The h Bar

More Anonymous

00:00

What? It was written by a polymath

Reddit the mob has spoken

"No. I was personally chastised by David Chalmers for not having read it. In other words, it's serious philosophy that Grad students (at least in phil. Mind) are supposed to have read. "

ACuriousMind

@MoreAnonymous So what? Doesn't mean it's not written at a deliberately informal level for a popular audience.

I'm not suggesting it's bad in some objective sense (after all, I haven't read it), just that nothing I've heard about it would entice me to want to read it

PM 2Ring

00:35

@MoreAnonymous See en.wikipedia.org/wiki/Word_embedding Also see the article "What Is ChatGPT Doing … and Why Does It Work?" by Stephen Wolfram linked at the end of my answer: meta.stackoverflow.com/a/422397/4014959

3

GPT-3.5 (aka the original ChatGPT) uses a higher dimensional space for tokens (words & certain word fragments, etc) than GPT-2 does. The details of GPT-4 are not public, but I've heard rumours that it actually uses a lower dimensional space than GPT-3.5 does.

@MoreAnonymous I read GEB when it was new, and I re-read it in around 2000 or so (my original copy, not the revised version). IMHO, it's certainly worth reading.

But getting back to word embedding spaces...

More Anonymous

@PM2Ring I recently read Douglas thinks LLMs makes him rethink GEB

PM 2Ring

An interesting geometrical fact of high dimensional balls is that most of the hypervolume is close to the surface. So when you do a random walk through the word space, you're mostly near the surface, and slightly weird things happen near the centre of the ball, since any random path is unlikely to spend much time near the centre of the ball.

@MoreAnonymous Yeah. I read a short article by Hofstadter on that about a year ago. I don't remember the details, but I vaguely remember thinking that what he said was reasonable, and that it was good that he was prepared to revise his opinions when presented with new data.

The old joke is "Never peel a 100 dimensional apple, unless you have a very sharp knife". :)

2

PM 2Ring

01:03

Mathematically, $\lim_{n\to\infty} (1-1/n)^n=1/e$ converges pretty quickly. So if you have a 1000 dimensional ball, and reduce its radius by 1 part in 1000, you reduce its volume to ~1/e of the original ball.

naturallyInconsistent

The version I got given of that fact is that the hypersurface of a n-D hypervolume goes as $L^{n-1}\mathrm dL$, so that if you plot this out, you will realise that "area under the curve" is mostly concentrated at the outer limit as $n\to\infty$

PM 2Ring

Apparently, GPT-3 uses vectors in a 12288 dimensional space. I can't remember where I saw the data for GPT-3.5...

@naturallyInconsistent Sure. But the "e" limit is a bit more quantitative. ;)

naturallyInconsistent

yes, im not disagreeing, merely pointing out an argument

PM 2Ring

01:23

Sadly, this question got closed as non-mainstream, despite my comment:

This question is not proposing a personal / non-mainstream theory. The OP wants to know if mainstream GR permits such gaps in time, and if not, why not. — PM 2Ring 4 hours ago

Allie

@TobiasFünke thank u. and everyone else who said congrats

naturallyInconsistent

03:00

congrats

Allie

thanks meow

naturallyInconsistent

m e o w ~

PM 2Ring

03:40

120

A: What's new in higher dimensions?

In high dimensions, almost all of the volume of a ball sits at its surface. More exactly, if $V_d(r)$ is the volume of the $d$-dimensional ball with radius $r$, then for any $\epsilon>0$, no matter how small, you have $$\lim_{d\to\infty} \frac{V_d(1-\epsilon)}{V_d(1)} = 0$$ Algebraically that's o...

Allie

meowing!

Slereah

07:58

> The 1930’s were a remarkable decade for foundational mathematics. At the time, mathematics was dominated by Germany to an extent that has never since been parallelled by any country.

