Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How inevitable is the concept of numbers?

writings.stephenwolfram.com

Post reply on HN
Print view View original

151–160 of 211 posts

Re: How inevitable is the concept of numbers?

#151

Post by function_seven »

lisper wrote: post #110
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…

> 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.

Is this the spoken form of a Church Numeral or something?

Re: How inevitable is the concept of numbers?

#152

Post by chmod775 »

ultrablack wrote: post #150

Numbers are inevitable. How many people are we? How many berries do we need to collect for each. Later: How many seeds do we need to sow. How big a foundation is needed for this building… How many suns until the weather gets warmer again? I suppose you could do without if you lived in a cave with endless food readily available outside.

> How many people are we?

We are Steven, Simon, and Sarah.

> How many berries do we need to collect for each.

A handful for each.

> How big a foundation is needed for this building.

What building? You haven't even built the foundation yet.

And so on. You can do without numbers. And in fact people did all of the above without measuring quantities in any meaningful way in the history of humanity.

Re: How inevitable is the concept of numbers?

#153

Post by lisper »

function_seven wrote: post #151
lisper wrote: post #110

Earlier quoted context omitted.

> 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.

Is this the spoken form of a Church Numeral or something?

Yes. Exactly. (You could also see it as a rendering of some of the Peano axioms.)

Re: How inevitable is the concept of numbers?

#154

Post by ad404b8a372f2b9 »

minikites wrote: post #106
zwkrt wrote: post #102

Earlier quoted context omitted.

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

Nature counts all the time: tree rings, the angles of petals or leaves, the packing shapes for seeds.

Venus flytraps even count the number of their spikes that were moved during a certain interval of time to know whether to close or stay open.

Re: How inevitable is the concept of numbers?

#155

Post by nonsen »

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…

5 means territory

Re: How inevitable is the concept of numbers?

#156

Post by daxfohl »

Odd, I was thinking about this earlier today. I came to the conclusion that an axiomatization of math sans numbers doesn't make sense because you have to have a certain number of axioms. I'm certain a counterargument could be made though.

Re: How inevitable is the concept of numbers?

#159

Post by slver »

coder-3 wrote: post #64
slver wrote: post #16

Earlier quoted context omitted.

When we train neural networks, we don't tell them what to think and how to think about it. We mostly focus on overall structure, layers and we want useful outcomes. And yet we see lots of patterns that repeat ways in which we think. I think if a lion could speak, we'd understand him, because we're much closer to "a speaking lion" ourselves than we realize. Our intelligence didn't just happen at the last mile between…

The way I see the universe is that all this complexity is just the interplay of a finite few axioms (the fundamental laws of physics). Given enough time and scale, the seemingly unique complexity converges back into a few (relatively speaking) patterns. If that wasn't the case the universe would be pure chaos.

Wouldn't it suck if you and I and the rest of the universe are the inevitable result of a tweet-long equation, and any change to the equation renders it unviable.

So everything is just one formula, and me picking my nose right now came from that formula.

Re: How inevitable is the concept of numbers?

#160

Post by avereveard »

Eh idk something that moves uses energy and something that uses energy needs to replenish said energy. A natural question becomes how many recharge traveling a path needs, of course you can think about it as positions, but the stops themselves are intrinsically countable
Post reply on HN