Mathematics and Sex

The purpose of the writing is to illustrate two important misconceptions in two very different domains, respectively. mathematics and sexuality.

It is precisely because they belong to areas that are so far apart that we can spot the extend to which we humans—who else can be so creative—can stick to old habits, even when presented with convincing knowledge that would otherwise cause us to integrate it, and then act on it.

Mathematics and sexuality play very different roles in our lives, even though they are both fundamentally indispensable: one because our physical world is based on it and the other because without it, we would not be here at all!

One difference between them can be that we do not really need to deal with mathematics, which is also considered by many as something quite dry and free from emotion: mathematical laws and statements can hardly be discussed, at least in the common world, where there is a consensus that two and two are four, regardless of gender, religion, or social status.

Sexuality, on the other hand, is one of the areas that most can be—is—marked by emotional undercurrents, and is so much influenced by culture, religion, and economic forces.

A final contextual detail, however: the misunderstanding in the domain of sexuality has been known for several millennia, as it has been described in the past, a long time ago, while the one mathematics has been first brought to the world's attention in 2001 (in an article, "π is wrong", written by Bob Palais, see here)!

Now that we have set the framework, let's look a little more in details—among others by mentioning the two misunderstandings—and afterwards examine the facts that point out that they are misunderstandings.

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1. Pi (π=3.14159...), despite its celebrity and the almost mystical interest it has aroused around the world for a very long time, is not the "fundamental number," we think it is!

A little explanation of my use of the term "fundamental number", with an example:

4, because it also can be expressed as 2 times 2, is not a fundamental number.

2, on the other hqnd, can be considered as fundamental because it cannot be broken down to something more fundamental. 2 is at least "more" fundamental than 4 (remember this statement, it is used again later).

Mathematics, moreover, occupies itself among others with finding what is most simple, most fundamental—and by the way, as a result, most elegant—and build on it.

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2. The ultimate purpose of sexuality—and here we are not talking about procreation, which is, seen from nature's point of view, the ultimate purpose of sexuality; rather, we talk about sexuality as an ability humans share with only a few other species: having sex for the sake of pleasure—is not that the man gets an ejaculation (in the context of this writing, we are talking only about heterosexual sexuality, other orientations are treated elsewhere—although an observation of human sexual activities from the outside, through literature, movies, porn, etc., appears to show that it is the purpose!

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If asked to say what π really is, then most of us will remember from our school days that the circumference of a circle is its diameter times π! This shows by the way the degree to which π pervade our surroundings: every time there is a circle, then π hides in the background: any wheel, any pipe—water, gas, etc.—a trumpet and many more, just to name the most visible appearances of π.

How can I say that π is a fraud!?

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As sketched out before, in other words, the convenient visitor from Mars—or Venus, or another planet—who should come to Earth and observe human sexuality would only come to the conclusion that a man's ejaculation is the highlight of any sexual encounter (remember we talk only about heterosexuality here), if only because a clear majority of these episodes end with some kind of outpouring of semen, visible or not.

* * *

Once we have passed the test of π's definition (circle's circumference / diameter), we are confronted with the question of how we draw a circle.

There are two different ways to draw a circle, I can take a glass or a round can, put it on a piece of paper and draw the circle's circumference. Or I can use a compas, or even the compass's predecessor, a piece of string with a pin at one end and a pencil on the other. I set the pin firmly on the paper and draw the circle with the pencil.

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Sexuality is of course, in some ways, more complicated than mathematics, precisely because it is about people and their emotions, which cannot, yet, be defined with as sharp a precision as mathematical concepts.

So here, instead of definitions, we can look at the equivalent for living beings, ie. how people are built, ie. Physiology—sexual physiology, as far as out topic is concerned.

In a man, the sexual physiology is (apparently) clearly associated with procreation because when the man has an orgasm, he gets also an ejaculation. Relatively few men get away without experiencing some fatigue after ejaculation: in fact, most men must rest before they can "perform" again.

In a woman, on the other hand, the sexual physiology is clearly free from procreation. In other words, a woman's body built to be able to experience orgasm after orgasm without there any reproduction-related requirements or adverse impact.

