The h Bar

Allie

02:47

If I take a classical system with N degrees of freedom and impose x holonomic constraints and y non-holomomic contstraints, is it true that the system will now have N-x dof?

That is, does a holonomic constraint always eliminate 1 dof while a nonholonomic constraint eliminates none?

Or are there exceptions

Ryder Rude

07:05

hi

Slereah

07:52

> We evidently must regard Time as passing with a steady flow ; therefore it must be compared with some handy steady motion, such as the motion of the stars, and especially of the Sun and the Moon ; such a comparison is generally accepted, and was born adapted for the purpose by the Divine design of God (Genesis i, 14).

Bible reference in an article

handan_toddler

hi

qwerty

@Slereah what are you reading :p

Slereah

@qwerty ia601604.us.archive.org/9/items/geometricallectu00barruoft/…

Tobias Fünke

08:10

good morning, everyone :)

qwerty

hello

handan_toddler

\o

qwerty

@Slereah published 1916. tsk tsk

Slereah

@qwerty 1690 actually

qwerty

haha

shouldve scrolled past the title

Ryder Rude

08:26

@Slereah i think the Bible might have borrowed it from earlier philosophers

handan_toddler

Separating the Science from the scientist @naturallyInconsistent he ends the book with a bang.

ACuriousMind

09:02

@Allie Depends on how pedantic you set up the question :P If you just say "n holonomic constraints", I could impose one constraint $f_1 = 0$ and then my other $n-1$ constraints are $2 f_1 = 0, 3 f_1 = 0,\dots n f_1 = 0$, obviously those altogether eliminate only 1 d.o.f., not $n$ and similarly obviously that's not what you meant ;P

handan_toddler

Separating the Science from the pedantry :P

ACuriousMind

what?

handan_toddler

re: the YouTube link

48 mins ago, by handan_toddler

Separating the Science from the scientist @naturallyInconsistent he ends the book with a bang.

ACuriousMind

I understand it's some kind of reference but I'm unclear on what you actually want to say

handan_toddler

09:17

I'm making a sarcastic joke about pedantry.

ACuriousMind

I think you and me have very different understandings of what sarcasm is :P

handan_toddler

Agreed.

Slereah

That book has "linelet" in it

Original latin for it was apparently "lineolis"

little line

handan_toddler

Ye Olde English gives me a headache.

Perhaps because I wasn't indoctrinated into Latin early in life.

qwerty

is old english supposed to be more Latin like? O.o

Slereah

09:29

it's not

That book was originally in latin

qwerty

@Slereah i know, i was asking handan_toddler the reason for their remark :P

handan_toddler

I've found out I'm wrong :(

> Old English is one of the West Germanic languages, with its closest relatives being Old Frisian and Old Saxon

I must be getting those headaches from overthinking...

qwerty

it's okay. it happens to all of us

ACuriousMind

That quote doesn't even explain anything, modern English is still a West Germanic language

The Latin/romance influence in modern English comes mostly via French, but it didn't turn English into a non-Germanic language

qwerty

apparently the bulk of our sk- words come from Norse

like skull, skin, etc

sky

John Rennie

09:41

@ACuriousMind British English is such a mongrel language I'm not sure you can still say it's a West Germanic language. It certainly retains many of the features of its original source but it has radically changed over the millenia.

handan_toddler

English isn't even the official language of England.

ACuriousMind

@JohnRennie You know, people like to say that, but English really just borrows words everywhere it goes. That's what all languages do to some extent, English just has travelled quite far. Syntactically it's still clearly a Germanic language, although compared to other modern Germanic languages it's lost more of the original case/verb form systems

qwerty

@qwerty even when I'm fairly confident about something, i usually phrase it as a question because it's much more polite, or maybe I'm confidently incorrect or misunderstanding what their point was. but sometimes it gets misinterpreted as not knowing altogether. i don't know if there's a better way though >.< ... but open to suggestions, as I'd rather not be misunderstood at all.

handan_toddler

Sorry for the confusion.

ACuriousMind

for instance, the strong/weak verb distinction and particularly the way the past tense of strong verbs is formed is one of the Germanic features which are very difficult for a language to pick up in the way it picks up vocabulary

qwerty

09:49

@handan_toddler no no, it's ok. it's just that something similar happened literally just before i logged onto hbar, at work :P

John Rennie

How much of the language has to change before you'd say it was a new language? Isn't that a matter of opinion?

handan_toddler

:: runs from the philosophy of language ::

John Rennie

As one who had to study Old English at school, it is utterly incomprehensible to a modern English speaker. Even Middle English is mostly incomprehensible.

