Galileo Redux

[elendil]

I tend to agree. I think for most people there's a beauty in the "simple" or "elegant" solution that "cuts to the heart of the matter" rather than "beating around the bush." That's what I meant about instinctively, almost, going for beauty, believing that there's truth in beauty. The Greek philosophers certainly believed it. And long before the Greeks began to philosophize they gave the name cosmos to the world. The root meaning, of course, is "order," but in order is beauty and so we also use that Greek word in precisely that sense: "cosmetic." The whole tendency of Pythagorean-Platonic thought was to find the simple principle to explain the harmony of the cosmos. And yet we also marvel at the complexities of the biological realm which somehow fit so harmoniously together and seem to work to redress any imbalance that arises, to restore that beautiful order.

[jim stone]

They (the sri lankans)
got it from Thomas Kuhn, The Structure of Scientific
Revolutions., which maintained that science moves
from paradigm to paradigm. Kuhn regretted for
the rest of his life what people made of this...
there's no objective reality, it all depends on
your paradigm.

Engineers make good philosophers.

There were some differences around Galileo's time
about whether simple theories were more likely
to be true. Some thought that God, being omnipotent,
could make things as baroque as he pleased.
This was Pope Urban's view, I think.
Why not epiciycles? There's no reason to believe
the universe would be particularly comprehensible
to us. A Copernican model might help us predict things
with fewer computations, but that's no reason to
infer that that's how things really are.

There really is a deep question: why believe the
simpler theory is more probably true?

[Lorenzo]

To put it bluntly (and cut out a most of the details) Galileo had a truly abrasive personality, and made a large number of political enemies.

There's two sides to every story like this one. I've known someone, since I was a teenager, that is viewed by many as having an abrasive personality. But, you know what...he never use to be that way, and he's not that way around other good scientists. He got that way from banging his head against a dumb brick wall most his life...people unqualified to understand. That same brick wall could have given Galileo an attitude.

If he became disgusted with people who "refused" to see the light, people of such shallow and superstitious intelligence that they considered his telescope an instrument of the devil...well, welcome home. There's people like that everywhere who "refuse" or are incapable for one reason or another. It's too bad that vested interests often have such a devastating influence, or guiding factor, on a person's thinking...many times it being some cherished religious view.

For the serious student, sincerely wanting to know what's what, Rice University did a massive and scholarly research project, unraveling theory from historical evidence. It's called The Galileo Project. http://es.rice.edu/ES/humsoc/Galileo/ If anyone disagrees with the analysis or conclusion of this project, it would be interesting to know why.

If one were faced with a choice of either trying to temper the public's perspective of the Church, re the historical account of the Galileo story, or celebrating with the NASA team today, with their success on Mars, no contest...you know where I'd be. Imagine what Galileo would think if he knew what we were doing today.

[jim stone]

I've known great intellectuals and there is a tendency
toward arrogance. Brilliant people doing important
stuff when they're young... Great accomplishments
are often driven by ego. There is good indication
that Galileo was arrogant from the first.
Also he wasn't dealing with idiots--in some of
his scientific debates with Jesuit astromoners
(e.g. about comets), they were right, he was wrong. best

[Lorenzo]

Yea, and doesn't it all depend on who's writing, or who's being written about? Excuse me while I slip into another more scientific web site for the latest pictures of something Galileo only could have dreamed of...

[elendil]

There really is a deep question: why believe the
simpler theory is more probably true?

My answer? Because we want things to be that way. I guess that's the simple answer.

Interesting about Kuhn's regrets. I read him back in the 60's. A lot of what he had to say seemed to me then to be basic common sense, but right from the start it seems people were trying to hitch him to their own agendas. Maybe the trouble was that people wanted to systematize his insights, whereas science rarely advances in a textbook methodic fashion. Which was a big part of what he was saying, I think.

[jim stone]

I think the book is beautifully written,
but in the last chapter Kuhn went a bit over the
top and seems to be saying that a scientific
paradigm creates the world in which science
is done. Later he wrote that he never meant
it in the way it was taken, but then it was
too late.

As to why simplicity might be a sign of truth,
we agree, I think, that God would have made
a world that we could understand scientifically, and
simplicity is more understandable than complexity.
The aesthetic virtue of simplicity is elegance,
and one supposes that God would make an
elegant universe, not something full of needless
clutter. Of course I'm supposing that God
appreciates beauty, but why not? If it is
a fact that some things are beautiful,
and he knows everything, he knows
that fact. Beauty is good, and he knows
that too, and so would be inclined
to create a beautiful universe.

For non-believers:

According to probability theory conjunctions
of propositions have a lower probabilty of
being true than one of the conjuncts taken
alone.

It will rain tomorrow

and

bush will be re-elected

have, alone, more likelihood of being true than

'It will rain tomorrow and Bush will be re-elected.'

Complicated theories, made of many propositions conjoined,
therefore, have a lower probabilty than simple theories,
all other things being equal.

Perhaps this helps...Best

[Wombat]

The reason why simplicity is a guide to theory acceptance is, at least in part, quite banal. Take any theory which you would take seriously as a scientific theory. Now generate a new theory by tacking on an obvious truth. It doesn't matter what the truth is just so long as it is obvious.

Theory 2 will be confirmed just in case theory 1 is. Theory 2 will be adeqaute if theory 1 is. The only criterion of theory acceptability that rules out these countless billions of silly theories is simplicity.

Of course, there is no reason why the only adequate theories might not be fairly complicated. But if we want to get rid of billions of adequate contenders, we need to use simplicity as a guide.

As for the idea that we like things to be simple, let me quote a conservative Roman Catholic writer (Mary Douglas) on a closely related desire.

