101–110 of 211 posts
Saying that the universe is irreducible with pockets of reducibility is a total oxymoron. It's not "irreducible" if parts of it are reducible. "This wall is impenetrable, except for the holes there. Don't mind them I'm making a point here!"
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…
If Mathematics is a language to describe reality, maybe numbers are not its whole alphabet. Inherent complexity, things that are not discrete, and emergent properties may not be described adequately with numbers, and maybe a different alphabet or even language is needed. Numbers may be (or not, it may depend on our biology) a good initial concept, but maybe something else may be developed, something more "correct" to…
Almost all of modern mathematics is not about numbers, although a lot of the objects studied can eventually be related to numbers in some way.
There may be entire categories of representational concepts which we abstract poorly, or don't abstract at all, or possibly don't perceive at all - because from our point of view the relationships are so complex and remote they're effectively invisible.
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.
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.
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.
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…
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…
Positive operations and numbers move you to the right. Negative operations and numbers move you to the left.
So a negative number is simply a count of a change in direction.
This works very literally. Ten miles west followed by five miles east is five miles west. There's nothing mysterious or weird about the "absence of westness" when you've turned around and started off in the opposite direction.
It generalises neatly to complex numbers where i is a rotation in the complex plane - instead of being pointlessly-weird-for-the-sake-of-it: "the square root of -1 which we've spent years telling you can't exist, and now we're telling you it can."
Technically this is a form of basis vector. Beyond that things get complicated.
But the idea is still valid - you define your direction markers (even if they're functions instead of constants) and then you can work out where you are in the space you're exploring, and what "movement", "counting" and "position" mean in that space.
Multiplying by zero is always a null movement of no distance.
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…
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.