Science and math.

[Corribus]

No, I'll argue that Newtonian Physics is wrong. Maybe it's just the mathematician in me speaking, but I view scientific theories in black and white - a theory is either right or wrong; there is no middleground. The 'middleground' is just the case when we don't know, when we can't label the theory right, or wrong. Since theories can never be proven, we can't ever say a theory is right as well; we can just have a lot of confidence that it is not wrong. Therefore, in some sense, all theories are wrong, or middleground, where we don't know if they are right.

My friend Banedon, nice to see you around again.

It's quite unfair to say that Newtonian Physics is wrong. I will explain the reason to you briefly.

(1) For classical systems (balls rolling down hills, cannons firing, pendula swinging, etc.) it models observation perfectly, or, at least, to within such a degree of perfection that nobody would criticize it. Certainly, in principle using quantum mechanics or relativity to describe the motion of a baseball would be better. But would it be practical to use quantum mechanics to describe wavelike motion of a baseball in motion? After all, the wavelength of a 150 g baseball moving at 40 meters per second (a fast pitch) is approximately 1.1 x 10 -34 m. For reference, the diameter of a proton is ~ 1.5 x 10-15 m. So you're talking about a wavelength that is as many orders of magnitude smaller than a proton, that my height is smaller than the diameter of the milky way galaxy (well, not quite, but you get the idea)! So, using "correct theories" is not really practical.

(2) People in high school cannot learn quantum mechanics or relativity before they learn Newtonian Mechanics. As I've stressed, science is cumulative. And you must build your knowledge in order to tackle modern problems Newtonian Physics has many useful concepts, is valuable for every day life, and its quantitative deviation from "reality" is so minute for every day phenomena that it would be absurd to use anything else.

That's the purely logical view, but even on the less logical level I'll still have to say that Newtonian Physics is wrong. It's wrong because the theory cannot be infinitely extended to all situations conceivable, and also because it assumes concepts like absolute time, which is not the case. This doesn't mean that Newtonian Physics is useless; it's obviously sufficient for 99% of everyday needs. Nonetheless, the core ideas it champions are inaccurate, and therefore the theory is wrong.

If that is your criteria for rightness, then every scientific theory we have is wrong, and we might as go back and worship trees. The theory is not wrong, it's right for a restricted volume of possible circumstances. Call its underlying principles assumptions or approximations - it doesn't really make much difference. The fact is that if it predicts 99% of phenomena correctly, than 99% of the time it is right. For the other 1% we use something better. I understand what you are getting at, but being a stickler for perfection is a not very productive mentality for a scientist. It's also confusing for nonscientists, and deepening the void between scientists and nonscientists is not something I endorse at all.

But I'm sure that if someone can consistently conjure a leaf (for example) from thin air the phenomenon will be studied, analyzed and eventually explained.

When something happens that is very unlikely, we call it a miracle. In fact, even the unlikeliest event is possible in statistics, given enough rolls of the dice. There are no miracles. Just rare occurances.

Similarly, Darwin's theory of evolution can only work when life already exists. What caused life?

The answer is this - we don't know, but it doesn't mean we will never know.

Actually there are several credible theories.

Now we know the Sun rises because of the Earth's orbit and rotation,

Did you use Newtonian mechanics to come to that deduction?

PS: This is a point Corribus in which I think you may be mistaken.

What is?

How do you know we can never prove there isn't an afterlife?

By which I mean, of course, heaven. And no, you cannot prove, using empirical science, the existence of a nonempirical place.

[protecyon]

Great discussion everyone, particularly I wished to respond to the following excerpt from Brendon's post by elaborating on what Corribus has said:

It's wrong because the theory cannot be infinitely extended to all situations conceivable, and also because it assumes concepts like absolute time, which is not the case.

