3 ms·

I want to look into this more, but I have to wonder- if you look hard enough for a number/ratio to appear, won't you find it almost everywhere? Seems kinda like

by tibbon 17y ago

I want to look into this more, but I have to wonder- if you look hard enough for a number/ratio to appear, won't you find it almost everywhere? Seems kinda like a fortune teller asking you to look for the number '3'. I am not a mathematician, so I also have no idea what I'm talking about- just gut instinct.

pohl 17y ago
That's a good question. I would imagine the probability to vary a great deal by what particular number one is looking for. That is, I would expect it to be very easy to find small integers, but extremely unlikely to accidentally find a very large prime number. I suspect it would be much harder to find (1 + sqrt(5)) / 2 everywhere you look than to find 3.
snorkel 17y ago
The value 1.618... is not as interesting as its recursive fraction form which happens to be = 1 + (1 + 1/ ( 1 + 1/ ( 1 + 1/ ... an infinite recursion based on the number 1 is somewhat interesting and could be insightful.
dc2k08 17y ago
I can recommend a book called: The Golden Ratio: The Story of Phi - the World's Most Astonishing Number. It gave me a bit of bit of a Phi fetish. It appears like a kernel of existence.
dandelany 17y ago
Not when the number is irrational. What's most interesting to me is that phi often occurs in recursive systems, so it's discovery often implies natural recursion.
Sukotto 17y ago
The thing about the golden number is that it really does appear just about everywhere. That's one of the reasons it's so cool.
ams6110 17y ago
In the quantum realm, doesn't looking for something make it appear?
- eru 17y ago
  It may work the other way round --- if you don't look it doesn't appear. But you can't just make any stuff appear.
jordanb 17y ago
Well, the set of all numbers is infinite, so you would wouldn't expect to find just any number appear in a lot of different contexts by chance. Some numbers do tend to show up over and over again. That makes those numbers special. φ is such a special number. But there are a lot of special things about 3 though too: It's an integer (which is a pretty special property for a number to have, considering there are an infinite number of real numbers between each integer). What's more, it's a very small integer (the fourth smallest) and it's the second smallest prime number. In fact, we could say that 3 is a very special number, in the scheme of things, and has lots of reasons to show up in particular contexts. Now φ being the golden ratio is pretty much all that's unique about it. Otherwise, it's just one of the uncountably infinite set of real numbers between 1 and 2. So if you find φ show up some place, almost surely you're dealing with the golden ratio. The same is true of π. It's just some real number that happens to be the ratio of a circle's circumference to its diameter. I've heard of mathematicians working on problems and having π appear in their calculations, and then suddenly realizing that they're working on a harmonics problem. The fallacy of numerology is getting attracted to numbers that have lots of reasons to show up in various problems (usually small integers, like 3) and then taking whatever one of their many properties is most convenient and treating it as an iron link to whatever they're trying to prove.

by tibbon 17y ago

pohl 17y ago

That's a good question. I would imagine the probability to vary a great deal by what particular number one is looking for. That is, I would expect it to be very easy to find small integers, but extremely unlikely to accidentally find a very large prime number. I suspect it would be much harder to find (1 + sqrt(5)) / 2 everywhere you look than to find 3.

snorkel 17y ago

The value 1.618... is not as interesting as its recursive fraction form which happens to be = 1 + (1 + 1/ ( 1 + 1/ ( 1 + 1/ ... an infinite recursion based on the number 1 is somewhat interesting and could be insightful.

dc2k08 17y ago

I can recommend a book called: The Golden Ratio: The Story of Phi - the World's Most Astonishing Number. It gave me a bit of bit of a Phi fetish. It appears like a kernel of existence.

dandelany 17y ago

Not when the number is irrational. What's most interesting to me is that phi often occurs in recursive systems, so it's discovery often implies natural recursion.

Sukotto 17y ago

The thing about the golden number is that it really does appear just about everywhere. That's one of the reasons it's so cool.

ams6110 17y ago

In the quantum realm, doesn't looking for something make it appear?

eru 17y ago
It may work the other way round --- if you don't look it doesn't appear. But you can't just make any stuff appear.

jordanb 17y ago

Well, the set of all numbers is infinite, so you would wouldn't expect to find just any number appear in a lot of different contexts by chance. Some numbers do tend to show up over and over again. That makes those numbers special. φ is such a special number. But there are a lot of special things about 3 though too: It's an integer (which is a pretty special property for a number to have, considering there are an infinite number of real numbers between each integer). What's more, it's a very small integer (the fourth smallest) and it's the second smallest prime number. In fact, we could say that 3 is a very special number, in the scheme of things, and has lots of reasons to show up in particular contexts. Now φ being the golden ratio is pretty much all that's unique about it. Otherwise, it's just one of the uncountably infinite set of real numbers between 1 and 2. So if you find φ show up some place, almost surely you're dealing with the golden ratio. The same is true of π. It's just some real number that happens to be the ratio of a circle's circumference to its diameter. I've heard of mathematicians working on problems and having π appear in their calculations, and then suddenly realizing that they're working on a harmonics problem. The fallacy of numerology is getting attracted to numbers that have lots of reasons to show up in various problems (usually small integers, like 3) and then taking whatever one of their many properties is most convenient and treating it as an iron link to whatever they're trying to prove.