Saturday, July 24, 2021

From the "Half-formed thoughts" file

It is commonly, but erroneously, believed that more information always reduces uncertainty and that more laws increase order. Note that I include information systems and laws in the same basket because both are intended to tame entropy and chaos and are, at there hearts, very similar.

Additionally, it is believed that each incremental piece of information reduces the amount of uncertainty by increasingly smaller amounts. Incidentally, this is capture in a mathematical concept called Bayes' Theorem.

By way of example, we intuitively believe that our ability to predict what somebody will do is very strongly correlated with how long we have known them. Given two different people, one I have known since childhood and another I just met...I are SURE that I can predict what the first will do with far more accuracy than the second.

Let me illustrate with a fun example.

 Behold: A Treasure Map. X marks the spot! (All maps from the fine folks at Google)
What information is captured in this map? There is a treasure buried on a beach near a body of water. If you could zoom in, you might deduce that the beach is not sand but stone cobbles and the treasure is buried where the water suddenly becomes shallow.

 An additional piece of information. The treasure is 3.54 miles from some town.
Still not very much to go on.
 Blimey! The pirates have different colours of ink.

In addition to the previous information, we can now deduce that the treasure is 3.54 miles west of some, unknown town near a body of water.

 Our pirates now tell us the name of the body-of-water but Lake Michigan is 300 miles north-to-south.

 There is now enough information for intelligent people to mount a search even though it does not describe, to-the-inch, the precise location of the treasure.

Where Bayes' Theorem fails
Bayes' Theorum fails when the additional "information" comes from dodgy sources. You cannot wash the turd out of the punch bowl using water from the septic tank.

Consider the modern high school student who borrowed his parent's vehicle. He/she ignored the idiot lights and it stopped working.

They called an equally ignorant friend who informed them that the engine is out of oil. Looking in the trunk, the intrepid motorists found two quarts of motor oil. They proceeded to add oil to every place under the hood where a cap can be pried off. It goes into the transmission, the radiator, the power steering, the windshield washer tank...some even went into the motor.

Then they poured the second quart of oil over the top of the engine.

Don't laugh. THIS HAPPENED (and continues to happen).

Miraculously, the engine started back up and after a bit later it ignited the oil that had dripped down onto the exhaust manifold.

Or it swells the seals in the transmission and it stops shifting. Or it sprays motor oil on the windshield and the loss of visibility causes a crash.

Calling a friend did not decrease the entropy/chaos but added to it.