Well if we quantify whether something is right or wrong based on whether it can be infinitely extended to all situations conceivable then I think every single theory(scientific or mathematical) ever devised by mankind is incorrect. I think a more proper way of looking at this is that every theory is aimed at solving or explaining a certain problem domain. To use your example of Newtonian Physics, think of it as a theory that solves problems in the domain between the extremely small, and the extremely large. Setting up this domain for the theory would be akin to specifying a domain for a mathematical equation. As with mathematics just because the equation works for a limited domain does not mean that it is wrong.

[Mytical]

Ok, again my sarcasm is mistaken for something else entirely. By 'laughing at' I meant to express the fact that some of the fundamental ideas that were believed 1000+ years have since changed. People observed such things as the sun rising and setting and based on that Empherical 'truth' decided that the earth stood still and the sun revoled around it. In a 1000+ years our current scientific theories might be as 'laughable' as that.

Mankind is very vain. We look at things and say ok this is this and that is that. If any other intelligent life exsists out there they will come to the same conclusion. You say math is a universal constant. So our very limited observations determine that we can't not be wrong? Sorry, that is vanity at it's finest. One of the major problems with science is bias. Every experiment conducted has bias in it regardless of the conductors intention. We have social bias, educational bias, and other biases. It may not be conscious, but it is there. These bias always tilt research, maybe not much, but even a little is too much.

Example. You have a area, everybody goes in that area dies. Over 1 million 'test subjects' prove this, for every one of them died. Does that mean the million and first will die? Statistacally yes, but there are exceptions to every rule. Now if somebody else 100 years down the road came to conduct experiments in that area he would 'know' that if they sent test subjects into that area they would die, and his research (even if subconsciously) would be done with that in mind. Or conversely he would do everything to prevent it happening, and his research would then be altered in another way.

This is why I do not think our 'math' is indeed universal. It is vanity in itself to say that our math is the only possible math.

[Caradoc]

Drat. I got here too late and all the good points have already been made. Except maybe that it is important to distinguish between the methodology of science and the body of currently accepted scientific theory.

A great reference on this subject is Alex Rosenburg's 'Philosophy of Science: a contemporary introduction.' (There goes the Amazon gift certificate.)

And a footnote on the Big Bang. I saw an article saying that there are now equations that support the possibility that the 'bang' started not from a singularity but a highly compressed glob of protomatter. The implication is that there may be a cycle of Big Bangs and Big Crunches.

[Gaidal Cain]

By empiricism I am referring to the axiom of science which states that any empirical observation - by which I mean, any phenomenon I observe, the observable world - has a rational explanation that can, in principle, be explained using logic, deductive reasoning, analysis, experimentation, and theories themselves based on all of the above. I see no violation of this principle in any of your examples.

Actually, empiricism usually means that one believe that what one percieves with ones senses is what's real. In the context of science, it means that theories has to be confirmed by some data. The existance of a rational truth is actually not required.

[Jolly Joker]

Right, GC and Caradoc.

The point is, that empiricism doesn't want to EXPLAIN. Empiricism wants to DESCRIBE only. Therefore empiricism doesn't do any explanations, it only tries to DESCRIBE the world around us. The explanations are something else completely.
For example, it's one thing to come up with (observe) quantum phenomena, but it's another to come up with a theory of quantum mechanics and yet another to deduce from it that foretelling the future is impossible, since it is not possible to completely and fully determine a given state of a system.

Empiricism is basically just an instrument, a METHOD, and to come back to the issue here in this thread, to make actual use of it you need another instrument that got anything to do with empiricism or observation at all: Math.

I'll give another example. The empiric method is giving us the following informations:
1) No matter the point in space you are, if you watch the big objects like galaxies you will see that they are all moving further apart from each other.
2) They seem to do it ever faster (it looks like they are accelerating their process of drifting apart).

This is far from explaining the structure of the universe. What is happening does seem to hint on something we have problems to IMAGINE, not to mention observe.
In fact, the more information we get the more it becomes clear that "things" are not what they seem.

