Archived threads in /sci/ - Science & Math - 1657. page

>>8094070
Lee's smooth manifolds. Spells everything out, hence very suitable for home study.

>>8094080
I just took a look at Lee. i think we aren't studying it so deep. We started with parametric curves in R^2 and R^3 (Tangent, Normal, binormal base). Then we got to elementary parametric surfaces with geodesic curves, first and second fundamental forms, asymptotic lines.
I need something like that for further reading

>>8094096
Sorry I didn't realize they had internet in the 19th century.

Rocket surgery

rocket science
t. not biased

brain surgery
t. not biased

>>8093942
>all military closed down

We'd have a huge surplus of burger-flippers, low-end wages would fall.
The increase in welfare spending would further politically divide the U.S.

>and the budget put into science and social research.
STEM job crisis ends, but the extra research mostly goes into stuff with marginal returns.

>>8093946
>STEM job crisis ends

There's a worldwide STEM job crisis?

>>8093952
h1b Pajeet outsourcing crisis

>>8093939
>Are there any other examples of actual randomness?
Everything that depends on quantum effects. Tunnelling (radio decay) is the easiest to explain, but basically all of quantum mechanics.

>>8093949
Layman here. Can we prove their randomness or we just don't know what happen behind the scenes and use this approximation?

>>8093949
Thanks, gonna read up on that and try to understand it at least a little bit

>>8093894
They tried to do it on mythbusters

>>8093894
Archimedes was straight balling.

>>8093894
It's unlikely that the wood will burn
You can however burn the sails

>>8093701
axioms are invented
the resulting objects and their properties are discovered.

Math wouldn't exist without us because our logic is not universal, it only makes sense to us. And that's what we use to do math.

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>>8093701
Philosophy is just structuring and formalizing in natural languages.

mathematics are about formalizations of your speculations (which you form from your desire to see things that you experience [the empirical world, once you chose to objectify what you feel] through induction, as similar or dissimilar) to the point that you have a structure more formalized than your speculations structured in natural languages.

Logic is just a the formalization of your speculations about *validity of inferences*, so here logic is a formal part of mathematics.

It turns out that plenty of mathematical structures are cast into some formal deductive logic (like set theory formalizes your structures of numbers).
I meant your usual set theory cast in FOL. Set theory is just a structure too and it turns out that you can interpret a part of this structure as some kind of numbers.


Science is just claiming that your formalized structures (in formal languages or not) gives you access to some *reality*, more or less hidden with respect to what you are conscious of[=the empirical world, once you choose to ''externalize, objectify'' what you feel].
Same thing for the religions which go beyond empiricism [=claiming that you feel and think is **not** enough from which you choose to dwell in your mental proliferations].

Some mathematicians, typically Brouwer, think that mathematics should, equally to the speculations (however formalized) of the scientists, talk about the empirical world. So typically, your formal symbols are real entities: these entities belong to some world and they connect or not back to the empirical world.
to be clearer, the symbols are names of real entities and, since you begin always from the empirical world, this world constrains you on the creation and usage of these real entities. then these real entities can or cannot belong to some other world as well.

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A lot of math, historically, came from "standard" (ie. euclidean) geometry.
So thats mostly discovery, because you can draw pictures and see how things work out.
(Our real world is approx. Euclidean 3d space)

However, once a certain formalism is established (like Cartesian coordinates, defining algebraic equations for plane curves, or axioms for deriving all known properties of geometry), one can twiddle around with that and invent new things.

Probably the most trivial example would be Euclidean 4d space, or more interesting, alternative axioms for geometry, in particular relaxing the parallel axiom in Euclidean geometry leads to hyperbolic geometry, which is a lot of fun.

pic related shows a bunch of lines going through some point and parallel to a given (thick) line, visualized in the poincare disk model of the hyperbolic plane.

>>8093608
Buggy as shit, could be worse. Homework on moodle can go suck every dick in existence though.

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>>8093618
Second

I hear Canvas is pretty good.

>>8093541
CO2 won't sustain alien life. Mg4O5(g) does. The Drake Equation (d×t×x) proves this.

>>8093541
Oh, just like that.

>>8093541

How would you do it?

