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How inevitable is the concept of numbers?

writings.stephenwolfram.com

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Re: How inevitable is the concept of numbers?

#181

Post by trashtester »

ornxka wrote: post #144
codeismath wrote: post #95

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…

Five's how many fingers I have.

Sorry to hear that... May I ask how you lost the other 5?

(My inner Asberger's could not resist.)

Re: How inevitable is the concept of numbers?

#182

Post by trashtester »

teachingassist wrote: post #116
slver wrote: post #8

I like that he keeps it open-minded, but I've thought a lot about this and to me the case for numbers being inevitable is decisively yes. Every adaptable system evolves to adapt to a changing environment by detecting "modes" (categories) and adapting to each mode. Then we start noticing categories come in instances. There's a tree, there are more trees. So now it's useful to count them... Then it's useful to have fra…

> There's a tree, there are more trees. So now it's useful to count them... It's not that useful to count them. My personal interactions with trees have likely never involved counting them; not even when I was involved in woodland management. Trees control their numbers according to whether or not they can reasonably live in a particular density of tree coverage. Only humans want to count trees, perhaps in general to…

Lets say, based on your nick, you are teaching two classes. Both consist of individuals.

If we were to count the classes, we would say that one class consist of 2 people, and the other of 20000.

But those are just numbers.

My point is that numbers are useful for us in understanding how to interact with the world. If you don't plan to interact with the trees, you probably don't need to count them. But if you are going to use them for firewood or building materials, the knowing the difference between 2 trees and 20000 is useful.

Re: How inevitable is the concept of numbers?

#183

Post by trashtester »

zwkrt wrote: post #102
slver wrote: post #8

I like that he keeps it open-minded, but I've thought a lot about this and to me the case for numbers being inevitable is decisively yes. Every adaptable system evolves to adapt to a changing environment by detecting "modes" (categories) and adapting to each mode. Then we start noticing categories come in instances. There's a tree, there are more trees. So now it's useful to count them... Then it's useful to have fra…

A tree adapts to its environment and I would bet money that trees in their phenomenology can’t count.

Well, in a very primitive and non-accurate sense, it counts/measures the number of (photo synthesis generating) photons hitting each leaves, and then grows in directions that maximizes its photo synthesis.

Since a tree has a much lower number of branches and leaves than there are photons, there has to be some aggregation of information involved in this computational process.

Re: How inevitable is the concept of numbers?

#184

Post by ayewo »

codeismath wrote: post #95

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…

> 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.

Re: How inevitable is the concept of numbers?

#186

Post by Radim »

esarbe wrote: post #179
Radim wrote: post #176

Earlier quoted context omitted.

> 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?

I'm not drawing a hard line at all; yes, imagination is part of the same system. And of course it has the capacity to affect the world. I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

But "world", "separate" and "parts" are all language concepts too. I feel the inconsistency in your (circular) argument is not getting through.

That divisions are arbitrary and "exist just in our imagination" doesn't line up with your admission that imagination is real, and using words to describe it. That line between "real" vs "arbitrary / imaginary" is not as clear cut as you (unconsciously, apparently) draw it.

Re: How inevitable is the concept of numbers?

#187

Post by teachingassist »

trashtester wrote: post #182
teachingassist wrote: post #116

Earlier quoted context omitted.

> There's a tree, there are more trees. So now it's useful to count them... It's not that useful to count them. My personal interactions with trees have likely never involved counting them; not even when I was involved in woodland management. Trees control their numbers according to whether or not they can reasonably live in a particular density of tree coverage. Only humans want to count trees, perhaps in general to…

Lets say, based on your nick, you are teaching two classes. Both consist of individuals. If we were to count the classes, we would say that one class consist of 2 people, and the other of 20000. But those are just numbers. My point is that numbers are useful for us in understanding how to interact with the world. If you don't plan to interact with the trees, you probably don't need to count them. But if you are going…

We agree that the difference between 2 and 20000 is significant, but I can easily observe this difference without counting all the way up to 20000.

Identifying the difference between 19,999 and 20,000 is certainly not significant in this way. 19,999 is already "too many" students; or, "plenty" of firewood. I don't need to count them to know this.

I'd say the difference between 5 and 6 is already relatively unimportant in these contexts.

Re: How inevitable is the concept of numbers?

#188

Post by trashtester »

teachingassist wrote: post #187
trashtester wrote: post #182

Earlier quoted context omitted.

Lets say, based on your nick, you are teaching two classes. Both consist of individuals. If we were to count the classes, we would say that one class consist of 2 people, and the other of 20000. But those are just numbers. My point is that numbers are useful for us in understanding how to interact with the world. If you don't plan to interact with the trees, you probably don't need to count them. But if you are going…

We agree that the difference between 2 and 20000 is significant, but I can easily observe this difference without counting all the way up to 20000. Identifying the difference between 19,999 and 20,000 is certainly not significant in this way. 19,999 is already "too many" students; or, "plenty" of firewood. I don't need to count them to know this. I'd say the difference between 5 and 6 is already relatively unimportan…

My point is not that you need the number to be exactly accurate, my claim is that for the number 2 you don't even condider the student body as a quantity, but for 20000 it very much becomes a quantity.

Also, if 20000 students need training, as a teacher you can still provide training, you just need to do so in other ways. Either, you can recruit more teachers to help you (and then it matters if the number is 10000 students or 20000 students), or you can switch to another medium (a book, a video, on-line training).

Treating a student body as a number will make it more managable for you to provide/organize training to them than just hireing more teachers at random until each student gets enough attention.

Likewise, 2 trees may keep you warm for a week, 20000 may keep you and half your (small) village warm for a year, with enough trees left over for the forest to replenish.

Re: How inevitable is the concept of numbers?

#189

Post by esarbe »

Radim wrote: post #186
esarbe wrote: post #179

Earlier quoted context omitted.

I'm not drawing a hard line at all; yes, imagination is part of the same system. And of course it has the capacity to affect the world. I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

But "world", "separate" and "parts" are all language concepts too. I feel the inconsistency in your (circular) argument is not getting through. That divisions are arbitrary and "exist just in our imagination" doesn't line up with your admission that imagination is real, and using words to describe it. That line between "real" vs "arbitrary / imaginary" is not as clear cut as you (unconsciously, apparently) draw it.

> I feel the inconsistency in your (circular) argument is not getting through.

I guess it's not, since I'm not convinced that mine is a circular argument.

My argument - to put is simply - is that we are all part of the same system and that there are no divisions. Without divisions, no numbers. I don't need any distinction between 'real' and 'arbitrary' for this to hold, that's a dichotomy you assume on your part.

Re: How inevitable is the concept of numbers?

#190

Post by Tainnor »

marcodiego wrote: post #97
Tainnor wrote: post #84

Earlier quoted context omitted.

Basically every single claim about Pirahã (not Piranha) needs to be taken with a huge grain of salt. There's just not enough people who have studied the language and the claims are so strong and unparalleled that we really ought to have more evidence between making any conclusive statements.

Hmmm... I stand corrected. Although I lived in the Amazon region for a few years (1993 to 2002 in Rondônia), never formally studied any native language and mostly blindly believed the wikipedia article on Pirahã people[0] and probably mixed things from the Hopi language time controversy. Thanks for such info. Ironically, my English was mostly learnt from people from Europe who came there to conduct researches. This i…

I'm not claiming that what Everett et al. are saying is wrong, just that the claims are so spectacular that I'd like to see more evidence before I believe them.
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