement must also be rejected. The expectation is this alternative approach will result in clarity in communication and increased precision in our understanding of our species, and in deciding what exactly justice is, and how it should be distributed.

The author and paper support the idea that increasing precision in measurement results in increasing accuracy concerning objects to be understood. Refusing to measure, and refusing to notice differences in measurement, for the purpose of avoiding the conclusion that the above propositions are true, is really equivalent to avoiding understanding, and avoiding complexity which exists in the subject of allocating resources to specific individuals.


  • 1.
    This note is in the primary book notes, Book and Journal of Mattanaw, here: notes.html#1
  • 2.
    This note is in the primary book notes, Book and Journal of Mattanaw, here: notes.html#2
  • 3.
    This note is in the primary book notes, Book and Journal of Mattanaw, here: notes.html#3
  • 4. Equality, in the uppercase form, in this article is the traditional project, and movment, which advocates an undefined but mutually communicated political and social equality, or social justice. When one hears about equality on the news, or “equality” in politics, it is this Equality that is referred to. It is treated respectfully with expectations of mutual agreement. This Equality is to be distinguished from mathematical equality, which will be written in lowercase, without quotation.
  • 5. Only when we switch from mathematics to politics and the social Equality project do these words get confused as being the same, or get utilized as synonyms for each other. When in mathematics, these words require very specific meanings in order to be as useful as they are, and the rules for doing math are different for each of these concepts. In the Equality project, these words suddenly become acceptable substitutes, that one uses when one feels one has been used too repetitively, or when one seems not quite fitting. “Not quite fitting” however, does not lead to usage that creates a social expectation that substitution is not permissible, but does lead sometimes to a usage which is slightly more clear, and closer to mathematical usage, but still not mathematical. Equivalent may be used when dissimilarities seem to make it a better word than equal, but may not be separate from the motive to use it, because the word equal has been overused in the same conversation.
  • 6. Seldom because in math one may still be interested in modeling forms of social fairness and justice, using precise mathematical techniques that would not really employ those same words. Mathematicians may be interested in using mathematical techniquest to explain what fairness might be in different contexts. In game theory, there are efforts to describe what fair games might be, using mathematical methods that use equalities.
  • 7. Equalitarian culture is here meant those cultures that use short non-specific slogans using “equal” in advocacy of social views concerning distribution of justice and resources. The author has in mind groups that are often thought to be “western style democracies”coming from a European, English speaking, or British heritage. The author is partly from the United States, and is thinking of the United States, and countries of similar ideals, when he writes about Equalitarian culture. The reason for using “Equalitarian” and not “democratic culture” or “western culture” is that currently, both seem somewhat non-globalist and partial. Equalitarian is also an unfortunate term to use, yet it does seem to capture the views of groups under consideration; those who want to advocate a kind of ambiguous equality that is assumed often in government documents, including the Declaration of Independence of the United States, but also government documents of other democratic nations. Equalitarian slogans used typically do not offer what equality is about, or which comparisons were made, or which measurements were under consideration, or which social program and objectives indicate an equal comparison. There is an assumption that such a comparison would not be required. Statements are short and are somewhat like “We believe in human equality” or “We are all created equal” and the like.
  • 5. When one has selected a candidate precision of a simple measurement of an object, that is expected to be somewhat accurate, it will be found the chosen measure for the task, which is not too granular, but granular enough for utility, which includes comparison, will be one that is of low precision, especially taken relativistically in comparison to how highly precise the measurement could be. As an example, one may choose centimeters or inches to measure a person’s height, thinking that usefully precise, and usable for comparisons. However, immediately one can see that it is low precision given what is available for measurement of lengths. Even using low precision of just inches, however, one can see that differences are anticipated in comparisons, which means what is really expected routinely at low precision is inequality. If inequality is not expected, comparisons would not be useful. The choise of measurement and to measure has some expectation at the precision quickly chosen, which is a low precision, that differences are detectable and are anticipated.
