The h Bar

12:00 AM

Apparently Carroll's book states that $dx^1\wedge...\wedge dx^n$ is not a n-form but a tensor density because upon a coordinate transformation it is expressed as $(\mathrm{det}\frac{\partial x}{\partial y}) dy^1\wedge...\wedge dy^n$. This is just a normal n-form transformation

Amit

volume forms are all n-forms

Mr. Feynman

Sure

Amit

well you wrote "..*but* a tensor density*

Mr. Feynman

I'm quoting Carroll

"Carroll's book states that [...]"

Amit

ah, no quotes i didn't understand that lol

ACuriousMind

12:09 AM

@Mr.Feynman what is the definition of a "tensor density" here if not an n-form?

Like, a density is something you can integrate over a volume to get a number. An n-form is something you can integrate over a volume to get a number. Not sure what distinction Carroll is trying to draw here, to me these are two words for the same concept

Mr. Feynman

This (according to Carroll)

Amit

i think it may just be the coefficient

Mr. Feynman

@ACuriousMind well, for non oriented manifolds the two things are indeed different

ACuriousMind

ahhhh

Mr. Feynman

Also, the highlighted result is different from how they define a density as there should be both the determinant and the various $\partial x^h/\partial y^k$ factors

Imo they just made a mess to express the simple fact that $dx^1\wedge...\wedge dx^n$ is not form-invariant under coordinate transformations and I wonder why such thing was never corrected in so many years

Amit

12:18 AM

Dirac takes a page and a half in his book to cover this lol

ACuriousMind

there's an annoying ambiguity in the language here

Mr. Feynman

Do you mean in the book?

Amit

This is the one case where perhaps the good old Jacobian is more intuitive than the fancy stuff

Mr. Feynman

Rigorous differential geometry is more intuitive

The pull back of a n-form between two n-manifolds makes the jacobian determinant "magically" appear

ACuriousMind

when the text says that $\mathrm{d}x^1\wedge \dots \wedge \mathrm{d}x^n$ is "not an n-form", it means indeed that this is not a coordinate-independent definition of an n-form.

Mr. Feynman

12:23 AM

That is, it's not form invariant

And we need the Riemannian volume form to make it form invariant

ACuriousMind

this is a common turn of phrase - people often also say e.g. that the Kronecker with two indices on the same level $\delta_{\mu\nu}$ is "not a tensor"

Amit

yeah it's probably a physicist thing. "not a vector", etc. lol

Mr. Feynman

@ACuriousMind Oh my, I hate this terminology :P

Amit

it's too long to write every time "this vector does not belong to the vector space we're interested in"

ACuriousMind

and the text is also "right" that $\tilde{\epsilon}_{\mu\dots}$ whatever is a "tensor density"

Mr. Feynman

12:26 AM

That is indeed ok

ACuriousMind

but I also agree that none of this matters at all, the point is just that $\mathrm{d}^n x$ isn't a coordinate-independent definition of anything :P

Mr. Feynman

I sent the picture as a comparison to show that the trasnformation was different from that of the n form

Aug 17, 2022 at 20:41, by Feynman_00

Talking about GR, my program has no differential geometry course, that's why I'm studying it. Next year I might suffer during the brief differential geometry introduction in the GR course

Amit

@Mr.Feynman Cool so my education is still lacking in that regard, I thought the tensor density is pulled out of a hat (or at least out of a volume form)

ACuriousMind

the text isn't wrong as such but this is a prime example of why thinking about diff. geo. entities primarily in terms of "how they transform" isn't always useful

Mr. Feynman

The pullback was just a fancy way of saying things here, you can just transform each $dx^i$ piece as you know and then take out a permutation sign from the n-form. The prefactor is the definition of the determinant

@ACuriousMind More than wrong I would say kind of sloppy in this bit(?)

