The h Bar

00:34

@imbAF When the RHS is zero or one, the square is equal to the square root.

@imbAF you misunderstand what is happening. If you are finding a basis, it is convenient to have orthonormal bases, so we will want to impose the condition that basis vectors be of unit length. That is one application of that integral. Each basis vector in QM is a particular quantum state, and each of them needs to be normalisable to unity. A different notion is that a general quantum state must also be normalisable; it is this one that, if you did not consider enough basis vectors, then

it can fail to be normalised.

It is this, that "less than the total amount of possible states, then it can happen that the probability is less than one" could apply.

Relativisticcucumber

01:15

@bolbteppa XD

Silly Goose

02:38

what is a good resource to learn about bell's and bell-like inequalities and this whole sphere of things related to EPR paradox?

it would be nice if such things were spoken of in math (not physics-ey) probability theoretic terms

perhaps Semiclassical knows...

naturallyInconsistent

03:07

There are good textbooks on quantum information that talk about the details of Bell's inequalities.

lucabtz

06:24

@fqq yeah if i did PhD it would be either because i may potentially stay in academia in the future or otherwise for the fun

its true that it wouldnt had basically anything to make finding a job easier, actually maybe its easier to get a better job in three years from now (which is the time i would finish phd at) by working this three years and having work experience

user 70432

Is there a combined professional and theoretical option like applied physics available at your university?

naturallyInconsistent

@fqq this connection did not appear to meow but it makes a lot of sense. Miao miao been concerned since back when Berlusconi was younger and already bossing things around for a decade plus, but never thought of why Italians would be so much into sciences.

Silly Goose

06:59

I think this (long) paper maybe is a nice discussion to my recent questions about what a quantum correlation really is: iopscience.iop.org/article/10.1088/1751-8113/49/47/473001/pdf

Mr. Feynman

07:14

@lucabtz ok, this sounds like one of those low level rumor but a couple of days ago, my friend told me that a friend of his got denied a job because he had done a PhD :P

That's the "you're overqualified" shit

lucabtz

@Mr.Feynman nice

Ryder Rude

07:29

phd is not necessary to do physics, i would say

lucabtz

@RyderRude if you want to stay in the academic world it basically is

Ryder Rude

for that, it is by definition, unless one is exceptional like Dyson

i like generality more. i hav no interest in researching something specific. so it depends on whether u like doing general physics or specific physics @lucabtz

lucabtz

@RyderRude any concrete research is specific usually

Ryder Rude

yes. if u want to research, u hav to like specific physics. like, too specific these days

but neither of general or specific phyics r necessarily betr in my opinion

if u just like learning anything physics, then go for general physics. specific physicists dont hav the time to learn anything they want @lucabtz

lucabtz

07:47

@RyderRude there does not exists a general physics phd, research is always specific nowadays

naturallyInconsistent

> ‘Insanity is doing the same thing over and over again and expecting different results.’ --- Rita Mae Brown

lucabtz

@naturallyInconsistent yeah right

naturallyInconsistent

@lucabtz hey, that can be sarcastic...

Ryder Rude

i meant "go for general physics" as a life path, rather than a university path @lucabtz

lucabtz

@naturallyInconsistent i understood what you mean

naturallyInconsistent

07:53

@lucabtz smirk

Ryder Rude

if u go for specific physics, u wont hav the time to learn anything u want. it depends on priorities

user 70432

m i a o ~

Ryder Rude

i like some physics, but nothing too specific

naturallyInconsistent

@user70432 M I A O ~

Ryder Rude

naturallyinconsistent is always grumpy

naturallyInconsistent

07:56

One cannot help but point out the "states' rights" vibe, whose appearance should always be replied by "states' rights to do what?"

user 70432

@RyderRude that quote is actually why memorization works.

naturallyInconsistent

@user70432 miao miao at least tried to search for the true quote source. It is most often attributed to Einstein, but that seems to be wrong.

user 70432

yes, searching for sources is frustrating

just accept it for what it is

naturallyInconsistent

But you might be more amused to note the irony of asserting that an obviously happily provided statement is somehow "always grumpy"

@user70432 that does not mean we should totally give up. You know, "be the change you want to see in the world". Miao miao can be inspirational hippie too

user 70432

Agreed, but miao miao once sent a letter to the OED to find the true source of the saying "I see you cannot see the forest for the trees"

I decided to

6 mins ago, by user 70432

just accept it for what it is

naturallyInconsistent

08:08

@user70432 lies

user 70432

I meant miao = me.

