Re: Request

Glenn wrote:

> "John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message
> news:kdrNe.1596$3F6.846@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
>>Glenn wrote:
>>
>>
>>>"John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message
>>>news:NXkNe.3172$Z87.191@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>>>
>>>
>>>>John Drayton wrote:
>>>>
>>>>
>>>>
>>>>>Glenn wrote:
>>>>>
>>>>>
>>>>>
>>>>>>"John Drayton" <bitbucket55@xxxxxxxxxxx> wrote in message
>>>>>>news:1124426995.530310.4020@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>>>>>
>>>>><snip>
>>>>>
>>>>>>>It's not a specialised meaning at all. Certainly not
>>>>>>>specialised for evolutionary theory, anyway. It's the
>>>>>>>regular mathematical meaning, no matter where this math
>>>>>>>is used: physics, chemistry, biology, economics ...
>>>>>>>
>>>>>>>Not only that, it agrees with most dictionary definitions
>>>>>>>I could find.
>>>>>>>
>>>>>>
>>>>>>If by "it" you refer to "all mutations are equally likely, "or "all
>>>>>>mutations are equally likely to be selected", then you are right. The only
>>>>>>quibble would be to add "any and all".
>>>>>>http://www.google.com/search?hl=en&lr=&oi=defmore&q=define:random
>>>>>
>>>>>
>>>>>I'm not sure what you're saying.
>>>>>
>>>>>I was saying that most definitions of "random" in dictionaries
>>>>>that I could find don't define it as "all outcomes equally
>>>>>likely", as you've shown in the link above.
>>>>
>>>>"Random" can mean "all outcomes equally likely", even for some
>>>>distributions that aren't flat, if you weasel "all outcomes" properly.
>>>>Taking the two dice example, 7 is much more likely than 3, but if you
>>>>define the outcomes as ordered pairs -- i.e. 3 = (2,1) or (1,2) -- then
>>>>all outcomes, all ordered pairs, are equally likely. I suppose this
>>>>would apply to mutations too, if you think of mutations as being drawn
>>>
>>>>from a bag that just happens to contain a lot more transitions than it
>>>
>>>>does transversions.
>>>>
>>>
>>>References to where 7 is "much more likely" than 3, or were you weaseling. Is
>
> this
>
>>>probability based on a mechanism, and testable?
>>
>>Indeed it is. It's based on two fair dice. There are 36 possible rolls,
>>from 1+1=2 to 6+6=12. There are 6 ways to get a 7, and only 2 ways to
>>get a 3; 7 is three times as likely as 3. If you don't believe this,
>>perhaps you would like to get together and play craps with me.
>
> But these numbers are just representations, in this case to mathematical sums. The
> relevance of "random" with dice is not in the particular combination of dots
> adding up to a particular sum, is it? Or would you claim that roled dice are not
> random?

I have no idea what you are trying to say here, so I will just explain
in your general direction. Rolling two dice and adding them gives you a
random number. That number is drawn from a particular distribution in
which 7 is much more likely than 3. The physical details do allow us to
determine what that distribution is quite simply. Rolled dice are random.

>>>I just rolled a series, and it
>>>didn't happen. How many series must I role?
>>
>>What didn't happen? How long a series? The more times you roll, the
>>closer your cumulative results will come to the theoretical
>>distribution, assuming you really do have two fair dice.
>
> How does that relate to mutations?

Well, the more sequence you assay, the closer the number of mutations
experienced per unit time will approach the expected distribution. This
is true for all random distributions one is ever likely to encounter:
the bigger the sample size, the smaller the percent standard deviation.
But really, the whole point of bringing up the dice was merely to show
Zoe that random distributions don't have to be uniform distributions.
That's all.

>>>I define the outcome of a role as the
>>>sum of the number of dots on the dice faces. What is the difference between
>
> that
>
>>>and "defining the outcome as ordered pairs"?
>>
>>In ordered pairs, 2+5 is different from 3+4 and also from 5+2. There are
>>36 different ordered pairs. Counting the number that sum to a given
>>amount and dividing by 36 will give you the probability of rolling any
>>given number on any single trial.
>
> Why is 2 and 5 an "ordered pair"?

It's an ordered pair because it's a pair of numbers, and it's ordered,
meaning that the order in which you give the numbers is important.
Surely you took algebra in high school. Can you try remembering that far
back? You may remember the notation (2,5) defining a point on a plane
whose x value is 2 and whose y value is 5. (5,2) is a different point.

.

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