by Marcus Loane
It is possible to write a computer program which has the answer to every meaningful question that has ever been asked and that ever could be asked. This program is really quite trivial and can be implemented in perhaps 10 lines of computer code. Imagine a program which outputs a sequence of letters. Let's say the sequence is set to 3 letters long. The program is written so it outputs every possible 3 letter sequence. This is easy to do. It starts with aaa then aab, aac and so on. It can work methodically through every possible 3 letter sequence. The output of this program will contain every English 3 letter word and also a lot of nonsense words. Now we can modify this simple program to also use spaces and punctuation marks as well as letters, and we can make the sequence longer than 3. We could make the length of the output sequence, say, 100,000 characters long. Again this is a really easy program to implement in just a few lines of code. Ask any computer programmer or even computer literate school kid and they will agree.
Included in the outputs of this program will be anything that can be written in 100,000 letters or less. Some of the outputs will contain a lot of gibberish but some will contain the answers to meaningful questions. It will contain all the novels and academic tomes ever written, that are not longer than 100,000 words. (It will also have everything ever written, that is longer than 100,000 characters except it will be broken into 100,000 character chunks.) It will contain a perfect copy of Macbeth, but also Macbeth with spelling mistakes and Macbeth with new exciting plot twists. It will contain the King James Bible and the Koran. It will contain witty intelligent discussions on every conceivable topic. It will contain the as yet unknown Unified Theory of physics if one exists. It might be difficult to express without mathematical symbols but it should be possible. It will contain your autobiography describing some of your most private thoughts and inner experiences and including things you have not done yet. A lot of this program's output will be nonsense but some of it will look like the work of the most knowledgeable and intelligent person who ever lived. Some of the 100,000 character sequences will contain profound new insights into the universe and the workings of the human mind. In addition, it will have all that, also written in French, Spanish and any other language which uses the 26 character alphabet.
All that intelligent output has been generated from a few lines of mindless computer code.
What is the catch? The catch is time, or the lack of it. As you may have guessed there are a lot of ways of arranging characters into 100,000 length sequences. If we use small and capital letters plus 10 different punctuation marks, there are 62 to the power of 100,000 outputs from our program. That is quite a large number. It is (approximately) a 1 followed by 180,000 zeros. It is a billion, billion, billion... (say "billion" 20,000 times). If we recruited every English speaker on earth to help us filter through the outputs to weed out the nonsense outputs and keep the good stuff, the universe will either have contracted again or undergone a heat death before we make even a tiny dent in the huge task. A much more efficient method would be to evolve organisms with brains who can produce more meaningful output than drivel. That only takes a few billion years.
Notice though, that both methods use mindless algorithms to produce intelligent outputs. The former uses a brute force approach and the latter uses the more discriminatory evolutionary algorithm.
For those not afraid of multi-dimensional spaces
The totality of all the 3 letter program's outputs could be visualised as a cube with the alphabet written along each edge. Each 3 letter output is represented by a location in the cube which has three coordinates such as (d,o,g). One corner would be (a,a,a) and the opposite one would be (z,z,z). Similarly the totality of the outputs of the second program can be visualised as a hypercube in 100,000 dimensions instead of the more familiar 3. There are 1 followed by 180,000 zeros locations in the hypercube. A minute proportion of these locations contain meaningful documents, and a minute proportion of those contain documents that already exist like Macbeth or the Bible. It can be hard for the human brain to comprehend such numbers. Even though we are talking about a minute proportion, this minute proportion is still an almost inconceivably vast number. However it is not infinite and it can written down as a meaningful number.
Think with your head
Now what is the point of all this? Not much really, but it shows that we can have difficulty grasping some things intuitively and we need mathematics to express them. We are not good at intuitively visualising very large numbers, or very large/small distances, velocities and times, or more than 3 spacial dimensions, or small probabilities. We evolved in a medium sized environment midway between the size of galaxies and the size of atoms. Our timescales are in decades. We are accustomed to medium velocities and rates of change. We are blind to very fast and very slow change. This makes it difficult for some to understand evolution because of the very long time scales and very slow rates of change. It also makes it difficult for some to understand how a vast universe could emerge out of something so small, and undergo huge changes in tiny fractions of a second at the beginning. We are lucky we stumbled upon mathematics because our brains are not equipped with the ability to intuitively grasp the truths outside of our own parochial earthly experience. Mathematics is the best tool to describe how the universe works. We should not expect common sense to help us describe galaxies or sub-atomic particles. Our brains are not truth detectors which can "tune in" to The Truth (whatever that is). There is a common fallacy that the truth should somehow "feel right" and be emotionally satisfying, but we never evolved to have such an ability. The truth may be complex or simple, satisfying or extremely dull and trivial. We cannot expect it to satisfy our evolved human desires - they are what they are because they helped our ancestors survive. The origin of the universe should not instinctively "feel right" to us. We grew up in our limited earthly environment with no need to quickly understand the behaviour of subatomic particles or space-time. We can only rely on the scientific method and accept (tentatively, of course) what it tells us, regardless of whether it satisfies.
On a personal note, I find the search for truth, regardless of the consequences, deeply satisfying but I feel I am in the minority.
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Marcus Loane