ACuriousMind

12:30 AM

if this was written by a mathematician, sure

for a physics text this is par for the course

Amit

ahh yes, and then I remember you have to compensate for that by 1 over the determinant so that the integrals be equal in overlapping charts, something like that

Mr. Feynman

@ACuriousMind Alright, I'm being a picky eater here :P

ACuriousMind

like, if you demand "non-sloppiness", you have to go to the mathematicians

Mr. Feynman

@Amit yes, you do that by introducing the Riemannian volume form

Amit

then the next step is partition of unity, those scare me a bit

Mr. Feynman

12:33 AM

@ACuriousMind I felt like doing that here because this is one of the cases where being more accurate would have taken the same space :P

Amit

when you need to cross a boundary of charts when integrating... it's like the closest thing you can give an integral to a passport

Mr. Feynman

@Amit Partitions of unity are very important in existence proofs

Amit

this is a very different use case i suspect

Mr. Feynman

And also to define integrals of differential forms

It turns out that whatever partition of unity you use, the integral is independent of it. I'm astonished by this result

Amit

it better be! :)

but why are you astonished, it's by construction so isn't it

i mean yeah it's an astonishing construction, i can agree with that

Mr. Feynman

12:40 AM

@Amit because I find amazing that we can build something independent on the choice using the partitions of unity

Good night, people

Amit

@Mr.Feynman yeah honestly I feel silly for coming across as passing judgement on what is / not amazing, regardless of the details

Good night!

antimony

12:57 AM

night

John Rennie

7:08 AM

That's annoying, it looks as if the ChatJax Chrome addon has been removed from the Chrome store. Back to the scripts I suppose.

Ryder Rude

7:45 AM

@bolbteppa @bolbteppa @Amit In this debate, I agreed with most of what James said. But he also advocates that math needs to changed to get rid of infinity. I didnt agree with that

I think the axiom of infinity is fine. Even the human feeling, that there exists a collection of objects that satisfies this axiom, is fine according to me

But we should also note that any actual APPLICATION of math only verifies truths about finite computations @Amit @bolbteppa

And about finite collections of objects

So we dont NEED to believe that an infinite collection has ontological existence in any sense, if we're being minimalist. But it may still be that spacetime or the number of planets is infinite

bolbteppa

8:25 AM

@NiharKarve Something like that seems to be going on, that's roughly what this book seems to do, if you find a clearer/simpler/easier description of it let me know

Tensor density

In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another (see tensor field), except that it is additionally multiplied or weighted by a power W of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities...

34

A: Explain densities to me please!

The basic concept is that of a density of weight $s$ (or just an $s$-density) for any $s\in \mathbb R$ on an $n$-dimensional real vector space $V$, which is a map $\mu\colon V\times\dots\times V\to \mathbb R$ that satisfies the following identity for every linear map $A\colon V\to V$: $$ \mu(AX_...

Slereah

Tensor densities pop up because of the representation theory of the general linear group

bolbteppa

8:44 AM

I can't make sense of the problem people are trying to pick with calling the volume element a tensor density, but it is a tensor density...

@RyderRude Every time I write down $\sqrt{2}$, I am writing down an infinite series $1.414...$, not a finite series, same with $1 = 1.0000...$, not a finite series, or $0.999.... = 1$ etc... you are using infinities everywhere, not finite series

The infinities are coming out of your eyeballs and there's nothing you can do about it, every integral involves these infinite series etc... you can't even define a notion of integration without them, everything collapses when you go down this crank rabbit hole of denying infinities

Mr. Feynman

9:16 AM

Is this notion of tensor density, which arises in many Physics book different from the tensor densities arising as "absolute values" of n-forms?

Ryder Rude

@bolbteppa but when you write 0.99999....=1, it is more precisely a proof in a formal axiomatic system. It's just string manipulation. Now, I admit that this string manipulation does tell us a verifiable truth about the real world, but that truth is ultimately about a finite computation on finite sets that we can verify

Mr. Feynman

To be clear, this is the second option.

