The h Bar

I found a great gif for next time drama breaks out:

@0celo7^

0celo7

12:49 AM

what

Q: Can I State a Thought About Physics and Ask for Comments

I'm promoting my new found meme.

I found another one, wanna see?

Anonymous

2:30 AM

Schrödinger's cat walks into the h-bar and doesn't.

4

Physics Meta

6:10 AM

0

I have what I think is an insight, based on a set theoretic analysis of the Riemann integral, regarding whether or not there are any physical variables that really are continuous, vs. discrete. For instance, in QM, energy is quantized but position and time are not yet known to be quantized. Howev...

discussion

6:24 AM

Possible Insight, Based on Set Theory, On Quantization of Position: The set of all integers is a countable infinity. The rational numbers are also a countable infinity but the irrational numbers are a non-countable infinity. You can make a one to one mapping of the infinity of all integers to the infinity of all rationals, and vice versa. You can even map the infinity of all integers to the infinity of all rationals that are between 0 and 1. The real numbers are the combination of the rationals and the irrationals and are represented by the real number line, such as the continuum of point…

Q: Is it possible for a physical object to have a irrational length?

6:36 AM

Your argument is surely only arguing that physical quantities cannot be irrational, not that they are necessarily quantised.

See for example:

8

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this caliper to measure any small object, would the caliper ever return an irrational number, or would the t...

mathematics measurements geometry

@JohnRennie Good morning John :)

Morning :-)

You had a bad interview?

Was it a job you really wanted?

Hi, well, even that they cannot be irrational is kind of a big thing and means that there are no physical variables that are truly a continua.

no, no interview. Do I sound cranky?

Oh, you are talking to Mr. Meurer

@David Yes

@JohnRennie Yeah, it was kind of the dream job going :/

And the interview was pretty horrible, I got blasted

But another interview, at another pretty cool company, went well, I think

And I have another one next week

6:42 AM

@David bear in mind that we physicists construct mathematical models that describe reality i.e. allow us to make predictions. All models are necessarily approximations and are eventually replaced by better models as we learn more. All models fail if pushed beyond their limits, and I would guess that arguing about whether physical quantities are rational or irrational is probably beyond the scope of the models we currently use.

@BernardoMeurer I had the idea you had a summer job lined up?

@JohnRennie Well, so did I, but I haven't heard anything from Waldorf in a while, which means I ought to be looking for other opportunities

What was the dream job?

@JohnRennie Thank you for your response. But there seems to be a contradiction by assuming that a variable takes on a continuum of values, but integration over that variable skipping the irrational ones. The link you provided assumes that position can have irrational values, so I think it is different than where I am coming from.

Car Hacker (literally that's the job title) at comma.ai

I interviewed with George Hotz himself!

It does look cool. Oh well. Was the interview hostile, or just that they asked questions you couldn't answer?

6:46 AM

Well, I wouldn't say hostile, but definitely "intense." They also asked a couple questions that I think are absolutely unreasonable to expect a CS undergrad to know

And I managed to figure those out too, but it did take me a while

My interview at standard.ai went much better, they even allowed me to go on a short rant about x86_64 and AVX512!

@BernardoMeurer :-)

Interviews work both ways.

They literally said "Tell us more about why you dislike x86"

If you go for an interview and they spend the whole time sniping you then you have to ask yourself if that is going to be a nice place to work.

And I asked "Are you sure you want this?"

And they said "We are positive"

Lol

(not exact quotes, but something like that"

@JohnRennie Well, Yeah, but I did learn more in the 30 minutes of Interview with comma than I have in some semester-long classes ;P

@JohnRennie But do you agree that it seems that Riemann integrals seems to skip over the irrational values of the variable of integration? I never learned that and think it is interesting and probably telling of something...

6:50 AM

@David no. I don't see how you can argue that.

@JohnRennie Could you please tell me where my reasoning went wrong, above?

The Riemann integral adds up intervals (areas) and those intervals contain the irrationals

x86 is great u jerk

but the function is never evaluated at the irrationals in calculating the areas.

Sam, I have a GR question for you (now is a good time to run away :-)

6:52 AM

@David The Riemann integral is defined over the Reals, which contain the Irrationals, what you are saying makes no sense

I never run away from a fight

@Slereah If you think x86 is great it's no wonder you're a physicist

Darn tootin

@Slereah Why is it that the solutions to the Einstein equation have a Lorentzian signature? Is it built into the equations? Can it have solutions that are Riemannian?

It is not built in the equations, no

The vacuum EFE could admit a flat Euclidian metric just as well as a flat Lorentzian metric

It's just built in the space of solutions

Or the initial values, I guess

6:57 AM

Hmm. So 1,1,1,1 is a solution of the vacuum equations?

