Monkey Business - Part III

You think we can get a lot of data stored in a memory chip, or a lot of data stored on a disk drive? Well, that's nothing compared to the potential storage of information available in a piece of matter.

A little look at the nature of digital information is in order first. Most all digital data is stored in bits. A bit is a two-valued piece of information. It can either be 0 or 1, on or off, yes or no, any two paired values. Virtually all digital information is stored this way. Two bits can store 4 possible values: 00, 01, 10, 11. Three bits can store 8 values: 000, 001, 010, 011, 100, 101, 110, 111. And so on. The characters that I am typing in my computer keyboard are generally represented by 8-bit chunks. This gives a possibility of 256 characters, upper and lower case letters, numbers, punctuation, and many special symbols. In computers these bits are generally stored by having section of a memory chip be either a high voltage or a low voltage, on or off. As you probably know, the amount of physical space it takes to store these massive arrays of bits has progressively grown smaller and smaller through the years since computing has become prominent. So what is the limit of how much can be stored in these small spaces?

It is possible to exploit methods of storage of data at a atomic and sub-atomic level. For example, an electron has a property called 'spin'. The spin can be 'up' or 'down' (picture your hand with the thumb up; the spin is the direction of the fingers curl, and it is up or down depending on whether thumb is pointing up or down). It turns out that the spin on an electron can be flipped easily by zapping it with a laser. This state of 'up' or 'down' can be detected, so a bit of data can be stored in this way. Basically, every changeable attribute of elementary particles such as electrons, photons, and other elements of atoms can theoretically be used to store information. Researchers have been able to store 1024 bits of information in a single molecule containing only 19 hydrogen atoms. So what is the ultimate amount of information that can be stored in a piece of matter?

Well, first, without going into the details of how it is figured out, estimates have been made that the human brain can store about a billion billion bits of information (that's 10 to the 18th power). So lets take a rock that weighs 1 kilogram (2.2 lbs). If all the molecules were used for storage how much information could you store? It is calculated to be 10 to the 27th power bits. That is on the same order of magnitude as all the human brains on the planet. And this is not even using all the available technology to squeeze more out of it, like supercooling. Furthermore, if the rock were used for computing, it could, in the ultimate theoretical state, do a million trillion trillion trillion computations per second (10 to the 42nd power) which is about 10 trillion times more powerful than and the human brain computing power on the planet.

And this is just a 2.2lb rock. Think if the whole planet was used for computing. What if the whole universe was a computer? Would this qualify as being God (or just a God computer)? I'll leave that philosophical question for you to ponder. But I will tell you that Mr. Lloyd, a very intelligent MIT professor, has developed theories to show that, and believes that, the whole universe is computing.

Monkey Business - Part II

Its all fine to monkey around with some typewriters, but what about where the monkeys came from; where did life come from, and in fact how did the universe get here? Was it by chance, random happenings like the monkey's typing randomly on the keyboards, or was there some non-random causative influence. What if the monkeys were typing in computer programs? Could computers execute the program? Well, Seth LLoyd in his book Programming the Universe has some very interesting revelations about this.

Actually, these questions concern some of the most heavy philosophical and religious questions ever posed by man, as well as questions in the areas of quantum physics and information theory. Did life evolve from a random collision of fundamental particles that by chance evolved into combinations that had survival potential? Current molecular biologists are working very hard to support this theory, and have made some convincing arguments for how some of the basic materials of life could have evolved. Yet, even they admit there are big holes in the theory for which they have no answers. I am going to cop out and not go into any details, because it is beyond the scope of this article, but Lloyd argues that the current state of the universe could not have come about by chance. He argues that there is much too much organization present to be accounted for by chance. He believes there were physical laws which governed its development. This brings me to one of the two topics I would like to take up though.

First, how the physical universe acts as a computer.



As in the classic experiment by Galileo, if you roll a ball down an inclined plane, the laws of the physical universe can actually compute for you. Let's say in the first second of travel down the inclined plane that the ball travels distance D. Then in the 2nd second of travel it will travel 3 times as far as the first second, or a total distance of 4D. In the third second, because its speed is accelerating, it will travel 5 times as far as in the first second, or a total distance of 9D. And so on. If we put this in a table we would see:



So, if we wanted to know the square of a number, we could easily calculate it with a ball and the inclined plane (if the plane were long enough). What is calculating the result? Its the physical law of the acceleration of gravity. The physical universe, with its law is calculating for us.

By extending this idea, we find this is how quantum computers work. Only this time it is laws concerning particles like electrons and how they behave. Though the laws get quite weird by our normal intuitive standards, like the fact particles are in multiple states simultaneously, they are nonetheless predictable laws of our universe. Notice that we could go about trying to get the inclined plane and ball to calculate for us, but whether we gave it an input and looked at the output, it would still be calculating.

Lloyd goes beyond the idea that humans have to be involved in giving input to one of these physical computing devices. This is not necessary to make it into a physical computer. He shows how things like electrons and atoms are computing all the time. They are in a certain state and based on what they encounter, and the physical laws of this universe, they change state, or compute, accordingly. And taken to the final conclusion, he believes the whole universe is computing constantly and its result is what we see observe as the physical universe. I know I have skipped a lot here, but read the book and you will be filled in on all the missing steps in logic. Its really a quite convincing theory.

Next, how physical matter, and the universe, stores data.

Monkey Business - Part I

I am sure we have all heard of the idea of having a million monkeys sitting at typewriters for 10 hours a day and typing for a year. We are told that they could, by random chance, write all the well-known text in the world, including the likes of Hamlet.

But first let's back up a bit and look where this interesting idea came from. It has often been falsely attributed to Thomas Huxley. In a debate with Bishop Wilberforce concerning Darwin's Origin of the Species the discussion wandered onto the topic of monkeys. Apparently, Wilberforce asked Huxley whether he was descended from a monkey on his grandmother's side or his grandfather's side. It seems Huxley was defending Darwin's idea that we were related to more primitive life forms. Huxley replied he would rather be related to a monkey than descended from a man of great intelligence who used his gifts in the service of falsehoods. But none of the records we have of the debate really discuss monkeys with typewriters.

The real origin of the idea came from Emile Borel, in the early 1900's. He was a French mathematician, and according to his calculations, he figured it was a very small chance the the million monkeys typing for a year wouldn't produce all the great volumes of writing that man has ever written. This novel idea was then taken up and written about by various scientists, and science fiction writers till it became a quite common idea.

So is it true? Not by a long shot. Let's do some math. There are about 50 keys on a keyboard. So there is a 1/50 chance that one monkey will hit a certain letter, say 'h'. The chance of the monkey typing 'ha' is 1/50 X 1/50, or 1/2500. The chance of him typing 'ham' would be 1/125000. And so on, and so on. So, the chance of the monkey typing a phrase with 22 characters in it are about 1 in 10 to the 38th power. That's:

1/100,000,000,000,000,000,000,000,000,000,000,000,000

Or another way to put it, it would take a billion billion monkeys, each typing 10 characters a second, for each of the billion billion seconds since the universe began to type the phrase, 'hamlet. act i, scene i.'

This example, and many many other interesting ideas about computing are to be found in a delightful book called Programming the Universe by Seth LLoyd. He is a quantum scientist and a Professor at MIT. His book has a very easy and natural style of describing the nature of computing, from a theoretical viewpoint. But he has much more profound things to say about evolution, the origin and nature of the universe, and the ultimate computer. More on that next time.