Eric Angelini <Eric.Angelini@kntv.be> wrote:
Thank you, Keith -- I've just bought on Amazon.fr the Greg Egan books you've indicated.
Which books? I mentioned two short stories, "Luminous" and "Dark Integers." The website isfdb.org will tell you what books and magazines they appear in. If you're read them in the week since you posted that, what do you think of them? I've been thinking about how Egan's conjecture could be tested. In its weakest form, that no conjecture is true or false until it somehow makes a difference to some physical system, it can't be. But what about in a slightly less weak form? My modest proposal is that someone try testing a large number of conjectures that have almost certainly never been tested, or made any difference to any physical system, ever before. For instance the conjecture that the thousandth binary digit of the fractional part of some random hundred-digit number is 1. Test many such hundred-digit numbers using several very different algorithms. See if there's any correlation between which algorithm is used and the odds of the conjecture being true. If there isn't, that doesn't prove or disprove anything, but if there is, then something is going on. Probably the something is an uninteresting bug in your program. But suppose that is ruled out. First, there's the "most intuitive" possibility that whichever algorithm determines its value first, any other algorithm run later will find the same value, even if the value is biased by the first algorithm. If so, this could be used for communications. The sender and recipient agree ahead of time on a bank of numbers for each bit of the message. How many numbers are needed per bit depends on how strong the bias is. The recipient has to agree not to test the numbers until after the scheduled transmission time. If, after that, he finds the bias using an algorithm with the opposite bias, then a 1-bit has been sent, otherwise a 0-bit has been sent. If that's how it works, what if the two algorithms are run simultaneously, in the sense that no light-speed signal could get from either computer after it starts the computation to the other computer until after it had finished the computation? Would you somehow cause a contradiction? Would the conjecture be both true and false? One possible solution to that paradox is that no bias appears unless the computation will *never* be done with the other algorithm. But this could give rise to classic time-travel paradoxes instead. By deciding to later test or not test the banks of numbers with the other algorithm depending on, say, what next week's winning lottery numbers will be, you could send messages to yourself back through time. (If the numbers are large enough, and if you are careful to leave no record of them, it's all but certain that if you don't calculate on them using the other algorithm, nobody else ever will.) Self-reference: Since Egan's conjecture is itself a conjecture, then by its own rule it's neither true nor false until tested, and maybe how we test it will change the odds of its being true or false. Which do we want it to be? The conjecture is of course absurd, and in the unlikely case that there's any bias in the digits of square roots it's shared by all algorithms. But I could be wrong, so it might be worth testing. Maybe I'll test it myself if I get a TUIT with fewer corners. If you hear that I've won the lottery....
Propuls? d'un aPhone
Was the question mark supposed to be an e with an acute accent? Nobody seems to have mentioned, in the recent discussion about UTF-8, that in the digest option all high-bit characters are replaced by question marks. So in the digest option, only plain old 7-bit ASCII works.