@user379685 it sounds achievable, bear in mind all physical (imperfect) light sensors will have a radial response curve

(as will sources too)

Could you elaborate what a radial response curve is?

@user379685 oh it is the relative intensity dependent on the angle of incidence formed by the geometry of the sensor itself, and the aperture from packaging, lens etc etc

i mention this if you plan to run this as an experiment

@ACuriousMind i was reading that very interesting wiki page on distribution (mathematics), and they say many times that it is different to the 'classical' sense

what does classical mean in mathematics? i'm familiar with classical vs quantum in physics, but not math

@antimony It just means the "normal" sense of being differentiable

ahh gotcha thanks Nihar :)

@antimony You have to read the entire phrase - the "classical notion of functions". The point is that while functions can be evaluated at points, distributions - even if we may notate them as $\delta(x)$ - cannot, they are instead evaluated at test functions and do not have a "value at a point"

^ (the differentiable thing was only in the context of the sentence "Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense", sorry)

This is a very weird question, but if we consider the set of all statements in math to be a poset with ordering $\Rightarrow$ (i.e. "implies"), could there exist a minimal element?

Like I was thinking our set of axioms would probably be the maximal elements but I'm dubious on a minimal one existing

Depends

@SirCumference implication is not a partial order

equivalent statements imply each other, so implication is not antisymmetric

In most mathematical formal systems, there is the trivial rule $A \Rightarrow A$

So you could go arbitrarily far back

@ACuriousMind yeah but that's kinda like how ≥ is a partial order despite equal numbers being ≥ to each other

@SirCumference no, it's not :P

also yeah

you have to quotient the set of all statements by the equivalence relation to get something where implication is a partial order

for instance, a lot of theorems can be used to derive the axiom of choice again

or the axiom of non-contradiction

@ACuriousMind ah crap

the result is the LT algebra

woah

never knew something like this existed

neat, thanks

@SirCumference however, passing to the quotient loses some of the structure of the actual logic, see the last paragraph here - the partial order is not actually a useful thing for logicians

Anyone feels like answering?

But If I check the transformation properties of $\epsilon_{x_1x_2...x_d}r^{x_{d-1}}p^{x_d}$ it is a (d-2) rank tensor..

the epsilon thing is the totally antisymmetric levi civita tensor in d dimensions

Sigh..."We don't do much with serifs anyway"...not much, as in, run entire sites like physics.SE with serif as their default font???

@ManasDogra $p$ and $d-p$ forms are Hodge dual to each other

I talk about that at some length w.r.t. angular momentum here

@ACuriousMind But they are not exactly the same...so Is L a 2 form or a d-2 form?

depends on your definition of it :P

since Hodge duality is an isomorphism, both forms are equally valid definitions

@ACuriousMind This is another thing I have noticed....Whenever there is an isomorphism sooner or later everyone treats them as the same...like vectors and 1st order differential operators...covectors and differentials(1-forms)...

it is a tricky thing to keep in mind

sure - since if you have a canonical (or just a fixed) isomorphism between $A$ and $B$ you always have a unique way to translate statements about elements of $A$ into statements about elements of $B$ and vice versa

in many senses, mathematical objects really just have an "identity" up to canonical isomorphisms

@ACuriousMind That's the meaning of an isomorphism anyway :)

I feel so disappointed that high school teachers usually don't warn about these tricky things...like Angular momentum is not a vector all the time..it's different in different dimensions and so on..

I don't think telling kids about the angular momentum as a Noether current would help them much

@ManasDogra why would high schoolers care about angular momentum in dimensions other than 3?

the unfortunate reality is that with increasing generality in physics the mathematical sophistication necessary to express the more general concepts also increases

and physics education generally operates on the principle to do the least sophisticated math they can get away with :P

this isn't always beneficial, but it is definitely reasonable to not bother the average high schooler with exterior algebras and Hodge duals :P

@ManasDogra well, for 2d you can get away with just embedding the 2d space as a plane in 3d space and using the usual angular momentum there

@ACuriousMind But it isn't told in that way :( embeddings and stuff...

the angular momentum will always be orthogonal to the plane, and hence only have one d.o.f., just like the intrinsic description as a pseudoscalar

@ACuriousMind Yes

@ManasDogra Here's a page that lets you play with a rotating 4D hypercube syntagmatic.github.io/hypercube/rotate You can make it rotate in 2 or more planes simultaneously. Here's a shiny hypercube that's somewhat interactive on a touchscreen. It might have more controls on a desktop: mikelortega.github.io/tesseract

@PM2Ring Wowww! Thanks for sharing!

