Anonymous at Tue, 2 Jul 2024 20:24:37 UTC No. 16264888

>>16264745
Hello sciencemen, I am stupid feller that would like to get intellectual. I want to understand string theory. My current understanding goes up to doppler effect kek, my math is pathetic but nobody understands math. Is there any hope for me, I am just a simple C programmer. Can you recommend me a book or a resource where I could begin my journey into the unknown realm of bosonic strings moving through a 26-dimensional spacetime?

Anonymous at Tue, 2 Jul 2024 20:44:57 UTC No. 16264908

>>16264888
You could read some popular science books on the topic but realistically that is as far as you are going to get. To truly understand them and where the ideas came from requires you to take post-graduate level physics courses.

Anonymous at Wed, 3 Jul 2024 04:50:55 UTC No. 16265458

>>16264908
I learn everything myself, all the knowledge is out there. Wouldn't you agree it's possible to learn it on my own? I do imagine I would go for a more academic approach should I hit a roadblock. Wouldn't hurt to try it on my own.

Anonymous at Wed, 3 Jul 2024 07:29:36 UTC No. 16265612

>>16265458
As a minimum you would need to teach yourself quantum mechanics, quantum field theory and general relativity - so that includes a hell of a lot of calculus, the calculus of variations / lagrangians, complex analysis, group theory, PDEs, Fourier transformations, path integrals, differential geometry. All that before you can start on String Theory.

Anonymous at Wed, 3 Jul 2024 07:53:10 UTC No. 16265624

>>16265612
Ah yes, the cult of quantum actively proselytizing again.

Read the holy scriptures! Bow down to the gods of materialist-mechanistic interpretations of our measurements; We are the sole arbitrators of truth! Sickening to behold...

https://www.youtube.com/watch?v=5IwgRNS1Frs

Anonymous at Wed, 3 Jul 2024 08:34:23 UTC No. 16265662

>>16265624
are you feeling alright anon? did a scientist touch you in a bad place when you were young?

Anonymous at Wed, 3 Jul 2024 08:36:20 UTC No. 16265668

>>16265612
Seems like a lot of stuff to learn. I will start with quantum mechanics. Thanks anon, this journey will be legendary.

Anonymous at Wed, 3 Jul 2024 08:44:23 UTC No. 16265681

>>16265668
Good luck. I'll tell you now you will fail on your journey. But hey, at least you might enjoy some of it until you give up.

Anonymous at Wed, 3 Jul 2024 14:06:03 UTC No. 16265959

>>16265681
do you understand string theory, if yes, how long did it take anon, quantum mechanics is already filtering me with my calculus, I am learning it right now kek.

Anonymous at Wed, 3 Jul 2024 15:18:54 UTC No. 16266057

Cantor draws diagonal on the set of numbers, adds 1 and says he created a new number that's not on the list.

But if there is an infinite ammount of numbers why wouldn't there be this precise "draw diagonal and add +1" number already on the list?

Anonymous at Wed, 3 Jul 2024 15:36:27 UTC No. 16266088

>>16266057
Just because the list is infinite doesn't mean every possibility is present.

Anonymous at Wed, 3 Jul 2024 15:39:52 UTC No. 16266092

>>16266088
Then infinite monkey theorem is incorrect?

Anonymous at Wed, 3 Jul 2024 15:46:38 UTC No. 16266101

>>16266092
No, the infinite monkey theorem is correct: It doesn't say that they're guaranteed to print Hamlet or whatever, just that they're "almost certain" to.

Anonymous at Wed, 3 Jul 2024 15:58:47 UTC No. 16266120

>>16266101
>In this context, "almost surely" is a mathematical term meaning the event happens with probability 1.

It does say such event will happen. "Sooner or later" would probably be more accurate description.

Anonymous at Wed, 3 Jul 2024 16:02:38 UTC No. 16266129

>>16266120
Probability 1 does not mean it's guaranteed. Neither does probability 0 mean impossible.

Anonymous at Wed, 3 Jul 2024 16:22:20 UTC No. 16266151

>>16266092
The basic diag argument finds one irrational number, whose decimal representation is infinitely long. The infinite monkeys are trying to type up a finite ordered list of letters/punctuation. Every rational number (one integer in the numerator and denominator) can be placed in Cantor's list.

Anonymous at Wed, 3 Jul 2024 17:45:52 UTC No. 16266279

>>16266057
like the other anon said, infinite does not imply all possible values. for example, the set of all even integers is infinite, but it doesnt contain 3.

Anonymous at Wed, 3 Jul 2024 18:04:34 UTC No. 16266313

>>16266279
>infinite does not imply all possible values
I just cannot accept. If there are infinite amount of rooms (all possible natural numbers), you can place infinite amount of guests in it (infinite possible sequences of digits which are of real numbers). There is always ∞+1 room (which is basically ∞) if you'd find another unique sequence.
>>16266151
If we want infinite monkeys with infinite amount of time to write digits of pi for eternity, one would eventually do it too.

Anonymous at Wed, 3 Jul 2024 18:46:34 UTC No. 16266362

>>16266313
>If we want infinite monkeys with infinite amount of time to write digits of pi for eternity, one would eventually do it too.
probability 1 does not imply certainty. thats a little hard to grasp, but the contrapositive is easier to understand: probability zero does not imply impossibility. for example, consider a dart board, where a dart lands on it with a uniform probability distribution, that is, the probability of a dart landing in a given area is proportional to the size of the area. consider a random point on the board. whats the probability of the dart hitting that point? well, points have an area of zero, so the probability of the dart hitting that point is zero. but you could say the same for all other points on the board. if every point has a 0% chance of the dart hitting it, then its impossible to hit the board with the dart. and yet, all you have to do is throw the dart to prove that wrong.

Anonymous at Wed, 3 Jul 2024 20:16:13 UTC No. 16266512

>>16266362
The dart board explanation is very sophisticated because of the premise that the point has an area of zero. One can also ask how many zeros there are in 1. The very question is rigged.

Anonymous at Wed, 3 Jul 2024 20:21:47 UTC No. 16266521

>>16266512
>the premise that the point has an area of zero
do you disagree that the point has an area of zero? do you disagree that there are infinitely many possible points on the board that the dart can hit? do you disagree that subdividing the distance between 0 and 1 infinitely many times, e.g.
[math] \displaystyle
\frac{1}{2}+\frac{1}{2} \\
\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4} \\
\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8} \\
\cdots
[/math]
will result in the divisions having a length (measure) smaller than any number larger than 0? you need to be a bit more specific about what youre hung up on.

Anonymous at Wed, 3 Jul 2024 20:24:09 UTC No. 16266527

>>16264888
Why do you want to get into string theory? As far as I know it's currently on ice - due to lack of verification by experiments. To be brutally honest with you, if you want to have any chance you'll have to build up a groundwork. You can do this alone, but it'll take some time. Concretely, you'll need to at least have a good grasp of calculus and linear algebra. You'll also want to be able to understand the basics of mechanics - otherwise, you'll have to learn it as you go along and that can be really frustrating. This alone is a year of work, if you're serious about it. I recommend "Mathematics for physicists" and Goldstein mechanics. If you have this done, you can comfortably start with quantum mechanics.

Anonymous at Wed, 3 Jul 2024 20:35:53 UTC No. 16266549

>>16265668
learning up to quantum on your own isnt too bad if youre serious.
>algebra (recap if you need it)
>calculus
>multivariate calculus
>ODEs
>PDEs
>mechanics
>electrodynamics
>quantum
you could probably do that in a year without much trouble if you were dedicated enough.

Anonymous at Wed, 3 Jul 2024 20:49:17 UTC No. 16266585

>>16266549
Agreed. Though you did miss linear alg. + eigenvalues + eigenvectors. I think with enough dedication someone could teach themselves QM in a year or two depending on their existing knowledge. GR though is when it gets exponentially harder but QFT... That's a few orders of magnitude more difficult still, at least to get to a level to start on String Theory. I'm not sure if it's possible for someone to self-learn that, not without some kind of assistance.

Anonymous at Wed, 3 Jul 2024 20:56:16 UTC No. 16266604

>>16266521
>do you disagree that the point has an area of zero? do you disagree that there are infinitely many possible points on the board that the dart can hit?
From the prospect of geometry it is true.
>do you disagree that subdividing the distance between 0 and 1 infinitely many times, e.g. will result in the divisions having a length (measure) smaller than any number larger than 0?
Of course it will, and as the series are infinite, they will more and more closely approach zero.

Anonymous at Wed, 3 Jul 2024 20:59:22 UTC No. 16266609

>>16266604
okay, now do you also agree that if [math] a \geq b [/math] and [math] a \leq b [/math] then it must be true that [math] a = b [/math]?

Anonymous at Wed, 3 Jul 2024 21:47:20 UTC No. 16266699

Is it possible to create synthetic diamonds with the impact toughness of carbonado diamonds?

Anonymous at Thu, 4 Jul 2024 03:58:15 UTC No. 16267168

>>16266609
If it's "or" instead of "and", then yes, it must be true.

Anonymous at Thu, 4 Jul 2024 05:38:37 UTC No. 16267257

>>16264888
https://sheafification.com/the-fast-track/

Anonymous at Thu, 4 Jul 2024 06:26:21 UTC No. 16267304

>>16267257
Every book but one is a meme. Nice work.

Anonymous at Thu, 4 Jul 2024 07:25:20 UTC No. 16267350

Okay, guys, how do i integrate the centrifugal force in a disc?

It's not a homework question but i can't help but think it would be.

Anonymous at Thu, 4 Jul 2024 07:51:11 UTC No. 16267368

>>16267350
Integrate over what? More info needed

Anonymous at Thu, 4 Jul 2024 09:39:27 UTC No. 16267418

Why does most of academia and the chemistry industry use a boring table to represent the catalog of elements?

Anonymous at Thu, 4 Jul 2024 10:54:09 UTC No. 16267461

I want to try to convert between one paper's figures for heterozygosity from a gene survey and another papers estimates of autozygosity (identical by descent) through relatedness from another paper in such a way that will allow me to see if the performance peak range of the two papers is in the same approximate effective range but my maths ability is too lacking to see how to do it myself

The figures from the first paper are peaking around 4.5 heterozygous pairs per 1000 while the relatedness autozygous estimates from the other paper correlate with a peak between about 1% and 0.1%
they seem nominally to be in a comparable range but I can't figure out how to actually assess how close they match

any suggestions?

Anonymous at Thu, 4 Jul 2024 17:41:40 UTC No. 16267838

Physics question.
When a car is making a scraping sound ONLY when turning left and it is known that it is the dust shield rubbing on the rotor, is that because of the centripetal force? My assumption is the rotor is rigid and the dust shield is a thin soft plate. So when the car is turning left, the shield bends towards the rotor. What I am not sure about is if it is moving towards the inside of the turning curve due to inertia or it is exactly the opposite. The centrifugal force perhaps?

Anonymous at Thu, 4 Jul 2024 19:18:07 UTC No. 16267955

>>16267350
I'm going to assume that the disk is "flat" meaning that the expansion of the disk in the [math]z[/math] direction can be neglected. The symbol [math]\mu[/math] denotes the homogeneous density of the object.

In this case, [eqn]F_{C} = 2\mu\, \mathbf{\omega} \times \dot{r} = 2\mu\, \omega\, \dot r = 2\mu \omega^2\, r,[/eqn]because the axis of rotation and the "tangential" velocity for the points on the disk are always orthogonal. Now I would go ahead and integrate [eqn]\int_0^R \int_0^{2\pi} dr\, d\varphi\, F_C(r) = 2\, \omega^2 \int_0^R \int_0^{2\pi} dr\, d\varphi\, \mu\, r = 2\, \omega^2 M.[/eqn]

No idea, if actually correct.

Anonymous at Thu, 4 Jul 2024 21:06:31 UTC No. 16268088

[math]\lim z->\infty\frac{(1-iz)^2}{(1-iz^2)}=-i[/math] how? I tried changing z to 1/z where z approaches 0 and I'm getting -1. How?

Anonymous at Thu, 4 Jul 2024 21:17:16 UTC No. 16268097

>>16268088
[math](1-iz)^2=-z^2-2iz+1[/math]
[math]\frac{-z^2-2iz+1}{1-iz^2} = \frac{-z^2}{1-iz^2} + \frac{-2iz}{1-iz^2} + \frac{1}{1-iz^2}[/math]
not going to bother demonstrating it rigorously but the last two terms obviously go to 0 as z goes to infinity since their denominator is a polynomial of a higher degree than their numerator
and the first one asymptotically approaches [math]\frac{-z^2}{-iz^2}=\frac{1}{i}=-i[/math]
are you by chance trying to square the [math]i[/math] in the denominator, too? not just the [math]z[/math]? because that does get you -1

Anonymous at Thu, 4 Jul 2024 21:39:17 UTC No. 16268120

>>16268088
[eqn]\lim_{z \to \infty} \frac{\left(1 - iz\right)^{2}}{1 - iz^{2}} = \lim_{z \to \infty} \frac{\left(1 - iz\right)^{2}\left(1 + iz^{2}\right)}{1 + z^{2}} = \lim_{z \to \infty} \frac{-iz^{4} + iA + B}{1 + z^{4}} = -i \lim_{z \to \infty} \frac{1}{\frac{1}{z^{4}} + 1} = -i[/eqn]Both [math]A[/math] and [math]B[/math] are real polynomials in [math]\mathbb{R}[x][/math] of order [math]\mathcal{O}(x^3)[/math]. Both of them go to zero as the limit approaches infinity.

Anonymous at Fri, 5 Jul 2024 09:28:12 UTC No. 16268744

Mathematical and physical prerequisites for reading this? Will I die if I haven’t read a book on the standard wave mechanics approach beforehand?

Anonymous at Fri, 5 Jul 2024 10:07:28 UTC No. 16268775

>>16268744
What do you mean by 'standard wave mechanics approach' ?