I should have used miao'

naturallyInconsistent

Ahhhh

two cats confused about references miehehehe

user 70432

The letter I got back said the quote goes back to 1533.

In the writings of Thomas More, if you're interested :-)

Silly Goose

08:32

shweggums

user 70432

h o n k

Mr. Feynman

@naturallyInconsistent Nah, that's Vaas from Far Cry 3

bolbteppa

08:51

@RyderRude In practice there is basically no serious research done by people without them, even by people with them who've left, because it involves the effort of a full-blown job (where people often 'work' longer hours than normal jobs) to do anything of value, as vixra can attest

Silly Goose

is working in a national lab considered academia

bolbteppa

Antony Garrett Lisi

Antony Garrett Lisi (born January 24, 1968), known as Garrett Lisi, is an American theoretical physicist. Lisi works as an independent researcher without an academic position. Lisi is known for "An Exceptionally Simple Theory of Everything," an unpublished preprint paper proposing a unified field theory based on the E8 Lie group, combining particle physics with Einstein's theory of gravitation. The theory is incomplete and has unresolved problems. The theory has been extensively criticized in the scientific community. == Biography == === Education and career === Lisi was born in Los Angeles and...

is what happens when there are no guardrails

From one of the vixra ToE's from the past month:

> In 2019 the author published the framework for a ToE or world formula in the form 12πc^3 =1. After 5 years of developing the framework further, the equation is now clearly explained using the Archimendian spiral and the physical background of the equation is illuminated.

5 years spent proving $12 \pi c^3 = 1$

Slereah

One pretty big red flag for a crank paper is when there is no derivatives anywhere

They are often big fans of elementary arithmetics

More Anonymous

@RyderRude ... Wanted to bounce this of you:

What is the negation of "I think therefore I am"

I don't have a background in philosophy however I don't think I fundamentally understand "I think therefore I am." Here's what confuses me. My idea is to assign a truth value to this statement. However, if I apply a negation I should get a false value to it's negation and equally non-trivial. So the negation could be:

"I think therefore I am not"

"I do not think therefore I am"

"I do not think therefore I am not"

bolbteppa

09:06

> The author declares that there are no conflicts of interest and that all his work specifically on the topic of "time" in physics (2008 – 2024) 2,3,4,5,6,7,8,9,10,11,12,13,14,15 has been created through self-funded projects and essentially refers only to the ideas of Isaac Newton and Albert Einstein

Slereah

@MoreAnonymous Negation of a material implication is $\neg (A \to B) = A \wedge \neg B$

It should be "I think and I am not"

More Anonymous

@Slereah what happened to therefore?

If the statement was I think and I am ... Im like meh .. who cares

@Slereah Or wait your saying negation works like that?

What is the negation of "I think and I am"?

Is that redundancy?

Slereah

Material implication can be defined as $A \to B = \neg A \vee B$

So "I think therefore I am" is an equivalent proposition to"I don't think or I am" (or both)

Ryder Rude

i agree with Slereah

Slereah

To do the negation you can just apply De Morgan's law

More Anonymous

09:12

@Slereah Isnt this non-sensical: "I don't think or I am"

Can you recommend a book for loigic?

bolbteppa

A discrete math book will go over this stuff

Ryder Rude

@bolbteppa yeah.. research is specific in nature. without phd, u can learn general physics but not research much. it's not necessarily worse than research, as researchers dont get the time to learn general physics

bolbteppa

Lecture 1 - Propositional Logic

►

Ryder Rude

@MoreAnonymous u hav to check that the truth tables r identical

More Anonymous

I am regardless weather I am thinking or not

The thinking is an extra conditional which may or may not be true when I am

So the or condition is irrelevant

Ryder Rude

09:17

@MoreAnonymous it is an inclusive OR

More Anonymous

@RyderRude what's an inclusive or?

