Home Forums FineTunedMac Community Lounge Unexplained Scientific Principles

In the previous lounge, during one of the long and vigorous discussions that evolved into faith versus science (I think it was a thread that started out talking about nature), someone mentioned two basic scientific principles that scientists are still unable to explain and which are accepted as "that's just the way it is".

Does anyone recall what they might have been or, barring recollection, just know what they are?

ryck

"Non-troubleshooting technical issues belong in the Lounge" was probably one of them.

I don't remember that specific thread but I can take a guess about one of those principles. Physics is based upon mathematical representations of reality. Obviously, the math is successful at predicting the behavior of physical objects. We couldn't get to the Moon, for example, if the opposite were true. AFAIK, nobody understands why physical objects follow mathematical rules. Math is a human invention, not an object.

"Actually", math/physics/etc is an deduction based on observable phenomena and then becomes inductive when used to predict phenomena.
And don't forget abduction ... and all things which pull stuff apart and then put it back together again.

You omitted seduction, which brings things together.

Mea culpa, although methinks that would fall into my last category.

Jon, it could be the other way around: It is not that objects follow our math rules, it is that the rules are tailored to the objects. We definitely are quite advanced in that domain, I guess. But coming back to the original post, we see that a lot in biology. The same molecule has different effects on different cell types having the same signaling machinery. The cell type-dependent effects are unexplained in general - this is just the way it is...

I'm not quite sure about this. Pure math is abstract and its own world. Yet, arithmetic, algebra, trigonometry, calculus, etc. seem to be involved in the "real" world. I don't think that mathematicians necessarily tailored their theorems to physical objects. (Of course, one could make that claim about geometry and trigonometry.)

Quantum mechanics is just plain weird by the standards of our everyday experience but it seems to predict sub-atomic behavior quite well. My violin student has a Ph.D. in physics and actually understands quantum theory. I made the remark that that theory is somewhat more comprehensible than the US Tax Code but he said that they were equal. Quantum Theory allows for parallel universes and the IRS seems to exist in one. I don't know where politicians fit into all this but that's for future generations to explain.

Macnerd10 has it right Jon. You have the cart before the horse. Physics is not based on mathematics it is based on observed physical phenomena which in turn can be modeled mathematically. Albert Einstein created his theories, and he was always careful to call them theories, by observing specific physical phenomena, working them out as a "story problem" describing why the phenomena might occur, and only then developing a mathematical formula to model his story. Of course if he could not model it mathematically he might have to rethink his story.

Virtually every physical, and even human activity, can be modeled mathematically. In some cases the model can be devolved into a single specific equation such as E=MC², others require a complex set of related equations, and still others require modeling using a mathematical heuristic. As the mathematics and the phenomena are better understood the more complex formulations tend to become simpler and less complex. I once took a course where we spent an entire semester understanding the implications of a 47 step equation modeling a single process. Two days before the final exam another researcher published a paper that reduced the 47 step equation into a single equation with 4 variables. (My professor humanely elected to hand out a copy of the new formula instead of the final exam and gave everyone in the class a Pass.)

The beauty of this is once the math has been worked out, it is possible to infer from that math phenomena that have not yet been observed and in fact may never be directly observable. The current very exciting theoretical physics work in string theory being a prime example of the latter.

Mathematical modeling is not limited to physics and the {i]hard[/i] sciences, but as macnerd10 has indicated can easily extended into the biological sciences or in fact virtually any field of study. How about modeling the behavior of customers in the line(s) at a MacDonalds -- been there, done that. the ultimate modeling is summed up in General Systems Theory.

Bingo. The math that is used in physics represents a model of the observed facts. We observe the way the physical world behaves, we construct models that match the observed reality, then we use those models to predict the behavior of the physical world and see how closely the world matches the models.

Some of these models are mathematical in nature. That doesn't mean the physical world is mathematical; it means that certain types of math can be used to construct models that match the behavior we see in the physical world. Not all of these models are mathematical, and not all math models the physical world.

Many thanks to macnerd10, joemikeb and Tacit for their clear, concise explanations. If only economists could come up with accurate equations...

but that has nothing to do with math. it's all voodoo!

Isn't that what I said, far more economically?

Actually Jon the class I mentioned was a graduate economics course. The primary economic models over the last 50 years been based on two critical assumptions first propounded by Keynes:

1. The markets are at their core rational and
2. the major players in the market would always act out of informed self-interest

Unfortunately as Alan Greenspan said, he never dreamed the big players greed would overwhelm their informed self-interest, but it did. Once that happened the markets were no longer acting in a rational manner or viewed another way, the collapse was a rational, albeit disastrous, reaction to an irrational system.