In other words, you need more than a method to actually EXPLAIN things.

[ThunderTitan]

It's quite unfair to say that Newtonian Physics is wrong.

So any mathematical formula that will always give the right result on a limited scale is right even if it has nothing to do with reality?

By which I mean, of course, heaven. And no, you cannot prove, using empirical science, the existence of a nonempirical place.

Hey, for all you know the Dead Gentlemen's Heaven Exploratory Society has observed and cataloged all the afterlife.... now all you need to do is die and find out.

[Veldrynus]

if for example someone miraculously recovers from AIDS after his parents pray for him, something may have happened on an esoteric level, where forces we have not even imagined and catalogued have come into play and somehow cured the patient.

Or the initial diagnosis of AIDS may have been wrong. Also, the patient could be genetically resistant to AIDS.

Esoteric? Crap.

[ThunderTitan]

Also, the patient could be genetically resistant to AIDS.

If he has he wouldn't have AIDS... he'd just be HIV positive. You can't be resistant to not having much of an immune system.

And you kinda missed Banedon's point btw.

[Corribus]

Ok, again my sarcasm is mistaken for something else entirely.

In dealing with serious subjects, perhaps sarcasm is best avoided, especially when it comes at the expense of precision in your language.

By 'laughing at' I meant to express the fact that some of the fundamental ideas that were believed 1000+ years have since changed. People observed such things as the sun rising and setting and based on that Empherical 'truth' decided that the earth stood still and the sun revoled around it. In a 1000+ years our current scientific theories might be as 'laughable' as that.

You clearly didn't read anything I wrote, or, if you did, you certainly didn't understand it. The geocentric model was not devised through experimentation or careful consideration of pre-existing empirical theories. It is not comparable to, say, quantum theory. To say that people from the future would treat today's version of quantum theory in the same way that we would treat the "theory" of geocentricism is just wrong. Quantum theory may be incomplete, but it was based on a large body of pre-existing experimentation and logical thought, and is able to correctly explain and predict an overwhelming amount of observable phenomena, from the behavior of superconductors to the structure of stars. Some have called it the most successful theory ever devised by humankind. Nobody would go back in time and laugh at it. Geocentricism predicts nothing, explains nothing, and was based on nothing except the very human assumption that we are the most important thing in the Universe. It is nonetheless important as a placeholder in the history of the origins of modern science. But that's about it.

Mankind is very vain. We look at things and say ok this is this and that is that.

You are very fond of saying this, but it's untrue.

You say math is a universal constant. So our very limited observations determine that we can't not be wrong?

You are putting words in peoples' mouths. In fact, I said quite the opposite.

One of the major problems with science is bias.

Yes, that's true, particularly before the advent of instrumentation and computers.

Every experiment conducted has bias in it regardless of the conductors intention.

No, that's not true at all. You *might* be able to get away with saying that interpretation of experimental results are open to bias, but a properly designed experiment is unbiased. You demonstrate a complete lack of understanding of the scientific method.

Example. You have a area, everybody goes in that area dies. Over 1 million 'test subjects' prove this, for every one of them died. Does that mean the million and first will die? Statistacally yes, but there are exceptions to every rule.

Statistically yes? What does that mean? Statistics don't tell you what WILL happen. They tell you what PROBABLY will happen. Statistics by themselves are also meaningless unless you know what gives rise to them.

This is why I do not think our 'math' is indeed universal. It is vanity in itself to say that our math is the only possible math.

YOu haven't demonstrated your point very well, because I don't see how you arrive at this conclusion from the rest of your post.

@Caradoc: Yes it's often referred to as the oscillating universe theory.

@GC: Isn't that basically what I said?

@JJ: I have given you my definition of what I am referring to as empiricism, and what I am arguing about. Do not redefine it for me and then try to use your definition to show that I am wrong. I already stated that I am not endeavoring to argue for the encyclopedic definition of the word, whatever that may be. If you want to try to argue that I am wrong, you may start with MY definition.

