right. very likely they wouldn't be even capable to instruct their faked 60 mill ai-managed profiles 'to like' Zuckerboi's own sentence for that matter ..
That's one explanation for the force. Another is that it's just the electrons/atoms in the two plates attracting each other. It's literally mentioned in the page you linked.
John Baez is actually quite level headed, one of my idols, and I see nothing wrong with that list.
However OP wasn't even asserting anything of a discovery or a revolution. He actually ended his post by asking a question: "Then, I suppose, the question further resolves to: which assumption makes our equations easier to work with?"
Any decent man would have explained to OP about how the best fitting generalizations/abstractions in mathematics and physics also fit the most specific cases. Instead we had a gatekeeper put OP down like a wild fox in a hen house. It's shit like that, that makes humanity stink of arrogance and petulance. It's people like that, that discourage positivity while dispersing platitudes. Their subscription to authority has no basis in merit, it is exactly like John Baez says: "Crackpot Index #9) List your credentials"
This is what epistemic status tries to make explicit. There’s a difference between serious conjecture and playful speculation. The former, I think, involves claiming an amount of status for oneself. People view the latter as the former and attack speculators for having insufficient status. It’s a shame, because speculation can be a useful learning activity/opportunity.
> the best fitting generalizations/abstractions in mathematics and physics also fit the most specific cases
Out of curiosity, how does this differ from the criteria of choosing the assumption which makes the equations easier to work with?
I feel as if they are the same, though perhaps lacking a careful qualification on my part: "which assumption makes our equations easier to work with (without introducing incorrect solutions)?"
Given the choice of abstractions, assuming each abstraction is apt as the next and none of them is "more wrong" than any other, wouldn't the choice of abstraction come down to ease? (or aesthetics, possibly)
I'd love your take, and doubly so if I seem to be coming at this backwards.
Yes, if there is no difference, then we'd likely use the one that is easier or more aesthetic. The heuristic would differ depending on the discipline and the culture of the science.
For instance, Matrix mechanics is equivalent to the Shrodinger wave formulation, but it did not catch on for reasons listed here.
Another system that did not catch on, is Nonstandard analysis, which uses infinitesimals. It is equivalent to the standard curriculum analysis that uses limits.
It's hard to pinpoint exactly why these systems weren't chosen. It's not just aesthetics or ease of use. It's a bit of arcane history too. Nonstandard analysis took a while to make rigorous. And by that time, standard analysis had already enveloped the "cult of science." Once standards are set, they rarely change if the current methods are "good enough." I've always sought intuition with everything, so I know about these alternative methods.
I find it sad that so many in academia resign themselves to symbol pushing without a real understanding, and then repeat the same misgivings on their pupils. If methods do exist to achieve better intuition, then we should promote them. Often, alternative yet equivalent formulations do provide that intuition.
HN is a bit of a cult of personality itself but ironically, about every month on the dot, a submission gets front paged - geometric / vector algebra or quaternions, and how they simplify and clarify the intuition behind 3D transformations.
Yet the same HN has curmudgeon gatekeepers that also pop up like clockwork in any science thread, just to make sure all lines of thought correlate to the rote symbol pushing they learned. They didn't gain intuition, so they must feel that it's either impossible to, or that no one else has the right to intuition either.
You did, thank you for the discussion! I actually have a first edition of Keisler's "Elementary Calculus," well-worn I assure you; throughout my mathematics degree, I sought various other methods of approaching the curricula. I'm very much a fan of Robinson's program of infinitesimals; occasionally, I'm treated to even more rarefied notions of these beloved ghosts of departed quantities.
Here's one I find particularly fun, wherein you disregard law of excluded middle to use nilpotents!
I'm currently trying to digest "Geometric Algebra: An Object-Oriented Approach." It is a real pleasure to see you mention some of my pet favorites; thank you, thank you, a hundred times over friend! You've put a song in my heart today.
EDIT: I was so wrapped up in having met a fellow traveler that I forgot to leave an "in," should you wish to continue this thread.
I also find it a tragedy that my foray into the constructivist and sundry corners of math was relegated to self-study. Having approached a few professors on this topic, the general consensus seems to be "why waste your time?"
To what do you think the intuitive power of these equivalent-but-alternative foundations is owed? Personally, I think it has something of the basis that colors the division of the analytically- vs algebraically-minded; yet even the cause of this is a mystery!
(However, let me be careful here: I don't wish to give the impression of undue competence. I'm broadly-read, but woefully underskilled.)
Thank you for sharing SDG. I haven't heard it mentioned in many years. The simplification power it provides is beautiful! [1]
I'm elated over having delighted and filled you with music. Your kind words have made me beam from ear to ear as well :-)
I think the intuitive power of these other formulations comes from the spatial/geometric imagery that these disciplines naturally provide. Another aspect is the conversion of unwieldy processes into simpler objects. Like nonstandard analysis replacing the limit process with the infinitesimal object.
The paradigm of replacing large processes with things that can be intuited might not be very profound if as programmers we bring up first class functions. A function is just an object anyhow! True but the human mind seems to be less efficient at composing functions than composing objects. So though it's all interchangable, we seem to work better when we are given mentally ergonomic foundations.
Back to what you said in your previous posts, the ease of manipulation in these alternative theories, it probably lends a bit from this exchange of complicated processes for simpler things.
No, I'm saying that griping about how things in social land are polarized isn't going to get us off this planet. If you have the brains to write these things, you have the brains to work on a solution that doesn't give a fuck about what some douchebag poser thinks about how reality works.
Though comprised of many good people, HR is just the de facto surveillance apparatus of management. This has been shown to be the case many times over.
HR. its in the name. Human Resources. Theyr job is to provide human resources to the company, not to defend employee rights. Thats what unions are for.
Ok, then what do you do once all these companies stop doing business with the US government? The US government will find someone else to buy these services from - maybe they will have to pay more... no big deal.
Governments pay more all the time for various social and political purposes. For Amazon and other tech companies "The government made us do it" is probably what they're after anyway. It allows them to service everyone and not have to face boycotts from anyone.
Drat, I didn't come up with a perfect plan, with no possible hypothetical what-if responses. Back to the drawing board.
It's a solution to keep corporations that grow big enough to cause societal issues, having grown that big through utilizing society's resources, somewhat more accountable. There might be issues, but I'd suspect there to be more issues with the current solution: being "nothing."
