eigenket

51 ms·

541.
by eigenket 3y ago
The easiest way to see it is to consider the time-reversed version. You chuck the ball up the shape so it perfectly stops balanced at the top. It turns out this is possible for the weird dome in question, but not for pretty much any other s
542.
by eigenket 3y ago
Ugh. Just a tiny bit of googling would have informed the scheme people that kawa is the Polish word for coffee.
543.
by eigenket 3y ago
I wouldn't describe that as sloppy. If it was written in isolation it would be a bit weird but given the context I think its completely fine.
544.
by eigenket 3y ago
For some reason computer programmers took the mathematical definition of "functions", used it for their things which are emphatically not mathematical functions, and are now complaining that they get confused by people talking ab
545.
by eigenket 3y ago
The article is by no means perfect, but that "howler" sees completely fine to me. If you want to prove something is a vector space the standard way would be to prove that all the vector space axioms hold for it.
546.
by eigenket 3y ago
I dont understand the point of this comment. You obviously need it to be a vector space before you can define an inner product. Inner product spaces are very special examples of vector spaces.
547.
by eigenket 3y ago
Perhaps it depends where you're from. I was born in the UK, and I don't see the HRE as particularly influencing my view of western vs non-western countries. Especially France, Spain, Portugal and the UK seem emphatically Western t
548.
by eigenket 3y ago
The Holy Roman Empire has very little do do with what is "the west", even within Europe. Spain, Poland, Portugal the UK were not part of it and only a small part of France was. France is (in my view) clearly significantly part of
549.
by eigenket 3y ago
Austrian neutrality has changed a lot over the years. They're part of the EU's common foreign and security policy, part of which is "Permanent Structured Cooperation" (because the EU, as much as I love it, absolutely suc
550.
by eigenket 3y ago
Legally Austria is part of the European Union and a founding member of the OECD. Its not just "allies with" the West. It is part of the west.
551.
by eigenket 3y ago
> Since then the sector has accumulated £53bn in debt while distributing £72bn to shareholders, the majority of whom are international investors Theres actually a pretty huge amount of "free ride" sitting there waiting to be ri
552.
by eigenket 3y ago
The Planck length does not mean anything like space quantization. It's just a length that pops out when you combine several physical constants. The values of those constants mean that the Planck scale is likely to be roughly where grav
553.
by eigenket 3y ago
That is certainly true. In fact you don't even need rational numbers, it is entirely possible that there are a finite number of positions on the universe, for example. Nevertheless physics seems to work very nicely when expressed in th
554.
by eigenket 3y ago
> I don’t know how someone is supposed to come up with evidence before a hypothesis Sure, this is usually how science works. A good example is the famous Michelson–Morley experiment which was performed in 1887 and was a key piece of evid
555.
by eigenket 3y ago
> In the decades since the establishment of these theories, both the continuous (classical) spacetime of general relativity and discrete matter of quantum mechanics, the world has changed in rather significant ways. It was essentially a
556.
by eigenket 3y ago
The Planck length and Planck's constans are both named after Max Planck. That doesn't mean they're the same thing. The Max Planck Institutes are also named after Planck, but they are neither lengths nor constants.
557.
by eigenket 3y ago
That isn't obvious to me - the equivalence principle works fine in classical GR, I'm not sure why it would break in Jonathan's model, but I'm very far from qualified to speak authoratively about his work!
558.
by eigenket 3y ago
Thats definitely a good question, and one that people have thought about before. I think its amazingly difficult to test it experimentally, even compared to something like directly measuring to see whether a massive object in superpositio
559.
by eigenket 3y ago
That is certainly a hypothesis, but there is no evidence for it.
560.
by eigenket 3y ago
I think this entire comment thread is using the wrong definition of the word "quantized". There are two relevant meanings of this word 1. Something split up into discrete chunks (like integers vs real numbers) 2. Something which a
561.
by eigenket 3y ago
I attended a talk by Jonathan Oppenheim a while back on this subject, and my understanding based on that is that in his model something (very) roughly like this happens. You put your massive object in superposition, it interacts with space-
562.
by eigenket 3y ago
Speaking as a physicist I think its very far from obvious that digital physics (or anything else) is the correct approach from a philosophical perspective. Real numbers are so ubiquitous in physics because space-time (and other quantities)
563.
by eigenket 3y ago
There is absolutely no evidence that the Planck length is anything like the smallest possible length or wavelength. Its "just" a length scale that pops out when you combine several physical constants. That combination of constants
564.
by eigenket 3y ago
x86 machine code is a type of program, which is interpreted by the processor, but distributing the binary of my program doesn't make it open source.
565.
by eigenket 3y ago
I would argue that dimensionful quantities are never used as arguments to power series, however you are correct that this does not imply that angles are dimensionless, since (like we do with other quantities, we can divide by whatever unit
566.
by eigenket 3y ago
Ok, you've replied to quite a lot of my comments, with some fairly confusingly worded responses. Some of your claims appear to be incompatible as far as I read them. For example you claim that angles are not dimensionless, but that dim
567.
by eigenket 3y ago
If you say "angles have units" I agree with you - obviously you can measure them in degrees or radians or whatever you want. I was responding to the claim > Angles aren't dimensionless any more than lengths are dimensionle
568.
by eigenket 3y ago
Units are not the same as dimensions, something can have a dimension of 1 (which is what we usually mean by "dimensionless") and still have different units, just as something can have a dimension of length but still be measured in
569.
by eigenket 3y ago
Angles are absolutely more dimensionless than lengths are. For an easy check you can't add quantities where the dimension differs, which means it doesn't make sense to add a length to its cube. On the other hand it does make sen
570.
by eigenket 3y ago
You appear to be confusing special relativity and general relativity. Mass-energy equivalence pops out of special relativity, and is part of general relativity because GR extends SR. Another class of theories which extend special relativity

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