There are lots of articles about math as a language.

http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx

https://en.m.wikipedia.org/wiki/Language_of_mathematics

Any language has a ‘listening’ part, a natural foundation that users of the language cannot build upon i.e., ‘a source’, and a ‘building’ part which is the superficial language itself i.e., words, grammar etc that contain information of various kinds developed into a sort of worldview. In other words any language can exist by itself, and two or more languages are mutually exclusive, they can’t exist together properly without conflict, but from a wider view there is a benefit to ‘many languages’, some hidden ‘wisdom’ that no one single language contains.

https://www.quantamagazine.org/how-physics-gifted-math-with-a-new-geometry-20200729/ 

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The following is copied from a comment about a Youtube video https://m.youtube.com/watch?v=ShdmErv5jvs

"One: Mathematics is the language of nature." 
"Two: Everything around us can be represented and understood through numbers." 
"Three: If you graph the numbers of any system, patterns emerge."

 That's a good way of saying that eventually ai development of sciences will use a 'number', instead of arbitrary code, to represent the elements of a science.

Another example.

https://m.youtube.com/watch?v=3vi7043z6tI

The first video has a person motivated by hunger, ambition, at a basic level. The second maybe a higher level or a level that is only important after the first level has been satisfied.

Whether a person agrees with either video specifically, there is evidence that the broader idea of all sciences containing mathematical progressions is accurate.

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When a non academic person references a quantity, they refer to a specific object, the number doesn't have to be articulated.

"How many oranges?"

"This many."

When a person starts to study mathematics specifically they start with integers. 1, 2, 3, 4, 5 etc. Not because integers accurately reflect any specific science, other than the science of math, but because they are easy to learn, communicate etc. You can always figure out the next integer by adding one. So, the 'science' of integers is easy.

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Sciences can be divided into

a) natural sciences, which are based on concrete realities in 'the common world' and are reducible to numbers, even if that is not generally done, and

b) paradigms which can be shown to be sciences because they reduce to numbers, even if their scientific validity is contradicted on some other grounds, and

c) hypothetical sciences which are generally considered sciences but which may in fact be just a product of the group that is defining what a science is i.e., a projection of some flaw in their understanding of the world.

Those three types of science are not 'official' of course, they are completely made up. Another website will say there are x different kinds of science distinguished by such and such.

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So, accepting that math is a science whose basic language is composed of integers, the way a written language is composed of letters, a person should ask if there would be a natural variation of that basic language that applies to other sciences. For example

integers are to the science of math, as

x number progression is to the science of y.

When a science starts, it begins with the elements that led to a rational, or scientific, pattern being identified. Chemistry started with the realization that there are numerous ‘root’ substances which have 'some' relationship. After a science develops then there becomes a visible overlap with other sciences.

https://en.m.wikipedia.org/wiki/Aether_(classical_element)

So, is there an overlap between the science of math and other sciences, a progression of numbers that corresponds to other sciences?

There are some people who would say definitively that there is, and there are others who don't know.

If a person accepts that there are number systems that correspond to natural sciences, as defined above, then it should be possible to work backwards as well, finding a natural progression of numbers and then deducing that it corresponds to a natural science, even if that natural science is not usually articulated exactly as the progression of numbers suggests it should be.

Math is a primitive science still. The only progression that has been sort of mastered is integers. 

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Prime numbers are perhaps the second most 'obvious' progression of numbers, after integers, but almost nothing is known yet about prime numbers.

Integers consist of some composite numbers and some new numbers.

For example ten consists of 5 twos or twenty consists of 10 twos or 4 fives, etc, but eleven is a new number, a prime.

Ten and Twenty can both be 'built' out of numbers previously used, but eleven cannot be communicated except as a new number or a combination of new numbers.

So even though common mathematics teaches that integers are the natural progression of numbers, a person can also be educated from infancy to believe prime numbers are the original progression, and integers derive from primes.

A person raised to order things by prime numbers, rather than integers, would not just count differently, they would reason differently and perceive the world in a way very unlike an integer person.

Likewise, a step further, when a third natural progression is found it would be possible to educate a person such that they would consider the third progression to be natural and original, with integers and primes derived from it,

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One other obvious number progression would involve natural numbers that occur as part of an order within a specific paradigm, or across paradigms, ‘constants’.

For example pi is the same for big objects, small objects, it is the same in every country or territory, but it may or may not be dependent on a common paradigm.

