Quantum Mechanics, Sudoku, and Sherlock Holmes

One is filled with mind-numbing mathematics, one is a game, one is Benedict Cumberbatch. OK OK…I was kidding about the last one. But you get the idea, they are seemingly unrelated. Why are these three together in the title of a blog post?

All three, at the beginning, come with information that you need to measure/deduce from/investigate. In the case of quantum mechanics, the act of measuring will result in causing a specific result, of all the possibilities, to be made apparent. In Sudoku, deduction causes a single option to remain, of all the possible options. In Sherlock Holmes, from all the possible suspects, Holmes homes (heh heh) in on the guilty one by using deduction from his investigations.

In each of the three, the process that works is the same – elimination.

As new information is collected or worked out, new hypothesis are placed, further information confirms or denies that hypothesis and refines the set of available possibilities. The refinement can be the eliminating of unlikely options and/or increasing the likelihood of a particular option.

Though it was not these three that made me realize the power of elimination. Some years back I underwent a massive personal upheaval (How massive? I was suicidal for three months and only wanted to hear the truth about that matter.). I was being fed a lot of stories from my source. They were all “consistent”. But consistency is not the same as “facts”, even lies can be consistent if they are arranged properly. I can say this is one time that my economics study had set me on the right scent. Years back I read about “stated” and “revealed” preferences. It was on placing all the information provided to me (stated preferences) and the actions that were being taken (revealed preferences) was I able to begin to understand what was not being told to me and who was orchestrating the entire theatrical play.

This was the beginning of realizing what the process of elimination could actually do, all that was required was to gather the necessary information or the patience to be handed the information (even indirectly). And yes, there will always be those “helpful idiots” who give away the “wrong” information.

It was then that I began to view everything¬† a little differently. Take the case of quantum mechanics. Simplest example is the momentum/position of a moving object. Let’s say your observation is by using a camera. If you take a time lapse picture, you will get the object at two different points, the momentum (speed) can then be calculated easily as you know how long it took to get from A to B. Did you notice that you lost track of exactly where the object is though? If you take a still image, you know exactly where it is but you lose information on its momentum because you don’t know how long the object took to get there from where. Each method of measurement will provide some information while obscuring others about the state of the object, putting everything together enables you to build a complete picture.

In Sudoku, only certain numbers are allowed to take up a position; any number from 0-9 can be present only ONCE in a row, column, and square. This automatically makes it a game of understanding probability, eg. if a number can occur in only two places in a square and they are horizontally aligned (because the other places are occupied or blocked off), you can eliminate all other options for that number in the remainder of that row.

Holmes on getting to the crime scene immediately begins to look for clues that give away characteristics of the criminal. The shoe-prints tell him how many people there were and a little about them, any unique objects (cigarette ash, burnt matchstick, etc.) tell something about the habits, marks on the wall or ground clue him in on what could have happened and what could be the progression of events.

In all three, you start with a range of options, and eliminate the ones the evidence is against. In quantum mechanics, there is an important twist, it makes a difference what it is you are looking for. Measuring one thing will result in some other thing being obscured. Placing everything in the correct logical order, as evidenced by the way Holmes operates, gives the entire story.

Generally, that is what is missing for us in many cases in our lives: the entire story.

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