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.