@antimony Not referring to that in fact, but I think there may be methods some day of watermarking a text to know if it is AI generated. Steganography may play into that, just musing, I don't really know
FWIW, Scott Aaronson has been working for OpenAI, developing techniques to robustly watermark ChatGPT output, but they haven't been implemented yet. See https://scottaaronson.blog/?p=6823
I'm actually a little surprised that they haven't implemented it yet, since it would be very useful to OpenAI. The Internet is being flooded with ChatGPT output, and surely they want to be able to easily identify that stuff so that they can ignore it (or at least give it a low weight) in future training data.
@Amit I've seen this concept get introduced in a QM books appendix page. I suppose that's where the inner product of functions come from, and the concept of orthonormality etc. It was a bit contrived for me though, but i smiled and accepted it without any thought. After yesterday's discussion ive purchased 2nd hand copies of halmos- "finite dimensional vector spaces" and HK linear algebra
So I was watching some videos. Over here Padmanabhan claims that in a zero cosmological constant universe setting $a =1 $ in the FLRW metric is quite non-trivial:
so there is a constant in the universe $a_0$ which you can determine
only if this a note is given but if Friedmann equations do not f...
There is this interesting thought experiment : You will be cloned once, with same memories and stuff. Both clones will b indistinguishable. One clone gets a billion dollars. Other clone gets brutally murdered
I personally find this cloning unacceptable cuz it guarantees u being brutally murdered
We can't prove or disprove a deterministic universe so yeah, I guess it's good to learn statistical methods in the event that we're all just playing a game of chance
@Obliv "causation" is a story we tell ourselves, not an intrinsic part of our scientific models (see Norton's "Causation as Folk Science")
@RyderRude the more fundamental thing here is a philosophy of identity - what does it mean for some person to be "me", and more generally for anything to "be" the same thing as another (see also ship of Theseus)
your cloning presents little conflict to me - I find killing one person in exchange for a billion dollars inacceptable regardless of whether the person being killed or receiving the money is "me"
@ACuriousMind I would say that deciding yourself to be brutally murdered is less morally troubling than deciding someone else to be
So there is an argument 2 b made that, since a person feels in charge of themselves, they can decide it for themselves without facing moral issues
I personally hate this cloing becuz im guaranteeing godawful pain on myself @ACuriousMind . If suppose the experiment was : the first clone gets deleted painlessly. The second clone gets 1 billion. then i wud agree to the cloning
@RyderRude see, that's why I said this is really about philosophy of identity: In what sense is the person deciding this the same person that's being killed? To answer this you must first develop a coherent theory of what it means to be the same person.
Yeah, we then get into the ship of theseus stuff. The only resolution ive found to that one is that i define "changes to the object" as resulting in a different object
So in this sense, we r deciding it for a different person, yes
@Obliv you can't do math this way "from the start"
because you'd have to know a list of all primes in advance to write any number like this
and even determining whether large numbers are prime is hard enough that in some applications people only use algorithms that tell you the number is probably prime because dealing with some "primes" that aren't primes is easier than investing the computing power necessary to tell for certain
What I meant was anytime you're using a number you factor it, and maybe by having done this from ye olden days we would be better at it or see some patterns
But im pretty sure there are no patterns so that point is moot
I wonder why quantum computers are able to factor big numbers better than classical ones
if you represented numbers by physical characteristics, (such as the decimal number system, or shapes) you could come to the conclusion that it's prime just from the information present
you think that's true because that's how school teaches you to do mechanics
but if this truly was "intuitive" then why did civilization exist for thousands of years until we actually wrote down Newtonian mechanics?
I think there is an argument to be made that Newtonian mechanics is easier to understand than something like relativistic mechanics because we can cannot it more directly to our everyday experience
I think because we weren't concerned with abstraction in that sense. It's one thing to understand trajectories for shooting an arrow with a bow, and another to write it down to use in other ways.
both are able to predict where an arrow might land, but they use very different inputs to do so and they use fundamentally different processes to arrive at their results
In application to skills, you can develop intuition for basic familiarity with the skill, but to get better you have to apply yourself to face unfamiliar situations and make them familiar
Like the archer, or a video game professional etc
I don't know if this method of learning makes sense for math/science
Which makes me question the motto "shut up and calculate"
But if we have no familiarity to begin with it can help get you started I guess.
Do skills degrade in DnD @Acuriousmind
I wonder if your character doesn't do anything for some time if he gets weaker, or if that's dependent on the DM
I guess in a way people made RPGs because they found a balance of realism that they liked. When we were kids our necessity for realism was greatly lower :P
Yeah. But ultimately we do agree on wut words intuitively mean, even if words can't be defined non-circularly. What do we intuitively mean by the word "existence"?
