Just because you can buy antacids at a 7/11 that doesn't mean 7/11s are pharmacies.

The interdisciplinary point was made. Thanks.

Lol ok

pass the wrench ... pls

ok ok ... here's a quote:
"In most sciences one generation tears down what another has built, and what one has established, another undoes. In Mathematics alone each generation adds a new storey to the old structure." ~ Hermann Hankel (1839-1873)

I would agree with most of what semck wrote. Math is separate from other sciences in that it is a body of knowledge that is acquired in a fundamentally different way, i.e. by logical reasoning from axioms (assumed truths) rather than by comparing theory with observations of nature. This does not make math better or worse than other sciences. It's just fundamentally different. You can go ahead and call math the mother of all sciences or just a tool for the other sciences but in the end that's just a subjective personal judgment. There are arguments to be made for either statement.

In math it is possible to pick another set of axioms and deduce a new but entirely consistent theory with completely different properties. Euclidean geometry versus non-Euclidean geometry would be an example. For many centuries mathematicians have tried to prove that the parallel axiom of Euclidean geometry follows from the other Euclidean axioms (which would make it a consequence rather than an axiom, or a redundant axiom if you will). It turned out however that the parallel axiom does not follow from the other axioms and that you can in fact construct geometries that meet all the other Euclidean axioms but violate the parallel axiom. And thus the parallel axiom is essential to Euclidean geometry.

Now there is no point in saying that Euclidean geometry is valid and non-Euclidean geometry isn't (or vice versa). They just follow from a different set of axioms. Neither makes any claims as to how nature works.

Now (natural) sciences most often formulate their hypotheses, models and theories in mathematical language. As such math can be used to figure out the consequences of hypotheses and thus help figure out ways to test them against observations. As such math is an important tool in applying the scientific method because the scientific method requires logical and consist reasoning which math is excellent in providing.

Conversely, nature has so far turned out to be remarkably consistent and logical and hence math is a great way to find and formulate theories that might describe nature correctly. That's basically what string theorist are doing. This approach has proven quite productive historically (although so far not so much for string theory). Still, after all the math has been done, scientifically the prove of the pudding is in the eating, which is to say in the comparison of the predictions with observation of nature. Newtonian mechanics for instance is a beautifully consistent theory from a purely mathematical perspective. In the end however, as measurement devices got more accurate, it still turned out that nature works quite different on small scales or at high speeds.

Now does that mean that string theorist aren't scientists? I would say that yes, they are scientist. They are just focused on a particular part of the scientific method (formulating falsifiable theories) and leave the actual falsifying to others. Saying that string theorists aren't scientists is IMO much like saying that goalies aren't soccer players. For with the same line of reasoning you could argue that experimental scientist that don't develop their own theories but just test theories proposed by others aren't scientist because they don't partake in certain aspects of the scientific method. Science is a team effort. As long as they work together there is no need for every scientist to play the entire field.

Math:
"The process of discovering new mathematics is much messier, full of the pursuit of directions which were naïve, fruitless or uninteresting.
So one should be unafraid to ask “stupid” questions, challenging conventional wisdom on a subject; the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing." ~ Terence Tao

"Science"
"Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed." ~ Blaise Pascal

Engineering:
"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction." ~ A. Einstein

Oscar,

Great post. On string theory, I don't have strong views, but I think that where the people who think it's not science would disagree with you is where you say that its creators have formulated *falsifiable* theories. People have yet to come with even a conceptual way where you could falsify string theory, so it's accused of being much like saying that there are 100 angels dancing on every atom, which also wouldn't seem to be falsifiable, and probably isn't science.

Anyway, this seems like a great time to post this classic article, by the physicist Eugene Wigner.

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

What I meant to say is they try to formulate falsifiable theories, but yeah not much in the way of success on that front so far.

"Science" isn't the be all end all of everything. People's self esteem is too attached to being science. Science doesn't really help in theory formulation, which is why string theorists shouldn't give a damn if their critics claim they aren't doing science.

