This series of postings combines puzzles, paradoxes, decision theory, statistics, and probability. This subject grouping is not arbitrary, but represents much of what I think is valuable in the world. Everyone likes to work puzzles, but not everyone likes to work the same type of puzzle. Every time we learn something new, we have solved a puzzle, but we might not think of it that way.

So for a person who values learning, finding puzzles that combine logical thinking with fun and an “aha!” experience is a godsend. Paradoxes are often approached as a type of puzzle that can facilitate greater understanding but in a different way.

One topic that should probably be added to my list is skepticism. Skeptics get a bad and undeserved press. I never understand why. For some reason people who accept the most outrageous assumptions on faith are often valued while their colleagues who question the basis of that faith are held to be in a lower social status. This tendency goes all the way back to Socrates and beyond. Doubting Thomas was a proto-scientist, and Icarus was an enthusiastic text engineer. Everything we learn starts with a skeptical thought.

The trouble starts when a skeptic (often with little or no tact) asks questions which show that we, the questioned, do not know what we think we know. Assuming that we know when we are really ignorant is a wonderful time-saving tool. Instead of taking the time to understand, just assume the results and press on. In fact, that type of assumption is absolutely necessary because we don’t have the time to independently check everything - besides, someone else has already checked it out, right? When some wise guy disturbs our tranquility by pointing out that we really don’t know what we think we know, then we get upset.

Which brings up the question of how do we know what we know? Books are written about that. Some books even write learnedly about how we cannot know anything (which leads to an interesting paradox). But for practical purposes, I maintain that one of the greatest things humankind has done is to learn how to learn. By developing logic, decision theory, statistics, and probability, we have been able to advance learning and slowly overcome the make-do assumptions our ancestors needed to live their daily lives.

Occasionally a reader will take me to task for overstepping the bounds of good science and making unsupported claims about topics that rightly are determined by religion. This usually happens when discussing evolution or similar issues that religionists think should be determined by their beliefs. However, I try to couch the results of various scientific investigations in the appropriate words. Those words usually convey the thought that no truth found in nature by scientific investigation can be shown to be absolutely true for all time. However, we surely know that some things are more true than others. That is why we fly successfully in airplanes and generally don’t try to fly on broomsticks.

The nature of the topics I present here are always aimed at developing practical methods of solving problems. That sentence contains a lot of assumptions such as there is a real world shared by a multitude of thinking beings who can exchange information, and that they want to exchange information about their surroundings. I try to avoid diversions such as asking what is the purpose of life or “is there an afterlife?” Those puzzles are fun to argue, but not as likely to lead to an accepted solution as the puzzle of the Sultan’s Daughters or resolution of the Barber Paradox.

So, having restated the ground rules, I am going back to the Internet to search for some more amusing puzzles of the sort that can be challenging and informative. This is not as easy to do as you might think. If any reader has a favorite that I have not featured in a past column, let me know and I will try to feature it.

In the meanwhile, a boy has a cylindrical pail. It holds five gallons. He is sent to get a gallon of milk for one family and ten quarts for another family. He only has the one pail so he has the seller put all the milk in it and manages to deliver the right amounts without using any other measuring devices. The families do not have calibrated vessels. How does he do it?

In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.

[tags]barber paradox, sultan’s daughters, decision theory, sherman deforest, faith, science[/tags]