Home > Human Limits > The Shannon Number, and the impossible hubris of city planning.

## The Shannon Number, and the impossible hubris of city planning.

Consider for a moment a simple chessboard.  8×8, or 64 alternately colored squares, occupied by 32 pieces, of only 6 categories of pieces.  In 1950, a man named Claude Shannon published an influential article entitled “Programming a Computer for Playing Chess” which is credited with fathering the field of computer chess.

Within this article, Shannon posited a number, which was an estimated lower bound on the number of legal chess positions, roughly put at 10^43.  The upper bound in a theoretical chess match was roughly 10^50, and the total game-tree complexity was estimated at 10^120, now called the Shannon Number.  In other words, the number of possible positions that any number of chesspieces could be in at any given point in a theoretical chess match falls somewhere between 10^43 and 10^50.  The number of possible games two theoretical players could play without repeating themselves is somewhere in the neighborhood of 10^120.  By comparison, the most common estimate for the number of atoms in the observable universe is somewhere around 10^80.

Think about that for a moment.  Chess is theoretically more detailed, in terms of game-tree complexity, than the observable universe is in terms of atoms.  Now consider the limitations imposed on the game of chess.  The pieces may not move beyond their 8×8 square.  The pieces may only move in certain directions.  One piece must be moved per turn.  Only one piece may occupy a single spot.  Chesspieces have no feelings, no motivations, no impulses.

The reason I bring this up is because today, November 8, is World Town Planning Day, according to a group of people who are far too arrogant for their own good.  They apparently do not see any problem with telling urban dwellers how to live their lives, despite the inherent complexity of the undertaking being far beyond that which even the sharpest mind could comprehend, let alone calculate.  In a world where we have no computer powerful enough to determine the exact number of possible unique games of chess, we nevertheless have a group of “city planning” enthusiasts who feel like they are smart enough to control the minutiae of millions of human lives from the top down.

Amazing advances have been made in computer chess.  Using retrograde computer analysis, one can fairly accurately pick a winner in a chess game  in which only 6 or 7  of the original 32 pieces remain on the board.  World champion Garry Kasparov has been defeated by supercomputers in the past.  However, no matter how much city planners want to treat the city’s residents as pawns in their little game, they will never encounter a single person with as many limitations as a chesspiece.  People have feelings.  People make stupid decisions, smart decisions, innocuous decisions.  People can immigrate and emigrate.  People can act and fail to act.

Even the smallest city, when populated by humans, will never be able to be planned.  The philosophical foundations for city planning are exactly the same as those which underpinned Marxism and Soviet-style socialism.  The idea that things can be planned from the top down is always proven spectacularly wrong.

City planning as a discipline is an arrogant, pseudoscientific fraud.  Its practitioners are the intellectual equivalents of astrologers but with real opportunity to do lasting damage to other, innocent people.  “World Town Planning Day” should be consigned to the dustbin of history.

***As an aside, I am by no means the first to tread this ground.  If you’re interested in the folly and failures of city planning at all stages, take a gander at Blight Ideas by David Willens, Best Laid Plans by Randal O’Toole, and many books by Thomas Sowell.

Categories: Human Limits
1. September 6, 2012 at 11:03 AM

Weather forecasting must blow your mind then.

• September 6, 2012 at 11:16 AM

Given how often it’s wrong, not really.

2. September 6, 2012 at 12:44 PM

So the fact that some planning has failed in the past means that all planning is doomed to fail?

I guess by that logic we can say science is doomed to fail since there has been failures in science in the past. Might as well give up NASA, its all a bunch of Marxists hocus pocus.

• September 6, 2012 at 1:02 PM

Misstatement of my position. My position is that ALL PLANNING FAILS. What seems to “work” is some combination of blind luck, survivorship bias, and causal density.

Perhaps the reason why you think it doesn’t fail is because you’re only looking at the world that obtained, and you see that it functions, after a fashion. I prefer to think of what might have been otherwise.

3. September 6, 2012 at 12:51 PM

Well thought out city-planning is what has made Chicago into the jewel it is today. Daniel Burnham’s plan. Is his plan really so arrogant and terrible?

• September 6, 2012 at 1:06 PM

I find causality to be far more difficult. You cannot attribute one cause to what Chicago “is.” That’s ridiculous on its face.

My contention is that what you’re doing is incorrect for its lack of complexity. You look out upon the city, see that it is good, and create a backward-looking narrative that fits your preconceived notions of what the cause should be. In reality you know nothing of what might have happened absent your purported cause.

Perhaps it would have been similar. Perhaps not. But it never seems to enter into your mind that it might have been better.

• September 6, 2012 at 1:19 PM

I can’t imagine a better place (except one with natural beauty to complement the artificial beauty) Sure, maybe the city would have centralized the way it did without the plan, but, this is one of the easiest cities on earth to navigate, Everything leads to downtown (or all the main routes, rail/road) so it is highly centralized, and very beautiful as a result of that centralization. Sure, there are many factors that have contributed to chicago being what it is, but I think one of the biggest is ease of transport/transport capacity. And that exists in this city in its current, highly effective manner, because of the plan laid out over 100 years ago. Something interesting about this particular city is that it has the least highway miles per capita of any city, yet its stands as our country’s third largest city, and has the 5th largest CBD on earth. People still get around fine in the city, just, it is so well laid out that it doesn’t need to waste resources on the overblown networks necessary to handle lesser traffic in other places.

• September 7, 2012 at 2:00 PM

I am glad you like where you live, but I feel as though we’re talking at cross purposes. My argument was never about whether Chicago (or any city) is a good or bad place to live, and it certainly was not about mass transit, though you can find my thoughts on that elsewhere. For the record, I do not live in Chicago. I find it a nice place to visit.

4. September 6, 2012 at 1:09 PM

By the way, this is why I stand by my contention that planning is pseudoscience. In the hard sciences, contra the NASA comment above, cause and effect are provable. We can isolate factors and repeat the result.

City planning does not allow for that, and the arguments I’ve been getting so far have all tried to prove a negative. Is it so hard to believe that you might be wrong?

• September 6, 2012 at 4:04 PM

Hard sciences can’t predict any better than urban planners. Sure, we can predict simple things like a ball dropping to the floor when it falls off a table, but good luck doing weather forecasts and sea level rise predictions with accuracy.

Does this mean climatology is a pseudo-science? No, it means it deals with complex issues unlike simple stuff such as gravity and planetary motion that is governed by very few basic laws. The same is true for urban planning.

• September 7, 2012 at 1:58 PM

The difference is one of causes and effects.

A chessboard has very few “causes” (moves, pieces, turns, spaces) and literally more effects than there are atoms in the universe.

Weather forecasting has orders of magnitude more causes, and just as innumerable effects. Simply because it is complicated does not make it less a science. After all, physics tells us that manipulating a molecule causes that molecule to act in particular, repeatable, provable ways. Thus, it is a science.

City planning has just as innumerable causes as weather forecasting, but – and here is the critical difference – no scientifically particular, repeatable, or provable effects. After all, a human being can act rationally, irrationally, or perhaps not at all. The “effect,” such as it is, may literally depend on what side of the bed the subject woke up on in the morning. That is the antithesis of science.

The complexity, or the usefulness of the forecasting based on it, has literally zero to do with it.

I feel like I addressed this pretty well in the post. Go back and reread the end of the third to last paragraph.

1. May 18, 2011 at 6:43 PM
2. December 27, 2012 at 8:51 PM