[Gaidal Cain]

@GC: Isn't that basically what I said?

Not quite. There is no assumption in empricism that there has to be a truth out there. It is more part of the method for finding out about the truth, than an idea of how that truth is - empiricism doesn't say that it can find out everything, but that which we find by doing it is what we "must" accept as true.

[Corribus]

Well as I've stated I freely acknowledge that my definition of the word, at least in practice in this thread, is probably not synonymous with the accepted definition. I don't subscribe to the rigid belief that everything MUST be explainable or predictable by physical science - although it would not surprise me if this turned out to be the case. As I've stated before, when I use the word "empiricism" I mean: if you make an observation, that observation has an explanation that in principle can be understood through empirical experimentation and the scientific method. That is, it is never necessary to invoke God or supernatural phenomena to explain an empirical observation. A corrolary to this is that, given an empirical understanding for a physical observation, I can predict the circumstances, again in principle, under which I might make that observation again. I leave open the question as to whether there are non-empirical phenomena out there - and in this regard I acknowledge the possibility that empirical science does not necessarily lead to any ultimate, universal truth - but insofar as nonempirical phenomena cannot be observed empirically, then as far as the observable universe is concerned, the principles of empiricism - my version of it anyway - are the best means to achieve understanding.

[Banedon]

My friend Banedon, nice to see you around again.

Oh my! Seriously Corribus, you're a Professor and I'm a first-year Undergraduate, it's really a bit unwarranted to call me 'friend'

If that is your criteria for rightness, then every scientific theory we have is wrong, and we might as go back and worship trees. The theory is not wrong, it's right for a restricted volume of possible circumstances. Call its underlying principles assumptions or approximations - it doesn't really make much difference. The fact is that if it predicts 99% of phenomena correctly, than 99% of the time it is right. For the other 1% we use something better. I understand what you are getting at, but being a stickler for perfection is a not very productive mentality for a scientist. It's also confusing for nonscientists, and deepening the void between scientists and nonscientists is not something I endorse at all.

Yes, it's the mentality I hold in the deeper recesses of my mind but I never operate with it. I happily learn Newtonian Mechanics and Quantum Theory even though they're flawed and I happily apply them to solve problems as well. It's just that when it gets to ultimate logic (which is something I really like by the way) you can only say that Newtonian Mechanics is wrong, that Quantum Theory is wrong, and we're just refining theories one-by-one looking for a Theory of Everything (which is the only theory that is 'right').

So any mathematical formula that will always give the right result on a limited scale is right even if it has nothing to do with reality?

I suppose by most scientists, yes, it would be 'right'. I should add though that a vital essence in scientific theories is that the theory must be falsifiable - that is, it must be possible to prove the theory wrong. If you come up with a theory that there're Little Green Men on Mars who somehow have the reflexes to hide the moment mankind begins to look for them, you will have come up with a non-falsifiable theory because, short of blowing Mars up and looking among the debris, there's no way to prove the theory wrong. It's because of this that scientists - at least when practising as a scientist - have to assume no supernatural influences. The theory that 'God did this' simply cannot be refuted.

[Corribus]

Oh my! Seriously Corribus, you're a Professor and I'm a first-year Undergraduate, it's really a bit unwarranted to call me 'friend'

Well as much as I love the thought, I'm not a Professor yet, at least by the American definition. Right now I'm just a post-doctoral fellow. But insofar as I care very much about education at all levels, particularly undergraduate, I have no such lofty airs that I can't associate with college students.

we're just refining theories one-by-one looking for a Theory of Everything (which is the only theory that is 'right').

It's also a pipe dream. Until you learn that science is all about making good approximations, you are doomed to a life of frustration. In fact, learning how to make approximations, and how to identify a good one, is really much harder than learning the scientific principles upon which the science is based. Because that art is not taught in any textbook.