  • 5. I have a strong disinclination to rely on examples which bring to mind real people. While these may make clear examples for the reader, I am strongly suspicious concerning the value of information which has been shared by media, and think that very likely their situations are not well understood. Furthermore, examples are easy to arrive at. We can create many examples which would easily reveal what we know on experience from actual examples which we need not speak of excessively. Furthermore, I want examples to be more abstract, to show that they generalize to some if not all other examples which have existed. In this way the reader is free to call to mind other examples and see that it applies more generally. My intention is not to focus only one one example but show how it relates to all the others also.
  • 6. Aggregates of equations may be used to support the inference that objects are the same. In programming, one may say that one object that is created under a class is equal to another object for being created with the same properties. This is more familiar and two objects may be tested for equality by checking all properties for their separate equality. Aggregating smaller equalities may be used for supporting propositions about rough equality of abstract objects or objects in nature, but more needs to be said about this later in this article.
  • 7.
  • 8. Certain measures will have a smaller scale, or only a few distinct selections. These still have precision related issues which conceal differences. Some will think, perhaps, that someone who has blood type A has an equal blood type to someone else who has blood type A, and so on. Another exmaple might be positive and negative charges. These examples are of greater interst in our section about what might be truly equal in world, later in this essay-chapter.
  • 9. Propositions are used to provide clarity to sentences making them more usable in more formal logical arguments. I do not subscribe to the idea that a propositional expression is one that is already atomistic regarding its logic and math, and that it cannot be subdivided further to include additional information completing the description, which would serve for the best logical and mathematical arguments possible. Typically, writers do not make the logic very clear. We can utilize propositions like this to create greater clarity; a clarity which is appropriate to the type of demonstration to be provided. What the reader should take from this note is that the author knows that it can be taken to a more detailed logical view, which the author knows supports his thesis. It is for this reason that it can be omitted unless it becomes necessary to show such detail, should it become more appropriate to do so.
  • 10.
  • 11.
  • 12. Deterministic theory is relevant to this discussion and will be treated elseewhere by the author. Briefly, deterministic theory points out the importance of physical causes which precede and exist within and around one’s life, governing one’s life and future. While this point of view is contented in some ways, it is not contentended in all ways. It is not hotly contended, for example, that one’s language and exposure to learning determines one’s mind, and that without education opportunities, one would not have the mind one has. Because one is born into a time in which education exists, one has access to learning that results in one’s mind. This is why we are able to confidently understand that we think the way we do because of our surrounding culture, and not like early primordial humans, becasue of the causal connection with the development of our culture, and the availability of our learning opportunities. Efforts are expended by people to learn well, but this does not diminish that if stimulation did not exist, the brain could not develop.
  • 13. The objective of this paper is not to go into the details of how to measure the power or influence of any person on their environment or on themselves, and does not deny that as humans grow, they increase these powers. It is also admitted that the powers that individuals have on themselves and their environment vary. The size of the variance appears to be relative to comparisons with other humans and babies. Compared with other potential forms of power it may seem quite negligible. Taking a zoological perspective, it is to be admitted that learning animals advance in measurable ways in their self-influence and the influence of their environment, but with certain animals it appears they have negligable gains as compared with humans. It may be the case that they vary quite greately if the relative comparisons are made with their own species.
  • 14. When two babies from very different genotypes and phenotypes are placed in the same cultural context, they eventually become adults that behave similarly, but the similarity is largely due to the cultural context, which makes it seem as though greater differences are more obvious and observable at birth, than later, when the cultural comparisons become more what we are interested in. The absence of the cultural difference too, is notable, however, which allows us to attend to baby behaviors, which also, create a greater appearance of similarity than which exists in the physiology. If we wanted to understand differences in human physiology, there is an interest in separating out cultural influences, somewhat to our interest in understanding animals in their natural contexts versus animals in zoos. There is much more to be explored on this topic, and the author believes lingering on this topic would inform the vague nature-nurture debates which have existed to date.
