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.

APPENDIX 8: The Falsification of Evolution by Natural Selection

After a great deal of work the penny finally dropped mid June 2019. All my computer simulation work was really doing was trying to reliably predict the mean or average work required (total number of mutations) to evolve a genome. The Second Law of Thermodynamics is a statement about the average behaviour of a system. As genome size increases the model should show both the power and the limit of what natural selection can do under the Second Law. The problem was to predict the mean of a distribution where the distribution has an unknown law and a large standard deviation. But now thanks to Richard Dawkins this problem has been solved! It is the model performed by Richard Dawkins in one of his Christmas lectures in the 1990's at the RI!

In the original demonstration an audience of about 120 children were asked to all stand and privately guess heads or tails. Another boy at the front was asked to toss a coin. All who got it wrong were asked to sit down. Honesty was as in all science basic to the success of the whole thing. This was repeated until there was only one child left standing at which point Dawkins pointed out he had just guessed seven H-T tosses correctly in a row demonstrating that improbable things are not so difficult to observe. It was of course a simulation of selection's power over pure chance but I don't recall Dawkins actually claiming that.

In this simple coin toss model there is NO TARGET! All simulations of evolution with a predetermined target are invalid because evolution has no target. Instead an external random event becomes the next test of survival for the last guess (mutation) which in a very simple way mimics response in a population to a change in an external fitness landscape. The model is purely a test of selection uncomplicated by other constraints. This model finally achieved my objective of having a model of mutation and selection in a population and I found it has an equation for the mean total number of mutations to evolve any code sequence of any given length. I believe this model has an equation because the true entropy cost is paid for up front by starting with a population which all gets culled so the outcome is predictable but only in entropy terms which is the cost of performing the total number of mutations.

Apendix 7.5 Modeling Evolution

It turns out there is a very good reason why its difficult to include realistic selection in an equation of probability of evolution over time. Selection causes the outcome of one random mutation event to affect that of the following event breaching independence. The general form would normally be a Poisson distribution but that is only valid for independent events.

So lets keep things very simple and run the model for a more realistic gene pattern based on the A, T, C, G nucleotide bases of the DNA molecule. Same 10 genes, same 100% selection of the top scoring 5 genes reproduced faithfully to maintain the population of 10. So if we start with one mutation per generation per gene what happens..

To give some statistical validity I averaged the total number of mutation events to achieve the pattern [ATCGATCGATCG.. repeated] for various length genes over 10 cycles and I got this..

Gene      Number of
Length    Mutations
 (L)            (N)           Log(N)
10               818         2.9129
15             4353         3.6388
20           22956         4.3609
25         108139         5.0339
30         918605         5.9631
35       2453687         6.3898
40     16080795         7.2063

Basically log(N) graphed against (L) gives a nice straight line as expected since the governing distribution would be exponential (Poisson). My computer would not solve beyond length 40 without taking too long to do 10 cycles of each.. (days)..

A simple linear regression of the straight line projected out to just 150 bases long gives a first approximation.. however standard deviation is quite large..

The answer is for a gene of just 130 DNA bases evolved as using this model with perfect selection of every single mutation.. If a mutation occurred every millisecond it would take 3.6 billion years on average to get there.. While this result is mathematically correct its not the the most favorable model for a real evolutionary algorithm. What I have done here is pit a severe mutation rate against the very best selection rate.. and while the former won it means I need a more realistic mutation rates v more realistic selection rate. Not simple as Fred Hoyle's work shows..

I obviously need a more powerful computer and a bit more statistical work to tidy it up as a paper..

Appendix 7.4 Modelling Evolution

It seems for the statistical simulation model the efficiency of selection is not completely set by one value of Sn (or as in the stat model, top % of population selected). It is affected by the methodology used.. So in the original Dr J model all strings of '01' or '10' were counted resulting in 2000 - 4000 generations (single mutation) to achieve the 100 long "010101.." pattern. I have settled on simply counting every correct digit (base) be it 0 or 1 or A or T or C or G etc in its correct position. Running this model 50 times the sample mean to 'evolve' the 100 pattern was 443 generations which with a 10 gene population = 4431 mutation events.. min 2021, max 12870. Now that's with one mutation, on a simple 2 code choice model with perfect selection/copy of the top 50% after each single mutation level. A fair way from reality.

