The h Bar - 2023-02-08 (page 2 of 3)

« first day (4479 days earlier) ← previous day next day → last day (451 days later) »

7:00 PM

that you can post like three sentences and I apparently have to do multiple hour analysis in order to understand what you mean when I'm reasonably well-read in philosophy means it's unlikely I'll be able to follow anything else you say after that quickly, either

But I gave Terrance deacon as a reference and he's a neuro anthropologist

Also apologies I suspect the real problem is I don't spend enough times with humans

@MoreAnonymous Yes. Why are we calling this a "system"? What exactly is a "phenomenon"? See, usually we start in epistemology with an analysis of what the relationship of sensual information (what I see, what I hear, what I smell, etc.) to things such as "a phenomenon" is

e.g. Hume thinks everything comes from the senses, while Kant thinks we need some intrinsic pure reason to even be able to organize sense data into things like distinct phenomena

and is an entirely internal experience, e.g. a dream, or doing math in my head, a "phenomenon" I "experience" in your sense?

that's a distinction likely to matter if what we want to do ultimately is discuss things like the relation of mathematical concepts to reality

According to classical Husserlian phenomenology, our experience is directed toward—represents or “intends”—things only through particular concepts, thoughts, ideas, images, etc. These make up the meaning or content of a given experience, and are distinct from the things they present or mean.

From Stanford (I agree with this)

but you also didn't really say what question exactly we're trying to tackle here so maybe I'm trying to interpret this entirely through the wrong lens

Question: is metaphysics meaningless as concluded by catnap?

Autocorrect :(((

@ACuriousMind u need to know how Terrance thinks of the world to understand the answer to this

7:08 PM

and why would I be interested in discussing Carnap, who was in some sense the "last" of the positivists, when I've repeatedly stated I (and the modern scientific method more broadly) are more on the side of Popperian falsificationism?

Ah ... I thought u thought metaphysics was meaningless (and sided with slereah)

oh, I do

Did I say such things

My bad

Didn't u recommend me a book of carnap?

@Slereah

There are many things in it

7:09 PM

He just complained that Popper wasn't the start of epistemology and that one might as well start with Carnap :P

@ACuriousMind then the question is relevant?

Ah okay my bad

@Slereah I thought u agreed with all of it ://

just because logical positivism isn't the best doesn't mean nothing in there is of use

@MoreAnonymous I mean, yes, the question "Is metaphysics meaningless?" is something we can discuss. So we need to first establish what "metaphysics" and "meaning" means.

My bad misread your intent

it is a nice enough books on logical foundations of physics

Plus it's like

A lot of the issues involved with that whole thing was trying to make everything like physics

But for physics itself it's mostly fine

7:11 PM

@ACuriousMind metaphysics is a sociological endeavour that aids the movement of a symbolic classification system to a prediction system

For instance, the sense in which I answer this question with "yes" is in the following: Meta-physics are non-falsifiable statements about reality (explanations or interpretations of physics that themselves are not directly testable), and it's meaningless in the sense that it is impossible to assign a truth value to it with any confidence since by the definition of falsificationism we generate "truth" (or confidence in "non-falsehood", rather) by testing predictions

if you define "metaphysics" or "meaning" differently, we're not so much disagreeing as talking about incommensurable things

@ACuriousMind I don't think meta physics is non falsifiable

@ACuriousMind Do you assign a truth value to verificationism

If it does not aid in scientific discovery

How does one explain why metaphysics influences science in the correct direction versus no metaphysics

The empirical probabilities can back me up here

@Slereah not really

but I see where you're going with this :P

@MoreAnonymous I don't even know what that claim means

7:16 PM

@ACuriousMind It's the oldest trick in the book

So basically if I have physics without the aid of metaphysics

you obviously use metaphysics to mean something different from what I mean, but you have given me no clue as to what that something different is

It will progress slower as to with the aid of it

What do you mean by metaphysics?

also "metaphysics" is a pretty broad term anyway

Fair

7:18 PM

@MoreAnonymous as I said, non-falsifiable statements about reality

For all we know you're talking about aesthetics!

the unloved child of metaphysics

But the statements u make like metaphysics is meaningless is falsifiable

?

in what I said, it's essentially a tautology

because I defined both in terms of falsifiability, I'm just saying "non-falsifiable things are non-falsifiable" :P

you can disagree with these definitions - and you apparently do - but you still haven't presented any alternative definitions

Im gonna ask what do you mean by meanin?