  • 15. This discussion on inequality and equality applies to the words same and different, and clarifies their usage as well. We need to have a limitation placed on precision in order to agree that any two things are “the same” unless we are focusing on one object, and say it is self-same, or identical to itself. Speaking of people, we say they have an identity, but only regarding themselves in their uniqueness. By restricting the word identity to specific individual people, and not allowing them to be shared, we have already admitted they are unequal. Again, this may seem an obvious point as we focus on it in this way, but when Equality arises in conversation in equalitarian culture, people revert to using vague ideas that people are somehow, or someplac “equal” to each other. Again and again on close inspection we find that this is not the case. Likewise, this applies to our usage of same and different, and explains why people sometimes successfully communicate regarding sames, and sometimes do not. Absolutely humans are different and diverse from each other, whereas we admit that when we are speaking only roughly, there are samenesses that support meaningful conversation.
  • 16. A mathematican, can come to believe, writing symbols on paper, that those symbols are “found” equal to one another, even if the mathemacian used the hands only.
  • 17. We call them identical twins, not because we are ready and prepared to provide them the same identity paperworks. We are not prepared to say they are the same person. Rather, they are the closest examples among humans to being the same. In math, an exact sameness is an “identity” or an “equality”. The name identical twins is a kind of misnomer. They are very similar but they are not really identical. This is the case even if they are the most similar examples of comparisons of animals we have available.
  • 18. Statistics here would be utilizing data collected on repeated comparisons of humans in total. Simply using vision, identical twins side-by-side, would have visible differences that humans would notice. These differences would be noticed quickly, and once noticed, would result in a judgement of “self-evidence”. “It is true just by looking.” On simple reflection of one’s experience, people know this to be the case, so a definite scientific experiment collecting such information is not really necessary. For purposes of establishing the conclusions of this paper, it certainly will not be performed, but it is expected that any confirming study would arrive at this result. Our resulting statistical inference on this data and experience would provide a true inductive input into our premises in our argument for the theseis of this paper, and for the proposition following this sentence, realting to this note. For those unexposed to logic, a sound argument is one that is not only valid logically, but has true premises, which sometimes require data related evidence and earlier inferences. Statistics is used to create the true premises and the sound argument. The complete formalization of this argument is omitted due to excess complication of the essay in its thesis which is true obviously on inspection. Again, a completely sound and formalized argument can be provided indicating the same results. It is not known whether the present author will have sufficient interest to carry out that effort, but is able to do so, and if it is performed by another, he would be grateful for confirmation in the scientific community. This type of separate work is standard in science either way, where people are not themselves assured that the work is obviously true in the way the author does (i.e. does not agree the paper is self-evidently true using their knowledge and experience).
  • 19. In manufacturing, and in other businesses wanting a very greate level of reliability, and quality assurance, six standard deviations from the mean might be the maximum allowable level in which defects may be found. The objective is to have reliablility approaching 100%, knowing that the reality is that 100% reliability cannot be attained. Here we see that in manufacture, there is a desire for extremely consistent product, but an understanding that no matter how precise, the complex objects will never one be equal to another. There are enough differences that at least one object will have too many defects, if the number of objects created is sufficiently large. With a sufficient number of poducts created, there is a high probability that one will be a six standard deviation defective product. The size of the number of products that must be created depends on the type of product and the statistical distribution.

Words of Interest

Below is a list of words of interest realting to the Equality project, or mathematics, or general conversation. General conversation forgets to use the mathematics as was used in math training, so is closer to usage in the historical equality movement. This makes sense as political discussion, and social debate, is often more conversational, and often does not utilize mathematics even when mathematics is required for clarity. However, it still borrows words from mathematics, and uses it in a lax, imprecise way, which is anathema to usage in math and the science.

From memory without concern for the word’s form:

Equality, equality, equivalence, equitability, egalitarian, congruence, parity, fair, just, mutual, same, invariation, undiverse, indifferent, interchangeable, substitutable, replaceable, unspecial, unexceptional, unnoteworthy, remarkable, similar, similitude, verisimilitude.

Inequality, difference, diversity, variation, non-interchangeability, irreplaceability, uniqueness, special, exceptional, noteworthy, unremarkable, dissimilar, dissimilitude.


The following are audio versions created during the editing process.