Biology, Geometry, & Platonic Rationalism

According to legend, Galileo proved that heavier objects do not fall faster than light objects by dropping two led balls off the Tower of Pisa.  One weighed ten times more than the other, yet they reached the ground at about the same time. 

It is uncertain whether Galileo actually did this or merely proposed doing it.  It doesn’t matter for two reasons.  One is that the experiment has been repeated (on the moon, if I remember right) and the results were the same.  The other is that Galileo already knew that heavy objects could not fall faster than lighter ones.  He knew this not by observation but by reason alone. 

Suppose that heavier objects do fall faster than lighter ones.  Bind a ten-pound weight and a one-pound weight with duct tape.  Now drop them off the top of the tower.  We can make two predictions. 

One, that the object should fall at a speed between the natural speed of the two; for the heavier one will speed up the lighter one by a bit and the lighter one will retard the heavier one by a bit. 

Okay.  So far so good. 

Two, that the two objects conjoined will be heavier together than the heavier one alone.  If so, then the two objects should fall faster than either would alone. 

The two predictions both seem to follow logically from the premise, yet they are contradictory.  When contradictory conclusions follow from the same premise, the premise is refuted. 

Galileo’s thought experiment is strong evidence for the position in epistemology known as rationalism.  Rationalist, like yours truly, agree with empiricists that we learn a lot of what we know from observation.  We insist, however, that we can know a lot of important things by reason alone. 

For example: how do I know that there is no highest number?  I can’t know that by observation, for I cannot observe an infinite series of numbers.  I know it because I can reason that for any number specified, I can always add one. 

Plato stands as the greatest defender of rationalism in the history of philosophy.  He thought that we know almost everything we know about the world by means of intelligence rather than observation.  See my previous post for an explanation of his view. 

I have been reading a wonderful book by Peter Godfrey-Smith, Other Minds: The Octopus, the Sea, and the Deep Origins of Consciousness.  You won’t find Plato in the index, but I submit that you will find an account of the octopus that is pregnant with Platonic reasoning. 

Platonic reasoning in evolutionary biology is most clearly expressed in Daniel Dennett’s account of design space.  According to Dennett, design space is the realm of all possible organic forms.  Design space is not infinite.  You can’t really have the giant spiders that crawl around in sci-fi movies.  You can, however, have a lot more organisms than those that have actually emerged.  Evolution is the process whereby lineages of organisms explore the library of forms that are potentially available. 

To get a handle on the idea of design space, consider some very simple geometry.  Start with a single geometric point.  This is an altogether dimensionless position in space.  Now push the point a short distance in one direction.  You get a line segment.  Now push the line segment in a direction perpendicular to itself.  You get a square and define a plane.  Now push the square in a direction perpendicular to the plane.  You get a cube.  That is the design space available for objects in a three-dimensional world.  Everything that we observe with our sensory apparatus is confined to that design space.  Fortunately for us, it is very broad. 

Godfrey-Smith, an academic philosopher, is intrigued by octopuses.  He gives us an account, early in the book, of the evolution of animals.  His account is pointed not toward us, but toward our very distant, eight-limbed relatives.  What caught my attention is that this account mirrors the geometry that I describe above. 

We begin, in this account, with relatively flat creatures crawling on the ocean floor.  How do we know they could crawl, rather than swim?  They are always found in the fossil record right side up.  If they were swimming, some of them would have face-planted.  These creatures were almost two dimensional. 

Next they began to rise, probably by means of producing gas in their bodies.  Eventually you get something like a jellyfish.  It has a top and a bottom, but no left or right or front or back. 

It is said to have radial symmetry

By contrast, we are bilaterians.  We have a front and a back and so a left and a right.  The evolution of animals in the beginning was a push into geometric as well as biological design space.  It followed the contours of Euclidian geometry. 

Of course, it was much more complicated than that.  For a long period in the evolution of animals, the lion laid down with the lamb.  There was peace.  The earliest animals had neither claws nor armor.  Some of them, however, found rich sources of nutrients in the decaying bodies of their brethren. 

The efficient scavengers developed better and better devices to exploit the dead and then some of them discovered that such device could be used against living organisms.  The age of peace was over forever. 

I humbly submit that the evolution of animals follows lines that are geometrically coherent.  That is very important.  All philosophy and science proceed on an assumption: that the principles by which human reasoning works are the same principles by which the external world works.  That is the basis of Plato’s theory of ideas.  So far, evolutionary biology supports Plato.  

