John,
Thanks a lot! A most interesting post. I'll look up your paper.
Even though I have approached these questions from a different angle ,
I wholly agree with your conlusion views on the nature of thirds. And
on the arguments offered by Peirce. - It has seemed to me, too, that he
did not solve these issues, but he pointed the ways on how to get on
solving them.
I do lack expertice on the topics you deal with. Still, I have been
groping for undestanding the connections between triadic thinking,
three-body problem & dissipative systems for a long time.
So,thanks & my very best regards,
Kirsti
John Collier kirjoitti 12.4.2017 23:45:
Three body problem is computable for any finite amount of time (like
all conservative systems). To get problems the end state must be
reached in a finite time. This can happen in dissipative systems.
There are many cases where you can’t even get approximate solutions,
though you can get probabilities of various solutions. For example,
Mercury is in a 3/2 rotation to revolution rate around the Sun. It was
expected to be 1:1 like the Moon around the Earth. A bit of a
surprise, since the 1-1 ratio is the lowest energy one. However,
everything near the 3/2 state is higher energy, so it is stable. Now
the interesting thig is that the boundaries between the attractors are
such that there are regions in which any two points in one attractor
has a point in the other attractor between them. So no degree of
accuracy of measurement can allow predicting which attractor the
system is in. So Frances Darwin’s explanation of why the Moon always
faces the Earth is incomplete, and can never be fully completed. There
is about 50% likelihood of 1-1 capture, 33% for 3-2 capture, and the
rest take up the remaining chances. Note that the end states aren’t
just a little bit different, but a lot different. Things get much more
complicated in evolution and development, where more factors are
involved. I argue that information dissipation (e.g., through death
eliminating genetic information) works the same way. I first published
on this as the first paper in the journal _Biology and Philosophy_ n
1986.
The main point is the problem is not one of our limited calculation
capacity. It holds in principle. Even Laplace’s demon, if they are
like a regular computer, but arbitrarily large, could not do the
calculations. Basically, there are far more functions that are not
Turing computable than are, and many of these give widely different
possible solutions. It’s really just another case of the number of
theorems being aleph 1, but the number of possible proofs is only
aleph 0.
I call systems like the Mercury –Sun system reductively explainable,
but not reductive. Physicalism is not violated, but reduction is not
possible. But we can get a good idea of what is going on, after the
fact (though our first guess in the Mercury-Sun case was wrong).
Personally, I think all thirds are of this nature, which is why they
can’t be reduced to dyads. I have never found Pierce’s arguments
convincing about the irreducibility.
John
FROM: Clark Goble [mailto:cl...@lextek.com]
SENT: Wednesday, 12 April 2017 1:47 PM
TO: Peirce-L <PEIRCE-L@list.iupui.edu>
SUBJECT: Re: [PEIRCE-L] Laws of Nature as Signs
On Apr 12, 2017, at 11:21 AM, John Collier <colli...@ukzn.ac.za>
wrote:
Some reductions are impossible because the functions are not
computable, even in Newtonian mechanics.
Are you talking about the problem in mathematics of solving things
like the three body problem? That’s not quite what I was thinking of
rather I was more thinking that any solution is approximate and the
errors can propagate in weird ways.
But that’s true of almost any real phenomena which is more complex
than we can calculate. It’s not just an issue of reduction although
it clearly manifests in the problem of reduction and emergence.
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