Does Common Descent Follow Logically From Darwin's Four Postulates?

Eugene Shubert said:
No. For mathematicians, probability theory has a precise set-theoretic formulation.
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In science, a probability of measure zero means impossible.
And the assumption that an evolutionary change of X -> Y has the same probability as Y -> X is ridiculous.
Eugene Shubert said:
For those not so frightened of learning something, the title Sanford's Genomic Degeneration Theorem is a link.
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That theorem is in conflict with the findings of research and observation.
 
iceaura said:
In science, a probability of measure zero means impossible.
And the assumption that an evolutionary change of X -> Y has the same probability as Y -> X is ridiculous.
That theorem is in conflict with the findings of research and observation.
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Find some mathematicians you trust and ask them.
 
iceaura said:
And the assumption that an evolutionary change of X -> Y has the same probability as Y -> X is ridiculous.
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X --> Y has same probability Y --> X

Pregnancy --> Birth

Birth --> ???

I don't think so

I'm with you iceaura

:)
 
Axiom 3: "The DNA copying process is imperfect; there are random, frequently occurring single-character misspellings, deletions, insertions, duplications, translocations and inversions."

Consequently, what is the probability for each specific error and what is the probability for each error to be undone? All I know is that if a transposition takes place with probability p, then the reverse transposition to fix that error also has a probability of p of happening.
 
Eugene Shubert said:
Find some mathematicians you trust and ask them.
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Like I said - all you need is a high school intro text in "Probability and Statistics". It will have a picture of a Galton Machine, for you to ponder. I linked one for you, on Wiki.

In more advanced classes, the 2nd Law of Thermodynamics is introduced - if you need something fancier than marbles in boxes.
Eugene Shubert said:
Consequently, what is the probability for each specific error and what is the probability for each error to be undone? All I know is that if a transposition takes place with probability p, then the reverse transposition to fix that error also has a probability of p of happening.
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That's not the case, in physical reality, for evolutionary processes.

We're not talking math, we're talking science. Physical reality. If your math model doesn't fit the facts, you discard it or change it.
 
Eugene Shubert said:
Axiom 3: "The DNA copying process is imperfect; there are random, frequently occurring single-character misspellings, deletions, insertions, duplications, translocations and inversions."

Consequently, what is the probability for each specific error and what is the probability for each error to be undone? All I know is that if a transposition takes place with probability p, then the reverse transposition to fix that error also has a probability of p of happening.
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Likewise, if an inversion takes place with probability q, then the probability to invert that inversion is also of probability q.
 
Eugene Shubert said:
Consequently, what is the probability for each specific error and what is the probability for each error to be undone? All I know is that if a transposition takes place with probability p, then the reverse transposition to fix that error also has a probability of p of happening.
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The probability of any particular transposition taking place is UNKNOWN and UNKNOWABLE

Hence the reverse of any particular transposition taking place is DOUBLE UNKNOWN and UNKNOWABLE

There MIGHT, only JUST might be a extremely high number just short of INFINITY but because of UNKNOWN imponderables is beyond calculation

If anybody out there has a formula or calculation method I would be happy to hear about it

I'll go with 1 in INFINITY

:)
 
Eugene Shubert said:
Likewise, if an inversion takes place with probability q, then the probability to invert that inversion is also of probability q.
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That's not true of evolutionary processes in physical reality. Your model is in conflict with research findings and observation. Change your model, or discard it.
Eugene Shubert said:
A Galton Machine has nothing to do with mutations.
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That's not true either - the basics of probability are best illustrated with simple models like that, and models of mutation frequency etc incorporate probabilities.
 
Michael 345 said:
The probability of any particular transposition taking place is UNKNOWN and UNKNOWABLE
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Given a string of n distinct characters, then the number of possible transpositions is exactly n(n-1)/2.

For example, AB is a string of two distinct characters. So n=2. Put that in the formula and you get 2(2-1)/2 =1. That's right, isn't it?
There is only 1 possible transposition for the string AB, which is BA.

Again, ABC is a string of three distinct characters. So n=3. Put that in the formula and you get 3(3-1)/2 =3. I'm right again.

So from ABC there are only 3 possible transpositions:

BAC
ACB
CBA

Here's a homework assignment for you. Check my formula for 4 distinct characters by listing all the possible transpositions to ABCD. There should be 4(4-1)/2 = 6 of them.
 
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Eugene Shubert said:
Axiom 3: "The DNA copying process is imperfect; there are random, frequently occurring single-character misspellings, deletions, insertions, duplications, translocations and inversions."

Consequently, what is the probability for each specific error and what is the probability for each error to be undone? All I know is that if a transposition takes place with probability p, then the reverse transposition to fix that error also has a probability of p of happening.
Click to expand...
In general, DNA polymerases are highly accurate, with an intrinsic error rate of less than one mistake for every 107 nucleotides added.[7] In addition, some DNA polymerases also have proofreading ability; they can remove nucleotides from the end of a growing strand in order to correct mismatched bases. Finally, post-replication mismatch repair mechanisms monitor the DNA for errors, being capable of distinguishing mismatches in the newly synthesized DNA strand from the original strand sequence. Together, these three discrimination steps enable replication fidelity of less than one mistake for every 109 nucleotides added.[7] (wikipedia)
 
iceaura said:
That's not true of evolutionary processes in physical reality. Your model is in conflict with research findings and observation.
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Toy models are just the playthings of mathematicians. Again, start with a string of n distinct characters and derive the formula for the number of possible inversions. Assign the same probability for each inversion. Do the math.
 
Eugene Shubert said:
Toy models are just the playthings of mathematicians. Again, start with a string of n distinct characters and derive the formula for the number of possible inversions. Assign the same probability for each inversion. Do the math.
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Is that real math or creationist math?
 
spidergoat said:
In general, DNA polymerases are highly accurate, with an intrinsic error rate of less than one mistake for every 107 nucleotides added.[7] In addition, some DNA polymerases also have proofreading ability; they can remove nucleotides from the end of a growing strand in order to correct mismatched bases. Finally, post-replication mismatch repair mechanisms monitor the DNA for errors, being capable of distinguishing mismatches in the newly synthesized DNA strand from the original strand sequence. Together, these three discrimination steps enable replication fidelity of less than one mistake for every 109 nucleotides added.[7] (wikipedia)
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Thank you for getting this show back on the road with some proper science, rather than puerile arguments based on a 5th former's grasp of probability.
 
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