What Even Is a Number? • Hacker News Board

Re: What Even Is a Number?

#171

Post by Nomentatus » Thu, Feb 21, 2019, 6:14 PM UTC

qubex wrote: post #169

Nomentatus wrote: post #167

Earlier quoted context omitted.

Now if you look up tangible... I think you're caviling, at this point.

“Tangible” means touchable and has a Latin root; “tangere” still means “to touch” (though somewhat archaic) in my native Italian. That same Latin root is why we call linear equations that share the gradient of a given curve evaluated at the point where they cross to be “tangential”. Look, we could go on with this all day. What’s your point? To show your terminology and grasp of topics is greater than mine? Is this so…

So, how do you pinch a democracy, physically? By avoiding answering my point in my last message, you're still caviling. One progresses to the end of a conversation by honestly answering the points made, and you aren't interested in doing that.

Re: What Even Is a Number?

#172

Post by Retra » Fri, Feb 22, 2019, 2:15 PM UTC

AgentME wrote: post #165

Retra wrote: post #160

Earlier quoted context omitted.

The concepts are also just symbols, just in different media. They are also a map. >if/when mathematics provides a complete map to that territory which is "the world", Then it will encode all the information that exists in the universe. Which will not fit in your head, and thus will not be mathematics. Just because a territory is trivially a map of itself doesn't mean it is useful to call it a map. >The description of…

>Reality isn't just the initial rules. It has state. That state must be described for you to have a complete description of reality. If reality is deterministic, then all the state is derivable from the rules and the initial state, and it's possible we could figure out the rules and initial state and become relatively sure of them. (We probably wouldn't be able to calculate the future, since evaluating the rules with…

Even if reality is deterministic, you still have to know which state to derive. And that process will have to account for all of the same information.

Re: What Even Is a Number?

#173

Post by chmod775 » Tue, Feb 26, 2019, 6:14 AM UTC

kazinator wrote: post #120

jakeinspace wrote: post #117

Earlier quoted context omitted.

My guess is that eventually, if we manage to ever reach that point of total knowledge, there are certain properties of the universe that exist for no reason; they just are. Whether that's at the level of today's fundamental particles/qft or much deeper is anyone's guess. Example: space-time exists in n(>=4) dimensions, there are several quantum fields that exist in that space-time and evolve/interact according to the…

> there are certain properties of the universe that exist for no reason; they just are. But we have that in math and logic: axioms! > Of course, we can never know for certain whether we've bottomed-out our description of reality That we do not know is a fact; but is it a fact that we can never know? What if one fine day we do know?

> But we have that in math and logic: axioms!

Yes and no. Axioms are chosen such that the math that is based on them makes sense to us (because the math reflects what we'd expect in the real world) and isn't self-contradictory.

So they do exist for a reason.

> That we do not know is a fact; but is it a fact that we can never know?

What if our universe actually has randomness that appears to come from "outside the system", i.e. there is really no way to predict the outcome of certain things from inside the system.

Picture you're sitting in a box trying to play Mikado. In theory you should be able to perfectly predict the outcome of every move you make - except there's a stranger shaking the box you're sitting in at truly random intervals.

For our reality this would mean that there's no way for us to develop an understanding of certain things and predict their behavior.

So essentially the end of the line for all sciences except theology and philosophy.

This possibility makes me somewhat uncomfortable.

On the other hand maybe everything is perfectly deterministic within our universe.