Why is the phase speed of a material wave being bigger than the speed of light not a contradiction to special relativity?

@MadSpaces see physics.stackexchange.com/q/6912/50583

Thanks

Suppose solving a system of ODE x'=f(x,y),y'=g(x,y) we get x=3,y=7 does the solution in x-y plane represent a point (3,7) or the full y=7x/3?

If there was a t dependence in the solution...we could have eliminated t and get the x-y equation and plotted it in the x-y plane...Why does this does not work in this case if the solution is not y=7x/3

the ' denotes time derivative

@ManasDogra What do you mean "we get $x=3, y=7$"? If $x$ and $y$ are constant, then this is only a solution if $f = g = 0$.

Yes

That's what I meant---It's a trivial system I know

So it should represent a point right?

yes

I'm not sure how you got to the "full $y = 7x/3$", either

@ACuriousMind What stops us from dividing the two equations...x=3,y=7 to give us x/y=3/7 and y=7x/3? What mathematical fact? (I understand we cannot do that somehow but "why" )

any choice of constant $x(t) = x_0, y(t) = y_0$ is a solution for your trivial system, not only those with a ratio of $x$ and $y$ of 7/3

@MadSpaces Also see this cute toy Greg Egan wrote 20 years ago: gregegan.net/APPLETS/20/20.html

@ACuriousMind Initial conditions are given

@ManasDogra In this case, your initial conditions are just the pair $(x_0, y_0)$

of course it is true that $x/y = x_0/y_0$ in this case, but I don't get why you want to look at that ratio in the first place

@ACuriousMind Just playing around actually...Look I want something fallatical going on here...Like x=1 implies x^2=-1 but it does not imply x=1 or -1 because we started with x=-1 itself...So has this got some name?

Similarly with x=3,y=7 does imply y=7x/3 but doesn't imply that we can take all the points on the line y=7x/3 cz we started with x=3,y=7

So what rule of rigorous mathematics prevents us...apart from the most common sense

@ManasDogra of course it does - the implication $A \implies A\vee B$ is always trivially true just by definition of 'or'

however $A\vee B$ does not imply $B$

i.e. the chain of implications $A\implies A\vee B \implies B$ is just not logically valid

@ACuriousMind This is the kind of statement I was looking for...Is there a term for this "chain of implications" thing?

I don't think it has any particular name

@ACuriousMind Oh..ok I will better use thiss term "chain of implications". Thanks

Now I see I chose a ridiculously complicated example for such a simple thing :p

@ACuriousMind Another quick question....for that system x'=0,y'=0..If no initial condition was given we would get a family of straight lines parallel to X axis and another family parallel to Y axis...these curve cut each other but they shouldn't do so in an autonomous system...So there exists certain f and g for which phase trajectories DO cut for autonomous systems of ODEs! Are f,g=0 the only ones?

I'm not sure what you mean - the general solution is $(x(t),y(t)) = (x_0,y_0)$, it's not a straight line, each "trajectory" is just a point in the x-y-plane

@ACuriousMind Ok I get it now...Yeah it makes sense, the solution is to be treated as a tuple..not independently.

I was speaking of plotting the x=x0 and y=y0 seperately and hence getting the confusion

But that doesn't make any sense here...

@ACuriousMind I gave it a thought and have this question--- is it a point or any point when x0 and y0 aren't given?

@ManasDogra each individual trajectory is a single point, but any point is a possible trajectory

@ACuriousMind Yes

Is this the right place for this

I think I found the great filter
so basically our civilization has gotten to the point where natural selection no longer occurs we do our best to make everyone live no matter what mutations they might have and because of that, we have stopped getting better as a species. so if something bad happens like an ice age or a mass extinction event we wont be prepared and this probably happens to all large species

sounds a lot better in my head

not sure why you think a physics chat room would be the "right place" for this, but if you think that evolution makes us "better" but only if we let people die you haven't understood that fitness is always relative to an environment and modern human civilization is just another environment in this context just like Galapagos islands or deserts :P

cant find a science room hoping yall could point me in the right directio

direction*

Well if everybody has equal fitness because nobody dies unless they have a really bad mutation favorable ones reproduce just as often as no mutations

@ACuriousMind

@CiurkitboyN fitness is not the probability of survival, it is the probability of reproduction

im not real smart about the terms

Why do they make it so you cant edit messages after a liitle while

in order to prevent abuse where people go back and retroactively change what they said during a discussion

Well if everybody has an equal chance of survival because nobody dies unless they have a really bad mutation favorable ones reproduce just as often as no mutations

fixed

you seem to have a strange idea of how humans work

I've survived for quite a while yet I have not reproduced. Plenty of people I know have. Survival is a necessary, not a sufficient condition for reproduction.

