111–120 of 250 posts
Earlier quoted context omitted.
It is discrete insofar as we're talking about sequences of thoughts, ie., reasoning. What offends the minds of some people is the world might not be like their mind at all. They want always to analogise everything to Reason. Everything should be countable, everything should be knowable, etc.
what's a sequence of thoughts?
Earlier quoted context omitted.
> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.
> computer science leaking out Planck constant would like to have a word with you. But it is true that CS shines a light on the matter of mapping the infinite into bounded spaces. This matter of ‘cognition’ is the entire matter (npi) of contention. What is the actual relationship between number and perceived phenomena ? What is the deeper meaning of the concordance of mathematics and physics? Where do these magical c…
Do you want to flesh this out? Are you suggesting that because phase space is quantized, position space must be quantized as well?
Earlier quoted context omitted.
Imagine there was a grid for space. For simplicity consider a regular grid of size 1unit in one direction and 1unit in a perpendicular direction. If such a grid existed, using one unit of ?something? would move you 1 unit along the axes of the grid, but you'd need 2 units of ?something? to move root2 units 45deg to the grid. Any discrete grid of any shape or size or pattern would have something like this, some sort o…
You don't have to imagine an ordered grid. If grid unit is small enough (say plank length 1,6 10^-35) and the grid is chaotic, for the distances of ~ 10^-16 that we can measure, everything will look the same in all directions. This happens the same way in which steel demonstrates isotropic behavior although its microscopic structure is anisotropic. So there is no easy way to prove or disprove continuity of space.
However, what's missed here is that discrete is a necessary but not sufficient condition.
Once you give any sort of plausible account of how reality could be discrete, as you've done here, you end up with non-computable aspects (eg., typically randomness). So the metagame is lost regardless: reality isnt a computer (/ no complete physical theories of reality are computable).
Though the meta-meta-game around "simulation" is probably internally incoherent in itself -- whether reality is a computer or not would really have nothing to do with whether any properties had by it (eg., mass) are simulated.
Since either you take reality to have this property and hence "simulation" doesn't make sense, or you take it to be faked. If it's faked, being computable or not is irrelevant. There's an infinite number of conceivable ways that, globally, all properties could be faked (eg., by a demon that is dreaming).
Maxwell didn't have the nice differential geometric notations that we use today, which allow us to write his equations in a very concise and easy to understand form. His original paper is way more convoluted, so at the time it must have been really difficult to understand for everyone except the subject matter experts. And he was of course building on the work of Faraday, Ampere and others. But like with other theori…
I really liked Kathy Joseph's historical reviews of vector physics and the people who developed it, which explain some of the reason's for how it's taught. Most texts don't even develop electrodynamics from relativistic electrostatics as a demonstration.
I think I fell down the rabbit hole from Freya Holmer's "why you can't multiply vectors".
The key being that all of the Hamiltonian fields can be found in a single quaternion equation, which is just what happens when you start multiplying vectors together.
Earlier quoted context omitted.
> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.
If it really was continuous so that physical quantities were real numbers as defined in mathematics, then it is in contradiction to maximal information density. Because almost all real numbers contain infinite amount of information. Full argument is elaborated here "Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real? by Nicolas Gisin": https://arxiv.org/abs/1803.06824
Earlier quoted context omitted.
> computer science leaking out Planck constant would like to have a word with you. But it is true that CS shines a light on the matter of mapping the infinite into bounded spaces. This matter of ‘cognition’ is the entire matter (npi) of contention. What is the actual relationship between number and perceived phenomena ? What is the deeper meaning of the concordance of mathematics and physics? Where do these magical c…
> Planck constant would like to have a word with you. Do you want to flesh this out? Are you suggesting that because phase space is quantized, position space must be quantized as well?
(My actual point is that Reality is neither continuous nor discreet - it is an infinitesimal point and it is our mind — that likes to name and number things and relies on duality to make ‘distinctions’ — that creates the universe, the subjective reality that we perceive as inhabiting.)
My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…
My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…
Earlier quoted context omitted.
Maxwell's Equations have already been superseded by Quantum Electrodynamics, in the same way that Newtonian gravity has been superseded by General Relativity. Both Newtonian gravity and Maxwell's Equations are still very good approximations in their regimes of validity.
we are commenting on an article which describes in depth how quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered. that's why my comment specifically talks about the 'maxwellian paradigm' and not 'maxwell's equations', which is, by the way, not a brand name i thought it was too obvious to be worth saying that classical physics is still an excellent approximation to reality, but hopef…
Are you commenting on the capitalization of "Maxwell"? It is a proper name, and it should be capitalized.
Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…
Are there any textbooks you would recommend for learning vector analysis / vector fields before studying EM?
Perhaps somebody who has read this book can comment in more detail.