"People have yet to come with even a conceptual way where you could falsify string theory"

Classic anti-string rant, Luboš Motl would say: http://physics.stackexchange.com/questions/15/what-experiment-would-disprove-string-theory/3177#3177

I fully agree that science has much to gain by embracing other disciplins and vica-versa. Archaelogy breing something that springs to mind. For example, if you have some time this is very good

https://www.youtube.com/watch?v=K60lChTkth8

@Putin

Although I get where you're coming from I don't entirely agree. Theoretical scientists don't work in a vacuum. The theories they formulate must at least match up with data observed so far or they would just be falsified immediately. For instance the theory of relativity matched the data that had until then been explained by classical mechanics.

It also often the case that observations that falsify an existing theory lead to theorist trying to formulate new theories that match the new data, i.e. sometimes new observations become before new theories and sometimes it's the other way around. In the latter case it is of course obvious that observations don't help theory formulation. In that case I'd say that practices from philosophy (in which you could include maths) are obviously more helpful than practices from the scientific method (or experimentation to be more precise).

True, ulytau, but Lubos is justly mocked for most of this stuff. The bulk of his "predictions" are actually predictions of other theories that string theory is supposed to encompass. What is needed is a unique or characteristic prediction of string theory. It's not enough to say, "Oh, string theory implies quantum mechanics, so if QM is wrong then so is ST."

fullham: "Archaelogy breing something that springs to mind."

Are you saying that Archeology isn't a science? It is.

Math is not a science. The reason is that with science, things are discovered. Math has a foundation on things we invent (the number line, base 10 counting system, etc) and then things we discover we can do with them.

Theorems are FAR different from theories. Math has the following:

Axioms: axioms are sets of rules we follow. We can decide on these rules and they are not proven true, merely true by decision.

Theorems are truths that have been proven based on a set of axioms. I can also prove other theorems to be true using other proven theorems.

Math theories we often call "conjectures"

Have you met Fulham? He doesn't think anything except his own field is a science.

"The theories they formulate must at least match up with data observed so far or they would just be falsified immediately"

We might not know enough about the data or be recording it correctly. I'm thinking for example of Neptune's orbit.

"True, ulytau, but Lubos is justly mocked for most of this stuff. The bulk of his "predictions" are actually predictions of other theories that string theory is supposed to encompass. What is needed is a unique or characteristic prediction of string theory. It's not enough to say, "Oh, string theory implies quantum mechanics, so if QM is wrong then so is ST.""

I'd say he's mostly mocked for being of the most "libertarian" physicists :) It's true that most of his suggestions would disprove QFT in the first place but that's because from a certain viewpoint, string theory is QFT with an upside. If we're only looking at testing predictions that are not part of established physics, I think his 6th point works.

What semck said...

If a new theory has no additional predictive capacity beyond what other theories already predict then Occam's razor should be applied, i.e. stick with the simplest explanation. In the case of string theory that means to not accept string theory at this point.

String theorist work on the premise that there must be a unifying theory that combines quantum field theory and general relativity. Although it's a very appealing premise, there is no basis for it in observation until a candidate unified theory actually predicts something that contradicts (at least one of the) separate existing theories.

Until then it might be nice to have a unifying theory that explains what we already know from existing theories, but as long as that unifying theory is much more complex than those other theories it really serves no purpose whatsoever except for the subjective appeal it has to some theorists.

@oscar, I am not sure. History is most definitely not a science. And yet it is the queen of logical subjects in my view ( even though it is not my field!). Hence, where archaelogy engages in historical discourse coming to likely conclusions, rather than facts I wonder. I also wonder about repeatable experiments, falsifiable data etc. but maybe I am being too rigid.

I fully take on board, however, that today's scientific facts are likely to be, what we call in England, tomorrow's chip paper.

@Putin

"We might not know enough about the data or be recording it correctly. I'm thinking for example of Neptune's orbit."

I don't see how this example contradicts my statements. People often say that Neptune was discovered because of irregularities in the orbit of Uranus that could not be explained by Newtonian mechanics. That's an entirely false statement though, they could be explained perfectly by them.

