
Why Math is deeper than Sociology [quote] - ced
"Mathematical statements are unambiguous, and so permit long chains of argument. Unfortunately, statements about society, as about evolution, have a degree of ambiguity. It follows that theories in these fields, if they are to be operative in the sense of leading to clear predictions, must be simple. Of course, it may be that no operative theories are possible in the social sciences."<p>- Maynard Smith and Szathmary, <i>The Major Transitions in Evolution</i>
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Xichekolas
While I don't disagree, neither do I see the point of statements like this,
other than to feed our pre-existing Nerd superiority complex. Although I guess
by poking fun at sociology and other "normal kid" majors, we are getting back
for not being popular in High School, or something...

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karzeem
I second that. These kinds of arguments often go pretty quickly from "social
sciences are hard to study properly" to "social sciences aren't worth
studying." That's usually the main problem at companies that suffer from a
tyranny of the engineers (these companies typically have lots of smart people
and terrible UIs).

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amichail
One could argue though that theories in the social sciences are of greater
importance than most mathematical statements, even though they are less
predictive.

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mynameishere
Rather striking that such a sentiment would find approval here. I'm not sure
how you might actually defend such a statement. I would defy you to produce
any fruits of sociology that are comparable to those of mathematics
(remembering that everything in science and engineering hedges upon math).

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Alex3917
I defy you to show me a math book that makes no use of the written word or
alternative forms of communication. Clearly linguistics is the most important
subject and mathematicians are just a bunch of derivative hacks. :-)

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eru
<http://nrich.maths.org/public/viewer.php?obj_id=1382>

(Not quite there, yet. But trying.)

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ced
Wow, it didn't even cross my mind that the quote was a "bash" on social
sciences. My title picked on sociology because it seemed like a clearer case,
but the quote lumps evolution among the "ambiguous sciences" as well. I very
much agree. I also think that evolution is much more beautiful than anything
I've seen in Maths so far.

I found it interesting, because it's the first time I internalized that
ambiguity _prevents_ long chains of arguments, because fuzziness is
multiplicative (so to say). As a corollary, if social behavior was not
ambiguous, sociology would be potentially just as deep as physics.

The quote actually has very little to do with the rest of the book. It was
merely a prelude to their discussion on the evolution of societies, which is
one of the Major Transitions.

The last remark is cool too, "it may be that no operative theories are
possible in the social sciences", because it applies to biology as well. We do
have _some_ operative theories on evolution, but there's absolutely no
guarantee that every phenomena has a simple holistic explanation. As far as
I'm concerned, we still don't have a proof that evolution (Darwin's axiom)
could lead to complex structures. We just have a lot of very convincing hand-
waving.

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iamwil
I don't know what the larger context of the quote it, but as commented by
others, it can certainly be taken out of context as support of a nerd-
superiority complex.

That aside, the nature of the "soft sciences" is that you can't very well
conduct controlled experiments, because it is unethical, or it is hard to
control all the variables. So current soft sciences plod about trying to
gather some type of predictablity in their theories, but often falling back to
trying to make causal statements of their experimental observations.

I think there's been attempts before, like cybernetics, that tries to model
human behavior using signal processing techniques. To my understanding, it's
since fallen out of favor. So while it's been tried before--and I don't know
for sure, but my gut says that there probably is mathematics, other than
statistics, to bring more analysis into the social sciences.

Otherwise, the math just hasn't been invented yet. Currently there are studies
in nonlinear systems, complex systems, and math of intervation and
manipulation. My shallowly informed guess is that one of these will help out.

Or else we just have to wait for a Physicist to help us out here.

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henning
the useful material in sociology is, evidently, phrases and ideas created by
sociologists that are now widely accepted and commonly used.

i have no reservations, however, declaring that by and large undergraduate
sociology education is bullshit.

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fauigerzigerk
Mathematical statements are not unambiguous if you mean anything more than
just syntactical consistency, which is by definition meaningless. Maths is a
means to make statements about the world and thus depends on analysis and
modeling. Modeling is by no means unambiguous as anyone who ever created a
data model will be able to confirm. So maths is either meaningless or
ambiguous if seen in its application context.

The issue goes even deeper. You could argue that the above argument is a
semantic trick, because modeling is outside the realm of maths as a science.
But even the formal foundations are in doubt if you consider Goedels
incompleteness theorems
([http://en.wikipedia.org/wiki/GAXdel%27s_incompleteness_theor...](http://en.wikipedia.org/wiki/GAXdel%27s_incompleteness_theorems))

Sorry, the link is broken. Apparently this forum doesn't support umlauts in
URLs

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ced
First, I do think that modelling is in the realm of physics, biology, etc.
Mathematicians might make unambiguous statements about these, but they never
claim that the model is a good representation of reality.

Second, Godel's incompleteness theorem is about incompleteness, not ambiguity.
The statement x = y + 10 is unambiguous in the sense that all mathematicians
would always interpret it in exactly the same way. There is no question that x
= 12, y = 2 is consistent with that statement, and x=y is not.

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awt
I'm a sociology nerd. If you want to understand how important sociology is,
and how clearly it can be reasoned about, read Eric Hoffer. If you want to
understand how important it is to understand how we evolved, read "Before the
Dawn."

Also, I like to look at sociology as the study of complex systems - extremely
complex systems. It is difficult to study systems over which you do not have
complete experimental control, however it is possible to view history as a
series of experiments.

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adamsmith
This statement, while true, doesn't make sociology unworthy of study or
investigation. One of my favorite political science professors in school
claimed on the first day of class that poly sci is a science. But they have
few data points, and can't perform experiments, so they actually have a harder
job.

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Jd
Natural language does not have to be ambiguous. Numerous scholastic movements
from Plato's Academy to the Confucians have attempted to enable us to speak
with greater precision.

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altay
Sociology's gonna get a lot more interesting -- and more math-like -- in the
coming next few years, now that we can quantify mass behavior and social
interactions.

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dfranke
I don't understand your comment. What has changed?

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danteembermage
Hari Seldon has finally completed his life's work?

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curi
But there isn't any ambiguity in the theory of evolution.

