Re: Sean PItman and nested hierarchy

Charles Brenner wrote:
On Mar 3, 8:27 am, John Harshman <jharshman.diespam...@xxxxxxxxxxx>
wrote:
Charles Brenner wrote:
On Mar 2, 8:21 pm, John Harshman <jharshman.diespam...@xxxxxxxxxxx>
wrote:
Charles Brenner wrote:
On Feb 26, 9:36 am, John Harshman <jharshman.diespam...@xxxxxxxxxxx>
wrote:
[I thought I'd start a new thread since Sean isn't replying in the old
one. ...
Sean Pitman:
> As far as I've been able to tell, your argument is basically that a
> nested hierarchical pattern implies common descent in all cases where
> it is found. This hypothesis does seem to hold true, as far as I can
> tell, for non-deliberate processes. It seems that non-deliberate
> processes cannot make a nested hierarchical pattern without the use of
> common descent. In fact, this particular hypothesis, is actually
> falsifiable. All one has to do to falsify this hypothesis is show a
> non-deliberate process producing a nested pattern without using common
> descent and this hypothesis would be falsified.
> However, this very predictable limitation is demonstrably *not* a
> necessity when intelligent design is involved.
I agree. Since there are no limits on intelligent design, anything is
possible and science is futile. I can't understand why you still cling
to it.
> In order to try to
> make it a necessity for when ID is demonstrably involved, you propose
> various limitations to all intelligent designers. You suggest that no
> intelligent designer would ever produce a nested pattern. You ask for
> a reason why an intelligent designer would create such a pattern.
> Don't you see, this is like asking why Picasso refuses to paint in the
> style of Michelangelo? It makes absolutely no sense to ask this
> question. If you don't see that, there simply is no further
> argument. It should be enough to speak for itself.
I agree. It makes absolutely no sense to ask any questions at all, given
your assumptions. We can't know anything through examination of the world.
> Your efforts to presuppose limits on all intelligent designers, even
> ones you do not know, reduces your hypothesis to a position of non-
> falsifiability. Given they way you describe your position, it is true
> by definition. It cannot be challenged, even in theory, because you
> defined what a designer can and cannot do.
No, in fact I haven't. Consider this in a likelihoodist framework: A
designer (hey, can I save typing by calling him "god" from now on?
Thanks.) has a flat probability distribution of expected result,
infinitely wide -- i.e. he could do anything. This means that the
probability of any one outcome -- e.g. a nested hierarchy -- is
arbitrarily close to zero. The likelihood of the data given the god
model is almost nil. Then again, the distribution for common descent is
sharply peaked; we strongly expect a nested hierarchy and little else.
So the likelihood of the nested hierarchy data given the common descent
model is quite high. In a likelihoodist framework we clearly pick common
descent as an explanation of the data. Similar reasoning would produce
similar results in bayesian or frequentist frameworks.
I'm glad you introduced this point. For me it's the most sensible way
to think of evidence. I wasn't very surprised when Sean clipped it
though; I suppose to many people it comes across a incomprehensible
technical gobbledy-gook -- and in a way it is. My objection is to the
concept of a "flat probability distribution" across all possible
things God might do.
How about "uniform distribution"? No? It merely means that all possible
outcomes have an equal probability. And since all probabilities must add
up to 1, the more possible outcomes the lower the chance of each. If
there are infinite outcomes, there is zero chance of each.
That's doesn't work except in severely limited and simple situations.
For example, you can't even make sense of the idea of a uniform
distribution on the integers. (Any method of choosing integers at
random must necessarily tend to favor small ones.)
Nor is this a mere mathematical curiosity. Assuming a "uniform
distribution" over a disorderly set of possibilities is even more
nonsensical. A creationist might accept your stipulation and argue as
follow:
Very well, the creator has an infinitude of possible ways to create
life and I accept that they are all equally likely. Let's examine
them. To begin, consider two broad categories: methods involving
common descent (which result in nested hierarchies), and methods of
separate creation (which might not). Each has infinitely many
subcases, and by the uniform distribution hypothesis each broad
category is 50% likely to be chosen, etc. etc. Hence the observed
nested hierarchy is quite a normal and expected result for a creator
to produce. Now, you can argue that my particular categories seem very
self-serving and you may be able to argue it very well. But
mathematics isn't going to help you. (To define a uniform prior on a
set of possibilities requires imposing a metric, and the metric can be
chosen arbitrarily.)
Ah, but the total of all possible nested hierarchies is in fact a very
large but finite set of patterns. So the creationist's initial
assumption is wrong. (Unless there are an infinite number of species,
that is.)

As I said above I object to a flat probability distribution "across
all things God might do" -- i.e. all of God's possible schemes for
creating life. Surely there are infinitely many possible schemes. But
you apparently have in mind quite a different probability space ...

Then again, the number of possible total patterns might not be
infinite either. Let's limit our list of patterns to possible sets of
connections among species, i.e. some sort of graph.