> it's meaningless in the sense that it is impossible to assign a truth value to it with any confidence since by the definition of falsificationism we generate "truth" (or confidence in "non-falsehood", rather) by testing predictions

already said that

7:21 PM

Maybe we should talk about aesthetics

Is physics beautiful

@ACuriousMind yes but empirical probability does do this to some extent

@Slereah no, I hate it :P

Its heuristic but who cares?

once again I have no idea what you mean. What "empirical probability" are you talking about and what does it have to do with metaphysics?

I mean what do u mean by metaphysics?

7:22 PM

I've already answered that twice

I also thought I answered it

11 mins ago, by More Anonymous

@ACuriousMind metaphysics is a sociological endeavour that aids the movement of a symbolic classification system to a prediction system

Scrolling up

This?

11 mins ago, by More Anonymous

@ACuriousMind metaphysics is a sociological endeavour that aids the movement of a symbolic classification system to a prediction system

Ignore

yes but I have no idea what you mean by "symbolic classification system " or "prediction system" since apparently I have to watch a 3h video to understand even what the word symbol means

Is the equivalence principle metaphysics?

(i like to think with examples)

extremely vague question because "the equivalence principle" can mean a lot of technically different statements

@ACuriousMind the book might be longer :p

@ACuriousMind acceleration is locally indistinguishable from gravity

7:25 PM

when doing stuff like this it's always useful to pick the simplest example you can think of

Been reading gr a bit here and there :p

Its also a recent example

In some sense

Acceleration is indistinguishable from gravity only at a single point, which I don't think is measurable

Good

So it's not falsifiable?

So for instance, a metaphysical belief about good old Newtonian mechanics would be something like "The laws of Newton objectively exist and are not just tools used by humans"

@Slereah can't we stick to this. Its obvious u have the edge here and understand things better

?

7:28 PM

I mean you can do a lot of nitpicking of a statement in many directions

points are probably not a meaningful notion experimentally

Yes but I already have planned my line of attack with that one

But also it's probably true within experimental precision, and if we can't detect a difference, maybe it's true!

Awww slerah don't beat me to a punchline

also how do you check an acceleration

;p

7:29 PM

You need to compare it to a free motion

by metaphysics I do not mean statements that are untestable merely because they're idealizations or whatever

Which requires assumptions that certain bodies are in free motion

@Slereah observables in gr???

@ACuriousMind so the equivalence principles truth value is?

I mean yeah, but there's a lot of hidden assumptions in between the math and the real world

the statement "an observer can't distinguish acceleration from gravity" isn't metaphysics unless it's impossible to come up with an experiment that could in principle show they're different

the only problem here is that "acceleration" and "gravity" might only be defined relative to the theory

7:31 PM

Well what does "in principle" mean

If you're talking about an experiment that could never actually be performed, is it really physics

You don't even need very fancy theories for that problem, really

Does anyone know for which $Z$ Moseley's law holds? Also, in the article it says that the square root of the frequency of the emitted radiation is approximately proportional to $Z$, however, I assume this only holds for $K_{\alpha}$ lines, see here.

Like here's a very basic one : what's a straight line in (physical) geometry?

@Slereah "never" due to limits on experiments the theory itself predicts or due to limitations on practical experiments

@ACuriousMind can we assume for sake of discussion it is so?

That: experiment cannot distinguish?

I mean...yes?