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If you are really paying attention, you can begin to see that there now are actually two ways to describe the relationship between a circle and its respectively diameter or radius: on the one hand we have the already mentioned "circumference is diameter times π" and now "the perimeter is all points lying at the same distance to a given point."

You may wonder: how can it be that π has been defined from the first formulation—the relationship between the diameter and the circumference—and not from the other—the relationship between the radius and the circumference?

* * *

You may wonder: if this description of the human sexual physiology holds—and there is not so much that can contradict it—so it appears that women and men are rather incompatible beings: one can get all the enjoyment, she wants, while the other is limited by the significant energy loss brought about by an ejaculation, and the next, and the next...

* * *

It is easy to understand that people have chosen the circumference/diameter definition for π, because we live first of all in the physical world, where our approach to a circle is more often through its diameter than through its radius: we have a good feel for how much water can flow through a pipe by looking at its diameter, we can "feel" a glass's diameter when we hold it in your hand. An example of where the radius is more visible is a vehicle's wheels.

Said in other words, it is because we have a primarily physical relationship to the world around us that we have "prioritized" the diameter over the radius. The physical world has blinded us and led us to give more attention to the diameter of a circle than to its radius, thereby forgetting mathematics' requirements of simplicity!

* * *

Here we have a clear difference with the π topic, although it is still about our skewed vision of the world around us that causes us to end up with a misunderstanding about sexuality.

And, as mentioned before, because sexuality can be affected by many more human factors than mathematics, we need to look at aspects of society that are so deeply rooted that we are no longer aware of them.

Our modern culture is largely based on male premises, ie. a man-centered culture where female interests are therefore suppressed, as they have been for millenia.

* * *

You may not even see how π could be "wrong", and what to use in its place!

However, it is simple: if you look at what the diameter is to the radius, then you have the answer: the radius is more fundamental than the diameter because the diameter can be expressed as twice the radius—like 4 is twice 2, as seen above. The radius, on the other hand, cannot be simplified further.

If we now take a circle and divide its circumference by its radius, we will find a number which of course is just 2 times π. And it is precisely this number, that is the fundamental number in the relationship between a circle's "roundness" (circumference) and its "linearity" (radius).

This number is called Tau: τ.

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If we look more closely at sexuality, it becomes clear that men get pleasure (hence ejaculations) too soon, while women get less enjoyment, precisely because their partners get theirs too soon, a kind of a vicious circle (!).

What corresponding to τ in sexuality is that men, during millennia, have been blinded by their relation to their enjoyment without regard to their partners.

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Well, will you say, this is not such a big problem. Fine, we know we were wrong. We do not need to eliminate π, because we would have to rewrite all the textbooks with the hassle and expense and confusion it would cause! It is not like when Sweden decided to switch from driving on the left lane to driving on the right. We have lived with π for centuries, and we can live on with it.

* * *

As for sexuality, it is perhaps the same: men can maybe become a little more aware of women's needs and then it should be okay.

Here also, we have lived with it for millennia!

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It is precisely one of the main points of this writing: to show that even with mathematics, where things must be either right or wrong—because it does not involve feelings or soft values—the worst aspects of what being human means sneak in, in the form to an inability to recognize one's mistakes, even when confronted with eloquent documentation.

Once a person has become aware of the "π problem", a review of some basic mathematical topics reinforces the argument that π should be replaced with τ/2.

* * *

Once a person has become aware of the sexual problem, it becomes increasingly clear that there is something we can do about it. And, as mentioned at the beginning, what we can do about it has been known for several millennium, unlike with π.

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The fact of looking at a the most simple definition of a circle is in my opinion already enough evidence:

When a circle is defined as the points that are at the same distance—the radius, from a given point, the circumference is then radius times τ.

There are moreover numerous examples where τ is more appropriate than π.

Firstly, it is clear that if we look at mathematical equations that involve π, virtually all of them actually invoke 2 times π, not π alone!

A simple example that does not require advanced mathematical knowledge is a circle of radius 1. By the current definition is the circle's circumference 2 times π. If we use τ instead of π, then the perimeter is 1 times τ. That is, one full circumference is one τ.

