What is "2"?

TillICollapse · May 7, 2015

Architeuthus said:
Yes.

Okay cool, on the same page.

I don't know how you could, although whatever it does seems to be consistent with our "2" (or, with the universal "2," if one believes in that).

With large mammals, brain scans etc. have shed some light on cognition, but (as Wittgenstein said), "If a lion could speak, we could not understand him."

You jumped to Wittgenstein

This is partially what I was approaching ... the idea there is no private language, and that "2" is basically just a symbol of language (which in this context would be a social phenomenon, not a private one), mapped to concepts we can demonstrate or utilize which we recognize and identify as "2" via language ... but via qualia we cannot coherently define it, because no private language would be coherent. It wouldn't be anymore coherent than a lion speaking to us, or the chickens trying to tell us what "2" is, even though they can demonstrate it, utilize it, etc.

Thus "2" would be an agreed upon symbol of language, mapped to concepts we can utilize and demonstrate and recognize as "2". But to find out precisely what "2" actually is, becomes more or less meaningless to pursue, for similar reasons as to why it would be more or less meaningless to ascertain what the chicken defines as "2".

The reason I'm pointing this out, is arguably because the no private language applies to the concept of "2" itself lol. We cannot ask "2" how it defines itself, and even if we could and "it" could communicate it to us, it would do so via a public language, not it's own qualia.

Architeuthus · May 7, 2015

Architeuthus said:
I don't know much about ants counting, I'm afraid (if they indeed do count). It does sound intriguing, though.

On thinking about it, ants probably don't have the neural machinery to actually count steps.

There's probably a chemical or electrical level somewhere that increases with each step, giving an approximate step count.

Architeuthus · May 7, 2015

TillICollapse said:
that "2" is basically just a symbol of language (which in this context would be a social phenomenon, not a private one)

That was my case (e), which I don't think can work, because animals don't share our language or culture, but do seem to have simple number concepts. Human language is private from birds (and vice versa).

TillICollapse said:
Thus "2" would be an agreed upon symbol of language, mapped to concepts we can utilize and demonstrate and recognize as "2". But to find out precisely what "2" actually is, becomes more or less meaningless to pursue

Like I said, I don't think the language/culture answer works, so I think "2" has to be actually be something else (or at least something more).

But thanks for tossing the conversational ball around.

TillICollapse · May 7, 2015

Architeuthus said:
On thinking about it, ants probably don't have the neural machinery to actually count steps.

There's probably a chemical or electrical level somewhere that increases with each step, giving an approximate step count.

I don't know ... I haven't researched what that article is referencing concerning the ants. I'm too lazy right now to fact check it and see more of the details about the claim But apparently they can do more than just count steps lol ...

When a desert ant leaves its nest in search of food, it has an important task: find its way back home. In almost any other part of the world, the ant can use one of two tricks for finding its way home, visual landmarks or scent trails. The windswept saltpans of Tunisia make it impossible to leave a scent trail, though. And the relatively featureless landscape doesn't provide much in the way of visual landmarks, other than perhaps the odd rock or weed. So evolution endowed the desert ant with a secret weapon: geometry. Armed with its mathematical know-how, the desert ant is able to path integrate. This means, according to ant navigation researchers Martin Muller and Rudiger Wehner, that it "is able to continuously compute its present location from its past trajectory and, as a consequence, to return to the starting point by choosing the direct route rather than retracing its outbound trajectory."

How does this work? These desert ants calculate the distance walked by counting steps. Researchers discovered this by strapping stilts made of pig hairs onto the legs of the ants. The ants stilts made each individual step longer than it would have otherwise been, making them overestimate the distance home. The ants calculate the direction they walk by calculating the angle of their path relative to the position of the sun, using the same rules of trigonometry that were taught to me in the tenth grade. And whats more, the ants constantly update their calculations to correct for the sun's march across the sky. All that in a nervous system comprised of as few as 250,000 neurons (compared to the approximately 85 billion neurons in the human).

TillICollapse · May 8, 2015

Architeuthus said:
That was my case (e), which I don't think can work, because animals don't share our language or culture, but do seem to have simple number concepts. Human language is private from birds (and vice versa).

