Which in turn comes from the German word "Thaler", which originally was an abbreviation of "Joachimsthaler", which is (the nominalization of) an adjective meaning "from Jochachimsthal".
The point is, if you assume that you can roll dice infinitely often, then a limit probability of 0 cannot mean that the sequence is impossible, because whatever sequence you get, you'll have probability 0 for that sequence. That is, the probability of getting a sequence with probability 0 is 1.
Of course, if you take that fact just as proof that it is impossible to roll dice infinitely often, then we don't get any more problems with interpreting probability 0 as impossible.
Well, until someone invents the infinite improbability generator, that is.:-)
Actually I just noticed that there are sequences which provably cannot be compressed. There are at least two of them: The one-bit sequence "0" and the one-bit sequence "1".
If there is a countably infinite number of dices, the probability is the same as with one die. And allowing any number instead of just 1 multiplies the limit probability by 6 (I'm assuming the condition that all dice show the same number remains). Calculating 6*0 is left as exercise for the reader.
If there's an uncountably infinite number of dice, I'm not sure if the question is well defined.
The claim was that it is impossible to get, because the probability is 0. However, if you could roll an infinite number of times, you'd get a distinct infinite series of numbers. Since every distinct infinite series of numbers gives 0 as limit probability, the conclusion would be that you just rolled an impossible sequence. Welcome in the restaurant at the end of the universe.
You seem to have a very wrong conception of what math is about. Hint: It's not about calculating numbers (although the definition of numbers and the corresponding operators is a genuinely mathematical topic). Being good at logic is a very large part of what it means to be good at math.
Doesn't the compressibility depend on the compression algorithm? Are there sequences where you can prove that no compression algorithm will compress this special sequence (versus just checking that none of the known compression algorithms does)?
Actually, if you don't take the size of the compression algorithm itself into account, it's already trivial to achieve it: Start with any conventional compression algorithm. Now our new algorithm is the following:
if (sequence to compress == special sequence)
write(0) else
write(1)
compress sequence with other algorithm
That way the sequence will always be compressed to 1 bit. However, at the cost that you have to store the sequence in the decompression algorithm, because otherwise the one-bit file cannot be decompressed. Therefore the size of the (executable) decompression algorithm should count towards the compressed size. However, that gives another problem: The size of the algorithm depends on the machine code it's implemented in. A space-optimized x86 implementation will need a different number of bytes than a space-optimized Alpha version. So what is the "correct size" of the algorithm?
A nice example is the number pi. Pi is assumed to be normal, i.e. its digits are "random"; that would naively translate into not compressible. However, pi is very well compressible, as any algorithm to calculate pi is a compression of the sequence.
Sort of looks like there are groups of character-types, but I guess it could be random.
Actually anything could be random, because by its very nature a random process can create anything, including "Sort of looks like there are groups of character-types, but I guess it could be random." However, it's still much more likely that you intentionally wrote that sentence, that that it just happened to be generated by a random process.
Just make a "no party" clause with huge monetary penalty for breaking. Make it bloody obvious from the beginning that this clause is there, and that it will be enforced if necessary.
Actually tyrants fear the people more than democrats. In a democracy, those in power mainly fear to get voted out of office. Tyrants fear to be forcefully removed, with high probability of being killed, and an assured uncomfortable life if he survives the revolution.
I think maybe they should put the USERS outside at -11C
For users, -11C is not a documented working temperature.
By the way, expressing common measurements like this, in units that are so stupidly useless is my main beef with the metric system. WTF is a negative degree in this context?
A negative degree is a temperature where water freezes. This means, at negative temperatures you have to expect
glace
bottles freezing and breaking
precipitation will go down as snow
existing snow will not melt
It's the single most useful distinction there is. Going outside an -2C and going out at +2C is very different. Going out at +8C and going out at +12C is not too different.
Slashdot Mirror
No, dollar comes from the Dutch word "daalder"
Which in turn comes from the German word "Thaler", which originally was an abbreviation of "Joachimsthaler", which is (the nominalization of) an adjective meaning "from Jochachimsthal".
The point is, if you assume that you can roll dice infinitely often, then a limit probability of 0 cannot mean that the sequence is impossible, because whatever sequence you get, you'll have probability 0 for that sequence. That is, the probability of getting a sequence with probability 0 is 1.
Of course, if you take that fact just as proof that it is impossible to roll dice infinitely often, then we don't get any more problems with interpreting probability 0 as impossible.