Ryder Rude

All of calculus results are formal string manipulation, without necessarily any interpretation. They are useful results because you can verify these results on finite sets @bolbteppa

I'm saying that you need not interpret this string manipulation as implying the existence of an infinite collection of objects

The axiom of infinity can just be taken as a rule for string manipulation, without any interpretation in terms of collections of objects

Mr. Feynman

@bolbteppa The first lines of the last link I posted should clarify what was the problem last night

bolbteppa

@RyderRude A formal axiomatic system called mathematics...

Ryder Rude

9:24 AM

Yeah, I'm fine with mathematics using the axiom of infinity. I just don't think we need to interpret this axiom in terms of an infinite collection of objects.

Now one may still say that infinite sets may exist as, say, the set of planets, even if u can never personally visit those planets

What I find weird about that camp is that : 1. It's not minimalist. It assumes more than we need to 2. It implies sets exist objectively. I think sets are more likely to be how humans interpret nature

But not just humans. It seems like other life forms like dogs definitely think in terms of objects. I think sets and numbers are an interpretation of nature among the life forms on earth

But what nature objectively is, is unknowable

bolbteppa

The set $\mathbb{N}$ is an infinite collection of objects, there's no way you're going to convince anybody (except Wildberger :p) that this is not an infinite set, if you try to say it's finite I just add $+1$ to the top number, I don't know how anybody can object to something this simple

In the real world, this traces back to the existence of an (infinite) time interval, if the time interval is not infinite it's only because of some contraction of the universe thing, but it doesn't change the mathematical fact that the time interval would be infinite if it wasn't for some GR/men-in-black thing ending the universe early

@Mr.Feynman I'm not sure, that post is just saying a power of a form leads to the determinant getting some power

Mr. Feynman

@bolbteppa Note that in the "math definition" there is an absolute value. I think that's what we call an even density

Ryder Rude

@bolbteppa but does "the set of spacetime points" objectively exist, or is it an interpretation of nature among earth's life forms? Would you say that the universe is objectively "the set of all spacetime points"?

Mr. Feynman

But even then the two concepts still look different

bolbteppa

power of a(n absolute value of a)*

Mr. Feynman

9:35 AM

While the "physicists' version" is tipically without absolute value

Ryder Rude

I think any interpretation of nature in terms of sets is just bound to our conscious experience

Mr. Feynman

cf e.g. the wiki article that you posted

Ryder Rude

I mean that sets arent nature

So u cant say that numbers exist out there

Mr. Feynman

At a first look I think the mathematicians' tensor densities are even scalar densities in our language

Ryder Rude

Becuz the nature of "out there" is unknowable. When we try to imagine the early universe, we are not imagining nature as it objectively is (whatever that means). We are only imagining it in terms of what we're used to experience, i.e sets

bolbteppa

9:39 AM

The wiki explains the absolute value, sometimes you have 'pseudo-tensors' i.e. one also gets an extra sign, and you can re-write it with these absolute value signs and the sign thing if you want, the physicist version just assumes you are working with a tensor not a pseudo-tensor

Ryder Rude

When we try to imagine state of the universe after, say, life gets wiped out, we're not imagining the objective universe that exists independent on life. Our imagination still commits to life's interpretation of the universe

These r the reasons I think we cant say that numbers r out there

Any number that exists r the ones we can encounter in our own experience

bolbteppa

@RyderRude none of this is convincing, you can always interpret everything in terms of infinite sets, space-time as an infinite set, the early universe as an infinite set, it's as simple as saying if something exists in 2D, it can be plotted on a page, similar in 4D

*Classically, QM adds curveballs but on measuring, things reduce to the classical picture, and all we care about are measurements at the end of the day

Ryder Rude

@bolbteppa In that case, I wud say that the objective existence of sets, either in the physical or Platonic universe, is a valid viewpoint to have

I wud just say that it's unnecessary, from a minimalistic pov. Our applications always involve finite sets. And all proofs involving infinites are just string manipulation

So I wud just say it's unnecessary, but a valid viewpoint

But also it's a useful viewpoint, becuz it helps with intuition about mathematics

