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The Remarkable Number 1/89 (2004)

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Re: The Remarkable Number 1/89 (2004)

#51

Post by foobarian »

chrismorgan wrote: post #49
NickHoff wrote: post #39

Earlier quoted context omitted.

I've always liked 1/7 as well, and I never realized that thing about doubling from 7 giving 14, 28, 56. People are always impressed when I can rattle off the digits of x/7. By the way, I appreciate your use of U+0305 combining overline. Did you enter those manually or do you have some neat way of doing it?

Heh, last time I spouted about 1⁄7 here someone asked about the overline too: https://news.ycombinator.com/item?id=24302104 . I love my Compose key.

How do you get one of those. Track down an old Sun keyboard? :)

Re: The Remarkable Number 1/89 (2004)

#52

Post by core-questions »

ckemere wrote: post #18

Presumably in a different number base (base 12, eg) it would be a different number that had this reciprocal property. Would it still be in the fibonacci series in that base?

This was my thought too. If 1/89 in base 10 works, and 89 in the 10th unique term of the series

> 1,1,2,3,5,8,13,21,34,55,89,144,...

then does 1/144 work in base 11, and 1/233 in base 12?

Assuming we of course translate the base-10 number 144 to the appropriate base-11 number (121) first. I'm too bad at math to do this anymore, maybe someone else can tell us ;)

Re: The Remarkable Number 1/89 (2004)

#53

Post by chrismorgan »

foobarian wrote: post #51
chrismorgan wrote: post #49

Earlier quoted context omitted.

Heh, last time I spouted about 1⁄7 here someone asked about the overline too: https://news.ycombinator.com/item?id=24302104 . I love my Compose key.

How do you get one of those. Track down an old Sun keyboard? :)

On my last laptop I used the Menu key as Compose. On this one I use Right Alt.

Re: The Remarkable Number 1/89 (2004)

#55

Post by core-questions »

Cullinet wrote: post #29
ckemere wrote: post #17

Presumably in a different number base, the number would be different. Would it still be in the aeries?

Without any basis whatsoever, and I really must one day put this idea out of its misery with some studying, I long suspected that quantum mechanics involved parallel universes where different bases more aptly fit with that other reality. My thought is surely crackpot but I'll explain how my idea arose : A fraction eg 1/3 describes a decimal number to infinite accuracy but creates a challenge for base 10 calculations.…

This is my favourite kind of pure speculation. You don't know what you're talking about, really, but you're clearly exploring vast areas of thought at the same time.

Remember, integers are integers are integers, because they represent the intrinsic "whole quantity" of something; this is as concrete as logic will get, the idea that there are "ones", it's pretty hard to imagine a universe that doesn't have that.

Once you have integers, then you're going to do math in an integer base; and making too high of a base has a diminishing value at at certain point, so it's unlikely we'd see higher than maybe 60. Non-integer bases exist - https://en.wikipedia.org/wiki/Non-integer_base_of_numeration - but it's clear to me that I'm too stupid to use them, and so probably most other people are too. This tells me that it's going to be a comparatively rare Many World that chooses to do this.

Choosing a number like 12 or 60 with a lot of divisors would have been nice. 1/3 in base 12 is "0.4", which is a lot nicer than 0.333... and would probably help make a lot of younger math education way easier.

Combining that with skipping "degrees" entirely and using radians from the start would probably have been wise choices. We'd have been much better equipped to divide things! I imagine a six-fingered being would have had an immediate advantage in that regard, but, alas.

Now, would some of those number constants look particularly different? Not really. Pi in base 12 is "3.184809493B91866", for instance, so it doesn't look like that would be much easier. E and other numbers similarly just end up with different expansions.

Remember, you can use whatever number base you want to, in this universe. The key is that it's just a way your brain interprets the symbols to represent a quantity; don't confuse the map for the territory. Five, the quality of having five whole entities, exists the same when it's 101 in binary or 10 in base 5 or 11 in base 4; either way it's all still just five, and so the right thing to do is to use the base system that most intuitively works for you so that it becomes transparent.

Re: The Remarkable Number 1/89 (2004)

#56

Post by pessimizer »

chrismorgan wrote: post #53
foobarian wrote: post #51

Earlier quoted context omitted.