Precisely ... and yet, animals utilize and seem to recognize what we describe as "2", even though they can't communicate it via language. Thus, "2" would be nothing more than a human construct. What it maps to, is a different story, but this is where I think there is a dead end, which is why I kept focusing on language ...

Like I said, I don't think the language/culture answer works, so I think "2" has to be actually be something else (or at least something more).

... and if "2" is something more, how would you define it absolutely ? What I'm saying is, I don't think you can. You can only describe it and define it so much, but then one will come up short ... because of two things:

1) The nature of language
2) The nature of experience

You cannot experience what it is like to be "2" lol, which is arguably the purest form of definitive "language". You can try and relate, and define this via language. Both fall short. And even if "2" were somehow an entity that could communicate ... that communication would still fall short, as would being able to experience what it would be like to be "2". So asking what something "is" only goes so far, before it gets lost in translation and cannot be understood any further. That's what I was thinking out-loud

Although I suppose if one could demonstrate that they were experiencing one and the same as another thing (i.e. "2"), then they could then define "2" at least via the experience, but I don't know that it could be demonstrated definitively to someone who wasn't experiencing that same thing.

But thanks for tossing the conversational ball around.

It's cool. And if you think this angle has reached it's limit, it's cool too I suppose

True Scotsman · May 8, 2015

TillICollapse said:
That's very interesting ... thanks for answering. Interesting to read the impact it had on you

Oh I've read some of her books I would probably say The Fountainhead (read when I was 17) is one of the best novels I have ever read.

I loved it when he told Toohey "but I don't think of you". I also loved it when he threw the baby sculpture and broke it and told him "don't ever do anything like this again." And when he grabbed the watercolor sketch and re-drew it to his original drawing in front of the whole office while the client and his boss watched. I wanted to cheer. His relationship with Cameron. Such a great book.

Have you read Atlas Shrugged? My favorite line from the book: Dagny: Do you suppose I've died and this is some other kind of existence. Galt: It is another kind of existence but as for dying, doesn't it seem like the other way around.

Architeuthus · May 8, 2015

(duplicate post deleted)

Architeuthus · May 8, 2015

TillICollapse said:
But apparently they can do more than just count steps lol ...

I really doubt that they count; I suspect that their "odometer" uses analog technology. The article is consistent with that, saying "some kind of step integrator, or 'step counter.'" Miller and Wehner support that too, finding that their ants used a simplified/approximate navigation algorithm.

TillICollapse said:
Precisely ... and yet, animals utilize and seem to recognize what we describe as "2", even though they can't communicate it via language. Thus, "2" would be nothing more than a human construct.

If they recognize what we describe as "2," then "2" must be more than just a "human construct," surely.

TillICollapse said:
... and if "2" is something more, how would you define it absolutely ? What I'm saying is, I don't think you can.

Historically, there have been attempts, hence my (a) to (e) list.

The other problem with the language/culture approach is that mathematics works too well. Bits of mathematics get invented/discovered, and then turn out useful a century later in branches of science completely unknown at the time of the invention/discovery.

TillICollapse said:
It's cool. And if you think this angle has reached it's limit, it's cool too I suppose

Oh, I certainly didn't say that.

KCfromNC · May 8, 2015

Resha Caner said:
It seems "2" can be anything I want it to be. How is this a useful concept?

I can call a dog a cat. That doesn't make the English language useless for everyone else who isn't intentionally trying to get in the way of communication.

quatona · May 8, 2015

KCfromNC said:
I can call a dog a cat. That doesn't make the English language useless for everyone else who isn't intentionally trying to get in the way of communication.

^ This.

KCfromNC · May 8, 2015

Resha Caner said:
As I recall, you don't like to debate the philosophy of such things. So I'm not sure if I should ask any follow-on questions of you. If I did, they would be:

1) If we began our number system with different assumptions, would we produce different results in the "real" world by using that different system?

Would the reality (whatever that is) of an insect be any different if we described it in Sanskrit?

2) If we're using numbers to describe real things - what I would call a "property" of those real things - are we describing something inherent to these real things?

Not sure what you mean. A bowling ball weighs 16 pounds. It also weighs 7.26kg. Which, if either, number is inherent in the real thing? Or are both just a convenient shorthand (with tons of implied shared knowledge) for communicating an observation?