Anonymous at Fri, 5 Jul 2024 10:57:35 UTC No. 16268803

>>16266057
Cantors proof is a proof by contradiction. We assume that the real numbers can be listed out in sequential order (meaning we can put them in one-to-one correspondence with the natural numbers, i.e. we can assign to each real number a number from the list 1,2,3,4,5…), and then find that any time we try to actually construct such a sequence we can find a real number that is not on the list. Even if you tacked the number constructed by the diagonal argument on to the list, you could still find another real number that isn’t on this new list, and so on ad infinitum. Since the assumption that it is possible to list ALL real numbers in a sequence leads us to a contradiction, we conclude that the assumption must be false. You can never construct such a list.

“ But if there is an infinite ammount of numbers why wouldn't there be this precise "draw diagonal and add +1" number already on the list?”

That’s the point, it SHOULD be on the list, because we assumed that the list contains all reals numbers. But because we can construct a number that clearly does not belong to the list, our starting assumption that our list contained all real numbers must be wrong.

Anonymous at Fri, 5 Jul 2024 11:06:51 UTC No. 16268809

>>16268803
Cont.
But you seem to have interpreted “infinite” as meaning “all encompassing”, when really all it means is “not finite”, i.e. unending. Let’s say that the hotel guests are autistic, and refuse to sleep in odd numbered rooms. You would still never run out of rooms, because the list 2,4,6,8,10… never ends - it is infinite. But the guest list would not include any guests in odd numbered rooms; even though there infinitely many guests, these guests do not take on EVERY possibility.

The point of cantor’s result is that there are different kinds of infinity, in the sense that 2,4,6,8,10… is the same kind of infinity as 1,2,3,4,5…, because we can make the association:
1 2 3 4 5…
2 4 6 8 10…

That is to say, if the hotel owner got sick of having so many empty, odd-numbered rooms, he could simply relabel the room numbered “n” with “2n”.

And if some even more autistic guests came along, each of which having a rational number tattooed to their forehead, and these guests asked to stay in the forehead number room, he could then relabel the rooms by drawing a spiral through an infinite rectangular grid.

But if a group of supremely autistic /sci/ posters came along, and each declared “I want a room that has a number in which the digit in the nth decimal place is different to the digit in the nth decimal place of the room which your nth guest is staying in“ he’d have to build some more fucken rooms. Uncountably many, that is. And he would not be able to list out the rooms in an order like 1,2,3,4,5… - he would instead have to assign the rooms a point on a line. So, real numbers are a different kind of infinity to natural numbers.

But if you really believe that it is possible to define a list of the real numbers in a sequence assigning each real number a natural number - go ahead, try to do so. But you will not be able to - because Cantor can always find a real number that is not on your list, no matter how you try.

Anonymous at Fri, 5 Jul 2024 12:45:59 UTC No. 16268894

>>16268809
Let w be a numbering system of radix 1.
A series of hash marks.
Now his argument fall apart.

Anonymous at Fri, 5 Jul 2024 13:16:02 UTC No. 16268930

>>16268894
It really doesn't.
You could twist things a bit to represent rational numbers (it'd look incredibly stupid, but it would at least be possible), but there's no way to construct a unary expansion of any irrational number.

Anonymous at Fri, 5 Jul 2024 15:06:27 UTC No. 16269017

>>16268930
We shall use Q10 as a representation of the unary counting system w. - = 1, -- = 2, --- = 3, etc
Now rationals can be described exactly as they are elsewhere, but they anchor to w. We don't have to have a burdensome notation like -------------, etc. And when logical contradictions arise, we can reduce them back to w to test their veracity.
So a change in a digit is translated to an addition or subtraction at some magnitude to the quotient Just for example. 0.33. . . . = 1 / 3
And suppose we are changing it. 0.34333... = 1/3 + 1/100
Each translates directly into hash mark arithmetic, which is captured in Q10 as 103/300.
There is no trickery here.
As for the claim about irrational numbers, the expression sqrt(---) is sufficient description.
You could do some Q-string expansion, but what is the point? You are only losing precision at the cut off.

Anonymous at Fri, 5 Jul 2024 15:21:17 UTC No. 16269027

>>16269017
>the expression sqrt(---) is sufficient description.
No, it definitely isn't. Not for the vast majority of irrationals, and certainly not for a diagonal argument.
Display [math]\sqrt{2}=1.414213...[/math] in a unary expansion, as a sum of integer multiples of powers of 1. Then we can talk about application of the diagonal argument to such a representation.

Anonymous at Fri, 5 Jul 2024 15:26:03 UTC No. 16269034

>>16269027
To be clear, you first have to fully define your expansion, which you haven't done. But up to your specified degree.

1 + 4/10 + 1/100 + 4/1000 + 2/10000 + 1/100000 + 3/1000000
- + ----/---------- + - / ----------^-- + ---- / ---------- ^ --- + -- / ---------- ^ ---- + - / ----------^----- + --- / ---------- ^ ------

Anonymous at Fri, 5 Jul 2024 15:32:32 UTC No. 16269041

>>16269034
>But up to your specified degree.
There is no specified degree. It's an irrational number. You're not just "losing precision", you're conflating uncountably many numbers together into one. The whole point of the diagonal argument is that you can't construct any of these; you don't just get to write them off as "precision errors".
Might as well as claim that there are only 10 integers, because you can classify them by their final digit in decimal, and you're only "losing precision" at the cut-off of any position beyond the order of [math]10^0[/math]

Anonymous at Fri, 5 Jul 2024 15:33:25 UTC No. 16269044

>>16269041
I take it that you can't list a number that can't be described by w.

Anonymous at Fri, 5 Jul 2024 16:15:45 UTC No. 16269104

Is atmospheric pressure bigger underground than on the ground? Like in the deep metro station.

Anonymous at Fri, 5 Jul 2024 20:25:50 UTC No. 16269431

>>16269104
According to
https://www.saimm.co.za/Journal/v105n06p387.pdf

>The total increase in barometric pressure while
descending from surface to a mining depth of
5 000 m would be approximately 0.55 ATA

raspberry pie at Fri, 5 Jul 2024 20:34:35 UTC No. 16269453

>>16268809
>even though there infinitely many guests
*there are infinity guests
Saying 'infinitely many' is a bloated and cluttered way of just saying what we already have a word for: Infinity. Anyone that ever uses the phrase 'infinitely many' is a turbo autist.

raspberry pie at Fri, 5 Jul 2024 20:38:52 UTC No. 16269465

>>16266129
retard
>>16266092
No, its just proof that .9... is not equal to 1

Anonymous at Fri, 5 Jul 2024 23:19:01 UTC No. 16269670

>>16264745
Could anyone prove part b? I think it involves repeated application of Rolle's theorem, but I can't see how.

Anonymous at Sat, 6 Jul 2024 00:04:30 UTC No. 16269709

>>16269670
Would it just be induction of the previous proof?

Anonymous at Sat, 6 Jul 2024 00:27:09 UTC No. 16269724

>>16269709
How would I apply induction though, as there are n+1 points each with different multiplicity k_i + 1.

Anonymous at Sat, 6 Jul 2024 02:22:06 UTC No. 16269830

>>16269453
Some might say that nitpicking about such things is is a sign of turbo autism.

raspberry pie at Sat, 6 Jul 2024 02:32:06 UTC No. 16269841

>>16269830
Some might yes but those some are turbo autists

Anonymous at Sat, 6 Jul 2024 03:13:00 UTC No. 16269892

>>16269044
It literally does not matter what numbering system you use. The point is that it is impossible to define a bijection between the real numbers and natural numbers. This property is completely independent of how you label the elements of each set. Cantor doesn’t even need to work in your ridiculously clumsy numbering system to find a missing number - if you can list out the real numbers in sequence with your system, he could then convert each number from your representation to its decimal representation to find an identical list of numbers and then apply the diagonal argument to that list. If a number is missing from one list, it is also missing from the other (if you dispute that we’ll have to change the diagnosis from mild to profound mental retardation).

>>16269017
Most irrationals are not expressible as square roots. The algebraic numbers (roots of polynomials over the rationals) are countable, it’s the transcendental numbers that make the reals as a whole uncountable.

>>16269034
This is just a decimal representation where you labeled the digits with dashes. You are using powers of ten, not powers of one. I really have no idea why you think using some obscure way to label numbers is going to help you.

>>16269044
Again, it is NOT ABOUT HOW YOU REPRESENT THE NUMBERS, it is about whether or not you can make a bijection/one-to-one correspondence between the real numbers and the natural numbers. It does not matter if your system can describe every real number, because you still cannot assign to each real number a unique natural number. If you think you can, describe a way to do so.

Can you even describe, in your own words, what cantor’s argument is actually saying?

Anonymous at Sat, 6 Jul 2024 03:15:53 UTC No. 16269899

>>16269841
I know you are but what am I

raspberry pie at Sat, 6 Jul 2024 04:41:37 UTC No. 16269962

>>16269899
please learn english before attempting to converse with me, because english is the only language I know, thank you

Anonymous at Sat, 6 Jul 2024 07:28:37 UTC No. 16270055

Bump >>16269670

Anonymous at Sat, 6 Jul 2024 08:28:56 UTC No. 16270073

>>16264745
[math]f[/math] vanishes with multiplicity [math]k_i + 1[/math] at [math]a_i[/math] for [math]i = 0, \dots, n[/math] and [math]a_0 < a_1 < \dots < a_n[/math], i.e. [math]f(a_i) = f'(a_i) = \dots = f^{(k)}(a_i) = 0[/math]. [math]f[/math] is [math]N = n + \sum_{i = 0}^{n} k_i[/math] times differentiable.

How do I prove the following:

Show that there exists [math]c \in (a_0, a_n)[/math] such that [math]f^{(N)}(c) = 0[/math].

Anonymous at Sat, 6 Jul 2024 10:02:14 UTC No. 16270127

>>16267304
Post your list

Anonymous at Sat, 6 Jul 2024 10:03:15 UTC No. 16270128

>>16266527
why even reply if you know fuck all about physics let alone string theory?

Anonymous at Sat, 6 Jul 2024 10:07:58 UTC No. 16270132

>>16264888
http://pastebin.com/sy2MbenC
clueless retards love to say it's a meme but it's actually very solid for gaining a deep understanding of the math behind string theory

Anonymous at Sat, 6 Jul 2024 10:52:30 UTC No. 16270155

>>16270132
The original website for this content seems to have been this guy's website (it is in Russian though):
http://imperium.lenin.ru/~verbit/MATH/programma.html

Anonymous at Sat, 6 Jul 2024 12:03:19 UTC No. 16270210

>>16269962
Sorry, I only speak American, not some gay limey language

Anonymous at Sat, 6 Jul 2024 12:21:16 UTC No. 16270225

>>16269892
Incorrect. Cantor's diagonalization argument rests squarely upon string representations abstraction boundary perversion. The reduction of a natural counting system is impervious to his manipulation. The ability to translate w into any integer based system is a feature, not a flaw.
Again, the burden is on you to show how you can diagonalize the following series:
-
--
---
----
-----
. . .
It is very clear here that Cantor has tricked everyone into thinking adding 1 an infinite number of times somehow generates a new infinity.
Additionally, the group w{n} presentation generalizes to the decimal version, with a parallel conclusion: adding k•10^n k,n varying an infinite times somehow generates new numbers. This is also absurd.

Anonymous at Sat, 6 Jul 2024 15:18:25 UTC No. 16270377

>>16270225
You're doing it backwards, let me explain.

A diagonal argument begins with a fixed set [math]A[/math]. From [math]A[/math], we construct a _countable_ subset [math]B[/math] of [math]A[/math]. By applying a diagonal argument (if possible, it's not always the case), we can construct an element of [math]A[/math] that is not in [math]B[/math].

What you're doing is defining a set [math]B[/math] using the 'unary counting system w.' Then, you claim that [math]A = B[/math], where [math]A[/math] is 'the set of numbers,' which I don't know what that is, but I guess that you mean that [math]B = \mathbb{R}[/math], the set of real numbers. In that case, it is not possible to construct an element of [math]B[/math] not in [math]A[/math], because these two sets are equal by your definition. For this reason, you would be correct that it is not possible to apply the diagonal argument here.

The issue is simple: you haven't shown anywhere that the set [math]B[/math] spanned by the 'unary counting system w' is the set of the real numbers, in particular, the burden is on you to show that [math]B[/math] is an ordered field with the least upper bound property. Otherwise, this discussion won't go anywhere.

Anonymous at Sat, 6 Jul 2024 15:24:23 UTC No. 16270382

>>16270377
(cont.)
In any case, if you really believe that there are no countable sets, I have a challenge for you.

Consider the set [math]F = \{f \, | \, f : \mathbb{N} \to \mathbb{N}\}[/math] the set of functions from the natural numbers to itself. Can you enumerate every element of [math]F[/math]?

Anonymous at Sat, 6 Jul 2024 15:24:24 UTC No. 16270383

>>16270377
You may as well stop posting. He will not accept being wrong and nothing will change his mind.

Anonymous at Sat, 6 Jul 2024 18:15:12 UTC No. 16270550

Two questions:

1. What's it called when you "rotate" a function in the xy-plane? Like say I wanted to rotate pic related CCW by 45 degrees

2. Have rotated triangle waves ever been used to analytically compute quantization stuff? Like how picrel, rotated by -45 degrees, is basically an x=y function quantized as some function of the frequency

Anonymous at Sat, 6 Jul 2024 18:57:17 UTC No. 16270589

>>16270377
Every real string can be represented in w, but we just don't merely forget w and start manipulating strings to see how we can break abstraction. As for construction of R, as rationals + irrationals, we can generate some basic phrases to get back to the string representation.
w{10} notation:
3.14. . . [string]
--- + -/---------- + ----/----------^-- [w]
--- . - , ---- , . . . [w{10}]
3. 1, 4, . . . [Qw10]
3.14. . . [string]
This demonstrates the idea of groupings, where w{10} is grouping our marks in groups of 0-9. Of course, w{n} can be grouped into any integer base. I am currently uncertain of non-integer bases.
So just translate every argument over R into the w formulation. This is simple because constructing n by diagonalization is just S + s, s is different magnitudes such that it is different from the real at that rank, and S is just the ongoing sum of s.
[math]
S = \sum s_r
[/math]
There are obviously no n that are of a form outside of w which maps to R.