Most exciting time in Germany indeed

Ryder Rude

09:13

do you think quantum mechanics is an anti realist theory?

hi

i had asked this question a while back philosophy.stackexchange.com/q/121408/27700 i got anti realism as the answer

ACuriousMind

@Slereah When I think "1930s' Germany" I think "mathematics"! (What is this from? :P)

handan_toddler

09:31

hi

Slereah

@ACuriousMind Some Lawvere theory paper

handan_toddler

09:51

Have you heard any rumors about a new volume of Éléments de Mathématique being released soon?

imbAF

I have a question. I am trying to have an understanding of internal symmetries. In an example that I read, the way I understand it is that a system has some sort of internal quantity that characterizes it and under certain transformation, this quantity/quality stays invariant. And we call that internal symmetry. Essentially the coordinates do not change. Does that mean that a gauge transformation is an internal one?

ACuriousMind

The technically correct answer would be "no" but for your purposes: Yes. :P

Signor Feynman

We're about to step in ACM's favorite territory

qwerty

uh oh

imbAF

@ACuriousMind is this a reply to my question?

ACuriousMind

10:03

@imbAF yes

all the gauge symmetries you will see in QFT will be internal

imbAF

Can you elaborate further?

ACuriousMind

on what?

Signor Feynman

In the context of QFT there is really nothing more to say. Gauge symmetries only act on the internal (the fields) degrees of freedom

imbAF

On what exactly is an internal symmetry

I said something about a "hidden" quantity/quanlity/ characteristics of a system

I.e isospin was an example given

How is this quality different than say charge

ACuriousMind

It's any symmetry that acts on something different than the spacetime coordinates. There isn't really anything more to say in general.

imbAF

10:07

Which also happens to be the conserved quantity under a certain transformation. U1 gauge i think

@ACuriousMind i see. But whether the change happens in the coordinate or not, the end result is the same, in the sense that some physical measurable quantity is conserved, right?

ACuriousMind

I don't know what you mean by "end result"

Symmetries are by definition just transformations that leave the action invariant

They are not necessarily associated with conserved quantities

imbAF

End result= the consequence of invariance of some transformation being the conversation of some quantity

ACuriousMind

No, that's too vague a statement, Noether's theorem is much more precise.

imbAF

I read it. That's what it says

Unless it doesn't

ACuriousMind

No, it doesn't. For instance there are no conserved quantities associated with discrete symmetry groups.

imbAF

10:12

Well, then I had to add continues in all my statements

But I took it as given, since we are talking about conserved quantities

Signor Feynman

@ACuriousMind Is there any problem with linking books available on the web archive?

(In a question)

ACuriousMind

@imbAF There are also no useful conserved quantities associated with the infinite-dimensional continuous groups of gauge symmetries, for those Noether's second theorem applies.

imbAF

Infinite-dimensional continues grous o gauge symmetries? I don't understand. I belive the rotational group is a continuees infinite group but it's not a gauge transformation. What do you mean with what you wrote?

ACuriousMind

@SignorFeynman I don't know if and how the archive checks the copyright status of materials on there, so I can't answer that. Generally I think if you cite the reference properly a link is really not that necessary, anyone can find the book by its title and author on their own (and your question should not need people to read the reference to understand it anyway).

Signor Feynman

Alright, I won't use the link in such case, just list the ref

ACuriousMind

10:24

@imbAF Gauge symmetries are given by functions of the form $\alpha : \mathbb{R}^4 \to G$ for some group $G$ (e.g. $G = \mathrm{U}(1)$). The group of all these functions is not finite-dimensional (in the usual sense of dimensionality of manifolds).

imbAF

Dimensionality of manifolds...and there it,.. differential geometry

Yeah I don't understand it. But hopefully once I see Frederik schuller video on the topic, I might

Tobias Fünke

10:37

morning

qwerty

hallo

Tobias Fünke

:)

Ryder Rude

10:51

how much of physics do you think is dependent on how the human mind is? i.e. a product of what a human is

the notation is certainly human dependent

what about the emphasis on modeling things to understand nature? is this a human specific need

and the idea that the models are based on mathematics. is this a consequence of the fact that the human mind indulges in classical reasoning

suppose an alien mind does not indulge in classical reasoning. then their approach to understanding nature would be much different? they wouldnt be building models?

by "classical reasoning", i mean language combined with classical logic. an alien mind need not have either of these aspects

Ryder Rude

11:31

separately, within QFT, is it logically coherent that, as we go higher and higher energies, we will always find new particles?

and, if yes, what does this say about a "final model to describe everything"? would it be that there is no such model? or would it be that there is such a model but we can never know it by doing experiments as experiments can only access finite energies?

