Friday, August 24, 2012

Telescope Mirrors, Washing Machines and Our Philosopher Kings

From time to time, I've been know to string together strange analogies around here, and tonight I present another one, involving going places no sane person goes for an obscure analogy.  But if you're up for a few minutes in a totally different world, pull up a seat and a cup of whatever.  

Let's talk about making a telescope mirror.  Do you know that an average person, who simply follows instructions well - you, for example - can make a telescope mirror with their own hands that is among the most precise things humanity knows how to make?  How precise?  Just to be functional, the surface of the mirror must be within 1/2 wavelength of light of the right shape, or within around 10 millionths of an inch.  The performance of a half wave mirror is so bad, though, that most amateur astronomers wouldn't stand it.  Instead, most experienced mirror makers turn out mirrors to better than 1/10 wave - often much better.  That's better than 2 millionths of an inch.  With your hands and extremely primitive tools - glass and abrasive grit. 

Furthermore, the average person is going to produce a more precise surface than most machines, unless a lot of thought went into the design of the surface.  Why?  Because a person can't make the same grinding stroke on the mirror every time while a machine can.  Because we're imperfect.

In a nutshell, here's how you grind a telescope mirror.  First, you put a hard ceramic or glass plate "tool" on the top of a stand of some sort (55 gallon drums are the ideal), sprinkle some abrasive on top of it, spritz some water, then put the glass for the mirror on top of this tool.  Now you stroke the mirror back and forth in a broad "W", turning the mirror a little and stepping sideways the opposite direction around the barrel.  Eventually, you wear a hollow depression in the piece on top, while the bottom piece wears down on the edges.  Once the curve is shaped, you clean up and switch to a smaller abrasive, grinding away the imperfections of the coarser grit.  Refine the surface like this a few times, followed by a polish and you have a surface ready for the real "magic", the optical figuring; making the surface meet the optical prescription.  This can be very easy or take weeks, but when it's done you have a telescope mirror.

We can make this nearly perfect surface because the thousands of strokes are all different in exactly how they work the surface.  The thousands of sprinkles of abrasive grit and water are never exactly the same amount.  The randomization of the actions produces a surface that's an average of the thousands of different strokes, much more perfect than can be produced by machine.  While all larger mirors are made by machine, smaller instruments are not, and the standard of excellence is still the hand-figured mirror. 

OK, now I can hear you saying, "that's moderately interesting, but I have no desire to make a telescope: why are you telling me this?" 

It's an extremely good analogy for the free market.  Millions of imperfect decisions being made by imperfect humans together form a more perfect decision than any machine, or in this case, more perfect than our "philosopher kings" - who are just one of those millions, after all - could ever make. 

Case in point is top-loading washing machines and the Department of Energy (source editorial here).  The DOE, of course, is driven by the agenda that energy efficiency is the single most important characteristic in any appliance, and if you consumers don't always buy the most efficient, then you're just too stupid and need to nudged into the right choices.  Consumers, however, seem to consider a wider variety of factors in choosing things to buy, not just the energy efficiency.  In reaction to how consumers were not always buying what their algorithms concluded were the most efficient machines, the DOE created rules that effectively eliminated top loading washing machines - protested by almost 3:1 among consumers.  One study showed that the average family does fewer loads of wash per week than the assumptions built into the rules did.  These folks saved far less money with the front-loading machines.  Consumers seem to be smarter than the DOE at figuring their total cost of ownership. 

This is just a subset of the study by Ted Gayer and W. Kip Viscusi of the Brookings Institute, called "Overriding Consumer Preferences with Energy Regulations".  (pdf)  It's a 46 page report, but interesting reading.

Consumers aren't perfect because humans aren't perfect.  They will buy a washing machine that isn't as "good" because it's on sale and they're short of money, say.  But they're better at figuring out what's best for them at that time, and the movement of millions of consumers, the market, is better than the models the government regulators  use. 
You're saving some petty bureaucrat's job. 


  1. Yep, I used to grind my own mirrors back in high-school, over 40 years ago.
    Took me a couple of times to get the silvering correct, but after I learned how to do it, I could also recoat them when the got damaged.
    MANY hours spent walking around the bench the blank was on, and keeping the compound "just right".

  2. It's been said, but not nearly often enough, that "one consumer is an idiot; a million consumers is genius."

  3. Brought to you by the same faceless autocrats who demanded 1 gallon flush toilets that need 2 flushes to do the job completely. LED bulbs, thermostats set at 82 in the summer, and 62 in the winter, smart meters for "your" energy consumption, removing any pesticides that are truly effective, going after the manufactures of legal products for extortion money, letting me know that THEY are smarter than I am so I should just lay back and relax, it will only hurt a little. Who elected these pinheads, and why are they commpelled to interfere in my buisness.

    1. Heh - you got that right. What do they say? "Lie down and take it for the Queen"?

      But to be serious a minute, I've heard that the toilet law actually came from the toilet manufacturers, who were getting hammered by different states proposing different standards, and they didn't want to stock 20 different tank sizes. So they asked Uncle Sugar to make one "law to bind them all".

  4. Great analogy re: function of a (truly) free market. Which we haven't had in many, many years.