11–20 of 211 posts
When my two year old can't count the items in front of him he just says it's "many".
But one two and three are also innate (immediately recognizable) quantities are they not? So does a person using such a number system actually count, or recognize and categorize only?
I 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.
When my two year old can't count the items in front of him he just says it's "many".
IIRC (edit: and as alluded in the article) there are languages which count as "one, two, three, many". But one two and three are also innate (immediately recognizable) quantities are they not? So does a person using such a number system actually count, or recognize and categorize only?
https://slate.com/podcasts/lexicon-valley/2021/03/english-la...
When my two year old can't count the items in front of him he just says it's "many".
IIRC (edit: and as alluded in the article) there are languages which count as "one, two, three, many". But one two and three are also innate (immediately recognizable) quantities are they not? So does a person using such a number system actually count, or recognize and categorize only?
I 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…
If I cover lunch for you, you would owe me $5.
In a way, you now have -$5. You won't have $0 until you pay me back the $5 you owe. We can also say you have $5 of debt. That makes the number positive while still representing the amount. But when reconciling your books, it'll be subtracted from your total.
‘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…
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 ape and humans. Our intelligence has been emerging from the simplest animal there is throughout our entire evolutionary history.
And even then we see birds, octopuses and so on use tools and solve problems very similarly to us, which have branched much earlier from us. There are many different types of minds that can evolve. But I believe the fundamentals will always be the same. They're fundamentals of information processing systems. And BTW, we know dolphins, parrots and so on can do basic math, like counting, and translating that count to another set of objects. So they understand numbers, that's what numbers are at their most basic.
We marvel at how enormous the universe is, and how varied life in it can be, how different the minds of aliens may be. But in that seemingly humble pondering, there underlies something very arrogant. We think our mind is special. We think it's unique. And other minds will think extremely differently.
I think we'll figure out sooner or later, that our mind is basically inevitable, the broad strokes will be replicated for every species throughout the universe. This doesn't mean it'll be immediately easy to figure out aliens and their culture. But those are the details, not the fundamentals.
I 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…
Earlier quoted context omitted.
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.
I’ve mentioned in a comment above, I find nothing natural in doing operations related to zero i.e. related to nothingness, meaning that I see “adding” and “zero times” as an oxymoron (you cannot associate an action, “adding”, to nothingness, i.e. to “zero”).