Well, until someone invents the infinite improbability generator, that is. :-)
Actually I just noticed that there are sequences which provably cannot be compressed. There are at least two of them: The one-bit sequence "0" and the one-bit sequence "1".
The cardinal numbers are not a subset of the real numbers, and definitely not a finite one. Indeed, there are more cardinal numbers than reals.
How do you know? He might have picked a random cherry.
If there is a countably infinite number of dices, the probability is the same as with one die. And allowing any number instead of just 1 multiplies the limit probability by 6 (I'm assuming the condition that all dice show the same number remains). Calculating 6*0 is left as exercise for the reader.
If there's an uncountably infinite number of dice, I'm not sure if the question is well defined.
The claim was that it is impossible to get, because the probability is 0. However, if you could roll an infinite number of times, you'd get a distinct infinite series of numbers. Since every distinct infinite series of numbers gives 0 as limit probability, the conclusion would be that you just rolled an impossible sequence. Welcome in the restaurant at the end of the universe.
Are you sure one cannot define the concept of a random cardinal number?
First: Heisenberg.
Second: Even Bell only proves randomness on the assumption of locality. Non-local deterministic theories are still possible.
For example, it allows you to write your bitmasks without performing the tedious binary->decimal conversion.
You seem to have a very wrong conception of what math is about. Hint: It's not about calculating numbers (although the definition of numbers and the corresponding operators is a genuinely mathematical topic). Being good at logic is a very large part of what it means to be good at math.
And I'd also say that an astronomer should know quite a bit about using telescopes.
Doesn't the compressibility depend on the compression algorithm? Are there sequences where you can prove that no compression algorithm will compress this special sequence (versus just checking that none of the known compression algorithms does)?
Actually, if you don't take the size of the compression algorithm itself into account, it's already trivial to achieve it: Start with any conventional compression algorithm. Now our new algorithm is the following:
That way the sequence will always be compressed to 1 bit. However, at the cost that you have to store the sequence in the decompression algorithm, because otherwise the one-bit file cannot be decompressed. Therefore the size of the (executable) decompression algorithm should count towards the compressed size. However, that gives another problem: The size of the algorithm depends on the machine code it's implemented in. A space-optimized x86 implementation will need a different number of bytes than a space-optimized Alpha version. So what is the "correct size" of the algorithm?
A nice example is the number pi. Pi is assumed to be normal, i.e. its digits are "random"; that would naively translate into not compressible. However, pi is very well compressible, as any algorithm to calculate pi is a compression of the sequence.
Of course that assumes independence of the bits. If there's a memory effect, the "debiased" data may still be biased.
Unless the password is used for generating the key (together with the random number, of course).
How about this as random?
Sr5&8w796Z6W9mVVM7HAuv43Yg8D523QwTf25646@SEKKEP3#m2t3f@2ap95295437852^5262S*qMK#b&B#^aXbxNfRQudSCz9P
Sort of looks like there are groups of character-types, but I guess it could be random.
Actually anything could be random, because by its very nature a random process can create anything, including "Sort of looks like there are groups of character-types, but I guess it could be random."
However, it's still much more likely that you intentionally wrote that sentence, that that it just happened to be generated by a random process.
Only if you think being so fixated on your job to dismiss more important things (the hostages, in this case) is a good thing.
Just make a "no party" clause with huge monetary penalty for breaking. Make it bloody obvious from the beginning that this clause is there, and that it will be enforced if necessary.
Damn, there go my plans of selling a Beowulf cluster of Spectrums ... :-)
I don't think Microsoft will sell them their patents.
What if they want both PHP and .NET? (Say, .NET for their own application, PHP to run an existing forum software on their web site)?
That was an observation, a bash would be: "Macs cannot play games". There is a difference.
That would be bashing Mac, not bashing Mac users.
Actually tyrants fear the people more than democrats. In a democracy, those in power mainly fear to get voted out of office. Tyrants fear to be forcefully removed, with high probability of being killed, and an assured uncomfortable life if he survives the revolution.
For users, -11C is not a documented working temperature.
A negative degree is a temperature where water freezes. This means, at negative temperatures you have to expect
It's the single most useful distinction there is. Going outside an -2C and going out at +2C is very different. Going out at +8C and going out at +12C is not too different.
And yet you buy Apple products.
*ducks*
Apple now produces ducks?