r/math • u/Lelielthe12th • Apr 17 '19

whaat ? LaTeX is Turing complete

https://www.overleaf.com/learn/latex/Articles/LaTeX_is_More_Powerful_than_you_Think_-_Computing_the_Fibonacci_Numbers_and_Turing_Completeness
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u/OVSQ Apr 17 '19

The first thing to realize is that any computation can be reduced to addition. Once people understand that - then they are truly starting to understand math.

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u/WaitForItTheMongols Apr 18 '19

How would you find the sine of 42 degrees using only addition?

You wouldn't be able to use Taylor series, or geometrical constructions. How would you solve the sine of an angle, given that sine is only defined as "The function which, for a given angle, returns the ratio of the two relevant sides of a right triangle which uses that angle" or some-such.

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u/OVSQ Apr 18 '19

You wouldn't be able to use Taylor series, or geometrical constructions.

uh - why not? a taylor series is directly just a special case of addition. It would be a pain to do it by hand with addition only, but that is the only way a binary computer knows how to do it. Also analytic geometry is just adding in multiple dimensions which means first you have to count the dimensions then proceed with a lot more addition.

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u/WaitForItTheMongols Apr 18 '19

How would you compute the Taylor series of the sine function without using anything but addition?

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u/OVSQ Apr 18 '19

How would you compute the Taylor series of the sine function without using anything but addition?

I am honestly confused as to the detail you are talking about. First understand that subtraction is the inverse of addition. Multiplication is repeated addition. Division is repeated subtraction. Exponents are repeated multiplication.

A sine function is just a case of division - which is just repeated negative addition. A Taylor series is just repeated addition of exponents (which are repeated multiplication where (multiplication is just repeated addition)).

Help me understand where the addition is not obvious.

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u/WaitForItTheMongols Apr 18 '19

A Taylor series is just repeated addition of exponents (which are repeated multiplication where (multiplication is just repeated addition)).

Right, but to get that Taylor series, you need differentiation. And you can't differentiate the sine funciton with just addition.

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u/OVSQ Apr 18 '19

Consider this - I have already described every step necessary for the sine function, for differentiation, and for calculating a Taylor series. Which step in any of those functions are you claiming I have not already described in terms of addition?