Saving Math from Plato

By Harry Binswanger
Mathematics is the headquarters of Platonism-the reification of abstractions and the primacy of concepts over percepts. Even Euclid defined “line” as “breadthless length,” something not of this world, and the moderns define “one” in terms of nonbeing (the null set). In this lecture, drawing on a few incisive statements by Ayn Rand, Dr. Binswanger gives perceptually based definitions of key mathematical concepts, such as quantity, measurement, one, number, point, line, infinite, and mathematics itself.
Delivered at OCON 2023 in Miami, Florida on July 3, 2023.
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[@KINGSLEYEZE-bn7bu]

One of my best lectures. 👌

[@ExistenceUniversity]

What is the nill thickness of the image of Dr. Binswanger on my screen? What about the thickness of the line I imagine in my head?

[@lmf9308]

The thickness of the image on your screen is nill. That is to say, it is negligible (in most contexts). The thickness of your imaginary image of a line is also nill (otherwise it wouldn't be an image of a line).

[@ExistenceUniversity]

@@lmf9308 What is that thickness?

[@zardozcys2912]

Awesome explanation of the meaning of imaginary numbers. So in reality they are vector numbers or direction numbers. Much more understandable that way.

[@TeaParty1776]

What about imaginary politics, eg, Biden and Trump?

[@alexhauser5043]

They're not vectors. The 'imaginary unit' is a rotational operator. All difficulties disappear once it is so characterized.

[@zardozcys2912]

@@alexhauser5043 complex numbers are vectors. Multiplying and dividing by an 'imaginary number' represents rotation but adding and subtracting represents movement perpendicular to the number line.

[@alexhauser5043]

@@zardozcys2912 "complex numbers are vectors." No, they're not. Complex number multiplication and vector multiplication are defined differently. The former can only be multiplied in one way, whereas the latter are 'multiplied' in two distinct ways (cross product and dot product). Complex numbers and vectors are operationally distinct, and only superficially similar.

[@science212]

Eric Temple Bell wrote good books about the subject.

[@geekonomist]

@ 37.25 The length of that line is 5 and 1/2. Ask any carpenter.

[@ExistenceUniversity]

9:10 Counterexample to Dr. Binswanger: Euclid also states a plane is length and breadth but no thickness, which might be equally alarming to Dr. Binswanger, but the shadow he is measuring is a mathematical plane, the shadow has no thickness. The shadow of a line has no breadth. Abstraction of a point has having no length as well is fine. Its a very small thing, smaller than any ruler can measure but exists at a place and time, like a point charge.

[@BalugaWhale37]

How is "a very small thing" different than the concept of nill that Dr. Binswanger described?

[@ORagnar]

A shadow is lack of light. It's more like an absence of a thing than a thing. o

[@jocr1971]

if a thing is of zero dimension along any of it's axes it can't be said to exist in space..and by extension, in time. something not in space or time is a non thing. or nonexistent.

[@ExistenceUniversity]

​@@BalugaWhale37 Well stars for example, to ancient mathematians, a star is just a point taking up essentially no room. If you want to teach geometry, you don't want to start with something with length and breadth and thickness as you haven't explained those yet. The square you eventually want to talk about needs a corner to start your drawing at, and that corner has no length or breadth or thickness. Sure the depression and ink or graphite does, but we don't want to discuss engineering friction of carbon on paper to talk about a square. Everyone can see a dot is that which has no length, or else we'd call it a line. Line-of-sight meaning straight ahead without breadth

[@ExistenceUniversity]

@@jocr1971 A point is THE PLACE that exists.

[@ExistenceUniversity]

In reality, we will (at some points) disagree about what counts as the past, the present, the future, and the distance between objects, and all that we will agree on is that causality is real. Given causality as the fundamental basis of all the rest, we will eventually need to give way to the fact that the aether exists and that time is a dimension alongside the 3 spatial dimensions, and that everything except causality is relative.

[@siyabongampongwana990]

Can someone please suggest any books, philosophers, and or mathemticians that hold this view of mathematics.

[@ExistenceUniversity]

What view?