With just 2 mutations however these simple models reveal a real problem.. so far none have completed the pattern. As it turns out a single mutation in a 2 code system has only a 25% chance of being detrimental similar to the Fred Hoyle analysis of the 'naive' single beneficial mutation. However with a second mutation that all changes as the second becomes predominantly detrimental.

So do two mutations acting on 100 base length of genome = 2% mutation rate? Imply a massive overstatement of the rate of mutation. Lets pose the question.. How many DNA changes generally occur in concert before a selectable trait is produced? Putting it another way.. Is every single DNA mutation normally selectable.. clearly not. By requiring just 2 mutations to act together before selection criteria is applied is actually a huge concession to what occurs in the real world. Recall I am only modelling the algorithm of evolution and artificially increasing the rate of mutation just facilitates a quicker result particularly since every beneficial change is selected.

Including realistic selection strengths in models and equations of evolution has proved very difficult. So to keep things simple I am going to assume 100% selection and reproduction of every beneficial change. Which may mean a more realistic number of mutations (ie 2) or larger population size. The objective is a rigorous, simple, verifiable test of the evolutionary algorithm to which end it is imperative I give every possible concession to evolution theory.

So what's the result..

Appendix 7.3 Modelling Evolution

The coin toss simulation is not a model of evolution but a model of the algorithm of evolution which allows exploration of the strength of natural selection to overcome the normal destructive effects of random mutation. Since natural selection does change the probability of a required outcome it would be nice to find an equation for that probability. In Appendix 5.1 I discovered a number which was effectively a boundary condition the 2nd Law imposes on the random assembly of any coded string from a finite alphabet. An equation for probability of evolving a given 'gene' after any number of generations including the effect of natural selection would allow me to relate the improbability of the state to the limit imposed by the Second Law.

I have an equation which on preliminary testing shows agreement with some statistical modelling, Fred Hoyle's results [The Mathematics of Evolution] and recently published papers like this..

[http://dx.doi.org/10.1371/journal.pone.0000096].. noting..
"Although a great deal is known about the landscape structure near the fitness peaks of native proteins [5], [7], [9], [15], little is known about structures near the bottom, which contain information regarding primordial protein evolution." and..
"Although it was shown to be possible for a single arbitrarily chosen polypeptide to evolve infectivity, the evolution stagnated after the 7th generation, which was probably due to the small mutant library size at each generation."

While such modelling does show some increase in fitness as complexity (sequence length) increases it effectively stagnates at some limiting value dependent upon the "mutant library size".. This is precisely what my Second Law boundary condition predicts..

The equation is proving difficult to verify and I initially had problems with software handling very large/small numbers (now solved).. I started defining selection success 'Sn' as the probability that positive mutations on average will succeed.. ie not die or get eaten before they can reproduce.  Sn varies like this..

Sn = 0  (no selection)   to   Sn = 1  (100% selection)

Some program confirmation of stagnation occurred for all values of Sn for large enough gene lengths. However the extreme sensitivity as Sn dropped even minutely below 1 for me urges caution so I'll hold that result until fully verified.

Appendix 7.2 Modeling Evolution

Well it turns out my 100 coin toss model exceeds all expectations.. Yes the one proposed in Appendix 5 and which Dr J programmed (see App 6).

The program demonstrates that with a single mutation applied at random to all 10 genes (each 100 long) and with 50% selection of the best(fittest = largest count of 0101.. sequence) the model converges on the target 100 long string of 0101.. pattern in 2000 to 4000 generations. The advantage of this pattern is that it has an equal number of heads/tails which makes the improbability only a function of the order and not the number of heads or tails which over any large random sample will be approximately equal. In absolute entropy terms it means the set of macrostates with the largest number of microstates.

If we now note that a single mutation (toss of coin) at a random position in the 100 long gene has 50% chance of being correct and 50% chance of being in the right place = 25% chance favorable. It also has 2 x 25% chance of being neutral so leaving only a 25% chance of being unfavorable. This approximates Hoyle's description of what he calls the naively simplistic model widely accepted by evolutionary biologists and their followers.. its the single favorable mutation model.. and yes it behaves exactly as predicted. But now following Hoyle what happens if we introduce a second mutation.. ie make 2 random mutations at random positions at each new generation while still selecting 50% = 5 best genes..

Go ahead.. run it..