ACuriousMind

@JohnRennie sure (I don't think anyone really claims you can draw exact lines between Old/Middle/Modern English), but I don't really think there's linguistic debates about whether or not modern English is a Germanic language - apart from the vocabulary all the other features are still just the Germanic ones

PM 2Ring

A language is a dialect with an army and navy

"A language is a dialect with an army and navy", sometimes called the Weinreich witticism, is a quip about the arbitrariness of the distinction between a dialect and a language. It points out the influence that social and political conditions can have over a community's perception of the status of a language or dialect. The facetious adage was popularized by the sociolinguist and Yiddish scholar Max Weinreich, who heard it from a member of the audience at one of his lectures in the 1940s. == Weinreich == This statement is usually attributed to Max Weinreich, a specialist in Yiddish linguistics...

handan_toddler

09:53

How much of Shakespeare did you have to memorize @JohnRennie

ACuriousMind

the incomprehensibility is just due to the large change in vocabulary + some particularly gnarly pronounciation shifts in English, not because something more fundamental about the language would have changed

John Rennie

Most of The Tempest!!!

handan_toddler

:O

PM 2Ring

So Swiss German is just a dialect because they don't have a navy. ;)

qwerty

@PM2Ring hbar conversation points seem to repeat xD chat.stackexchange.com/transcript/71?m=66685699#66685699

handan_toddler

09:55

LoL

qwerty

@ACuriousMind you just need to listen to dutch or frisian, I'm told, to figure it out.

John Rennie

I wasn't keen on any subject that wasn't science, but in retrospect being forced to study English was probably a good thing. If you get too focussed I think it can end up lessening your enjoyment of life.

Though I found it a massive pain at the time :-)

PM 2Ring

I love the sound of Dutch. But in written form, it looks hilarious. It seems to be pretty common with closely related languages that they look or sound a bit silly.

handan_toddler

No French, German, or Russian @JohnRennie

ACuriousMind

@qwerty Well, Dutch is (or at least was when it still existed) part of the West Germanic dialect continuum (English escaped by going to an island). So to a large extent, the boundary between Dutch and German is very artificial to begin with - there are many "German" dialects in the border region to the Netherlands that are more mutually intellegible with Dutch than they are with Standard German

qwerty

09:59

John Rennie

@handan_toddler I studied German and French for the UK O level exam. That was two years so I got reasonably good at both languages, though it was 50 years ago and I've now forgotten most of both.

ACuriousMind

But a Standard German speaker and a Standard Dutch speaker can only communicate with effort, it's not that they can not understand each other but it's also too much too say that they understand each other :P

John Rennie

This was pretty standard for UK schools in the 1970s. I don't know whether the languages are still studied in modern schools.

qwerty

^ @PM2Ring that reminded me of "ich bin kaputt" lol

Slereah

> However useful it may have been in practice, the concept of infinitesimal could scarcely withstand logical scrutiny. Derided by Berkeley in the eighteenth century as “Ghosts of departed Quantities” (1734: 59), in the nineteenth century execrated by Cantor as “cholera-bacilli” infecting mathematics (1893 [1965: 505], translated by Fisher 1981: 116), and in the twentieth roundly condemned by Bertrand Russell as “unnecessary, erroneous, and self-contradictory” (1903: 345)

lol

handan_toddler

10:03

The evils of dividing by 0.

PM 2Ring

@ACuriousMind How do you go with the various German dialects? A YouTube clip I saw recently claimed that they are mostly dying out due to to the prevalence of Standard High German.

ACuriousMind

yes, they're dying out, which is why the dialect continuum is more and more a historical thing rather than a description of current reality

Tobias Fünke

:d

ACuriousMind

Some regions have a very strong regional identity linked to their dialect (it's unlikely Bavarian or Swabian will leave us soon :P), but many dialects that aren't like that are being forgotten

Tobias Fünke

also eastern Germany

a lot of people still have a strong dialect, although I don't know how it will evolve in the future

qwerty

10:06

@Slereah i recently heard a claim that ancient greeks were like, what dyou mean you can add a bunch of infinitesimals and get anything finite? and that is why they didn't invent calculus. I don't know how true a story that is though lol

John Rennie

@PM2Ring I think that is probably happening everywhere. When my family moved to Somerset in 1969 I couldn't understand some of the old people because the English they spoke was significantly different from the BBC English I had grown up with. When I go back to Somerset these days the English I hear is standard English, albeit sometimes with a strong accent.

Slereah

@qwerty It is somehow true yeah

Like some greeks used infinitesimals

But Eudoxus said he was against it or something

handan_toddler

Archimedes was kind of ok with it.

