5 ms·

I think numbers are wonderful and cool abstract thingies. We grow up being taught them (in my case Arabic numerals in base 10) and they become such part of our

I think numbers are wonderful and cool abstract thingies. We grow up being taught them (in my case Arabic numerals in base 10) and they become such part of our being that we start to think that we know what “5” is. Then I was introduced to Roman Numerals. Didn’t like those much. That one taught me that 4 is more related to 5 than it is 3. Then some of us learn a base 2 number system or base 16 number system and for a brief moment we question whether we actually knew what “5” was. And then we may learn about Peano and the successor(s…) of zero. Did we really know what “5” was then? What is five-ness really? Perhaps fiveness is a set within a set within a set… Every interaction our human minds have with fiveness is with a representation or encoding of 5. With each new representation, I’ve experienced fiveness slightly differently. But I like computers and math. For me, the best to experience oneness with the fiveness is through computation with Lambda Calculus and Church Numerals. Very fond of that encoding.

routerl 5y ago
In fact, you're talking about digits and numerals, not numbers. But this actually drives your point home, I think.
lisper 5y ago
> What is five-ness really? It is everything that has some relation to something that has that same relation to something that has that same relation to something that has that same relation to something that has that same relation to some unique thing that does NOT have that same relation to anything.
- function_seven 5y ago
  Is this the spoken form of a Church Numeral or something?
  - lisper 5y ago
    Yes. Exactly. (You could also see it as a rendering of some of the Peano axioms.)
- BBC-vs-neolibs 5y ago
  Username checks out. :)
Koshkin 5y ago
> Did we really know what “5” was then? What is five-ness really? Ah, but we do, and it’s very simple: it is what five cows an five fingers have in common in the most obvious sense. There’s no mystery there. Or, stated in another way, “fiveness is something you’ll be very sad not to see when you look at your hand.”
- orthonormal 5y ago
  I lost one of my fingers when i was a child, so after getting used to it i don't experience sadness when i look at it. That statement also checks out for four, in this case.
  - lazydud 5y ago
    Ok
- esarbe 5y ago
  This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition. I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system. So, given that there are no categories to put discrete things into - they just exist in our imagination - and there are probably not even discrete things - these also just exist in our imagination - the question of five-ness is not really answered.
  - Radim 5y ago
    > You cannot separate a river from the ocean - it's part of the same system. > discrete things - these also just exist in our imagination What leads you to separate "imagination" from "exists"? Isn't imagination also "part of the same system"? Imagination definitely has the capacity to affect the world, so it's not obvious in what way it's "not real". Why do you draw a hard line there?
saeranv 5y ago
Does the base really have anything to do with 5? I can represent 5 in base 10 as 5, or I can represent it in base 2 as 101, but both encode the same information. Using different bases, to me, is just about storing information. How many symbols do you want to create before you increase the length of your number and start re-using them.
ornxka 5y ago
Five's how many fingers I have.
- trashtester 5y ago
  Sorry to hear that... May I ask how you lost the other 5? (My inner Asberger's could not resist.)
nonsen 5y ago
5 means territory
LudwigNagasena 5y ago
I would say that positional notation, Zermelo ordinals and Church numerals are just ways to encode numbers. I would never call them numbers in the strictest sense of this word. Just how your C code is not an algorithm. I would say I knew what 5 was even before I learned any notation or written language whatsoever.
jychang 5y ago
Five Five Five Five Five There is no Antimemetics Division
stareatgoats 5y ago
Yes; the difference between token and denoted concept. They are not the same thing (as René Magritte probably wanted to say with his "This is not a pipe" painting). In computer contexts: each representation of 5, in whatever base or language would point to the same element in a lookup-table. But for us humans, the tokens and concepts blend to some degree: maybe not so much with regards to numerals (although there seem to be exceptions ...). So even if 'Amour', 'Love' and 'Liebe' essentially point to the same concept, we might conceive of them differently, ever so slightly, depending on the language we chose to use. Which gives an inkling of the vast difference between computers and humans, at the current stage.
ayewo 5y ago
> Did we really know what “5” was then? What is five-ness really? Perhaps fiveness is a set within a set within a set… The reason it seems mushy is because there are two related concepts at play: a numeral vs. a number. A numeral is the symbol: 5 in Arabic numerals in Latin script or ٥ in Arabic script; V in Roman numerals etc. A number is the quantity, the amount being expressed: five (English), ḫamsa (Arabic), cinq (French) etc.