I let it run for two days and over 40 million generations and NO it does not converge just as Fred Hoyle's math analysis predicted.. The second mutation becomes overwhelmingly unfavorable to the completion of the whole series beyond a certain point.

You may think that a rather strange result.. by adding just one more mutation it completely annuls the power of 50% perfect selection..! So the real question it raises is; what exactly is the power of selection to 'create'? Consistent with standard probability rules the length of the genome has a big effect on the improbability of the final outcome as convergence can easily be obtained for say a 50 long string even with 2 mutations. Although it now becomes a statistical analysis problem.. it starts to look very much like it supports my original falsification in Ch 9 on the basis selection 'bias' may be so small as to be negligent for large genomes with large numbers of unfavorable mutations.. ie Fred Hoyle's conclusion.

Appendix 7.1 Modeling Evolution

Fred Hoyle was a brilliant mathematician.. Professor of mathematics at Cambridge.. solved the nuclear synthesis of the heavy elements in the center of stars.. He was an anti-creationist and made a genuine attempt to math model the evolutionary algorithm analytically.. He differs from what he calls the "new believers" (in evolution by natural selection).. in one characteristic.. He told the truth in "The Mathematics of Evolution".. You need to hear what he had to say..

"Let us start naively with the feedback equation..
dx/dt = s.x    (t = time)  (1.1)

in which x is considered to be the fraction of some large population that possesses a particular property, 'A' say, the remaining fraction (1 - x) possessing a different property 'a', all the other individuals being otherwise similar to each other."

After integration to find x and some elaboration on the reproductive outcomes of this model for A being advantageous (s > 0) he gets..
x = xoexp(st)

"So it is agreed for s > 0, with A then a favorable property, that x rises to unity with all members of the population coming to possess it in a time span of ln xo/s generations..  ...  And if s < 0 the solution dies away in a time span of the order 1/s generations, thereby implying that if A is unfavorable it will be quickly rejected.

I am convinced it is this almost trivial simplicity that explains why the Darwinian theory of evolution is so widely accepted, why it has penetrated through the educational system so completely. As one student text puts it.. 'The theory is a two step process. First variation must exist in a population. Second the fittest members of the population have a selective advantage and are more likely to transmit their genes to the next generation.'

But what if individuals with a good gene A carry a bad gene B having the larger value of |s|. Does the bad gene not carry the good one down to disaster? What of the situation that bad mutations must enormously exceed good ones in number?"  (A fact acknowledged by all the research).. and so after some work he gets..
x  ~=  xo/( xo + exp(-st))      (1.6)

Unlike the solution to (1.1) for s > 0, x does not increase to unity ... but only to 1/2... Property A does not "fix" itself in the species in any finite number of generations. A residuum of individuals remain with the disadvantageous property 'a'."

My verification of this next..

Appendix 7 Modelling Evolution

First a note about probability and entropy..

The probability of any 'event' is determined by the 'prior' expectation of it (by a given process). (ie if coins are intelligently placed in order (HTHT.. etc.) then the probability of that arrangement would appear to be 1 because the outcome is certain). So by this it would appear the probability of achieving a state of matter depends upon how it is produced (process). But the absolute entropy of any state of matter is independent of the process that produced it! So it would appear the entropy cost of producing an end state is independent of the absolute entropy of the state itself.! Yet we know they must be dependently linked because any low entropy state must be accounted for by an increase in entropy (in the surroundings) and the only available way to get it is the process that produced it..?

How do we reconcile this apparent contradiction..

If the improbability of a state is reduced by a natural bias (like selection) or even direct intelligence the entropy of that state is not changed and the cost of that state must still be accounted for.. The answer must lie in that fact I have only considering the final steps (the placing or tossing of the coins) of a process which is in fact the result of a much larger 'system' that makes the outcome possible..

The considerations of where did the coins (or dice) come from.. what about the table, the room and even the person doing the placing. So is it valid to calculate the improbability simply by looking at the end result. That answer is in the term conditional probability. The probability of A given B is written Pr(A|B), (Noting that improbability is just 1/probability). So when I am calculating the probability of a sequence of 100 coins (leave the DNA for now).. It is actually..

Pr(100 HT pattern | coins, table, room, person, land, earth etc etc.) with all those 'givens'..

