How inevitable is the concept of numbers?
writings.stephenwolfram.com
How inevitable is the concept of numbers?
1–10 of 211 posts
Re: How inevitable is the concept of numbers?
#2I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero.
Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you multiply a number (no matter how big) by zero you get zero as a result.
Maybe there’s some Wittgenstein-like material somewhere that will better explain this, in which case I’ll very happy for some references.
Re: How inevitable is the concept of numbers?
#3I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero. Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you mu…
Isn't multiplication by 0 natural?
If i'm at a party and everybody wants 2 beers, then if there is 1 person I need 2 beers (1 * 2), 2 people need 4 beers (2 * 2), but 0 people need 0 beers (0 * 2).
Re: How inevitable is the concept of numbers?
#4While 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 depth in one area or another, rather than a conflation of ideas providing food for thought. Otherwise there are far too many variables to consider for a worthwhile analysis.
Re: How inevitable is the concept of numbers?
#5I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero. Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you mu…
Because multiplication is just the number of times you add something to 0. If you add 2 to 0 3 times you get 6, if you add 2 to 0 0 times you get zero.
Re: How inevitable is the concept of numbers?
#6When my two year old can't count the items in front of him he just says it's "many".
Re: How inevitable is the concept of numbers?
#7‘If a lion could speak, we could not understand him’.
- Wittgenstein
So even things we understand as fundamental truths of the universe are so deeply rooted in human experience that it's possible another living entity could be so different than ourselves that the capacity to sympathize with one another about certain things may simply not exist. Would a lion understand a corsage? Would an alien know what 12 x 12 means? The universe is just one hella big ¯\_( ͡° ͜ʖ ͡°)_/¯
Re: How inevitable is the concept of numbers?
#8I 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 fractions. And measurements (like weight and length). Basic operations like + - emerge, and with that multiplication. And with that division... and so on.
I think the fundamental properties of math are one of those things that will keep emerging for every thinking system. Not because numbers are fundamental to the universe. Rather they're fundamental aspect of intelligently adapting to (i.e. thinking about and making predictions about) the universe.
Re: How inevitable is the concept of numbers?
#9I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero. Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you mu…
No need for Wittgenstein.
Fish have 0 legs. So how many legs do N fish have? N*0 = 0.
Now division by zero, that is Devil's idea.
Re: How inevitable is the concept of numbers?
#10I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero. Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you mu…
Isn't multiplication by 0 natural? If i'm at a party and everybody wants 2 beers, then if there is 1 person I need 2 beers (1 * 2), 2 people need 4 beers (2 * 2), but 0 people need 0 beers (0 * 2).
“Zero people” and “needing” is an oxymoron, nothing (zero) can’t be associated to any natural thing (like “needing”), that’s what I was trying to say in my not so clear comment above.
Writing this down I realized we’re still trying to write in fancier words what the pre-Socratics had a clear understanding of 2500+ years ago, and speaking of the Greeks is too bad that Wolfram didn’t mention Plato by name in the first few paragraphs, the chair example is practically taken from him (expecting a Parmenides quote would have probably been too much).