Signor Feynman

11:55

@imbAF Think about the $\mathrm{U}(1)$ case: it amounts to choosing a phase transformation that depends on the spacetime point (this is the function ACM was talking about). You have "many" (infinite) phase transformation functions you can apply

Signor Feynman

12:37

I recently learned that MO and SO are not the only SE sites not carrying "stackexchange" in the link, there is also askubuntu

ACuriousMind

@SignorFeynman also superuser and serverfault (SO and those two were the first sites)

Signor Feynman

I wonder why a "Physics Overflow" was never created on SE

naturallyInconsistent

@SignorFeynman the people who started it were already suspicious of SE. They were P.SE veterans

ACuriousMind

@SignorFeynman There was a TheoreticalPhysics.SE once. It failed and was folded into physics.SE. You can search our meta for old discussions about that

(this was before my time, all I know is from reading meta, too)

Signor Feynman

And was it purely academic like MO?

ACuriousMind

12:43

Their ambition was definitely to be like MO (and several of the same people who wanted that site then went on to create PO outside of the SE network).

Signor Feynman

@naturallyInconsistent Oh yes, I have heard about the "frictions". What I meant is that why the physics community of SE doesn't feel the necessity of an academic version of PSE, like people have it on MO for Math.

naturallyInconsistent

it is purely by chance that miao miao happens to know one of the original founders of PO

Signor Feynman

@naturallyInconsistent Plot twist

Is there some blood in your story?

Slereah

This is stack exchange, not Highlander

ACuriousMind

@SignorFeynman Personally, I like that physics.SE sits very much in the middle ground between what math.SE and MO are.

I don't think there's really a lot of benefit to trying to emulate that separation - they didn't design math.SE and MO as complementary sites, SE started math.SE, some academics started MO, and then MO was folded into the SE network at some point

it's not that MO split off from math.SE or vice versa

naturallyInconsistent

12:47

@SignorFeynman no, he is extremely nice too, but maybe not as nice as ACM

Signor Feynman

Do you think it sits on the middle ground? Probably rule-wise (i.e. what posts are allowed), but is the average level of questions and answers really different? We get questions at all levels here, like MSE and we also have a fair share of people with remarkable knowledge like MSE.

Oh, I see, Math.SE was created by SE directly

naturallyInconsistent

But because of the exodus, he aint working with simple questions

at least for now

ACuriousMind

@SignorFeynman Very difficult to compare because math.SE also has a lot more traffic than physics.SE

Signor Feynman

Oh, I didn't know that

ACuriousMind

see stackexchange.com/sites#questionsperday

math.SE is the second-busiest site on the network with 168 questions/day, we're the 4th-busiest site with only 39

that's also a reason why the network can sustain two math sites but not two physics sites - there's just much more traffic for math

Tobias Fünke

12:56

SO 1.3k/day

ok lol

crazy

Slereah

To be fair, we do have several physics sites

Physics, astronomy, quantum computing and earth science

Tobias Fünke

which ones do you mean?

matter modeling is probably half physics, half chemistry

ACuriousMind

also matter modelling, but yeah

Slereah

yeah that too

Tobias Fünke

but yeah, you are right

Slereah

12:57

Nobody thinks of those poor berks at Earth Science

Their third most popular tag is "climate change"

Dooooom

ACuriousMind

but as you can see on the list, all those sites are another order of magnitude below physics.SE in traffic

Signor Feynman

@ACuriousMind Oh my, we're so smaller than I thought

I will consider myself as part of an elite from now on :P

Tobias Fünke

lol

Slereah

We're still 4th overall

Tobias Fünke

well, from my perspective 30+ questions per day is quite good. IDK what the SE bosses think about that, though

Signor Feynman

13:00

The thing I can say is that the hBar is definitely the most welcoming chat

Slereah

They would probably disagree because from late decisions they seem decided to kill the site

Tobias Fünke

I hope SE will never shut down for one reason or the other at some point

Signor Feynman

The math chat is good too but the atmosphere feels a little... cold?