It is therefore possible to simply state the absolute entropy of the state is not changed by the process its just that I am calculating the conditional probability (or improbability) of the last part of the process (system) that produced it. Most important here is the fact that each conditional part in the process must result in an entropy increase which exceeds the drop in entropy that it creates. So the drop in entropy resulting from a person placing the coins in order is different to the drop in entropy resulting from tossing the coins randomly to get the same order. But the absolute entropy (~probability) of the final state is the same in both cases. They simply have a different set of 'givens'.

I hope that is clear enough..

Appendix 6.1 Dr J Verifies

So my 100 coin toss model of evolution turns out to be a reasonable illustration of how selection and replication work. By adjusting the parameters of the model it should be possible to plot the 2nd Law boundary which ultimately limits what any natural process can achieve.. Which is what Fred Hoyle actually showed in "The Mathematics of Evolution".. He said..

"evolution is correct in the small but not in the large.."  Introduction p6

Dr J's program of my model shows that my assumption: selection and reproduction have no effect on the probability of the final outcome is wrong!

However by mapping the effect of selection and reproduction I may be able to establish a relationship between (+ve mutation rates ~ selection strength ~ reproductive success) to the limits imposed by the 2nd Law. This should be possible because I discovered the unique number which sets the boundary for violation of the second law in any system where the improbability can be calculated (like with DNA). It may in the end require a fairly rigorous statistical approach but overall to date my 2nd Law boundary theory indicates it should agree quite well with Fred Hoyle's results in "The Mathematics of Evolution"..

So was my 'falsification' Ch 9 correct or not.. As far as the (corrected) program of the model goes.. I have to say not yet for evolution by natural selection, (but it should falsify the abio-genesis protein first model).

I now need to summarize the basic principles underlying all this..

(1)   The total improbability of any state of matter is quantified by its absolute entropy. For any ordered state of matter it represents the decrease in entropy from the state of complete disorder (equilibrium).  All forms of order are included.. physical (structure) and logical (information).

(2)   By the second law there must be a corresponding increase in entropy of the surroundings of the system which must be a direct consequence of the processes and events that created the state of order.

(3)   The rule of conditional probability allows the process to be analysed in parts which themselves must each obey the second law when all contributing processes are included.

Richard Feynman 1975 Caltech address warned scientists "before going public consider every conceivable way we might be wrong"..
Popular Science May 2015 "Nothing but the Truth".. strongly agree.

Appendix 6 Dr J Verifies

I do not normally respond to people who conceal their name.. but here's an exception..

Dr J programmed an enhanced (100 long genomes instead of 10) model at [https://t.co/k0WLnZyyTR] complete with results showing successful 'evolution' of 1x100 long 01' (or HT') sequence after some 2000 - 4000 generations. Its not the 10x10 as originally proposed but lets face it 1x100 is the same thing, ok.. Then there was the Python problem..

I programmed the same model and my answer was NO.. My Python program had to be terminated at over 10000 generations.. with no tendency to converge on the specified pattern.. I thought Dr J's program was doing something else. On re-checking I discovered the Python program was flawed because unknown to me copies of elements of Python lists are not real copies.. they are pointers.. When corrected for this my Python translation of DrJ's program of the model does converge exactly as Dr J's program does for a single mutation with 75% chance of being favorable or neutral.

So is this a model of evolution.. not according to Fred Hoyle.. with rates of +ve mutation averaging 25% and perfect selection but I think it has all the required elements.. It turns out to be an excellent way of verifying Hoyle's analytical results by adjusting the parameters (no of mutations, selection/reproduction strength) and by re-running many times I should be able to plot the boundary which I predict must exist imposed by the 2nd Law.

Clearly natural selection in combination with built in repair and redundancy elements of the genetic code are effective in the preservation of DNA in real populations. We only need to look at familiar small mammals - voles, mice & rabbits to tell us that. What the model may show is the relationship between mutation frequency and selection strength to overcome normal adverse statistical events and what degree of evolution if any may occur. What degree, is the very same question tackled by Fred Hoyle in "The Mathematics of Evolution". His analysis is by rigorous analytical math modelling, as opposed to second law limitations as I have done . However he as a convinced evolutionist came to the same conclusion I and many others have. His words..

"When ideas are based on observations, as the Darwinian theory certainly is, it is usual for those ideas to be valid at least within the range of those observations. It is when extrapolations are made outside the range of observations that troubles may arise. So the issue that presented itself was to determine just how far the theory was valid and exactly why beyond a certain point it became invalid."  Introduction p5

Thankful to Dr J for getting involved..

