/sci/ - Science & Math

[The Polymath No.14872042]

Polymath here. I challenge you to hit me with your hardest questions.

Rules:
>I will not do your homework (e.g. "What's the derivative of ...?").
>I will not write more than one post as an answer. Don't expect an entire textbook from me.
>I will not bother with questions that can be easily googled (e.g. " When did ... happen?")
>Don't waste your time asking me about unsolved problems like Navier-Stokes.

[Anonymous No.14872047]

>>14872042
n = np?

[Anonymous No.14872059]

What sorts of parallels, if any, do you observe between the behavior of matter on the micro scale (particle physics etc.) and the macro scale (astrophysics)

[Anonymous No.14872090]

>>14872042
Why doesn't the dependence on pi change when calculating properties of a sphere (surface area, volume) vs. a circle (circumference, area)? The volume and area of a 4-sphere depends on pi^2, same for a 5-sphere. The dependence jumps every even dimension, but not the odd dimension.

Do you have an intuitive explanation for why this is so?

[Anonymous No.14872098]

>>14872042
What do Laver Tables have to do with large cardinals?

[Anonymous No.14872112]

>>14872090
...because...the nature of the math expands linearly moving from odd to even but quadratically[?] when moving from even to odd

[Anonymous No.14872119]

>>14872042
Prove that if X is a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

[Anonymous No.14872124]

>>14872112
when you move from 1D to 2D you're just taking the same line and rotating it, so it's just circle math, but when you add the z-axis shit explodes because now you just created infinity xy-planes so then it's real mf exponent hours

[Anonymous No.14872130]

>>14872042
why do you think we don't see any aliens?
(large) planets are not rare, and i suspect we will find small habitable planets are not rare either as our tech becomes able to detect them easily
do you think life is rare? is life common but intelligence and/or technology rare (my guess)? is ftl truly impossible meaning no species bothers? are we just early?

[Anonymous No.14872133]

>>14872124
building an additional plane introduces significantly less complexity than rotating it

[Anonymous No.14872142]

>>14872042
Write a multilateration algorithm or equations using n static receivers and a transmitter moving. Ignore any backscatering, multipaths, etc, but if the algorithm includes error it should be taken into account in the solution (analytical or approximation within a d).

It's more about the geometric algorithm than EM itself.

[Anonymous No.14872162]

>>14872130
life is either exceedingly common, or exceedingly rare - it's highly unlikely to be a "sort of probable" event given the scale of the universe. since we have not made contact with any life yet, the likely answer is that life is exceedingly rare. we are lucky.

[Anonymous No.14872168]

>>14872042
How profitable is your knowledge?

[Anonymous No.14872179]

>>14872042
Describe a method whereby a neural network's model can be reconstructed through carefully constructed queries and prove an upper bound on how many such queries are required to reconstruct a model of fidelity x (0 <= x <= 1).

[Anonymous No.14872190]

>>14872162
Certain UAP (formerly UFOs) could actually be aliens though. It can be rationalized like this: civilisations that develop technology go down a similar route, that is to say they miniaturise and mobilize their tech. The same way we can put a ventilator in ambulance that was previously so big it had to be in a building, and the ambulance vehicle itself has gotten faster, more powerful etc. If this trend is followed to it's logical conclusion, it means bulky spaceships will one day be made of materials with ridiculous (to current standards) strength weight ratios, engines, etc, and then we may one day zip around the solar system in small but powerful craft, perhaps near the limits of the laws of physics and exploring the galaxy. Going back to the UAPs, it would be like an uncontacted tribe witnessing a jet fly overhead. It's speculation to say if this is really the case for any individual event we see, but the reasoning is sound IMO.

[Anonymous No.14872193]

>>14872162
>since we have not made contact with any life yet, the likely answer is that life is exceedingly rare
Or the aliens capable of transsolar travel have a subtler policy for introducing themselves to primitive species than just slamming a UFO down in times square and going HAY GUIZ WUTS GOIN ON IN THIS THRED