There are an unlimited number of constants that exist within any paradigm, but their ‘progression’ may be different from integers and primes, for example. They may not progress from ‘close to 0’ to ‘close to 100’ to ‘close to 10,000’ etc.

What their progression would be, whether one constant would be ‘higher’ or ‘lower’ than another, might only become visible when certain sciences have moved forward a bit. For example, there isn’t currently a science of paradigms in popular culture. People usually perceive other paradigms as flaws in their own paradigm rather than a necessary balance to some bigger paradigm, just as people view foreign cultures as flawed reflections of their own culture rather than as ‘other’ cultures which are internally consistent in a way their culture is not. Once the bigger view is available, ‘a science describing paradigms’, then constants that form the boundaries of paradigms can be arranged in some coherent order.

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'Primeness' isn't just a mathematical idea. You can say anything has 'elements'. Colors for example can be reduced to some primes from which other colors are made etc.

Another point is that the 'logic' of metaphysics and mystical traditions is in primes, not integers, so a person could say that prime numbers are the math progression of those sciences, and allow a person to both learn accurately, extrapolate, and spot errors or 'ignore accurately'.

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AI in computer networks will ultimately involve using numbers to represent the elements of a natural science.

Representing scientific elements or other aspects of a science is done today by first translating 'element a' of 'science b' to a number by giving it an arbitrary mathematical term in the binary code of computers.

For example if you want to use the concept of hydrogen on a computer you would start with the word hydrogen, or some variation, then give that word a representative symbol in arbitrary computer code. In fact everything in computer code is first filtered through a written language, so it would be done automatically.

But if hydrogen were known to have a certain position in a natural progression, around which there was a logical framework, then instead of translating

a) object to b) word to c) arbitrary value, a person could use the actual numerical value of hydrogen, for example

a) object to b) actual value within the specific science being developed.

At first that kind of function would need to use a program which converted the 'computer environment' to some sort of architecture in which the symbols like 'hydrogen' acted properly, but eventually a computer could itself be designed for each science environment. A computer that can have 'hydrogen' as an element, or 'bit', and whose architecture is symbolic of how elements interact.

Then using the corresponding number pattern the science could be developed 'accurately' as long as it is first defined properly. So 'developing' the foundation of a science would be easy, and mastering it within a network would be easy.

What would be next?

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https://www.vice.com/en_us/article/pa8dw8/prime-number-pattern-mimics-crystal-patterns

https://iopscience.iop.org/article/10.1088/1742-5468/aad6be/meta

This page mentions math as a language that is useful for unifying sciences, but in fact there are many disciplines that various cultures develop to provide a connection between their sciences. Another interesting one, besides math, is syllables in Tibetan studies. When Tibet was fairly independent they developed an unusual science of syllables which became a field of study connecting other of their arcane sciences. Anagariko Govinda was one of the few outsiders to record some of that science.

https://en.m.wikipedia.org/wiki/Anagarika_Govinda

Since the Chinese invasion and occupation, Tibetans scholars have begun eliminating sciences like that, as tribal groups do when they are being melting potted.

Around the world, every day, more and more elaborate ancient sciences which have never been cataloged nor translated are disappearing, destroyed by melting pots.

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The Jung Number Archetype

This is not an archetype Jung specifically mentions, but it is clear from his writing that he treats numbers as archetypes.

'One' would correspond to his Self archetype, among other 'things'.

'Two', dualism, is the 'non physical' viewed through the physical, among other things. Dualism here is not referring to the common dictionary definition, but to the fact that any 'non physical' or 'spiritual' fact can only be expressed physically by the relation of two opposites. In other words everything physically expressable has an opposite and to express something non physical requires using two opposites.

The first archetype in this list 'one' or 'self' refers to a totality or completeness that is not physical, but it does not refer to something specific, so Jung tried to make it a singular object for ease of communicating. It is equivalent to a singular 'god', which of course cannot be communicated. In some foreign traditions there is a well developed version of this https://en.wikipedia.org/wiki/Neti_neti 

'Three', a trinity, includes, for example, the Christian and Hindu trinities.

Four, quaternity, can symbolize death, wholeness, etc.

Odd numbers and even numbers refer to broader concepts.

These are clear Jungian archetypes which are often abused/modified by individuals or groups for their own reasons.

 

 

In Progress

 

 

https://www.quantamagazine.org/landmark-math-proof-clears-hurdle-in-top-erdos-conjecture-20200803/