#121
yeah it doesnt really answer the question but i appreciate the effort
#122
i wish i had an irl math/coding study buddy. toyotathon you still wanna team up?
#123
yup let's do visual group theory. should i catch up to ch 6?
#124

tears posted:

yeah it doesnt really answer the question but i appreciate the effort


This is really something that many serious physicists have struggled with. "Is the wavefunction real?" is a question that has seen a decent amount of back and forth over the years by physicists studying quantum phenomena

#125

toyotathon posted:

yup let's do visual group theory. should i catch up to ch 6?


sounds good to me

#126
TIL in topology book that the set symbols (⊆ means 'is a subset of, or is equal to') can be analogous to < & >, like

A ⊆ A for every A
x ≤ x for every x,

A ⊆ B and B ⊆ A, therefore, A = B
x ≤ y and y ≤ x, therefore, x = y,

and,
A ⊆ B and B ⊆ C, therefore A ⊆ C
x ≤ y and y ≤ z, therefore, x ≤ z.

so it's like, A = {1,2,3}, B = {1,2,3}, C = {1,2,3,4,5,6,7}
#127
Yep! That actually something that can be made totally rigorous and very general, its called a partial order
#128
ooh that is relevant to this topologic CAD program, point-ordering. currently the topological space is lexicographic (s0,t0),(s0,t1),...(s0,tN),(s1,t0)..., because it is most convenient to the renderer, which needs to know whether t loops in a circle or terminates in a line. but i think, if the points were re-ordered, it could be fed to the renderer with a little modification, interesting.
#129
Im not sure!
#130
I'm working through Linear Algebra by Friedberg
#131
i'm using trigonometry on the lathe, in order to make a profile of the lathe bed.

drawing out the trig problem. all this machining stuff's just a lot of trig.:

you use the hypotenuse measured on a steel rule, and the known radius of a pin. then take a picture using a level camera, and use software to determine the angle of the rule. that lets you determine the X and Y distance of the feature on the lathe bed, to the lathe centerline.

example pictures:



it's nice that the skewed reflection kind of 'hones in' on the steel rule and pin contact point.

the measurement, the pin radius, and the angle, make two right triangles with a same angle, so you can get the distances. results were pretty good! the steel rule measures 1/64" or 0.5mm, and of the measurements that should be the same, the formula gives: 98.50mm and 98.62mm, 105.27mm and 105.20mm, and 104.43mm and 104.66mm.

it's to make an accurate jig with a V-channel to hold bar stock, which can slide along the lathe bed and kind of dock into the lathe chuck already along an eccentric centerline, then the 4-jaw chuck tightens down on it. otherwise it's basically hard to chuck something at a precise angle, and off-center in the lathe. this is so it sets a specified angle on a specific radius, to drill into the face of bar stock, except off-center. at least hopefully, who knows.

this is what the jig looks like:



fingers crossed that it more or less works...
#132
https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115/

Always inspiring to see an independent researcher come up with something new.

In this case the 'amateur' has a PHD in physics but it still gives me hope lol
#133
speaking of... https://www.quantamagazine.org/sci-fi-writer-greg-egan-and-anonymous-math-whiz-advance-permutation-problem-20181105/

On September 16, 2011, an anime fan posted a math question to the online bulletin board 4chan about the cult classic television series The Melancholy of Haruhi Suzumiya. Season one of the show, which involves time travel, had originally aired in nonchronological order, and a re-broadcast and a DVD version had each further rearranged the episodes. Fans were arguing online about the best order to watch the episodes, and the 4chan poster wondered: If viewers wanted to see the series in every possible order, what is the shortest list of episodes they’d have to watch?

In less than an hour, an anonymous person offered an answer — not a complete solution, but a lower bound on the number of episodes required. The argument, which covered series with any number of episodes, showed that for the 14-episode first season of Haruhi, viewers would have to watch at least 93,884,313,611 episodes to see all possible orderings. “Please look over for any loopholes I might have missed,” the anonymous poster wrote.



edit: also saw a shoutout today to the science of exact constraint: https://hackaday.com/2018/11/16/expanding-3d-printer-bed-stays-true-under-fire/
this guy who built it is a VERY irritating man, and a dentist. and he also picked the wrong coupling. Kelvin's 1-2-3 is known to be not very good w/ thermal expansion. if the distance between his 3-constraint (socket) ball and 2-constraint (vee) ball grows, like during thermal expansion, then the bed will rotate in the socket, along the path of the vee, until it compensates itself for the increased distance. unless he machined it exactly parallel to the line between them. part of the point of exact constraint is you don't need expensive stuff like 'exactly parallel' anymore... it's why maxwell made the 2-2-2 that everybody uses...

