Re: Sean PItman and nested hierarchy

On Mar 3, 6:59 pm, John Harshman <jharshman.diespam...@xxxxxxxxxxx>
wrote:
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.

We're talking about a likelihood ratio framework. Data of life or
fossils is observed and there are two hypotheses about how it came
about --

Hn = common descent from natural processes
Hg = God created life

The salient and interesting fact about the data is that it indicates a
nested hierarchy (NS). NS is a more or less inevitable consequence of
Hn, but only one possible consequence of Hg. So the data supports Hn
over Hg, but by a lot or by a little? If the NS property of the data
is improbable under Hg, then the data is strong evidence supporting Hn
over Hg.

In order to get a handle on how improbable NS is as a consequence of
Hg, you posit the universe of all possible data states and imagine
them to be equally likely. That's quite unlike what one does in real
life (and most of my work is related to the theory or practice of
likelihoods of DNA data), but I've agreed to play along with your
point of view -- though of course I argue that the "equally likely"
provision doesn't make sense (mathematically, let alone
scientifically). However, if God created life then the patterns in the
data correspond to what God did -- the scheme that God chose. Are we
agreed so far?

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.

There is an infinitude of possible data sets. It's natural to want to
bin the data to cope with it. In your case part of the motive for
doing so is to have a finite set, because for a finite set at least
the concept of "uniform probability distribution" is well-defined.
However, lifting this distribution from the finite set back to the
real data does not impose a uniform distribution on the real data --
just some arbitrary distribution that is tailored for the purpose of
your argument.

In short, what you call a "simplification" is a way of being sneaky.

(It's also very bizarre. Unless I quite misunderstand, a few of the
graphs are trees representing natural hierarchies, which might
actually come about as a consequence of some God-scheme we could think
of.

Only a few of these patterns would be trees,
which of course would correspond to nested hierarchies.

(The vast majority consist of a bunch of random edges here and there
including tangles and loops, and these correspond, to put it mildly,
to no obvious kind of God-scheme so my guess is that they have
probability about zero. On the other hand, a very obvious category of
God-schemes wherein God tosses completely different random DNA into
every different species, corresponds to the empty graph. Hence to
suppose equal probabilities for all the different graphs is pretty
odd. Recall my baseball analogy.)

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.

I'm not increasing, I'm comprehending. You're decreasing.

The data is what it is. However, to consider the probability of the
data (="likelihood of Hg" as RA Fisher would say) we've agreed to put
it alongside all other things it might have been and compare their
probabilities. The other things that it might have been include
chemistry other than we actually see. Certainly there are infinitely
many possibilities.

There still will not be infinitely many possibilities unless there is
some infinite dimension.

Sorry, but that's a little too fuzzy for me to understand. Suppose for
example that the data can be regarded as described by a finite
sequence of English words, each of which is composed of the finite set
of typographical symbols. There are infinitely many of such
descriptions. It's not clear to me what "infinite dimension" you would
have in mind.

[...]

The big problem I see is that we really can't characterize the
distribution of results expected from creation at all.

I agree.

The uniform distribution is often used to represent ignorance of the true
distribution. But it isn't really, is it?

I agree with that too. Even when the "uniform distribution" is
perfectly well-defined, it is often nonsensical to invoke it.

.

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