Appendix 5.3 Richard Dawkins Verifies

This is actually by way of answer to Dr J (a keen supporter of Mr Dawkins) on Twitter.. It falls under this heading however as it is still in that sphere of simple probability modelling of supposed evolutionary processes oft referred to by Richard himself.

First the model Richard re-tweeted [tunartphoto.com].. Yes he's a photographer.. Title

Understanding Evolution With A Handful Of Dice

Take a handful of dice throw them.. select all but the 6's throw only them.. repeat.. voila all 6's = evolution..!  Really.. The end state is known and the probability of getting it = 1..!!

I think all this serves to demonstrate is an appalling state of ignorance.. undeserving of one who held the seat of Professor for Public Education in Britain..!

Dr J commented something very similar..

Repeat audience guessing of a coin toss.. kill all that get it wrong (about half) each time replace with 'descendants' = copies of those who got it right.. toss again replace those who got it wrong etc.. and repeat..

So by 2nd audience all are parents or 'descendants' of those who guessed right once..

By 3rd audience all are parents or 'descendants' of those who guessed right twice..

By nth audience all are parents or 'descendants' of those who guessed right n-1 times..

Firstly we must decide what Mr DJ means by 'breed'.. is that like a clone of a person who guessed right implying they have inherited the 'gene' for guessing coin tosses. If so how does this 'gene' work.. are they more likely to guess right.. Well in Dr J's own words "about half" will be eliminated each round.. so NO they do not have any greater chance of guessing the next toss right. Which all means you end up with exactly what you started with after each round.. About half get it right and half get eliminated.. In other words ITS GOING NOWHERE..!

Secondly the implication each successive half that guess right are also those who guessed right previously is clearly incorrect so in the end you cannot say how many any one of that audience guessed right in a row..

Here's A BETTER EXAMPLE.. Evolve a 100 coins into a HTHTHTHT.. pattern.

(The end result is only improbable because of the order not the count of Heads)

Take a population of 10 'genes' of 100 coins.. Toss all for starters..

1 - Score and Kill the 5 groups with least total runs of HTHT.. etc.

2 - Duplicate the top 5 so we have 10 with longest runs of HTHT..etc

3 - Randomly toss 1 or more coins from each gene. [no protected areas]

4 - Go back to 1 and repeat. [Top 5 mutated groups (genes) are retained]

What do you think happens..?

Appendix 5.2 Richard Dawkins Verifies

These derivations go like this.. First you set the problem up in words.. then you translate those into math symbols, work the math to get an answer and then translate it back into words. So here goes..

                (n) 
E =  N .  \               1            =     N .  (2^n  -  1)        =        2N . (2^n  -  1)
               /          2^(m-1)                     2^(n-1)                                   2^n
               m=1

Now for n large enough (number of correct guesses ~ 8 will do) 
(2^n  - 1)  approx ~=   2^n   leaving     E   ~=  2N

Now for n = 8 (RD's example where he noted the audience was about 100)

E (from actual calculation above) = N . (255/128)

From simple probability..  n correct guesses at random will occur once every 2^n tosses if averaged over a very large number of tosses.

Hence the expected value of E is 2^8 = 256 so putting this value in above we get..

N . (255/128)  =  256    Therefore N = 128.502   or    129  (whole people)
This corresponds well with Richard Dawkins estimate at the time. Now look at this table..

n                  N                    2^n = E  
8                 129                  256
10               513                1024
15           16385              32768
20       524289          1048576

So N (rounded up) ~= E/2.. The audience number N determines E (the number of events) which (by my proof) = the required number to pay the entropy debt for the low entropy result (a number of heads guessed in a row)..
The simulation verifies how the entropy debt is paid for by the process.. QED

Appendix 5.1 Richard Dawkins Verifies

This is all about an experiment Richard Dawkins did with an audience of young people to demonstrate improbable events happen all the time and the inclination to see the supernatural is in fact illogical.. Ref: [https://www.youtube.com/watch?v=H1TxH0zf07w]..

So lets see what this same experiment reveals when analysed as to conformance with the second law.. the basis of my falsification.. First I must say I agree the outcome is in no way supernatural.. and you do end up with an apparently remarkable result.. in the case given guessing 8 times in a row the outcome of the toss of a coin. But what does this actually demonstrate..?

