If the evolutionary algorithm as simple and elegant as it sounds actually violates the Second Law and is therefore impossible.. there should be some significant contrary observations linked to this seemingly incredible assertion.
All scientific theories embody foundational assumptions which must be independently verifiable. For evolution there are at least three.
(1) - Mathematical Assumption
Evolutionary changes which are mathematically impossible in a single mutation event are claimed to be made possible by a large number of only slightly improbable mutation events. (R Dawkins "crane" in Climbing Mount Improbable)
This assumption relies on the true observation that Natural Selection will preserve or 'quarantine' a population from the steady occurrence of damaging mutations. The group need only wait until a beneficial one comes along.. which when it does appear spreads through the population simply because their prodigy are more successful. Then all you have to do is wait for the next one.. and voilà evolution. It could be true.. except for..
(a) Entropy being a state variable.. like any improbability (low entropy state) it is irrelevant how you got there the improbability is the same. For 100 heads it makes no difference if you toss 100 coins at once or one coin 100 times. Mount improbable is just as forbidding.
(b) Codes of DNA put a finite limit on 'small' they are not infinitesimal.. (its a real process not quasi-static as R Dawkins erroneously claims "take any change as small as you like" - Climbing Mount Improbable).
Note natural selection is a SELECTION process for what random mutations have ALREADY PRODUCED.. so logically cannot influence those mutations.
So if the evolutionary process assumes (as I did) every atom of the universe for every millisecond in 14 billion years is applied to a single protein molecule and still it falls massively short .. ie predicts you cannot get enough beneficial changes (correct DNA to make the protein).. the protein remains impossible.
moving on..
Friday, August 16, 2013
Wednesday, August 14, 2013
Appendix 1.5 Entropy
I could not find the Boltzmann Gibbs equation for absolute entropy applied to DNA like this anywhere. It challenges the naturalistic assumption that semantic information can evolve from a chance combination of mass and energy.. by definition DNA is a low entropy state.. which must be paid for..
The Second Law condition for the random assembly of a string of semantic information of length p from an alphabet of m possible codes is..
n = m^p random trials.
(eg to throw a double [6] with 2 dice n = 6^2 = 36 throws or
for a string of 10 bases of DNA n = 4^10 = 1048576 random mutations)
It is the average occurrence of a specific sequence in an infinite number of random trials that determines the minimum number of trials (entropy cost) to meet the second law requirement, entropy must increase.
The probability of getting at least one occurrence of a specific string of length p codes from an alphabet of m possibilities in n = m^p random trials is..
Pr(at least one) = 1 - Pr(not getting any) = 1 - [(n-1) /n]^n
So for at least one (two heads) from n = 4 throws of a coin..
Pr(at least one 2xhead) = 1 - [(4 - 1) / 4]^4 = 0.6836
For at least one [double 6] from 2 dice in n = 6^6 = 36 throws..
Pr(at least one) = 1 - (35/36)^36 = 0.6372
For at least one 10 base DNA string from 1048576 random mutations..
Pr(at least one) = 1 - (1048575)/1048576]^1048576 = 0.6321
Note the probability of at least one occurrence as n gets large asymptotes toward a certain LIMITING value.. So what is it?
the limit of [1 - [ (n-1) / n ] ^ n] = 1 - 1/e approx = 0.6321
for n -> infinity
Its my number so.. The 'Bellamy limit' = 1 - 1/e is the lowest probability demanded by the Second Law for a randomly assembled string of semantic information length p from m codes in n = m^p tries to make it PROBABLE ENOUGH NOT to violate that law (for large n say > 50).
(Jan 2015: I now believe it applies to all logical states ie.. microstates)
The Second Law condition for the random assembly of a string of semantic information of length p from an alphabet of m possible codes is..
n = m^p random trials.
(eg to throw a double [6] with 2 dice n = 6^2 = 36 throws or
for a string of 10 bases of DNA n = 4^10 = 1048576 random mutations)
It is the average occurrence of a specific sequence in an infinite number of random trials that determines the minimum number of trials (entropy cost) to meet the second law requirement, entropy must increase.
The probability of getting at least one occurrence of a specific string of length p codes from an alphabet of m possibilities in n = m^p random trials is..
Pr(at least one) = 1 - Pr(not getting any) = 1 - [(n-1) /n]^n
So for at least one (two heads) from n = 4 throws of a coin..
Pr(at least one 2xhead) = 1 - [(4 - 1) / 4]^4 = 0.6836
For at least one [double 6] from 2 dice in n = 6^6 = 36 throws..
Pr(at least one) = 1 - (35/36)^36 = 0.6372
For at least one 10 base DNA string from 1048576 random mutations..
