Random Mutations

[Micaiah]

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?

I presume when you talk about quantum you mean what we refer to as discrete. I just posted an example of an event with an outcome that is discrete and not random, though each toss of the 'fair dice' is random.

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.

Not sure why we are discussing this at length apart from it being a bit of a spitting match.

If you draw out the probability tree you can confirm that the probability of throwing a coin 'n' times and getting a tail after consecutive heads is indeed the same as throwing a coin 'n' times and getting all head which is calculated as:

P(a tail after a string of heads) = (1/2)^n

I think it is less confusing to express n as the number of throws and does the same thing.

I'm not sure of the significance of the number 'n' being what you call a random variable. It is just a variable, and as such can be any number within a defined domain.

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.

Lighting is not random. As you noted, it has a greater chance of striking some locations than others.

Either mutations are random or they are biased by God in which case they are not random. You have to make a choice.

 

[Micaiah]

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.

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.

If you look at the example on tossing two coins it gives a binomial pattern similar to the genetics example of which you spoke.

(a+b) (a+b)= a.a+a.b+b.a+b.b= a.a+2a.b+b.b which is a binomial expression.

The sum of the probability of all outcomes is equal to one and as you stated does not impact on the definition of random. It was something I threw in at no extra cost since I thought people would find it interesting.

 

[random_guy]

Are random variables random, Miciah? For example, with the coin tossing experiment, Let X=0 if you flip a head, and X=1 if you flip a tail, is X a random variable? Does this mean X takes on a random value, ) or 1? Why or why not?

It seems that you're using an incorrect definition of random.

 

[gluadys]

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.

Yes they are random.

If you look at the example on tossing two coins it gives a binomial pattern similar to the genetics example of which you spoke.

(a+b) (a+b)= a.a+a.b+b.a+b.b= a.a+2a.b+b.b which is a binomial expression.

The sum of the probability of all outcomes is equal to one and as you stated does not impact on the definition of random. It was something I threw in at no extra cost since I thought people would find it interesting.

Yes, they are similar. And the outcome is random.

It is when you do not get the binomial result that you look for an influence (like natural selection) that is not random and is skewing the results.

 

[random_guy]

Wow, talk about coincidence. Right after I posted, I left to class where my professor talked about random variables. The weird thing is, this is a biology course. Anyway, while he was discussing how we model gene activation with random variables, I thought of a great example.

According to Miciah's definition of random, roulette is not random since all outcomes are not equally likely. Red and Black each have 19/40 chance of showing up, Green has 2/40 chance of showing up.

 

[Saucy]

I believe the answer to the question is very simple. It's the curse placed on all creation. Life is no longer perfect. The lion no longer lies with the lamb. Now life is about survival.

 

[DailyBlessings]

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?

Sort of? Some aspects of genetic recombination, including mutations, are random, at least insofar as anything is random. But this would be true whether evoution were valid or not- even most creationists accept the basic workings of genetics. And if randonimity were the only factor, evolution would not really occur, because genes would retain the same frequencies, except for adding new mutations at an equal and predictable rate.

Now, what randonimity really means is a matter for quantum physicists, not me. I'm content to presume that whatever randonimity is, it is a result of the physical nature of the universe. Since God created the universe and every part of it intentionally, an event can be completely random from the eyes of scientists and still be in accordance with the will of God, who set the original parameters and nature of random events.

I see the Creation as a continuing process, not a single act a long time ago, and evolution an aspect of that creative process along with all other physical processes.

 

[shernren]

Let me get this right, Micaiah. According to your definition, the outcome of tossing one coin is random, but the outcome of tossing two coins is not. Are you serious??

What I meant by fair vs. random was this:

Let's imagine a weighted die. It is weighted so that the probability of it giving a 6 is artificially inflated, say 1/2, and the other probabilities remain equal at 1/10 each. (In real life with real die the other probabilities would have different relative frequencies too, but this is a bluff die so I'm calling the shots! ) This is what we mean by "unfair". A fair die would give 1/6 for 1, 1/6 for 2, 1/6 for 3 ... etc. but an unfair die has a larger probability for a given outcome, 6 in this case. Is it still random? By your definition no. However the generally defined view would be that it is still partially random. Here's a good overview:

http://en.wikipedia.org/wiki/Random

(P.S. the actual probability is 1/2^n. I was wrong earlier. It is the probability of getting n-1 consecutive heads times the possibility of getting a tail next.)

Either mutations are random or they are biased by God in which case they are not random. You have to make a choice.

Nope, I don't have to. I don't like unanswered theological questions but this is one of them. Predestination vs. free will. On the one hand:

People make their own decisions, therefore they are responsible for their own decisions.