Tobias Fünke

all this knowledge

Signor Feynman

@TobiasFünke ACM promised me that he will take the servers with him in the next universe

Tobias Fünke

13:01

ah ok haha

Slereah

How big is the whole PSE database I wonder

that might be on the database part of SE

Signor Feynman

I can't find that message though

Tobias Fünke

Is there a good/efficient way to save several individual posts somehow?

Signor Feynman

I wonder, even if SE collapsed, wouldn't we have the archive to see questions?

ACuriousMind

@Slereah You can look at how large the data dumps are they upload regularly (when they aren't trying to go back on that :P)

Slereah

13:03

data.stackexchange.com/physics/query/1880314/…

6 GB

It's not that big

and posts themselves are about 2 GB

ACuriousMind

@TobiasFünke Individual posts manually, no. But you can just download the entire site in your user settings (Settings -> Access -> Data dump access)

physics.SE is 697 MB

Tobias Fünke

whut

Signor Feynman

I don't know why this is funny

Ryder Rude

@TobiasFünke several at once?

Tobias Fünke

yeah

Ryder Rude

13:05

i just follow several posts

but u can't follow at once

Tobias Fünke

(I cannot do it right now): do you know which format the data is?

RR, no that's not what I mean

I mean to save the posts locally

Ryder Rude

i should keep that too

Signor Feynman

I'm befuddled. Plane waves?

ACuriousMind

@TobiasFünke I think it's an XML with the same data/tables as the data.SE explorer

Tobias Fünke

thanks

ACuriousMind

13:08

the db schema is explained at meta.stackexchange.com/q/2677/263383

Tobias Fünke

thank you. So I guess one can, with a bit of work, recover the site?

Ryder Rude

@SignorFeynman strange that they have $\psi ^{\dagger}$ in this

ACuriousMind

@TobiasFünke yes, the data dump contains everything you need to in principle host a perfect copy of all the questions and answers

Tobias Fünke

"in principle" :d

I did not know about this feature. Thank you all. Interesting

Ryder Rude

in bra-ket, this becomes, $|\psi\rangle +\langle \psi |$. It doesn't make sense

Signor Feynman

13:11

It comes from the field Heisenberg EoM with some assumptions that are not relevant now. The equation is correct. The plane wave remark is confusing

Ryder Rude

nvm it makes sense

it is an operator equation, not a state equation

one can indeed add $A+A^{\dagger}$

Signor Feynman

I know it makes sense. I didn't ask if the equation is right; it is.

Judging from what happens below I think that the author wanted to say that he tries a free ansatz

Ryder Rude

i cant find plane wave solutions of this equation. did they solve this explicitly in the book

Signor Feynman

Clearly misguided :P

Ryder Rude

yes. If the dagger was absent, then one can find plane wave solutions of this

@SignorFeynman what field is this equation used in

field as in physics field

Tobias Fünke

13:24

seems like Gross Pitaevskii or so, no?

Ryder Rude

emergent level fields are much stranger than fundamental fields

all sorts of strange equations

@TobiasFünke oh

Signor Feynman

@TobiasFünke Yes, that's the context (superfluid condensate). I don't understand that "We see that plane waves satisfy this equation". That is not a free equation

Tobias Fünke

yeah, I don't get it either

which book is it?

naturallyInconsistent

The book is correct. Even if there are both $b$ and $b^\dagger$, you definitely can solve for the solution in terms of both, at specific $\vec k$ values. The resultant is indeed a plane wave

Signor Feynman

@TobiasFünke Nazarov, Advanced QM. Chapter 6.

naturallyInconsistent

13:29

Sure, you might have to have both $\vec k$ and $-\vec k$ appearing, but it is still, in principle, a plane wave solution

Signor Feynman

Ah, I don't think I really understand how. This "plane wave" doesn't look like the usual $\exp\bigg[i(kx-\hbar k^2t/2m )\bigg]$, does it?

Because this one clearly does not satisfy $(6.19)$

You said at specific $k$ values though

$\mu\cos(kx-\omega(k)t)=0$ values?