It necessarily follows that any proof resting on Cantor's diagonalization is void. If the proposed problem uses Cantor's arguments to be uncountable, then it requires still some other argumentation to validate it. This does not forbid uncountability, but just forbids Cantor's abstraction breaking.
It should also be noted that we don't even need R to generate uncountable sets by Cantor's logic. You can start with just a list of all natural numbers and generate a number that is not on that list by the same diagonalization fraud. It is the result of the digit span squaring up with string span at infinity - everywhere else, you land at just another N. This is abstraction breaking.
I was thinking p-adic fuckers got it, but they go resting on Cantor's claim anyways.

retarded 13 year old at Sat, 6 Jul 2024 20:05:06 UTC No. 16270672

To rotate a graph on the xy plane use a rotation matrix. namely, to rotate a graph by theta degrees counterclockwise, replace x and y with xcos(theta)+ysin(theta) and -xsin(theta)+ycos(theta) respectively

Anonymous at Sat, 6 Jul 2024 21:32:54 UTC No. 16270772

>>16268809
>Let’s say that the hotel guests are autistic
oh, hadn't heard that take before
>>16270589
>diagonalization fraud
oh, you do know the diagonal argument is used in turing's proof of the halting problem?, are you asserting that the machine that "can determine if a given program halt" exists?
https://www.youtube.com/watch?v=7N3iKB0OnOs
https://www.youtube.com/watch?v=dwNxVpbEVcc
also, do you know that dedekind cuts are sequences of rational numbers, and given that they are a construction of the real numbers, that says that the sequences of rationals(with the proper restrictions to be dedekind cuts, although given that in he case of the rationals themselves and their numerability with N, it is very similar in the sense that both the full n/m combination grid and the reduced fractions have the same cardinality, and so given that the dedekind cuts have the cardinality of the reals, it is easy to see that the full unrestricted set of rational sequences also has the cardinality of the reals) are also of the cardinality of the reals?, and the very funny think is that we can have unary https://en.wikipedia.org/wiki/Bijective_numeration , but given its nature it cant represent the rationals positionally, but it is very clear that we can simply write the rationals only using the / such:
11/111=2/3
this then gives us access to the rationals using unary, from which we can then build dedekind cuts, which as you know has the cardinality of the reals
i must say, you finitist are really funny, you really are the flat earthers of mathematics
>pdf
oh, the p-adics(and obviouly the n-adics) are diagonalizatable as well, and obviouly have the same cardinality as the reals, boy you are funny

Anonymous at Sat, 6 Jul 2024 21:44:36 UTC No. 16270785

>>16270225
You still do not understand what cantors argument is saying. Do you understand what a one-to-one correspondence/bijection is. Can you define what countability means.

“Again, the burden is on you to show how you can diagonalize the following series:”

Jesus Fucking Christ you are stupid lmao. There is no need to apply the diagonal argument here because that sequence obviously does not go through every real number. It literally just counts 1,2,3,4,5…

You need to give a function from the reals to the naturals that specifies a unique natural number for each real number, or a function from the naturals to the reals that goes through every possible value.

“The ability to translate w into any integer based system is a feature, not a flaw.”
Yes, that is a feature which can be exploited when you try to write down a sequence of real numbers in your system that includes every real number. Simply convert the sequence to its decimal representation and diagonalize that sequence instead. This will find a number that exists in both number systems, but is not in either sequence.

String representations of numbers are not needed. You can construct an uncountable set out of a countable infinite set just by considering its power set, because it is impossible to create a bijection between a set and its power set. This alone is enough to prove that there are different kinds of infinity.

“It is very clear here that Cantor has tricked everyone into thinking adding 1 an infinite number of times somehow generates a new infinity.“

No you moron, the “new infinity” was already “generated” when the real numbers were constructed, the diagonal argument simply demonstrates that this infinity is different from the infinity of the naturals. It does not “generate new numbers”, it just shows that any SEQUENCE of real numbers cannot possibly contain all real numbers, i.e. it is impossible to construct a bijection between the reals an the naturals.

Anonymous at Sat, 6 Jul 2024 21:48:59 UTC No. 16270793

>>16270383
Arguing with stupid people is fun, it’s more challenging than arguing with smart people.

Anonymous at Sun, 7 Jul 2024 10:36:19 UTC No. 16271342

>>16270772
The refutation of a premise of an argument does not mean that a conclusion is false. It just means that it is unsupported by the premise. The conclusion could be true, but has gone unproven due to error. In this case, diagonalization substitutes fantastical thinking about abstractions, not backed by anything stated by the basic mathematics. Anyways, you let me know when you find a number that isn't a natural number, but is some whole number distance away from one.
>>16270785
Sure, if you have a proof of uncountability not following Cantor's flawed reasoning, I am sure Turing would like to know it to apparently support his position on the halting problem. Though, unlike what the previous poster said, I thought the proof involved finding a pathological case where a halting machine couldn't exist.

Anonymous at Sun, 7 Jul 2024 10:44:08 UTC No. 16271346

>>16270550
>1
there's no way to guarantee that a rotated graph is still the graph of a function
>2
what?

Anonymous at Sun, 7 Jul 2024 11:27:41 UTC No. 16271377

>>16270589
Do you agree that there can be no surjective function from [math]\mathbb N[/math] to [math]2^{\mathbb N}[/math]?

Anonymous at Sun, 7 Jul 2024 12:19:56 UTC No. 16271403

Will this stupid barren old hag ever stop blabbering on about muh ebul climate change?

No wonder she didn't make it in academia lmao

Anonymous at Sun, 7 Jul 2024 12:39:06 UTC No. 16271421

Would printing a math textbook using a pdf with something like lulu.com be a good idea?
Could some of the writing get fucked and other issues like that?
It would end up being cheaper and less time consuming than looking for used textbooks, I've already spent a lot, in retrospect, not that I regret it but I'd rather save some money now.
(I know I can just pirate but I can't study math in front of a pc)

Anonymous at Sun, 7 Jul 2024 13:10:19 UTC No. 16271448

>>16271421
I've had math textbooks printed at a print shop before and they came out fine
Imo I'd get it printed without binding and just put it into a ring binder, then you can also insert your notes directly into the binder

Anonymous at Sun, 7 Jul 2024 14:10:34 UTC No. 16271492

>>16271421
I've done this a few times, not with textbooks, but lecture note sets. If you are going to do it, make sure to find a PDF that looks like it was compiled fresh from the source, and not stitched together from 300 shoddy scans.

I printed at my uni, and used their tools to bind it with those plastic ring binder spine things - beware that they only fit like 50 pages tops though. Though I think that it's a better idea (like the other guy said) to just insert the pages in a regular binder, so you can interleave with your own notes etc.

Anonymous at Sun, 7 Jul 2024 15:30:02 UTC No. 16271555

f is a polynomial. This is not norm on the vector space of polynomials, right? Because it's not multiplicative in the way a norm is supposed to be.

Anonymous at Sun, 7 Jul 2024 16:55:38 UTC No. 16271631

>>16271346
>>what?
A stairstep function is basically just a quantized version of the identity function, y=x. If you multiply any smooth continuous function by a stairstep function, wouldn't that essentially quantize it?

Anonymous at Sun, 7 Jul 2024 17:10:32 UTC No. 16271642

>>16271448
>>16271492
I found a local option that's very cheap and I'll be using a binder like you suggested, that's a great idea. Thanks anons.

Anonymous at Sun, 7 Jul 2024 17:19:18 UTC No. 16271649

>>16271555
yes

Anonymous at Sun, 7 Jul 2024 17:38:22 UTC No. 16271674

>>16266057
It differs from every number on the list at every digit

Anonymous at Sun, 7 Jul 2024 18:40:09 UTC No. 16271769

if the speed of light was faster, would the relative distances of universes/all material in the universe be in a similar relative distance from each other (using the speed of light as your normalizing distance, for example)
I.e., it sucks the speed of light is so "slow" for transmission and trying to view other stuff in the galaxy but let's say the limit was higher, would everything after the big bang just have expanded further out in proportion to this faster speed of light difference and we'd be at square one anyways or am I retarded?

fuck reach at Sun, 7 Jul 2024 18:54:39 UTC No. 16271790

>>16271769
You are retarded for believing in the big bang

raspberry pie at Sun, 7 Jul 2024 18:58:05 UTC No. 16271793

>>16270210
Thank you for admitting to being retarded

Anonymous at Sun, 7 Jul 2024 19:00:02 UTC No. 16271797

Does there exist a space-filling rhombic disphenoid?

Anonymous at Sun, 7 Jul 2024 19:21:39 UTC No. 16271812

>>16264745
not really if someone here can answer this but in a house, does an open floor keep air cooler/warmer more efficiently than traditional floor plans?

i feel like since there is more space for air to occupy the hvac system has to work harder

Anonymous at Sun, 7 Jul 2024 19:51:46 UTC No. 16271844

>>16271769
It would not be that simple and it's hard to say precisely what would happen and depends on how much you vary 'c'.

Our universe exists in its present state because of a complex interaction between all the fundamental constants. The speed of light does not just affect space and distance, it appears in multiple equations. For example: [math]E=mc^2[/math] and [math]E = hc / \lambda[/math], the amount of energy in rest mass or a photon would be altered, the frequency + wavelength for a given energy would be not be the same as we know. The fine structure constant [math]\alpha = \dfrac{e^2}{4\pi\epsilon_0\hbar c}[/math] would have a different value affecting all of nuclear physics. Fusion may no longer be possible, stars might not be able to form. In the extreme case atoms might no longer even exist. If the speed of light was fast enough it could still be greater than the expansion rate of the universe, space and the night sky would no longer be black, but entirely filled with the light from every star in the universe that has no longer been red-shifted enough.

Anonymous at Sun, 7 Jul 2024 21:50:00 UTC No. 16272009

>>16271793
Thank you for putting your autism on full display

Anonymous at Sun, 7 Jul 2024 22:02:40 UTC No. 16272031

>>16271844
These are all good points. ty fren.

Anonymous at Sun, 7 Jul 2024 22:11:56 UTC No. 16272052

>>16271377
Sure.

Anonymous at Mon, 8 Jul 2024 01:25:51 UTC No. 16272297

>>16264745
Does the magnetic permeability drop to 1 after ferromagnetic saturation. Why no textbook mentions what happens to it after saturation? All they say that it drops abruptly but does it drop to one such that the material effectively becomes air? If yes how can you prove this?

raspberry pie at Mon, 8 Jul 2024 01:43:57 UTC No. 16272310

>>16272009
Autism? At least I am not a retard like (You)

Anonymous at Mon, 8 Jul 2024 02:07:39 UTC No. 16272339

>>16272297
Magnetic domain theory is the current explanation. At one level, the domains are coming under alignment but the next layer are aligning atomic/molecular geometries.
The permeability goes to 1 because after saturation the excess is going through air instead of the core. This would be leakage.
Steinmetz discusses saturation and various impacts on circuit behaviors. Page 43, 125.
https://archive.org/details/in.ernet.dli.2015.162619/page/n5/mode/2up

Anonymous at Mon, 8 Jul 2024 05:16:49 UTC No. 16272488

Say an especially lazy and unmotivated person was preparing for the upcoming all-star tournament of a game show in about 6-8 months. Besides just studying and playing a lot of practice games, how else could they improve their chances and be less tired and have better reflexes?

Anonymous at Mon, 8 Jul 2024 07:30:30 UTC No. 16272560

>Given four numbers, combine the numbers using + - * / in such a way that you get fifth number
What's the quick strategy to solve these? Do I just have to write a solver?

Anonymous at Mon, 8 Jul 2024 07:47:19 UTC No. 16272565

>>16272560
The 'quick' way would depend on the fifth number. You could remove a lot of the possible options depending if it is odd or even, it's last digit, what factors does it have, is it a square number, and so on. But yeah, the simplest and most general method would be to just iterate all the combinations.

Anonymous at Mon, 8 Jul 2024 08:13:09 UTC No. 16272585

Why is a quarter of the board missing, what got spammed?

Anonymous at Mon, 8 Jul 2024 08:14:11 UTC No. 16272587

>>16272488
run sprints

Anonymous at Mon, 8 Jul 2024 14:07:18 UTC No. 16272810

math/cs/stats folks itt, I'm sort of an average joe, midwit, autodidact ig and I wish to learn analysis and discrete math, but I only know pre calc algebra. I've got some questions regarding this.
For calculus and analysis:
>Should I just complete calc1,2,3 b4 doing analysis or can I go straight ahead?
>What are the best texts from a theory & problem solving perspective for learning calc 1,2,3 and analysis? I did search a little bit and found baby rudin and apostol being recommended. I was also able to find some not so often recommended texts like Courant's calculus, or Keisler's elementary calculus. What do?
>Any good place for finding problem sets & lecture notes that may really help in improving my grasp of applications based calculus and analysis? What about books like schaum series, as in do they have a nice variety of problems? How about previous year GRE papers, putnam, etc.?
For discrete math:
>Again, what books do I use from theory & problem solving perspective? CL Liu? Kenneth Rosen? Don knuth's concrete math? something else?
>where do I find good problem sets & lecture notes that are really useful and again, is schaum's series, previous year GRE papers useful?
>Do I have to spent incredible amounts of time trying to study topics like combinatorics & number theory independently if my aim is to do machine learning?

Anonymous at Mon, 8 Jul 2024 15:02:27 UTC No. 16272848

>>16272585
The usual. It's just jannies doing their job.

Anonymous at Mon, 8 Jul 2024 15:04:06 UTC No. 16272849

>>16272848
so the jannies spam the board then remove it to give themselves something to do?