Sure

The Christoffel symbols are 0 and so is the Riemann tensor

So $G = 0$

Any constant metric whatever the signature is a solution of the vacuum EFE

we just constrain the solution to be Lorentzian

that's why when you're writing a metric solution you always check the signature before solving the EFE

Otherwise anything goes

Even the degenerate metric 0

@JohnRennie Perhaps what I can say is that the Riemann integral, along an interval of the x axis, is not a generalization of a discrete sum, consisting of a finite number of terms, into "continuum sum”, that is a sum containing a non-countable number of terms. It is, rather, a generalization of a discrete sum, containing a finite number of terms into a sum containing a countably infinite number of terms.

That isn't true. We don't insist that the Riemann integral use only the rationals.

@Slereah Thanks. I don't know why this has never occurred to me before.

can be tough when the metric components change sign!

@David The opposite is true, the Riemann Integral only works as a summation over a set with countably many discontinuities, therefore although you can not-define it in a discrete manner, the summation, and the integral, itself must be done over an uncountable set, and therefore non-discrete

c.f. Thomae's function and it's 0-valued existing Riemann integral

@David If what you were saying was true, then it would imply Thomae's function isn't Riemann integrable --- which it is

The proof, IIRC, uses the Lebesgue criterion. Since the discontinuous set is a countable subset of R, it has measure 0, which implies the function is Riemann integrable

@0celo7 ^ Are you proud?

7:17 AM

@tatan Assuming the string lengths are the same, and the system is perfect, etc; I think it should read 0. Alas you better wait for someone who actually knows physics to answer you

I think it should be 100N as this case is same as that of the spring balance being attached to the wall (here one block is providing the reaction that the wall provides if one end is tied to a block and the other to a wall)...

Actually, come to think of it

?

100N sounds right; you can think of the scale in the middle as a spring; which measures force by length changes, which makes it a bit easier to think about

7:22 AM

Yeah... ofcourse its a spring balance

::goes back to doing category theory::

haha

what category theory are you learning?

(I am not rude.. plz note) @BernardoMeurer

@JoshuaLin Intro, reading Pierce's intro for computer scientists, I have some lecture notes too, and then I want to try Mac Lane

I'm trying to understand Topos Theory in the end

@tatan Oh, I didn't think you were rude :)

7:25 AM

;-)

Oh like category theory for compsci? I've never really understood how it helps lol tbh
Like.. type theory? Is that the right thing?

Apparently Cat Theory blends in with $\lambda\text{-calculi}$ somehow

Which, yes, in the end is a part of type theory

I've heard about homotopy type theory and like 'thinking about the space of statements, with paths in this space being logical deductions, and thinking about homotopy classes of these paths as different proofs' (thats probably really botched)

this is more like theoretical compsci though right?

ah, Category theory has very little to do with HoTT directly, afaik

Not "more like" it's just like :P

like day to day programming you, probably dont need category theory?

lol

actually wait; I heard some people saying like "category theory is helpful for haskell" (or maybe it was the other way around... hmm)

7:28 AM

Well, knowing CT might help you argue about some things, specially if you work with a functional paradigm :)

It's definitely both ways

Monads and Functors are all elements of CT

And well used in Haskell

wait wow really? dang

wait has pierce talked about Yoneda lemma? I've proved that thing like 3 times over; and I still don't have a mental image of what it's even saying

Yeah a monad is just a monoid in a category of endofunctors, which is part of CT!

He hasn't mentioned Yoneda's lemma yet

7:43 AM

@rob o/

7:55 AM

Last night dream, fell inside a black hole which has the following scenery

I then have 5s before whatever structure I am trapped in hits the singularity, and everywhere then gone white

@Secret Have you ever taken LSD?

nope

I'm not sure whether to say you should or you shouldn't

Why would anyone need LSD when there is quantum mechanics?

@JohnRennie If you do QM on the beach everyone thinks you're a nerd

8:02 AM

do my love of quantum mechanics caused all these weird dreams?

also, I found I kept dreamt about falling into a blackhole and dying that way recently, this is weird...

Absolutely. Quantum mechanics is destroying your brain.

It does that.

I honestly think QM is worse than LSD for your health

An LSD trip ends eventually :-)

Hybrid: Polaris

►

There might also be a possibility to do with the stuff I listened to recently, which is distinctivey unhuman

Balarka Sen

8:18 AM

@0celo7 LOL

Jesus

8:39 AM

@BalarkaSen What are you going to get me for my birthday?

@BernardoMeurer tuberculosis

I'm Brazilian, I already have that

@Slereah Do you know algebra?