It's strictly unnecessary but a helpful viewpoint

bolbteppa

10:09 AM

When I write down $e^0 = 1$, or $e^1 = e$ etc..., my number is only found by computing an infinite series, I can't write down the number without invoking infinity here, all of quantum mechanics etc... is gone if this infinity is gone, in no way are we using finite sets here

Ryder Rude

@bolbteppa when i say "our applications only involve finite sets", I mean that we never encounter an infinite collection of objects in any application. Ofc we do string manipulation that we believe is to be interpreted as statements about an infinite collection of objects. But that belief isnt necessary

Notice that any computation involving e only involves a finite collection of objects

And the rules of limits are just rules of manipulation. There need not be any interpreration involving an infinite collection of objects

bolbteppa

Every time I write down $e^{...}$ I am working with an infinite collection of objects, it's just notation for an infinite sum, the notation $\sum_n (...)^n/n!$ is also just a shorthand notation for an infinite sum, it's still an infinite collection. Any number can be interpreted in this way too, same as writing $1 = 1.000...$ the infinities are coming out of your eyeballs

Ryder Rude

@bolbteppa But it is a belief that that notation is shorthand for some collection that exists. There is nothing infinite about strings

Ok let's agree to disagree :)

I agree that it is a useful and valid belief tho

bolbteppa

Right, you have to start denying numbers like $e^1 = e$ or $\sqrt{2}$ exist down this rabbit hole, which means denying the real numbers etc... so everything is gone

Ryder Rude

I wud never deny any math we've done using strings

:P

But Norman thinks that we need to dispose of these parts of mathematics, yes. I disgree with him there

Amit

11:09 AM

I'm very careful not to code infinite loops

I rather assume they exist to remain careful, lol

ACuriousMind

what

almost every interactive program is technically an infinite loop

sometimes you need functions that never return, that's why many type systems have an empty bottom type

Amit

Hmm, that's cheating a bit, yes it's an infinite loop but once you've built the input handler into it, it's a different beast. I know, the power button is also an input :) But what happens when the thing runs on the chip of an airplane or something...

Or a satellite, that can come very near to infinite lol

Anyway I only pointed it out to say, even as a programmer that doesn't do mathematical things, I think it's more natural to assume that "infinity" does exist, as part of thinking on how to avoid hanging your system

ACuriousMind

The notion of functions that never return doesn't need a notion of "infinity"

from the perspective of the caller, whether the function doesn't return because it's stuck in an infinite loop or because it exploded the computer doesn't matter

Amit

I claim that every time the phrase in our mind of the type: "no matter how many times we do X then still we won't finish" we are implicitly assuming infinity exists

ACuriousMind

what does that even mean

Amit

11:18 AM

Yes, I am speaking only on the mental level, technically you are correct of course

ACuriousMind

what is the material difference between infinity "existing" or "not existing"

Amit

It means that I don't think we'll get rid of thinking in terms of infinity

ACuriousMind

when I think about the number $\pi$ I'm not "assuming its existence"

I don't even know what it means for $\pi$ to "exist"

let alone for infinity

Amit

Well thought is a material process so there is a difference there

Slereah

what does it mean for $2^{100}$ to exist

Amit

11:20 AM

When I start thinking about the digits of pi I can'f help but assume infinity

ACuriousMind

@Slereah what does it mean for 0 or 1 to exist?!

Slereah

what does "it" mean

Amit

String manipulation

ACuriousMind

I feel conversations of this type first need to very carefully think about their general epistemology because if we don't agree on what existence means it's completely pointless to discuss whether or not specific things exist

Slereah

Don't u mean ontology

ACuriousMind

11:21 AM

both, probably

you need to know what you mean by existence and how you figure out that things actually exist

Amit

@ACuriousMind agreed

Slereah

Show me on this chart where the infinite is

ACuriousMind

it's easy to maneuver yourself into a situation where your ontological ideas aren't verifiable/falsifiable - and then what's the point of the discussion?

