The Hindu Business Line : Ten billion monkeys typing out <I>Hamlet</I>!

IN Hamlet, soon after delving into the dilemma of `to be or not to be,' the prince confuses Ophelia with a paradox - that the power of beauty will sooner transform honesty than the force of honesty can translate beauty into his likeness.

More on Hamlet, later, but Erich Fromm says that in love the paradox occurs that two beings become one and yet remain two. On that there can be many views, such as that of John Fowles, who says that most marriages recognise the paradox of passion destroying passion; for, "we want what puts an end to wanting what we want."

There seems to be no dearth of paradox in news. For instance, www.line56.com speaks about `IBM's Paradox of Banking 2015'. Susan L. Miller has written a new book, Victims as Offenders: The Paradox of Women's Violence in Relationships. And Rob Hof writes on www.businessweek.com about `Wikipedia's Paradox'. The word seems to be popular in headlines, as in `Playing with paradox' (London Free Press, Canada); `The Pantech paradox' (Mobilemag.com); `Paradox over cost of justice' (Scotsman); `The Hong Kong paradox' (Mathaba.Net); and `A Polish paradox' (Jerusalem Post).

There is a paradox up in the brain, too, as one learns from a recent paper titled Complexity, information and biological organisation by Attila Grandpierre of the Konkoly Observatory of the Hungarian Academy of Sciences Budapest, Hungary.

It is `information paradox,' which is about `an apparent conflict between physics and biology': the genetic complexity of the human organism (including the brain) is smaller than the algorithmic capacity of the human brain.

Brain's complexity can be measured in terms of neurons and synaptic connections, writes Attila. Neurons number 10{+1}{+1} to 10{+1}{+3}, and interconnections are a few thousand per neuron, and so the brain's complexity can be put at 10{+1}{+5} to 10{+1}{+7}. Assuming that a connection (synapse) represents one bit of information, the information measure of the brain's complexity is 10{+1}{+5} to 10{+1}{+7} bit.

That's almost equal to the memory of `the biggest supercomputer today, Blue Gene/L,' which has a memory capacity of 64 TB (corresponding roughly to 5·10{+1}{+4} bit).

Compared to such an algorithmic complexity, the genetic complexity only adds up to 10{+9} bit, taking into account `30,000 genes indicated to be present in the whole human genome'.

Measuring `operations per second' is relevant for `dynamic complexity', says Attila and compares the brain to Blue Gene/L, which operates at 367 Teraflops (trillion floating point operations) per second. "Considering that the visual input into the brain comes through the 10{+8} retinal cells, and 10{+6} retinal cells are connected to the brain with axons sending 100 spikes of action potentials per second, regarded as carrying 1 bit of information each, one obtains 10{+8} bit per second for the visual input into the brain," writes Attila. Assuming processing to be at 100 operations per second per neuron, he computes speed to be 10{+1}{+3} - 10{+1}{+5} `neural operations' per second.

You can read in the paper about the biological efficiency of cellular respiration (which is about 40 per cent), and the thermodynamic capacity of the human organism; and also learn that `to solve the Rubik cube by one random step in every second, it would take 1,35·10{+1}{+2} years.'

But let me move on to `a popular example of monkeys that can type Shakespeare's complete oeuvre on a typewriter,' cited in the paper. "Actually, to type only one sentence from the Hamlet, consisting of 40 letters, each selected from 30 possibilities, it would be necessary to realise 30{+4}{+0}-10{+5}{+9} trials," explains the author.

"Let us assume that we have ten billion monkeys - that is, rather more monkeys than there are currently people in the world. And let us imagine each monkey hits one key per second. Let us further assume that they never stop to sleep or eat or anything else. It will still take more than 10{+4}{+9} seconds before one of the monkeys has the luck to hit on the right sequence. Now, one year is about 32 million seconds, so it will take our world population of monkeys about 3·10{+4}{+1} years to get there."

Leaving the monkeys to their job, let us return to the paradox. What's the solution? There are two possible answers to `the fundamental information paradox,' says Attila. Look for it, therefore, "either in the chemical evolution of inheritance in abiogenesis, or in the existence of an autonomous biological principle allowing the production of information beyond physics."

Beyond understanding?

SayCheek@TheHindu.co.in