7:34 PM

Alright proceeding feel free to accuse me of sleight of hand

@schn Yes, Moseley's law is for $K_\alpha$ lines

Now did this belief in assigning a truth value of 1

Aid GR?

I have no idea what that question means

(regardless of what the actual truth value is)

presumably the equivalence principle is just part of/a prediction of GR

7:35 PM

So basically einstien thought the equivalence principle was true and developed ge

"gr

You got the casual order wrong

I did not claim a causal order

Ah okay

I don't care how someone developed a theory

But your "metaphysics is meaningless" statement cannot describe this phenomenon then?

what does any of this have to do with metaphysics?

7:37 PM

Equivalence principle the specific statement made is considered metaphysics

And I already told you my definition of metaphysics

@ACuriousMind Hi, i wanted to ask something that yesterday I didn;t fully understand. How is the statistical ensemble (which is an abstract concept of having N identical copies of the same system) tied to the phase space of a system?

So I'm not sure if this is logically equivalent

also you're talking philosophy, you don't need to use 1 for truth values :p

But it sounds like what ur saying implies the equivalence principle is meaningless

This isn't CS

7:39 PM

21 hours ago, by ACuriousMind

@imbAF classically you represent the ensemble by a probability distribution on phase space, quantumly by a density matrix on Hilbert space

Since most people consider it a subset of metaphysics

@MoreAnonymous I didn't agree that the equivalence principle is metaphysics

@ACuriousMind so I guess $Z\geq 3$, since lithium should have a $K_\alpha$ line.

so, a point in phase space= one of the indentical copies of the system?

@imbAF no, not at all

7:40 PM

Fair but I don't see for argument sake why it can't be considered. Feel free to tell me where my slight of hand is. U can replace equivalence principle with theory X

I have no idea why you think it's metaphysics

If phase space is some sort of mathematical concept of A dynamic SYSTEM, I don't get where the ensemble,a bunch of identical copies of the system, comes into play

Its more helpful when u tell me what's lacking?

@imbAF consider an ensemble of $N$ dice that are being thrown. We assume the dice are fair and being thrown randomly. So each die has a probability $1/6$ to land on any of the sides. The state space of a single die has 6 points (the 6 sides), but we still can talk about the frequency of outcomes of the ensemble with a probability distribution on that space of a single die, i.e. $p(n) = 1/6$

30 mins ago, by More Anonymous

@ACuriousMind metaphysics is a sociological endeavour that aids the movement of a symbolic classification system to a prediction system

7:43 PM

@MoreAnonymous look we can go in circles all you want but if your problem with my statement that metaphysics is meaningless is that you neither agree with my definition of metaphysics nor my definition of meaning then I don't know what purpose you think this discussion has

maybe with your definitions "metaphysics" isn't "meaningless"

why would I care, and conversely why would you care that I define these things differently?

Okay here's what I see:

what is the meaning of meaning 🤯

Metaphysics is meaningless

And meaningless is that which can't assign a truth value to

U define metaphysics as non falsifiable statments

yes, and I'm using falsificationism where confidence in the "truth" of a statement is generated by it failing to be falsified, i.e. there are observations where the statement implies a specific outcome and that's the outcome we actually observe

so this is a tautology: We cannot by definition generate confidence in the truth of a non-falsifiable statement, by definition statements for which we can't do that are meaningless, hence metaphysics is meaningless

of course you can simply choose to define either of these two words differently and then "metaphysics" might be no longer "meaningless"

So naively I can't disprove u since this is logically consistent however this does not tell me is what is metaphysics as since I can say ... But then to claim that this ant relevance to anything like the equivalence principle or many worlds (for that matter) is beyond me

Ignore this does not tell me what metaphysics is

7:47 PM

a meaingful discussion about this would be to argue why either my definition of metaphysics or my definition of meaning isn't useful

@ACuriousMind agreed

or you have to argue that falsificationism itself is the wrong scientific methods

but just saying "I disagree, here's my definition of metaphysics and in that definition you're wrong" is rather useless

No I asked for an example cause when u commit to an example I think u overreach

though admittedly a lot of low-quality philosophical discourse does look like that

I only believe in divine revelation

7:49 PM

@Slereah oh tell me prophet :p

"but we still can talk about the frequency of outcomes of the ensemble with a probability distribution on that space of a single die, i.e. $p(n) = 1/6$" is there a reason why we would focus on the probability of an outcome for the ensemble? Since we mostly want to focus on a system, and not N copies of it ? Is there a benefit?