Anonymous at Mon, 8 Jul 2024 15:29:07 UTC No. 16272867

>>16272810
>Should I just complete calc1,2,3 b4 doing analysis or can I go straight ahead?
You should do at least calc 1 (derivatives and integrals in 1 variable) before analysis otherwise doesn't matter
>GRE subject papers, putnam
Overkill if you want to do ML, only top math majors prepare for these
>Do I have to spent incredible amounts of time trying to study topics like combinatorics & number theory
Absolutely not, for ML these are not needed
>Best texts
Imo choice of textbook doesn't matter that much, just follow a syllabus from a reputable university
>Problem sets & lecture notes
google search for .edu domains

Anonymous at Tue, 9 Jul 2024 01:44:06 UTC No. 16273571

>>16271342
Once again you ignore all the points that expose the flaws in your argument, and you still haven’t shown that you even understand the basic mathematical concepts involved.

“proof of uncountability”
I’ll spell it out with as much handholding as possible. Consider the power set P(N) which consists of all subsets of N, where N is the set of natural numbers. Now suppose that we can put P(N) is countable, i.e. there exists a bijective function f that maps numbers from N to P(N). Consider the subset A of N such that n ∈ N if and only if n ∉ f(n). Since f is a bijective function, there must be some a ∈ N such that f(a) = A. One of a ∈ f(a) or a ∉ f(a) must be true. If a ∈ f(a), then a ∈ A since A = f(a) which implies a ∉ f(a) by the definition of A, which is a contradiction. If a ∉ f(a), then by the definition of A we have a ∈ A. But since A = f(a), we have a ∈ f(a), which is a contradiction. To summarise, supposing the existence of a bijective function f : N -> P(N) leads us to a contradictory conclusion, so no such function may exist. Hence P(N) is uncountable, so uncountable sets exist. P(N) can easily be shown to have the same cardinal it as the reals.

“not following Cantor's flawed reasoning”
Your definition of flawed reasoning is any reasoning that you are incapable of understanding. Cantor’s reasoning is not flawed and you have not demonstrated any flaws in his reasoning.

“fantastical thinking about abstractions“
All mathematics is based on abstraction. Even the idea of numbers themselves is an abstraction. If you are incapable of thinking about abstractions, mathematics is not for you.

“Anyways, you let me know when you find a number that isn't a natural number, but is some whole number distance away from one.”
The fuck are you even on about, this has nothing to do with the uncountability of the reals

Anonymous at Tue, 9 Jul 2024 05:16:08 UTC No. 16273737

Am I retarded if I can't multitask? For example, my friend plays video games while listening to podcasts or history videos. I can't imagine doing this regularly, because I've tried to do something similar and I never get much out of either when they're both prying for my attention. Is this a problem? Obviously video games and podcasts are not important, but it feels like a lot of the recreational AND professional world has put such a high emphasis on multitasking these days, or at least that's what it feels like. I just like doing one thing at a time with 100% focus. I don't even want to listen to music when I read.

Anonymous at Tue, 9 Jul 2024 05:19:54 UTC No. 16273740

>>16273737
>Am I retarded
Didn't read your post but yes you are

Anonymous at Tue, 9 Jul 2024 05:21:13 UTC No. 16273741

>>16272810
I quite like Calculus - Infinitesimal Approach by Keisler. Occasionally it was unclear at which point I cross referenced Apostol's Calculus volumes 1-2

Anonymous at Tue, 9 Jul 2024 05:22:51 UTC No. 16273745

>>16273737
Chances are the multitaskers are just half assing both. So probably they are the retarded ones. Save the rare person who actually is hyperintelligent

Anonymous at Tue, 9 Jul 2024 12:48:56 UTC No. 16274066

What could cause a dead animal to not stink? For months I’ve been finding dead animals that don’t stink. Two days ago I found a seemingly intact dead bluejay, I checked on it this morning and despite being out in a 100+ Fahrenheit heatwave for two days I couldn’t smell it at all. I can smell plenty of other things so I don’t think I’m noseblind.

Anonymous at Tue, 9 Jul 2024 12:51:55 UTC No. 16274069

>>16273571
Your argument has nothing to do with diagonalization. Very strange. And your defense of cantor is meaningless and does not follow from it. There is nothing wrong with abstraction, except when applying it invalidly. As an example, when separating decimal representations from those abstractions which underlie their construction. You apparently have no problem with there being integers greater than 0 that aren't naturals, just like you think there are some some reals that are like reals in every other way, except they only exist at infinity. As I would expect form someone completely avoiding the problem.

Anonymous at Tue, 9 Jul 2024 20:14:36 UTC No. 16274922

It is commonly said that, in a vacuum, objects of different mass fall at the same speed, and I've seen a video where this was shown with a bowling ball and a feather. But if gravity attracts heavier objects harder, shouldn't the bowling ball still fall slightly faster?

Anonymous at Tue, 9 Jul 2024 20:24:32 UTC No. 16274943

>>16274922
>But if gravity attracts heavier objects harder, shouldn't the bowling ball still fall slightly faster?
No.
[math]F=ma[/math], so while the force of the gravity acting on the bowling ball will be stronger, it has nothing to do with a difference the acceleration (and thus rate of descent). That's independent of the mass.

Anonymous at Tue, 9 Jul 2024 20:25:02 UTC No. 16274945

Here's some recreational math

A semi-circle is inside of a quarter circle like in picrelated. The semi-circle touches the edge of the quarter circle in three points.

Prove that the intersection point between the vertical line (drawn through the bottom vertex of the semi-circle) and the arc of the quarter circle is the same as the intersection point between the arcs of the semi and quarter circles.

Anonymous at Tue, 9 Jul 2024 20:29:33 UTC No. 16274950

>>16274922
They fall at the same speed, but the more massive object falls with more force - you understand this intuitively, even if you aren't aware of it.
Imagine someone dropping a 20kg metal ball and a 20g styrofoam ball from high up in a tall vacuum chamber.
If the styrofoam ball lands on your head, you'll barely feel it. If the metal ball lands on your head, you'll never feel anything again.

Anonymous at Tue, 9 Jul 2024 20:32:55 UTC No. 16274955

>>16274066
>I checked on it this morning and despite being out in a 100+ Fahrenheit heatwave for two days I couldn’t smell it at all.
If the dead animal (and the surrounding air mass) has been dehydrated by a 100+ F heatwave, then there will be little smell.
The volatile organic compounds and other chemicals that give things their smells tend to be very water soluble, so when the object is wet or the air around it is humid, then more particles are carried into the air with the water vapour.
Wet dog smell etc.

Anonymous at Tue, 9 Jul 2024 20:42:43 UTC No. 16274974

Are any youtube experimenters accepted on /sci/ or just amateur philosophers and simp magnets?
https://www.youtube.com/watch?v=PDapGJ9jWZk

Anonymous at Tue, 9 Jul 2024 20:50:33 UTC No. 16274984

>>16274974
Dr. Fire is always welcome.

Anonymous at Tue, 9 Jul 2024 21:00:51 UTC No. 16274999

>>16274922

tard level answer is heavy = fast.

we intuitively accept that because what we see around us is air resistance everywhere.
you can counter this intuition by accepting heavy objects are harder to get moving.
so, they are pulled more, hence them being heavy, but they are harder to move, so they take time to get up to speed.

midwit level answer is all acceleration is equal.
g, gravitational acceleration is a constant
some good answers in this thread, such as >>16274943 & >>16274950
also lots of resources online.

genius tier answer is heavy = fast.
do not attempt this unless you understand midwit tier answer.
earth is massive, and each object is attracted to it equally. however, earth is also attracted to each of the small objects as well. the attraction is negligible, as the earth is massive. however, if the object were the size of, say, jupiter, with gravitational acceleration greater than earth (about 2.5x), then you'd feel it, yeah.

Anonymous at Tue, 9 Jul 2024 21:16:30 UTC No. 16275017

>>16274950
>>16274999
Thanks, those explanations make sense.

>earth is massive, and each object is attracted to it equally. however, earth is also attracted to each of the small objects as well. the attraction is negligible, as the earth is massive
Yeah, this is also part of what I thought, I guess it is indeed negligible due to the difference in mass of a bowling ball and the earth, but technically, the bowling ball is moving a negligible amount faster.

Anonymous at Wed, 10 Jul 2024 02:14:09 UTC No. 16275479

>>16275017
It's far easier than >>16274943 and the others are trying to explain to you.

Gravitation force: [math]F = \dfrac{GmM}{r^2}[/math] (where M is the mass of the Earth)

Then use the 1st Law of Motion: [math]ma = \dfrac{GmM}{r^2} \implies a = \dfrac{GM}{r^2}[/math].

So the acceleration felt by the falling object due to gravity does not depend on its mass, only on the mass of the planet.

Anonymous at Wed, 10 Jul 2024 04:16:13 UTC No. 16275570

>>16274922
Gonna add, say you and your twin decide to jump off a cliff together. Do you fall faster if both of you decide to hold hands? Obviously not. The point is, gravity pulls on you both the same, regardless or not if both of you are connected.

>Extra
I would also like to add that saying gravity is the same is more cause the earth is huge and we are much smaller, so we approximate acceleration to be a constant 9.8 m/s^2 near the earth's surface.
But obviously if you're a million miles away from earth, it ain't 9.8 m/s^2; technically earth's pull does depend on distance from the center (for a smaller-than-earth object like a person or a bowling ball), but we say it's approximately constant.
If you're falling into a black hole though, your foot WILL feel a larger acceleration than your head (streeeeeeetch).

Anonymous at Wed, 10 Jul 2024 16:21:37 UTC No. 16276129

In the category of path connected nondegenerately based spaces we are given
[math]f_0, f_1 :A\to X[/math]
[math]g: X \to Z[/math] s.t. [math]g \circ f_0 \simeq g \circ f_1 [/math]
For all spaces [math]Z'[/math] and maps [math]h: X \to Z'[/math], if [math]h \circ f_0 \simeq h \circ f_1[/math],
then [math]\exists k:Z \to Z', h \simeq k \circ g[/math].
Let [math]z \in H^q(X, x_0, G)[/math] be such that [math]f_0^*(z) = f_1^*(z) \in H^q(A, a_0, G)[/math].
Can you help me prove that
[math]\exists w \in H^q(Z, z_0, G), g^*(w) = z[/math]?

Anonymous at Wed, 10 Jul 2024 17:05:49 UTC No. 16276179

>>16275479
nta but wouldn't that apply to the planet too? [math]F = Ma = \frac{GmM}{r^2}[/math] ==> [math]a = \frac{Gm}{r^2}[/math], meaning the acceleration felt by the earth due to the falling object depends on its mass

Anonymous at Wed, 10 Jul 2024 17:06:50 UTC No. 16276180

>>16276129
what do you nerds even get out of this

Anonymous at Wed, 10 Jul 2024 17:11:32 UTC No. 16276184

>>16276179
Correct, both objects will exert a force and attract each other. But remember that [math]m \ll M[/math], and G is already a very small number so the pull / acceleration from the object compared to the planet will be minuscule.

Anonymous at Wed, 10 Jul 2024 18:48:55 UTC No. 16276313

Anyone got any experience with TI microcontrollers? My uni received a supply of MSP430fr2433s and gave them out to any comp sci/engineering students interested in one. It's my first time with a low level development board and the official userguide (about 600+ pages) is throwing me for a loop. So far I've gotten the LEDs to blink in assembly and want to move to C, but I'm having trouble wrapping my head around all the acronyms, schematics and how it all connects desu . Are there any video courses or other resources related to the board that anyone would recommend? For reference I'm taking a computer architecture class but the prof is well...I'll just say pretty disorganized. My only experience with microcontrollers is programming a raspberry pi with an arduino but that's not as close to "bare metal" programming like the msp430.

Anonymous at Wed, 10 Jul 2024 19:31:17 UTC No. 16276356

i know its a little hard to see but im wondering what are equations M_a and M_b are showing

Anonymous at Wed, 10 Jul 2024 20:26:36 UTC No. 16276470

>>16276356
looks like the mass of a sphere with density [math]\rho[/math]
[math]m_a = \frac{4}{3} \rho \pi a^3[/math]
for some reason they're using "a" and "b" as the radius

Anonymous at Wed, 10 Jul 2024 21:37:03 UTC No. 16276578

>>16276470
does that mean that is the true mass of the object since they are accounting for density?

Anonymous at Wed, 10 Jul 2024 22:14:09 UTC No. 16276632

>>16276578
uhh sure
the next equation has them being subtracted though, which makes no sense

Anonymous at Wed, 10 Jul 2024 22:28:09 UTC No. 16276642

What are some good learning materials (youtube playlists, books and others) to git gud at Linear Algebra?

Anonymous at Thu, 11 Jul 2024 00:27:37 UTC No. 16276749

What even is an eigenvalue or an eigenvector? Like isn't it literally just the scaling factor of a vector?

Anonymous at Thu, 11 Jul 2024 01:57:28 UTC No. 16276808

>>16276749
If you multiply a square matrix by one of its eigenvectors, you get the same matrix multiplied by a constant.
That constant is the eigenvalue corresponding to the eigenvector in question.
So, yeah, the eigenvalue is pretty much a scaling factor.

Anonymous at Thu, 11 Jul 2024 03:26:59 UTC No. 16276862

>>16276356
whenever you see 4/3 pi x^3, that means volume of a sphere. The rho p next to it is mass/volume, so multiplying it by volume is the total mass. When you subtract two spheres of different size, you get a spherical shell of thickness a-b.

2/5 m a^2 has units of mass * distance^2. Those are units of moment of inertia. I dont wanna look it up, but it prob is it. Idk off the top of my head what the moment for a sphere is tho.

Anonymous at Thu, 11 Jul 2024 03:32:44 UTC No. 16276864

On Zill's Advanced Engineering Mathematics, but applies to all textbooks for self-learning
1) Are you supposed to solve all problems?
2) If no, when to stop?
3) Should I solve once and then use the formula for other problems?
The book explicitly says you shouldn't memorize them. So there is building familiarity in redoing vs time waste.
4) What to do when you can't find the answer?
I currently use litsolutions, but a lot of the time they're wrong.
I dislike the trope of
>no solutions for you so you can try harder
when it is mostly done for instructors to assign homework. I'm already afraid I've picked up misunderstandings and bad habits because of the lack of feedback.

