Abandoning Equality

Friday, August 5th, 2022, at 8:42 PM Alaska Time



Author: Mattanaw, Christopher Matthew Cavanaugh

Former Chief Architect, Adobe Systems

Current President/Advisor, Social Architects and Economists International.



This paper discusses the thesis that the clearest treatment of human similarities and differences assumes propositions that are quite contrary to what has been assumed in popular culture. These propositions include that people taken individually are unequal on almost any individual measure that is of interest regarding their traits. Taking people to be complex objects which are the complete combination of their measurable traits, they are clearly unequal as wholes also. Diversity is an expression of specific inequalities of traits, and not equalities. 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 needs to market for social justice 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 or 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 needs 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. Since this extends to all people universally, the author notes that welfare has not been distributed to their natures and situations in a way that is based on human designs or plans, as much as natural pathways of history and pre-history. Humans individually can be randomly taken and distributed across regions, and by this method it can be demonstrated that their receiving of goods is unrelated to their later efforts, which are also dependent on those earlier goods. Those who are able to imagine themselves being unfortunate in a way outside their control like another baby grown adult, and also recognizing, that their benefits also were also outside their control., being themselves babies grown adult, they may feel care and concern, for all to whom misfortune and lack of control applies. Since lack of control applies to everyone, it is known that misfortunes were distributed not according to any demerit, and from there is concern about how their lives could be made better more deliberately.

Additionally, the author covers 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 developemnts 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.


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. 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.


One thing I have found that blocks careful thinking about the topic we are going to develop is the way we talk about it as a social ideal with meanings that are somehow separate from the words we are using. I will resist, from this point on, saying things such as, “Human equality” or just Equality, capitalized to indicate it is a kind of social institution, or collective assumption. Whereas, the phrase, and the capitalized form of equality, really does use the word “equal” 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, and justness, equivalence, and even alternative usages which are quickly taken to be synonymous, like egalitarian, equitable, fair, and similar words, which really are not synonymous. These terms are employed when one seems overused in the same conversation, or when one does not appear completely fitting. For example, if “equal” seems too strong, one may rely on equitable, as an admission that “in this usage it is known it cannot be precisely equal, but something closer to fair seems possible.” Balanced, proportional, congruous, and other terms may be employed to a similar effect.

Notice that all of these terms, except “just”, or “fair” really do have a usage which is from mathematics or the sciences. 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 reaonsable 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 negotation 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 relats 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 captilize it. Conversation cannot go futher 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 unerstanding 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 belive 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, perahps 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 agains 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 admissable. The purpose of this usage is to give the reader the impression that such statemetns 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 separatd 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.

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 thse which I pointed out earlier.

Babies and Amorphous Beginnings

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.

I think this perspective is really useful, if it is understood in detail, and not extended to mean something more and additional than what it really means or implies. There are useful consequences and uncomfortable consequences to this point of view that bring clarity to one’s thinking about politics and morality. Here is a brief list of points which extend from what is true about facts related to our beginnings as babies:

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. 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.

It appears to me that democratic nations have grown from this more accurate and detailed fact, that we were all babies, 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.

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

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.

However, words like equality, in mathematics, do have a special precision. In mathematics, it has even been overlooked for the trustworthiness that it really does have. In other writings on mathematics, 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. 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.

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

For this 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.

In competition, we want to see and experince 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 differnt, 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 disasterous. 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.

In many ways I think it is irrefutable that we really do not think people are equal, 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 recieved 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.

What I wish to say is that I don’t want to dwell on this side too long. 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 improvemetn 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 measuable 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 themselve 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.

This is a point where I hope the reader recognizes what I have stated earlier. This is a well tested view. 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.

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.

Notice that when thinking about sports and competition in that context there is a kind of clarity about inequality. 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 wordlview.

However, a 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. This is where vagueness creeps into the topic, which seemsm to come in the form of 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 contxt.

For example, 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 speciment 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, andclear ways of comparing which exist within the sport. In social life we are much more confused about how justice is to be allocated, particularly becasue 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 gone into the vaguest of locations, partly because the topic is huge. 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 convercing 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 agreeement 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 Justice

Here, once again, I feel that I need to articulate that I am on the side of furthering social justice, and not taking away from it. 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 ofmy 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 realted 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 defintely exists. Some may confusingly and vaguels 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, involvings starving children, and extreme wealth differences which appear unjustified. Such an admission would forget, that onen’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

“equality” is a word that does not stand on its own. The mathematical trust and precision that we have given to it implies that there has been an evaluation anytime it is used. The reader is used to this, from school, and would not object to this idea, that equality expects a comparison, and is often understood in shorthand using the equality symbol, placed between two values. Note this means that it is not used when no valuation has happened. In other words you don’t use equality when a measurement has not happened or is not expected to happen.

