Forum: Science, Mathematics, Medicine, and Technology
2nd August 2014, 04:13 PM
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Replies: 2,104
Views: 221,008
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Forum: Science, Mathematics, Medicine, and Technology
27th July 2014, 04:01 PM
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Replies: 13
Views: 1,261
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Forum: Science, Mathematics, Medicine, and Technology
12th July 2014, 07:42 AM
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Replies: 84
Views: 4,339
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Forum: Science, Mathematics, Medicine, and Technology
24th June 2014, 03:15 AM
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Replies: 8
Views: 1,069
Bell's theorem says that a quantum theory can't...
Bell's theorem says that a quantum theory can't have locality, counterfactual-definiteness, and realism all at once. Denying CFD doesn't automatically bring about locality.
MWI says that there's a...
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Forum: Science, Mathematics, Medicine, and Technology
23rd June 2014, 08:32 AM
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Replies: 8
Views: 1,069
In classical mechanics, trying to make a...
In classical mechanics, trying to make a superposition of eigenstates gets you something indistinguishable from a mixed state, which you can then interpret as your lack of knowledge about the...
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Forum: Science, Mathematics, Medicine, and Technology
27th April 2014, 05:38 PM
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Replies: 1,631
Views: 91,465
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Forum: Science, Mathematics, Medicine, and Technology
27th April 2014, 05:10 PM
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Replies: 1,631
Views: 91,465
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Forum: Science, Mathematics, Medicine, and Technology
27th April 2014, 04:53 PM
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Replies: 1,631
Views: 91,465
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Forum: Science, Mathematics, Medicine, and Technology
27th April 2014, 03:06 PM
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Replies: 2,104
Views: 221,008
Just another way Maxwell's equations become...
Just another way Maxwell's equations become prettier with magnetic monopoles than without...
One can do a bit better if one treats the relationship between the EM tensor and its dual as a...
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Forum: Science, Mathematics, Medicine, and Technology
26th April 2014, 11:09 AM
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Replies: 2,104
Views: 221,008
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Forum: Science, Mathematics, Medicine, and Technology
25th April 2014, 03:59 AM
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Replies: 2,104
Views: 221,008
A somewhat more faithful transcription of...
A somewhat more faithful transcription of Heaviside's paper follows (Ụ should have dot above):
Finally, the appearance of V is to indicate that vector product that follows it is the vector (i.e.,...
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Forum: Science, Mathematics, Medicine, and Technology
12th April 2014, 06:49 PM
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Replies: 1,631
Views: 91,465
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Forum: Science, Mathematics, Medicine, and Technology
25th March 2014, 07:38 AM
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Replies: 2,104
Views: 221,008
The "right-hand rule" is just an artifact of...
The "right-hand rule" is just an artifact of using pseudovectors in place of bivectors (http://en.wikipedia.org/wiki/Bivector). In three dimensions, standard Hodge duality maps bivectors to vectors...
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Forum: Science, Mathematics, Medicine, and Technology
22nd March 2014, 05:16 AM
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Replies: 2,104
Views: 221,008
This is not only of dubious relevance, but...
This is not only of dubious relevance, but manages to the the direct opposite of the facts.
Benko gave up his spot for Fischer because Fischer refused to participate in the 1969 US Championship...
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Forum: Science, Mathematics, Medicine, and Technology
2nd March 2014, 11:22 PM
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Replies: 45
Views: 3,630
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Forum: Science, Mathematics, Medicine, and Technology
1st March 2014, 01:16 PM
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Replies: 2,104
Views: 221,008
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Forum: Science, Mathematics, Medicine, and Technology
28th February 2014, 02:16 PM
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Replies: 2,104
Views: 221,008
The essence of the Newtonian intuition...
...
The essence of the Newtonian intuition...
carries over into GTR: if you have two geodesics with four-velocity u and a nearby geodesic connected with n connecting points of equal affine...
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Forum: Science, Mathematics, Medicine, and Technology
16th February 2014, 03:56 PM
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Replies: 159
Views: 9,569
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Forum: Science, Mathematics, Medicine, and Technology
16th February 2014, 03:13 PM
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Replies: 159
Views: 9,569
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Forum: Science, Mathematics, Medicine, and Technology
15th February 2014, 11:11 PM
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Replies: 159
Views: 9,569
I've never said that gravity moves...