Pr(at least one) = 1 - (1048575)/1048576]^1048576 = 0.6321
Note the probability of at least one occurrence as n gets large asymptotes toward a certain LIMITING value.. So what is it?
the limit of [1 - [ (n-1) / n ] ^ n] = 1 - 1/e approx = 0.6321
for n -> infinity
Its my number so.. The 'Bellamy limit' = 1 - 1/e is the lowest probability demanded by the Second Law for a randomly assembled string of semantic information length p from m codes in n = m^p tries to make it PROBABLE ENOUGH NOT to violate that law (for large n say > 50).
(Jan 2015: I now believe it applies to all logical states ie.. microstates)
Sunday, August 11, 2013
Appendix 1.4 Entropy
Now..
MASS + ENERGY = INFORMATION
is the EQUATION of LIFE..
It's the basis of the assumption that life will evolve on Earth like planets.. so
ROCK + LIQUID WATER + HEAT = DNA
MUST be true for life to evolve.. To fail to question this assumption is to fail to do science.
2. Entropy is an EXTRINSIC property.. meaning its value depends on factors which are not inherent to the mass of the system.
Weight is an extrinsic property of mass because its value depends upon the strength of the gravitational acceleration where it is being measured.
The absolute entropy of any system depends upon only ONE thing.. 'W' the thermodynamic probability of the system. It is the number of micro-states in that macro-state.. Given all micro-states are equally likely a system (of particles) will tend to move to a macro-state with more micro-states and so entropy increases.
The absolute entropy of the dice is a combination of both the PHYSICAL state and the LOGICAL state (ie double 3). The Clausius equation for entropy change can account for the physical state during the process of manufacture but only the Boltzmann equation can account for the logical state which is extrinsic because it is not dependent on the mass of the dice.
The important thing to understand about the Second Law is systems left to themselves will tend to move to a more probable state. All we need is a probability calculation to determine the STRENGTH of that tendency. For a large system it is not sufficient for it just to be POSSIBLE, it must be PROBABLE..
For DNA (large book, even for bacteria) the total number of possible arrangements is what determines its absolute entropy and the possibility of that state arising from random mutations (mass + energy).
So does the Second Law define a boundary between possible and probable?
one more on this..
MASS + ENERGY = INFORMATION
is the EQUATION of LIFE..
It's the basis of the assumption that life will evolve on Earth like planets.. so
ROCK + LIQUID WATER + HEAT = DNA
MUST be true for life to evolve.. To fail to question this assumption is to fail to do science.
2. Entropy is an EXTRINSIC property.. meaning its value depends on factors which are not inherent to the mass of the system.
Weight is an extrinsic property of mass because its value depends upon the strength of the gravitational acceleration where it is being measured.
The absolute entropy of any system depends upon only ONE thing.. 'W' the thermodynamic probability of the system. It is the number of micro-states in that macro-state.. Given all micro-states are equally likely a system (of particles) will tend to move to a macro-state with more micro-states and so entropy increases.
The absolute entropy of the dice is a combination of both the PHYSICAL state and the LOGICAL state (ie double 3). The Clausius equation for entropy change can account for the physical state during the process of manufacture but only the Boltzmann equation can account for the logical state which is extrinsic because it is not dependent on the mass of the dice.
The important thing to understand about the Second Law is systems left to themselves will tend to move to a more probable state. All we need is a probability calculation to determine the STRENGTH of that tendency. For a large system it is not sufficient for it just to be POSSIBLE, it must be PROBABLE..
For DNA (large book, even for bacteria) the total number of possible arrangements is what determines its absolute entropy and the possibility of that state arising from random mutations (mass + energy).
So does the Second Law define a boundary between possible and probable?
one more on this..
Appendix 1.3 Entropy
The fact that entropy is a STATE variable (does not care about the process that got the system to where it is) does not mean the process can violate the Second Law..
Consider two pairs of dice.. first a pair of plastic dice on the kitchen table, second a pair of 1 metre square steel cubes at the bottom of a 10 metre high sand dune..
Now both exist.. so their physical form (low absolute entropy state of matter) has been accounted for by a larger increase in the entropy of the surroundings by their manufacturing processes and obeys Second Law..
Now throw both pairs 9972 times.. Their is a crane and dump truck at the bottom of the sand dune..
Counting the number of [3].[3].. We know it will be 277, average once every 36 times for both. But the absolute entropy for the LOGICAL state of [3].[3] is the SAME for both (actually zero because there is only one way to get it). However the heat energy and consequential entropy increase in the surroundings is massively bigger for one than the other..