Lets take the number of people participating as  = N
the number of correct guesses in a row  =  n

The total number of guess 'events' = N + N/2 + N/4 + ... +N/2^(n-1)  =  (lets call this) E

                (n) 
E =  N .  \                1          {ie N x (sum of the series  1/2^(n-1)  (n) times)}
               /             2^(m-1)
               m=1

Assuming half sit down after each toss of the coin.. because they got it wrong.

Now my falsification is based on the observation that the number of random changes (events or tosses of coin) required on average to get a certain improbable outcome is how the process balances the entropy decrease of that outcome (state) with an entropy increase in the surroundings. Its the entropy cost of the low entropy state which by the second law must be paid by that process.

So now we have the end result being the low entropy state of 8 correct guesses in a row which is equivalent to tossing 8 heads in a row or tossing 8 coins and ending up with 8 heads.

The probability of this outcome = 1/2^8  (or 1/2^n for 'n' correct guesses in a row)

So the question is, what is the audience size N to give enough events to pay the cost..?

Appendix 4.3 Other Laws

5. The Rational Mind
Any theory predicting the random assembly of the human brain (the most orderly state of matter in the known universe) as 'rational', 'logical' and therefore capable of discerning truth and therefore doing 'science'.. must itself be unreliable.. not capable of doing science.

Gödel was a convinced theist.^[22] He rejected the notion of others like his friend Albert Einstein that God was impersonal.
He believed firmly in an afterlife, stating: "Of course this supposes that there are many relationships which today's science and received wisdom haven't any inkling of. But I am convinced of this [the afterlife], independently of any theology." It is "possible today to perceive, by pure reasoning" that it "is entirely consistent with known facts." "If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife]."^[23]
...
[Wikipedia - Kurt Godel]

I think God is an uncomfortable truth for everyone actually.. but in the end truth is what we need and what good science is all about. It cannot be left to a bunch of theophobics to make it up to suit their beliefs. They have brought science into disrepute and most certainly misled society into thinking you can forget about God (and by implication truth)..

Absolutes do exist.. Temperature has one, Entropy has one, Velocity has one.. so it should not surprise you to know that Law and Morality have them (since they are based on the existence of truth). Truth is by definition an absolute which cannot be avoided and only fools try to fight.

Please read 9.1-2 'The Falsification of Evolution'.. if you agree I suggest you also look at "Who is God" at [vh-who.blogspot.com.au]. If you do not understand or accept the falsification case.. leave a comment.

I am sincerely trying to help you..

Thank you..

Appendix 4.2 Other Laws

These points are not so much other laws but where evolutionary thinking fails in its application..

3. The First Star

After the mega blast of energy and mass, many times the size of the universe, the extremely high initial temperature produces a rapidly expanding ball of protons.. (hydrogen nuclei).. After a little more cooling the protons gain a couple of electrons and voilà - a massive ball of hydrogen.. (cosmic sand).

By definition that process becomes an adiabatic expansion of gas. Its adiabatic because there is no 'space' outside it for any of the heat to transfer or radiate into.. it is expanding as fast as the radiation itself. Which all means it begins as a low entropy state.. highly concentrated very hot.. and moves to being a high entropy state.. cool and fairly evenly distributed.

Now density fluctuations are theorised to cause the collapse of one or more regions under the action of their collective gravity to eventually form the first massive stars. But compared to a cool ball of hydrogen in space a massive star is a much lower entropy state.!! Oh No.. not that Second Law again.

So gravity MUST overcome the Second Law.. I don't think so.. I should be able to prove that.. (to come)

4. The Simple can explain the Complex

From a mathematical - logic point of view.. this was proved to be impossible by Kurt Godel in his 1931 Incompleteness Theorems. There is always a 'remainder'. It's equivalent to saying the whole can be explained by examining the parts.. basic reductionism.. Its false.

An aeroplane may comprise 15000 parts.. none of which can fly..

In technological terms.. the whole is more than the sum of the parts.

Godel's theorems give meaning to the word 'design' as a Functional State of Matter.. meaning a design always has an overall purpose.. which can only be the product of a mind.

Think about it..

Appendix 4.1 Other Laws

If the theory of evolution by natural selection violates the Second Law of Thermodynamics it should not be too surprising to find that ideas and theories founded on the same thinking may also be shown to violate other laws of physics. The scope of influence of evolutionary thinking cannot be underestimated as to its effects on almost every aspect of science and education from medicine to economics.. so what if its wrong!!

