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The Marxists famously took a deterministic view of the world. They saw the evolution of society as one where certain stages of development were inevitable. So, they believed that capitalism emerged, but that it too must evolve into the next order, which they of course understood to be full-blown socialism. They were wrong.

However, there is a contingent of folks out there who believe in individual psychological determinism (i.e. we have no free will). Whatever your view on that is, let’s think about the implications. If it is true that all behavior is deterministic, then it must be be the case that we can theoretically design a powerful computer that understands our every last hope and desire, our every last ability, and in fact can figure out how to mesh our hopes, ambitions and desires with those of everyone else on the planet to create an order that is beyond anything we can imagine.

It sounds great (for some, not me). But it is patently absurd. And we know it is patently absurd because of simple statistics that a grade schooler could figure out once someone taught them scientific notation. Take the size of the population on planet as fixed forever at 7 billion, or 7.0 x 10e9. The folks who subscribe to the planning view think we can take all of these brains, download them into a computer, and go ahead and solve some equations. My point is, even if it is theoretically feasible, it is not physically feasible. Literally, the laws of physics do not allow it.

Suppose that each of these individuals has only one choice to make in their entire lives (such as where to work) and that you want to allow a lot of heterogeneity in the population, such that there are not 7 billion different people-choices, but perhaps only 1 million (i.e. person one chooses between career A and B, person two chooses between C and D and so forth). The relevant question for our computer programmer is to figure out how to mimic the choices of these million different “choice groups” (remember, they represent the entire 7 billion, so we are already assuming that we can do such a grouping — presumably the smart computer could do this). How many different permutations of choices exist among a million “people” choosing their careers? How about 1 million factorial. That is, 1 million times 999,999 times 999,998 times 999,997, times …. times 2, times 1.

How big is this? I don’t have a piece of software on my computer that is able to calculate it! In fact, if you assume that there are only 100 such choosers, then my computer can handle the calculation. How big is the number of possible outcomes that society may demonstrate? Well, 100! (factorial) is roughly equal to 9.3 x 10e157. Yes, that is 9.3 with 156 zeros after it. For reference sake, that is much larger than a Googol. OK, so you might not be overwhelmed, because you believe that computing power will improve enough to be able to process the “desirability” of each of these 9.3e157 possible outcomes and then spit out the “best” one.

This is problematic for two reasons. First, and I will write more about this in the future, we’d have to pre-program this machine to understand what could possible be “good” versus not good. It’s not a matter of adding up the good and bad from each individual’s choices, because my thoughts on good are a function of what everyone else is doing. Second, and this is the point of today’s post – is that physics suggests (to me) that it is impossible to design such a computer.

Why? Because there are “only” approximately 10e89 total particles in the entire universe. In other words, I wonder whether it is possible to run combinatorial calculations on numbers that exceed this base number. I need to think this through some more. But consider it from a different angle. What limitations does the speed of electro-magnetic radiation force on such a computer. Suppose that it can analyze each decision in the time in takes light to travel the smallest length you might think a computer chip can be engineered down to (perhaps a nanometer, or 10e-9 meters). How long does it take light to travel this distance? Well, light travels at about 3e8 meters per second. And we know that the time it takes for something to happen is the distance traveled divided by the velocity, so we have:

Time for EM to travel on a chip = 1e-9 / 3e8 = 0.33e-17

In other words, it will take about 3.3e-16 seconds to make each calculation. In a second, the computer could make a little over 33 pentillion calculations. If there are 86,400 seconds per day, our computer could make about 3 million pentillion calculations per day (about 3e21). So, how long would it take to process the 9.3e157 calculations that only a 100 choice world would entail? How about 3.1e142 seconds. Well, there are 32 million seconds in a year, and the universe is about 20 billion years old. Therefore, the universe has had about 640 million billion seconds tick away since its start – or about 6.4e17 seconds. In other words, if we asked our supercomputer to start this calculation with the Big Bang, and it processed the choices at the speed of light, but today it would still have only made an infinitesimally small fraction of the way through all of the possible choices we’d have to analyse.

The actual “calculation problem” is much worse than that of course, because 7 billion of us have tens of thousands of decisions to make over the course of 80 years, and our preferences and constraints are changing from second to second as well. I do not mean by this to argue that what we all choose to do here in the spontaneous order it “optimal” but rather that the concept of optimality is beyond comprehension, and beyond this, the idea that a computer could get anywhere near optimal is silly. But it’s worse – the computer is unlikely to stumble upon anything that would resemble tolerable, even if we brushed aside the impossibility of making the calculations.

Here is Nozick’s experience machine idea.

3 Responses to “Pithy Proof Against Planning”

  1. Busterdog says:

    “Well, light travels at about 3e8 meters per second squared”

    I don’t think you want the word “squared” in that sentence. That would imply acceleration.

  2. Harry says:

    You do not have to convince me.

    Anyone who hangs out with people wearing suits knows about “Strategic Planning” which every MBA is taught is among the highest of management pursuits, often done at retreats. Often the product of these efforts is a Five Year Plan, four inches thick and put into a three-ring binder.

    While one has to plan, certainly for the next month or two to make sure the machines have enough backlog not to be idle and be reasonably sure the sales department thinks you will be able to sell whatever is going out the door, it is a neat trick to make all that happen.

    Two questions:

    1) Is the interest in a five- or even a three-year plan an idea of progressive academia? (Did Andrew Carnegie concern himself with such things?)

    2) Didn’t Goedel prove that computers can’t do metaphysics?

  3. Rod says:

    It seems to me that the best managers are the ones who can adjust to continually changing conditions, and not shoehorn every choice into the model of a strategic plan.

    Our local chamber of commerce recently spent $50,000 of state grant money (the kind of money that grows on trees in Harrisburg) on a study of our local valley’s economic scene, the PERK UP project. The cleverness of that choice of acronym (stands for Perkiomen Economic Redevelopment something or other) betrays the emptyheadeness of the study, which was done by a band of clueless planners from Carlisle. While in some cases there might be a virtue in having outsiders offer some fresh ideas, this group began its study by transcribing much of our bureaucrat-written comprehensive plan into theirs.

    When the Carlisle planners presented a draft of their plan to the executive director of the chamber of commerce, she called me up to ask me to “clean it up” grammatically and structurally so it would not be a total embarasment to the chamber of commerce. I hardly knew where to start. Absolutely none of their findings were anything more than what the members of the chamber of commerce already knew. Worse, however, were the broad conclusions they made for the chamber to foster prosperity.

    The first recommendation was that the chamber encourage the development of “eco-tourism.” The idea was that yuppies from the suburbs (including employees of the Montgomery County Planning Commission) would flock to our area for the “amenities” of our public parks. Kayakers would tool around the reservoir (the water turns green in the summer and emits a sulfurous odor) and then stay at a bed-and-breakfast and have a meal at one of our local fine dining restaurants. By making the area a mecca for nature lovers, the regional planning commission would then be able to justify zoning fewer acres of land for real economic development where a business brings in money by the truckload. Everyone would be happy, then. And a bonus: fewer carbon emissions and a happier planet! (Will one be able to transport that kayak on top of a Smart Car? Sure, you can fit at least ten clowns in that car!)

    The PERK UP Plan, like all similar plans, now sits in a pile of useless plans. The worst part is that fifty grand of taxpayer money got spent on this. Those planners from Carlisle should get real jobs in the private economy, where they might have an opportunity to add and not subtract from this nation’s wealth.

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