Ryder Rude

the sentence "A OR B" is true if at least one of them is true

More Anonymous

@RyderRude Yes

Ryder Rude

an exclusive or is A exclusiveOR B

naturallyInconsistent

@user70432 definitely interested. Thanks~

Ryder Rude

09:19

this is true when exactly one of A and Bis true

More Anonymous

I dont see why "I do not think or I am" is a false statement

I am = True

I do not think = True (maybe I'm sleeping)

Slereah

@MoreAnonymous That's the true statement

The false statement is "I think and I am not"

which is indeed a contradiction

Ryder Rude

@MoreAnonymous so u obtained True OR True, which is True

More Anonymous

Here's another false statement is "I do not think and I am not"

@RyderRude I thought I was suppose to get a contradiction for my negation

Ryder Rude

i dont know what u r doing.. let's start from the beginning

More Anonymous

09:26

Either way my point was the initial statement is ...
I think therefore I am ...
The negation according to Slereah is:
"I think and I am not" ...
I argue the "I think is irrelevant" since I can also say:
"I do not think and I am not" is also a false statement

Slereah

Is it

I think therefore I am does not imply that non-thinking things exist

More Anonymous

Whats the equivalent statement of "I do not think and I am not"?

Slereah

I think or I am

De Morgan's law

Silly Goose

why is it that one can only think or not think

Slereah

$\neg(A \wedge B) = \neg A \vee \neg B$

Silly Goose

09:29

what if one can quasi-think

Slereah

@RyderRude does that a lot

More Anonymous

@SillyGoose rofl

Ryder Rude

i dont

Silly Goose

this "law of excluded middle" seems sort of fishy

Slereah

Sorry there is a no intuitionist policy here

Silly Goose

09:31

xD

how can the law of excluded middle seem natural

Ryder Rude

@MoreAnonymous the equivalent statement in terms of implication wud b "I don't think does not imply I am"

Slereah

@SillyGoose It is either natural or it isn't

Silly Goose

Lol

Ryder Rude

is Not (A --->B) the same as A does not imply B?

@MoreAnonymous i took (A and B) which is Not (Not A or Not B) which is Not ( A implies Not B) which is A does not imply Not B

More Anonymous

@RyderRude I see ... Im analysing this ... I still think its fishy

Ryder Rude

09:35

oh

More Anonymous

But isnt this a true statement as well?

"I don't think does not imply I am"

Slereah

Beware of not confusing material implication with causal implication

More Anonymous

@Slereah Ah ... whats the difference between the two

Slereah

Material implication is a purely logical thing

PM 2Ring

@Slereah Speaking of cranks, the push gravity guy has returned to Space.SE. space.stackexchange.com/a/66062/38535 i posted an answer to his question before I realised that he was looking for evidence for his BS.

Slereah

09:38

It does not at all concern itself with whether the two statements imply each other in the causal sense

ie. The sky is blue $\to 1+1 = 2$ is a correct material implication

Even though there is no causation

Ryder Rude

very interesting

Dannyu NDos

Relevance logic is paraconsistent tho.

More Anonymous

I think Decartes intended a casual implication no? Otherwise ... what was he on about?

PM 2Ring

If it rains, I will get wet. But I may also get wet from some other water source.

Ryder Rude

No, thinking does not cause existence

Descartes is simply deducing that he exists

More Anonymous

09:40

What was he on about?

Then say I exist

Why say I think hence I exist?

Ryder Rude

But he doubted it initually

his existenxe

Slereah

well the negation of causation would simply be that I think does not imply that I am

Ryder Rude

but to doubt his existence, he wud hav to exist. therefore, he cannot correctly doubt his existence

Slereah

So whether you're thinking or not thinking does not have any bearing on whether or not you are

Ryder Rude

therefore any such doubt must be incorrect

therefore he exists

this is Descartes's argument

i recently felt that it was circular. lemme rememeber

some philosophers regard it as circular

Descartes is only saying that he can doubt the correctness of all his knowledge but not of his existence @MoreAnonymous

maybe all his knowledge is incorrect becuz a demon is deceiving him

PM 2Ring

09:43

Or he's a Boltzmann brain

Ryder Rude

ok so i felt it was circular in a recent philosophical conversation

More Anonymous

@RyderRude Thats a coherent interpretation ... But it does make you speculate about things ... does self-existence fall under the domain of knowlegde

Ryder Rude

it's because "I think" assumes "I am"

if he is doubting "I am", he shud b doubting "I think"

but i proceeded to conclude that my objection was wrong

More Anonymous

I remember Buddhist philosophers dont think too highly of "I think therefore I am"

Ryder Rude

@MoreAnonymous yes... it's definitely weird to call it knowledge

@PM2Ring hi. Descartes does not conclude anything about the existence of his body. he is only able to conclude that his subjective experience exists

he isnt even able to conclude that his brain exists

@MoreAnonymous oh

PM 2Ring

09:48

Of course. And he has to take it on faith that God isn't malicious or a trickster.

