Randomness

Psuedorandomness

When people talked about “random”, they usually thought of something that is unpredictable. However, in the field of computer science, randomness is not as simple as it seems. In fact, it is a very complex and interesting topic.

Let’s start with take a look from the Python documentation about random:

random — Generate pseudo-random numbers

This module implements pseudo-random number generators for various distributions.

Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne Twister is one of the most extensively tested random number generators in existence. However, being completely deterministic, it is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.

In this paragraph, we found a keyword “pseudo-random”, which the concpet of random is probably not as simple as we thought. The Mersenne Twister is a pseudo-random number generator, which means that it generates numbers that appear to be random, but are actually deterministic. For most purposes, the numbers generated by a Mersenne Twister are good enough, but in some cases, they are not suitable.

Warning The pseudo-random generators of this module should not be used for security purposes. For security or cryptographic uses, see the secrets module.

The basic random() function maybe sometimes not enough for some purposes, due the the fact that it is deterministic. For example, if you want to generate a random number for a lottery, you don’t want the number to be predictable. In this case, you should use the secrets module, which is designed for security purposes. Let’s talk another look at the secrets page:

secrets — Generate secure random numbers for managing secrets

The secrets module is used for generating cryptographically strong random numbers suitable for managing data such as passwords, account authentication, security tokens, and related secrets.

Here we got another term “cryptographically strong random numbers”. This means that the numbers generated by the secrets module are not only random, but also unpredictable for us. Our devices has a feature called “entropy pool”, which is a source of randomness. The secrets module uses the entropy pool and algorithms to generate random numbers that are suitable for security purposes.

However, it seemed that the secrets module is not generating truly random numbers. If we are strong enough to control the same environment to the entropy pool, the numbers generated by the secrets module are still predictable. If everything is determined, isn’t there any chaos in the computer world?

GPT and the Chaos

GPT is the technology used AI to generate text. It is based on a complex system which use large text data and neural networks to generate text that is similar to human writing. The response generated by GPT looks not deterministic but it uses an existing model and some seeds to generate the text. If we use the same model and the same seed, we will get the same response, which is not truly random. If we ask GPT to generate a random number, will it be able to do that?

The parameter behind GPT is too complex which is like a block box to human.

For some interesting purposes, I wanted to ask GPT to create an artwork with me, which is like that the artwork is generated randomly but can’t tell that it’s really chaos.

I used a p5.js small program I designed before that features interconnected hexagonal patterns. Users can use keyboard inputs to generate some colors on the patterns, such as typing g31. In this input format, the first character g represents the position, the second character 3 indicates the color, and the third character 1 determines the range of its influence. By inputting multiple such commands consecutively, users can create a patch with various colors.

I then asked GPT to randomly generate 20 sets, each containing 15 such inputs, resulting in 20 uniquely colored patches. Using these patches, I combined them based on their colors, then to create a larger piece.

I wonder if these results are truely random. I can’t really tell whether the random inputs generated by GPT are truely random. Perhaps, when I submit a prompt to GPT, it’s the multiverse that determines the outcome. As a human, all I did was assemble the patches generated by GPT into a larger piece. So, who is the true creator of the artwork? Is it me, using GPT as a tool? Is it the GPT model itself? Or perhaps it’s the multiverse, splitting into different branches the moment I hit the submit button, that brought this creation into being?

determinism randomness computation