I'm afraid you have to do the journey yourself

@ACuriousMind I'll pass on meta conversation conversations for later

@Slereah the tao of slereah :p

Just read the Lesser Keys of Salomon

Plenty of demons are specialized in astronomy

@Slereah somewhere i can believe u have read it

7:51 PM

When you go back far enough in time, the difference between science and magic kind of blurs I fear

Newton discovered the philosophers stone!!! Its a conspiracy that he didn't :p

I mean magic contradicts first law of thermodynamics, how's the line between the two blurry ?

@imbAF what does it mean to focus on a system?

Okay I gotta sleep 😴

I'll bounce in a while

@ACuriousMind would u like to continue another day?

Ancient greek science people tended to have very broad worldviews in their theories

7:53 PM

@ACuriousMind Well, we usually focus on a thermodynamic or a system, most of the times,no?

About nature, the gods, the human soul, etc

@imbAF if you're saying you just want to focus on the "probability" of the system to be in a specific state, can you define what you mean by "probability" without talking about an ensemble of identically prepared system?

Observe the same one system N times

or N copies at the same time

the latter is the ensemble

observing $N$ copies at the same time is talking about the frequency of outcomes in an ensemble, is it not?

it is

7:54 PM

so why are you objecting to me using that connection between the notion of "probability of outcome for a single system" and "frequency of outcome for an ensemble of identical systems"

(if you were a ::gasp:: Bayesian you'd have objected much earlier :P)

I am not xD

I don't know why I objected

I'm just using the standard frequentist definition of probability

ahaa

The only thing that I cannot link

so hold on

the phase space pdf is the ensemble ?

or I am making no sense

@imbAF are you asking why are time averages and spatial averages the same?

No no

7:57 PM

Ah okay

I'll try my best to put it into words

Just checking.

@imbAF with the probability density you can compute probabilities for subsets of states (remember a single point has zero probability!), and these probabilities are the frequency with which a state in that subset occurs in the ensemble

I haven't fully understood what you just said, but one thing

isn't the computation of the probability with the help of pdf, the probability of the system occupying a microstate that belongs to the region, in which we integrated?

yes

7:59 PM

Ok

and we just discussed that these two ways to look at a probability are the same, did we not?

which two ways?

"a probability is the probability of a system to be in a particular state" and "a probability is the frequency with which that particular state would occur in an ensemble of the systems"

Frequentist and a theoretical prediction?

as I said, the latter is essentially the frequentist definition of what the former means

unless you're a Bayesian these are literally the same thing

8:02 PM

Does anyone know if the $K_\alpha$ line of lithium has ever been determined experimentally?

I can see the similarity definitely, I am simply working something in my head, a sec please

I don't see this any different from saying a dice should show heads one sixth of the time and then rolling it a million times and calculating the empirical probability?

Yes I understand the frequentistic probability

empirical frequency

basically the mean, if I can say so

No

I can't say so xD

So

8:06 PM

So do rae me sa fa lo :p

fa so la si do xD

@imbAF there we go!

