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Why Math is deeper than Sociology [quote]

12 points by ced ↗ HN
"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."

- Maynard Smith and Szathmary, The Major Transitions in Evolution

26 comments

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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.

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).
kcl
I don't read this as fuel for the hard-science superiority complex. It seems more like a defense for the methodology sociology uses.
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.
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).
amichail
Web 2.0 is one huge sociology experiment. Its scientists are entrepreneurs trying out new ideas and tweaking others with the goal of maximizing traffic.

As for more traditional sociology research, see:

http://en.wikipedia.org/wiki/Sociological_theory

mynameishere
Web 2.0 is one huge sociology experiment

It is...perhaps...a thing that falls under the rubric of "socialogical phenomena", but that doesn't really regard the science as such. It's just it's self-declared field of study. The science itself could have never existed and people would have still made webpages of various types.

Again, I don't think I need to point out that mathematics are a necessary condition (10,000 times over) for "web 2.0" to even exist.

amichail
Again, I don't think I need to point out that mathematics are a necessary condition (10,000 times over) for "web 2.0" to even exist.

I think it's more helpful to consider whether mathematics is at the core of most web 2.0 services or whether it is somewhat removed (e.g., part of an encryption library used by the service, part of building a computer, etc.).

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. :-)
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.
dfranke
I don't understand your comment. What has changed?
fauigerzigerk
I think he might be right, because what we see now is that a lot more social interaction in the broadest sense is conducted electronically and produces huge amounts of data. So, at lest, we get a chance to apply algorithmic techniques to these things. However, we're not very far along. It's more complicated to analyse biographies of criminals to devise effective crime prevention/rehabilitation measures than to figure out buying patterns in supermarkets.
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.
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.

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.
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...)

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

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.

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

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.