Slereah

He was kind of okay with it

He proved some things with it but with the caveat that it is infinitesimal methods and therefore sspiscious

qwerty

what would be the key to convincing the ancient greeks that integration is possible?

Ryder Rude

10:09

an infinitesimal is greater than 0 but smaller than all real numbers >0

PM 2Ring

I guess it makes communication easier when a standard dialect replaces local dialects. But I hate the loss of cultural & linguistic diversity.

All of the weird & wonderful language quirks carry important information about how humans have learned to preserve and communicate information and world views. It's tragic for that stuff to be lost.

Slereah

@qwerty lots of work on the notion of infinites, I guess

handan_toddler

Can all Australians understand all New Zealanders?

qwerty

@Slereah I mean like conceptually was there something in particular they were missing?

Ryder Rude

Aaronson says free will is an empirical question

qwerty

10:11

@handan_toddler sometimes we make them say six for fun

handan_toddler

:D

PM 2Ring

@qwerty It didn't seem to bother Archimedes. His proof for the volume of the sphere is pretty impressive. But not easy to read, unless you're very good at 3D geometry.

Slereah

@qwerty I mean we didn't make calculus rigorous until the 19th century ourselves

It's not an easy thing :p

Tobias Fünke

@PM2Ring :( yes

Ryder Rude

i think epsilon delta stuff is really easy to come up with. it is more like the earlier generations didn't understand the importance of well defined things

Tobias Fünke

10:13

In hindsight most things seem easy

Ryder Rude

as soon as people understood that math needed to be objective and well defined, they were able to make it that way

qwerty

@Slereah i just like to daydream about what I would have to say to convince the people from an earlier time period of modern results xD

PM 2Ring

@handan_toddler Admittedly, some of the South Island accents can be difficult, even when you're used to the extreme vowel shifts.

handan_toddler

🤔 Hmm

Ryder Rude

earlier people conflated math with metaphysics. they thought mathematics rules came from the heavens

they didn't know that they could invent the rules

which is why so many debates on the parallel postulate or infinitesimals

and also imaginary numbers

qwerty

10:15

imaginary numbers are just so so badly named

Ryder Rude

they thought these things could only be valid if they were true in some metaphysical sense

handan_toddler

@qwerty 100% agreed 👍💯

Ryder Rude

once math was separated from metaphysics, its nature became well understood

handan_toddler

How about i-numbers?

qwerty

I believe Euler called them lateral numbers en.wikipedia.org/wiki/Complex_number#History

*Gauss?

handan_toddler

10:22

LoL "mental torture"

qwerty

hsm.stackexchange.com/questions/13333/… according to this reference euler also called them imaginary

PM 2Ring

@qwerty One of my nephews loves numbers. When he was about 10 I introduced him to imaginary and complex integers. I did it in reference to the number line and I called the imaginary integers "sideways numbers". He had no trouble understanding how multiplication by i gave a 90° rotation.

qwerty

@PM2Ring your nephew is lucky to have you as a mentor :)

PM 2Ring

Thanks. :)

Ryder Rude

u can also teach him.p-adic numbers

PM 2Ring

10:31

People used negative numbers for centuries before they were considered to be legitimate numbers in their own right. They were treated as just a bookkeeping trick. The usefulness & acceptance of complex numbers kinda forced the acceptance of negatives.

qwerty

similar story with 0 in some cultures

PM 2Ring

The ancient Greeks didn't even consider 1 to be a number, since there's only one of 'em. ;)

qwerty

this guy doesnt like irrationals en.wikipedia.org/wiki/…

once again the conversation returns xD chat.stackexchange.com/transcript/71?m=66978067#66978067

PM 2Ring

@qwerty Yeah. He's just down the road from me, assuming he still has an office at UNSW...

Speaking of irrationals...

in Mathematics, Jan 25 at 16:05, by PM 2Ring

Given any irrational real number $r$ it's possible to find a linear Diophantine approximation for any other incommensurable irrational $s$ in the form $z=ar+b$ with integers $a,b$ such that $|s-z|<\epsilon$ for any given $\epsilon>0$. I have a fairly simple algorithm to find $a,b$ pairs, based on the continued fraction convergents of $r$ and the extended Euclidean algorithm. But I'm not sure how optimal it is, and I'm curious about alternative algorithms.

I didn't get any verbal responses to that post (but I did get a star).

Eg, $-489030\sqrt{2} + 691596 \approx 3.141592685 \approx \pi$

handan_toddler

Have you @PM2Ring fully recovered from your health issue?

qwerty

10:45

@PM2Ring did you catch my message before I removed it? :)

PM 2Ring

@handan_toddler No. But at least I can now sleep for 4 hours or so at a stretch. It's not fun when you can't sleep for an hour...

