The Landscapes of Science

 I have always been interested in the concept of a "landscape" in scientific theories.  A "landscape" is a representation of a higher dimensioned potential energy surface in a simplified three dimensional plot.  A couple of years ago I posted this comment in a thread about Conrad Hal Waddington's ideas on epigenetics (his term for developmental processes in biology not to be confused with the current misuse and abuse of the terminology):

"I can still remember the shock of insight from seeing a diagram of the epigenetic landscape in one of C.H. Waddington’s books when reading it over 40 years ago now.

I am impressed to this day by the usefulness of the “landscape” concept in diverse fields of science. In chemistry the potential energy surfaces of molecules and reactions are a landscape representation. In evolutionary theory there are of course fitness landscapes and finally on the grandest scale the cosmological landscape of string theory.

They are all of course higher dimensioned potential energy surfaces simplified to a 3-D representation in a 2-D projection. I wish the current evolutionary biologists would draw them the right way though, like physicists, chemists and the late great C. H. Waddingtion did. The vertical axis is potential energy and stable states are the lowest levels on this axis. So there are fitness valleys not fitness hills. A test “marble”, “ping-pong ball” atom or organism will tend to roll down to the lowest level in the metaphor of terrestrial gravity operating in a landscape."

 Comment in Why Evolution Is True

I have continued to think about the landscape metaphor in science.  The landscape is a simplified representation of a mathematical object in a potentially highly dimensioned hyperspace.  The usefulness of the concept in such diverse scientific fields  must represent some underlying similarities of the mathematics involved.

An example of a chemical potential energy surface from the article When is a Minimum not a Minimum

Here is Waddington's epigentic landscape from 1957 showing the potential developmental pathways for the ball (embryonic cell) as it rolls down the landscape.

What is the fundamental difference between difference between the two landscape representations ?  More to come.