If we would integrate the pdf for an arbitrary region, and the computed probability, obviously, one, then by upholding to what this statement says: "with the probability density you can compute probabilities for subsets of states (remember a single point has zero probability!), and these probabilities are the frequency with which a state in that subset occurs in the ensemble", then there's 100% probability that a state in that subset (region of integration) occurs in the ensemble?

why is the result of that integral "obviously one"?

it's only obviously one if you integrate over the entire phase space, not just a subset of it

well, I am constantly assuming the MCE, where \rho is non zero somewhere, and zero elsewhere

and this somewhere region, if you integrate over it, you'd get one

8:11 PM

Me sleeping guys

Thanks @ACuriousMind for the conversation:)

@imbAF sure

but that's just saying "of all the possible states, the system is in one"

and, in "ensemble terms": "every state in the ensemble is one of the possible state"

quite a tautological observation :P

Well, this is what we get from the statement made above, in addition to the fact that we are having a MCE

because as you said

Actually

but you could also integrate the pdf over some region that's smaller than the "somewhere"

could you?

and then you'd get probabilities that are neither one nor zero

8:14 PM

ahaaa

ahaaa I see

this is math, we can integrate functions over any subsets we want!

yes I know xD

(pls don't pull out non-measureable sets Slereah)

One thing, for clarification

as we said, the probability of a point (in phase space) is zero

compute probabilities for subsets of states

so you can't make probability claims for a single state

but for a set of them

I see

And, if , as an example, you get x value as the probability of a subset of states

then what I can say is that the system can occupy one of these states with x-value probability

or am I expressing myself wrong>

no, that sounds fine to me

8:21 PM

But no claims for individual microstates

probability wise I mean

no claim or zero

really a question of your statistical philosophy which of the two is "right" :P

I mean, eventually you end up in that exact spot

One final thing

yesterday you said probability distribution

I asked whether you meant phase space pdf

and you said, the same thing

Here: en.wikipedia.org/wiki/Distribution_function_(physics)

I found about what you were talking

I have one question

In molecular kinetic theory in physics, a system's distribution function is a function of seven variables,
f(x,y,z,t;v_{x},v_{y},v_{z}), which gives the number of particles per unit volume in single-particle phase space.

This is what I find so abstract and hard to comprehend

First of all, can I say that the phase space is an abstract mathematical concept?

Would this be a somehow correct assessment?

if you want to :D

i mean

it's not a physical thing

is this gonna descend into a philosophy discussion, too?

8:27 PM

or a biological

No it won't

100% it wont

but sure, the phase space is an abstract concept

Ok, then

is phase space always a manifold

hopefully

In the statement above, we have a system, which is comprised of a single particle. As any system, we can creat/generate/represent it's phase space, where in it's phase space, the "volume" is filled with points, which are the microstates. So how does the probability distribution, as the statement claims, give us the number of particles per unit volume in it's phase space? Phase space=abstract non existen concept, the particles are physical, real objects.

The phase space is filled with points(microstates), not physical objects, in this case particles. I was also going to add, why multiple particles, when we are talking about the the phase space of a single one, but I guess, these is the ensemble of our system,

8:32 PM

XD hopefully as in presumed to be the case but not proven?

you promised this wouldn't be a philosophy discussion :D

but it isn't

@SillyGoose serious answer: Yes, the usual general definition of "a phase space" is as a symplectic or Poisson manifold

there is a claim made, about physical objects in a abstract mathematical object, wth is that even?

@imbAF math in physical theories makes statements about physical objects all the time

that's what a theory is

8:33 PM

phase space is fillied with points, that represent physically a microstate, not with physical particles

but I'm a bit confused what you mean by the "probability distribution, as the statement claims, give us the number of particles per unit volume in it's phase space!"

who claimed that?

so,what? the phase space of a single particle system, is filled with physical/material particles, instead with points, that are microstate?

no one is saying that "phase space is filled with particles"

well

\rho which gives the number of particles per unit volume in single-particle phase space.

or, well, so far I haven't been saying that, at least

@imbAF where does that come from?