Also, what is a "bad" mutation?

anything that makes living actively harder

Evolution has no notion of "good" or "bad". You're probably trying to justify a personal value judgement here.

not very common

ok

@ACuriousMind So are you are not married?

I'm probably worse at fighting lions than some of my ancestors were. That doesn't make me "better" or "worse" than them, it just makes me better suited to an environment where I don't have to fight lions

@ManasDogra I didn't say that, but no I'm not married, either :P

Exactly w have gotten so used to this envirement where If anything suddenly happened we wouldn't be prepared

"Suddenly, lions attack" is pretty low on my list of things that are or could go wrong with the world.

@ACuriousMind OMG...that's why you are so happy and that's why you get so much time to study physics :p

not specifaclly lions

(Married people here---just kidding)

im too young to get married im 14 lol

aquard silence lol

no idea how to spell akward

@ManasDogra I actually spend very little of my time studying physics :P

@ACuriousMind I rarely study physicks except quantum mechanics I find them very intereting

physics*

@ACuriousMind I know now you develop softwares...But then I must say you have got a god-gifted brain! Or maybe once upon a time you studied physics a lot:-)

well, I did study it for about 6 years :P

Right now I am watching this youtube.com/watch?v=OqkrONVO_Sg Quantum physics are very cool

I just looked at this link and now im confused syntagmatic.github.io/hypercube/rotate lol

@ACuriousMind That too...say..40+ years ago?

Hm? I'm 28.

lol im very small compared to yall

@ACuriousMind What?...everyone says you are old...like John Rennie!!!

who's saying that? let them come out and fight me :P

A year ago someone threw some disrepsectful words at you and someone came out with your true name(which I am lucky to know but won't tell here) and said that you are more than 4 times his age(which was ~20) so...you are 80!...

But now you say you are 28..and yet so good at everything! OMG

I'm pretty sure you misunderstood a joke there (or that someone simply didn't know me)

I wish I could be like you one day :)

that's flattering, thanks, but you don't know what you're wishing for there :P

@ACuriousMind Is it that bad? :p

nah, I like my life as it is

yall started ignoring me when I said I was 14?

@ACuriousMind Anyway goodnight...It's already 1AM in the night here in India :-)

@CiurkitboyN Hey i am 17

g'night

cya

yah I was jokin its just yall stopped reacting to what I said lol

sup

hello. may i please request assistance with this question to which i posted the accepted answer? the question is certainly not a homework question and i'm not sure why it was marked off-topic as such

looks like a pretty clear case of a check-my-work question to me

how about this one physics.stackexchange.com/questions/631467/…

and thanks for the guidance @ACuriousMind

let us assume that the original intention of the questions is to check-my-work or homework-type. if i edited the body of the OP to 'appear' to not fall into those categories, does a moderated then step in to 'reopen' the closed question?

@kbakshi314 the first edit after closure automatically enqueues the question for review in the reopen queue

thanks for the info @ACuriousMind. if possible please comment on the second question I was hoping to receive advice on

Both of these are questions that are pretty clearly off-topic by our current policies. The effort you put in is commendable, but in general you shouldn't answer such questions

no worries @ACuriousMind and thanks for the compliment. i like posting explicit answers since implicit and brief answers which avoid quantitative analysis seem to avoid addressing the intent of the OP, in my opinion. your comments helped me understand the policy on off-topic questions and answers. thanks.

@kbakshi314 there is an automatic deletion routine called the roomba, the exact conditions for deletion are here

additionally, we do often delete complete or near-complete answers to homework-like questions when they are flagged as such, but doing so long after the OP has seen them serves little purpose

i see @ACuriousMind. as per the link you provided, am i right to conclude that this question marked closed because of being homework-like off-topic would have been deleted (because it has been 14 days > 9 days since it has been closed) would have been deleted if it had 'score of 0 or less', 'no answers with a score > 0' and 'no accepted answer'?

yes

thanks for the link. in the case of the posts we discussed, i am not inclined to delete the answers since the concepts explained are quite deep and require subtle thinking. i'll leave it up to the moderators to make an assessment on those

but i'll keep in mind that the site discourages answering homework-like questions henceforth.

oh thanks @ACuriousMind for the clarification re. ""classical notion of functions"" i still don't quite understand, but now at least know what it is i don't understand so i can do some more reading :)