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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?

#111

Post by anoncow »

mensetmanusman wrote: post #92
swagasaurus-rex wrote: post #90

Earlier quoted context omitted.

Another perspective could be that we are creatures emergent out of the physical and chemical processes of the universe. There is some similarity or equivalence to some of these processes with mathematics, which allows us to model a subset of physics/chemistry with mathematics. Because physics/chemistry can create us using rules that follow math (or even some undiscovered rules), this same physics/chemistry gives us t…

Physics creates us, universe creates physics, … creates universe

Math creates universe? The answer normally lies in the open. (I don't know though)

Re: How inevitable is the concept of numbers?

#112

Post by jayd16 »

contravariant wrote: post #28
SquibblesRedux wrote: post #4

While the post covers quite a bit of ground, it feels (to me) like it conflates knowledge representation, language, biological systems (i.e., the messiness of implementation), computability, and realism. Regarding numbers in particular, there are a practically uncountably infinite number of mathematical truths that apply equally to numbers or to other abstract (non-numerical) mathematical ideas. I would rather see de…

Because of the limitation of language there's only a countable number of mathematical truths that can be proven or written down. So for all practical purposes there's countably many.

But we can make new words.

Re: How inevitable is the concept of numbers?

#113

Post by dane-pgp »

alcover wrote: post #37
pjettter wrote: post #19

The word "finger" did not occur so I skipped it.

It's certainly a big reason why we're so adept at counting but don't you think speech plays a big role too (and could be sufficient) ? I mean numbers are fingers but they're also a kind of song "one two three.." you map on things.

> also a kind of song "one two three.." you map on things.

Apparently it's as easy as "A, B, C...".

Re: How inevitable is the concept of numbers?

#114

Post by taotau »

I've always thought of numbers, and the broader system of mathematics as equivalent to the Newtonian understanding of physics - an adequate tool to explain observed reality - but the edge cases that break the system are starting to pile up, and we are just waiting for someone to discover the Quantum/General Relativity theory of mathematics.

Re: How inevitable is the concept of numbers?

#115

Post by slver »

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.

Lots of animals have been verified to understand and use abstract count which is what numbers are at their basics.

Plants are much less adaptive than animals by definition. The problem isn’t whether they know numbers but how do you even test what plants “know”.

Re: How inevitable is the concept of numbers?

#116

Post by teachingassist »

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 claim (abstract) ownership of a particular large number.

Re: How inevitable is the concept of numbers?

#117

Post by slver »

mrfox321 wrote: post #73
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…

Your argument is tautological. Do we really know if adaptation is responding to discrete classifications of environmental pressure? There could be other ways to describe how systems adapt. You are ascribing a lot to how you think it emerged. I think your opinions are great, but I just have a hard time having beliefs about things that are as fundamental as numbers.

> Do we really know if adaptation is responding to discrete classifications of environmental pressure?

Yeah we do know.

Take any system of variables that interact, and change them smoothly, and inflection points will emerge. This is true literally any way you look at it. In space. In time.

Heck aggregate states of matter represent "categorical adaptation" of matter to smooth alteration of temperature.

Point being this process happens even before we even can call a system "thinking". It's absolutely inevitable.

We can keep our options open forever and say "I don't know", that's fine. But if we analyze what we do know... turns out we DO do know.

Re: How inevitable is the concept of numbers?

#118

Post by rrao »

taotau wrote: post #114

I've always thought of numbers, and the broader system of mathematics as equivalent to the Newtonian understanding of physics - an adequate tool to explain observed reality - but the edge cases that break the system are starting to pile up, and we are just waiting for someone to discover the Quantum/General Relativity theory of mathematics.

As someone who has recently started diving deeper into math recently, that is very interesting and something I was totally unaware of. Could you point me to some of these edge cases?

Re: How inevitable is the concept of numbers?

#119

Post by mrfox321 »

slver wrote: post #117
mrfox321 wrote: post #73

Earlier quoted context omitted.

Your argument is tautological. Do we really know if adaptation is responding to discrete classifications of environmental pressure? There could be other ways to describe how systems adapt. You are ascribing a lot to how you think it emerged. I think your opinions are great, but I just have a hard time having beliefs about things that are as fundamental as numbers.

> Do we really know if adaptation is responding to discrete classifications of environmental pressure? Yeah we do know. Take any system of variables that interact, and change them smoothly, and inflection points will emerge. This is true literally any way you look at it. In space. In time. Heck aggregate states of matter represent "categorical adaptation" of matter to smooth alteration of temperature. Point being thi…

You are just saying that interacting systems have phase transitions.

I think this is a far cry from "emergent numbers".

Edit: Maybe self organizing matter that lives on a phase transition boundary benefits from being aware of the boundary? Thats the only analogy I could think of that could logically connect.

Re: How inevitable is the concept of numbers?

#120

Post by [deleted] »

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…

[deleted]
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