Anonymous at Thu, 11 Jul 2024 03:46:17 UTC No. 16276870

Is wavelength quantized? In other words, is there a minimum difference in wavelength that two photons can have, without having an identical wavelength?

Anonymous at Thu, 11 Jul 2024 04:26:04 UTC No. 16276890

>>16276870
No. Quantization occurs when there is some kind of constraint or boundary condition on a system. There is neither for an photon in free space, so they can have any energy.

Anonymous at Thu, 11 Jul 2024 05:18:08 UTC No. 16276925

I have to do the Fourier transform of the function of the pic, using the attached table. At some point, I get that I have to solve the Fourier transform of [math]\frac{1}{1+\frac{u}{2}^2}[/math]
I guess I could use the Fourier transform of f(ax+b), with a=1/2 and b=0. And the one of 1/(1+x^2). So the Fourier transform would be [math]\pi 2 e^{-|2t|}[/math].
But I checked it with Wolfram and I got [math]\sqrt{2\pi}e^{-2|t|}.[/math]
Where am I wrong?

Anonymous at Thu, 11 Jul 2024 05:18:54 UTC No. 16276926

>>16264745
Is there any good place to go where good faith discussions about science can be had?
I'm tired of /sci/ and 4chan in general.
Its just full of arrogant and uneducated idiots shitting up every thread with their worthless ignorant opinions. Not everyone here is like that and there are occasionally some good threads, but they are far too rare. Most threads just degenerate once the little assholes start posting.
I need some place where posters are genuine and knoweldegable but the topics aren't too high level academic and too much group think between people already in agreement. So people can follow a discussion in areas outside their specialties and weight different opinions. Somewhere where there is some degree of moderation to keep the little assholes, shitposters, and schizos out but where educated and rational people who can offer intriguing questions and differing views without being blanket censored. Informed debate without the idiots and shit posters. Does such a place even exist?

Anonymous at Thu, 11 Jul 2024 05:46:09 UTC No. 16276937

>>16276926
there's some public discord servers that are academically oriented where people outside of the general channels are generally discussing in good faith and chilling

Anonymous at Thu, 11 Jul 2024 08:41:31 UTC No. 16277034

>>16276864
>Are you supposed to solve all problems?
You should only solve the ones you don't know how to do :-).
That is, you should seriously attempt them. Of course it happens (often) that you fail to solve something (I'm projecting).
>If no, when to stop?
I usually stop when it's been an hour or I'm out of ideas, whichever happens last.
>Should I solve once and then use the formula for other problems?
Not sure what you mean but I wouldn't memorize a formula if you can derive it quickly yourself when needed.
>What to do when you can't find the answer?
Look online or ask here or anywhere else.
>I'm already afraid I've picked up misunderstandings and bad habits because of the lack of feedback.
You can try a different book which has similar topics and solutions available, if it exists. If not, see above.

Anonymous at Thu, 11 Jul 2024 11:56:26 UTC No. 16277203

>>16276926
Have you tried r/atheism? Of course, you don't get to talk about any spicy topics that are worth talking about, but you also won't get bitched at for formatting or being a faggot.

Anonymous at Thu, 11 Jul 2024 13:16:26 UTC No. 16277275

Is there a way to compute the orbital period (or equiv. semi major axis) from the velocity and position of a given celestian body without simulating a whole orbital period? Like a simple formula or such, within a two-body system where the celestial body has neglegible mass.

Anonymous at Thu, 11 Jul 2024 13:32:14 UTC No. 16277290

>>16277275
Wouldn't the approximation just be from Keplers second law as the area swept is equal over a time frame? Divide total area by the area swept at the velocity measured and then multiply by the time it took to sweep that area. There is probably some integral form of this.
https://youtu.be/dsttEhQr4Sc?si=ynmpTVTNSrrYacwf

Anonymous at Thu, 11 Jul 2024 14:23:27 UTC No. 16277326

>>16277275
Nevermind, I found an answer:
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/09%3A_The_Two_Body_Problem_in_Two_Dimensions/9.08%3A_Orbital_Elements_and_Velocity_Vector#mjx-eqn-9.5.31

Anonymous at Thu, 11 Jul 2024 14:53:20 UTC No. 16277354

>>16276925
Mathematica has a different convention of Fourier transform than the one you are using. Just trust the table you were given if you can't derive it yourself

🗑️ Anonymous at Thu, 11 Jul 2024 15:07:10 UTC No. 16277368

Can /sci/ do the guillotine math? How much does the force on the blade increase is the blade is slanted by a given number of degrees?

Anonymous at Thu, 11 Jul 2024 15:09:53 UTC No. 16277371

Can /sci/ do guillotine math? How much does the force on the blade increase if the blade is slanted by a given number of degrees?

Anonymous at Thu, 11 Jul 2024 16:06:06 UTC No. 16277455

Surely I'm always allowed to say this right? and if so by what principal?
[math]5xy+4xz=\phi_1(x,y)+\phi_2(x,z)\implies(\phi_1(x,y),\phi_2(x,z))=(5xy,4xz).[/math]

Anonymous at Thu, 11 Jul 2024 16:13:13 UTC No. 16277463

>>16277371
The slant doesn't increase force it just makes it better at cutting with the same force.

Anonymous at Thu, 11 Jul 2024 16:22:13 UTC No. 16277473

>>16277455
The left side does not imply the right side. If f1(x,y) = 5xy + 1 and f2(x,z) = 4xz - 1, the left side is satisfied but not the right.

Anonymous at Thu, 11 Jul 2024 16:45:47 UTC No. 16277489

>>16277473
Fuck, you're right. What about up to some function in their shared variable x?
[math]5xy+4xz=\phi_1(x,y)+\phi_2(x,z)\implies(\phi_1(x,y),\phi_2(x,z))=(5xy+f(x),4xz-f(x)).[/math]
Does that make logical sense and if so how?

Anonymous at Thu, 11 Jul 2024 17:55:43 UTC No. 16277586

>>16277489
h(x,y,z) = f1(x,y) + f2(x,z)
Now do partial derivatives for x,y, and z. Three equations, three unknowns. Both left and right hand sides are equivalent.

Anonymous at Thu, 11 Jul 2024 18:02:01 UTC No. 16277592

>>16277586
you don't need to do partial for x, my b, that would be using a 4th equation. The original counts as the first

Anonymous at Thu, 11 Jul 2024 18:31:38 UTC No. 16277634

"Find all the singularities of [math]\frac{z^3e^{\frac{1}{z^2}}}{(z^2+4)^2}[/math], classify them, and find each residue"
I found that +-2i are poles of order two. I was able to calculate its residues.
I found that in 0 it has an essential singularity, and afaik to calculate that sort of residue I have to do the Laurent series and find a_(-1) which can be a pain in the ass. So i was like ok I will use that the sum of the residues is equal to minus the residue at infinity no prob.
Then I found that in infinity it has an essential singularity. Even though essentials singularities have 0 as residue, this doesn't apply to the ones in infinity but I can calculate them using that Res(f(z), inf)=Res(1/z^2 f(1/z), 0).
Usually in this sort of exercise I get that the function at that point is holomorphic so the residue is 0 and I'm done, but in this one i got that:
[math]\frac{1}{z^2} f(\frac 1 z ) = \frac{ e^{z^2}}{z(1+ z^2 4)^2}[/math]
And this is not holomorphic at 0. So how do I have to calculate its residue?

Anonymous at Thu, 11 Jul 2024 18:43:33 UTC No. 16277649

>>16277634
At infinity has a removable singularity* typo
A friend told me that I could just do the limit of z to infinity of f(z) as if I were working with real numbers, is it that simple?

Barkon Approved Post at Thu, 11 Jul 2024 19:01:33 UTC No. 16277679

I feel bad when I feel surrounded by enemies, but these are good protocols. What's the intellectual benefit of awkward situations?

Anonymous at Thu, 11 Jul 2024 19:06:23 UTC No. 16277685

>>16277586
>>16277592
So do we really need partials or not? For some reason I feel like there is a more fundamental reason why >>16277489 may be true if it is. Almost like how [math]P(x)=Q(x)[math] implies that they have the same coefficients for each power. You don't need calculus to prove that, do you?

Anonymous at Thu, 11 Jul 2024 19:32:49 UTC No. 16277736

>>16277634
You calculate the Laurent series.
I think the residue should be
[eqn]1 - \frac{5}{4} e^{-\frac{1}{4}}[/eqn]

Anonymous at Thu, 11 Jul 2024 19:35:57 UTC No. 16277739

>>16277685
[eqn]\phi_1(x,y) - 5xy = 4xz - \phi_2(x,z) [/eqn]
The LHS does not depend on z and the RHS does not depend on y. Since they are equal neither of them can depend on either y or z.

Anonymous at Thu, 11 Jul 2024 19:42:00 UTC No. 16277749

>>16277679
sex

Barkon Approved Post at Thu, 11 Jul 2024 19:45:32 UTC No. 16277751

>>16277749
I will contact you before sex, sure. Don't worry, this is nothing like I'm in mind. I'm very very very very ordered in mind.

Anonymous at Thu, 11 Jul 2024 19:49:39 UTC No. 16277760

>>16277739
What? Not him but 4xz-phi2 clearly does depend on z and phi1-5xy on y.

Anonymous at Thu, 11 Jul 2024 20:14:04 UTC No. 16277797

>>16277685
This >>16277739 is pretty much the same, but the form might be easier to think about. The LHS is a function of y, and the RHS is a function of z. But y and z are supposed to be independent variables (this is shown easily when you do a partial derivatives in y and then in z, since one side will always be equal to 0.) The only way this works out is if both the LHS and RHS are equal to the same function of x, and no other variable.

Anonymous at Thu, 11 Jul 2024 20:22:43 UTC No. 16277808

Let v be some vector on a unit sphere in 3D. I want to rotate it using the Rodrigues formula such that it becomes the point (0,0,1). I figured out that the axis is simply the vector orthogonal to the plane given by ((0,0,1),v) but I thought the angle should be simply arccos(z/r), i.e. the [math]\theta[/math] in spherical coordinates, but it does not seem to be that way. How do I find the angle?

Anonymous at Thu, 11 Jul 2024 20:49:55 UTC No. 16277848

>>16277808
A x B gives to normal vector of the plane of rotation. A dot B gives AB*cos(theta), where theta is the angle in between

Anonymous at Thu, 11 Jul 2024 20:52:09 UTC No. 16277851

This question >>16277827 if anyone can answer it

Anonymous at Thu, 11 Jul 2024 22:10:21 UTC No. 16277919

>>16277851
A homeomorphism is a continuous bijection with continuous inverse.
It seems to me the first sentence breaks down if x^{-1} isn't continuous.

Anonymous at Thu, 11 Jul 2024 22:15:25 UTC No. 16277924

>>16277919
The proof shows that if X and Y are cont and differentiable (infinitely, for this book), the h = F^{-1} o Y is differentiable since F^{-1} and Y are differentiable. The same proof would show that h^{-1} = F^{-1} o X is differentiable since F^{-1} and X are differentiable. Why does continuity of X^{-1} or Y^{-1} matter here?

Anonymous at Thu, 11 Jul 2024 22:18:12 UTC No. 16277926

>>16277924
the second F^{-1} is for Y, i should've used a subscript or something, like (F_x)^{-1} o Y and (F_y)^{-1} o X

Anonymous at Fri, 12 Jul 2024 03:44:23 UTC No. 16278190

I have suddenly at 30 years old awakened to a desire to better myself. I want to learn math again from the ground up. What do you suggest for a guy who basically scraped by his college algebra class? Where do I begin?

Anonymous at Fri, 12 Jul 2024 03:47:31 UTC No. 16278191

>>16278190
how about reviewing some college algebra?

Anonymous at Fri, 12 Jul 2024 03:51:08 UTC No. 16278194

>>16278191
I honestly don't know where to start. I don't really remember much of anything and my ability to understand math logic was severely dysfunctional back then. I have a better mind now. I just want to start from the beginning but don't know where that is.

Anonymous at Fri, 12 Jul 2024 03:53:20 UTC No. 16278195

>>16278194
generally you pick a subject and then read a book or maybe some online lecture series on the subject. people on here like to recommend khan academy but ive never used it personally so i couldnt tell ya.

Anonymous at Fri, 12 Jul 2024 03:55:18 UTC No. 16278199

>>16278195
I see. I keep going in circles on this because I don't know where to begin. I'll try KA.
I've always been more interested in the history and humanities side of life so this is definitely something that will be tough.

Anonymous at Fri, 12 Jul 2024 03:56:20 UTC No. 16278201

>>16278199
good luck fren. ill be here if you have questions.

Anonymous at Fri, 12 Jul 2024 03:56:38 UTC No. 16278202

>>16278195
Also thank you, I'm sorry I forgot to say thank you.
>>16277679
An opportunity to explore your ability to navigate such a situation. It can be very good experience.

Anonymous at Fri, 12 Jul 2024 03:57:34 UTC No. 16278203

>>16278202
<3
also i dont know if youre new here but all the namefags are schizos, dont reply to them.

Anonymous at Fri, 12 Jul 2024 04:09:34 UTC No. 16278205

>>16278203
Yes I'm new here, I usually browse other boards but I feel really desperate to reclaim some semblance of nobility as an intellectual that isn't rooted just in historical allegories, religious doctrine and social maneuverability. Those things are very comfortable for me. I picked up terrible habits from childhood on that did not support a perfectly well rounded education. Sorry to ramble like that, I wanted to tell someone the truth for why I came here. I want to feel noble for having turned toward scholarship rather than just succumbing to indulgence. I thought perhaps this board would give me an honest shot at that. Thank you again.

What subjects did you learn in your free time? Any you would recommend?