KCfromNC · May 8, 2015

Resha Caner said:
Agreed. Instrumentalism has long been my view. Yet for some reason you seem to believe there is something "out there" that is "reality". How did you come to that conclusion if not by forming an idea from your perceptions?

Are you wrong that reality is out there?

Could be, but it is the simplest explanation for our ability to make consistent observations.

And this is still related to number. I still await a comment on 3E8. I know it's not "2", but hopefully it's still sexy enough to talk about that number as well.

Are you aware that c=1 is used to simplify the physics in many problems? Seems to cast some light on specific numbers being some magical identity when we can change them so freely and still get useful work done.

KCfromNC · May 8, 2015

Architeuthus said:
If they recognize what we describe as "2," then "2" must be more than just a "human construct," surely.

No more than if any non-humans recognize what we describe as green, or sugar, or a flower. They're all labels which more or less successfully describe something. That another non-human animal can identify things in the real world seems to be a separate question from the labels we ourselves put them - unless those non-humans have independently created the exact same labels. Which they haven't, since you don't find a lot of e.g. earthworms doing algebra.

The other problem with the language/culture approach is that mathematics works too well. Bits of mathematics get invented/discovered, and then turn out useful a century later in branches of science completely unknown at the time of the invention/discovery.

It isn't as if we generally teach all of the math which doesn't work for any useful purpose, so this seems a bit circular to me.

Resha Caner · May 8, 2015

GrimKingGrim said:
Looking for the point

In part I was feeling a bit precocious and wanted to demonstrate how easy it is to create confusion if that is one's objective.

For the other part, read on a bit.

KCfromNC said:
I can call a dog a cat. That doesn't make the English language useless for everyone else who isn't intentionally trying to get in the way of communication.

Exactly. I agree.

Architeuthus said:
The foundations of mathematics are actually not quite so obvious as they seem to be. Especially since we all recognise "2" when we see an instance of it, and we haven't struggled with small integers since kindergarten.

But if it was simple, we would all be able to agree on what exactly "2" was. And Russell and Whitehead wouldn't have needed more than 300 pages to prove that 1 + 1 = 2

Yep. This was the other part. Oversimplifying the problem doesn't mean you've given a good answer. If we can't agree on what "2" means, how can we even dare to consider what "3" means? (For those who don't like subtlety, that's a reference to the Trinity)

essentialsaltes said:
This may surprise you, but meters and seconds are also things we invented to describe the world. I'm not sure what comment you want me to make on 3E8. If we describe things in meters and seconds, then that's roughly the quantity that correctly describes the thing we have defined as velocity for light in vacuum.

I can change the raw number to 186,000 or 1 quite easily by describing the universe in different manmade units.

So, it appears the conversation ran on for quite awhile without me. But using the above as a summary along with Architeuthus' comment that numbers are the territory let me address a few things:

1) I'm aware we can change the numerals via a change of units, but that doesn't change what we're trying to describe. So let's not confuse the numerals with the number. If you prefer representing the number as "c", that's fine. If you prefer using "quantity" rather than number, that's fine.

2) Is velocity a property of light or isn't it? I say it is.

3) Do we use number to describe velocity or don't we? I say we do.

So let's get over the symbology and address the property. Light has a constant property whose value is a quantity. To me "constant" means never-changing and unending. We can add the "as far as we know" disclaimer to that, but so what. As far as we know that property is never-changing and unending. So, it seems it exists eternally.

essentialsaltes · May 8, 2015

Resha Caner said:
along with Architeuthus' comment that numbers are the territory

Numbers are the territory when we're doing mathematics. But that territory is not real, it is invented.

2) Is velocity a property of light or isn't it? I say it is.

Velocity is one way we describe the world. We can use it to predict things that actually happen in the real world. But our model of reality is not reality itself.

3) Do we use number to describe velocity or don't we? I say we do.

Yes, we use numbers to describe many things about the real world.

So let's get over the symbology and address the property. Light has a constant property whose value is a quantity. To me "constant" means never-changing and unending. We can add the "as far as we know" disclaimer to that, but so what. As far as we know that property is never-changing and unending. So, it seems it exists eternally.

What, the number? No, that's just our description that we made.

Hydrogen has 1 and exactly 1 proton in its nucleus. This was true long before there were any humans. But there were no 1's present at that time. Just hydrogen atoms. There are no 1's present today as real things; they are 'just' ideas in our heads.

