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motion, in which one takes a small grain, say of pollen, puts it in a liquid, and then looks at its motion under a microscope.

What one finds is that the grain jumps around in an apparently random way. And as was suspected when this was first noticed in the 1820s, what is going on is that molecules in the liquid are continually hitting the grain and causing it to move. But even in a tiny volume of liquid there are already an immense number of molecules. And since one certainly does not even know at any given time exactly where all these molecules are, the details of their effect on the motion of the grain will inevitably seem quite random.

But to observe random Brownian motion, one needs a microscope. And one might imagine that randomness produced by any similar molecular process would also be too small to be of relevance in everyday life. But in fact such randomness is quite obvious in the operation of many kinds of electronic devices.

As an example, consider a radio receiver that is tuned to the wrong frequency or has no antenna connected. The radio receiver is built to amplify any signal that it receives. But what happens when there is no signal for it to amplify?

The answer is that the receiver produces noise. And it turns out that in most cases this noise is nothing other than a highly amplified version of microscopic processes going on inside the receiver.

In practice, such noise is usually considered a nuisance, and indeed modern digital electronics systems are typically designed to get rid of it at every stage. But since at least the 1940s, there have been various devices built for the specific purpose of generating randomness using electronic noise.

Typically these devices work by operating fairly standard electronic components in extreme conditions where there is usually no output signal, but where microscopic fluctuations can cause breakdown processes to occur which yield large output signals.

A large-scale example is a pair of metal plates with air in between. Usually no current flows across this air gap, but when the voltage between the plates is large enough, the air can break down, sparks can be generated, and spikes of current can occur. But exactly when and

From Stephen Wolfram: A New Kind of Science [citation]