I've been reading "Godel, Escher, Bach" by Douglas Hofstadter and it's got me thinking a lot about the definition of life.
As I've mentioned in previous posts, if we want to find life, we need to think outside of the box.
We need to focus on finding systems far-from-equilibrium.
The early Earth would have had the following components far-from-equilibrium: sunlight, volcanoes and lightning. (And probably more)
Initials studies of life (Urey-Miller), took advantage of lightning to create a molecules in concentrations that are not-in-equilibrium with an environment at 300 K. The lightning (plasma) creates species that may be in equilibrium at 3000 K, but are not-in-equilibrium when the system cools down to 300 K. The lightning relies on the non-equilibrium formation of clouds and electron transport via droplets, which is in turn driven by the real source of non-equilibrium in the solar system (the Sun).
The questions that remain for me are:
Where else are there far-from-equilibrium situations?
How do life structures store exergy? When I see non-equilibrium dissipative structures (like Jupiter's Red Eye, or a hurricane, or Rayleigh-Benard convection cells), I don't see them as capable of storing exergy or self-replicating.
We need to find the differential equations (and the symmetries inside the DifEq's) that allow for self-replication and storage of information or exergy.
In a previous blog, I mentioned that I think that the symmetries have to be quite large (the smallest building blog is probably A5...a group with 60 symmetry operations.) My feeling is that A5 is just the smallest building block, and the actual differential equations that model life has even larger group structures.
My gut feeling (since I have no way yet to prove it) is that the group of symmetries of the differential equations is so complex that Godel's Theorem applies. (For example, the "integers under addition" is not complicated enough for Godel's theorem to apply, but when you include multiplication and other functions, then you get to the point at which there is an automorphism between the numbers and the operators. Somehow, this allows the system to self-replicate...don't worry if you don't follow me it because I don't understand this is either. I'm still trying to figure out how automorphism could lead to self-replication. (Let me know if you have any thoughts.)
Because...ultimately, we need to be able to describe biology in terms of chemistry and in terms of differential equations. So, we have to start looking for symmetries or building blocks inside of the equations (not just the physical chemicals themselves...such as RNA or DNA). Clearly, if you just look for the molecules (RNA or DNA), then you end up with a chicken or the egg argument. (i.e. is life just RNA/DNA or did life make RNA?)
We need to find the symmetries inside the differential equations just as we can find certain symmetries inside of the differential equations that allow for dissipative structures, such as Rayleigh-Benard cells or perhaps such as the ~ 11 (22) year cycles in the number/location of sunspots.
In the end, life structures use their ability to store exergy and to replicate in order to speed up the production of entropy to bring the universe closer to equilibrium.