>>8093523
a^2+b^2=c^2 is the best avenue of solving that equation.

>>8093523
[math]10\nmid(k^{2}+2k+2)(k+1)[/math] though, try n=3, you get 17*4 which is 68.

>>8093528
Incorrect.

k+1=60
60-1=k
K=59

>>8093425
Standard gravity is inferred directly from the density of the earth at given points. This isn't the 19th century any more senpai, we don't use pendula to measure g. So if you were to drop a particle it would undergo an accelerating less than g because of the coriolis force.

>>8093425
https://en.m.wikipedia.org/wiki/Gravity_of_Earth

Check out the part in apparent gravity. It also varies by a little bit depending on your distance from the earth's axis of rotation.

>>8093459
>>8093461
Also, the percentage would be pretty small, considering the force of gravity is dependent on the mass of the Earth, while the centripetal force is dependent on your mass (or whatever you're measuring) which will be quite a lot smaller than Earth.

>>8093364
Mechanics C is the only useful one.

The "algebra-based" ones are retarded.

E&M needs mv-calc to be done correctly. So E&M C isn't very useful.

>>8093376
Thank you for your input.

>>8093364
It has an abismal passing percent, only 30% get a 3 or higher. I took it and it was very hard but very informative. Take it with no expectation to get college credits but just to learn. I'd recommend it.

>>8093359
math exists whether or not we discovered the "rules"

they aren't invented they're discovered, please commit sudoku

>>8093368
This. Math is discovered, not invented.

You can in fact define your own sets of mathematical rules across a space you define, and this is often done in fields such as modeling. However, such systems will either be a subset of an overall vector space, or will be inconsistent.

(Took linear algebra 101 eight years ago so I know what I'm talking about)

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(cont'd)

While Newtonian gravity expressed the interaction of bodies in a basically acausal, yet simultaneous way, GR suggests that the bodies (represented by the stress-energy tensor) have an effect on the geometry of spacetime (the metric tensor), which then affects the bodies in turn (the geodetic equations). This might not be a problem, except for the fact that their exist valid solutions like the van Stocktum, Gödel, and Alcubierrie metrics allow you to create a circle of events which are still seperated by timelike intervals (closed timelike curves), which means you could have a seemingly paradoxical cyclic causality. To date, all responses to these metrics have been the suggestion of ad-hoc conjectures that invoke causality as some kind of universal force field, something which strikes me as desperate and unsound.

When one tries to natively combine the equations of relativity and QM, we get the timeless, acasual, and nonlocal Wheeler-DeWitt equation. This is presently interpreted as showing some essential incompatibility between GR and QM, but what if what that equation has been demonstrating, and we've been ignoring, is that this is precisely how the universe operates? That time, space, and therefore causality and locality, are merely emergent properties of laws which are have none of those things?

What would the implications be of ditching the reliance on causality? Is it even possible to make a coherent theory without it? Can we even prove that the universe is logically consistent in the first place?

because we have absolutely no experimental evidence for acausality

also metrics such as godel's do obey causality, and also just because it's a mathematical solution doesn't mean it's in any way a good physical solution

EFE break down at certain extremes, we already know this. is meme theory the way to fix that breakdown? probably not, but it sounds like you don't actually care about physics being a science (rather than physics being a study of mathematics), so i guess you'll be a great meme theorist

>>8093369
I didn't say acausality as such had been observed, certainly not at normal scales. My question is if it's possible that causality might a) be an emergent phenomenon of something which is acausal, and b) if that causality might itself break down under extreme conditions.

As for the "not all mathematical solutions are good physical solutions", well, then we still have to explain what those constraints are and why they exist. Physics tends to follow the math quite closely. No one had ever observed antimatter when Paul Dirac first wondered what would happen if he did't discard the negative solution to a particular quadratic term in the relativistic Schrödinger equation.

Good. Women have become so cancerous to this species that we'd better be extinct than let this continue.

>>8093291
>implying half the world's population doesn't sill live under 19th century conditions.

>>8093291
seewhatyoudidthar

yes there does

>>8093289
yes

>muh rigor

That's the only reason, OP. """"Higher level"""""" math is just mental S&M