I've never said that gravity moves instantly--actually, I've explicitly said it does not.
I've never said that they didn't decay. I've merely said that they don't decay fast enough to crash into...
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Forum: Science, Mathematics, Medicine, and Technology
15th February 2014, 12:19 PM
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Replies: 159
Views: 9,569
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Forum: Science, Mathematics, Medicine, and Technology
15th February 2014, 11:25 AM
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Replies: 159
Views: 9,569
Nonsense. The only claim I've made about the...
Nonsense. The only claim I've made about the stability of orbits here is that they're stable enough for the Earth not to spiral into the Sun on the timescale of a handful of centuries. This is very...
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Forum: Science, Mathematics, Medicine, and Technology
15th February 2014, 05:26 AM
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Replies: 159
Views: 9,569
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Forum: Science, Mathematics, Medicine, and Technology
15th February 2014, 01:46 AM
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Replies: 159
Views: 9,569
For the motivating analogy of electromagnetic...
For the motivating analogy of electromagnetic field of a uniformly moving charge, see just about any EM textbook that discusses the Lorentz transformation. The electric field is directed toward its...
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Forum: Science, Mathematics, Medicine, and Technology
14th February 2014, 10:51 PM
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Replies: 159
Views: 9,569
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Forum: Science, Mathematics, Medicine, and Technology
14th February 2014, 09:02 PM
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Replies: 159
Views: 9,569
That doesn't happen. Putting in an eight-minute...
That doesn't happen. Putting in an eight-minute delay puts a force component on Earth that makes it orbit unstable on the order of a few centuries. This is very tough to reconcile with the historical...
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Forum: Science, Mathematics, Medicine, and Technology
11th February 2014, 09:59 PM
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Replies: 15
Views: 2,960
His conclusions would be wrong-headed even if...
His conclusions would be wrong-headed even if that claim were true, which can be argued separately*, but in fact it is false. While the claim does the describe the four most famous of black hole...
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Forum: Science, Mathematics, Medicine, and Technology
28th January 2014, 12:25 PM
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Replies: 18
Views: 885
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Forum: Science, Mathematics, Medicine, and Technology
28th January 2014, 01:07 AM
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Replies: 18
Views: 885
There's an ambiguity here. Does this mean you...
There's an ambiguity here. Does this mean you evaluate both series (by whichever method if not the conventional definition), then subtract? If the value is finite, then yes. Otherwise, undefined.
...
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Forum: Science, Mathematics, Medicine, and Technology
26th January 2014, 03:46 AM
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Replies: 68
Views: 3,529
If you ask yourself what justifies the quoted...
If you ask yourself what justifies the quoted step, you'd probably want a principle like "I can rearrange the order of the sequence I'm summing arbitrarily without affecting the sum."
It is true...
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Forum: Science, Mathematics, Medicine, and Technology
26th January 2014, 03:04 AM
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Replies: 68
Views: 3,529
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Forum: Science, Mathematics, Medicine, and Technology
22nd January 2014, 11:34 PM
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Replies: 584
Views: 17,723
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Forum: Science, Mathematics, Medicine, and Technology
22nd January 2014, 09:31 PM
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Replies: 584
Views: 17,723
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Forum: Science, Mathematics, Medicine, and Technology
22nd January 2014, 10:43 AM
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Replies: 584
Views: 17,723
Number of object doesn't matter. STR is as...
Number of object doesn't matter. STR is as consistent as Euclidean geometry, since Minkowski spacetime is just a sign flip in the metric away from Euclidean space.
This is especially obvious in...
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Forum: Science, Mathematics, Medicine, and Technology
21st January 2014, 01:56 AM
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Replies: 68
Views: 3,529
I gave definitions of both explicitly* and...
I gave definitions of both explicitly* and explained some of the motivation for having something other than the common definition of a series sum.
I kept on using explicit names for them because...