On the other hand:

God knows the future, so God knows every decision that is made before it is made. Furthermore, God actively directs and works through the decisions of man as shown several times in the Bible.

So, how? If God knows what I choose before I choose it doesn't that mean I have no actual say over the matter of what I choose? When Paul faced this in Romans the first thing he said was "Don't talk back!" and I won't. But this situation is exactly parallel to what we have here.

Mutations are random.

However, God knows the future, so He knows every mutation that will happen. Not only that, God actively directs and works through mutations to bring about the evolution of a perfect habitat for humans (which we promptly set about dismantling, sadly).

I will freely admit that my intellect is not enough for this particular dilemma.

 

[Saucy]

I believe the answer to the question is very simple. It's the curse placed on all creation. Life is no longer perfect. The lion no longer lies with the lamb. Now life is about survival.

 

[random_guy]

I think two of the biggest problems is many times, Creationists get the scientific or mathematical meanings of definitions wrong, and two, seldom will they admit to it.

I'm almost positive that random events do not require equal probability in order to be random. Heck, even flipping a coin wouldn't be random since the curves on the surface would bias the coin in a certain direction.

 

[ebia]

I think two of the biggest problems is many times, Creationists get the scientific or mathematical meanings of definitions wrong, and two, seldom will they admit to it.

I'm almost positive that random events do not require equal probability in order to be random. Heck, even flipping a coin wouldn't be random since the curves on the surface would bias the coin in a certain direction.

To (hopefully) answer this definitively:

A random experiment is a process with a well-defined set of possible outcomes but whose outcome in any given running of the process cannot be determined in advance.​

[...]
In many experiments, all of the possible outcomes are equally likely.

emphaisis mine. Many experiments, not all.

 

[random_guy]

To (hopefully) answer this definitively:


emphaisis mine. Many experiments, not all.

That's a weird way of putting it. To be honest, I'm actually not sure what random actually means, either. I know what a random variable is, but not random. It's one of those words you think you know until you try to describe it to someone else.

 

[shernren]

A random experiment is a process with a well-defined set of possible outcomes but whose outcome in any given running of the process cannot be determined in advance.

I think this almost hits it on the nail, but I would replace "cannot" with "is very hard to" or "is computationally unfeasible to". For example, it should be possible, given a well written program and a gamers' computer, to predict the outcome of roulette. But to the casual gambler it is random.

 

[Micaiah]

That's a weird way of putting it. To be honest, I'm actually not sure what random actually means, either. I know what a random variable is, but not random. It's one of those words you think you know until you try to describe it to someone else.

Does anyone see the humour of someone dismissing others definitions as wrong and at the same time displaying a high degree of uncertainty in the mathematics they post and then admitting they don't really know the definition.

As stated at the start of this thread random means different things to different people. The mathematical ideal is an event where all outcomes have an equal probability of occuring. Tossing a coin approximates that well.

At the other end of the spectrum are those who define it as loosely as something that cannot be predictable with any certainty. The definitions we've seen to date fall all along this continuum.

Suppose you were on one of those TV games shows where their was one of those spinning wheels with lots of numbers. Some numbers were repeated, and the wheel tended to roll around to a certain position as it slowed down and stopped. Most people would be very cynical of anyone claiming this kind of wheel could give a random outcome.

The idea of variation resulting from random mutation was an important one for those who formulated the Neo-Darwinian Theory of evolution. They had specific requirements for the type of mutation which could be admitted to being responsible for evolution. It had to occur in small steps as they recognised the getting a beneficial mutation involving many nucleotides was implausible. It could not be the result of intelligent design, and it could not arise due to environmental factors. It had to be random.

So in this context, what did the scientists who formulated the NDT mean by the concept of random mutation?

 

[gluadys]

So in this context, what did the scientists who formulated the NDT mean by the concept of random mutation?

They meant that the occurrence of a mutation was not related to the need for an adaptive variation.

A mutation with adaptive value in current circumstances will not occur simply because it would be useful. Neither will it not occur simply because there is no current usefulness for it.

They also meant that it is not possible/feasible to calculate in advance which nucleotide(s) will be affected by a mutation at any given point in time.

 

[random_guy]

Does anyone see the humour of someone dismissing others definitions as wrong and at the same time displaying a high degree of uncertainty in the mathematics they post and then admitting they don't really know the definition.

Just because I can't exactly explain what random means, doesn't mean I can't tell if a definition is wrong. It's like art, hard to describe, but I know it when I see it. According to you, flipping a coin is not random since it doesn't have 50-50 chance of heads or tails, nor is rolling a dice since each side doesn't have 1-6 chance of showing (all due to non-uniform density distributions). So in your definition, nothing is random.