8:34 PM

Distribution function (physics)

This article describes the distribution function as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, f ( x , y , z , t ; v x , v y , v...

first sentence here

okay, so what they mean is just my statement about the distribution of the probability density encoding the frequency of the states in the ensemble

in the language we've used so far, you could phrase that as "gives the number of systems in the ensemble per unit volume"

any distinction between these two statements is really purely philosophical, we're not disagreeing about the physical meaning of the probability density here

and this number of system

systems

belonging to the ensemble

I assume must be equal to the number of points in the unit volume in the phase space?

see that's why I don't like this language because it makes things awkward :P

what does "number of points in the unit volume" even mean?

My way of expressing things?

no, this is indeed common language among some physicists

8:40 PM

well the space in phase space is like a fluid

this fluid is made out of something

@ACuriousMind from earlier, then is the statement unitarily varying choice of hamiltonian $THT^{-1}$ and $T'HT'^{-1]$ with the same spectrum redundant?

a volume is a subset of continuous phase space that typically contains infinitely many points (e.g. any subset of $\mathbb{R}^3$ with non-zero volume contains uncountably many)

in the phase space, this something is a point

because since the hamiltonians connected by such unitary transformations, it is implied the hamiltonians are isospectral?

@imbAF now we're doing either philosophy or weird analogy again

@SillyGoose depends on whether there are other things beside the Hamiltonian spectrum you care about or not

e.g. $H=x^2$ and $H=p^2$ have the same spectrum, but certainly it's physically relevant whether the eigenstates of the Hamiltonian are eigenstates of the position or of the momentum operator

8:43 PM

hm it seems in this paper we only care about whether the hamiltonian is local or not which it is argued can be recovered by the spectrum usually

then you probably don't care

what's the question?

if calling hamiltonians connected by unitary transformations also isospectral is redundant

ohohoh

i see

"gives the number of systems in the ensemble per unit volume"

the next part of the paper is about dualities XD where hamiltonians may have the same spectrum (and thus both be local) but not be related by unitary transformations and so are not equivalent

per unit volume in the phase space?

8:44 PM

okay so itt is necessary because same spectrum does not imply related by unitary trans

@imbAF the "per unit volume" is just because it's a density, right?

but the other way around is true i see

the relevant thing is this thing assigns probabilities to volumes when we integrate it

@ACuriousMind yes

so we say that the thing we integrate is "probability per unit volume"

8:45 PM

mayn this paper is v cool :D

as we discussed probability and "number of systems in the ensemble in a state" are the same notion, so this means we have to say something like "number of systems in the ensemble per unit volume"

@ACuriousMind which is what the pdf is

I don't really like that kind of phrasing but I also don't see why it's necessary to talk about it

the probability density is used to assign probabilities to regions

I don't really care what anyone thinks the density itself "is"

same like mass density

or charge

But let me read what you wrote xD

sure, what does "charge per unit volume" mean?

8:47 PM

the amount of charge located in a unit of volume

what does that means

like, say I have $\rho(x) = 1/2 C$ in some volume and 0 outside that volume

take a point on the boundary where it is just non-zero.

how much charge is stored, in the space, that we consider as unit of volume, depending on what our definition of length is

I guess

what are you saying when you're saying "at this point there's 1/2 Coulomb per unit volume"

I think you're subjecting the probability density in phase space to much more scrutiny than any other density :P

I am just trying to make sense to all the mess that statistical and quantum statistical mechanics is

I am trying hard to have a fundamental understanding

and I am extremely aware , that my brain is just superficially touching on it, in difference from before, when I could think deeper, if one can say so

Must have been tough to be a math nerd in antiquity if you weren't into astronomy

A lot of it was astronomy stuff

8:58 PM

@ACuriousMind
as we discussed probability and "number of systems in the ensemble in a state" are the same notion, so this means we have to say something like "number of systems in the ensemble per unit volume", should you in the last statement say number of systems in the ensemble in a state per unit volume, or no?

probably?

that's why I said this kind of language is awkward

and I prefer to just think about the probability density as something that assigns probabilities to sets of states

« first day (4479 days earlier) ← previous day next day → last day (451 days later) »

Transcript for

Feb '238

The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

site design / logo © 2024 Stack Exchange Inc; legal

mobile