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Forum: Science, Mathematics, Medicine, and Technology
20th January 2014, 10:01 PM
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Replies: 68
Views: 3,529
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Forum: Science, Mathematics, Medicine, and Technology
19th January 2014, 03:08 PM
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Replies: 68
Views: 3,529
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Forum: Science, Mathematics, Medicine, and Technology
19th January 2014, 06:16 AM
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Replies: 68
Views: 3,529
I'm afraid not.
A convergent series will...
I'm afraid not.
A convergent series will have only one limit of partial sums, and phrasing this condition more precisely illustrates exactly where some of the other possibilities lie.
For...
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Forum: Science, Mathematics, Medicine, and Technology
18th January 2014, 01:14 PM
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Replies: 68
Views: 3,529
You're mis-diagonising the problem, and as a...
You're mis-diagonising the problem, and as a result missing some interesting mathematics. This is bad, because the point of mathematics (qua mathematics) is to explore interesting abstract structure....
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Forum: Science, Mathematics, Medicine, and Technology
18th January 2014, 08:30 AM
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Replies: 68
Views: 3,529
Why would that end discussion? There are many...
Why would that end discussion? There are many ways to assign a value to an infinite series, of which the common meaning is just one. As long as we're careful not to equivocate between them, there's...
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Forum: Science, Mathematics, Medicine, and Technology
18th January 2014, 12:31 AM
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Replies: 68
Views: 3,529
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Forum: Science, Mathematics, Medicine, and Technology
17th January 2014, 11:10 PM
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Replies: 68
Views: 3,529
The sum doesn't exist because the series is...
The sum doesn't exist because the series is divergent, and the sum of the series means the limit of the partial sums.
That doesn't mean we can't have concepts that acts analogously to the sum of...
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Forum: Science, Mathematics, Medicine, and Technology
16th January 2014, 02:22 PM
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Replies: 12
Views: 1,181
I think I have to slightly disagree with...
I think I have to slightly disagree with Ziggurat's point. Not about the utility of relativistic mass (it's indeed redundant and pointlessly confusing), or the reasoning that bare facts should be...
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Forum: Science, Mathematics, Medicine, and Technology
28th November 2013, 06:25 PM
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Replies: 31
Views: 1,043
This isn't really correct. As a particular...
This isn't really correct. As a particular example, if you have completely Euclidean constant-time slices, as in,
[1] ds² = -(1+2Φ)dt² + (dx²+dy²+dz²)
where Φ is small and time-independent, then to...
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Forum: Science, Mathematics, Medicine, and Technology
10th November 2013, 04:45 AM
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Replies: 60
Views: 6,330
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Forum: Science, Mathematics, Medicine, and Technology
10th November 2013, 02:34 AM
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Replies: 60
Views: 6,330
Completely disagree.
No, it is both...
Completely disagree.
No, it is both correct and fair. Eddington ca. 1930s and was a crank. Bohr, Fowler, Gamow, Kramers, von Neumann, Rosenfeld, and Wigner all knew it at the time, although they...
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Forum: Science, Mathematics, Medicine, and Technology
9th November 2013, 04:52 PM
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Replies: 60
Views: 6,330
I'd call it "confirmation bias" instead, but...
I'd call it "confirmation bias" instead, but otherwise yes.
Eddington's story was itself caused by Eddington inventing reasons to confirm his belief about 136 or 137 being special, so it itself was...
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Forum: Science, Mathematics, Medicine, and Technology
9th November 2013, 04:08 PM
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Replies: 60
Views: 6,330
That's just wrong. Well, at best, that's...
That's just wrong. Well, at best, that's extremely misleading.
There never was a time when it looked it might be "exactly 1/137", at least not in the sense of there having ever been an even...
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Forum: Science, Mathematics, Medicine, and Technology
8th November 2013, 09:17 AM
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Replies: 20
Views: 1,087
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Forum: Science, Mathematics, Medicine, and Technology
2nd November 2013, 07:26 AM
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Replies: 116
Views: 7,327
That's almost but not strictly speaking true....
That's almost but not strictly speaking true. Intel processors have had the RDRAND instruction since Ivy Bridge, and it generates random numbers non-deterministically, at least in the sense of having...
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