Nah, I'm making no sense, this is a spacetime dependent condition

naturallyInconsistent

That is not what defines a plane wave. A plane wave in x,t has no y,z dependence. It does not have to be the usual basic plane wave that you are considering. For example, the EM plane wave does not have $\omega=\hslash^2k^2/2m$ but instead has $\omega=ck$

Signor Feynman

(Yeah, of course mine was 1D) You're corrent about the dispersion relation, I was misguided in using the free particle one

naturallyInconsistent

The idea is that you have wavefronts that are planes

Ryder Rude

i think one needs to diagonalise this equation by taking linear combinations of $b_k$ and $b^{\dagger} _k$. then one might turn this into a plane wave equation

but the book must have solved this explicitly, unless they leave it as exercise

Signor Feynman

13:39

So, you're saying that a plane wave doesn't necessarily have the form $\exp\{i(\vec{k}\cdot\vec{r}-\omega_{\vec{k}}t)\}$?

With $\omega_k$ a generic dispersion relation

Ryder Rude

i think the equation we have is a coupled system of ODEs

when there r finitely many ODEs, one does matrix diagonalisation

we should treat $b_k$ and $b^{\dagger} _k$ as independent

so we need the expression for $d/dt b^{\dagger} _k$ before doing matrix diagonalisation

i think that expression can be found by taking dagger on both sides of the equation for $d/dt b_k$

then we would have a system of ODEs with constant coefficients. this would correspond to a matrix equation

ACuriousMind

@SignorFeynman I'm stuck right at the start: In what sense does the r.h.s. of (6.20) depend on $t$?

Ryder Rude

@ACuriousMind i think it is a typo

@SignorFeynman they mean to substitute this

but it is not a plane wave equation. one needs to do matrix diagonalisation first

Signor Feynman

@ACuriousMind great question, they clearly forgot the evolution (or just wanted to consider the $t=0$ solution

ACuriousMind

@SignorFeynman But the value at $t=0$ would be an initial condition, not a solution :P

overall this does not seem to be carefully written :P

Ryder Rude

13:51

it is a typo

i think the book should proceed with matrix diagonalisation

ACuriousMind

@SignorFeynman If one works backwards from (6.22), I think they want the time-dependence to be in the $b_k$

i.e. that should be a $b_k(t)$ in there

Ryder Rude

@ACuriousMind this makes more sense, yes

Signor Feynman

Oh, right. I'm dummy. Those are operators, so of course the creation gets the time dependence, not the plane wave factor

ACuriousMind

and then the ansatz also makes sense - what they mean by it being "solved by plane waves" is that the spatial part of the solution is a plane wave $\mathrm{e}^{\mathrm{i}kr}$

Ryder Rude

wow

Signor Feynman

13:55

@ACuriousMind By solution do you mean $(6.20)$?

ACuriousMind

yes

as they show after that, that is a solution for any $b_k(t)$ that obeys (6.22)

Ryder Rude

still, i think it is poor writing. if one leave b_k(t) arbitrary, one can substitute plane waves into many equations

Signor Feynman

So, what I mean is that the author probably wanted to say that "we can find a solution that can be expanded in plane waves", not that "we see that plane waves are a solution". I'm not trying to do semantics, it really seems convoluted in the phrasing :P

Ryder Rude

they make it sound like this particular equation admits plane waves

@SignorFeynman yes

Tobias Fünke

@SignorFeynman oh, I actually remember this book. It was quite nice in my memory :d

Signor Feynman

13:58

I mean, I may be the one who's not nice :P

Ryder Rude

e.g. the solutions of Schrodinger equation with arbitrary V(x) can be expanded in the plane wave basis

it is bad writing to say that the solutions are plane waves

ACuriousMind

@SignorFeynman honestly I would just write something like "this equation is easier to solve in Fourier space" instead of talking confusingly about plane waves :P

Ryder Rude

yes

Tobias Fünke

as I anyway want to point out in many such discussions here: one should always consult a) a possible erratum or b) a different book with a similar content

ACuriousMind

This isn't even really an ansatz, it's just replacing the $\psi(t,r)$ by its Fourier series with coefficients $b_k(t)$

Signor Feynman

14:00

@TobiasFünke I did a) and couldn't find any :P

Ryder Rude

yes. it can be done in just about any equation

u just have to assume the solution is L^2(R)

Tobias Fünke

I meant it as a general statement :) many books have one, where typos and vague phrasings are corrected, too