And are platonism and mathematical universe using that word in a meaningful sense
I have one intuitive meaning of what it means to exist : I say everything in my own subjective experience exists @Obliv . This is how im defining this word
So all of my thoughts exist as thoughts, and my qualia exist
@ACuriousMind I think it's not a mainstream position :) . Most philosophers i chatted with today were more sure about the outside world than their perceptions
But idk. It seemed like they were not defining what it meant for the outside world to exist
They took it as their starting point @ACuriousMind
@PrateekMourya see e.g. math.stackexchange.com/q/770915/143136 for a proof that there are no functions that are eigenfunctions of the multiplication operator
@RyderRude that's not exactly a counterpoint to my statement
Philosophy is like frantically trying to build a sandcastle while the waves just wash it away every time. Like it seems like an exercise in futility but bolsters your reasoning skills
It's very much what I'd call an "operational definition" - yes, I agree this is how it works in practice like 99% of the time but I mean if that's what we're doing then I'm not sure why we're doing philosophy at all :P
@PrateekMourya We just want the analog of $\hat{H} \psi_{E_n}(q) = E_n \psi_{E_n}(q)$ for the position operator $\hat{q}$, where the action of this operator on functions $f(x)$ is via multiplication by $q$: $\hat{q} f(x) = q f(x)$. We thus need to find solutions to $\hat{q} f_{q_0}(q) = q_0 f_{q_0}(q)$ i.e. $q f_{q_0}(q) = q_0 f_{q_0}(q)$.
Either $f_{q_0}(q) = 0$ or $q = q_0$ solve this, so we need a 'function' $f_{q_0}(q)$ which is $0$ everywhere except at $q_0$ which is also normalized i.e. integrates to $1$, only a delta function $f_{q_0}(q) = \delta(q - q_0)$ does this, i.e. a distribution, which is not a function, and indeed $q f_{q_0}(q) = q \delta(q - q_0) = q_0 \delta(q - q_0) = q_0 f_{q_0}(q)$ holds.
@PrateekMourya so, we've shown any solution must be zero except at the single point $x=\lambda$. But a function that's only non-zero at a single point has zero integral, $\int f = 0$
all epistemologies essentially fall into two categories: Realism or idealism
idealists believe only "ideas", i.e. mind- or perception-dependent things exist, while realists believe there is such a thing as an independent external world - reality
But idk. I think this philosophy's starting point is an assertion we cant verify or falsify. They say that infants believe in objects before they r sentient
So objects exist before sentience
And sentience is a product of interacting with objects
@PrateekMourya you essentially have a choice here of "how mathematical" you want to be: You can ignore the distinction between a function and a distribution and just go with "$\delta(x)$ are eigenfunctions but not in the Hilbert space", you can learn what a distribution is and how they relate to the Hilbert space, or you can do any number of even more abstract stuff
in the end it depends on what you want to do with this - generally I would not worry too much about the nature of position "eigenstates" in introductory QM
@PrateekMourya the problem is that a Hilbert space is not the correct language if a wave function is not square integrable, i.e. the math is the wrong language
@RyderRude You see, at this point you must already have decided to believe in physicalism: Not only does an external physical world exist, but our minds are functions of it - of the physical processes in our brain - and thus observing the development of children's mental abilities is somehow a valid argument for how our minds work
@PrateekMourya it's not that it's not square-integrable, it's that the integral is zero (if it was a function)!
because we've shown it is zero everywhere except at $\lambda$
If a coin came up heads 9 times in a row, but you're assured it's a balanced and fair coin, would you bet heads or tails on the next throw for a million dollars?
In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$
(cf. last formula on p. 101). He then says that these eigenfunctions are not square integrable because
$$\int_{-\in...
@ACuriousMind yes. I too thought it was circular to say that they studied a child's brain and found the child believed in objects before they had subjective experience!
In Griffiths Introduction to Quantum Mechanics on page 102 it is shown, that the eigenfunctions of the position operator $\hat{x}=x$ are not normalizable.
$$\int_{-\infty}^{\infty}g_{\lambda}\left(x\right)^{*}g_{\lambda}\left(x\right)dx
~=~\left|B_{\lambda}\right|^{2}\int_{-\infty}^{\infty}\del...
@DIRAC1930 Why are the studying the exact propagator around the start of that chapter, where is it coming from? They define it out of thin air, but following their logic, where does it come from and what does it do
Right, but in the way they set things up, they pull (103.1) out of thin air (at best motivated by (73.3)), never explain how it arises or how it relates to what they did previously (as far as I can see), and intensely use this stuff in the next chapter without explaining the link (in what I remember)
The way they introduce (73.3) is a small side-step in the bigger problem of solving the bigger perturbation problem, yet here they take this as the fundamental quantity and never explain why or how it helps solve higher order corrections (as far as I can see) or how to use this to do the earlier stuff at higher orders, unless I'm missing something in the exposition (which is possible)
The series was originally released in 2 volumes with the second volume starting at the chapter 'Exact Propagators and Vertex Parts'. I've only really used the 2nd volume so I'm not sure
If you're just studying properties of Green functions that chapter is fine, in the larger QFT context I just can't believe they wrote it in this confusing way for such important stuff and am surely missing something (...)
One of the writers wrote another QED book and there too it's a mess on this topic
"While Heitler was at Göttingen, Adolf Hitler came to power in 1933. With the rising prominence of anti-Semitism under Hitler, Born took it upon himself to take the younger Jewish generation under his wing.[18] In doing so, Born arranged for Heitler to get a position that year as a Research Fellow at the University of Bristol, with Nevill Francis Mott." - Wikipedia
In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$
(cf. last formula on p. 101). He then says that these eigenfunctions are not square integrable because
$$\int_{-\in...
In Griffiths Introduction to Quantum Mechanics on page 102 it is shown, that the eigenfunctions of the position operator $\hat{x}=x$ are not normalizable.
$$\int_{-\infty}^{\infty}g_{\lambda}\left(x\right)^{*}g_{\lambda}\left(x\right)dx
~=~\left|B_{\lambda}\right|^{2}\int_{-\infty}^{\infty}\del...