8:55 AM

that's a pretty broad question

Namely, what's the signature of an algebra?

Is it just the operations defined within it?

"In universal algebra, a signature lists the operations that characterize an algebraic structure."

apparently so, yes

i.e. the operations that characterize the algebra

Oh

Dope

Signature (logic)

In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures are used for both purposes. Signatures play the same role in mathematics as type signatures in computer programming. They are rarely made explicit in more philosophical treatments of logic. == Definition == Formally, a (single-sorted) signature can be defined as a triple σ = (Sfunc, Srel, ar), where Sfunc and Srel are disjoint sets not containing any other...

yeah, I've just grown distrustful of Wikipedia for things

9:11 AM

do the usual trick

Go to the article

check the bibliography

Almost forgot, last night dream also have a scene where a woman fancies an english gentleman, but the gentleman has no feelings for her. He then said that he is sorry he cannot have dinner with her, but perhaps they can catch up by having something spicy instead

@Secret That's me and @JohnRennie's relationship

He's been promising to make me spicy curry for ages

The next scene showed something that looks like a shopping list contain at least 6 lines, which the woman deduced based on there are no free slots and that she don't eat spicy food, deduce in proposition logic style that this is basically the gentleman's extremely convoluted way of saying no

^ What

-_-

9:21 AM

@Secret What you wrote makes literally no sense

I feel like I'm reading JS source

no offence intended, pal

@Cows Given how cocky your bio description is, I'd expect that Java's memory model would be something you can decipher while juggling chainsaws and playing Flappy Bird on your toes

Put it simply, the gentleman said "they will catch up having spicy food". But the problem is that the context of this respond can never be fulfilled

because she don't eat spicy food nor there are actually anymore free time

so in other words, that's a "no" in disguise and the gentleman knew that when he made that response

For some strange reasons, my dreams are very good at finding very convoluted ways to kill me or other people, or to reject or to put forward a plan

Yup, sounds like John R :P

this is in contrast to reality where things are a lot more straightforward

9:24 AM

@Cows But to answer your question, no it does not touch the heap. As in most other languages primitive allocations are done on the stack. If you tried to malloc some memory, or whatever the Java analogous is, that would happen on the heap. Some languages provide means for you to make small vector-like structures on the stack, like Rust's SmallVec, since stack access is significantly faster.

@skullpatrol Well, I believe Johnrennie is nicer because even when he made those englishman responses, it is still direct enough in that you don't need proposition logic to deduce he is saying no in a convouted way

@Secret you might say that but I couldn't possibly comment

indeed

Since when do beliefs have anything to do with dreams?

I have no idea, a lot of things in my dream seemed to have no diret real life analogue

in paritcular, why is the dream so hellbent at killing me and my friends?

9:30 AM

I'm just saying, it's not uncommon advice to say, "don't take your dreams too seriously."

well, the only dreams that are useful to me are the idea dreams, but they are not as common

Unless, of course they are recurring nightmares.

As far I knew, my dreams have many recurring themes, but never actually recur.

and there are no sequel dreams eithe (dreams that continues where the last dream left off)

I'd pay attention to the recurring themes then, pal :-)

well as far I knew, death of my friends, myself and my family is one of them, sometimes video game style in that there is some notion of "lifes remaining"

In particular, I have a lot of dreams recently that involve me falling into a black hole and then killed by speghettification or hitting the singularity

Anonymous

9:36 AM

@Secret "a lot of things in my dream seemed to have no direct real life analogue". Yes, often dreams have no connection at all with the real world, and not even related to what you were thinking in your conscious or subconscious mind. I have experienced that too. It's pretty much a myth that dreams always have something to do with real life. I think this issue is well discussed clinical psychology.

Anonymous

Tbh, I find dreams to be very weird, and if given a chance, I'd like to learn more about this area of psychology.

well my dreams used to be a lot more traceable until that week long visit 2 months ago by one of my close friends. Somehow, the emotion of reunion have altered my dreamscape completely, as if it has undergone a phase transition

Anonymous

@Secret Maybe keep noting them down. You might be able to connect the dots in the future. :P

Sublimation?

I have been logging my dreams for 8 years already, I just don't have enough time to do a full analysis

But so far, my dream seemed to have undergone at least 6 phase transitions

Anonymous

9:41 AM

@Secret It would surely be an interesting case study

Anonymous

Maybe, discuss it with a psychology department professor, if you ever get the chance/time.

will see if I can catch up with them

Anonymous

@Secret Heh, same here I guess. Previously I only used to have nightmares.

Ask on CogSci Stackexchange

Anonymous

There are some interesting questions here: psychology.stackexchange.com/questions/tagged/dreams