Is the pi constant the proof of the Demiurge's existence? [closed]

Question

Consider the following infinite continued fraction for pi:

The pattern is obvious. Can this fraction be the proof of the Demiurge's existence?

Answer 1

No. Mathematical constants like pi do not provide any direct proof of the existence of any mythical creature.

Answer 2

This an infinite formula series like the Madhava–Leibniz series https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80 , Many other similar converging infinite series approaching pi exist. https://math.stackexchange.com/questions/14113/series-that-converge-to-pi-quickly

More precisely, it is an infinite continued fraction https://en.wikipedia.org/wiki/Continued_fraction

It seems there are multiple known infinite continued fractions equal to pi:

• https://en.wikipedia.org/wiki/William_Brouncker,_2nd_Viscount_Brouncker
• https://en.wikipedia.org/wiki/Euler%27s_continued_fraction_formula

As wikipedia states, this is an infinite converging series that converges on pi in the infinite. In practice by calculating it to a certain degree, one can approximate pi. It is not the only known series to describe pi, nor the best (in terms of how quickly it approaches pi with each additional fraction).

It is called an "converging series" because it will never exactly reach PI, but over time get closer to it.

This can be related to the ancient dilemma of "squaring the circle" https://en.wikipedia.org/wiki/Squaring_the_circle

Pi is one of several so-called transcendental numbers (https://en.wikipedia.org/wiki/Transcendental_number) whose value is proven not to be calculable using only finite "simple" operations.

The fact that certain transcendental numbers can still be approximated using "regular-looking" infinite series may be somewhat surprising initially, but maybe not overly so since the famous ones are grounded in geometry, and geometry is typically what made mathematicians come up with approximations. And geometry would have a lot of symmetries which in math would tend to look like regular series.

As an example, the area of a circle can be approached by first finding the smallest triangle outside a circle and the biggest triangle inside the circle. Then the same with squares. Then the same with 5-sided polygon (pentagon), then with 6-sided, 7-side, 8-sided and so on. Each would be more "circle-like" than the previous. So by increasing the number of edges, we can get closer and closer to pi. This in turn can be used to describe an infinite series that gets closer and closer to pi by "adding whats missing" from the inside polygon or "removing what's too much" on the outside polygon. So we can expect to find some approximations of pi as infinite series which look "regular" to the human mind.

However those approximations are not necessarily the "best" ones that maths could find. They rather reveal limitations of the human mind in problem solving and show some creativity using maths and infinite series.

Trying to find evidence of the supernatural in Maths is related to Numerology, and trying to pin this onto a specific supernatural entity would best be discussed in the subsite dealing with that given cult or religion, as those superstitions are not part of philosophy.

Answer 3

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series