The Infinite Monkey Theorem & biology

Today in my logic class we discussed probability calculations as a way of illustrating inductive arguments.  I amused my students and myself by discussing the infinite monkey theorem and, better yet, actually calculating the odds.  It occurs to me tonight that this has some bearing on one of the big questions in biology. 

The IMT is a famous thought problem in philosophy.  If you had a number of monkeys randomly typing on keyboards, could they eventually produce a copy of one of Shakespeare’s plays?  The IMT is a good test of rationality.  Some students simply refuse to agree that it would be possible, even given infinite numbers of monkeys and time.  That suggests a mental block.  Given those assumptions, the outcome is not only possible but inevitable.  It is also a good illustration of the difference between logical possibility (which the IMT demonstrates) and causal possibility (which the IMT demonstrably fails). 

The monkeys in the theorem are, of course, metaphors for random signal generators.  They are also cute.  To explain my test, I’ll employ metaphorical chimpanzees (they’re easier to train).  I stipulate the following:

a constant team of 100 chimps;

each has a keyboard with twenty-six letters (no other symbols or spaces);

each chimpanzee has an equal chance of hitting any of the twenty-six keys on each keystroke;

each chimpanzee types exactly twenty-six characters per minute;

a full team of 100 primates is working at the stipulated speed twenty-four hours a day;

all the keystrokes are entered in a single line that we test for results;

there is no time limit on how long I can keep the experiment going. 

If you think that these stipulations are unrealistic, you think correctly; it’s a thought problem. 

Now: forget about a whole play; let’s just ask our simian team to produce

Now is the winter of our discontent made glorious summer by this son of York. 

One of my favorite lines, opening Richard III if memory serves.  That doesn’t look so hard.  If my apes are following the above stated rules, each will produce an “n” about once every minute.  To get the first and second letters in the right order, we have to multiply the probability of each: 26 x 26.  So, each 676 keystrokes will produce “no” and our team will produce about four examples every minute.  That’s pretty good.  We’ll be done by lunch.  Bananas all around!

The team will produce the first word in the line about every seven minutes.  Unfortunately, the wonders of geometrical progressions slow us down precipitously.  To get the first two words will require three full days.  Better alert the[KB1]  caterer. 

It gets worse fast.  Given our stipulations, the first three words “nowisthe” are going to appear in order, somewhere in our line, about once every 153 years.  Just to get the next three letters of the fourth word in order will require our team to work for about three million years. 

So how long will it take to get the first four words out?  Forty-seven billion, two hundred and six million, one hundred and four thousand, eight hundred and ninety-four years.  We are going to need a lot of chimpanzees and a lot of bananas.  Unfortunately, the Kosmos is only fourteen billion years old. 

I submit that our thought problem demonstrates two things.  One is that it is logically possible for our chimpanzees to produce Richard III.  Given enough animals, bananas, and time, they could produce the entire corpus.  The other is that it is causally impossible.  Vast stretches of time beyond calculation are necessary even to get going. 

There have been two recent attempts to play out the scenario.  One involved a number of macaque monkeys.  After two months, they failed to produce a single English word (they did have an inexplicable fondness for “s”); they broke the computer and pissed on the keyboard. 

The other was actually interesting.  Someone created a very large number of virtual monkeys, using the cloud to borrow computer time.   He claims to have produced almost the entire Shakespearean corpus by this method.  However…he cheated.  Whenever his virtual monkeys produced nine letters that appeared consecutively anywhere in the corpus, the program took them out and put them in their place.  The monkeys would not have to produce that string again. 

That is cheating because it means that our monkeys can produce Shakespeare only if they begin with Shakespeare as a forced sorting device, even with vast resources.  One might argue that it is analogous to divine intervention. 

It occurs to me that this is analogous to natural selection.  Instead of monkeys we have random changes in DNA.  Very large numbers of organisms constantly reproducing result in very large strings of genetic characters.  Natural selection saves the ones that code for viable traits.  That is how natural selection eventually builds a Shakespeare. 

But what about the UR organism, the first genuine replicator?  Is the simplest such organism that science can yet imagine more or less complex than the Bard’s Dickey Three?  Allow me to suggest that the answer is “more”.  How do you get from inorganic processes to even the simplest organic processes without some kind of preordained sorting? 

I don’t know and neither do you.  No one knows.  I have previously blogged on one attempt to answer that question.  Andreas Wagner argues that evolution worked because nature had a preexisting library of Platonic forms.  As a Platonist, I like that idea and I am pretty sure he is right.  I am just wondering who, precisely, was the librarian? 

