Do you guys watch Star Trek TNG? Of course you do. Well hopefully you will remember this episode called Conundrum as well as I do. The is the historic episode in which Data is defeated in chess (3D chess) by Deanna Troi. I remember seeing this when I was in middle school and kinda scoffing… Yeah right as if she could ever beat Data. Data seems surprised that she devised a completely “new” strategy to an already well-researched sequence of moves. Troi explained that chess is a game of intuition… (Something Data’s programming cannot provide.)

I revisited by episode again when I was in college as I was watching the show again, and I was completely APPALLED! Humans can’t even beat computers now (Circa 2006), and Data is a million times more sophisticated then today’s machines. What are they trying to do in this stupid episode!? Suggest that Troi is better at chess than the most powerful computer in the universe (arguably)? Surely chess will be completely solved by then, don’t these writers know anything? Didn’t the scientists on staff who help with the script know anything!?

I must admit, later I found out that solving chess isn’t as easy as I originally thought. It isn’t simply a matter of time, there truly are more possible game-states than atoms in the universe.

Let’s take a short detour to really analyze why it might be impossible to solve chess. If you watch the Numberphile video you will see the mention of Shannon’s number, which although is pretty simplistic is most well known estimate for the complexity of chess. Shannon theorized that there are 10^120 possible different games of chess. Scientists estimate that the entire known universe “only” contains 10^80 atoms. This means if we assign one chess game per atom, we will not have enough to contain them all!

For a computer, storage space would be the first problem. As of 2012 it takes 1 million atoms to store a single bit of information. Let’s say someday we get that down to one atom per bit. Even if we could store an entire game of chess in a single bit (a bit only stores a 0 or a 1) we would need to harvest every atom in the universe and still not be able to create a large enough hard drive.

But what if we could! Well if you take every atom in the universe and put it into a line, that line would be 10^70 meters long (diameter of an atom is 0.1 nanometer). Traveling at the speed of light, it would take 10^54 years to travel from one end of this line of atoms to the other. That means if a computer wanted to access all of these bits of data just a single time, that is how long it would take the computer just to travel to each bit, let alone access it. (Thanks to @FreddyZ for the math help.)

So maybe it isn’t THAT obvious that Data should win. But he still should right? Troi has never been recognized as an exceptional chess player, or any kind of strategist at all. I suppose she would be stronger than your average human given her empathic abilities, perhaps being able to read the next move but Data is immune to such nonsense.

During the Alpha Go vs Lee Sedol Go match it finally dawned on me! Computers weren’t always so amazing at chess! I need to check the dates:

This episode originally aired in 1992. Deep Blue didn’t defeat Kasperov until 1996! The writers (and scientists) at the time were probably working on the assumption that computers will never be better than humans at chess. They probably tried to look it up too, and the only thing they found was Shannon’s Number (more games than atoms in the universe) and concluded, because computers can’t brute-force chess, they can never beat the best human players.

I still think it was pretty bad writing, because during the scene Data lists the correct named response to his named attack. If his attack, and resulting defense are both named move sequences then they have been well studied, surely Data would know the entire “book” on both maneuvers. Which means he would not be surprised by any defense. Even if it was not what he anticipated. But he reported the correct response to his attack, which means that must be the BEST defense. Obviously it isn’t if Troi completely countered the defense and set up Checkmate in the next few moves, that doesn’t make sense. Also, Data clearly puts Troi in check, but she does NOT move her king out of check. In the next move Data can simply capture her king. I suppose the rules of 3D chess are never canonically explained, so I guess we need to accept that “checking the king” doesn’t actually mean anything in this game?

Oh well, I suppose suspension of disbelief should ease my mind of this. The idea that computers lack “intuition” and 3D chess is more complicated than regular chess in some strange way are probably enough voodoo science fiction to make it possible for Troi to win. But it is very interesting for me to get into the mind of the writers at the time and really wonder what they were thinking when they wrote this scene.

3 replies
  1. imppress
    imppress says:

    When you check the king, you need to reflect on the human frailties of your parents. Data has no mother so is exempt from the rule. Troi is a 3D chess beast.


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