Random Mutations

[Micaiah]

I've noticed in recent threads some TE's are claiming that the variation that is supposed to occur in evolution is the result of random mutation to some extent guided by God.

TE's, please advise:

1. Is this your view?

2. Define random.

3. Provide references to support your ideas, or is this a home grown theory?

 

[notto]

Not my view. That is more of the intelligent design view. God tinkering with specific mutations and DNA of certain generations is what is proposed by ID pseudoscience.

 

[Rusticus]

I've noticed in recent threads some TE's are claiming that the variation that is supposed to occur in evolution is the result of random mutation to some extent guided by God.

Not my view either. Sounds like pseudo-scientific claptrap. Fee, Fi, Fo Fum: Do I smell the blood of a ... Straw-Man???

 

[random_guy]

Not my view, either.

As for random, it's a way of guessing what the outcome will be due to lack of information. Of course, this definition needs to be modified for Quantum Mechanics.

For example, rolling a dice, there's a 1/6 chance of it being 1, in the absense of any information, but if we knew the precise angle, velocity, coefficient of friction, etc..., we'd realize the process isn't very random, but has a determined outcome (again, in classical physics).

 

[Micaiah]

Random is a statistical term that indicates all outcomes of an event have an equal probability of occuring.

The probability of an event occuring = Number of outcomes / Number of possible outcomes.

In the case of a dice, the probability of throwing a given number is 1/6. The more times you roll a dice, the closer the experimental results will approximate the theoretical results.

When it comes to evolution, if you had an insertion sequence (IS) that was entirely random, it would mean the IS would have an equal chance of being inserted any where in the DNA. Unfortunately random insertions of this nature usually has disasterous results for the host. Similarly, a point mutation would be something that could occur anywhere in the DNA. In this case a single nucleotide changes. It is much easier to conceive that this could happen without adverse consequences to the host. That is why NDT assumes variation is the result of point mutations in gametes.

 

[gluadys]

Random is a statistical term that indicates all outcomes of an event have an equal probability of occuring.

Are you sure about that? Might it not be a known probability of occurring?

I am thinking here of Mendelian inheritance. If two F1 individuals are heterozygous for a character trait, the probability is 0.5 that any one offspring will also be heterozygous, but 0.25 that it will be homozygous for either the dominant or recessive form of the character trait.

So the probabilities are not equal, but they are still random, right?

 

[ebia]

Random is a statistical term that indicates all outcomes of an event have an equal probability of occuring.

Wrong.

 

[Micaiah]

Are you sure about that? Might it not be a known probability of occurring?

I am thinking here of Mendelian inheritance. If two F1 individuals are heterozygous for a character trait, the probability is 0.5 that any one offspring will also be heterozygous, but 0.25 that it will be homozygous for either the dominant or recessive form of the character trait.

So the probabilities are not equal, but they are still random, right?

Since all possible outcomes are do not have the same probability of occuring it is not random.

 

[random_guy]

Since all possible outcomes are do not have the same probability of occuring it is not random.

Definitely false. Have you studied random variables? Suppose I want to study X, where X is the number of tails I flip before a heads occur. X is a random variable taking on values from 0,1,..infinity. However, all values do not have equal probability.

FYI, for fun, can anyone give the probability for P(X)=x (probability it takes x flips before a heads occurs)?

 

[ebia]

Since all possible outcomes are do not have the same probability of occuring it is not random.

Can you provide a source for this assertion from a serious work on probability theory? Unfortunately I didn't keep my texts or notes from University on probability, but from what I remember of it, you'll be lucky to find a sound mathematical definition of random that is understandable without some University level maths, let alone amounts to what you claim.

 

[ebia]

FYI, for fun, can anyone give the probability for P(X)=x (probability it takes x flips before a heads occurs)?

eh?

I don't think you wrote what you meant to write.
Since x has to be a positive integer, and P(x) is a real number between 0 and 1 inclusive, the only overlap is the value 1, but when x is 1, P(x) does not equal 1.
So there is no x such that P(x) = x

 

[random_guy]

eh?

I don't think you wrote what you meant to write.
Since x has to be a positive integer, and P(x) is a real number between 0 and 1 inclusive, the only overlap is the value 1, but when x is 1, P(x) does not equal 1.
So there is no x such that P(x) = x

Whoops, you're right. It should read P(X=x) = ?. It's been a while since I've done probability.

 

[Micaiah]

Definitely false. Have you studied random variables? Suppose I want to study X, where X is the number of tails I flip before a heads occur. X is a random variable taking on values from 0,1,..infinity. However, all values do not have equal probability

Tossing a coin is a good example of a random event. All outcomes have equal probability of occuring which is why we often toss a coin to settle a dispute. Notice that the sum of all outcomes sum to one so that in the case of an event with two possible outcomes, each must have a probability of 0.5. This is basic high school mathematics which I once taught.