Silly Goose

maybe god is a trickster on tuesdays

Ryder Rude

yes... to be able to trust all his knowledge other than his existence, he has to trust god

descartes's philosophy is not as subtle in other aspects. he believs that animals dont have soul but humans do

More Anonymous

@RyderRude Im not an expert on it ... But yes they dont like it

PM 2Ring

@MoreAnonymous Sure. The point of meditation is to transcend the intrinsically dualistic platform of thought.

Ryder Rude

@MoreAnonymous whats their objection

More Anonymous

09:50

@RyderRude Nagarjuana has some idea of emptiness which I once understood

But then got drugged outta me

@PM2Ring yea ...

Ryder Rude

oh

i made this dualism based philosophy a year ago philosophy.stackexchange.com/q/98490/27700

PM 2Ring

Any fool with a brain can think. But learning to have non-dual awareness that transcends thought takes a lot of practice. And it helps to have a good teacher.

Ryder Rude

the philosophy is based on how toddlers would figure out the world

Dannyu NDos

No offense, but as a South Korean ex-Christian, I'm not quite in favor of Buddhism either. As far as I know, they advocate paraconsistent logic without any motivation.

Ryder Rude

@PM2Ring do u do meditation practice

More Anonymous

09:54

@DannyuNDos None taken ...

I happen to be buddhist

Ryder Rude

@MoreAnonymous do u do meditation practice

Dannyu NDos

Though, there is one discipline of logic I'm particularly into, namely linear logic.

PM 2Ring

The mind apprehends the world by cutting it into parts. But maybe something gets damaged in that cutting process. And the mind can't help but impose its own structure to some extent on the structures its analysing.

More Anonymous

@RyderRude well in my sect of buddhism its really different ... For one they say one can manifest enlightment in this lifetime

We chant ..

Ryder Rude

oh

PM 2Ring

09:56

@RyderRude I have in the past. But not so much these days.

More Anonymous

Yea ... Instead of sayin we should detach ourselves from the world in this one we go like: "Earthly desires are enlightenment"

Ryder Rude

@PM2Ring my recent philosophy is about how mind imposes mathematical structure on the world

Slereah

@MoreAnonymous Why would you trust a guy that doesn't think

More Anonymous

@RyderRude Do you write books?

Ryder Rude

i have rejected dualism now. it's only a stepping stone to truth

@MoreAnonymous no..

More Anonymous

09:57

@Slereah Buddhists were serious and strange logicians

Anyway I gtg

Ryder Rude

@MoreAnonymous hav u read Hume's philisophy

PM 2Ring

It's like imposing a coordinate system. It's certainly useful / practical. But there are benefits in not imposing a coordinate system, too.

Ryder Rude

@PM2Ring yes. thats a great analogy

in my philosophy, we obtain a non-mathematical or a semi-mathematical structure after going co ordinate free or mind independent

Silly Goose

@DannyuNDos every school of thought or institution is fundamentally unmotivated :D

someone decided to convince many people that an arbitrary thought was meaningful, important, or useful and the rest was history

Dannyu NDos

Here I, a hyper-Darwinist say, may the nature select you. 🙏

More Anonymous

10:02

@RyderRude nope ...

Dannyu NDos

I mean, I claim that all survived disciplines are consequences of natural selection.

Silly Goose

@Relativisticcucumber a friend has appeared hehe

Ryder Rude

@MoreAnonymous there is this book files.ethz.ch/isn/125487/5010_Hume_Treatise_Human_Nature.pdf

2

it's really short. im going to read it

@MoreAnonymous we can both read and discuss maybe

PM 2Ring

@DannyuNDos All organised religions have questionable beliefs & practices. But IMHO the Buddhists generally have a better track record than the Christians. ;) OTOH, some Buddhist theocracies have been very strict, and persisted well into modern times.