I'm slowly improving, but still quite short of breath.

@qwerty Yes.

handan_toddler

Okay, take it slowly 🙏

PM 2Ring

A solution of $x^2 + 60592445159x - 164707342625 = 0$ is a good approximation of $e$, to ~24 significant figures. But you need high precision arithmetic to demonstrate that.

handan_toddler

@qwerty thanks for the link

qwerty

@PM2Ring take care and I hope you continue to feel better

PM 2Ring

10:54

Thanks

Ryder Rude

11:42

take care

Ryder Rude

13:03

Do you prefer a chaotic Feynman onion universe or a regular Feynman onion universe?

chaotic - entire theories have to get updated forever

regular - theories get updated forever but they all stay within a fixed framework

Signor Feynman

Honestly, I never liked onion that much

Ryder Rude

chaotic meaning - say, we go from QFT to string theory to something else unrelated to something that's not even QM to something else... Repeat forever

Signor Feynman

But I guess it's better than garlic

Slereah

@SignorFeynman Enemy of France

Ryder Rude

regular meaning - we go from standard model QFT to another QFT to another QFT ... Repeat forever

Signor Feynman

13:07

@Slereah Which makes me a good Italian :P

But the garlic thing makes me enemy of half this planet

ACuriousMind

I'm pretty sure Italian cooking is also full of onions and garlic, no? :P

Ryder Rude

which of the two ideas I have described would u prefer for the universe to be like

please answer

ACuriousMind

Signor Feynman over there just eating his spaghetti olio (he rejected the aglio)

handan_toddler

what?

Ryder Rude

i think garlic is better than onion

but anyway, Feynman's idea is about an onion

@handan_toddler i have described two ways the future history of physics could be. which way do you prefer

a chaotic onion is when we keep updating from one theory to another unrelated theory with entirely different structure

a regular onion is when we keep updating but it always stays in the same structure (like, say, QFT)

it is at its heart a question of how you would like the universe to be

handan_toddler

13:14

I believe my preference makes no difference.

Ryder Rude

yes. but U can still state a preference. i am not saying that ur preference will cause the universe to be that way

especially since we r talking about unknown physics. so it is okay to state a preference

handan_toddler

Sort of like the whole "learning styles" myth.

Ryder Rude

@handan_toddler it is not...

qwerty

@SignorFeynman you might get along with the Buddhists

and vampires

Count Feynman

Signor Feynman

@qwerty I mean, who'd fight with a Buddhist monk? :P

Ryder Rude

13:18

@ACuriousMind which idea would you prefer

ACuriousMind

@SignorFeynman the Chinese state? :P

Signor Feynman

@ACuriousMind Your knowledge impresses me, young one. I do not reject garlic completely, I just do not like to get a massive quantity of it. Spaghetti aglio e olio is the only exception, though :P

Fair point

handan_toddler

@RyderRude do you have an evidence-based reason for that belief

Signor Feynman

@ACuriousMind Yes, it is. Although, except a few dishes (like the one above and Pici all'aglione) it's usually there just as "background", not preponderant. On the other hand, some cuisines tend to be less forgiving with garlic. It happens a lot in Eastern Europe for example

Ryder Rude

@handan_toddler i think the learning styles myth is about different ways of learning

Signor Feynman

13:22

But I guess that keeps vampires away

qwerty

@RyderRude I don't think ppl have a preference

Ryder Rude

@qwerty but I do have a slight preference towards the regular onion. i think other people might do too

i think Carroll is def someone who wouldn't want the chaotic onion

he likes the say the universe is a wavefunction. he would be reluctant to the chaotic onion

Signor Feynman

I prefer shallot.

qwerty

I like caramelised onion

Ryder Rude

i think the people who need final answers go with the regular onion

Signor Feynman

13:25

I agree, qwerty, that would be a great onion choice for the structure of the universe

Ryder Rude

people who like mystery go with the chaotic onion

qwerty

researchgate.net/figure/…

onion shaped light cones are a thing

Signor Feynman

I guess you should never let hungry physicists write papers

qwerty

I imagine those as raw onions

Signor Feynman

This chat is so unhinged, I love that :P

2

qwerty

13:31

a former prime minister was mocked forever for biting into a raw onion like an apple

qwerty

13:47

this whole conversation reminds me of glass onion

m.imdb.com/title/tt11564570/quotes/…

User198

14:26

@SignorFeynman Spaghetti aglio oglio peperoncino top 3 ways to eat spaghetti for sure.