[@siyabongampongwana990]

The one expressed by the speaker "Harry Binswanger" in this video.@@ExistenceUniversity

[@ExistenceUniversity]

@@siyabongampongwana990 Tell me what argument he made here at all? I love Harry Binswanger, but this was not a lecture or an argument. It was pedantic nitpicking with no solution and no saving from Plato at all

[@IanGilmore]

I think Dr. Binswanger is working on a book, but there is "Mathematics is about the world" by Robert Knapp. Dr. Binswanger has discussed that book in the past, and has some disagreements with it, but is examining similar ideas.

[@alexhauser5043]

You might appreciate the work of N.J. Wildberger. Vladimir Arnold also comes to mind.

[@science212]

George Gale wrote against Russell and logical positivism.

[@ExistenceUniversity]

Allow me to correct the definitions of "point", "line", and "plane"/"surface". Point: a location in space and/or time, omitting the various measurements of length, breadth, and depth of the representation marker. Or A point is that which occupies a space but has its parts omitted. Line: a line is length with the differences in length and the other dimensions in general are omitted. Surface: a surface is that with length and breadth with the differences in length, breadth and depth in general are omitted.

[@science212]

Read Penelope Maddy. She is for mathematical naturalism and realism.

[@siroutrage1045]

If math, as done by humans at least, is independent of experience why don’t all people become great mathematicians?

[@diegomorales8616]

I asked so many math professors, "What does this mean?" at the end of an example problem, and every time like a mantra they all answered, "The answer to the problem is (the answer they calculated)."

[@jocr1971]

math has no meaning without the context to which or from which it is applied or derived.

[@ExistenceUniversityStudentClub]

Why would ask that question? Were you not paying attention to the lesson when they were explaining why they are calculating this example. Presumably the example was the purpose and meaning behind the math of solving the problem. Like this is how I imagine it going: Teacher: To find the height of the tree from the length of the shadow it casts, we can you trigonometry and use this formula to find the height. You: What does this mean? Teacher: it means we can find the height of the tree using its shadow. Were you hoping for a different response?

[@TeaParty1776]

@@ExistenceUniversityStudentClub What is reality and mind such that from some facts, other facts are facts? What kind of universe has a necessary height/shadow relation?

[@micchaelsanders6286]

59:00

[@ExistenceUniversity]

Unfortunately the argument leads to this: For anything to exist it must have non-nill thickness in infinitely many dimensions. If the volume is a cube, it has six surfaces, but a surface having nill thickness means it is itself a volume, which would have surfaces, but every surface is a volume, which has surfaces... etc. This means there cannot be a "cent". Another issue. If you draw a triangle on a piece of paper the line drawing of the triangle has a thickness we agree, but the negative space of the drawing has created a second triangle inside the graphite lines. That triangle has a surface without thickness and exists itself as a plane without thickness. That triangle is not the paper.

[@lmf9308]

You didn't even explain which argument you are referring to.

[@ExistenceUniversity]

@@lmf9308 What argument did he even ever make?

[@lmf9308]

@@ExistenceUniversity You tell me. You are the one who referred to "the argument" and then started talking about what it leads to.

[@ExistenceUniversity]

@@lmf9308 LOL are you slow? I mean, what was Dr. Binswanger's purpose in this lecture? What was the main argument of his lecture? What was the moral of the story? All I heard was he didn't like some definitions and replaced them with worse ones. What was the point of the whole lecture?

[@hellothere-hx5by]

I would say irrational numbers represent real quantities, it’s just that they can’t be written as ratios. The definition of The sqrt(2) is the quantity of length of a right triangle when both sides are of length 1. PI is not 3.1415…… because infinity doesn’t actually exist. PI is just PI, a particular quantity that may only be written as a number as PI. It is that number that is the limit of the perimeter of a unit-lengthed n-gon (n*sin(180/n)) as n goes to “infinity”, i.e. it approaches this quantity as n keeps increasing, and we call it PI. (as n increases, there is a pattern of it going closer and closer, but never beyond, this quantity we call PI). Real numbers describe quantity due to the continuous nature of the world.

[@TeaParty1776]

>infinity doesn’t actually exist. Infinity is s potential that never sctualizes. -Aristotle

[@ExistenceUniversity]

@@TeaParty1776 By your argument however, nothing exists. Everything is quantum foam. So what are you going to do about that?