How do you get one of those. Track down an old Sun keyboard? :)

On my last laptop I used the Menu key as Compose. On this one I use Right Alt.

I use CapsLock; lowest usefulness to size ratio possible.

Re: The Remarkable Number 1/89 (2004)

#57

Post by dontcarethrow2 »

chrismorgan wrote: post #34

On the decimal expansion part, 1⁄7 has always fascinated me, having something very similar going on. Doubling from 7, you get 14, 28, 56; and 1⁄7 is 0.1̅4̅2̅8̅5̅7̅, 2⁄7 is 0.2̅8̅5̅7̅1̅4̅, 3⁄7 is 0.4̅2̅8̅5̅7̅1̅, &c. (just changing which digit you start the recurring sequence with). https://en.wikipedia.org/wiki/142,857 talks about it a bit more; the doubling sequence thing is covered in the section 1⁄7 as an infinite…

Which also makes it easier to find the patterns in its multiple(or just divide by the extra multiple) say 1/14 starts .07142857142857. Multiples with 3 don't give us the common repeating 1428 but still repeats in its own way.. but 1/49 is pretty cool. 1/49 looks to do what 1/89 is doing but with the powers of 2. Nice!

edit: Dont know the format for proofs but heres a try.

1/49 = i=1 towards inf

sum 2^i*100^-i

Re: The Remarkable Number 1/89 (2004)

#58

Post by munificent »

kazinator wrote: post #47
alisonkisk wrote: post #23

Earlier quoted context omitted.

It's a bit silly to chase down original authorship of an idea that is a minor detail visible to many people who work in a field. It's like asking who was the first person to discover that all multiples of 11 have the same parity in the respective sums of their odd and even digits.

Since there had to be a first person who discovered that all multiples of 11 have the same parity in the respective sums of their odd and even digits, that question is obviously interesting to some historians. Due to what circumstances was that person first? What hindered others before that person? How long was the lag before use of decimal and the discovery?

It's important to remember that while technically there is a chronologically first person to discover X for all X, that doesn't imply that that person is the only person to discover X. For sufficiently obvious X, there are likely to be many independent discoverers and highlighting the chronologically first one heaps praise somewhat arbitrarily on one of them.

Re: The Remarkable Number 1/89 (2004)

#59

Post by dylan604 »

chrismorgan wrote: post #34

On the decimal expansion part, 1⁄7 has always fascinated me, having something very similar going on. Doubling from 7, you get 14, 28, 56; and 1⁄7 is 0.1̅4̅2̅8̅5̅7̅, 2⁄7 is 0.2̅8̅5̅7̅1̅4̅, 3⁄7 is 0.4̅2̅8̅5̅7̅1̅, &c. (just changing which digit you start the recurring sequence with). https://en.wikipedia.org/wiki/142,857 talks about it a bit more; the doubling sequence thing is covered in the section 1⁄7 as an infinite…

Coming from video, I've always been a fan of 1/1001. 30000/1001 = 29.970029797002997 and 24000/1001 = 23.97600239760023976. There's something about it's clean repeating that I liked. I hear people confusing frame rates by saying something like 29.976. I also don't like 23.98 as that rounding is going to cause problems later.

However, you have to be a special math something to have any of these kind of number "oddities" be anything meaningful. I wear mine like a badge of honour

Re: The Remarkable Number 1/89 (2004)

#60

Post by phizy »

DeusExMachina wrote: post #24
benrbray wrote: post #9

Earlier quoted context omitted.

There's a "theorem" about this: > The interesting number paradox is a semi-humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smal…

This is not a paradox though, as your copy and paste states. It's just a theorem (as you stated) with a proof by contradiction. A paradox must be self-contradictory under all circumstances.

It is a paradox. It assumes you have a definition of uninteresting number such that you can select the least uninteresting number, and then retroactively defines that number to be interesting by brand new criteria, which contradicts that you would have ever selected it in the first place. Thus the axioms invoked are mutually contradictory: the axioms that allow you to identify the least uninteresting number, and the axioms you invoke to declare it interesting are in conflict.
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