@ACuriousMind xD

Ryder Rude

Jurassic World Rebirth | Official Trailer

►

they have made another Jurassic park lol

Signor Feynman

14:56

@User198 there is no denying

Allie

16:08

@ACuriousMind Lol of course, and you could write that the constraint is 0 = 0 and that wouldnt reduce any dof either. In the case where the constraints dont imply eachother

ACuriousMind

@Allie Then yes, if you have n independent holonomic constraints, they reduce the number of d.o.f. by n

DIRAC1930

What are everyones favourite particles

Allie

And nonholonomic constraints can never reduce dof, right?

DIRAC1930

Mine is the electron

Allie

Electron because im a computational chemist :P

ACuriousMind

16:14

@Allie I wouldn't dare to be so general, since the usual definition of "non-holonomic" is usually just "literally not holonomic, i.e. not given by an equation $f(x) = 0$" but usually nonholonomic constraints are not d.o.f. reducers yes

Allie

I dont like usually

But im not gonna get lost splitting hairs here

Thanks

DIRAC1930

16:28

There is a new Veritasium video

What if you just keep zooming in?

►

Allie

16:50

I dont like his vibes

Idk what it is

Maybe it was the self driving cars video

DIRAC1930

Some of his videos I don't find interesting but most I do

He recently had a video on the action principle which you may find interesting as you were just doing classical mech

The Closest We’ve Come to a Theory of Everything

►

Signor Feynman

17:07

@DIRAC1930 Of course neutrinos

DIRAC1930

Lol I don't think I would have thought anyone would have said neutrinos

Ryder Rude

@DIRAC1930 photon

@DIRAC1930 i haven't seen it yet

looks like a great premise

Veritasium is the best communicator. he tells stories

DIRAC1930

The photon is pretty great

Tobias Fünke

17:23

Hello

DIRAC1930

I hope in my lifetime, people find out what inside an electron

ACuriousMind

That would be surprising, given that electrons are point-like without substructure to the best of our current knowledge, i.e. no one believes they have anything "inside"

Ryder Rude

@ACuriousMind why can't we know for sure that it is a point particle

DIRAC1930

Well don't people researching string theory implicitly believe that there is a substructure i.e. strings?

ACuriousMind

no, not really

strings are not substructures of particles in string theory

DIRAC1930

17:36

Well I hope that there is a substructure lol

ACuriousMind

Why? Why would you have any personal preference for whether electrons are atomic or not at all?

2

Either the electron has substructure or not, currently the evidence overwhelmingly points to "not", so the scientific position is just to believe that it has no substructure unless contradicting evidence comes in

Tobias Fünke

I don't believe in electrons anyway :)

DIRAC1930

How can there be that much evidence though? One would need to be able to view the electron at crazy high energy scales which one cannot currently do

ACuriousMind

@DIRAC1930 It's not only the form factors (though that is a big part - we should be seeing some indication the electron isn't pointlike already at low energies) Think of the history of the proton/neutron and how many weird things about them fall into place when you realize they're bound states of quarks and many of their decay processes operate on the level of the quarks and not the hadron. And then think of the total absence of things like that for the electron.

DIRAC1930

Yes but a substructure doesn't have to mean that the electron contains other particles. It could just be some stable structure that elucidates what an electron actually is

Or, I would be happy if there was an explanation behind the mass to charge ratio of an electron

ACuriousMind

17:48

I don't know what that means. With standard QFT there is no such notion of "structure". And if you actually hope that we discover a theory so different from QFT that it provides such a notion, you hid an extremely big hope beyond the small "I hope the electron has a substructure"

DIRAC1930

Yes I don't believe QFT is the final theory

Signor Feynman

18:28

@DIRAC1930 Think about it: they don't having boring EM interactions and they don't have that EW mess that QCD is. BIG EW

If I had to call a particle "cute" that would be neutrinos

DIRAC1930

18:56

@SignorFeynman EM interactions are not boring lol

Allie

Hiya tobias

Tobias Fünke

19:42

heyho

Allie

19:59

Im not a ho

At least not anymore

Signor Feynman

@DIRAC1930 I mean, QED is my favorite gauge theory because $\math{U}(1)$ is the best Lie group, but Electrodynamics is such a bummer. It has a classical version ewwww

Tobias Fünke

lol

DIRAC1930

20:17

I think QED is probably more interesting in a quantum optics context

Tobias Fünke

20:45

@Allie Do you still study DFT? :)

and have you had time to think about the natural orbital stuff?

naturallyInconsistent

21:03

@handan_toddler yay

imbAF

22:40

Do the group generators play the same role as basis element of some arbitrary space, for the group elements?

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