A binary string is said to be random in
algorithmic information theory (my area of mathematics)
if it is not significantly compressible.
(I won't get into exactly what this means here
but you get the idea...)
Anyway,
anything that is compressible by a factor of
100 must have a huge amount of structure for
the compressor to take advantage of, and so
is highly non-random by definition. Clearly then their "virtually
random" data is not random in the slightest.
In fact in order to be compressible by this
factor it must be EXTREMELY non-random!
With a masters degree in the mathematics of Kolmogorov complexity theory (on which the theory behind this challenged is based) I have a few
comments. Yes, it is impossible to compress
a random string, in fact if you accept the Kolmogorov notion of randomness then it's
true just by definition. However you have to
be really really careful in defining the problem
not to let any additional information slip in
from anywhere -- even the mathematicians made
a mistake here when they first did it in that
they didn't properly account of the information
in the length of the compressed string(s) (Solomonoff's original definition didn't account for this - not to detract from his genius!).
Patrick used exactly the same trick here and
Mike was just too careless and let Patrick's
trick slip by. Mike had a basic idea right,
but in agreeing to allow multiple files without
explaining in great detail how he was going to
measure total file size he slipped up. Well done Patrick!:)
Brazil has had a computerized voting system for
years which uses machines that are sort of like
touch screen ATMs. It works fine, and has
done so for many years. After all it's hardly
hardly rocket science...
Slashdot Mirror
A binary string is said to be random in
algorithmic information theory (my area of mathematics)
if it is not significantly compressible.
(I won't get into exactly what this means here
but you get the idea...)
Anyway,
anything that is compressible by a factor of
100 must have a huge amount of structure for
the compressor to take advantage of, and so
is highly non-random by definition. Clearly then their "virtually
random" data is not random in the slightest.
In fact in order to be compressible by this
factor it must be EXTREMELY non-random!
With a masters degree in the mathematics of Kolmogorov complexity theory (on which the theory behind this challenged is based) I have a few comments. Yes, it is impossible to compress a random string, in fact if you accept the Kolmogorov notion of randomness then it's true just by definition. However you have to be really really careful in defining the problem not to let any additional information slip in from anywhere -- even the mathematicians made a mistake here when they first did it in that they didn't properly account of the information in the length of the compressed string(s) (Solomonoff's original definition didn't account for this - not to detract from his genius!). Patrick used exactly the same trick here and Mike was just too careless and let Patrick's trick slip by. Mike had a basic idea right, but in agreeing to allow multiple files without explaining in great detail how he was going to measure total file size he slipped up. Well done Patrick! :)
Brazil has had a computerized voting system for years which uses machines that are sort of like touch screen ATMs. It works fine, and has done so for many years. After all it's hardly hardly rocket science...