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1.6 Theory of Life
Discussion
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I believe that if we were to find life on other planets, the number of possible states for life would only be as large as the complexity of its structural components. This lecture made me reflect on what makes a crystal so fundamentally simple: its periodicity, or ability to be repeated across all of its constituent matter. Thus, there exists a symmetrical property that limits the amount of diversity a crystal may have. On the other hand, the aperiodic nature of the nitrogenous base pairs which make up our DNA allows for our genetic information to be highly variable, thus giving rise to the seemingly infinite number of evolutionary species, as well as variations among organisms of the same species. Were this genetic information to be limited to a finite number of repeated sequences such as the set {TATA, CCGC, ACTG}, there would not be nearly as much diversity as that which our planet currently supports.
Thus, any imposing property on the structural components of life limits the amount of diversity available to living matter. This result is very similar to the idea of Kolmogorov complexity in algorithmic information theory. In some sense, we can measure the amount of computational resources required to virtually simulate concrete or hypothetical life forms, which allows us to integrate mathematics and computer science into the field of biophysics.
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Hi Richard,
I am extremely impressed with these ideas! Realizing that symmetry and complexity are two sides of the same coin is a very profound insight. I would also like to throw the idea of randomness into this discussion. If you have a completely random system you probably won’t get life, yet random systems have the highest Kolmogorov complexity! Thus, Kolmogorov complexity fails in some regard because truly random systems allow a very simple statistical description. There are other, however, other measures of complexity that capture the notion that both purely periodic and completely random systems are both relatively simple to understand and it is somewhere in between that captures true complexity.
This actually brings me to my next point, which is that complexity is really well understood at an intuitive level but really poorly understood at a mathematical level. You mention both the structural components and the patterns that the components create as contributing to the overall complexity and recognizing that these are both factors is important. However, this component/pattern duality makes it difficult to assign a measure of complexity to a system. Is a complicated structure made of one component more complex than a simple structure made of many components?
Do you have any thoughts as to how to assess the amount of complexity a planet can support? Is earth close to its theoretical capacity?
Thanks for the great thoughts,
Jake
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