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 [KB1]

The City without Gods: on Noir Fiction

Last week I had dinner at John’s Grill in San Francisco, with several friends from the APSA convention I was attending.  I ordered “Sam Spade’s Lamb Chops” from the menu, because I like lamb chops and noir fiction.  It was superb.  Six or seven lamb chops with a baked potato and sliced tomato.  In Dashiell Hammett’s most famous work‑The Maltese Falcon‑that is what Spade ate in that venue.  The restaurant had a small shrine to Hammett’s novel in the back, toward the latrine where everyone would pass it.  I didn't know it at the time, but I was constantly on streets mentioned in the novel: Stockten, Bush, Geary, and Kearny.  

Later, alone, I walked up Kearny to the Occidental Cigar Bar.  This is one of the last civilized places in California.  Apparently, it was “grandfathered in” when the same wise solons who are trying to promote the smoking of marijuana were trying to stamp out the smoking of tobacco. 

It is a narrow room with tables and chairs arranged in the space not occupied by the bar.  When I entered, there were two men dressed in pin stripped suits and hats smoking at the bar.  I had more or less walked my way into Hammett’s world. 

I sat at a table next to the big window, where I could watch people walk or drive by.  I lit a fine, square bodied cigar with a Maduro rapper and sipped on an excellent IPA.  The scotch was unaffordable.  I downloaded the first chapter of The Maltese Falcon and read, occasionally looking up at the passersby.  That is how I do San Francisco.

I have a theory about genres.  Each is centered on some essential idea, usually attached to certain special signs.  Westerns, for example, are essentially about the frontier: the grey land between civilization and the utter lawlessness of the uncivilized territories, coupled with the signs of horses, hats, and handguns.  The samurai movie genre is very similar, if you trade swords for guns and modify the architecture.  Horror is about the idea that evil can be a real force in the world, like gravity or electricity.  Science fiction rests on the idea of a constantly expanding scientific view of the Kosmos and the surprises that such a view might hold. 

So, what about noir fiction?  I submit that the genre is centered on the city without gods.  Almost all of the noir films I have seen or fiction I have read take place in modern cities.  Even those that take place outside it presuppose a larger civilization.  The city is a relatively recent innovation in human history, meaning that it appears only about 12,000 years ago.  For most of that time, cities were watched over by gods.  To be a citizen of ancient Athens was to be a member of the cult of Athena Nike, the goddess of wisdom and victory.  The gods reinforced the social contract on which each city depends and give the citizens‑those who must stand against the city’s enemies‑some reason for confidence and comfort. 

Noir fiction takes place in a realm that is utterly demythologized.  There are neither gods nor ghosts in world laid out by Raymond Chandler or Dashiell Hammett.  The streets are dark and foggy, with nothing but black overhead.  Death is a constant presence, but there is not even a hint of anything beyond it.  Death is the big sleep. 

Evil, on the other hand, is very real.  Nearly everyone is morally comprised and knows it.  “I’ve been bad,” says Brigid O'Shaughnessy to Sam Spade.  What is true of Brigid is true of both the gaggle of lowlifes and the police.  There is no sense of any higher order, no confidence in patriotism, the rule of law, etc.  One wonders what meaning evil might have if there is nothing else in the human world. 

But of course, there is something else.  That is the hero.  Chandler’s Philip Marlowe and Hammett’s Spade are heroes.  Neither is a saint or the ideal boy scout.  Yet each has a set of moral rules that he strictly follows and each is the best man in the story.  Both of these heroes risk their lives to defend those who deserve to be defended, or mostly deserve it. 

When I was, very briefly and a long time ago, a psychology major, I was taught that morality was socially constructed.  We only behaved according to moral rules because we were taught to do so by the other human beings amongst whom we lived.  If that were true, noir fiction would be impossible.  The bad would have no sense that they were bad and the good, no sense of what it means to be good. 

Human beings are moral animals.  We think in terms of right and wrong as naturally as we think in terms of pain and pleasure.  Even in a city without gods, we still act as though we are obligated to someone or something with authority over us.  Biosocial theory can explain how we came to be such creatures. 

It cannot tell us whether we can make morality work in the absence of gods or God.  In noir fiction, the hero is a small island in a sea of iniquity.  That is small comfort.  It is nonetheless comforting.  We love the story because the hero is beautiful.  That, perhaps, is what we have to concentrate on.