Silly Goose

i wonder what it's like to feel like one is approaching the truth of a thing (can be experienced necessarily only by someone who believes in there existing a truth of a thing)

Dannyu NDos

10:05

^ This.

Ryder Rude

to me, forming clear philisophies is exciting only for a few moments, and then these philosophies feel worthless

but i get similar feelings about learning new physics

Dannyu NDos

We cannot reach the truth, but nonetheless, we're approaching it. Take the limit, as we've learnt in calculus.

PM 2Ring

@DannyuNDos Definitely. Institutional / organised religions have very strong memes. And lots of people who found those memes unacceptable failed to reproduce, for various reasons...

Ryder Rude

but these days, i can spot errors in philosophical debates. so i think it's not worthless even tho it feels that way

maybe it's just that the novelty of knowledge is gone

e.g. when people say "if p-zombies behave the same, then whats the difference between this universe and their universe", i can spot the error

Dannyu NDos

@PM2Ring Oh, I meant much broader spectrum of meanings of "disciplines". Scientific theories, or even mathematical axiomatic systems.

More Anonymous

10:10

@RyderRude I'll give it a look

PM 2Ring

@DannyuNDos Ok. That works, too.

Ryder Rude

@MoreAnonymous okay :)

Dannyu NDos

Those who thought 1+1=3 were wiped away by natural selection, for instance.

user 70432

338 pages is not "short" :-/

Ryder Rude

or when people say "consciousness is emergent in the same way oceans are emergent". when u havnt thought about it, u feel as if there is an error in there, but u cant pinpoint it

Dannyu NDos

10:13

And for a future instance, maybe someday the nature will force us to select amongst the continuum hypothesis and its negation.

Ryder Rude

but the exact error there is a categorical error

PM 2Ring

But at least with mathematics & modern science, some attempt is made to be logical, and consistent with empirical experience. Whereas religions can happily maintain beliefs that are downright delusional. ;)

Dannyu NDos

Yeah, but it's the nature that decided what's "logical".

Ryder Rude

@user70432 it is only in english tho... no math i hope

Dannyu NDos

What was bestowed can be also confiscated.

Silly Goose

10:18

@PM2Ring some would think that one needs to be delusional to believe in the foundations of science

if you would like to put institutions/schools of thought on a spectrum, that is conceivable. but to to a litmus test of "delusional" or "not delusional", I think everything is necessarily delusional

PM 2Ring

@DannyuNDos I'm not sure about that. I don't think any empirical experience can involve the kind of infinite sets that the continuum hypothesis and the Axiom of Choice require. On a simpler level, you can't build a Turing machine that has an actually infinite tape.

Ryder Rude

@PM2Ring they take a leap of faith... a logical denfense of their position can be that empiricism is not provenly the only path to truth.. and they may appeal to intuition as the path to truth

from a scientists's perspective, this defense does not really mean much

i dont think this defense applies in most cases. most cases of religious beliefs are caused by childhood beliefs imposed by authority figures

PM 2Ring

Oh, I don't claim that empiricism will lead us to the Truth. But it's certainly a useful path to dealing with the physical world. And although there's still a lot of crap going on in the world, in many parts things are a hell of a lot better than they were back in the day when religion had a much stronger hold over societies.

Dannyu NDos

@PM2Ring Who knows? I'm saying this only for fictional purposes, but maybe an extra-universal being will modify the physical laws to allow us to build a physically working Turing machine.

naturallyInconsistent

@SillyGoose what would you consider as a delusional belief that is taken as accepted as a foundation of science?

Ryder Rude

10:25

@PM2Ring yes. thats an understandable position.

PM 2Ring

@RyderRude But where did the oddball religious beliefs come from in the first place? I suspect that many major religious founders had some form of psychotic delusional experience. And in their mania, other people got swept up into their delusional belief system.

naturallyInconsistent

@PM2Ring Where do oddball scientific beliefs come from?

PM 2Ring

Of course, every religion also has non-oddball stuff, like love thy neighbour, and don't murder people. :)

Ryder Rude

@PM2Ring yes.. thats true. i think the defense mostly applies to deism, rather than to organised religion

but people who believe in organised religion may do so due to intuition and life experiences

so it applies to some cases of organised religion

PM 2Ring

@naturallyInconsistent The difference is that science has ways of testing crazy ideas. And there's a difference between creative, inspirational thinking and flat-out psychotic delusion.

