Diverse Thoughts

How much information is in here:

• It is a fine day.

Let’s measure the information by the number of characters. There are 17 characters, so the amount of information is 17.

How much information is in here:

• It is a fine day. It is a fine day. It is a fine day. It is a fine day. It is a fine day.

The same sentence is repeated five times. Is the amount of information 17 x 5 = 85? Answer: No. The extra four sentences don’t say anything new. The information that is present is this:

• Repeat 5 times: It is a fine day.

The number of characters in this is: 33

How much information is in here:

• 3.1415 …

This is the value of pi. Suppose one million digits are displayed. None of the digits repeat, so you might be tempted to say that the amount of information is one million. Not so. The information can be represented succinctly as:

• Pi to one million digits

Now the amount of information is just 24.

How much information is in here:

• dkdl;eekrkpeosfdlzdmc;dsfkdopkfospkfs;dlkflas;krwe0q0–03ospaaj

This is just a random sequence of 63 characters. If any random characters will do, then the information can be represented simply as:

• Random sequence of 63 characters

There are 33 characters.

Something is “information” if it is meaningful, non-random, and unpredictable [1].

How much information is in a rock? If we were to characterize all the properties (location, angular momentum, spin, velocity, and so on) of every atom in the rock, we would have a vast amount of information. A one-kilogram rock has 100000000000000000000000000000 (29 zeros) atoms. That’s one hundred million billion times more information than the genetic code of a human race. But for most common purposes, the bulk of this information is largely random and of little consequence. So we characterize the rock for most purposes with far less information just by specifying its shape, location, and the type of material of which it is made. Thus, it is reasonable to consider the information of an ordinary rock to be far less than that of a human even though the rock theoretically contains vast amounts of information.

[1] If you know what’s going to be said (i.e. it’s predictable) then it’s not information.

– – Extracted from The Singularity is Near by Ray Kurzweil

This entry was posted on August 18, 2007 at 9:48 am and is filed under Complexity, DNA, Genetic Code, Information, Information Theory, Random, Random Information, Ray Kurzweil, Rock. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.