[@hellothere-hx5by]

@@TeaParty1776 agreed

[@TeaParty1776]

@@ExistenceUniversity quantum foam thus exists. Why exclude it from existence? What about disco music? If anything is excluded from existence, then surely its disco music. Everything exists, equally and within or as a limit.

[@ExistenceUniversity]

@@TeaParty1776 What are you trying to say? You are making no sense whatsoever.

[@ExistenceUniversity]

Leonard Peikoff's "History of Philosophy: Aristotle: Epistemology" lecture, especially at the 10 minute mark, explains what Binswanger has done wrong in this lecture. Binswanger is being Platonic, or anti-Platonic. As Jean Mulroney's anti-value theory works, Harry has held the Platonic world as true, but rejects it outright and therefore just refuses to use abstractions, but this is exactly Plato's problem. Peikoff lecture, knocks down this lecture by showing that the thinking is the same: "That because the world is actually always 3 dimensional, that lines and surfaces cannot exist and therefore world of forms. Plato and Binswanger both accept this premise, but Plato embraces abstractions as real and king, and Binswanger rejects the abstractions and embraces over defining concepts such that they always represent one of the members of the kind.

[@TeaParty1776]

I have the written transcript from decades ago of Peikoffs Aristotle lectures. Ihave Peikoffs recent Hist Phil book. Binswanger is not mentioned > [Binswanger]defining concepts such that they always represent one of the members of the kind. In his How We Know, he does not say this. He implicitly agrees w/Rand that kind=concept and that concepts are mental integrations of units, ,not a representation of a member. Your claims are more bizarre than false

[@drstrangelove09]

to me math is a way of modelling reality... and so the operations are analogs to things in reality... we can combine objects and so we have addition I think that you are wrong about it not being true that between two points there is another point... I think that is true I also think that there are infinities

[@user-qm4ev6jb7d]

When he says "numbers don't really exist, they're conceptual tools", I would say: numbers don't really exist, they are *fictional characters,* which are *sometimes* used as conceptual tools. And, indeed, much of math was invented specifically *for* the sake of using it as a tool. But that doesn't mean that it's in any way "wrong" to talk about those mathematical objects which _only exist in the fictional story,_ like infinities, dimensionless points, and the empty set. There's nothing wrong with continuing the story for story's sake, and maybe eventually discovering that the newly invented characters have a practical use. Just like it happened with complex numbers.

[@ExistenceUniversity]

Right?! I was thinking this the whole time, like does he know Hank Rearden doesn't actually have a weight and height and therefore Ayn Rand wasted her time making up a story about reality instead of just describing reality including the thickness of every surface. He throw the baby out with the bathwater.

[@lmf9308]

Interesting perspective, thanks for sharing.

[@TeaParty1776]

Numbers are valid methods used by the mind in identifying reality. They are not products of imagination, eg, the characters in a novel. The mind has definite properties which thus act in a definite way. Reality is what it is and man can know it from many perspectives, eg, concrete, abstract. Man can know concrete trees as concrete trees or know them as forest. In both cases he knows concrete trees. But a different kind of knowing. Eg, a near-sighted person uses eyeglasses or not. Reality remains. Blurriness is a perspective. Reality is not blurry.

[@user-qm4ev6jb7d]

@@TeaParty1776 Since when are *methods,* in general, *not* products of imagination? Methods are first invented by the mind, then checked on known data (also in the mind), and only then checked in reality, to see if they can help in unknown situations. It is a "different kind of knowing", yes, and it's a completely *manufactured* kind of knowing. None of it is about reality, up until it's empirically checked. "It does not make any difference how beautiful your guess is, it does not make any difference how smart you are, who made the guess, or what his name is - if it disagrees with experiment, it is wrong." - R. Feynman

[@TeaParty1776]

@@user-qm4ev6jb7d >Since when are methods, in general, not products of imagination? Since the Greeks discovered the mind and its powers of knowing reality. Look out at reality, not inward. Focus your mind. The Your hidden context, the unfocused mind, is a random mental junkpile of mysticism and subjectivism , not knowledge of reality. Man knows reality by some means, with some method. Your hidden context is the pre-scientific mind/reality split in which knowledge of reality is impossible (subjectivism, Leftism) or possible without mental effort, means or method (mysticism, conservatism). Western civ, inc/the Enlightenment, is not part of your ideas. Intro. To Objectivist Epistemology-Ayn Rand >if it disagrees with experiment, it is wrong." - Disagrees in what context? Knowledge is contextual, ie, reality as known. There is no escaping philosophy, the study of reality as a whole. Man needs a framework for his mind. Yours is mindless empiricism, a chaos of logically and causally isolated and changing concretes known by statistics, ie, mindless counting. The atomic theory was opposed for decades because Logical Positivism accepted only immediate, unconceptualized experience.

