Appendix 8.3 The Falsification of Evolution

To set our model up to do the same task that evolution must actually do; that is evolve a new gene by mutation and selection we change the alphabet of possible values from [H or T] to [ A, T, C, G ] four possibilities. I apply a 30% redundancy factor as for real proteins by dividing 4 by 1.44 to give the probability of a successful mutation equal to 1 in 2.78 instead of 1 in 4 which is a 30.5% increase in probability. At each event the population is given a point mutation as a single DNA code which is compared with an external random pick of one code. The population is then compared to the external code and all who do not match are culled leaving a reduced population for the next mutation event. Those left after each event have accumulated a series of beneficial mutations for the total number of events to that point. This is equivalent growing a gene of DNA codes by mutation and selection equal in length to the number of events. I then plot the resulting points in groups of three to indicate whole codons but the numbers being so large the scale of total mutation count is logarithmic.

Now to something quite obvious I am deliberately omitting any consideration of function! So every match from the very first codon equivalent to one amino acid is considered equally selectable and functional. The reason for this is simple because where function begins in terms of gene size is unknown and actually irrelevant for the testing of selection alone. While the change to function by any mutation is obviously important for selection in the wild by ignoring function here I am making a huge concession to evolution by natural selection which does face that challenge. It means if this model cannot evolve a gene of reasonable size in the assumed time of earths evolutionary history then the natural case being far less efficient also could not and this is the essence of falsification as a violation of the second law.

Appendix 8.2 The Falsification of Evolution

Now things start to get interesting but let me first examine the coin toss model;  

To guess 7 H-T tosses in a row we note there is 2^7 or 128 ways of arranging 7 coins which actually means this will occur on average every 128 tosses of seven coins for a total of 896 coin tosses and that is the work required to both create the order and pay the entropy cost required by the second law for that state of order in that system and by that process. It is vital you understand the connection with entropy at this point since entropy is a measure of disorder and disorder is the probability of a state of matter existing. That is from Boltzmann's [ s = k.logW ] Disorder = W/Wtot where W is the number of microstates in a chosen macrostate and Wtot is the total number of microstates in the system. In this case W = 1 (one way to get an exact sequence of H-T) out of Wtot = 128 (possible arrangements) and the disorder is the probability of that state = 1/128 = 0.0078 while the entropy is log 1 = 0 as it is the most ordered state you can get from that system. There is something else; we know work is the only form of energy that can create thermodynamic order. Work is also a product of vectors which have direction as well as magnitude implying a choice has to be made. So work is directed energy while heat is random energy and creates only disorder unless directed. 

Note however to get one arrangement of 7 in a row starting with an audience (population) and using selection to cull it only took 7 generations of selection events. Knowing the chance of selection 0.5 we can predict the population required since it is on average halved 7 times from an initial starting population = 2^7 or 128. The total number of coin tosses (mutations) = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 254 so selection reduced the number of mutations required by (896 - 254)/896 x 100% = 71.6% revealing the power of selection over pure chance. The model tests survival in response to a changing environment. By starting with a population and introducing successive random mutations then selecting survivors matching an external random event and culling the rest it is a model of pure highly optimised selection. All we need now is to give this model the same task that evolution in the wild must have had, i.e. grow a new gene with no target to aim for just a fitness landscape to respond to.

Appendix 8.1The Falsification of Evolution by Natural Selection

Finding the mean total number of mutation events was vital as it is this that is directly proportional to the improbability or entropy of the state and hence the Entropy Cost of achieving that state under the second law. Let me illustrate what I mean by Entropy Cost with two dice: The probability of [6][6] is 1/36 but this does not mean we cannot throw [6][6] on the very first throw nor does it mean we are guaranteed to get [6][6] after 36 throws. What it really means is [6][6] will occur on average once every 36 throws of two dice if we just keep throwing the dice. The longer we keep doing it the closer will the ratio of total number of throws divided by occurrences of [6][6] approach 36 which is what the Law of Large Numbers predicts.

What that means is 36 throws of two dice is the minimum work required or entropy cost of the state of order of [6][6] in that system by the second law. Heavier dice simply increase the energy required but in no way does that affect the entropy cost measured as the number of throws of two dice = 72  demonstrating that entropy has nothing to do with energy. There is a paper yet to be published on that subject but let it suffice to know the second law imposes a minimum average number of random events to create a state of order by those events and it is equal to the improbability of the state. If any theory requires a state of order with less  random events to pay the entropy cost it is falsified by the 2nd Law.

The Dawkins coin toss model can be modified to be made generally applicable to any code base with any probabilities for selection and cull desired or even introduce code redundancies effectively moderating mutation probabilities for deselection etc. Noting that real evolution must in the end grow genes made up of an alphabet of bases A, T, C, G with certain probabilities of mutation it occurred to me the model could be configured to do exactly what evolution in the wild must do to grow a gene.