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Intrinsic mathematics
I didn't miss it, I just hadn't gotten around to it yet.
I'm not sure what you're trying to say here.
Oh, there's many. If you want to know more I recommend you study mathematics.
It's interesting, isn't it? It's not difficult to wow an idiot, but there are things that are so complex that an idiot isn't smart enough to understand enough to be amazed by. So, I guess a person is amazed by things that are slightly more complex than they can understand, and bored by things much less complex.
| I'm not a professional, though perhaps this hexagonal number nth term is proof, as the sum of consecutive numbers would strictly be n^3 if I am not mistaken. n^3 - (n-1)^3 |
| I don't reckon you're aware of a hidden gem? |
| what is the level of mental ability demonstrated when someone demonstrates a high level of interest and awe when seeing an example of the given intrinsic mathematics. Is he demonstrating a low mental ability, as in truth it is merely a particular intentional arrangement of already established laws? (Assuming he is not enthralled by the aesthetically pleasing element, rather he is astounded by the fact maths just possessed such intrinsic ideas) (admittedly, that was partially copied) |
| If your test for something special is based on its opposition to something else then you'll be waiting a long time. |
Also, while we're at it, you apparently don't know what "definition" means, because the perimeter of the mandelbrot set is not its definition; the definition is simply the set of points C that make the iteration Z <= Z^2 + C not diverge.
I have a perfect understanding of the term ‘definition’ and what it means. I didn’t define the set as its perimeter. I did however comment on carols reference to its perimeter which due to its fractal nature is infinite in length. That in turn is based on Benoit Mandelbrot 101. cf his introductory comments on rulers and measuring the distance around the coastline of England.
Phi is special for all the historical, aesthetic, architectural, mathematical reasons well known to most people and easily discovered by anybody who doesn’t know who isn’t lazy. Try googling it perhaps? I already know and appreciate its intrinsic beauty and application
Phi is special for all the historical, aesthetic, architectural, mathematical reasons well known to most people and easily discovered by anybody who doesn’t know who isn’t lazy. Try googling it perhaps? I already know and appreciate its intrinsic beauty and application
| I have a perfect understanding of the term ‘definition’ and what it means. I didn’t define the set as its perimeter. I did however comment on carols reference to its perimeter which due to its fractal nature is infinite in length. That in turn is based on Benoit Mandelbrot 101. cf his introductory comments on rulers and measuring the distance around the coastline of England. |
You then brazenly replied
| Excluding the fact that it resides in the complex plane and that it has an infinite 'perimeter', in fact no perimeter whatsoever. |
Right, so the context with phi was that the discussion was the aesthetic part of it. The full quote that you originally replied to was:
| I don't subscribe to the idea that there's anything special about phi. I've yet to see any convincing arguments for it being applicable in art and having any special aesthetic properties. I've seen far more evidence in favor of 3 being aesthetically pleasing. https://en.wikipedia.org/wiki/Rule_of_three_(writing) https://tvtropes.org/pmwiki/pmwiki.php/Main/RuleOfThree https://en.wikipedia.org/wiki/Rule_of_thirds This could be cultural, though, not an intrinsic property of the human mind. |
To re-iterate on this point, there's nothing that shows that a ratio of phi is more aesthetic to people than other ratios, e.g. 1/3, 3/4.
In addition, a lot of the arguments I hear about the golden ratio involve it supposedly showing up in nature more often than other ratios, e.g. in mollusk shells, but my understanding is that this is confirmation bias/overfitting the data to match pre-existing beliefs, and that the proportions are often significantly off of being the golden ratio.
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| Try googling it perhaps? |
The complex plane is 'just two numbers'. How absurdly wrong is that!
What pre-existing beliefs would they be? Perhaps at a stretch intrinsic appreciation of beauty. Word salad more likely.
Of course if you mix the spiral mollusc shell observations, among many others related natural phenomena, to the Fibonacci series and its relationship in the limit with phi you end up with a completely chopped and tossed salad like the above Gonadian tosser philosophy complete with that bias and prejudice.
| but my understanding is that this is confirmation bias/overfitting the data to match pre-existing beliefs, |
Of course if you mix the spiral mollusc shell observations, among many others related natural phenomena, to the Fibonacci series and its relationship in the limit with phi you end up with a completely chopped and tossed salad like the above Gonadian tosser philosophy complete with that bias and prejudice.
"Phi is beautiful. It just is you guys, trust me. Oh, you don't agree? Well, that's because you're dumb! Neener neener!"
So weak.
So weak.
First, I wasn't hoping anything. I want to know if he can. Anyone can find curious sequences that appear to match up. Skill in mathematics is all about proving statements.
