Every 7 kittens born, 6 are normal size and 1 special size!

[Tad Carlucci]

When working with randomly sampled data, the idea is to select a sample size sufficiently large that the sampling error becomes low enough for your intended use.

I've seen some medical studies, where the study group was only 5 or 6 patients. At first glance, this seemed ridiculously low. But, on examining deeper, it was apparent this was sufficient for the intended use. The full dataset, in the most recent, was not 'all humans', but rather 'patients exhibiting' a relatively narrow set of symptoms. And the intended use of the study was to test whether a larger test was warranted. As it turned out, the results indicated nothing could be gained from the larger study, and the research moved on to another area.

'Intended use' is critical. We've seen, in this thread, some comments about how it's not 'true random' but a 'pseudo-random' function. Yes, that is correct. But what is the intended use? If you're talking about taking a series of random 0's and 1's and producing Gender, does it really matter that, after, say, 1,000,000,000,000,000 offspring, there is a CHANCE that a pattern will develop?

The question is NOT, "Is this truly random?"

The question is, "Given the limited data anyone is likely to see, does this appear random?"

In cryptography, we need a number of factors. Speed (who is going to wait an hour to read their email?) is one of them. Complexity, another. The goal is to produce a function with is sufficiently fast it can be used, but complex enough that it cannot be attacked in REASONABLE time. We often speak of the attack speed in 'years' .. as if one would set a single computer to the task and await the result. The reality, given the size of the Internet, however, is that it is quite possible to set a huge number of computers to the task. So, we see cryptographic systems, in use today, which, given current computing power, should take millions upon millions of millions of years, simply because we recognize that (1) it is EASY, now-a-days, to marshal millions of computers to a task, and (2) Moore's Law tells us computers tomorrow will be significantly faster than today.

["Moore's law" is the observation that, over the history of computing hardware, the number of transistors in a dense integrated circuit doubles approximately every two years. The observation is named after Gordon E. Moore, co-founder of the Intel Corporation, who described the trend in his 1965 paper.] [As as aside, here, Moore's Law has been wrong for most of the past decade, computers today are NOT significantly faster than they were a decade ago. They just appear so because we're throwing more computers at the problem .. your new laptop is not "a" computer .. it's 4 or 6 of them .. so the box seems 6 times faster not because the computers are faster, but because you're using more computers. But recent research indicates that will soon end, and Moore's Law may become wrong to the other side .. computers a looking to become significantly faster, at a higher rate, assuming the research can be feasibly applied.]

But, we're not talking about millions of computers and millions upon millions of KittyCatS. We're talking about maybe 30,000 people, and somewhere around 6 or 7 million KittyCatS.

So, even though, yes, it's possible, over the course of the next couple millennia, the randomness of KittyCatS will break down and we MIGHT be able to prove a pattern, given the current conditions, and likely future and lifetime of the product, the results produced by even a weak pseudo-random number generator (such as the in-world llFrand() function or PHP mt_rand()) will pass most, if not all, tests we might apply in an attempt to prove "not random"