/sci/ - Science & Math

>>12118731
>If we can find so much interesting structure on topological spaces, why can't we do that on measurable spaces too?
I don't quite thank that this statement as posed is correct,
but I'll say that defining a topology is easy (you just need pullbacks and pretty much every framework let's you build arbitrary unions anyway), while the definition of a measure space involves something like fucking R.

>>11506330
To may contrast this with a positive example, let Y be the set of all natural numbers bigger than 3 (formally, Y:={x | x>3})

Then one may prove
>for all n in Y, it's the case that n^5 > 2

Once proven, we're allowed to instantiate any element of Y and thus prove individual cases.
E.g. t=80 is in Y, so having the above theorem, we can instantiate
80^5 > 2
(we have now thus proven a simpler theorem, a special case that also has a proof that doesn't need the induction axiom. We could have just proven it by rewriting mutliplication and using m=m being true for all m by axiom)

But again, we can't instantiate any t in X. So there's no standalone
>[statement]
in that case

https://en.wikipedia.org/wiki/Universal_instantiation

Alright, it seems that some people don't really see clamping from the broader scope, and I think it comes down to not entirely grasping the idea of "levels of organization" in a machine. It starts at the level of particles or a unit of some kind, goes up to molecules, then macrostructures, cells, groups of cells, tissues, organs, body regions, human or other organism, group, town, city, state, country, macro region, planet. Whether and the extent to which an object at any level of organization truly can be considered self contained and discrete is irrelevant.

In looking at one's own body, what we first find is organization. Your epidermis in not lining your bones, it is constituting your outer surface, because this allows it to perform its function relative to the overall system. When you digest food, it goes into a sack in which bile, enzymes, etc are secreted into an environment of low pH. The food particles don't dump into circulation because you don't want all that digestive activity and potential happening arbitrarily throughout the body. Likewise, the heart does not "choose" to beat, the muscle does not choose to move.
[...]

>>11454913
And, Anonymous:
>Unclamp

>>10886553
You just posted a somewhat subtly sexualized child.

>>10863873
>Time is an illusion
Never understood this. If there was no time, how would you have change? Time isn't a "description" of anything, all of our descriptions are based around time. Everything is state. Time is the medium for change of state. Without time there is no change, only a constant and unchaging state.

Yeah, I don't get it. I think a lot of this stems from relativity and the notion that there exists A spacetime, as in a physical object that exists rather than a concept for description and reasoning. If you think about the fundamentals you can see and experience, reality is pretty much a flipbook. Change is probably quantized. Who knows.

Honestly, this "time doesn't exist" shit actually pisses me off. It really does. Never before have I seen such a bold and massive statement made so often, yet literally, never, explained. In any detail. With any metaphor, allegory, "lateral thinking". It's just said, smugly. As though the supporting framework to understand it is on some plane where it's not feasible to make anyone understand.

Yeah. Prove me wrong and say something substantive, or fuck off kiddo.

>>10352916
This needs to be stickied. Bitching when someone tells you what to look for because they didn't spoonfeed you should be a bannable offense. I don't understand what's the matter with these people or why they're here if they have no personal initiative or curiosity.

>>7735972
From the thumbnail, I thought this was Re-L cosplay. Now that I've entered this thread, I am thoroughly disappointed.

Hidden, reported, and saged. Enjoy your symbolic downvote.

>>7684330
Delete this.

>>7385372
Been casually watching this conversation. Just adding my two cents to say not only am I not impressed, I am disappointed. Get yourself together, anon.