This not only shows why the absolute entropy of a system must be independent of the process that got it there BUT also the absolute entropy of any LOGICAL state such as semantic information is independent of the mass of the system.. Demonstrating semantic information is a separate and distinctly different entity to mass or energy.. and cannot be a product of them..
MAS + ENERGY # INFORMATION (live DNA)
more to come..
Consider two pairs of dice.. first a pair of plastic dice on the kitchen table, second a pair of 1 metre square steel cubes at the bottom of a 10 metre high sand dune..
Now both exist.. so their physical form (low absolute entropy state of matter) has been accounted for by a larger increase in the entropy of the surroundings by their manufacturing processes and obeys Second Law..
Now throw both pairs 9972 times.. Their is a crane and dump truck at the bottom of the sand dune..
Counting the number of [3].[3].. We know it will be 277, average once every 36 times for both. But the absolute entropy for the LOGICAL state of [3].[3] is the SAME for both (actually zero because there is only one way to get it). However the heat energy and consequential entropy increase in the surroundings is massively bigger for one than the other..
This not only shows why the absolute entropy of a system must be independent of the process that got it there BUT also the absolute entropy of any LOGICAL state such as semantic information is independent of the mass of the system.. Demonstrating semantic information is a separate and distinctly different entity to mass or energy.. and cannot be a product of them..
MAS + ENERGY # INFORMATION (live DNA)
more to come..
Appendix 1.2 Entropy
Now we need to get some fundamentals sorted out.. particularly concerning the two equations used for calculating entropy which have been all mixed up thanks to the very distorted article in the Wikipedia. I tried to fix it.. I really did but the self proclaimed 'moderator'.. used his knowledge of physics to put up a smoke screen of techno-bable to fend me off... all I can say is.. I'LL BE BACK.!
1. Entropy is a STATE variable meaning its absolute value is independent of the path by which it got there.. we know this from the Boltzmann Gibbs equation for absolute entropy which reveals it is directly (not linearly) and exclusively based on the probability of that particular state existing.
The Rudolf Clausius 'heat' equation is the integral sum (meaning by infinitesimally small amounts added up) of heat crossing a system boundary divided by the temperature at that point and moment on the boundary. It calculates the CHANGE in entropy of the system inside the boundary for a given quantity of heat transferred. Heat IN is positive increasing entropy, heart OUT is negative decreases entropy. Not only does this not say anything about the absolute entropy of the system but it totally misses logical states like semantic information such as a book or molecule of DNA.
The problem with absolute entropy is the calculation of the thermodynamic probability term "W". It requires the IDENTIFICATION of every particle or logical place holder in the system and the calculation for each state called a macro-state {set of energy states or logical sequences} the entire count of all possible combinations when every particle is swapped with every other particle in the system.. which is mind bogglingly big for any more than a few particles.
Engineers are mostly interested in the change of entropy during a process anyway so Clausius is the big winner here. His equation came in about 1865 just in time for the industrial revolution and steam power where it was needed most.
more to come
1. Entropy is a STATE variable meaning its absolute value is independent of the path by which it got there.. we know this from the Boltzmann Gibbs equation for absolute entropy which reveals it is directly (not linearly) and exclusively based on the probability of that particular state existing.
The Rudolf Clausius 'heat' equation is the integral sum (meaning by infinitesimally small amounts added up) of heat crossing a system boundary divided by the temperature at that point and moment on the boundary. It calculates the CHANGE in entropy of the system inside the boundary for a given quantity of heat transferred. Heat IN is positive increasing entropy, heart OUT is negative decreases entropy. Not only does this not say anything about the absolute entropy of the system but it totally misses logical states like semantic information such as a book or molecule of DNA.
The problem with absolute entropy is the calculation of the thermodynamic probability term "W". It requires the IDENTIFICATION of every particle or logical place holder in the system and the calculation for each state called a macro-state {set of energy states or logical sequences} the entire count of all possible combinations when every particle is swapped with every other particle in the system.. which is mind bogglingly big for any more than a few particles.
Engineers are mostly interested in the change of entropy during a process anyway so Clausius is the big winner here. His equation came in about 1865 just in time for the industrial revolution and steam power where it was needed most.
more to come
Sunday, August 4, 2013
Appendix 1.1 Entropy
I visited the London Science Museum a few years ago and saw they had an entire floor devoted to 'ENERGY', so I asked "Where's the floor devoted to 'ENTROPY'.. a sort of stunned silence followed by "What's entropy?".
Guess what.. There is a reason why nobody seems to know or care what 'entropy' is or means.. it is an embarrassment to the naturalists.. who control the agenda of modern science.