Second, just because there's a simple proof doesn't mean Rascake can do it.
Second, just because there's a simple proof doesn't mean Rascake can do it.
Well he can prove it, especially since I posted the proof.
Anyone can find such things? Well you didn’t.
It depends on which branch of mathematics what skills are required. Proving statements is only part of it.
Anyone can find such things? Well you didn’t.
It depends on which branch of mathematics what skills are required. Proving statements is only part of it.
| Well he can prove it, especially since I posted the proof. |
| Anyone can find such things? Well you didn’t. |
closed account (E8A4Nwbp)
| helios wrote: |
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| Oh, there's many hidden gems. If you want to know more I recommend you study mathematics. |
| I'm not sure what you're trying to say here. |
| So, I guess a person is amazed by things that are slightly more complex than they can understand, and bored by things much less complex. |
I am yet to confirm online what I have been informed, in person, regarding phi, however, paying regards to pi, it is said colliding blocks compute pi. The following explanation is from here: https://codereview.stackexchange.com/questions/211882/simulating-a-two-body-collision-problem-to-find-digits-of-pi
https://imgur.com/a/ISASS4a
The setup is as above. A "small" body of unit mass is at rest on the left and a "large" body on the right is moving towards the left (the initial positions and velocities are irrelevant). Assuming perfectly elastic collisions and that the large body's mass to be the n-th power of 100, where n is a natural number, the total number of collisions is always pi*10^n rounded down.
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Well, most people don't anything about actual mathematics. They think all mathematics is is running arithmetic algorithms.
Here's a couple interesting tidbits I found while looking at old emails with a discrete mathematics classmate:
* For all natural or zero n, ((2^n)+2)! is divisible by 2^(2^n)
* Let f(x) = x^n + x^(n-1) + ... + x + 1. f(x) = 0 if and only if x != 0 and x^(n+1) = 1
EDIT:
That formula was derived after proving that the sum of consecutive hexagonal numbers is a cubic number. The actual direct formula for hexagonal numbers is 1+3*(n^2+n).
Weird. You see? The only times phi comes up in surprising ways like that is because someone put it there. Even sqrt(2) has more significance.
Here's a couple interesting tidbits I found while looking at old emails with a discrete mathematics classmate:
* For all natural or zero n, ((2^n)+2)! is divisible by 2^(2^n)
* Let f(x) = x^n + x^(n-1) + ... + x + 1. f(x) = 0 if and only if x != 0 and x^(n+1) = 1
EDIT:
| The formula is the nth term for hexagonal numbers. |
| https://codereview.stackexchange.com/questions/211882/simulating-a-two-body-collision-problem-to-find-digits-of-pi https://imgur.com/a/ISASS4a The setup is as above. A "small" body of unit mass is at rest on the left and a "large" body on the right is moving towards the left (the initial positions and velocities are irrelevant). Assuming perfectly elastic collisions and that the large body's mass to be the n-th power of 100, where n is a natural number, the total number of collisions is always pi*10^n rounded down. |
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Once again Carol has completely blitzed herself in her foot. The few times phi crops up in comparison with pi just goes to show how special and intrinsically beautiful phi is.
There is no Buffon Needle Problem for phi, But for pi, like the collider, there is. Carol can keep knitting. Ha, ha ha!
There is no Buffon Needle Problem for phi, But for pi, like the collider, there is. Carol can keep knitting. Ha, ha ha!
I think I've had just about enough of you. You're not interesting enough to warrant seeing your stupidity, so I'm going to bring back that old GreaseMonkey script that let me hide users by name. I hope you had your fun, because this will be my last response to you.
closed account (E8A4Nwbp)
| * For all natural or zero n, ((2^n)+2)! is divisible by 2^(2^n) * Let f(x) = x^n + x^(n-1) + ... + x + 1. f(x) = 0 if and only if x != 0 and x^(n+1) = 1 |
| Weird. You see? The only times phi comes up in surprising ways like that is because someone put it there. |
| Even sqrt(2) has more significance. |
| I suppose some initiative may been essential for encountering the occurrences, however, it is these initiatives which make the encountering of reward, often. |
More relevantly for computer scientists, how DNA and the proteins that process it are analogous to a program tape and the reading head of a Turing machine, and how the cell as a whole is analogous to a von Neumann universal constructor. In a weird form of synchronicity, molecular biology and computer science were being almost at the same time in the early twentieth century.
| We are simply oblivious, and can't confirm which is of greater significance |
The turing machine and Carol’s first shawl knitting project are another example of very weird synchronicity.