[@science212]

Logic is Aristotle philosophy. And boolean logic. Not "multi-values" in analytic school.

[@science212]

Plato, Kant, Russell, Mach, Carnap, Kripke, Lewis, Quine, etc. All of them anti reason.

[@alexhauser5043]

Plato - His method is dialectical. Have you ever read one of his dialogues? They consist of very careful, logical refutations of misbegotten notions. Kant - Kant is unreadable. I'm not convinced that he and Hegel weren't schizophrenic, so I'll give you this one. Russell - To call Russell 'anti-reason' is absurd. Superficial, unoriginal and uninteresting? Absolutely. Mach - A very capable working physicist. There's nothing irrational about insisting that our physics should be based on the perceptually given as opposed to opaque and mysterious theorized entities. Carnap - Logical Positivism was a dead end, certainly. Anti-reason? A philosophy that dismisses empty speculation and verbal masturbation? The charge is risible. Kripke - Too technical; haven't read. Lewis - Admittedly goofy in his views on modals. Quine - Critiqued the Analytic/Synthetic Dichotomy before Peikoff did.

[@TeaParty1776]

@@alexhauser5043 > Kant is unreadable Not if youre stoned.

[@science212]

Hempel, the ugly philosophy. @@alexhauser5043

[@science212]

Russell, Canap, Mach- Listen to Stephen Hicks@@TeaParty1776

[@HBinswanger]

@alexhauser5043 Plato's arguments are, by modern standards, uncareful and only surface logical. Kant was explicitly anti-reason (see the famous quote from the preface to the 2nd edition of the Critique of Pure Reason). Kant is brain-crackingly hard to read but Hegel is truly unreadable. Russell did not intend to be anti-reason, and he's all over the place in his views (except for the right view). I agree he's superficial. Mach, I have (like you) some respect for. His relativism bears thinking about. Carnap is silly. Kripke, from the little I've read, is on the right track. Lewis, I was actually a co-student with him (and his former wife Stefanie) in Hilary Putnam's class on meta-ethics at MIT. I don't recall his views. Quine, terrible, but also didn't think he was anti-reason. His "critique" of the Analytic/Synthetic Dichotomy ("Two Dogmas of Empiricism") is coo-coo. His criticism of the a/s is weak (viz., no one has given a clear definition of it), and that's the essay where he famously says that physical objects are comparable, epistemologically, to the gods of Homer.

[@ExistenceUniversity]

"The science of inferring some measurements from others" From other what? From other measurements... from what? It's measurements all the way down. To say that math does not describe things while showing the formula which describes how the length of a ruler and the length of the tree and the length of their shadows and the relationship they share.

[@alexhauser5043]

I don't know why Objectivists are so opposed to characterizing mathematics as the science of magnitudes. Rand obviously knew next to nothing about mathematics, and Peikoff seems to know nothing at all about it. As far as I'm aware, there are virtually no (if any) Objectivists with doctoral degrees in mathematics or one of the hard sciences.

[@ExistenceUniversity]

The three quotes Harry uses at the start are both entirely and abusively taken out of context, as well as actually supporting his thesis. Russell, despite his issues, is agreeing with Binswanger, there are no real lines without breadth, at least for the common man on earth, and therefore math is a subject where we use lines and points and it works but since lines and points don't really exist then how can we know what we did was true? This is what Binswanger is saying the whole time (whether he knows that or not). The Kline quote was abised heavily! Kline is literally attacking the Platonists, and how they Platonists believe in contradictions because they need the world of forms. Kline is saying exactly what Binswanger is saying. Einstein is also stating the same thing. He also is agreeing with Binswanger. He is saying, lines don't actually exist, we cannot experience them, and yet they work for abstracting and producing machines that operate perfectly well given a subject matter which is so abstract that its contents don't actually exist. This out-of-context strawmanning is the worst part. I don't even know what to say about that dishonest approach, except to say that he clearly knew followers won't check his sources...