It is possible to anticipate irrational behavior in a system and there were many who were predicting the eventual crash but they were uniformly ignored because their rational arguments carried little or no weight in a system that had become almost totally irrational.

You mean that IRS takes our money in this universe and spends it on something in the parallel one?

Ah, that's a horse of a different color. Economics bears no resemblance to science of any kind. Your arguments vis-a-vis mathematics may be correct but your example is not a good one.

Perhaps someone can answer the original question in this thread.

Thanks Jon:

This thread is a good example of what has always made the Lounge shine, IMHO. You can ask about one thing and then get a great education in something related.

I may have phrased my question poorly. As I recall, the previous thread had got to a point where there was back-and-forth about the wisdom of believing in things that can't be proven. Someone made the point that such reliance on accepting the unproven existed in science.

I seems to be me that they mentioned two particular principles or theories - may even have been The Theory of ______ and The Theory of ______, - on which a lot of ensuing science didn't work unless you first accepted these two unknowns as true.

ryck

That was me; I argued then, and continue to argue now, that accepting things on faith, without evidence, is a mistake.

The argument that science accepts things that aren't proven is often made by those who favor believing in things on faith, but it isn't a good argument. There are axioms in mathematics that can't be proven formally (such as a thing is always equal to itself), but the body of human scientific knowledge does not rest on these axioms; it rests on observation. Any theory is only as good as the next bit of evidence that refutes it.

A scientist does not accept "the earth's gravity imparts an acceleration on an object equivalent to 9.8 meters per second squared" as an axiom; he goes out and measures it. Again and again and again and again. And then he refines his tools and increases the precision of his measurements, and measures it again.

The force of gravity is not math; the math describes the behavior of gravity. There's a difference. The animal that lives in my house is not a big black dog; "big" and "black" and "dog" are simply arbitrary sounds used to describe it, but it is an animal that exists without those words, so arguments about semantics do not change the reality of its existence any more than arguments about axioms in mathematics change the way that gravity behaves. Even in a different language, the pet in my house would be the same; even in a different mathematical system, gravity would act the same way. It's important not to confuse a thing with the model or language that we use to describe the thing. Attacks on axioms of a mathematical language do not mean that the universe's properties are based on things that can't be proved.

Faith is believing in something without evidence to support that belief. We have evidence to support the belief that gravity behaves in thus-and-such a way; we do not have evidence to believe that there is an invisible man who lives in the sky and spends a great deal of time thinking about what kind of clothes people should wear and how people should have sex.

One of the problems with accepting any belief without evidence is that you have no referent to decide whether or not that belief has any bearing on reality or not, as the world's thousands of religious faiths can demonstrate--they can not possibly all be right.

And to use your own philosophical principles against that: such things as "an invisible man who lives in the sky" could exist... whether or not any proof can be demonstrated. If there is a 'Creator' out there somewhere, he/she/it doesn't need **your** belief in order to exist. The real problems arise when mankind tries to politicize the debate with dogma (and dictatorship, and war, etc).

Though it got bad reviews from the critics, i do remember enjoying the book "The Tao of Physics"  a few decades back.

I cannot recall the quote precisely but the great mathematician and physicist, Albert Einstein, was quoted as saying something to the effect that no amount of experimentation could prove any of his work to be true and it would take but a single experiment to prove it false.

We accept scientific evidence and the mathematical models as true until a better explanation comes along, we learn more about the observed phenomena, or it is proven to be wrong. In that sense I contend we do take scientific theory on faith based on what we know and can explain at any given point in our understanding. I was taught atoms were the smallest elements of matter, then there were protons, neutrons, and electrons, that lasted until quarks came along, and today the theoretical physicists are working on string theory as the one in the same largest and smallest elements of matter and energy.

It strikes me that all scientific knowledge is genuinely a working hypothesis that we accept on faith as true until more or better understanding comes along.

Not responding to Hal, just contributing to the thread . . .

Mathematical modelling of the physical world is bound to have a "faith" component. I'm not talking about an Old Man With A Beard, or the Flying Spaghetti Monster.

Suppose there is an isomorphism between a complete mathematical model, and the physical laws of the universe. Then by Gödel's Incompleteness Theorem, our mathematical model must have unproveable truths, and this would, by our isomorphism, mean that the real world must also have unproveable truths - i.e. things that must be taken on "faith".