Ryder Rude

There r two camps u can be in : 1. Zfc is just string manipulation which models finite real world collections or 2. ZFC's axioms r truths about infinite sets that ontologically exist

I find the second camp really weird

There is no infinite real world collection u will ever encounter

ACuriousMind

I don't think any statement about finite sets depends on AC

bolbteppa

11:23 AM

The real question is this

2

A: What symmetry causes the Runge-Lenz vector to be conserved?

Looking at https://arxiv.org/abs/1207.5001 one gets a very nice solution. If one is not very keen into mathematics, their basic idea is to use the infinitesimal transformation $$\delta x^i=\epsilon L^{ik}$$ where $L^{ik}=\dot{x}^ix^k-\dot{x}^k x^i$. Since angular momentum is conserved, kinetic en...

Where the hell does this $\delta \mathbf{r}$ come from

Slereah

The axiom of choice can be proven from ZF in the case of finite sets

Ryder Rude

@ACuriousMind yeah, i mean it sometimes model finite collections. String manipulation games can have no models too

They're just games at their heart

ACuriousMind

@RyderRude my point is the moment where you claim that this is just about finite sets the difference between ZF and ZFC is nil

Ryder Rude

Now, some people say that they're not games and their models ontologically exist even if we can never encounter them

ACuriousMind

so as far as modelling stuff goes ZFC is not meaningfully a "model of finite real world collections", that's just ZF

Slereah

11:25 AM

I don't think math is fundamentally about string manipulation

there are math models not involving strings

Also people have been doing math since before symbolic notation

or writing

Ryder Rude

But idk what it could mean for a set to ontologically exist @Slereah this is wut i find weird about the other camp

Arent sets just a human interpretation of nature

Then how can sets b an objective description of universe

Slereah

well I don't know if human interpretation of nature has to be string manipulation :p

Ryder Rude

Oh yeah, we can use natural lanaguage too

ACuriousMind

it's just platonism

Plato thought that for every object there existed an "ideal" version of that object in an abstract immaterial realm

Ryder Rude

@ACuriousMind Yeah, but isnt platonism conflating how life forms on earth experience the universe with how universe objectively is?

ACuriousMind

11:29 AM

mathematical Platonists believe the same thing about mathematical laws and objects: they have immaterial existence

@RyderRude I mean, that's one possible criticism of it

Ryder Rude

Maybe theres a life form that cant comprehend natural numbers

Maybe sets dont make sense to some forms of existence

ACuriousMind

you need to separate your attempt at understanding philosophies from your attempt at judging them

Ryder Rude

Yeah, this is why i say that their viewpoint is valid too

And also helpful

It's one consistent way to look at things

But it's not a necessary viewpoint. It assumes unnecessary things, even if they're helpful for mathematical intuition

Slereah

Plato didn't invent mathematical objects being real

ACuriousMind

generally I think the problem here is really just that people want to use the word "existence" for different things

Ryder Rude

11:33 AM

I must say that I find it impossible to imagine a form of existence without a notion of sets. And even animals can think in terms of objects

So i think platonists have some point

ACuriousMind

and mostly I think this difference is sociological and aesthetic

Ryder Rude

Maaaybe sets are nature

It seems like there is some universality to the idea of sets

ACuriousMind

like, the finitists like restricting math to finite sets, okay - but why do we have to argue about the "existence" of infinite sets? Because the people who try to argue for their "non-existence" really want to say "that's not the kind of math we should be doing!"

many of these discussions aren't about "existence", they're about trying to establish some sort of judgement of merit

Ryder Rude

Oh:P

ACuriousMind

if you're doing the kind of math that's about things that are non-existent, then you're lesser

this is the worst kind of ontology, but also the most common

Ryder Rude

11:36 AM

Math involving infinity definitely have merit. There's no argument about that

Amit

Not only lesser, possibly also wrong

Ryder Rude

Yeah, this is what Normal advocates

ACuriousMind

one of the oldest rhetorical tricks is to transfer your value judgement into an objective-sounding judgement like " that doesn't exist" or "that's not natural"