I need a new blog.. "What's Missing from Science".. later
ENTROPY.. according to the Cambridge Encyclopedia
"A quantitative measure of disorder" not bad.. but it would help if they defined 'disorder'.. Is it what you would naturally think of? Like 'a mess on the desk'.. well almost.
But there is a proviso.. Disorder in the thermodynamic context means not just jumbled up but uniformly jumbled up.. So the papers in neat piles by subject and in date order would correspond to the minimum entropy state for that system. Still in 'piles' but not in date order.. higher entropy.. all piled up on one side of the desk still higher entropy and evenly spread over the desk in random fashion would be the highest entropy state. Note both PHYSICAL and LOGICAL order affects the value of the absolute entropy of a system.
Because semantic information is always stored in physical matter (even an idea in your head is a circuit in physical neurons) it is also subject to the Law of Increasing Entropy.. or increasing disorder.
When energy finally ends up as heat, (or radiation), it spreads out evenly moving from higher concentration (hot) to lower concentration (cool).. driven by the most powerful axiom of probability.. a disordered state is a more probable state because there are far more of them than ordered states.
Think of a working motorcycle of 5000 parts.. How many ways could those parts be connected together.. and for how many would it still work?
next time
Guess what.. There is a reason why nobody seems to know or care what 'entropy' is or means.. it is an embarrassment to the naturalists.. who control the agenda of modern science.
I need a new blog.. "What's Missing from Science".. later
ENTROPY.. according to the Cambridge Encyclopedia
"A quantitative measure of disorder" not bad.. but it would help if they defined 'disorder'.. Is it what you would naturally think of? Like 'a mess on the desk'.. well almost.
But there is a proviso.. Disorder in the thermodynamic context means not just jumbled up but uniformly jumbled up.. So the papers in neat piles by subject and in date order would correspond to the minimum entropy state for that system. Still in 'piles' but not in date order.. higher entropy.. all piled up on one side of the desk still higher entropy and evenly spread over the desk in random fashion would be the highest entropy state. Note both PHYSICAL and LOGICAL order affects the value of the absolute entropy of a system.
Because semantic information is always stored in physical matter (even an idea in your head is a circuit in physical neurons) it is also subject to the Law of Increasing Entropy.. or increasing disorder.
When energy finally ends up as heat, (or radiation), it spreads out evenly moving from higher concentration (hot) to lower concentration (cool).. driven by the most powerful axiom of probability.. a disordered state is a more probable state because there are far more of them than ordered states.
Think of a working motorcycle of 5000 parts.. How many ways could those parts be connected together.. and for how many would it still work?
next time
Tuesday, April 12, 2011
9.2 CAN EVOLUTION BE FALSIFICATION
6. Semantic information is a non repeating, non random, ordered set and as such for any given length it is a macrostate with only one microstate or the least likely of any arrangement. DNA is semantic information and in relation to the specification of protein represents a decrease in Boltzmann entropy by virtue of its improbability. The size of the entropy drop is not important, it is the second law requirement for that process to balance the entropy books.
7. Myoglobin was the first protein sequenced and has 153 (or 154) amino acids each coded by a 3 DNA based codon. The effective improbability of a codon is 162 counting chirality (handedness) and redundancy of codons. By the second law the evolutionary system that got it to that state must also pay for it which means the capacity for the execution of 153^162 = 10^338 random changes or mutations if selection and reproduction do not affect the improbability(1).
8. Since the total event capacity of the universe is 10^100 atom milliseconds this would clearly be insufficient to cover the entropy debt for the myoglobin protein molecule. In truth the opportunities for mutation events capable of evolving such a state of matter as myoglobin are limited to the surface of planets like earth. To falsify the theory of evolution it is necessary to show the evolutionary process cannot pay the entropy debt for proteins like myoglobin.
9. The entropy argument is saying that the number of possibilities (improbability) is by far too big for random mutations to string together the required series of complimentary beneficial changes. Lets look at another quote from the Wikipedia regarding what they call the Fitness Function concerning trying to 'evolve' an optimum truck delivery rout.
“Evolutionary optimization techniques are particularly useful in situations in which it is easy to determine the quality of a single solution, but hard to go through all possible solutions one by one (it is easy to determine the driving time for a particular route of the delivery truck, but it is almost impossible to check all possible routes once the number of destinations grows to more than a handful).”
(1) After correction (Feb 2016) the simple model I proposed in Dec 2015 has demonstrated that selection and replication reduce the improbability. [see Dr J verifies]
I do hope you have a nice day..
Mike Bellamy BE (Aero) UNSW 1972
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