'it is part of our condition that the purity for which we strive and sacrifice so much turns out to be hard and dead when we get it .... Purity is the enemy of change, of ambiguity and compromise.'

[Ridseard]

"Everything should be made as simple as possible, but not simpler."
-- Albert Einstein

[Darwin]

Complicated theories, made of many propositions conjoined, therefore, have a lower probabilty than simple theories, all other things being equal.

So, another way of stating Occam's Razor is "Given two competing theories, begin by testing the one that requires the fewest assumptions." That's simple resource economics.

By the way, I like Feynman's point that a crucial aspect of science is the acceptance of ultimate uncertainty. In contrast, religion is often about offering certainties. When someone told a fundamentalist friend that the discontinued Texas supercollider might have provided clues about the origins of the universe, my friend said, "We don't need a supercollider for that. We have the Bible."

It seems that real-life scientists find certainties just as appealing as anyone else. Although it's true, as Feynman also pointed out, that once you start testing a theory, you need to commit to it, there seems to be a tendency to forget that all theories are subject to eventual disproof or modification. I have my own personal conventional-cosmology-is-probably-all-wet hobby horse that I won't ride here.

[Ridseard]

When someone told a fundamentalist friend that the discontinued Texas supercollider might have provided clues about the origins of the universe, my friend said, "We don't need a supercollider for that. We have the Bible."

There's something so sad and hopeless about that anecdote. There's absolutely nothing you could say to your friend to convince him otherwise. <sigh>

[elendil]

In contrast, religion is often about offering certainties. When someone told a fundamentalist friend that the discontinued Texas supercollider might have provided clues about the origins of the universe, my friend said, "We don't need a supercollider for that. We have the Bible."

I imagine the same could be said for all those people who went out and butchered their neighbors in the name of Marx, Lenin, Stalin, Mao, et alios, in the hope that it would bring about the dictatorship of the proletariat. It's all "religion" in my book, which is why it's become a largely pointless words in discussions like this. You need to make precisions about the type of religion. Obviously, the Jesuit astronomers had a different religion than your fundamentalist friend. But I was forgetting myself--on another thread I said I didn't like that word either.

[Wombat]

Complicated theories, made of many propositions conjoined,
therefore, have a lower probabilty than simple theories,
all other things being equal.

Perhaps this helps...Best

The appeal to the lower probablity of conjunctions doesn't help here Jim. If all of the conjuncts are required to explain the experimental data, we need them all for the theory to be adequate. If, on the other hand, one of them can be dispensed with because the others do all the explanatory work by themselves, then we dispense with the additional conjunct because it is idling, not because it renders the whole less probable. The extra conjunct might be logically true in which case conjoining it to the explanatory portion does not result in a proposition with lower probablility. The more complex theory is still to be rejected in favour of the more simple theory.

[jim stone]

Certainly there is no essential connection between
conservative christianity and certainty. C. S. Lewis,
an apologist for conservative Christianity,
was emphatic that 'Christians are taking a chance.'

Of course there are scientific claims of which most
people are certain, e.g. that the planet isn't flat.
And I believe there are fundamentalists
who believe that what they believe isn't
certain, though there are compelling reasons
to believe it. So I know fundamentalists who
argue that the Bible is true on grounds that
they think would persuade atheists, e.g.
Biblical prophecies keep coming true,
the Biblical story progresses rationally
over centuries and has the ring of truth,
historical claims in the
Bible keep being vindicated by archeology,
and so on. Further the Bible makes the most
sense taken literally, alleged contradictions
turn out to make perfect sense on a
careful reading, and there are grounds
for believing in God independent of scripture...
and so on. Anybody intelligent (and these
people are highly intellegent) who argues in
this way knows that he is vulnerable in principle to
refutation (e.g. we learn that the archeological
evidence that supposedly vindicates
Biblical historical claims was fabricated, etc.).

Fallibilism is the idea that even our justified
claims to knowlege are in principle
subject to being overturned by new developments.
I think there are fundamentalists who
are fallibilists. I like to take these people
at their best.

About simplicity as a guide to truth:
In probability theory, probability is represented
on a scale between 0 and 1, where 1 is certainty
given the evidence and 0 is certainly false.
A probability of .5 is fifty fifty that the proposition
is true. Anything better than .5 is a good bet.

The probability of a conjunction is the probability of
the conjuncts multiplied.

So if p has a probabiltiy of .5 and q the same,
'p and q' has a probability of .25, much less
likely. A consequence of this is that the
conjunction of two likely conjuncts can be
unlikely. So if p has a probability of .7 and
q the same, 'p and q' has a probility of .49,
a bad bet.

Now Wombat's point might be put this way.
If p has a probabilty of .6 and q is a dead certainty,
.1, 'p and q' will have a probabilty of .6 .
So tacking on certainities ('It is raining or it isn't')
will produce a multiplicity
of theories with the same likelihood.
Simplicity, therefore, is a way of selecting
between these equally likely theories.

Note, too, that if we tack on something less than
certain but highly likely, a probability of .9,
say, the resulting theory will be less likely
than .6. So probability theory also gives us
a non-banal reason to prefer simplicity.
If a theory is a real one, it's complexity
won't be a matter of tacking on truisms,
and so its probability will diminish with
complexity. Best

[Caj]

Jim,

You might be interested to know that there is another mathematical justification for Occam's Razor, using information theory. I've seen it mentioned in a few places, including Cover & Thomas's fabulous textbook on the subject.

It's somewhat like your argument, except instead of the complexity of a theory, the argument addresses the complexity of the underlying mechanism which the theory presupposes. Under plenty of simplifying assumtions, we have that for a given string of observations, the most probable mechanism that outputs that string is the simplest one.

Caj