[@lmf9308]

You make the very serious accusation that Harry Binswanger has dishonestly straw-manned Russell, Kline, and Einstein. I am quite familiar with the ideas of Russell and Einstein, and I disagree with you. You didn't actually argue in support of your accusation. You did not explain why you think the quotes from Russell, Kline, and Einstein meant something other than what Binswanger implied that they meant.

[@ExistenceUniversity]

@@lmf9308 He clearly took them out of context. I went to the original source and read them. I am sure you are capable of doing the same

[@TeaParty1776]

Points and lines are methods of knowing reality.

[@ExistenceUniversity]

@@TeaParty1776 Units are methods of knowing reality. What is your point?

[@ExistenceUniversity]

@@TeaParty1776 Are you under the impression that I think points and lines exist in a world of forms? Lol. What is the point to your comment? Yes, a point is a method of knowing reality and it is defined as that without parts, it is the place in the universe that is not an other point in the universe. Two unique points can have a line, a length with no breadth, between them. Those abstractions help me know reality. So what is your follow up. Points are a method of knowing reality, now what?

[@ExistenceUniversity]

Ayn Rand: "With the grasp of the (implicit) concept “unit,” man reaches the conceptual level of cognition which consists of two interrelated fields: the conceptual and the mathematical. The process of concept-formation is, in large part, a mathematical process." "Let us now examine the process of forming the simplest concept, the concept of a single attribute (chronologically, this is not the first concept that a child would grasp; but it is the simplest one epistemologically)-for instance, the concept “length.” If a child considers a match, a pencil and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement. In order to form the concept “length,” the child’s mind retains the attribute and omits its particular measurements. Or, more precisely, if the process were identified in words, it would consist of the following: “Length must exist in some quantity, but may exist in any quantity. I shall identify as ‘length’ that attribute of any existent possessing it which can be quantitatively related to a unit of length, without specifying the quantity.” The child does not think in such words (he has, as yet, no knowledge of words), but that is the nature of the process which his mind performs wordlessly. And that is the principle which his mind follows, when, having grasped the concept “length” by observing the three objects, he uses it to identify the attribute of length in a piece of string, a ribbon, a belt, a corridor or a street. The same principle directs the process of forming concepts of entities-for instance, the concept “table.” The child’s mind isolates two or more tables from other objects, by focusing on their distinctive characteristic: their shape. He observes that their shapes vary, but have one characteristic in common: a flat, level surface and support(s). He forms the concept “table” by retaining that characteristic and omitting all particular measurements, not only the measurements of the shape, but of all the other characteristics of tables (many of which he is not aware of at the time)." "Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit. Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables-i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted. Please note the fact that a given shape represents a certain category or set of geometrical measurements. Shape is an attribute; differences of shape-whether cubes, spheres, cones or any complex combinations-are a matter of differing measurements; any shape can be reduced to or expressed by a set of figures in terms of linear measurement. When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity. Similarity is grasped perceptually; in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philosophy and of science to identify that fact."

[@science212]

Morris Kline was not a good writer. Carl Boyer was. Isaac Asimov knew that.

[@1surfer12]

We don't know what Plato thought about mathematics, as he wrote dialogues in which he did not express his own opinion. HIs dialogues are dialectical exercises intended to challenge the reader to think critically and rationally. Platonists are people who read his dialogues as if one or other character is Plato, and this leads to problems, to say the least.

[@science212]

Mathematics is real. Read Robert Knapp.

[@Holmnielsen-]

lol, there is another Robert Knapp so you might want to add a link

[@jiriinuk]

Just out of curiosity: Did you find any fundamental difference between Dr. Binswanger's and Dr. Knapp's approach to the philosophy of math?

[@jiriinuk]

I know he is, I haven't read him yet. His book is on my shelf waiting to be read.@@science212

[@science212]

Knapp is a very rational scholar. @@jiriinuk

[@science212]

Knapp and Binswanger are the same. They're for logic. @@jiriinuk

[@kyjo72682]

"There is no concept of nothing." - There is. It's the absence of everything.