Ryder Rude

That we should abandom the current math

If it's so sucessful, how can it not have merit :P

Amit

It's a clash of metaphysical principles

"But if only you'd done things my way we'd be faaaar more successful" lol

Ryder Rude

11:39 AM

Lol

ACuriousMind

and so I really think taking these ontological discussions at face value - that they are really about whether or not something "exists" - is probably not the most enlightening way to understand what's going on

Slereah

what about if the mathematical object is forbidden

cursed

Amit

😂

Ryder Rude

Maybe Norman says omega is cursed 😂

ACuriousMind

like, in this cynical view, original platonism with it's notion of the "ideals" existing immaterially and eternally independent of us really wanted that to be the case so that the ideals of virtue - the things we should strive for - had independent existence and so were more important than any in-the-moment human decisions

Amit

11:41 AM

Mathematicians rush in where angels fear to sum

Slereah

scp-wiki.wikidot.com/scp-033

ACuriousMind

the point isn't whether or not the virtues "really exist" - the point is that you should follow them!

Ryder Rude

It's like a cult lol

ACuriousMind

I feel this way about a lot of "philosophical" debates, they're really just debates about value judgements while pretending to be about something else

Slereah

platonism was basically catholicism of ancient greece

Ryder Rude

11:43 AM

Im personally only exploring the philosophy. I dont propose any change to the practice of math :P

@Slereah did they worship shapes

I wudnt b surprised

Slereah

no the shapes were basically like God's blueprints

also they are called forms

Ryder Rude

I never understood what their universe is. A society of numbers and shapes lol

Amit

@ACuriousMind but people tend to assume their judgements also have virtue. So perhaps it's not a matter of pretending, rather of identifying the judgement with virtue

Slereah

they were basically trying to reconcile the concept of a category of objects in their mind and their relations with actual objects in the real world

Why can you recognize different physical objects as the same thing

ACuriousMind

@Amit oh, the "pretending" doesn't have to be deceptive - I think in a lot of cases people aren't consciously aware of what they're doing

Amit

11:49 AM

Ah, yeah agreed

Slereah

Platonists thought that some categories were not arbitrary

They were naturally exisiting

ACuriousMind

we're surrounded by this type of argumentation so pervasively that it's very hard to stop - just think about how many debates about what is "natural" or "unnatural" aren't really about what exists in nature, the point is usually that the "unnatural" thing is evil and the "natural" thing is good

Slereah

what did Sextus Empiricus say on forms anyway

LEt's see

Ryder Rude

@Slereah but i never got what they meant by "existing". Existence is always the subjective interpretation of nature by some self aware entity. I dont know what it could mean to objectively exist

Slereah

@RyderRude That is our modern conception certainly

or at least of some people

Not really something people held back then

Amit

11:54 AM

@RyderRude You may wanna check what Popper, Lokatos thought about the subject

Lakatos*

Ryder Rude

I will check it out @Amit

As soon as we say that self aware beings can interpret nature, nature itself must objectively exist tho. But does nature have any other objective properties other than "it exists"?

I guess nature is "something" and "one thing". This makes its properties different from " Nothing"

Maybe the concept of ONE objectively exists. Becuz u cant have anything without one

The question "why is there something instead of nothing" is very crazy

Amit

That's why metaphysics is hard, there are too many possibilities lol

And on many levels we can't really choose our metaphysics, it has a lot to do with cultural social background probably

Slereah

> he doesn't get his metaphysics from revelations of supernatural entities

Amit

12:11 PM

But he does from their ontology?? 😇

Chatting on phone is ontologically unpleasant

Ryder Rude

I think nature itself has to have some properties. If nature itself were nothing, how could our interpretation of it be "something"?