Ryder Rude

10:48

do u think basing the argument on "I think" already assumes "I am", thereby making Descartes's first meditation a circular argument

user 70432

Yes.

Ryder Rude

and do u think it's problematic or bad reasoning @user70432

i think it's circular but good reasoning

91

Q: Could 'cogito ergo sum' possibly be false?

I've heard it postulated by some people that "we can't truly know anything". While that does seem to apply to the vast majority of things, I can't see how 'cogito ergo sum' can possibly be false. No matter what I am, no matter in what way I'm being tricked, no matter how I may be deluded, I mu...

user 70432

It must be recognized as a starting point like an axiom.

At some point we have to accept that we need to be circular in the sense of using accepted "common" words to define words.

Or else, as Feynman says, the philosopher dies of starvation, arguing about the "existence" of the steak.

Ryder Rude

11:07

@user70432 i have the same view...

@user70432 lol

user 70432

Richard Feynman on - philosophy, Why question, Modern science and Mathematics.avi

►

Relativisticcucumber

11:21

why is the Church–Turing–Deutsch principle not absurd

user 70432

Richard Feynman on hungry philosophers (or do we see objects or only their light)

►

Relativisticcucumber

also it seems this hypothesis "naturally" builds upon the church-turing thesis and that this motivated the idea of a quantum computer. but it seems to me a computer was meant to do computations and that a quantum computer does this, but just faster. so what does this have to do with simulating physical processes?

i mean obviously a quantum computer works via physical processes, but the jump to suggesting it can simulate physical systems generally goes over my head

user 70432

11:44

Here is a link in the top video to the entire lecture series, if you're interested.

PM 2Ring

@Relativisticcucumber If you can model some quantum system with n qubits, and your quantum computer has n qbits, then you can run a quantum model of that system. But that may not have a huge advantage over classical simulation techniques. Especially on current quantum computers which only have a fairly small pool of logical qubits, and which are limited by noise problems in resolving the states of those qubits.

user 70432

vega.org.uk/video/programme/45

PM 2Ring

Maybe take a look at some of Scott Aaronson's stuff. He wrote a book, Quantum Computing Since Democritus, but there are tons of free resources linked on his blog scottaaronson.blog

Relativisticcucumber

@PM2Ring "If you can model some quantum system with n qubits, and your quantum computer has n qubits, then you can run a quantum model of that system." hm why is this true?

Ryder Rude

@user70432 thanks

Feynman was pretty bad at philosophy

Relativisticcucumber

11:58

@PM2Ring will do ~~~

Mr. Feynman

Hey Ditto

::throws Pokéball

user 70432

He was a very "Practical Man."

Ryder Rude

yes. he believed in a pragmatic approach

user 70432

He started his study in math with practical guides.

Relativisticcucumber

@Mr.Feynman CHOMP

Ryder Rude

12:15

@user70432 oh

Slereah

my head

fqq

@PM2Ring the book is great

Ryder Rude

what is its purpose @Slereah

user 70432

Richard Feynman's Math Books

►

Slereah

Linear logic

Mr. Feynman

12:31

@Relativisticcucumber what is "Chomp"? :(

Did you eat my pokéball?

PM 2Ring

12:54

@Relativisticcucumber Because a qubit captures the "central mystery" of quantum mechanics. From The One Mystery of Quantum Mechanics

> We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.

> I will take just this one experiment, which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature one hundred per cent. Any other situation in quantum mechanics, it turns out, can always be explained by saying, 'You remember the case of the experiment with the two holes? It's the same thing'.