In any case, when Newton proposed his laws of motion those irregularities were yet unknown and thus his laws did in fact fit the then known data. In addition his laws were confirmed by many decades of further observations (new data).

And again, those irregularities in the orbit of Uranus could in fact be explained perfectly by Newtonian mechanics as well. One had simply to assume (theorize) the existence of an additional planet. That's exactly how the Newton's theories were used to predict Neptune's existence, i.e. if the theory is correct there must be an additional planet. This prediction was later confirmed by observation (new data) thus confirming, again, the validity of Newtonian mechanics.

Oscar makes good points. There's also sometimes some ambiguity along these lines for awhile. Dark matter is a great example. The simple interpretation of dark matter is that all of our theories of gravitation have been spectacularly falsified. Because there's so much data to the contrary, we prefer to posit so-far unknowable dark matter. Science is never as clean as we would prefer.

"I don't see how this example contradicts my statements."

It contradicts crude falsification notions of theory building/ testing. Just because there was an anomaly, doesn't mean the theory is "falsified" anymore than a new theory must account cleanly for all existing data else it is "falsified" from the get-go. They set up auxiliary hypotheses that took into account the anomaly - the planet of Neptune.

@fullham

"Hence, where archaelogy engages in historical discourse coming to likely conclusions, rather than facts I wonder."

All sciences come to likely conclusions rather than facts though. A part of being scientific is to be aware of and open and honest about the likelihood of your conclusions. Archeology is no exception there.

Theories in archeology are substantiated with very accurate measurements such as carbon dating and geological theories to date objects; biology, biomechanics and material sciences to deduce living circumstances, diets and habits from objects (tools, buildings) and (perserved) bodies of humans and their animals (for instance wear and tear of teeth and bones). In addition accurate information can be gathered about the region of origin of objects and materials providing information about cultural and economic interactions and migrations... Need I go on?

And surely, archeology also has a significant narrative aspect to it, that is less of a "hard" science (and what laymen tend to focus on mostly when they read about the subject). But still, any self-respecting archaeologist will make sure that his narratives fit the underlying data and venture into speculation only where the data allows it.

How is archaeology less scientific than anatomy? Or is anatomy not a science either?

I agree generally with Putin's statement that an anomaly does not falsify an entire theory. In a stable paradigm, a few anomalies are indicative that maybe not all the variables have been taken into account. When we start getting several anomalies and it seems like we have to start adding in more and more complicated subtheories or ideas to explain them, then the paradigm isn't stable anymore (non-normal state). If there is a competing theory with fewer complications that can explain the data as well if not better, then that's the one that's most likely to be true. Think geocentrism versus heliocentrism. I mean you can make the math work for an earth center system but it is complicated as hell and for each new heavenly body, it is likely that you have to add some more "auxiliary" hypotheses.

I can't agree more with semck's statement that "science is never as clean as we would prefer."

@Putin

Still, if a new theory doesn't fit the existing data then in order for it to be taken seriously it must have some testable hypothesis to explain the discrepancy. And yes hypothesizing that the existing data is incorrect rather then that the new theory is incorrect is one way to go. However you can only do that with small discrepancies. You can still not expect a new theory that is in wild contradiction with a vast amount of existing data to be taken seriously, which was the only point I was trying to make when I said new theories must fit existing data.

A "superior" theory has to do at least one of the following:
1. Explain the data in a "simpler" fashion (this mostly means mathematically for me since I was trained as a physicist).
2. Be able to predict something that the other theory could not, or predict something correctly that the other theory couldn't.

Or is that too simple?

I would argue that "conceptually simpler" might be a better criterion than "mathematically simpler," zultar. It presumably would be possible to create a really hideous theory of gravity using only high-school calculus and algebra, which would be as predictive as GR for the things we can observe (though it might require frequent updating); it would therefore be mathematically simpler than GR (which is mathematically very challenging), but it would be a complete kludge.

Just a thought.