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Comment by jl6 | Hacker News Reader

Mathematicians are locked in bitter struggle between the Zeroastrians who believe additive identity blesses 0 as truly the most foundational and therefore interesting integer, while the Unitarians favor multiplicative identity and thus champion 1. Uncountable souls have been lost to the conflict between these two groups.

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We Pragmaticists (some would say "abject pragmaticists") advocate for a compromise solution between Zeroastrians and Unitarians by taking h=½ as the fundamental constant. It satisfies several interesting identities involving other constants, like i^i=e^(-hπ), ∫e^(x^(1/h))dx=π^h, ∑n^(-1/h)=hπ^(1/h)/3, the celebrated inequality (a+b)h≥(ab)^h or the curious fact that 1/h is the smallest prime number.

Pragmaticists brought a fraction to an integer competition and lost

they lost the competition, but in the end it was them who paid the prize

Ah, but they won the Pi versus Tau competition ;-)

Halfasstrians?

Ugh, must we relate every thread about integer fascination back to Zerry/Unny zealotry? It’s been going on for centuries now, nobody’s changing their opinion at this point.

because numbers have a natural meaning. roughly speaking each integer has as many meanings as its value. so 0 and 1 are just the very beginning.

zero's natural meaning is special, it's the void. sometimes the 'variable' stands in as having this meaning, sometimes the variable is zero.

one is the easiest simplest to grasp. its meaning is "I", ego.

two is duality in the broadest imaginable sense. wars are being fought right now over the precise meaning of 3

This feels closer to a tarot reading than mathematics, and I’m here for it

The Tao Produced One;

The One Produced Two;

The Two Produced Three

And The Three Produced All Things.

Sounds very close to the firstness, secondness and thirdness categories from Charles Sanders Peirce.

(Which I think are nothing but nonsense from a madman =)

He was an awfully pragmatic madman. He also discovered the universal and existential quantifiers independently of Frege, albeit a few years later.

No offense intended, but to the extent his work feels mad to you, it might be a “you problem.” That said, he never did reduce firstness, secondness, and thirdness to unity to his own satisfaction either. His work is truly tantalizing.

Oh and abduction has had some conceptual influence too.

Sad that the Arisbe fansite got deleted.

I agree this must be a "me" problem.

I just have never found these three "universal" categories useful for anything whatsoever except for a semiotics class in university where he was one of the study subjects.

Umberto Eco on the other hand... every single thing he wrote was immediately interesting and useful.

Or funny. His Lolita's parody, Granita, was Pratchett and Adams levels of funny. He was awesome.

we can be more precise now:

the three produced the equation, which pretended that all things were (could be) equalized into equivalence. they called this algebra and parised some monotheistic god; they called this magic and GOTO one.

thats funny i always heard it was an origin with two other orthogonal roles

unless youre a dirty filioquist

Perhaps 0 and 1 are the same. If there only exists the entity called 1, lacking all properties or relations to other entities, what is left? A void called 1, no different than 0. The true mystery is: how did plurality arise?

> Perhaps 0 and 1 are the same.

Compare https://en.wikipedia.org/wiki/Field_with_one_element

Consider for a moment that Aristotle, and thus most likely all the ancients, made a distinction between nothing and void.

I, for one, think zero good will come of it…

Two soon?

> It’s been going on for centuries now, nobody’s changing their opinion at this point.

Sure, but one side can still out-breed the other.

My favorite is 2: Shared joy is a double joy, and shared sorrow is half sorrow.

My spouse often claims that two is the best prime because she knows it annoys me. Or perhaps she is truly insane. Clearly 2 is the WORST prime, amirite?

Well, it's definitely the primest prime.

I've always felt 2 was the most important as well, if only because for there to be something (1) there has to be nothing (0), and thus the existence of anything defines 2 states, being and non-being. Without the pair (0, 1) there is no distinguishing anything in the universe.

In modern math all numbers are built on set theory which has the empty set as it's foundation.

Empty set is more like 0 than 1. Check mate Unitarians.

The empty set is 1 set. Can’t have 0 without 1.

The empty set is the set with nothing, i e. no thing. So it doesn't need 1.

;)

Wouldn’t the set without nothing be more fundamental?

Does the set of sets that exclude themselves exclude itself?

That's a well-known old paradox, or close. Good on you, cobber. (AU slang :)

See Russells's paradox:

https://en.m.wikipedia.org/wiki/Russell%27s_paradox

No, because it isn't a set, but rather a class.

A concept created at least partially to resolve this paradox.

Brilliant. Go to the top of the class, er, set. Oops, forgot, sets have no order. List, then.

Ordered list, I mean.

You start from 1 empty set though.

If you could start from 0 empty sets, you'd have a point.

>You start from 1 empty set though.

Sez who, zigactly? If you are coldtea, I am coldertea. As in, I love my tea colder than you do yours. And starts who? Not me.

Don't kid around, dude. I dik around.

>If you could start from 0 empty sets, you'd have a point.

What if the set of empty sets has no element? :)

Was the first comment under the influence of drugs?

In any case, for the second comment: even if the set of empty sets has no elements, it's still ONE set.

>Was the first comment under the influence of drugs?

No, it was not. Regarding this whole subthread in which I participated, I did it for some mutual logic-chopping fun.

But if you thought there was a chance it was, you shouldn't have replied to the second comment, because I would have been equally under the influence of the drugs for the second, if I had been so for the first comment. (Don't reply to a druggie.) After all, they were both done in one atomic comment transaction.

If I start from 0 empty sets, how do I have A point?

>> The empty set is the set with nothing

So it is A set. In fact it's "the set" that makes it a rather special one.

No. Set theory is just one possible way you can build up numbers and mathematics.

You can just as well build up numbers and the rest of mathematics from different foundations. They are all equivalent.

Just like running your programs on ARM or on x86 or a toaster is all the same, thanks to emulators. (That's assuming you have an arbitrary amount of memory, and don't mind differences in runtime length.)

Which is more foundational: the wheel or the axle? Sets aren't worth much if you can't take unions, which is where 1 comes from.

0 and 1 are interesting as integers in the same way that a blank canvas is interesting as a painting. Very foundational, very useful but also very plain.

Pretty interesting if you work in an industry where you use them to represent every other number.

In my limited math experience, I really found an appreciation of the number one. My favorite part of high school algebra was realizing that "solving for x" was often just a repeated exercise of multiplying each side of the equation by a "clever form of one."

Solving for x often entails multiplying both sides by the same number, not necessarily one. Perhaps you're referring to simplifying fractions where you do often multiply by a clever form of one?

Ah, yes, you are absolutely correct. The _clever form of one_ trick did not apply as often as I recalled!

not in binary notation they're not

Must be an integer number of souls, though, so even in a conflict of infinite time, it won't be uncountable.

One of my professors would often refer to this struggle as taking place between the Nihilists and Unitarians.

Surely addition is more foundational than multiplication? Multiplication is just repeated addition.

Is this a reference for some fiction? Or you just made it up?

ℵ0 uncountable?

You missed the Dualitarians, the Trialitarians, and so on through to the Infinitarians ... whoops, forgot Cantor!

https://en.m.wikipedia.org/wiki/Georg_Cantor

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