I generally agree but the word "faith" makes me uneasy. When we say in papers "we believe" it does not imply that it is our faith, rather our understanding. This is why a lot of science people like the expression "working hypothesis, which implies that it mimics the real-life situation reasonably well but has room to be changed if new evidence is obtained. The original post was about "it is just as it is", which again is not about faith but about our total lack of understanding the phenomenon, whether we can describe it, measure, or create a model of it using math. Bottom line, I guess, we are all fairly correct and on the same ground.
Just one word of defense for John. When physicists describe some, say, new particle, as a prediction using a mathematical apparatus, and then discover it by experimentation, it is very easy to believe that the object obeys our reasoning and calculations. Most would say that the prediction was correct because we knew enough to make it, and the object is just still on its own, but we were able to model it correctly. This is one of the definitions of scientific discipline - whether it can make testable predictions. But it is so tempting to believe that if our model is advanced and accurate enough, the world may follow it by some higher law. Who knows?

Indeed, such an entity could exist. And it is unquestionably true that if such an entity exists, it will continue to exist regardless of whether or not I or anyone else believes in it.

One of the fundamental axioms of science, though, is that one does not benefit from believing that something exists when one has absolutely, positively no evidence to support that belief. There are literally billions of things that could possibly exist--a secret alien base on the far side of the moon, a gigantic omnipotent sky-dragon that called existence into being with a flap of its mighty wings, a caterpillar with an infinite number of legs wrapped in a ball around space-time outside the bounds of the physical universe, a cloned reproduction of Elvis Presley sealed in a ball of lucite in orbit around Alpha Centauri...I could, if I wanted to, spend months coming up with lists of things that could exist.

Hell, I could posit that the entire universe was created just exactly as it was about three hundred milliseconds before you read this post by being sneezed out of the nose of a supernatural, all-powerful being with a bad head cold. That could be the case; all of our memories could have been created along with us just a scant instant ago.

But the point is, without any evidence, there is no reason that you should believe any of these things. And in fact, you don't. Even the most faithful person does not accept 99.99999% of all the things which have been accepted on faith throughout human history. When we're talking about beliefs which are not supported by evidence and for which no proof can ever exist, what tool do you use to decide which ones to believe and which ones to reject? How can you tell?



Not as long as you don't confuse the model with reality, nor believe that the model is a perfectly complete, perfectly accurate reflection of reality.

Models are useful precisely because they model only a portion of reality. As human beings, we can not understand the whole of the physical world all at once, so we create models that help us to understand specific bits of it at a time. The model E=mC^2 is useful in helping us to understand the relationship between matter and energy; the model Fg=g(m1 m2)/r^2 is a model that helps us understand the gravitational attraction between two bodies; the proton-proton chain is a model that helps us understand how hydrogen fuses into helium in a star.

None of these things is an attempt to completely model the physical world. Gödel's Incompleteness Theorem states that a formal mathematical system must be incomplete in terms of provable theses and internal consistency, but mathematical systems are not the same thing as models; models of the physical world are specific subsets of mathematics, and not all models are mathematical in nature.

No benefit? Who says so? AFAIK, scientists haven't derived any equations for love either... so what do they know? Put all the geniuses on the planet into a [sterile] building and supply them with barrels containing every element in the universe, plus an unlimited amount of every type of energy. With all that, they couldn't even create a cockroach. Life and love are supposed to remain mysterious wonders. Believe anything you want. Your guess is as good as mine (maybe).



"Reality" in terms of anything meaningful is what we perceive through our five senses. Take those away and not much matters. And i suspect our senses are far from perfect anyway (and are thus probably inadequate to truly define something as subjective as "reality").

Horatio:
O day and night, but this is wondrous strange!

Hamlet:
And therefore as a stranger give it welcome.
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

   --Hamlet; Act 1, scene 5

I also disagree. Many physics and chemistry predictions of the last century were based upon some theoretical calculations and conclusions but not on any evidence. When the new particles are discovered in physics, chances are that they have been predicted but no real evidence existed. We are not talking about star or planet discoveries because in many cases the orbits of the neighboring bodies were not as they should have been should no star/planet be present there. You may be right about benefits because they are hard to define, but this is definitely not a fundamental axiom of science. Suspicions and abstract mathematical predictions cannot generally be classified as evidence.