ACuriousMind

which you can always do, but it's only useful if this yields an uncoupled equation for each $b_k$ (or some other easy to solve system)

which is the case here

Signor Feynman

@ACuriousMind You're right. I called it ansatz because in general the basis you use is not always the plane wave basis but yeah, it is correct

With the risk of sounding stingy, this is one of the cases in which a book seems voluntarily convoluted in the phrasing :P

Tobias Fünke

yeah I know what you mean

it wants you to read the text critically :p

Signor Feynman

14:05

"I was making sure you were listening" :P

Tobias Fünke

exactly hehe

Silly Goose

14:43

@MoreAnonymous is there a need to approximate? I would think we just need a bijection $\text{word}: \text{words} \to \mathbb{R}^n$.

Slereah

Most things can be approximated by vectors in $\mathbb{R}^n$

It is a blessed space

More Anonymous

@SillyGoose I just don't think of words as mathematical objects

Mapping a non mathematical object to R^n seems like black magic to me

Ryder Rude

15:02

it is a bit strange

but it is just a model for language generation. it is not supposed to capture it entirely maybe

i think of language as something that comes before mathematics. as mathematics is a subset of language. language and meaning and stuff are much broader than math

but at the same time, one can model the human mind as a computation. and then language generation becomes model-able as a computation. and computation is a subset of math

ACuriousMind

@SillyGoose do you think there are uncountably many words :P

Ryder Rude

it reminds me of Hegel's distinction between order of being and order of explanation

More Anonymous

@ACuriousMind good point! :p

Ryder Rude

> For Hegel, the universal is always first in the order of explanation even if what is naturally particular is first in the order of being

e.g. language is first in the order of explanation (from a human perspective). but math/computation is first in the order of being

ACuriousMind

It's not a bijection, you just take N words and send them to N points in some $\mathbb{R}^k$ ($N\neq k$!). The only non-trivial aspect here is that you can do this in a way so that vector addition/subtraction and distance encodes information about the statistical correlations between those words.

More Anonymous

15:10

I find it spooky because in physics all theories are approximations of deeper and even more richer theories (and it seems endless) ... but in LLM land this doesn't seem to be true (or maybe it is and there is some more richer theory of language we don't know about)

Slereah

I know that in some models the "basis" is semantics

Adding some woman to my grampa

Ryder Rude

i think LLM is just a model for language. it does not mean it is deeper than language. u need to know language in the first place to build the model

ACuriousMind

@Slereah poor boy, has only 2 age and 1 gender while the grandmother has 9 age and 9 gender.

Slereah

We've all been there

ACuriousMind

...old people hoarding all the genders?

Slereah

15:13

Although it's not typically a vector space even then because semantics is bounded

You don't have words of arbitrary gender or royalty

More Anonymous

@ACuriousMind do you think Wittgenstien would have been surprised that some aspects of language can be captured by a formal system.

Slereah

king, super king, mega king, giga king, etc

More Anonymous

He's one of my favourite philosophers

@RyderRude have you heard of him?

Ryder Rude

@MoreAnonymous yes. but i haven't read his works

i am planning to

ACuriousMind

@MoreAnonymous you should at least spell his name correctly, then :P

Slereah

15:15

also I think typically when we try to think of a "combination" of two words semantically, we're more likely to think of an average than a sum

or maybe not idk

What is the sum of two grampas

More Anonymous

@ACuriousMind my bad ...Wittgenstein

Slereah

The sum is typically gonna be on a few axis anyway

The sum of two grampas may be very old, but is it even less royalty and even manlier

Ryder Rude

i find it similar to idea that the human mind can be modelled as a computation. it follows directly from physics, as physics is computable stuff, and the brain is physical

so i don't find it surprising that language can be modelled like this

neuroscientists work with computation models

More Anonymous

@RyderRude I doubt all philosophers agree on this

Ryder Rude

but it is just a model. the map is not the territory. i would say all aspects of human experience (including language) are more fundamental than any model. models themselves are part of human experience

ACuriousMind

15:18

@Slereah isn't there some normalization or whatever implicit here? Like, the image you posted has the origin such that if you add 9 boys to each other, you get something that's as female as a girl, but I don't think that's how the actual math in the model works

Ryder Rude

@MoreAnonymous i think it is not a matter of philosophy anymore. u can model mind and human decision and stuff using computation models. it should be science by now

but again, it is just an approximate model

More Anonymous

@RyderRude The question becomes is there phenomena that cannot be modelled in a meaningful way.