So any mathematical formula that will always give the right result on a limited scale is right even if it has nothing to do with reality?

I'm sorry, I didn't see this before until Banedon quoted it. To give a more rigorous explanation - yes, TT that is often true. As I mentioned above, practical science is all about approximation. When I teach quantum chemistry, it always comes as a surprise to my students when I tell them that, for any system more complex than a hydrogen atom (actually, any system with more than one electron), exact solutions are fundamentally impossible to achieve. It is not worth getting into why at this time but the point is that when I say this, I get sort of hopeless, annoyed expressions which basically are asking me: "Well then why are we here?" After all, if exact solutions are impossible, isn't quantum mechanics useless?

Obviously it's not useless. So how do we solve this seeming paradox? An example is as follows: the position (and other observable information) of a particle in motion - say an electron - is described neatly by a mathematical entity called a wavefunction. A simple wave function describes the probability of finding a particle at a certain position at a certain time (or over all times). It also hides information about a particle's energy, momentum, etc., if appropriate equations are used in conjunction with the wavefunction. Obviously predicting these observable values is thus contingent upon knowing the wavefunction. But this is easier said than done because - as I said - for real multielectronic chemical systems the true functional form of the wavefunction is not possible to really know, and the differential equations are impossible to solve analytically.

Thankfully, there exist a number of very useful approximation theorems. In essence, these approximation methods allow us to "guess at" the wavefunction and arrive at prediciton for observable quantities that are so good as to be almost exactly the same as the real values. In some cases, these "trial functions" have some basis in physical reality. For example, Molecular Orbital Theory, a theory central to the modern way that chemical physicists understand molecular structure and bonding, is based upon constructing molecular wave-functions using combinations of atomic wave-functions which themselves are exactly solve-able. However a "trial function" need not have such a rational origin. It is perfectly reasonable to pick any random mathematical function that behaves in a manner similar to the way that the unknown wavefunction in question would be expected to behave. Such functions have no basis in reality except for the fact that they offer a realiable approximation of the true, natural function that describes the system in question. They are also usually of limited use, because they are tailor-chosen for the system in question. Nevertheless, they are "right" in the sense that they can be used to predict real, macroscopic observable phenomena - on a limited scale - with quite impressive degrees of accuracy. This is done fairly routinely.

So, if that was a bit too technical for you I apologize, but mathematical tools do not have to have a basis in reality to be very useful to scientists to aid in our understanding of reality. The important thing is to know that an approximation is being used and how, if need be, the approximation can be improved.

[asandir]

holy christ .... my eyes are spinning around and around, and around, and around .... and I'm out of that trance .... good god man, go to a pub

Here I am starting to teach my son about adding and subtracting apples and oranges .... he's three btw

[Corribus]

Apples and oranges can have wavefunctions, too.

[asandir]

sometimes they fly as well, into my kids mouths like an airoplane .... but that's neither here nor there

[Mytical]

The addition of computers may have aliviated some bias, but they only know what was programmed into them. Unfortunately, bias does exsist in every experiment. It may be small, and barely effect the experiment, but unfortunately it is there. Lets take one experiment done by two different entities.

Lets say there is a drug A. Experiment from lab 1 shows that drug A has limited side effects and is well tolerated. They study 1000 people, documenting their findings.

Lab 2 however, shows a lot more side effects, and even 1 or 2 fatalities. They also study 1000 people.

Now the first question is why two experiments conducted identically would show different results. The reason is bias. Of the possible millions of people who might benifit from the drug the researchers select people (maybe subconsciously) that they think would either (in lab 1) be more likely to tolerate it or (in lab 2) be less likely too. Any experiment is the same. It may be very minor, and even not seen by the naked eye, but there is always some bias. Even experiments done by computers, for they only know what they are told.

[winterfate]

So true Misty!

[asandir]

it is a truism that the outcome of any study depends purely on who is conducting it