Question: If you toss a coin once and then toss it again and consider this one outcome, how many outcomes are possible and are outcomes random?

I wonder if you are getting mixed up with random numbers. The random number generator of say an Excel spreadsheet is called such because all numbers generated in a range have an equal probabiliity of occuring. The probability distribution curve is a horizontal line. Again if you integrate the area under the curve it sums to one.

The other thing that may be causing confusion is the way we use the term in everyday language where the meaning roughly equates to the idea that an event is random if you cannot predict the outcome. That is okay, but when using the term in a mathematical context, it is not adequate. If you look in a good dictionary, you will find both definitions provided.

As stated above this idea of randomness is important in current evolutionary theory. It is asserted that the variation theorised by Darwin is the result of random genetic mutations which by definition all have equal probability of occuring. To claim that God somehow then itervened so that the probability distribution became anything other than a straight line over the range of all possible outcomes is contrary to what most scientists currently believe.

My understanding of TE's is that they accept the general consensus of scientists when it comes to evolution as the most authoritative souce of information on such matters. To be consistent they should then accept the general scientific consensus. As we learn more about the genome the idea that it all resulted from random variation and natural selection is becoming increasingly absurd which is obviously why some TE's feel the need for God's intervention.

Of course if you believe the historical account of origins given in Genesis, it is obvious that this fantastic piece of anatomy is the product of a Creator. Intuitively that is what you conclude.

 

[ebia]

Tossing a coin is a good example of a random event. All outcomes have equal probability of occuring which is why we often toss a coin to settle a dispute. Notice that the sum of all outcomes sum to one so that in the case of an event with two possible outcomes, each must have a probability of 0.5. This is basic high school mathematics which I once taught.

"Basic Highschool Maths" is frequently wrong, especially around limits, set theory, concepts of infinity, and probability theory (which is a much more involved subject than you can possibly convey at high school).

So, I ask again, can you give a proper mathematical definition of random, with citation? Unless you can, you are not on solid ground.

 

[Micaiah]

FYI, for fun, can anyone give the probability for P(X)=x (probability it takes x flips before a heads occurs)?

If I toss a dice and make the outcome all integer numbers between one and six inclusive, the probability of this occuring is one. In that case the probability that an event will occur is the same as the number of throws it will takes to get the event which is 1. It cannot happen when tossing a coin as someone noted above.

Unless you are talking about probability distributions, when doing probability problems X in P(X) is usually a specification of the outcome you are seeking.

eg. P(red ball) is say the probability of choosing a red ball from a bag containing 2 green balls and 5 red balls.

P(X)=x is a hybrid of probabiltiy and functional notation. This is further confused by the post that changes it to P(x)=x which implies functional notation and has different definitions of x on either side of the equations which of course is not allowed.

This does highlight one of the fundamental problems with using mathematics in discussions such as these. It can look and sound impressive to the uninitiated but can be fundamentally wrong. You would have been better to stay with a simple verbal description of what you were trying to say.

This is one of the reasons I am reluctant to post a mathematical procedure for defining information gain. We have trouble understanding simple probability. Debating the mathematics defining information gain would in my estinmation be a farce for most people, including myself, on this forum .

 

[ebia]

This does highlight one of the fundamental problems with using mathematics in discussions such as these. It can look and sound impressive to the uninitiated but can be fundamentally wrong. You would have been better to stay with a simple verbal description of what you were trying to say.

The trouble is, you are just as likely (probably more) to get things wrong, it's just harder to see and show when that is the case.

This is one of the reasons I am reluctant to post a mathematical procedure for defining information gain. We have trouble understanding simple probability. Debating the mathematics defining information gain would in my estinmation be a farce for most people, including myself, on this forum .

Looks rather like "I'd rather stick to waffle, because science and maths will show up my errors".

 

[gluadys]

Tossing a coin is a good example of a random event. All outcomes have equal probability of occuring which is why we often toss a coin to settle a dispute. Notice that the sum of all outcomes sum to one so that in the case of an event with two possible outcomes, each must have a probability of 0.5. This is basic high school mathematics which I once taught.

I am not up on probabilities, and can't follow more than the simplest math. But I think you are confusing the fact that all probable outcomes must sum to one, with the notion of equal outcomes. The two do not necessarily correlate. If of two possible outcomes, one occurs in 1 out of 5 cases and the other in 4 out of five cases, their respective probabilities (0.2 + 0.8) do sum up to one. Why would this be any less random than a distribution of (0.5 + 0.5)?

In respect to biology and evolution, have you checked out the probability equations in the Hardy-Weinburg equilibrium

This includes both non-equal but random probabilities, and also how to calculate the way selection affects the probabilities in a non-random manner.