> I am going to tell you about the experiment with the two holes. It does contain the general mystery; I am avoiding nothing; I am baring nature in her most elegant and difficult form. - The Character of Physical Law, chapter 6

Slereah

14:24

Apparently the exponential operator in linear logic corresponds in the QI case to sending the set of points of the Hilbert space to a new Hilbert space with those points as a basis

But why

For instance if you have the trivial Hilbert space $\mathbb{C}$, its exponential is some infinite dimensional Hilbert space witha basis indexed by $\mathbb{C}$

Slereah

14:39

Its nickname is the "of course" operator but it is not enlightening

Ryder Rude

ive seen an operation like this in the context of tensor products. a tensor product of two vector spaces $V$ and $W$ can b thought of as a quotient space of the vector space whose basis is the cartesian product $V\times W$

Slereah

Yes, it is the free functor

Ryder Rude

oh

Slereah

Mapping a set of points to a vector space of that dimension

Ryder Rude

it sounds like a ridiculous operation to me

didnt know it had a use

Slereah

14:50

It's the adjoint to the forgetful functor $\mathbf{Vect} \to \mathbf{Set}$

Ryder Rude

oh

so we takw the vector space, forget the vector space structure, get the set

i forgot what adjoint meant

Slereah

a complicated thing :p

Ryder Rude

yeh i probably never learned it :P

category theory has crazy constructions

Slereah

It is a weaker notion to the inverse of a functor

The two functors aren't inverse of each other but they have some properties of the inverse

Ryder Rude

oh

in homotopy, we hav the concept of "almost inverses"

Slereah

14:54

Sort of like that

Ryder Rude

oh

Slereah

Instead of being the identity, they give you something with a natural transformation to the identity

Ryder Rude

yeah, homotopy has a similar idea

i saw this crazy construction which had morphisms has objects and natural transformations as morphisms. it was bizarre

maybe it wud b clearer with an example

like morphisms between morphisms

Slereah

The forgetful functor is the right adjoint, mapping vectors to points, and the free functor is the left adjoint, mapping points to vector spaces of dimension dim(V) = card(S)

If you have say the set of one element, the free functor is $\{\bullet \} \to \mathbb{R}$, and the forgetful functor is $\mathbb{R}$ to $\mathbb{R}$ (but a set)

Ryder Rude

really beautiful

Slereah

15:00

So there is some natural transformation between the set of one element and $\mathbb{R}$

Or the set of $n$ element and $\mathbb{R}^n$ more generally

Ryder Rude

oh

so if we compose left and right adjoints, we get a functor from vector spaces to vector spaces, or from sets to sets

Slereah

and conversely you can do it the other way, although it is less pretty since you're mapping $\mathbb{R}$ to the set $\mathbb{R}$ and then the set $\mathbb{R}$ to some vector space of infinite dimension

Yes

Ryder Rude

this means left and right adjoints r not inverses of each other

the mapping to the vector spaces shud also take a field as input

Slereah

They're not, or more accurately if they are then they are equivalent, a condition stronger than adjoint

But their composition has a natural transformation to the identity functor

Ryder Rude

ooh

Slereah

15:07

The adjoints have a generally complementary vibe

Ryder Rude

the idea of converting a set into a group shows up in homology, and we hav the freedom to take a ring as input there

e.g. homology over Z vs R

Slereah

The adjoint of the inclusion of integers into R is the floor function

Ryder Rude

oh

i guess this idea does show up in QM...e.g. classical mech has a set which is the configuration space while QM has a vector space labelled by the configuration space

but to apply apply this idea twice would give something ridiculous

like a vector space of functionals i guess

Ryder Rude

15:27

@Slereah oh i get it now. it's because the composition is either identity or "almost identity"

user 70432

@RyderRude don't take these books too seriously, they are just collectors items :-)

Ryder Rude

@user70432 yeah... i dont read historical.books anyway :P

i wud like to learn category theory with examples

user 70432

You may find something useful here

for learning, in general.

Ryder Rude

@user70432 it has some useful techniques. i hav saved it

user 70432

ok

naturallyInconsistent

15:40

@PM2Ring of course. You wont find meow meow conflating scientific strokes of ingenuity with delusions.

@user70432 The Vega science trust version that is a full lecture, is also wonderful.

@Relativisticcucumber There are a few facts you have to assemble: 1) Normal computers using classical logic have been mathematically proved to take extremely long to simulate quantum computers, because all the various entanglement possibilities grow the "classical state space" far faster than a linear increase in number of qubits.

user 70432

ok

naturallyInconsistent

2) Quite many physical simulations, e.g. of solid state physics, is originally of quantum materials doing quantum stuff and obeying quantum logic. Be it protein folding, solving for atomic and molecular bonds and so forth; using something that already obeys quantum logic, to model a thing that obeys quantum logic, is vastly easier and faster than a classical simulation thereof.

