Is this a new trend in math?

[Philosophy Explorer]

Superficially two different areas in math may seem to have nothing to do with one another. This was the case with elliptic equations and modular forms.

Back in the 1950's a mathematician named Taniyama, after converting some elliptic equations and modular forms into their DNA forms, found those examples to be the same. His partner, Shimura, found more examples and led him and others to propose these two areas were the same. Finally Andrew Wiles in the 1990's formally proved that elliptic equations and modular forms are the same (as explained in Simon Singh's book Fermat's Enigma). This accomplishment removed the biggest puzzle in math going back over 350 years.

I've been reading about other areas of math that superficially seem different, yet may be the same. My questions are how many seemingly different areas of math are there, but are actually the same? Can you provide examples? Could this lead to new foundations of math?

PhilX

[Eodnhoj7]

Superficially two different areas in math may seem to have nothing to do with one another. This was the case with elliptic equations and modular forms.

Back in the 1950's a mathematician named Taniyama, after converting some elliptic equations and modular forms into their DNA forms, found those examples to be the same. His partner, Shimura, found more examples and led him and others to propose these two areas were the same. Finally Andrew Wiles in the 1990's formally proved that elliptic equations and modular forms are the same (as explained in Simon Singh's book Fermat's Enigma). This accomplishment removed the biggest puzzle in math going back over 350 years.

I've been reading about other areas of math that superficially seem different, yet may be the same. My questions are how many seemingly different areas of math are there, but are actually the same? Can you provide examples? Could this lead to new foundations of math?

PhilX

This would go back, theoretically, to the mirror function I argued for a while where all realities exist through a continuous mirror effect. This "mirror function" would be not just the origin of number but the primary means in which it constitutes itself as both an abstract and concrete reality.

[Philosophy Explorer]

From my online encyclopedia:

"A mirror is an object that reflects light in such a way that, for incident light in some range of wavelengths, the reflected light preserves many or most of the detailed physical characteristics of the original light, called specular reflection."

I don't think that's what you had in mind.

PhilX

[Eodnhoj7]

From my online encyclopedia:

"A mirror is an object that reflects light in such a way that, for incident light in some range of wavelengths, the reflected light preserves many or most of the detailed physical characteristics of the original light, called specular reflection."

I don't think that's what you had in mind.

PhilX

It wasn't because I prefer dictionaries:

Mirror verb:

"(of a reflective surface) show a reflection of."


This is more of what I had in mind:

Reflection (mirroring as verb):

(of a surface or body) throw back (heat, light, or sound) without absorbing it.
"when the sun's rays hit the Earth a lot of the heat is reflected back into space" · [more]
synonyms: send back · throw back · cast back · give back · bounce back · [more]

(of a mirror or shiny surface) show an image of.
"he could see himself reflected in Keith's mirrored glasses"
synonyms: send back · throw back · cast back · give back · bounce back · [more]
embody or represent (something) in a faithful or appropriate way.
"schools should reflect cultural differences" · [more]
synonyms: indicate · show · display · demonstrate · be evidence of · register · [more]

https://www.bing.com/search?q=reflect+d ... C7D238EB3E

Reflection, or "mirroring", would be a duplication through repitition of an inherent symmetry with this "replication" being a form of approximation of original form by allowing multiplicity.

[Philosophy Explorer]

I've tried doing a search for mirror functions on the internet and unable to turn up anything. This would lead me to assume that mirror functions are your own ideas or theories.

What do you think would make the best foundation for math? Mirror functions?

PhilX

[Eodnhoj7]

I've tried doing a search for mirror functions on the internet and unable to turn up anything. This would lead me to assume that mirror functions are your own ideas or theories.

What do you think would make the best foundation for math? Mirror functions?

In my limited opinion, I want to emphasize limited strongly, it would be one of three in theory.

The mirror function would observe the self-reflective capacity of all number manifesting further number while maintaining the original number in the form of a set of answers (you can see this in the MDR thread loosely). Hence "set theory", while certain fundamental axioms may be "turned" a little, is inherent within the basic act of arithmetic.

This reflective capacity of numbers would be what I call, and this is strictly me only, an origin function in the respect that the form (number) and function (addition, subtraction, etc.) are integrated as 1 in such a manner that both form and function are inseperable. Now this origin function, that of "mirroring", would presuppose that a function exists prior to the unified form/function dichotomy of all number, but I do not believe this to be the case as "mirroring" in itself is both a form/function resulting in further form functions. Hence 1 form/function results in another form/function to put it loosely and we are pointed in the direction of metamathematics.

As said on the other threads, where standard arithmetic views a percieved seperation of "1", "+" in "1+1", mirror theory would argue that "1" and "+" are not separate at all.

So 1+2=3 would convert to:

⨀(+1,+2) ⧂ (+1,+2,+3,*1,*2,*3)

Where:
⨀ = Mirroring
⧂ = Mirrored in Structure (equals)

All positives, as addition, inseperable from the number themselves in turn mirror into "multiplicatives" (as multiplication is the addition of addition) and in themselves are inseparable from the numbers. The form and function of the number replicate, not just the number itself, hence we are able to better observe the origin of number as a form of reflective alternation (similar to an expanding circle). In simpler terms the question comes: Which came first the form or function? Does 1x result in addition/subtraction/etc. or is it vice versa? Mirror theory takes the stance both happen simultaneously from a higher form/function through which all number extends from.


Now as to being 1 of 3:

1) The mirror function is about 95% done and contains about 120+ algrebraic expressions. However because I am not quoting anyone, do not have a master's, and generally speaking it may appear "insane" from a traditional point of view it is not published...yet.

2) The folding function is (expressed in numbers as linear unit particulate thread) is not complete...most likely at the 40-50% stage. It deals with number originating, relativistically, from a folding process where "1" folds through itself under an act of simultaneous multiplication and division and what we understand of numbers as units may in fact originate from fractals rather than whole numbers. Number may not begin with "1" or "0" on the number line but possibly from fractals perpetually approaching infinity.

3) The "synthetic function" I have not gotten into yet due to a variety of factors but it would be a mathematization of the process of synthesis of symbols. In simpler terms "imagination", or the process of imaging, has mathematical qualities and may be more "rational" than what we previously thought it to be. This is just strict opinion however, and can be briefly in very limited mathematical sense, be observe in "imagination as a negative dimension thread".

PhilX

I was arguing they were original from the beginning, however I believe they are not original in the respect that I "created them" but rather existed all along. A brief premise to this would be in observing Pythagoras foundations for the universe as dependent upon a mirroring process of the circle (one can argue point) which exists quantitatively as 1. Pythagoras observed everything extended from a mirroring process, the question occurs how this process and be defined through symbols.

The issues of all structure in itself is the replication of boundaries. Math, as you observed in more depth than I have, follows this same format if one is to look at the nature of number as a "boundary" in itself. The question is how do numbers, and their corresponding function through which they manifest, "replicate" to form the symmetry which both maintains and expands them?

Now forumula's, as extensions of the very same numbers which manifest these replicative properties, in theory should continually replicate symmetrical versions of themselves as approximates of an original formula. So this mirroring function, while premised in the origin of number, extends to the very same things the numbers manifests (ie formulas, equations, etc.). A philosophy of "as above so below and as below so above" would observe this philosophy further where this replication occurs as a form of self-reflective alternation.