Anonymous at Fri, 12 Jul 2024 04:16:45 UTC No. 16278208

>>16278205
>Sorry to ramble like that
no worries, i can be a bit of a rambler myself.
>Thank you again.
no prob bob.
>What subjects did you learn in your free time?
i learned quite a bit in school so i was only left with some of the more esoteric stuff for fun-study. i learned a lot about algebraic geometry and elliptic curves in my spare time just cause i think its so interesting and cool.
>Any you would recommend?
youre going to want to at least learn differential and integral calculus (oft called calc 1 and 2) and linear algebra before you start looking at anything else. get comfortable with "college algebra" and then pick either one to move on to.

Anonymous at Fri, 12 Jul 2024 04:21:17 UTC No. 16278209

>>16278205
actually, if you want me to recommend something other than the "basics", id say control theory is probably the single most useful thing you can learn in all of mathematics.

Anonymous at Fri, 12 Jul 2024 06:30:07 UTC No. 16278347

Let [math]X[/math] be a real/complex vector space. Let [math]T: X \to X[/math] be a function that is "convex-linear" in the sense that [math]T(\sum_{i=1}^n t_i x_i) = \sum_{i=1}^n t_i T(x_i)[/math] for any choice of vectors [math]x_1 \dots x_n \in X[/math] and coefficients of a convex combination [math]t_1 \dots t_n \in [0,1][/math].

Is there a characterization of all such maps? I don't mind imposing additional structure on [math]X[/math] (e.g. a Hilbert space structure) if it helps.

Anonymous at Fri, 12 Jul 2024 09:27:17 UTC No. 16278501

>>16278347
Can you give an example of such a function T that is not just an affine transformation?

Anonymous at Fri, 12 Jul 2024 09:40:43 UTC No. 16278513

Just a question, because I am not really fond in category theory, but interested in the following.
Let F:C -> D be an additive functor between abelian (or at least additive) categories. Furthermore let F be such, that there exists a short exact sequence, say 0-> A -> B -> C -> 0, such that F is neither right- nor left-exact.
What is the relation between the left- and right-derived functors of F?
Are there some explicit examples? Maybe something like Hom(tensor(-,M),N) of some torison modules that are not projective? But I guess the adjunction of Hom and tensor get's in the way here?

Anonymous at Fri, 12 Jul 2024 09:44:49 UTC No. 16278517

>>16278501
I can't. Are you implying that these are the only examples? (If that's the case, I don't see why)

Anonymous at Fri, 12 Jul 2024 11:51:44 UTC No. 16278613

>>16278205
here's a list for physics and math
https://sheafification.com/the-fast-track/

Anonymous at Fri, 12 Jul 2024 11:56:38 UTC No. 16278621

>>16278613
Stop trying to push that meme list.

Anonymous at Fri, 12 Jul 2024 12:38:37 UTC No. 16278663

not a stupid question
i just realized 4chan threads are all top heavy. the posts at the top get the most attention. what a horrible senseless bias. nothing to be done, but it's true

Anonymous at Fri, 12 Jul 2024 13:41:57 UTC No. 16278734

>>16277473
>>16277586
>>16277592
>>16277739
>>16277797
Got it. Thanks :^)

Anonymous at Fri, 12 Jul 2024 14:15:01 UTC No. 16278785

>>16278347
>>16278517
Those are precisely affine maps. You should be able to find the proof in any linear algebra book, but intuitively it satisfies Jensen and the inverse Jensen inequality at every point so it's concave and convex everywhere, which is a property only affine shapes hold

Anonymous at Fri, 12 Jul 2024 15:34:04 UTC No. 16278880

>>16278785
Jensen requires some kind of ordering on X.

Anonymous at Fri, 12 Jul 2024 16:19:43 UTC No. 16278929

>>16278621
how's it a meme

Anonymous at Fri, 12 Jul 2024 16:39:28 UTC No. 16278946

If you want a pencil to stay upright like this for one hour before it finally tips over, how close to 90 degrees would the angle need to be?

Assuming that the pencil is mathematically modeled as a straight line with some mass and length.

Anonymous at Fri, 12 Jul 2024 16:54:43 UTC No. 16278967

>>16278946
https://www.mathpages.com/home/kmath259/kmath259.htm

Anonymous at Fri, 12 Jul 2024 17:28:12 UTC No. 16279009

>>16278967
Tried making a graph of this where the x-axis is 1/10^x:th of a degree that the pencil is tilted from vertical position and y-axis is the time it takes to fall into horizontal position. The function is almost too much for desmos to handle lol

Anonymous at Fri, 12 Jul 2024 17:34:08 UTC No. 16279018

>>16279009
Yup. Looks like you are possibly hitting numerical accuracy problems.

Anonymous at Fri, 12 Jul 2024 17:45:07 UTC No. 16279029

>>16279018
Yeah something is messed up. For x>6, the value stays at constant 2.19699 and it never changes from that for x-values grater than six which is an angle smaller than one millionth of a degree. Doesn't even work with wolfram alpha if you try that small of an angle.

🗑️ Barkon Approved Post at Fri, 12 Jul 2024 17:52:24 UTC No. 16279038

>>16279029
There's weird faggy energies coming from this post. I think a fag made it.

Anonymous at Fri, 12 Jul 2024 17:56:55 UTC No. 16279042

https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/pages/syllabus/
>Format
>...students are given a set of flashcards to bring to each lecture. They are used during class sessions to vote on answers to questions...
1. What do those "flashcards" look like?
2. What makes Organic Chemistry Tutor so good? His lessons are structured with little exposition and a lot of, progressively harder, examples. What more?

Anonymous at Fri, 12 Jul 2024 18:15:23 UTC No. 16279065

>>16279029
Trying using one of the last two equations instead, though they require loops rather than brute force calculation.

Anonymous at Fri, 12 Jul 2024 18:31:01 UTC No. 16279084

>>16278347
>>16278880
Idk wtf is your problem and why you're being so annoying and bitchy but I'll spoonfeed you. It's affine iff it's affine on finite dimensional subspaces.
Let [math]G(x) := T(x) - T(0)[/math]
By [math]T(\lambda x + (1-\lambda) 0) = \lambda (T(x) - T(0)) + T(0)[/math] we get
[math]G(\lambda x) = \lambda G(x) \ \ \forall \lambda \in [0,1][/math]
Therefore [math]G(\lambda x) = \lambda G(x) \ \ \forall \lambda \in [0, \infty][/math]
Using this property, we easily get [math]G(-x) = -G(x)[/math]. Therefore
[math]G(a+b) = G(1/2 (2a) + 1/2 (2b)) = 1/2 G(2a) + 1/2 G(2b) = G(a) +
G(b)[/math]
Combining these properties, we see that G is linear and therefore F is affine.

Anonymous at Fri, 12 Jul 2024 19:10:11 UTC No. 16279159

>>16279084
For the record, I'm >>16278347 but >>16278880 is someone else. Thanks anyhow

Anonymous at Fri, 12 Jul 2024 19:35:50 UTC No. 16279206

>>16264745
is there anything like karnaugh map but for logic sentences?

Anonymous at Fri, 12 Jul 2024 21:28:33 UTC No. 16279385

not /sci/ but dunno where to put it.
is it weird/bad to ask for feedback on your CV when you've been successful and invited to an assessment day?

Anonymous at Fri, 12 Jul 2024 21:37:29 UTC No. 16279399

>>16279009
It's no accident it looks like a straight line up to the point where it fails due to numerical error. The slope of your graph for large x is
[math] \sqrt{\frac{2L}{3g}}\ln 10 \approx .268 [/math]
(if any of you anons think you're smart, derive this)

Anonymous at Fri, 12 Jul 2024 21:54:41 UTC No. 16279428

>>16279399
>(if any of you anons think you're smart, derive this)
Oh nevermind they basically do it in the other guy's link

Anonymous at Sat, 13 Jul 2024 07:33:51 UTC No. 16280005

Isn't astrology technically true if the universe is infinite? As you can find some combination of celestial events that could be used to predict any finite human life?

Anonymous at Sat, 13 Jul 2024 08:51:27 UTC No. 16280046

>>16280005
No, that doesn't make any sense.

Anonymous at Sat, 13 Jul 2024 09:47:19 UTC No. 16280088

I used to look at an image like this and think "Oh all the other stuff is stars in the background" but it only recently occurred to me that makes no sense. So there's M32 and M110, but besides that, are all the light spots stars in the FOREGROUND?

Anonymous at Sat, 13 Jul 2024 09:51:18 UTC No. 16280092

>>16280088
stars from our own galaxy dummy

Anonymous at Sat, 13 Jul 2024 09:55:49 UTC No. 16280093

>>16280092
God I feel like such a dumbass for not considering the scale of how fucking massive a galaxy is and how big something would have to be to shine that brightly BEHIND it...

Anonymous at Sat, 13 Jul 2024 10:01:36 UTC No. 16280096

>>16280092
So they're like really really close to us, too.

Anonymous at Sat, 13 Jul 2024 10:04:32 UTC No. 16280099

>>16280096
on an astronomical scale, yes Andromeda is fairly close to us

Anonymous at Sat, 13 Jul 2024 10:06:40 UTC No. 16280103

>>16280099
But also the stars in this >>16280088 that are not Andromeda, M32, or M110 are super close to us. Or are some of them are satellite galaxies of Andromeda?

Anonymous at Sat, 13 Jul 2024 11:18:53 UTC No. 16280154

Any good resources to go from retard to actually good at math? Something that will teach me like I’m a caveman idiot starting from like elementary school division & multiplication, shit with fractions and decimals too, like that level and take me all the way to smarter than most college students able to do algebra and some trig and all that shit?
I actually don’t hate math, I was just always lazy during school and found it uninteresting. I got through highschool and some college without ever having learned long division. I thought myself how to do long division a year ago and I was kind of proud at how easy it was. Same with essays, I didn’t write a single essay in high or middle school.


I dropped out of college because I had forgotten what little algebra I learned in highschool and took an alternative (stats) but it was the same issue I had forgotten all the fundamentals or I straight up never learned them. I hate that my brain if it can find a way to get through or technically succeed without doing any parts of the crucial work it absolutely will find that route. It’s come in clutch for me, but fucked myself over far too many times. I’m not stupid, I CAN learn stuff, I’m just guilty of being a retard a lot.
I find khan helpful at times but I’m looking for more resources because sometimes his shit just doesnt click and make sense with me


>doesn’t click
That’s the other thing, idk how to describe this but I need to fully understand every little step and to be able to actually see how I went from the start of the problem to the solution or else I cant grasp it or understand. I need to see how I went from the question to setting it up, to how the numbers and any variables all interact in every step of the way and I need to know why they’re interacting like that and how it’s gonna lead me to the next step and so on, to understand and learn. I can’t just be told “do this then that baddabam baddaboom wash your penis clean your room

🗑️ Barkon, Vard and Worl at Sat, 13 Jul 2024 11:20:00 UTC No. 16280156

>>16280154
Gluey hair right.

Anonymous at Sat, 13 Jul 2024 12:45:12 UTC No. 16280206

>>16264745
Question: what is a good, safe substance to help relax the mind and the body?
>no marijuana, I don't like the high
>no alcohol, it clouds the mind and damages the body
>most teas are useless, but I'm open to advice

Anonymous at Sat, 13 Jul 2024 13:10:34 UTC No. 16280220

>>16280206
Meditation

Anonymous at Sat, 13 Jul 2024 13:11:42 UTC No. 16280221

>>16280220
Meditation is not relaxing lmao. Also it gives you insomnia.

Anonymous at Sat, 13 Jul 2024 15:59:24 UTC No. 16280345

>>16280206
I have heard Passion flower, either in tea form or smoked, makes for a very calm and pleasant slightly euphoric high. People use it to sleep. But it apparently doesn’t sedate you doesn’t make you high like weed does you feel totally normal just chill and good, from what I’ve read.
There was another plant which I forget the name of but it sounded perfect. It was supposed to create a nearly identical high to weed but none of the visual parts of it if that makes sense. Like you’d still feel competent and not freaking out you wouldn’t have that slight haze in your vision or however you wanna describe the visual part of weed. No paranoia. But you’d feel all the pros that you’d want. I wish I could remember it, it had like 2 species of plant and one was better for this the other was weaker and more hit or miss. It was a plant you would find in a nursery that people use for decoration. Had little kind of elongated flowers. Was called like red lions dick or something like that.


T. Looking for the same, something I can smoke and relax with without getting blasted. Weed stopped being enjoyable for me after I turned 18.

Anonymous at Sat, 13 Jul 2024 17:59:54 UTC No. 16280419

>>16280046
Why? Astrologers say there's no causation it's just a correlation of celestial events to events on earth. So you could find a correlation to a series of finite events with infinite options easily.

Anonymous at Sat, 13 Jul 2024 18:02:32 UTC No. 16280422

>>16276129
Anyone?

Anonymous at Sat, 13 Jul 2024 18:05:46 UTC No. 16280424

>>16278208
I fell back into my old ways and in Khan Academy immediately lost interest in math to go learn American history...

Anonymous at Sat, 13 Jul 2024 18:16:19 UTC No. 16280437

>>16280419
>So you could find a correlation to a series of finite events with infinite options easily.
Not necessarily true, unless you're being incredibly vague with what the phenomena are supposed to "predict".
Which, to be fair, is exactly what astrology does anyway.

Just because you have an infinite number of options does not mean that every possibility will be accounted for.

Anonymous at Sat, 13 Jul 2024 19:09:19 UTC No. 16280529

>>16272810
but it disstn its always phycians who do matz.

Anonymous at Sat, 13 Jul 2024 19:12:10 UTC No. 16280534

>>16280529
Why do you post ugly AI slop?

Anonymous at Sun, 14 Jul 2024 14:53:28 UTC No. 16281390

>>16280437
They only have to cover human behaviors to be more useful than any modern psychometric.