Resha Caner · May 8, 2015

essentialsaltes said:
Velocity is one way we describe the world. We can use it to predict things that actually happen in the real world. But our model of reality is not reality itself.

Yes, I already agreed to that.

essentialsaltes said:
Numbers are the territory when we're doing mathematics. But that territory is not real, it is invented.

Then you would agree with Hartry Field that science can be done without numbers. I'm still not sure you're distinguishing between number and numeral, but if that is your claim you'll need to prove it.

IMO Field didn't succeed. Such a claim would require avoiding the concept of quantity. If you can't avoid quantity, then maybe it is inherent in reality.

essentialsaltes said:
Hydrogen has 1 and exactly 1 proton in its nucleus. This was true long before there were any humans. But there were no 1's present at that time. Just hydrogen atoms.

Yes, so call it what you like, that quantity has existed for a very long time - as has the constant speed of light.

essentialsaltes · May 8, 2015

Resha Caner said:
Yes, so call it what you like, that quantity has existed for a very long time - as has the constant speed of light.

No, hydrogen has existed for a very long time. Quantity is an idea.

Reality just is. It is not imprinted with labels. We do the labelling.

Resha Caner · May 8, 2015

essentialsaltes said:
Reality just is. It is not imprinted with labels. We do the labelling.

Yes, you've said that several times now. Repeating it doesn't make it more convincing. In fact, I've not disagreed with this statement.

So I guess we'll have to slow down and take smaller steps.

First questions: Am I part of reality? Are interactions part of reality?

TillICollapse · May 8, 2015

True Scotsman said:
I loved it when he told Toohey "but I don't think of you". I also loved it when he threw the baby sculpture and broke it and told him "don't ever do anything like this again." And when he grabbed the watercolor sketch and re-drew it to his original drawing in front of the whole office while the client and his boss watched. I wanted to cheer. His relationship with Cameron. Such a great book.

Yeah it's been probably 15 years since I read it ... I've read it twice, but it may be time for a re-read

I won't wax too poetic on what I remember of it or the effect it had on me at the time, but it did have a huge impact. It was as though I already had a key in the lock of a door in my life at that time, and that book helped to show me which way to turn the key to get the door open And the relationship between Roark and Dominique ... I could have written that myself, all the dynamics between them as I remember it.

But as I said, it was quite awhile ago, I would need to refresh myself on the specifics.

Have you read Atlas Shrugged? My favorite line from the book: Dagny: Do you suppose I've died and this is some other kind of existence. Galt: It is another kind of existence but as for dying, doesn't it seem like the other way around.

A very fitting line

Yes I've read Atlas Shrugged, and a bit of the Virtue of Selfishness, and bits and pieces of some of her other stuff but no in their entirety. The Fountainhead was the one that I found the most value in, as a combination of the timing on me reading it was integral and dead on accurate in my life.

TillICollapse · May 8, 2015

Architeuthus said:
If they recognize what we describe as "2," then "2" must be more than just a "human construct," surely.

Focusing on this part of your post, I believe essentialsaltes said it most succinctly:

essentialsaltes said:
Reality just is. It is not imprinted with labels. We do the labelling.

"2" is the human construct, the label/symbol thing we map or associate with whatever "2" actually is.

But whatever "2" actually is (and this arguably goes for most things, not just "2") ... it is what it is lol. Whether we call an apple a peach or not, it's still "whatever it actually is". Language is limited.

Things are not defined by us, IOW. They are defined intrinsically, "beyond language". What is defined by us, are our attempts to understand them, identify them, communicate about them, use them, etc.

Forget for a moment the number aspect of "2" and it being mapped to concepts involving only math. Is "1" the lonliest number ? Is "2" actually BETTER than 1 ? Is that part of the definition ? Because we often map that idea to those numbers. And what does "2" feel like (Wittgenstein ) ... if I win 2 free tickets to a game, I may be happy. So does 2 make a person feel happy every time? We map the concept of "2" to more than just whatever it actually is, because "2" is the construct. Whatever it is ... it is what it is.

I'm not sure we can definitively know what another thing is, unless we can experience what it is like to be that thing directly. And that makes for another set of issues.

What is "2"?

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