Not least because in (1), the entanglement possibilities can be captured. It can be as easy as setting up an equivalent problem in a quantum computer and letting the settling down to ground state solve the problem for us. Note that translating a problem from one expression in the real world, into an equivalent one in a quantum computer, can be fruitful and drastically different.

3) just like how Shor's algorithm combined the quantum version of FFT and entanglement and both constructive and destructive interference and so many more, a quantum computer gets to leverage many mathematical, computer science, and new quantum tricks, that will let us punch our way through difficult problems much faster than the straightforward methods

More Anonymous

15:55

@RyderRude ... I think the argument in Buddhism is the self too is a relational object

Are all things empty? - Nagarjuna & The Buddhist Middle Way

►

I found this ^

Obliv

16:37

"The heat flux to a system in any process (at constant mole numbers) is simply the difference in internal energy between the final and initial states, diminished by the work done in that process." We can measure work done on a system (enclosed by adiabatic impermeable walls) as a way to measure the difference in internal energy between two states, but that doesn't really give us a value of the "net" internal energy of a system

Slereah

Oh apparently the exponential operator maps a Hilbert space to its Fock space

I guess it is indeed exponential in that sense

I'm not sure if it is actually useful for quantum computing or if it just occurs in the internal logic of the full category

Seems like it would be a lot of qubits to have a Fock state

Obliv

I guess I'm just nitpicking here because I know later on we can derive the equipartition theorem but this section claims to define heat but all it's given is that it's the change in energy of a system not due to work..

I wonder if later on heat can be specified as QM/EM interactions

Slereah

It probably fits some specific property of operators in quantum logic since coherent states are states which can be copied and deleted

Obliv

You're doing quantum computing now? @Slereah

Slereah

I may be getting a job in the field soon-ish

Obliv

16:44

Nice

It ain't GR but I hope it's interesting enough for you

Slereah

Should be more interesting than doing data stuff

ah yes

ACuriousMind

@naturallyInconsistent I think all these statements about quantum computers being "faster" always need the caveat that this is a statement about the theoretical complexity of the computation, not about the real-world speed of the computation on a real-world machine - last time I checked, we were far away from any actual quantum computer outperforming an actual classical computer on any practicfal computation, marketing claims notwithstanding;

also you can do any computation a quantum computer can do to any accuracy on a classical computer, simply by simulating the quantum computer, there is no computation that's impossible on an ideal classical computer but possible on a quantum computer

naturallyInconsistent

@ACuriousMind that is heavily implied, for the fact that, as you correctly pointed out, we do not yet have such a computer available.

ACuriousMind

in this sense I agree with @Relativisticcucumber that the way the CTD thesis is often described in popular media (like "classical computers can't simulate all physical systems, but quantum computers can") is incoherent

naturallyInconsistent

@ACuriousMind not quickly

@ACuriousMind concur

Slereah

16:52

Tricky to determine because state preparation is also a thing

All the cool algorithms just make gigantic entangled states which is a lot of prep

naturallyInconsistent

@Obliv You are misunderstanding. This is just a wordy form of 1st law. $$\mathrm dE=đQ+đW\qquad\Leftrightarrow\qquad đQ=dE-đW$$ and the statement you quoted is just the latter form

Obliv

I'm a sucker for analogies and the farmer pond one in Callen is pretty great :P

naturallyInconsistent

yay

Obliv

Pond of water (U) = Water entering/leaving via stream (dW) + water entering/leaving via rain/evaporation (dQ) and controlling with adiabatic impermeable walls (Tarp) and dams. You can have flow meters for the streams and pretty much get the first law from this setup

naturallyInconsistent

@Obliv Anyway, note that the direction Callen is taking is actually the vastly superior one, even though we are always more used to doing energy first. The fact of the matter is that, when you are trying to learn thermodynamics, we should already understand energy in its other forms. It is heat transfer, and entropy, that we must newly learn, and so we should be defining heat transfer via that latter form, and defining $S(E,V,N)$, rather than $E(S,V,N)$

i.e. the newly introduced in terms of the understood, not the other way around.

Obliv

16:59

Yeah he appears to put a lot of emphasis on "building from the ground up"

Transcript for