Anonymous at Sun, 14 Jul 2024 15:46:45 UTC No. 16281423

>>16280154
http://sheafification.com/the-fast-track/ or the /mg/ chart

Anonymous at Sun, 14 Jul 2024 17:14:02 UTC No. 16281484

How does one understand pressure at any given point in a gas?

Like, don't you need to understand pressure in a comparative sense?

Perhaps you could understand a given region of gas in terms of density and frequency of collisions, right?

What are some terms i can look up about this subject?

Anonymous at Sun, 14 Jul 2024 17:14:18 UTC No. 16281485

>>16281423
This is a meme btw (both lists).

Anonymous at Sun, 14 Jul 2024 21:47:42 UTC No. 16281658

My degree was light on maths- basically single-variable calc and then individual topics as needed for whatever we were doing (e.g. covered partial derivatives but not multiple integration, covered various linear algebra topics but not very rigorously).
But now I want to learn about electromagnetism, because I'm interested in electronics and particularly signals/communications (and because Maxwell's equations seem to be very broadly applicable).

I know I've got quite a bit of catching up to do.
My plan is to spend several months working through udemy classes covering multivar/vector calc and other topics I missed, and then pick up Griffiths' Electrodynamics and work through it for however long that takes.

Is this realistic? I'm mainly worried that I'm underestimating how long it'll take to get my maths up to scratch, or that Griffiths will just be impenetrable without other undergrad physics foundations.

Anonymous at Sun, 14 Jul 2024 22:23:59 UTC No. 16281688

>>16265624
That video is really bad support to your argument.

Anonymous at Sun, 14 Jul 2024 22:31:00 UTC No. 16281692

>>16266362
>points have an area of zero

Anonymous at Mon, 15 Jul 2024 01:22:09 UTC No. 16281851

>>16280424
happens. its not like you *need* to learn math, plenty of people dont.
>>16281692
im not sure what you dont like about that statement, but if you define probability as the ratio of "success" points (one, in the case youre trying to hit a single point) to the number of other points you could it, you arrive at the same conclusion.

Anonymous at Mon, 15 Jul 2024 02:02:10 UTC No. 16281873

I have four points that form a tetrahedron in 3D space, how do I find four vectors normal to its faces? I don't know what order the points are given in, so if I take a cross product some of the vectors could be pointing the wrong way.

Anonymous at Mon, 15 Jul 2024 05:51:31 UTC No. 16282048

>>16281485
how so

Anonymous at Mon, 15 Jul 2024 05:58:46 UTC No. 16282053

>>16281658
Griffiths is pure garbage. I don't get why retards write books that offer nothing new, even Maxwell's original book on EM is better.
There's a difference between trying to write something for a course vs trying to actually explain physics well.
Landau starts in 4d special relativity in his second book while most other EM ones have that at the end for no reason whatsoever. Landau continues writing down how a 4 dim. EM vector potential acts on a charged particle; only this way can it be seen that there is one single observer independent EM field and the equations simplify DRAMATICALLY.
Those other books, Griffith's worthless pile of shit included, write down electric and magnetic fields seperately in 3d instead and derive stupidly complicated formulae with many corrections to account for the implicit change of observer frame.
ON TOP OF THAT, they randomly insert chapters about how the forces are modified inside of materials (to please engineers forced to take the course?) and it ends up just being a scatterbrained mess. Landau has all that stuff in vol.8 and treats it much better too
>working through udemy classes covering multivar/vector calc and other topics I missed
just watch https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

Anonymous at Mon, 15 Jul 2024 06:25:29 UTC No. 16282066

Is it just me, or has it really become expensive to do science?
Back in the 1900s, broke people like Nikola Tesla were able to get made huge and intricate machines like turbines and generators but now, even with advancements like 3d printing, making anything bigger than a desk toy or winding a small transformer is ultra expensive.

Heck. Even making lenses for Galilean telescope will cost you an arm and a leg just to get a glass cut in a circle and for diamond paste.

You can't buy chemicals even if you have money for it.

Even after spending a lot of money, you fail to get stuff to work somehow, like drill bits failing to drill into stainless steel. Lathes not having enough power to cut anything but brass. The metal strip that you bought, thinking to be nickel, turns acid to brown instead of green as expected, indicating it to be something else.

Anonymous at Mon, 15 Jul 2024 06:26:59 UTC No. 16282068

>>16282066
>You can't buy chemicals even if you have money for it.
What chemicals can't you buy? I do a lot of photography and get tons of chemicals.

Anonymous at Mon, 15 Jul 2024 08:44:22 UTC No. 16282148

Suicide suicide suicide

Anonymous at Mon, 15 Jul 2024 08:46:26 UTC No. 16282150

>>16282148
I was an emergency soldier with the 'keys' to get out of anything and save my population who was hell'd after lost war. I had about 10000 killion to spend. Lots of this was predicted. Right down to Trumps bullet.

Anonymous at Mon, 15 Jul 2024 09:03:15 UTC No. 16282164

>>16282066
>just to get a glass cut
cut your own damn glass

Anonymous at Mon, 15 Jul 2024 09:52:16 UTC No. 16282193

>>16282164
It over now we won, they're safe and refreshed.

Soon, you will be taken to the electrocube to your new home and universe.

The biosphere and electrocube are synonymous, in an electrocube you're in control/above biosphere.

It's an important part of your intellect.

Anonymous at Mon, 15 Jul 2024 10:48:27 UTC No. 16282232

>>16280154
There is no shortcut to learning math aside from just picking a book and doing problems. Math builds upon itself so you need to start from the beginning like the basics of exponents,how to work with fractions etc

Professor leonhard and organic chem tutor go through math problems step by step so they're a good resource to start with.

Anonymous at Mon, 15 Jul 2024 12:36:08 UTC No. 16282319

should i do my bsc thesis in neuro informatics or NLP?

Anonymous at Mon, 15 Jul 2024 12:39:33 UTC No. 16282323

>>16282066
imo capitalism has made professional manufacturing for civilians/individuals impossible. you have to be a company to get the good stuff at a reasonable price

Garrote at Mon, 15 Jul 2024 13:02:06 UTC No. 16282340

>>16281873
You could find the median of the points to find an internal point.
Then, say you get
N_a = (P1 - P2) x (P3 - P2)
while
M=(P1+P2+P3+P4)/4
Then if N_a has the same sign as (M-P2) you know it is wrong,
that is, if (M-P2).Na=|M-P2| |Na| cos(theta) > 0

Anonymous at Mon, 15 Jul 2024 13:55:11 UTC No. 16282381

>>16264888
Literally in the sticky >>15833832

Anonymous at Mon, 15 Jul 2024 14:12:29 UTC No. 16282394

>>16280154
http://pastebin.com/sy2MbenC

Anonymous at Mon, 15 Jul 2024 14:49:02 UTC No. 16282445

>>16282319
pick something that will get you a job

Anonymous at Mon, 15 Jul 2024 15:37:51 UTC No. 16282495

>>16282053
Thanks for your reply anon. I'm curious- how long ago did you learn about electromagnetism, and was it as part of a physics degree or some other way?
I ask because it's safe to say that you understand EM very well, and I wonder if you might have forgotten what it was like to learn it for the first time, and/or you might have covered topics like relativity before EM. I haven't studied relativity and don't really plan to- I'm interested specifically in EM, not in teaching myself physics more broadly. So I think starting with resources that involve relativity might not be the right move for me. (Although you say Landau's SECOND book covers that- is his first strictly classical?)

Similarly, the maths playlist you listed looks very interesting for what it is, but it's quite far down the abstract pure maths rabbit hole. I'm currently trying to learn the equivalent of Calc 3 so you'll appreciate that I'm quite far removed from understanding those lectures.

Anonymous at Mon, 15 Jul 2024 17:49:26 UTC No. 16282620

>>16282495
Don't listen to that anon, he has his head stuck up his ass. Griffiths wrote a very thorough and pedagogical textbook and Landau and Lifshitz is not a good read.

Anonymous at Mon, 15 Jul 2024 18:14:06 UTC No. 16282652

>>16282620
This. Landau and Lifshitz is a meme, and only useful as reference material. Also in no standard classes teaching physics do you learn relativity before electromagnetism.

B at Mon, 15 Jul 2024 18:21:48 UTC No. 16282662

>>16264745
Why do all the media in society have hidden super intellectual meaning that only zeta-minds like myself are able to interpret and see the true quality of such media?

Such as FarCry 4. Pagan Min represents a rich and powerful man in control of the most powerful country but he's making a small characteristic error and the whole game is about a coup involving a enemy country capitalising on this characteristic error with perfect force?

Anonymous at Mon, 15 Jul 2024 18:22:45 UTC No. 16282663

V is a vector space and S is a linearly dependent set of vectors such that for every vector w in S, the set S \ {w} is independent.

Is it true that for every vector w in S, S is contained in Span(S \ {w})?

Anonymous at Mon, 15 Jul 2024 18:24:30 UTC No. 16282666

>>16282662
Occam's Razor: actually you're a fucking idiot.

Anonymous at Mon, 15 Jul 2024 19:04:01 UTC No. 16282709

Does the universe have an exit and an entrance?

Can we leave and come back?

Is the Job 'Gatekeeper' available?

Are there other high jobs?

How do we sign up?

Anonymous at Mon, 15 Jul 2024 19:17:46 UTC No. 16282724

>>16282663
Yes. This is so trivial am am obliged to ask: did you even try thinking about it?

Anonymous at Mon, 15 Jul 2024 19:46:53 UTC No. 16282752

>>16282620
>>16282652
Neither of you have read Landau and I don't care enough to educate dishonest undergrad shitposters. Griffiths books are all terrible without exception and do not cover anything Landau doesn't. In fact, reference book fits Griffiths quite well: that retard does nothing but write down equations and how to solve them in his QM book all while explaining no physics whatsoever (e.g. angular momentum and Clebsch Gordon coefficients are particularly bad); they're glorified cookbooks. Meanwhile Landau starts talking about the kinds of experiments that came about and made necessary the generalization to the wave function
>>16282495
The first volume only treats classical mechanics and introduces the two fundamental formulations of mechanics.
>might have covered topics like relativity before EM
I have not. Vol. 2 introduces relativity.
>I think starting with resources that involve relativity might not be the right move for me.
note that Landau 2 still is about 200 pages shorter than Griffiths in spite of that. The calculus in that book is also straightforward. You're more than prepared to read it with calc and mechanics under your belt and if you beg to differ please point out where in Vol. 2 one has to use more than that.
Generally speaking, compromising introducing special relativity compromises the entire subject of electromagnetism and prevents teaching the main results. A 3D analysis of Maxwell's equations does not lead to understanding the engineering of the electrical grid or fields produced by semiconductors in computers. It's a question of whether you want to understand physics or not
>quite far down the abstract pure maths rabbit hole
It starts with extremely basic propositional logic and set theory. All the topics discussed are relevant for physics. I don't see any pure math rabbit hole. It's all clearly applied and Schuller regularly throws in physical examples. In fact, the final few lectures are just physics

Anonymous at Mon, 15 Jul 2024 20:05:12 UTC No. 16282764

>>16282445
both equally wont get me a job I think

Anonymous at Mon, 15 Jul 2024 20:24:57 UTC No. 16282785

Hello,
I'm asking here since I'm not sure how to exactly approach it. I'm looking for the formula for spherical coordinates from any point of the unit sphere.
The usual formula, for p = (x,y,z) on a unit sphere, is:
[math]
\phi = \arccos(\frac{z}{|p|}) \\
\theta = \text{sgn} ({y}) \arccos{\frac{x}{\sqrt{x^2 + y^2}}}
[/math]
This works everywhere except (0,0,1) (and (0,0,-1)) which is the "center" of the coordinates. I want to find an explicit formula (using elementary functions plus trigonometric and inverse trigonometric functions) for the same thing with an arbitrary point on the unit sphere as the "center".
I tried finding a composition of the formula above with rotations but that requires a lot of vector math (cross products etc) that I think could be avoided potentially.

Anonymous at Mon, 15 Jul 2024 20:35:07 UTC No. 16282793

>>16282752
Don't listen to this anon, Landau is trash, only shilled by clueless undergrads who think mentioning them makes them look impressive (it doesn't to anyone who has a clue).

Anonymous at Mon, 15 Jul 2024 20:36:33 UTC No. 16282795

>>16282752
Sorry but based on your reply, either (a) I still haven't clearly communicated where I'm at and what I want to learn, or (b) your conclusion is that I'm very far behind where I need to be and you're trying to tell me that without saying it.

When you first referred to Landau's first and second books, I assumed you meant he wrote two books about electromagnetism (with the first treating it classically and the second involving relativity). Having researched it, I realise what you meant.
"Landau and Lifshitz" refers to a series of 10 books.
Vol. 2 is called "The Classical Theory of Fields" but, despite the title, appears to involve relativity extensively and throughout.
Vol. 8 is about electrodynamics and comes after such volumes as "relativistic quantum theory".
Wikipedia says all his books are advanced and suitable for physics grad students.

I'm a CS grad from a low-tier uni who felt comfortable with maths whenever it came up but hasn't actually learned much of it. I'm currently teaching myself about divergence and curl! So the books you're recommending just seem entirely unsuitable for me.
My goal is to first study some essential vector calculus and related topics, and then work through some kind of approachable undergrad treatment of EM. I have not studied physics beyond high school level and, aside from any topics that are strict prereqs for EM, I don't intend to. So I'm hoping to dodge relativity, quantum mechanics, etc.

>It starts with extremely basic propositional logic and set theory.
Yes, and I'm comfortable with that since it was very important in CS. But those lectures rapidly move on to "Topological manifolds and manifold bundles" and "principal fibre bundles". One of the application lectures at the end is "Quantum mechanics on curved spaces".

Maybe your argument is that these topics are essential to truly understand EM. If that's the case, your opinion is appreciated but it seems to be a very unusual one.

Anonymous at Mon, 15 Jul 2024 20:40:35 UTC No. 16282800

>>16282620
>>16282793
Thanks anon(s). Currently I'm leaning towards sticking with my initial plan of maths udemy followed by Griffiths. I'm definitely open to alternative recommendations though.