Question: If you toss a coin once and then toss it again and consider this one outcome, how many outcomes are possible and are outcomes random?

Of course the outcomes are random. But they are not equal. There are three possible outcomes: both heads, both tails or one of each. And the last will probably occur twice as often as either of the others.

As stated above this idea of randomness is important in current evolutionary theory. It is asserted that the variation theorised by Darwin is the result of random genetic mutations which by definition all have equal probability of occuring. To claim that God somehow then itervened so that the probability distribution became anything other than a straight line over the range of all possible outcomes is contrary to what most scientists currently believe.

I don't think that is what is being claimed.

My understanding of TE's is that they accept the general consensus of scientists when it comes to evolution as the most authoritative souce of information on such matters. To be consistent they should then accept the general scientific consensus. As we learn more about the genome the idea that it all resulted from random variation and natural selection is becoming increasingly absurd which is obviously why some TE's feel the need for God's intervention.

I think this is a misunderstanding of both science and theistic evolution. It is certainly not the way I am coming at it.

Of course if you believe the historical account of origins given in Genesis, it is obvious that this fantastic piece of anatomy is the product of a Creator. Intuitively that is what you conclude.

Even if you do not believe the Genesis account is historical, it is still obvious (to a believer) that this fantastic piece of anatomy is the product of a Creator. Evolution is not a denial of creation. It is a method of creation.

 

[random_guy]

Tossing a coin is a good example of a random event. All outcomes have equal probability of occuring which is why we often toss a coin to settle a dispute. Notice that the sum of all outcomes sum to one so that in the case of an event with two possible outcomes, each must have a probability of 0.5. This is basic high school mathematics which I once taught.

This is wrong. My example is also a random event. How many heads does it take before a tail first appears.

Randomness is nothing more than predictions based on incomplete information. Even flipping a coin isn't 50% equal probability since a coin has different ridges on each side affecting the friction as it flips through the air. If we had information about friction, force, and gravity, etc, the event is no longer random since we can predict what the outcome is. However, we don't have all this information. All we have is a coin that we assume has 50% chance of heads or tails.

Anyway, back to my example, if all we know is we have an unbiased coin, then X is random. We don't know what value X can take on, but we can take a guess.

P(X=0) = P(T) = .5
P(X=1) = P(H)*P(T) = .5^2
P(X=2) = P(H)*P(H)*P(T) = .5^3
P(X=N) = P(H)^N*P(T) = .5^(N+1)

 

[shernren]

Random is a statistical term that indicates all outcomes of an event have an equal probability of occuring.

False. Quantum phenomena are mostly random yet for most quantum phenomena there are fixed ratios of probabilities of given outcomes that are not 1:1. What is your source?

Random guy: the probability of flipping a fair coin (fair is the better term for equal probabilities, not random - an unfair coin-flip is still random) and only getting a head on the nth flip = probability of flipping a fair coin and getting n-1 consecutive tails, which is equal to 1/2^(n-1). As I recall.

There is a difference between

a) controlled by God, but random, and
b) controlled by God, and yet not random.

The easiest example is lightning strikes. Apart from obvious anomalies (say, a skyscraper in the middle of the desert) the location on which lightning will strike is pretty much random. And yet God takes credit for the weather. How come - isn't it random?

This is predestination-free will all over again, except that it concerns the occurrence of natural events instead of human decisions, which can anyway be interpreted naturalistically. I don't have time so someone else will have to flesh this out.

In short, I believe most TEs would possibly believe a), but definitely not b). I'm somewhere in between.

 

[Micaiah]

Not much to add here fellas (and girls). I stand by the generally accepted, standard, orthodox, and might I say correct definition of random which I've have reprinted for you.

I went to a quizz night once. We had a contest as to who could remain standing the longest based on the following test:

Two coins were tossed. You had to place a hand on your head or tail (as in bottom) to indicate what you thought the outcome would be. If you got it right, you remained standing, otherwise you sat down. Mr Smarty Pants did some quick probability calculations and determined the most likely outcome, and won I might add. My great claim to fame.

Here is how it works ladies and gentlemen.

Possible outcomes from tossing two coins. (Cringe everytime I say that after teaching highschool students who would normally break out into a disorderly ruckus after that statement.)

Let H=Head
Let T=Tail

Outcomes: HH, HT, TH, TT

P(HH) = 1/4
P(HT or TH since only require the probabiltiy of a head or tail) = 2/4 = 1/2
P(TT) = 1/4

So the probability of tossing a head and tail or tail and head is 1/2, so the outcomes are not equal and hence not random.

If I had a million dollars on offer for predicting the outcome of tossing two coins I know which I'd be calling.