ACuriousMind

or that might be how it extremely literally works, but the algorithm would never consider this kind of sum, i.e. there's a lot of implicit stuff invisible in the simple "the words are in a vector space" picture

More Anonymous

Like next I'll hear consciousness can also be mapped to R^n

Ryder Rude

@MoreAnonymous there might be some absurd phenomena that can't be modeled, yes. it is possible

@MoreAnonymous it depends on what we mean. if I map the experience of multiple colors to the real line (the EM spectrum), have I mapped an aspect of consciousness to numbers?

i had a debate about this long ago

Slereah

15:24

@ACuriousMind I think the 0 is meant to be at 5 :p

The No gender point

maybe idk

But then what is at the origin of the vector space of words?

Ryder Rude

similarly, if I map a person's subjective experience to a mathematical model of neurons, have I mapped consciousness to math

Slereah

What is the word that is neutral to every semantics?

Ryder Rude

i think these mappings are possible

from an idealist perspective, these mappings are not problematic at all

More Anonymous

@RyderRude it's not as simple as that... or should I say reductive as that

Anyway I gtg .. I'll continue this discussion later

Ryder Rude

ok :) thanks for discussing

ACuriousMind

15:26

@Slereah the Ur-Word :P

Ryder Rude

i just want to say that idealist would just say the map is not the territory. so these mappings are not problematic at all

ACuriousMind

if you speak it you glimpse the face of god

Slereah

just monkey noises

Ryder Rude

we have only mapped consciousness. we haven't reduced consciousness

map is not the territory

ACuriousMind

@Slereah extremely silly choice of labeling, then :P

Slereah

15:27

@ACuriousMind I guess that fits the whole negative theology thing

God has no attributes

@ACuriousMind Data science is a mickey mouse science

Signor Feynman

15:46

I've just learned that a "four of a kind" is not called "poker" like in Italy D:

Silly Goose

16:50

@ACuriousMind i think that the number of words is not well-defined in two senses. one, on large timescales the number of words in say a dictionary does change non-negligibly (new words AND new meanings of old words). two, of course we cannot account for the words that have not been established yet.

@ACuriousMind so boy that you're a girl

Ryder Rude

17:11

Why Super Glue Is Perfect For Gluing Skin

►

it is from Veritasium

Signor Feynman

17:26

superconductors, superfluids and now SUPERGLUESJJDJ

I need a superbreak

Ryder Rude

3

Q: Before Evolution was proposed by Charles Darwin, what were the leading secular theories to explain how life developed?

Outside of evolution, what were the leading scientific schools of thought that Charles Darwin contented with when he published his evolution theory as way of natural selection in 1859?

@SignorFeynman it is good for the mind

Arjun

18:04

@SignorFeynman and @ACuriousMind take a look at this..

@SignorFeynman Yes page 68 of volume two, 4th revised english edition

@ACuriousMind pls take a look at the above image from LnL

Also I was wondering when the Abraham-Lorentz-Dirac forces become significant,i.e non-negligible compared to the lorentz force acting on a particle.

Signor Feynman

18:21

I see, it's not the edition that I knew. I thought L&L didn't have many, in any case I could find that part. I don't have much time to research old notes and think about it now, but it's related to expressing the EM field in terms of the invariants. Roughly speaking, you boost to a frame in which the fields are simple enough that you can express both in terms of the two invariants. I will let you know if I find something

Arjun

sure thanks ; )

Signor Feynman

18:36

So, @Arjun the electric field and the magnetic field are two vectors, so we have $6$ degrees of freedom before considering constraints

I'll wait for your replies before going on

Arjun

18:51

@SignorFeynman Hi,I'm here

@SignorFeynman Absolutely,the two constraint equations render 6-2=4 independent dof

Signor Feynman

19:23

@Arjun okay, I'm back

Now, let's consider $\vec{E}\cdot\vec{H}\neq0$

It can be seen that in such case there exists a Lorentz boost such that the fields in the new frame they are parallel

Arjun

Sure

Signor Feynman

Here you can find such boost

Now, a boost costs 3 degrees of freedom (choose a velocity vector)

Arjun

@SignorFeynman I'm totally fine with finding a reference frame in which E and H could be made parallel

my issue was the statement he made above it

which says: By means of a Lorentz transformation we can always give E and H arbitrary values

(given of course the two constraints are satisfied)

This seems non-plausible to me since a lorentz boost which has 3 dof can not result in arbitray E and H, which, when are made to obey the two constarint relations result in 4 DOF!