_______ = ___________

Looking at our familiar math, we can see something is expected on the left, and on the right, and those things would be numbers, which would come from measurements in the world, which are compared. Suppose we have two athletes, one is 165 centimeters tall, and the other is 166 centimeters tall. We would not be able to use equality for those:

165 != 166

In school we would say that 165 is not equal to 166. If, however, we took measures, and it was 165 for each athlete, we would say:

165 = 165

And we would say that the two objects in the world, the two people, who are athletes, are equal in height. That is an example of an 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 eons of math, the discipline which itself depends on it, as self-evident. Outside of math, in a vague social territory, 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.

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. There are exeptions, in mutual perceptions of events, in whih two people pereceiving the same thing, can mutually admit as a datum, that that thing was perceived or happend. 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.

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. 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 to a point when people are treated more fairly, using those measures. Consider again, that comparing two athletes who do the same type of sport, at the same position if it is a team sport, are compared on more than height. Sowe move to other comparisons which may or may not be equal. Suppose we measure the athletes on weight, and find that they are both 68 kilograms. We can say on that they are roughly equal too, and now we are making a list of statistics or metrics which are common to what is prepared for competitive athletes:

68 kilograms weight 166 centimeters height

Now let’s just say they are 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 leanmass - 60 percent lean mass

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 copmarison 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.

However, if I was the reader, by the time we were at 5 measures, I’d start to get annoyed by making them equal. I would anticipate that as we were taking measurements, that some would be different. 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, would have measures that are differnt. 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.

This suspicioun 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, becasue 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 existe 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 equal even on one measure, and certainly not when all of them are unequal and totaled together. This means that Equality is to be greatly distrusted, once gain, because it borrows a mathematical concept which an opposing viewpoint uses. The opposing viewpoint is the one that createes clarity, and not vague Equality.

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-mathematicans 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 atheletes, 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 knowlege 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 appers 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 peopl 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 corrrect 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 explailn 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 acceping Inequality is self-evident.”

Saying inequality is self-evident feels similar to calling everone 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 marketingn 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 beter 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 becasue 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 differnces, 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.

[Edit above]

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 alterantive 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 vlue 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 aheive more balanced well-being, and not equal distribution.

[More on this when not tired]

Truly Equal Things

Moving towards a greater precision in understanding the entire topic, let’s take some time to talk about what really can be equal. I did mention that those two checks from the government with the same amount of money written on them would be equal in a way. Let’s consider some things that are equal and then come back to this check, and see how it is equal, and how not, since there really are ways that matter to everyone, in how they are unequal.

An intereseting consideration supporting the current thesis is that equality is not the simplest thing to find, even if one searches carefully. There are strange realizations revealing that other things thought to be equal, still are not on greater consideration.

Simple measurements at high precision that still result in the same values might be said to be approaching equality. These are measurements, narrowly considered, for things that themselves are likely much more complex. However, measuring two things, and finding them to have equal length, at extreme precision, which 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. One that one measure, going ever more precise, one would find that they still are not equal down to the elemental level. 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. A physicist would say that certainly these two things are not equal in an ultimate way. A mathematician, however, comparing two values, without any units specified, might be lead to believe, falsely, that an equality exists, corresponding to the equation. 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. Howver 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.

Notice, however, that chips in a manufacuturing center really are mostly interchangeable, not only in the width of the chip, but in the total function along all relevant measures of the chip. You buy a computer and it works, and someone else buys the same model, and it works. 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 total equality.

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.

One might say, however, there are aspects of the two devices which are equal in ways that are more resistant to this type of differnce finding. This might be the design of the device which migh 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.

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. Humans could never have the similarity and interchangeability as chips, and since those are unequal already, we know there can be no equality in total among humans.

But back to our present topic of finding things that are equal. 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. But there is a recurring issue about inequalities that would be found at the elemental level. If we are comparing two electrial 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 functioning, and consistency of dimensions, we would still find that they do not have the same elemental configuations. Calculating variety on elemental configurations of gold in gold wires, 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.

This brings us to the consideration of something that does seem to have the candidate requirements of equality in nature based on what we know: this is chemical elemental interchangeability, at the single element level. We except 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 different lifetimes.

For our purposes though, this is really about as close to equality as we will get. 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.

In other words, equality in nature cannot be confirmed for any two things compared.

Certain equations in nature seem to have a greater exactitude than perhaps what this kind of measuring with instrumentation canconfirm. Some will say, on this basis, that it appears that nature is following what can be found on paper very elegantly. Forexample, 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 verificaition with instruments is not possible. Such a thing might indicate that in the physical-mathematical formulas we can see equalities which cannot beseen 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 physicsits, mathematicans, 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 consistecy 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, appearst 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 conventially 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 havea 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 achieveable in science or in math. Self-evidence and precision do exist, but that’s due to gradual work in the sciences and using measurment 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 considing 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 righly 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 conversastion 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 alredy 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 expectatation 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 simimlar measurements, similar DNA, similardata, 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:

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

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.

It is the position of the author, and this paper, that we ought to abandon the idea of human equality as we have inherited it in tradition. This would be akin to continuing and promoting a program of vague Equality, which is contrary to the above propositions which are really close to self-evident. It is better instead, to speak of human diversity and to utilize measurements, and to assume the above propositions, which are antithesis to assumptions that people are equal. The expectation is this alternative approach will result in clarity in communication.

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.