| bits? Does entropy have a hard objective definition here, or is it subjective?
Here is another showerthought. Different compression idea.
Every possible sequence of every possible
It is definitely objective in my example. Think of it this way, instead of 100 coinflips, do 2, so in binary: 00,01,10,11. And try to map the info into 1 bit: 0 or 1.
You can map 0 to 00 and 1 to 01, but then what do you map to 10 and 11? If you know that 10 and 11 never occurs, sure, you have compressed the data, but you do not.
This is proof that you cannot reduce entropy, only change the dataformat (and often add some entropy). Even a compression algorithm will INCREASE entropy of a totally random dataset.
About compression: For a given special dataset it may indeed decrease size, but if you use it over and over for different random datasets, you will spend more space than uncompressed.
That is, it is "proof" (not very rigorous and mathematically clear) that you cannot reduce entropy by a whole (information-)bit. It could easily be generalized to be more fine grained.
| number lives on irrational and transcendental numbers such as pi, right? (Nevermind the unfeasiblity, we just care about whether or not its logically possible). Could we not identify
| a string of data represented in numbers as an index position of pi? For example, '14159265' could be p[1:8]. Is that not potential for insane bit reduction, theoretically? (If the
| numbers get too big, no biggie, numbers can also be expressed as equations or in scientific notation).
I think all we gotta do to prove it is to do it once, and show results we
So you use some Pi magic to compress, and when it doesn't work you use some more magic. I am sorry, it will not help you, "the devil is in the details" here
| otherwise wouldn't be able to yield, correct?
I don't believe in a free lunch, but my mind is open.
People have bought me free lunch lots of times lol.
Ah, but if they bought the lunch, was it REALLY free? Huh? The plot thickens.
