patternCritical
Is von Neumann's randomness in sin quote no longer applicable?
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Problem
Some chap said the following:
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
That's always taken to mean that you can't generate true random numbers with just a computer. And he said that when computers were the equivalent size of a single Intel 8080 microprocessor (~6000 valves). Computers have gotten more complex, and I believe that von Von Neumann's statement may no longer be true. Consider that an implemented software only algorithm is impossible. They run on physical hardware. True random number generators and their entropy sources are also made of hardware.
This Java fragment put into a loop:
can create a data file which I've represented as an image:
You can see structure, but with a lot of randomness as well. The thing of interest is that this PNG file is 232KB in size, yet contains 250,000 grey scale pixels. The PNG compression level was maximum. That's only a compression ratio of 7%, ie. fairly non compressible. What's also interesting is that the file is unique. Every generation of this file is a slightly different pattern and has similar ~7% compressibility. I highlight this as it's critical to my argument. That's ~7bits/byte entropy. That will reduce of course upon use of a stronger compression algorithm. But not reduce to anything near 0 bits/byte. A better impression can be had by taking the above image and substituting its colour map for a random one:-
Most of the structure (in the top half) disappears as it was just sequences of similar but marginally different values. Is this a true entropy source created by just executing a Java program on a multi taking operating system? Not a uniformly distributed random number generator, but the entropy source for one? An entropy source built of software running on physical hardware that just happens to be a PC.
Supplemental
In order to confirm that every image gener
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
That's always taken to mean that you can't generate true random numbers with just a computer. And he said that when computers were the equivalent size of a single Intel 8080 microprocessor (~6000 valves). Computers have gotten more complex, and I believe that von Von Neumann's statement may no longer be true. Consider that an implemented software only algorithm is impossible. They run on physical hardware. True random number generators and their entropy sources are also made of hardware.
This Java fragment put into a loop:
file.writeByte((byte) (System.nanoTime() & 0xff));can create a data file which I've represented as an image:
You can see structure, but with a lot of randomness as well. The thing of interest is that this PNG file is 232KB in size, yet contains 250,000 grey scale pixels. The PNG compression level was maximum. That's only a compression ratio of 7%, ie. fairly non compressible. What's also interesting is that the file is unique. Every generation of this file is a slightly different pattern and has similar ~7% compressibility. I highlight this as it's critical to my argument. That's ~7bits/byte entropy. That will reduce of course upon use of a stronger compression algorithm. But not reduce to anything near 0 bits/byte. A better impression can be had by taking the above image and substituting its colour map for a random one:-
Most of the structure (in the top half) disappears as it was just sequences of similar but marginally different values. Is this a true entropy source created by just executing a Java program on a multi taking operating system? Not a uniformly distributed random number generator, but the entropy source for one? An entropy source built of software running on physical hardware that just happens to be a PC.
Supplemental
In order to confirm that every image gener
Solution
If you're using some hardware source of entropy/randomness, you're not "attempting to generate randomness by deterministic means" (my emphasis). If you're not using any hardware source of entropy/randomness, then a more powerful computer just means you can commit more sins per second.
Context
StackExchange Computer Science Q#89865, answer score: 101
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