Quote:
Originally Posted by NewOldGuy
That sounds exactly like a normal random deal.
People think random means evenly distributed but it doesn't. Lots of clustering is how randomness behaves.
This point is important and generally not well understood.
I may have told this story before but it may be a story worth retelling. In my introductory probability class, the teacher gave each student a single dice (a die). He said that all of the dice were regular normal dice except for one die which was special in a way that he would explain later.
Each student then rolled their die for several minutes and recorded each roll on a piece of paper. After awhile the teacher asked us to stop. He then asked anyone who thought they may have the special die to raise their hand.
Around half the class raised their hand! The teacher asked each student who had raised their hand to guess what the property of the special die was. Some students were very specific ("a 4 always follows a 2 except if the roll preceding the 2 was another 2"). Some students were more general ("odd numbers come in groups of 3 while even numbers come in groups of 2 or 4"). One student was positive that he had the special die since he had observed a sequence of one one followed by two twos followed by three threes.
Anyway, you can surely anticipate which student the teacher said had the special die. None of them. All the dice were regular normal dice. After the howls of disbelief subsided, the teacher then led a discussion on what the "experiment" demonstrated:
- Pure randomness generates clustering
- Relatedly, regularity is quite rare (for example, no student rolled exactly one of each of the numbers one through six in their first six rolls)
- There are an unending supply of "patterns" that random sequences can generate
- Humans are constantly pattern-seeking (it is virtually impossible for humans to turn off the pattern-seeking part of their brain).
I don't remember much of what I learned in high school, but I definitely remember that lesson.