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You might be interested in the last section of Motion Mountain, the free online physics textbook. It presents absolute limits for various measures of the universe, derived from quantum mechanics and general relativity. It appears that we live in a finite universe, though all of this stuff is pretty speculative.
circular sunglasses that have two polarized disks
(1) Circular sunglasses sem to be out of fashion at the moment.
(2) the polarization of sunglasses is chosen to eliminate glare from reflections of a rain-soaked street.
"Once upon a time, the notion of the scientific method - updating beliefs based on experimental evidence - was a philosophical notion."
"But back in Galileo's era, it was solely vague verbal arguments that said you should try to produce numerical predictions of experimental results, rather than consulting the Bible or Aristotle."
As far as I know, the first hints of the scientific method (testing theories by experiment) appear in the writings of Roger Bacon (who liven a few hundred years before the Francis Bacon people seem to confuse him with). He argued that when interpreting Aristotle, instead of arguing what the modern translation of an obscure Greek word was, you should use experiments to try out the alternative meanings. Experiment was conceived as a method of consulting Aristotle.
Humble beginnings.
Grey Area asked, "For instance, Cox's theorem states that plausibility is a real number. Why should it be a real number?" For that matter, why should the plausibility of the negation of a statement depend only on the plausibility of the statement? Mightn't the statement itself be relevant?
Any complex number? I.e. you're invoking an uncountable infinity for explaining the lowest known layer of physics? How does that fit in with being an infinite-set atheist - assuming you still hold that position?
In case you didn't notice, he's talking about a complex number, not all the complex numbers.
There's a long story at the then of The Mind's Eye (or is it The Mind's I? in which someone asks a question:
"What colour is this book.?"
"I believe it's red."
"Wrong"
There follows a wonderfully convoluted dialogue. The point seems to be that someone who believes the book is red would say "It's red," rather than "I believe it's red."
I'm in the middle of reading a wonderful fantasy. It's John Crowley's four-volume series Aegypt (not to be confused with his one-volume book Aegypt published a decade or two ago.) It is about a man who discovers that (here's the fantasy) there is more than one history of the world. Only a few hundred years ago, the Earth was at the centre of the universe. It was when people started to realise this wasn't so that the universe changed. Before that, the Earth was at the centre of the universe, and always had been so. After that the Earth wasn't at the centre, and had never been there.
This book excites my sense of wonder, even though I know it isn't so.
I'm also reading articles on how category theory is applied to quantum mechanics, and how this brings with it a whole set of nonclassical logics -- logics in which proof by contradiction fail, and in which 'and' and 'or' don't distribute (which I believe plays havoc with Bayes' theorem). Fascinating stuff.
In the sixties I was drunk on Cantor's theories of transfinite numbers, just intoxicated with an appreciation of their sheer, unimaginable hugeness. Don't tell me that mathematics is dry, and there is no sense of wonder there.
In the seventies I became a constructivist. Gone were all those transfinite objects. But the sense of wonder remains, and I keep finding new things to amaze me -- the sheer intricate details of finite things, and of merely countable infinity. The boundary between finite representations of the infinite and the infinite things represented is wonderfully intricate in detail.
The sense of wonder is innate. It attaches itself to things that exist and things that don't. There's no need to give it up merely because you've felt the divine in things that are unreal. It's still there, even if the things aren't. It's still there, even if the things are.
But is it important to distinguish what is real and what is not.
Eliezer could assert that the technology to beat the CAPTCHAs exists and is understood
Id does. In fact, most of the commonly used CAPTCHAs can be more reliably decoded by a machine than by a human being.
-- hendrik
It's not about what the bug-eyed monster considers sexy. It's about what the human reader considers sexy.
other people were near-perfect "eidetic" imagers
I read a report in the Scientific American a few years ago in which they were doing experiments with rend0m-dot stereograms -- the kind of thing where if you just look at one image or the other you just see random dots, but if you look at one with one eye and the other with the other eye you see a square full of random dots floating above a background with random dots.
Some people could be shown one image one week, and the other the next week, each by itself, and suddenly get it. Evidently they had remembered the entire first-week image in memory to scompare with the second a week later.
I was impressed. This seemed eidetic enough for me.
Let's take Bayes seriously.
Sometime ago there was a posting about something like "If all you knew was that the past 5 mornings the sun rose, what would you assign the probability the that sun would rise next morning? It came out so something like 5/6 or 4/5 or so.
But of course that's not all we know, and so we'd get different numbers.
Now what's given here is that Omega has been correct on a hundred occasions so far. If that's all we know, we should estimate the probability of him being right next time at about 99%. So if you're a one-boxer your expectation would be $990,000 and a two-boxer would have an expectation of $11,000.
But the whole argument seems to be about what extra knowledge you have; in particular, Can causation work in reverse? or Is Omega really superintelligent? or even Are the conditions stated in the problem logically inconsistent (which would justify any answer.)
Perhaps someone who enjoys these kinds of odds calculations could investigate the extent to which we know these things and how it affects the outcome?