... related to the number of ways the species might be arranged as a
graph or pattern of some sort.

Originally you wrote of "a flat probability distribution of expected
result, infinitely wide -- i.e. [God] could do anything". I was
slightly careless to equate possible "results" with possible schemes
for producing results, but anyway to the extent that they are
different (e.g. several slightly different schemes correspond to
identical observed data -- "result"), I don't see why it makes more
sense to imagine that probabilities would be uniform on the latter
rather than on the former. In fact to the contrary -- it is easier for
me to imagine God selecting a scheme from among many than to imagine
God selecting the data that the scheme creates from among many
possibilities. Analogy: a pitcher throws a ball using a complicated
strategy involving intentions and muscle groups. Listening to the game
on the radio our only data is that the pitch is a ball or a strike.
50% each way? Odd view.

I don't know how to
calculate the number of possible graphs among points, but it's clearly
astronomically larger than the number of possible trees.

For several reasons it seems to me irrelevant. One, it seems you are
assuming that the possible kinds of things God might do somehow
corresponds to possible patterns or "graphs" connecting the species.

The distributions Sean and I are arguing about are distributions of expected result or pattern in the data -- thing we could observe in the present day. They are not distributions of processes or intentions or any such thing. Let's at least agree on what we're talking about.

And we're specifically talking about the patterns in character data, i.e. similarities and differences among species. These in turn imply connections among the species, or perhaps lack thereof. So I have simplified by reducing the possible patterns to different assemblies of connections among species. Only a few of these patterns would be trees, which of course would correspond to nested hierarchies.

I
don't understand that but am willing to leave it aside. Two, it's an
artificial assumption that the set of species necessarily had to be
the ones that actually occurred. In other words, even granting that
only a finite number of species can exist, they are potentially drawn
from an infinitude of possible species. Hence infinitely many possible
"graphs." Three, it seems to me arbitrary and contrived to reduce the
observed data to the nested hierarchy or other connection pattern
which it implies, ignoring all other details. An alternative and
plausible point of view says that a single different base pair
somewhere in the voluminous collection of sequences, although
suggesting the same "graph", is a different "result". Not to mention
that even a DNA life-form was not pre-ordained -- there are infinitely
many possible ways the data could have looked with no natural way to
categorize them; certainly no way to say what is a "uniform
probability distribution."

You may of course choose to increase the complexity of the problem. There still will not be infinitely many possibilities unless there is some infinite dimension. Is there any parameter that might actually be infinite? Is there really an infinitude of possible species? True only if a genome could be arbitrarily large. But I suspect there is some limit to genome size.

Another problem is that your distribution mixes causation into what's
intended to be a distribution of pattern.

Are you just saying that you found my categories to be contrived?

Yes, though more to the point I found them not to be categories to be located in the sort of distributions I've been talking about.

The flat distribution in
question doesn't involve common descent at all, so the division into
common descent and non-common descent makes no sense.

Even if I (acting as consigliere for the creationist) agree to defer
to your judgment about which ideas are sensible to discard, you won't
get vary far toward finding the elusive "uniform distribution" by
throwing out things you don't like. It's really an impossible goal.

I'm not throwing out things I don't like. I'm throwing out things that don't have to do with the distribution under discussion. You could have rephrased it as "shows nested hierarchy" and "doesn't show nested hierarchy", but I think by any measure there are more patterns that don't than there are that do, so that wouldn't have worked.

The big problem I see is that we really can't characterize the distribution of results expected from creation at all. The uniform distribution is often used to represent ignorance of the true distribution. But it isn't really, is it?

.

Relevant Pages

  • Re: Sean PItman and nested hierarchy
    ... > processes cannot make a nested hierarchical pattern without the use of ... the distribution for common descent is ... concept of a "flat probability distribution" across all possible ... there are infinite outcomes, there is zero chance of each. ...
    (talk.origins)
  • Re: Sean PItman and nested hierarchy
    ... The likelihood of the data given the god ... the distribution for common descent is ... So the likelihood of the nested hierarchy data given the common descent ... there are infinite outcomes, there is zero chance of each. ...
    (talk.origins)
  • Re: Sean PItman and nested hierarchy
    ... > nested hierarchical pattern implies common descent in all cases where ... > processes cannot make a nested hierarchical pattern without the use of ... the distribution for common descent is ... So the likelihood of the nested hierarchy data given the common descent ...
    (talk.origins)
  • Re: "Logic" trumps science?
    ... I've already explained what a nested hierarchy is. ... overall pattern of nests within nests. ... are fractals, not that fractals are nested hierarchies. ... The tree of life is self-similar only in the most trivial and uninteresting ways, and the self-similarity is not a particularly important feature of its structure. ...
    (talk.origins)
  • Re: Sean Pitman and nested hierarchy
    ... You don't know the definition of a nested hierarchy. ... "Nature has nested hierarchial fractal-like organization." ... A fractal-type pattern need not have exact self-similarity, ... Let's start with the NHP of random mutations. ...
    (talk.origins)