If we take a half circle, it corresponds to a half τ (with π, it would be one π for a half circle). And so on.

There are many more examples showing that some mathematical topics that are rather cumbersome when we use π, becomes much more manageable when we take τ instead.

A clear example thereof is how we name various angles that are fractions of a full circle trigonometry (sine, cosine, etc.).

The following image shows a full circle and how different angles are called in different "languages".

Image of angles in various units

This clearly shows that when τ is used, the angles use of the same fraction than the circle divisions use. That is, a right angle, which is a quarter of a circle, corresponding to τ/4, while when using π, it becomes π/2!

This has unnecessarily confused many generations of students.

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The extent of the side effects of our misconceptions of sexuality is much broader than for π!

If we look at gender relations in our days, we ended in a place we could call paradoxical (in my opinion, our use of the word "paradoxical" reveals our lack of knowledge about what we are talking about. Had we that knowledge, so we would talk about contradictions instead): although women have an much greater innate sexual potential than men, it is men who apparently are obsessed with sex; men who sexually assault women; and women who in many cases have given up sex.

Over the centuries, the millennia, women have learned that they are not going to get the pleasure their bodies otherwise could allow, so they have had to suppress their sexuality.

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Despite all the very convincing considerations about π and τ (Michael Hart launched The τ manifesto in 2010, see www.tauday.com/tau-manifesto), the traditional scientific community has been very critical of the idea of τ. It must be because it is afraid to change a mistake of the past, and prefers to stick to something that has been shown to not work, instead of acknowledging the confusion and making life much easier for future generations of students, who cannot understand the reason why a right angle, which is 1/4 of a circle should be called π/2 instead of τ/4!

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When it comes to sexuality, the solution is also very clearly, if we dare—especially men—to be confronted with it. Men must reconsider their relationship with ejaculation.

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You have probably noticed that the neat symmetry, this writing began with has progressively deteriorated little by little along the way. This reflects the fact that our relationship to sexuality is ultimately more important than whether we keep π or replace it with τ.

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Final notes about π.

Perhaps one of the main reasons why it is hard for us to get rid π is that this number has achieved a near-mystical dimension over time.

Think of all those poor people who have for decades tried to interpret the bible and other sacred texts with π. Think of all those poor people who search specific sequences of numbers in π, be it social security numbers, telephone numbers, birth dates, etc., in the hope that it will make sense!

Then they must all start over with τ!

Michael Hart himself, in one of his videos, shows that he had learned many decimals of π by heart (and now he has også learned many decimals of τ!).

I would almost guess that people might find more "meaning" by examining τ than they ever will with π.

Because τ is a fundamental number!

* * *

Last remarks about sexuality (this issue is elaborated on elsewhere).

We have seen that there are good reasons to replace π by τ.

Similarly, there are good reasons to encourage men to limit their ejaculations.

It may seem almost crazy to have to do without some of the best we men can experience!

It is actually more that it is scary, especially because men who have not tried it imagine that they end up getting less enjoyment.

Men who have tried it, on the other hand, know that a man who has gained control of his ejaculations end up getting MANY times more pleasure than with ejaculations!

It's the same as with π: We live with a misunderstanding about how we relate to the world around us!

When men understand that ejaculations would be best reserved for procreation, they can enjoy a fuller sexuality in the long term and also give their women more enjoyment.

I am convinced that before long it will become just as unpopular for men to get ejaculations outside reproduction than it has become for people to smoke!

* * *

Is it a mere coincidence that Michael Hartl has chosen to associate τ with Taoism, as the following picture shows?

He came to it for obvious reasons: the letter τ is pronounced as "Tao", which is not that far from "Tao-ism". And as can be seen at the end of "The Tau Manifesto," this association has been a good source of puns that can compensate for the loss of the puns that have been built around π.

This writing takes a whole new dimension when it becomes known that Taoism is precisely one of the two most known ancient philosophies that have recommended for several millennia that men consider another form of sexuality, among others by limiting their ejaculations...