Anonymous at Mon, 15 Jul 2024 20:43:25 UTC No. 16282802

>>16282752
>>16282795 (Me)
>Maybe your argument is that these topics are essential to truly understand EM. If that's the case, your opinion is appreciated but it seems to be a very unusual one.
That's not what I meant to say actually... it's perfectly reasonable that extensive grad-level content would be involved when trying to "truly" understand something.
Let me try again:
>Maybe your argument is that these topics are essential to gain a reasonable undergrad understanding of EM. If that's the case, your opinion is appreciated but it seems to be a very unusual one.

Anonymous at Mon, 15 Jul 2024 20:46:54 UTC No. 16282811

>>16282800
Landau's books are genuinely full of nonsense and falsities. Since I see so many Landau fanboys, I made a thread in which I asked what Landau meant by something obviously nonsensical, and none of them could explain. None of the Landau fans on /sci/ actually carefully read his books, they just like to namedrop them because he's seen as a ebin russian physicist.

Anonymous at Mon, 15 Jul 2024 21:02:46 UTC No. 16282828

>>16282785
Just pick orthonormal unit vectors \hat{x}, \hat{y}, and \hat{z} representing the axes. Define x,y,z through dot products of the axes with the unit vector p
[math] z\equiv \hat{z}\cdot p,[/math] etc.
and then use the formulas for angles in your post.

This allows you to use any unit vector you want for \hat{z}, not just (0,0,1).

Anonymous at Mon, 15 Jul 2024 21:09:11 UTC No. 16282838

>>16282811
> I made a thread in which I asked what Landau meant by something obviously nonsensical, and none of them could explain
What was it? I'm one of the pro-Griffiths guys, but I think it's quite possible you and the few people reading your thread simply didn't understand the intent.

Anonymous at Mon, 15 Jul 2024 21:17:50 UTC No. 16282844

>>16282838
Take this for example https://warosu.org/sci/thread/16264709

Anonymous at Mon, 15 Jul 2024 21:51:32 UTC No. 16282878

>>16264745
Oh you have a severed spine?
No problem, let me get the super glue.

Anonymous at Mon, 15 Jul 2024 21:57:14 UTC No. 16282884

>>16282844
Let's just do it in one dimension for clarity. The term in question is
[math]\delta L = 2\epsilon \frac{\partial L}{\partial v^2} v[/math]
A general time derivative is
[math]\frac{d}{dt}F(x,v)=\frac{\partial F}{\partial x}v+\frac{\partial F}{\partial v}\dot{v} [/math]
So if \delta L can be expressed as a time derivative of F, F must have no explicit dependence on v (since the \dot{v} term is not there). This means that the coefficient dF/dx must also have no v dependence, so if \delta L is a time derivative dL/dv^2 can only be a constant (since we just argued it can't depend on v, and L doesn't depend on x either)

Anonymous at Mon, 15 Jul 2024 23:29:35 UTC No. 16282991

>>16282884
Good job proving you don't understand shit about the math. The only way you could've said this nonsense is if you didn't actually understand what you've read (either in the thread or in Landau's book).
Hint: there's a reason why Landau only considered functions f(q,t) and not f(q, q', t). What you wrote is unequivocally nonsense.

Anonymous at Mon, 15 Jul 2024 23:31:13 UTC No. 16282993

>>16282884
Also if you've read the thread you would've realized that this issue was already explained (not with your retarded gibberish argument though).
The problem I asked for is how Landau gets the implication B=>A when all he's proved is A=>B.

Anonymous at Mon, 15 Jul 2024 23:32:34 UTC No. 16282997

>>16282884
Oh but let me guess, you haven't actually read Landau and don't actually know any math, you're just a newbie and that's why you make all these elementary math mistakes in your posts.

Anonymous at Mon, 15 Jul 2024 23:36:33 UTC No. 16283000

>>16282884
Here's a few questions you might ask yourself to realize why you wrote is nonsense
1. What is a lagrangian
2. What is a total time derivative of a function
and from 1 and 2 derive the answer to
3. What does it mean for the lagrangian to be a total time derivative.

Anonymous at Tue, 16 Jul 2024 14:09:57 UTC No. 16283508

>>16282991
I explained the comment in Landau and Lifshitz which you failed to understand. There are no mistakes in my explanation, and if you think there are, I am sorry but you still aren't understanding.

I was not rude to you when I gave the explanation, so I don't understand the vitriol. Please lose the unjustified superiority complex. It isn't a good look especially when you are wrong (as you are).

Anonymous at Tue, 16 Jul 2024 14:43:29 UTC No. 16283539

How the fuck do we prove this:
[math]\lim_{n\to\infty}\frac{(-1)^n}{n}=0.[/math]
without resorting to epsilon-delta? because that gives me zero intuition or even just a useful rule or logic to use to solve future problems like this.

Anonymous at Tue, 16 Jul 2024 14:46:50 UTC No. 16283547

>>16283539
Nevermind actually, I think I just saw it in my mind. a ball teleporting back and forth between two points which are getting smaller and smaller and hence aproaching zero but I don't know, I would still like the argument.

Anonymous at Tue, 16 Jul 2024 15:28:34 UTC No. 16283593

>>16283547
You essentially described the squeeze theorem. The limit you want to prove L(n) has to sit between [eqn]\lim_{n \to \infty} -\frac{1}{n} \le L(n) \le \lim_{n \to \infty} \frac{1}{n}[/eqn]

And since both those limits tend to zero then so must L(n)

Anonymous at Tue, 16 Jul 2024 16:42:50 UTC No. 16283694

>>16283508
The total derivative w.r.t t of a function [math][f(x_i)]_{i \in I}[/math] is a functional (I use R here but you could use more general subsets of the reals)
[eqn]((q_i): \mathbb{R} \to \mathbb{R}^I) \mapsto \frac{d}{dt}f\circ (q_i) :\mathbb{R} \to \mathbb{R}[/eqn]

Landau repeatedly in the book confuses between the meaning of the lagrangian as a functional that takes coordinates as a function of time and outputs another function as a function of time, and the notion of the lagrangian as a real function of several variables.
These are not the same and cannot be the same. It makes sense to say that the first notion differs by a time derivative of a function (as both are functionals of the same type) and can be added/subtracted.
However, in the lagrangian as a functional the input space is restricted to the subspace in which the derivative of the first few functions are the following functions.
Even in this subspace, the time derivatives of a functional are more general than the functions of the form
[math]f(q,\dot q, t) = \partial_q g(q,t) \dot q + \partial_t g(q,t)[/math], which landau assumes are the only possible time derivatives. He also takes this functional f, and writes it as a function of three arguments (which are actually specially distinguished, since this is not an actual function but supposed to be part of a functional in which the arguments are related in a specific way by a derivative).

One stupid thing in your post is that you claim your function F is a general time derivative, but it doesn't contain the time as an argument. It also cannot be dependent on v because after taking the derivative you cannot do that stupid trick anymore where you identify the time derivative (which is a functional) with the function, because you run out of the special arguments (there is no special argument in the function form which is the second derivative of x).

None of this is ever explained in Landau.

Anonymous at Tue, 16 Jul 2024 16:47:05 UTC No. 16283700

>>16283508
Now explain how Landau gets that two Lagrangians give the same equations of motion only if they differ by a total time derivative of a function of coordinates and time (nevermind the fact that multiplying the lagrangian by constant also gives the same equations of motion).

Of course, you're not going to respond, because you don't know what the fuck you're talking about and you don't know shit about physics (none of you landau fans do). Go back to reading your retarded popsci books.

Anonymous at Tue, 16 Jul 2024 16:50:08 UTC No. 16283702

>>16283508
The reason I'm vitriolic is that I cannot stand it when people pretend to be smarter than me but are obviously wrong and do not realize it because they're too lazy to actually think for a minute or two about what they're saying. Yes, that includes you.

Anonymous at Tue, 16 Jul 2024 17:13:53 UTC No. 16283739

>>16283694
>which landau assumes are the only possible time derivatives
No. Did you read my explanation? You can begin by assuming that your function f (which I wrote as F) has \dot{q} dependence, but this will lead to a term proportional to \ddot{q}. There are no such terms in the derivative of the Lagrangian, so your f can not in fact have \dot{q} dependence.

>One stupid thing in your post is that you claim your function F is a general time derivative, but it doesn't contain the time as an argument
Just for clarity. Sure stick in explicit time dependence, this leads to a term with no dependence on v at all (given that F can't depend on v, by the argument I gave), and we are matching to something that is at least linearly dependent on v.

I'm sorry but ultimately this is a physical argument. Start with a "free" Lagrangian that is an arbitrary function of v^2, then impose Galilean invariance and you will see that a Lagrangian proportional to v^2 is the only one that works. If you are so sure LL are wrong can you find a counterexample?

Anonymous at Tue, 16 Jul 2024 17:18:37 UTC No. 16283746

>>16283700
>none of you landau fans do
I'm fairly sure you are the same guy who was promoting Landau and Lifshitz over Griffiths fwiw, the writing style is similar

>Now explain how Landau gets that two Lagrangians give the same equations of motion only if they differ by a total time derivative of a function of coordinates and time
Read the discussion of symmetry in the second chapter of Conformal Field Theory by diFrancesco et al if you like fancy books. It is very clear.

Anonymous at Tue, 16 Jul 2024 17:27:15 UTC No. 16283754

>>16283739
>No. Did you read my explanation?
Was it you in that thread? I didn't know that.
>>16283746
This is literally described as trivial in the first 10 pages of Landau's first book on elementary physics. I guess you accept that he lied about proving it (when he's only shown the converse). Also, if you actually understood it you would be able to explain it here right now, but you don't so you won't, which proves my point about Landau fans being clueless pseuds.

Anonymous at Tue, 16 Jul 2024 17:31:02 UTC No. 16283759

>>16283539
>resorting to epsilon-delta
Please do not use ridiculous expressions like that. Resorting to the definition is not a thing. The definition is not something you resort to, it's the first strategy you have to prove something.

Anonymous at Tue, 16 Jul 2024 21:54:44 UTC No. 16284153

>>16274945
bro just draw a line from the intersection of the two arcs to the center of the quarter-circle -> rectangle with diagonals

Anonymous at Wed, 17 Jul 2024 00:03:33 UTC No. 16284281

>>16283539
>without resorting to epsilon-delta
for any number k with magnitude larger than zero, there is eventually an n such that [math] | \frac{(-1)^n}{n} | [/math] is less than k, and its easy to see that every subsequent n will also yield a quotient will smaller magnitude than k.
thats basically episilon-delta.

Anonymous at Wed, 17 Jul 2024 00:46:14 UTC No. 16284321

>>16283539
well simply by profing an mathematical event horizon, by profing an limit to any eintelligence.

>>16283759
time for your ketamine does if you have nothing usefull to say.

Anonymous at Wed, 17 Jul 2024 00:57:14 UTC No. 16284330

Hi all. So why the fuck can my cell phone still receive text messages inside a Faraday sleeve while wrapped in 2 layers of aluminum foil?

I have lab experience (NRL arch) with testing these kinds of things, and my sample of reflective fabric was 100% reflective at -40dBm.

Are there some deep electromagnetic transmission principles at work with the foil resonating with the phone case or something, or is the cell tower signal really strong enough to pass through multiple layers of reflector?

🗑️ Anonymous at Wed, 17 Jul 2024 01:12:17 UTC No. 16284345

Integrals are fascinating although I don't know anything about them lol. But when thinking about it I came up with a question.

If you have a half of an ellipse like in picrelated, and then you slice it by vertical lines from the points a and b. Is it possible to have some kind of a formula that calculates the area of the slice based on the variables a and b?

If you just put in some arbitrary numbers, for example a=-1/11 and b=1/8, you get a crazy number that has square roots and trgonometric functions all over the place. How do you actually calculate all that and is it possible to do it more generally?

Anonymous at Wed, 17 Jul 2024 12:08:10 UTC No. 16284827

Would the western interior seaway have had tornadoes as frequently as the great plains do?

Anonymous at Wed, 17 Jul 2024 13:15:45 UTC No. 16284907

>>16283593
Thanks, this makes sense.
>>16283759
Pretty sure epsilon-delta isn't the only way to approach this especially since historically it was developed so late.
>>16284281
Thanks, I was avoiding this sort of argument.

Anonymous at Wed, 17 Jul 2024 21:21:36 UTC No. 16285578

What is the derivative of this function?

Anonymous at Wed, 17 Jul 2024 21:27:23 UTC No. 16285582

>>16285578
x^x if the derivative is w.r.t x

Anonymous at Thu, 18 Jul 2024 04:10:10 UTC No. 16286013

>>16282340
Thanks, that's it.

Anonymous at Thu, 18 Jul 2024 16:57:07 UTC No. 16287438

>>16264745
I'm bored. What's a study that would make me feel incredibly hopeless about all this sapience business.

Anonymous at Thu, 18 Jul 2024 23:11:33 UTC No. 16287860

>>16284330
Nothing is 100%. -40dBm is still quite a lot. You can have relatively poor signal strength at -100dBm.

Anonymous at Fri, 19 Jul 2024 15:44:24 UTC No. 16288482

>>16287438
study the mirror, and then your life's achievements

Anonymous at Fri, 19 Jul 2024 16:17:01 UTC No. 16288513

why isn't there a big religion where numbers are considered god?
numbers have lots of godlike attributes: they're everywhere, they're absolute, they define everything around us, their "word" is the law, etc.
and mathematics is like theology, trying to understand their divine nature
it would only make sense that numbers would be worshiped, yet majority of people prefer fairy tales
in fact, a number based religion could led to an increase of overall wisdom and intelligence because people would have regular contact with logic and reasoning

Anonymous at Fri, 19 Jul 2024 17:20:24 UTC No. 16288580

>>16288513
kill yourself unironically

Anonymous at Sat, 20 Jul 2024 18:27:18 UTC No. 16289893

What happens when infinite voltage and infinite resistance meets?