routerl 5y ago

In fact, you're talking about digits and numerals, not numbers. But this actually drives your point home, I think.

lisper 5y ago

> What is five-ness really? It is everything that has some relation to something that has that same relation to something that has that same relation to something that has that same relation to something that has that same relation to some unique thing that does NOT have that same relation to anything.

function_seven 5y ago
Is this the spoken form of a Church Numeral or something?
- lisper 5y ago
  Yes. Exactly. (You could also see it as a rendering of some of the Peano axioms.)
BBC-vs-neolibs 5y ago
Username checks out. :)

Koshkin 5y ago

> Did we really know what “5” was then? What is five-ness really? Ah, but we do, and it’s very simple: it is what five cows an five fingers have in common in the most obvious sense. There’s no mystery there. Or, stated in another way, “fiveness is something you’ll be very sad not to see when you look at your hand.”

orthonormal 5y ago
I lost one of my fingers when i was a child, so after getting used to it i don't experience sadness when i look at it. That statement also checks out for four, in this case.
- lazydud 5y ago
  Ok
esarbe 5y ago
This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition. I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system. So, given that there are no categories to put discrete things into - they just exist in our imagination - and there are probably not even discrete things - these also just exist in our imagination - the question of five-ness is not really answered.
- Radim 5y ago
  > You cannot separate a river from the ocean - it's part of the same system. > discrete things - these also just exist in our imagination What leads you to separate "imagination" from "exists"? Isn't imagination also "part of the same system"? Imagination definitely has the capacity to affect the world, so it's not obvious in what way it's "not real". Why do you draw a hard line there?

saeranv 5y ago

Does the base really have anything to do with 5? I can represent 5 in base 10 as 5, or I can represent it in base 2 as 101, but both encode the same information. Using different bases, to me, is just about storing information. How many symbols do you want to create before you increase the length of your number and start re-using them.

ornxka 5y ago

Five's how many fingers I have.

trashtester 5y ago
Sorry to hear that... May I ask how you lost the other 5? (My inner Asberger's could not resist.)

nonsen 5y ago

5 means territory

LudwigNagasena 5y ago

I would say that positional notation, Zermelo ordinals and Church numerals are just ways to encode numbers. I would never call them numbers in the strictest sense of this word. Just how your C code is not an algorithm. I would say I knew what 5 was even before I learned any notation or written language whatsoever.

jychang 5y ago

Five Five Five Five Five There is no Antimemetics Division

stareatgoats 5y ago

Yes; the difference between token and denoted concept. They are not the same thing (as René Magritte probably wanted to say with his "This is not a pipe" painting). In computer contexts: each representation of 5, in whatever base or language would point to the same element in a lookup-table. But for us humans, the tokens and concepts blend to some degree: maybe not so much with regards to numerals (although there seem to be exceptions ...). So even if 'Amour', 'Love' and 'Liebe' essentially point to the same concept, we might conceive of them differently, ever so slightly, depending on the language we chose to use. Which gives an inkling of the vast difference between computers and humans, at the current stage.

ayewo 5y ago

> Did we really know what “5” was then? What is five-ness really? Perhaps fiveness is a set within a set within a set… The reason it seems mushy is because there are two related concepts at play: a numeral vs. a number. A numeral is the symbol: 5 in Arabic numerals in Latin script or ٥ in Arabic script; V in Roman numerals etc. A number is the quantity, the amount being expressed: five (English), ḫamsa (Arabic), cinq (French) etc.