Edited by toyotathon ()

#134
fine ill learn your stupid maths





#135
hell yea. iirc that avogadro molar weighing of gases was a major piece of the evidence for molecular theory, back in the day, vs a continuum of matter. because like your text excerpt says, they'd boil a volume and pressure and temperature of a purified substance and then weigh it, and had this tabulation of all the values that the same experiments all over the world were confirming. and they'd notice how after reacting the gases, well if you were agnostic to whether molecules existed or not, you'd have no reason to suspect that they'd combine into neat ratios, like 2 hydrogen to 1 oxygen. no reason to suspect the chemical world should be neatly organized like that, except thru atomic/molecule theory. seeing molecules without seeing them! i could be misremembering the history tho...

Edited by toyotathon ()

#136
cant find weed on the periodic table
#137
Might as well call this the pretty note taking thread
#138
Yeah for real these make my notebooks look like dog trash
#139
#140
beautiful notes are very important for a Marxist. just as important: ugly notes, memorizing entire tables of grain production figures and thinking about them while squinting and nodding
#141
writing small is a good prison skill

Edited by toyotathon ()

#142
i've been focusing on programming but wanna get back to the math soon
#143

Belphegor posted:

I'm working through Linear Algebra by Friedberg



how are you liking friedberg? we're slowly working thru halmos, but it might be too abstract for us..

#144
yeah, it's slow but steady. I'm trying to do every problem. So far they are all doable, the main prerequisite has been calculus.

It's more rigorous/theoretical than the type of linear algebra I learned in Uni, which was very much applied, whereas Friedberg covers generalized vector spaces, not just the 'spatial' ones in R^n

I'm going to go do some right now!
#145
i've been reading about the replicability crisis in social sciences (only one problem of an obvious many). on the one hand, so-called experts are saying that this is not a problem of a blind faith in p-values, but other so-called experts are saying that p-values can no longer be reliably used in research. came across bayesian statistics, and am wondering if anyone has any thoughts/experience about this approach to research or its usefulness in general? is this just another attempt to rationalize poor methods?
#146
had a math-specific question, well 2.

first is about curvature on a 2D surface. if you take the set of normal vectors at every point on a 2D surface (call it A), and multiply them by a scalar r, it makes a new surface (call it B). could you find the radius of curvature of A, by looking at where B intersects itself, for a given r? if you look at my old exact constraint notes maybe you can see what i'm getting at, and why...

another's about spheres. if you're standing on a sphere, holding a compass facing forward, is it possible to walk a path on the sphere and come back to where you started, w/o the compass doing a full rotation, either its needle, or spinning around its N/S axis, or E/W axis?
#147

toyotathon posted:

another's about spheres. if you're standing on a sphere, holding a compass facing forward, is it possible to walk a path on the sphere and come back to where you started, w/o the compass doing a full rotation, either its needle, or spinning around its N/S axis, or E/W axis?


just put your finger on the needle as you walk around

#148

toyotathon posted:

had a math-specific question, well 2.

first is about curvature on a 2D surface. if you take the set of normal vectors at every point on a 2D surface (call it A), and multiply them by a scalar r, it makes a new surface (call it B). could you find the radius of curvature of A, by looking at where B intersects itself, for a given r? if you look at my old exact constraint notes maybe you can see what i'm getting at, and why...



why would B necessarily intersect with itself? it sounds like you're just talking about rescaling the surface A by r, which wouldnt by itself introduce any sort of self-intersections that werent in A to begin with.

another's about spheres. if you're standing on a sphere, holding a compass facing forward, is it possible to walk a path on the sphere and come back to where you started, w/o the compass doing a full rotation, either its needle, or spinning around its N/S axis, or E/W axis?


theres nothing stopping you from holding the compass still, facing the same direction, while you walk in a very small circle. if you want to mark a point on the compass and align that with your velocity then you will always make a full rotation.

#149

c_man posted:

c_man posted:
why would B necessarily intersect with itself? it sounds like you're just talking about rescaling the surface A by r, which wouldnt by itself introduce any sort of self-intersections that werent in A to begin with.



no no not rescaling. i'm probably not explaining it properly. making a new surface (B) out of the tips of the surface normals of A, the normals all the same height, determined by some scalar r. B's the normal plane.

this example may or may not clarify what i mean.. If surface A is a flat plane, but has a half-sphere indentation in it of radius r, then the radius of curvature there is r (right?). all the normals of A will meet at a single point (looking down at A, if the normals are length r, it's the center of the circle that's formed by the equator... the rest of the normals are just above A making another plane, distance r away). greater than r and there will be a self-intersection of B (even if A is well-behaved), less than r and no intersection. so you can kind of imagine B changing as r changes, gradually growing off the surface like blades of grass, and when the grass inside the half-sphere is length r (or greater) they touch.

#150
I see what you mean now but I think you need to define the surface A more narrowly than 'any given 2-manifold'.

Like c-man says, B is not guaranteed to have intersections.

On which 'side' do we draw the blades of grass? The top or the bottom?

Also, imagine you have an elliptical indent. Which radius are we interested in, the minor one or the major one? What would the 'correct' radius of curvature be, as you call it?

#151
yeah nvm on this. once the manifold becomes non-symmetrical, it's no longer = to the radius of curvature, it's something different, but still related to the curvature. i feel like i need to stop visualizing, and start calculating some examples in 2D.