Let's say all forms of self aware existence can comprehend natural numbers and sets. Maybe we can then say that sets and numbers objectively exist in nature

Slereah

Babies can't comprehend numbers and sets

Ryder Rude

That's a good argument. Babies lack basic skills like "object permanence"

I dont understand how we cud interpret sets out of nature if nature doesnt have anything equivalent to sets

U cant get something out of nothing

Slereah

can't you

Ryder Rude

But the objective nature of nature is unknowable

Amit

12:27 PM

If you postulate the drive to survive the rest will flow

I need to put the zebra and the lion in different sets

So fear is the root axiom of all! Mwahahah lol

One axiom to rule em all

Ryder Rude

This means nature objectively has FEAR :P

Amit

If we accept that our experiences are part of nature, yes

They also have a chemical basis

Slereah

You only know that they have a chemical basis from the conclusions of others, also based on their metaphysics

Amit

@Slereah agreed I am glad you caught that

Physics Meta

0

Q: Why is there so much string theory in physics stack exchange?

At my university, string theory courses are restricted to people who have taken about two years of courses on quantum field theory and the standard model. Only theory PhD students would ever take the class (a very small fraction of physicists). But there's so much string theory on physics stack e...

discussion

Slereah

12:31 PM

what if induction is wrong

see also

Amit

We need to make a special axiom to rule out solipsism, cuz I think it is lame lol. I got no other justification

Ryder Rude

I need to google solipsism

So this is the "problem of other mids" stuff

Amit

Lol its funny @Slereah

Ryder Rude

I guess thats the easiest way to deal with the problm of what objectively exists

Just say that ur own experience is the only thing that exiss

If a self aware being dies, the universe becomes nothing from their first person PoV

Slereah

you can probably just read a book on metaphysics rather than try to rediscover it all on your own

It may take a while otherwise

Ryder Rude

12:36 PM

Lol

Yeah, i will def study this stuff

Slereah

How will you even come up with swampman on your own

Amit

Socrates was against reading

Slereah

and now he's dead

Amit

Lol his spirit lives on in various chat rooms

Slereah

he also thought that slavery was rad

Ryder Rude

12:44 PM

Wut is a comprehensive book for the modern theories on this stuff? I mean, their equivalent of QFT

Amit

Who knows Plato may be lying. Another advantage of not writing lol

Bertrand russell has this book

Slereah

the only philosophy book I have that's not physics is this one : stafforini.com/broad/…

it is not general metaphysics tho

Amit

A history of western philosophy

Ryder Rude

Thank u

Does philosophy of mathematics come under metaphysics

Slereah

usually

Amit

12:47 PM

Read Lakatos he specialized in that

Ryder Rude

What is the most mindblowing theory to come out of this field

Anything crazy

Amit

He has this amusing book where he imagines a teacher and his students proving a geometry theorem

Slereah

probably any pythagorean nonsense

Ryder Rude

@Amit whats it called

@Slereah like, what nonsense?

Amit

Proofs and refutations

Ryder Rude

12:51 PM

Okay

Slereah

you can read up the weird mathematical cosmology of pythagoreans if u wish

with monads and dyads and whatnot

Amit

And vierbeins

Ryder Rude

@Slereah i googled this but some satanic ritual showed up

Amit

😂😂

Slereah

numbers are fundamentally evil

Ryder Rude

12:55 PM

Lol

Amit

He warned you of forbidden knowledgez

Slereah

there is a demon in the Ars Goetia that apparently can teach you forbidden mathematics that was known of Noah

they don't specify what it's about though

Ryder Rude

Maybe IUTT

Im convinced Mozichuki got that theory from satan

Slereah

> According to Pseudomonarchia Daemonum, Ham, son of Noah, was the first in invoking him after the flood, and wrote a book on mathematics with his help.

Amit

But Noah had all the elephants, they are supposed to be the wisest

Slereah

1:05 PM

He only had two, famously

Amit

Lol, that's four manifolds! One per ear

Slereah

> The Dictionnaire Infernal states that to summon Beleth, the person should hold a silver ring on the middle finger of the left hand against his face, to pay respect to Beleth's rank as king.

