Re: Is evolution more then mutation and selection?


"Bob Kolker" <nowhere@xxxxxxxxxxx> wrote in message
news:enc306$1msv$1@xxxxxxxxxxxxxxxxxxxxxx
John Edser wrote:


So what in principle remains new? Nothing much. Galileo (1564-1642)
invested
frames of reference rather a long time ago. It was Popper who required
them
to remain refutable so it was Popper was discarded by the mathematicians
because they do not wish to be told that mathematics is not a science.

Mathematics is not a science. Mathematics done abstractly (so called
"pure mathematics") has not an iota of empircal content. Its only
constraint is consistency.

Pure Mathematics is validated only by consistency and promoted purely by
the aesthetics of its output.

Bob Kolker

Bob,

Having read a few good books on *theory of mathematics*, such as one of my
favorites:
Fundamentals of Mathematics, by M. Richardson, Ph.D, the Macmillan Company
(copyright date of my copy 1958), your comments above seem right on.

My layman's view... math is what math IS; and it strikes me as both futile
and pointless to argue that.

Regarding the statement:

Pure Mathematics is validated only by consistency and promoted purely by
the aesthetics of its output.

This is an attractive thesis, and one I find both intuitive for me, by one
choice of definitions, on the one hand and vulnerable to question by another
definition, on the other.

I'm sorry... not meaning to be a fence straddle. But how one wishes to
define things amounts to intellectual freedom... and sometimes I appreciate
having a choice of being able to define something for my own satisfaction in
more ways than one.

That explanation muddle through, let me offer in total objectivity, and
freedom to look at a single thing from more than one perspective...

I ALSO can appreciate pure mathematics (in my imagination) in much the same
way I would appreciate a steel
wheel with symmetrical ridges on its exterior. That PARTICULAR object,
assuming it is small enough, might be applied as a gear in a wind-up watch.
Or it might be applied as a gear in the odometer of an automobile. Or, it
might be used as a gear between the motor and the drive shaft of a cassette
deck. Or, it could be put on a tiny gold chain and worn as a part of a
pendant. Or, it could be used in an intricate collage of objects in an
abstract art piece.
Then, too, it might simply be stored for possible future use until the end
of the universe, and never applied to anything.

Many, many times pure mathematical models have existed *as such* for a while
and suddenly BINGO, they may be found to fit an application that no one ever
thought could be explained. (I feel you already know examples... but I
could look up some and cite them, if you wish.)

So, the point is, I find myself able to view pure mathematics... and even
all mathematics... as having the potential to be used... even if no human
ever were to be smart enough to use it.

Where do I see fallacies in some people's thinking about pure and applied
mathematics? Well, here are some...

1. When two people argue about what math is, and the only differences I
see between them lie in the fact that one
is talking about a definition that appeals to him, and the other is
doing likewise, but preferring another
definition of the same thing which... also works;

2. When a thinker begins to CLAIM to have a theory which fits the facts
of something he claims to understand,
but that thinker is letting the mathematical formula drive his
thinking about the physical system. Often when
this happens... or I perceive it to... the thinker will be insisting
upon ignoring things that do not fit the
algorithm.

One evening, as I sat enjoying a discussion between two newspaper reporters
who also happened to be friends of mine, one of them made the statement that
"two and two always make four."

I felt compelled to intercede and say that this depends upon one's choice of
applications.

"No, you're WRONG," the one reporter exclaimed. You cannot give me ANY
example of an application in which
two and two are not four!"

"Well," I responded, "Yes, I think I can, if you will consider the algebra
of sets. Two members of one set and two members of another set can share
what, in the algebra of sets, is called intersection. Depending upon the
possibilities of intersection, two and two can combine into a third set
comprised of two, three or four members."

The reporter was red in the face at this point and getting loud. He said,
"Well in those cases it's not two and two."

So I tried an application, saying, "If you have two friends, John and Henry,
and Bill, there, has two friends, Jack and Henry, and I were to ask you how
many friends you and Bill have together, then how many are there... if there
is only one Henry?"

The reporter said, "That's not what I'm talking about."

"I know," I replied. "And that is the problem. You are arguing with Bill
over what amounts to two different applications of a single idea."

"Bull***!" the reporter pronounced. "Two and two is four, and you can't
change that."

Since it made no difference to me who was right; and since I never have felt
my ego demanded being DEEMED right... whether I am or am not... I just sat
back and said, "Okay. You win."

We both won, as far as I can see.

I understood his way of thinking about two and two; so I did not roll over
and play dead for him to make a false statement based upon what he wanted to
view as the whole picture.

My whole view of the picture is one I have had in many, many conversations
and situations in life. I see many different views of things sometimes...
not just in math, politics, economics... etc. Many times I have see
solutions to problems an employer had, and could have effected a solution,
if allowed to... but had a superior over me who
viewed the problem as that reported did... from one perspective and one
definitive stance, only. And I had to back down.

When given the responsibility and the authority to make changes, during my
working years, I have come up with solutions to some issues that absolutely
astounded some people... some people who said I was lucky or, less
derogatorily, "Damn, I'd've never thought THAT would have worked.

I'm not a math expert, by a long shot. But I love math... for its esthetic
value... for its consistency... but, also, as a reservoir of models to
consider, when a solution is needed for something that has someone else
stumped, and they are willing to relax and look at something from one or
more perspectives other than one they might be trapped in.

g

But






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