Signor Feynman

But it turns out that such boost not only makes them parallel, but they are also orthogonal to your boost velocity vector

@Arjun so, clearly the Lorentz degrees of freedom are reflected in parallelism (parallelism for vectors amounts to 3 conditions). The other condition is that you know in what plane they are

Because they are perpendicular to $v$

Now you have 2 degrees of freedom remaining and you can fix them via the constraints

Arjun

Sure that is fine,I'm fine with that case

Look at the part where he talks about assigning E and H arbitrary values and not necessarily making them parallel

Signor Feynman

19:36

The way I understand that part is just saying this in a very Landau way :P

That's what I'm saying

He's saying that the constraints fix the fields (and what I said about making them parallel was the operative way to do it)

Arjun

@SignorFeynman The part where he says there always exists a frame to which one could boost into to make E and H parallel to each other is fine ,but what troubled me was him saying in the general case we could always find a boost which results in E and H taking any arbitrary values(not necessarily parallel to each other) given ofcourse these values satisfy the constraints

Maybe it's a misinterpretation of landau from my side lol

Maybe he is only talking about the parallel case

(put the complete page,just in case)

Signor Feynman

I have digital and physical L&L :P

Arjun

XD It's 1:20 am at my place and I have physics lab at 8 am tomorrow : '(

Gotta hit the sack,we'll continue this discussion some time later ; )

Gn

Signor Feynman

19:52

@Arjun I'm sorry that I'm not able to interpret Lifshitz's words (not a word of Landau and not a thought of Lifshitz), but the overall meaning of that part, as far as I understand it (and considering some old notes of mine) is just that Landau wants to motivate that the Lagrangian - which is an invariant function - can be constructed using those invariants. What is mean is: why are those invariants good enough? Do they contain all the EM field? Yes, they do

Good night!

User198

20:58

In what theories have you encountered a Hamiltonian that was not quadratic? Is it always quadratic because that is a really good aprox. for dynamics around a minimum?

Signor Feynman

21:17

@User198 in the context of QFT quadratic Hamiltonians describe free fields, non quadratic terms are interaction terms. In the context of classical mechanics, one example is the Hamiltonian of a harmonic oscillator with an anharmonic term

Quadratic things are easier to solve, for sure :P

User198

@SignorFeynman Thanks

qwerty

21:37

@Slereah idk but sum a few more you get the académie française? chat.stackexchange.com/transcript/71?m=67041487#67041487

@Slereah in which case it is not less royalty lol

Tobias Fünke

22:29

@SignorFeynman also in the QM case! a classical example of perturbation theory is the quartic perturbation of a QHO... ofc, this is very similar to a $\varphi^4$ interaction in QFT

Signor Feynman

Indeed, also the cubic anharmonic term sometimes appears

Damn qubits!!

User198

What is the quantum version of the Poisson algebra? Is it the same, but we just replace that $q,p=1$ with $q,p=i \hbar$?

All other axioms remain the same?

Is the Poisson algebra a subset of Lie algebra?

Tobias Fünke

22:48

hehe

Signor Feynman

23:01

hhhh

Did you know that this is the Chinese "hahaha"? :P

imbAF

Hi, can someone help me with the following setup. In the lecture we considered the decay of an initial particle with 4-momenta $P$ and mass M into 3 particles of no mass. In order to solve the problem we considered an artificial massive particle. We have $P\rightarrow p_1 + p_{23}$. And $p_{23}\rightarrow p_2 + p_3$.

$P\rightarrow p_1 + p_{23}$If we focus on the com of P. Is it possible for us to consider this

because, since we are REST frame of particle P, because of momenta conservation $\vec p_1=-\vec p_{23}$

But since one of the particles is massive and one is massless

how can that occur?

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