If u need to brush up on your forbidden maths

Amit

Where is all this juicy info from

Slereah

the forbidden tome of wikipedia

List of demons in the Ars Goetia

The demons' names (given below) are taken from the Ars Goetia, which differs in terms of number and ranking from the Pseudomonarchia Daemonum of Johann Weyer. As a result of multiple translations, there are multiple spellings for some of the names, explained in more detail in the articles concerning them. The sole demon which appears in Pseudomonarchia Daemonum but not in the Ars Goetia is Pruflas. The 72 Angels of the Shem Hamephorash are considered the opposite and balancing force against these demons. == Demons == === Kings === According to the Grand Grimoire, Baal (or Bael) is the head of...

Amit

Lol

There is a metaphysical approach that says demons exist for those who believe they exist

Without extending the same principle to other stuff

Obama2020

1:19 PM

I recently asked a question about deriving the form of the reflected spherical modes from black hole in the hawking effect. It was about an intermediate step of writing down the interior schwartzchild coordinate in terms of the exterior one along a collapsing sphere. My reference (Birrel Davies) skips over the steps to get that. Does anyone know of any reference that derives the effect (for reflection off of black hole) without skipping over too many steps?

Jim

2:01 PM

@Obama2020 My experience is that every oft cited source skips too many steps. But I would have thought Birrel Davies would be at least sort of followable

Obama2020

2:57 PM

@

Ryder Rude

Ok there is a great reason to subscribe to the idea that infinite collections of objects exist, even if we can never encounter them. If we interpreted ZFC axioms as not merely string manipulation games, but as truths about some collection, then ZFC is guaranteed to be consistent by Godel's completeness theorem

Obama2020

You would think, but from what I have read many steps are skipped (for example, the one calculating the rate of change of the exterior metric). I asked an unanswered question about that one, too, and thankfully was able to figure it out sometime later. If only more textbooks didn't omit so many steps. It's why I appreciate Schwittenburg's books.

Ryder Rude

So this cud explain the great success of ZFC. We have to believe in a model. A model witnesses that a theory is consistent

But now, I again run into the problem of the meaning of "existence of a collection" if u can never encounter the collection in your experience

If ZFC is so successful, then maybe its model objectively exists out there in nature. It's just that a conscious life form can never encounter that model becuz of life's limitations

But it also means that sets objectively exist in nature

I'm now defining nature the collection of the platonic universes of every consistent set theory

Crazy how I convert back to Platonism within hours

Maybe I'll keep oscillating in my opinion

Amit

3:39 PM

You can oscillate even without an opinion

Slereah

Ryder Rude

3:53 PM

I want 2 get the best of both opinions in a single opinion

Existence of infinite collections can prove ZFC is consistent, but it doesnt make sense for a collection to exist if it literally cant exist in ur experience

Ok i guess infinite models dont actually exist. But it is a nice trick to pretend they exist and write down what axioms they wud satisfy if they existed, so that our theory is hopefully consistent

Becuz this trick yields useful theories to prove truths about finite collections that actually exist

user250478

Hello to all users I'm disconnected in next hours, good afternoon. I add the link to Wikipedia Theory of everything, the section Arguments against if some user wants to read it en.wikipedia.org/wiki/Theory_of_everything#Arguments_against

Amit

4:10 PM

"Take a trite example that also troubled me as a student. In the calculus we postulate the
existence of divergence of functions, and we allow our variable(s) to vary from minus to
plus infinity. Yet we postulate one point at infinity. In affine geometry we postulate a line
at infinity. This is puzzling. It is more puzzling if we know that measure theory postulates
two points of infinity for each variable, but I did not know this then. I asked my math
professor why the difference between the calculus and affine geometry. He said, the one

Nihar Karve

@bolbteppa chapter 7 of that book has a review of Regge trajectories, wasn't expecting that

given how opaque the literature generally is on this stuff

but yeah they seem to have fleshed out that exact argument, where's the catch?

bolbteppa

4:37 PM

@NiharKarve last time I went through it, it got very messy when going into the details

PM 2Ring

6:42 PM

@bolbteppa Greg Egan has a page about LRL conservation. gregegan.net/SCIENCE/LRL/LRL.html He starts by showing a simpler vector which is also conserved.

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