Jaynes is first mentioned on p. 221 of Consciousness Explained, and I haven’t got that far yet. I’m really rather perplexed about this; I have a distinct memory of reading about Jaynes’ bicameral mind, in some detail, in something by Dennett (around the same time I was reading Neal Stephenson’s Snow Crash, oddly enough—which was late last fall, I think). The slight reference in DDI that I can find almost certainly wouldn’t have been enough to prompt me to look it up (although I looked up and learned about a lot of things as a result of reading that book).
false_vacuum
Sorry, didn’t see this right away for some reason. Yeah, I think I’d like to read it at some point. And I don’t see it on the internet, so I’ll take you up on your offer. Could you send a copy to [email address redacted]?
Thanks!
This is exactly right except that the space in which Liouville’s theorem holds is called phase space. Phase space is the cotangent bundle over configuration space; i.e., if the configuration space is an n-dimensional manifold M, then for every point in M there is a copy of an n-dimensional vector space. These n-vectors* represent momenta, and both a configuration and a momentum are necessary to uniquely specify a state of a classical (Hamiltonian) system.
* More precisely, they are one-forms—linear functions of n-vectors; i.e. they eat n-vectors and spit out scalars. One-forms are also called covariant vectors, whence the other kind are called contravariant. They are dual to each other (for a given n), and thus (contravariant) vectors can equivalently be considered linear functions of one-forms instead.
I think it would be nice if the post were edited to reflect this distinction. It wouldn’t take much effort; just a sentence inserted at the point where it switches from talking about configuration space to talking about phase space, and appropriate tweaks to a few subsequent sentences. The Wikipedia article Configuration space links here, by the way.
Is this a standard term? I’ve only seen it in Alastair Reynolds’s writing.
immanent --> imminent
I don’t know much about politicians, really, but I don’t find it difficult to imagine that many of them could believe they are doing neither good nor harm on any significant scale—perhaps that they could not do significant good or harm--, but by means of some combination of seeking benefit for their allies and doing what they feel is necessary to be politically successful are in fact doing more harm than they imagine, at least by comparison with a hypothetical replacement of greater intelligence/integrity/courage/rationality/etc. I’m just speculating, though, and I’m not sure what could be offered in response except anecdotal (and indirect) evidence.
Here’s the output of my proofreading algorithm, which runs whenever I read something.
In the section Cardinal arithmetic, you have that the set X×Y is the cartesian product of A and B.
In The extended [positive] real line you have ‘with a an infinity element’.
In Hyperreal numbers you have ‘”the” hypperreal numbers’.
In your footnote to The surreal numbers you have ‘some a set of characteristic 0 “infinity kitchen sinks”’.
In Cardinal numbers (again), the words ‘set of’ should be used one more or at least 4 fewer times.
The world needed this article. I’m so glad you wrote it. It obviously needs to be in a more prominent place, and making it a wiki seems like a good idea.
How do I get the × html entity?
I suspect that partial orders are one of the most generally useful abstract tools that math-oriented people possess and others lack.
Also, looking forward to the aside on choice.
I’ll try that now.
It worked! (At least for me.)
Somebody should point out that TheOtherDave’s comment was a joke. (At least, I’m 95% confident it was so intended, and also I found it amusing.)
The Singularity is more analogous to the event horizon of a black hole; that used to be called the Schwarzschild singularity, but since its singular behaviour was an artifact of co-ordinate systems (as was first clearly shown by David Finkelstein), this terminology has fallen out of use. One imagines that eventually historical Singularities (which are really just prediction horizons) cease to be so called after they are past.
The singularity at the center of a black hole is presumably equally illusory; general relativity simply breaks down there, giving nonsensical answers (infinities). Singularities are in the map, not the territory. (Am I the first to say that?)
The contest announcement only refers to SI(AI) as ‘the Singularity Institute’, so clearly the prepositional phrase is foredoomed to wither on the vine. This seems a reasonable decision, all things considered; the shorter name seems higher-status to me.
I for one would get some utility from any further information about what sorts of designs were rejected and why. I’ve been working on SI logos for much of the last two days, but have no way to guess if I’m on the right track (other than that I like them, of course).
Has SI really got such a poor image that they’d want to consider abandoning their identity? I am certainly unaware of any such problem (but then, I don’t pay attention to a lot of things...).
For my part, I’m delighted to have the opportunity to try and create some distinctive imagery for SI. I’ve been fortunate enough to have what I think are some good ideas. And now I can be confident that SI will have a logo at least as good as the one I designed! Also, I’m using this as the perfect excuse to finally learn how to use Inkscape; that will be sufficient remuneration for my efforts. (I vaguely agree with the general point about contests tending to devalue labour, though.)
The event horizon is a co-ordinate singularity—like the North Pole. (Wikipedia has an article on the types of ‘mathematical’ singularity. I haven’t read it, so I don’t know how good it is.) Yes, in some sense it was a mistake to call the event horizon a ‘singularity’; that’s why they stopped.
Otherwise, we appear to agree. As you say, ‘If you divide by zero in your model, that just shows that your model is broken.’ I share your interest in good terminology; but it looks to me like it’s probably far too late to get rid of ‘The Singularity’. So I just adopt it, but with a certain air of amused detachment. Sure, it’s just a co-ordinate singularity at most.
I wonder if Ulam was thinking of the Schwarzschild singularity in 1958; that’s the same year Finkelstein’s co-ordinates were introduced, so he may or may not have absorbed the illusory nature of the horizon at that point, but probably he wasn’t thinking of the singularity at the centre of the hole. But I’m not much of an historian, and would welcome corrections from those better informed.
Yes, I think you’re right, concerning contemporary usage; but it’s not clear to me that either Ulam or Vinge had that connotation in mind.
ETA: Or von Neumann.
This presumably refers to Julian Jaynes and The Origins of Consciousness in the Breakdown of the Bicameral Mind. (I haven’t read it; I was sure until I checked that Dennett discussed it extensively in Darwin’s Dangerous Idea, but I can’t find such a discussion now, and thus have no idea why I know about it.)