[@zardozcys2912]

Concepts are formed by abstraction from referrents. The complete absence of everything is not an existing thing to abstract from. So you cannot sign a concept for it. It is what we call an invalid concept. Like a square circle. You can form those words but you cannot hold a referent in your mind that IS both a square and a circle just like you cannot picture an existent nothing.

[@kyjo72682]

I fail to see what the ability to picture something in one's mind has to do with any of this. Can you hold 100 objects in your mind? No.. only a few at a time, like 5 or 6. Does that mean that the number 100 is an "invalid concept"? No.. Can you imagine "everything"? Obviously not. Does that mean that the concept of infinity doesn't exist? No.. We're talking about the concept of existence and non-existence itself. Saying it's an invalid concept is like saying that the predicate logic is invalid because its quantifiers ∃ and ∀ are invalid concepts. Meanwhile predicate logic being extremely successful and basically forming the foundation of all modern mathematics. Because it works.

[@TeaParty1776]

@@kyjo72682 > picture something in one's mind concepts are identifications of reality, not copies of reality. Rand has a radically new theory of concepts

[@TeaParty1776]

@@kyjo72682 Pragmatism is false. Mans needs a focused mind

[@scottwolf8633]

Mathematics is a language/Science of what MAY actually be occurring. Then the Empiricists devise tests to observe whether the Mathematics is correct or not. If correct, We've learned something new about how Reality operates. If not, throw it out and start over.

[@alexanderscott2456]

666591278421000030059276 was exactly the same number I thinking of!

[@11kravitzn]

Maybe next time consult with a mathematician and a philosopher of mathematics so you don't go and make a total ass of yourself. But then, this is about as mathematically sophisticated as Ayn herself, which is to say sophomoric.

[@TeaParty1776]

Evidence?

[@ExistenceUniversity]

@@TeaParty1776 Evidence of what? What are you asking here? What would you accept as evidence that Dr. Binswanger should have consulted a professional mathematician? The only evidence one can really present is the knowledge of mathematics and why this video was, sadly, an embarrassment.

[@alexhauser5043]

I've long found Rand's near total lack of knowledge of mathematics and the physical sciences bizarre. How can someone glorify reason and rationality endlessly while having no working knowledge of its most perfect products?

[@TeaParty1776]

@@alexhauser5043 Rand is a philosopher, not scientist. Philosophy is the base of all knowledge because its based on common human experience, not specialized knowledge. Claims that contradict common human experience are false. Science begins in mans sense experience of the concrete , material universe, not in conjectures and refutations. Scientists, like all people, are man facing the universe, not brains in a vat pumping out statistics based on arbitrary, subjective ideas. Thats the mentality of primitive savages prior to the discovery of scientific method by the first scientist, the philosopher, Aristotle. A human being cannot live his life moment by moment; a human consciousness preserves a certain continuity and demands a certain degree of integration, whether a man seeks it or not. A human being needs a frame of reference, a comprehensive view of existence, no matter how rudimentary, -Ayn Rand

[@alexhauser5043]

@@TeaParty1776 "Rand is a philosopher, not scientist." Rand was a polemicist above all else. Her writing lacks the argumentative rigor and analytic character of genuine philosophy. I expect ALL intelligent persons to have some interest in mathematics. Indifference to the subject is the virtual sine qua non of the pseudo-intellectual. Please refrain from lecturing me with Randist copypasta in your subsequent replies; I read Rand extensively when I was a teenager. Nothing I wrote implies that philosophy is superfluous or inferior to science.

[@emanuellasker3650]

Mathematics derives from the Creator's purpose which is to limit the Eternal Chaos. This purpose is formulated from The Mystery of the Light. And He insured that Man would discover mathematics by constructing Man from the very essence of God Himself, once removed through transmutation. So, through the imperative of the divine purpose from which he was created, Man discovers mathematics in order to describe the Creation around him. And there can be only one commodity which can limit the Chaos.

[@TeaParty1776]

The content of the unfocused mind is horrible and terrible.

[@TeaParty1776]

The Creator hides your minds chaos.