1. The Law of Biogenesis Louis Pasteur circa 1860
Inorganic chemistry.. molecules are supposed to have 'competed' for fitness, resulting in greater size and complexity in the primordial soup on an ancient earth cooling down from its assumed hot beginning. All leading to a self replicating RNA or DNA molecule or a proto-protein capable of replication. That's the essence of 'abiogenesis', however.

Last night on the BBC Story of Science Power, Proof and Passion program 23rd Aug 2013, Michael J Mosley made a watershed admission.. DNA can only exist within a cell, complete with all its complex systems that maintain it and make it work. The observation was simply put "living cells come from living cells".. and he concluded life started.. complex not simple.

Biogenesis is back on the podium.. (Omni vitum ex vita).

2. The First Law - the baryon number problem
After Einstein we knew mass was a concentrated form of energy and it could be converted directly into energy as confirmed by the atomic bomb. Conversely energy can be 'concentrated' to form mass. However.. the law of conservation dictates that whenever this happens you always get an equal number of anti-matter particles and matter particles (baryons - matter particles).

So the postulate of a big bang creating matter from energy means you not only get a universe.. but also an anti-universe!! Which means they should both annihilate one another and return to energy.! So it is postulated this universe is just the 'ashes' left over from a very much bigger bang than anyone can imagine.. meaning the universe is just the tiny 'error'.

Laws would breakdown at a big bang singularity.. however the energy -> mass conversion occurs after the singularity. The assumption of a baryon number error the size of this universe has to qualify as a violation of the 1st law.

There's more.

Appendix 3.3 Evolutionary Predictions

Last but not least is..

(3) Computer Simulation

From Darwin 1857 to about 1990 it was not possible to do really big model simulation and the only method was complex algebra and later calculus to find analytic solutions (formula with general applicability). But many problems have no analytic solution.

In the 1990's massively parallel computers became available allowing for simulation of such things as the weather.. and the solution of very large structural problems..  (economics is apparently still out of reach :*()

Surely evolution... bunch of replicating things.. subject to occasional random change.. in an environment with a few enemies, a few different foods, a few ecological niches etc. let it run and see what survives.. a lot easier than the weather I would imagine. Checking the Wiki..(Evolutionary Algorithm)

"Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes. The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics." (complete with spelling error.. mutation.. hmm)

Hint.. "macroevolution" means create new information.. "attempt" means NO its not been done..

In 'Climbing Mount Improbable' Richard Dawkins promised this prediction would be fulfilled within ten years.. that was 1996. From my falsification I can confidently say it will never be done.. because macro-evolution implies a violation of the Second Law for any DNA coding protein type life on any Earth like planet.

The humble honey bee routinely does problems we need a supercomputer to solve?

A little humility is probably in order for us..

Appendix 3.2 Evolutionary Predictions

(2) Systematic Taxonomy

The evolutionary algorithm is a theory of limitless and constant change.. long periods of 'stasis' are cited for such creatures as crocodiles simply because their fossils cover a theoretical 200 million years.. However other fossil deposits demand very 'rapid' evolutionary change. The problem is the science is vague and accords more with convenient storytelling.

Human beings are described as having opted out of evolution.. But it was not so long ago black indigenous native people were considered less than human, primitive savages in evolutionary terms. Certainly Charles Darwin expressed this opinion and thought they would eventually die out.


The question is how does a system of continuous change produce a living kingdom which conforms to an enduring classification system of distinct types with identifiable groupings. The original idea actually came from the bible.. by a creationist (like all theists of his day) and it is still with us! Carl Linnaeus was the first to create the binomial naming system of classification.. its changed but his classification of large animals remains essentially unchanged.

Species is an inadequate term to talk about immutability but at the higher family level it accords rather well with the bible's use of the word 'kind'. Creatures reproduce after their kind and the flesh of one kind is different to the flesh of another kind.. accords well with observation and the Law of Biogenesis..

"Pasteur demonstrated that fermentation is caused by the growth of micro-organisms, and the emergent growth of bacteria in nutrient broths is due not to spontaneous generation, but rather to biogenesis (Omne vivum ex vivo "all life from life")." [from Wikipedia article Louis Pasteur]

must move on..