So in this context, what did the scientists who formulated the NDT mean by the concept of random mutation?

This I know. Random is used to describe processes in which we have too little information, or when a condition is very sensitive to initial parameters meaning we can't predict it. We use random all the time in this context. Rolling a dice seems random because we don't have all the information and a slight change in force vector leads to different outcome.

EDIT:

A neat quote that applies here:
Persi Diaconis (a statistician) : "We know what randomness isn't. We don't know what it is."

 

[ebia]

That's a weird way of putting it. To be honest, I'm actually not sure what random actually means, either. I know what a random variable is, but not random. It's one of those words you think you know until you try to describe it to someone else.

That's probability theory for you. The proper mathematical definitions of things in probability theory tends to have people going "huh?".

 

[ebia]

Does anyone see the humour of someone dismissing others definitions as wrong and at the same time displaying a high degree of uncertainty in the mathematics they post and then admitting they don't really know the definition.

I just posted you a definition from a university professor of maths and stats. I chose that one, because it's the only I could find that anyone without some degree level maths would understand. It's quite clear that outcomes do not have to have equal probability.

As stated at the start of this thread random means different things to different people. The mathematical ideal is an event where all outcomes have an equal probability of occuring.

This is simply wrong. The maths is much easier when the outcomes are equally likely (which is why you aren't going to look at much else at high-school), but it is not "mathematically ideal".

At the other end of the spectrum are those who define it as loosely as something that cannot be predictable with any certainty. The definitions we've seen to date fall all along this continuum.

Suppose you were on one of those TV games shows where their was one of those spinning wheels with lots of numbers. Some numbers were repeated, and the wheel tended to roll around to a certain position as it slowed down and stopped. Most people would be very cynical of anyone claiming this kind of wheel could give a random outcome.

You are confusing "fair" and "random". And, as far as probability is concerned "most people" have absolutely no idea what they are talking about, so they aren't a very authorititive source to cite.

I've cited you a defintion from an expert source. If you are going to continue to claim that your definition is correct, you must do likewise.

 

[shernren]

As stated at the start of this thread random means different things to different people. The mathematical ideal is an event where all outcomes have an equal probability of occuring. Tossing a coin approximates that well.

Nope. You yourself admitted that by your definition, tossing one coin is random whereas tossing two coins is not. Is there a causal link between a coin's first toss and its second?

Also, many things conventionally defined as random would not be. For example, when you toss a coin 10 times, you'd expect a fair coin to give 5 heads and 5 tails. But you will only see that, on average, once in every four trials of 10 tosses each. Does that mean that coin tosses are never fair or random? No, it is precisely what is predicted by the binomial distribution [X~Bin(0.5,10); P(X=5) = 10C5(0.5)^10 = 0.246]. But by your definition, since a large number of coin toss experiments would give you, say, 4 heads and 6 tails out of 10 tosses, therefore many coin tosses are not random. Furthermore, if the same coin gives 5 heads - 5 tails in one toss experiment, and 4 heads - 6 tails in another, then theoretically that coin is random in the first experiment and not in the second.

Are you really sure your definition holds up well? At all?

The idea of variation resulting from random mutation was an important one for those who formulated the Neo-Darwinian Theory of evolution. They had specific requirements for the type of mutation which could be admitted to being responsible for evolution. It had to occur in small steps as they recognised the getting a beneficial mutation involving many nucleotides was implausible. It could not be the result of intelligent design, and it could not arise due to environmental factors. It had to be random.

So in this context, what did the scientists who formulated the NDT mean by the concept of random mutation?

I think gluadys is on the mark here. In addition by using ebia's definition, it would mean that the occurrence of the mutation could not be predicted in advance were there human observers present at the time the mutation occurred. The mutation's location and nature (and even occurrence) would not be predictable, and only by its resulting effects on the child offspring would it be detectable. This is, by the way, precisely what we see with most typical mutation experiments.

 

[Micaiah]

Some further things to ponder.

1. Suppose in the example above of the tossing of two coins I write down the outcomes of each on a piece of paper. I number each outcome as follows:

1. HH
2. HT
3. TH
4. TT

If I then put each piece of paper into a bag, shake up the bag and remove one piece, the chance of me getting any one of the four events is equal. However, the chance of getting a head and tail is different to getting a tail and tail, or head and head. By my definition, the first event specified is random, the second is not.

2. Suppose there is an animal that has for arguments sake 1,000,000 nucleotides in its DNA. Assuming NDT, what is the probability that a point mutation occurs in a certain nucleotide?