Is the Unification of Sciences Possible?

[Fra]

What is your opinion that every different science, physics, mathematics, phychology are different views of the same thing.

Interesting question.

I have several times caught myself in a deja vu situation when thinking about seemingly unrelated problems. For example, I had a project some years ago trying to understand how a yeast cell works. And I eventually noticed that my own thinking converged into an abstraction of the "problem" that I had definitely seen before. And it came from thinking about foundational physics 10 years ago. The feeling I got is that the everyday problems at hand for me, and for a yeast cell are not that alienated. A cell need to regulated his metabolic systems for maximum benefit, I need to regulated my everyday activities for maximum benefit. So should I trivialized the problem of the cell, because my brain is much bigger? I think not. I came to think that, perhaps my problems are not much harder than the cells. My problems may be more complex, but OTOH my brain is bigger so perahaps the difficulty measures in some vague ratio complexity/cpupower is similar?

If we are considering methodologies, I think there is a lot in common. And I tend to think of mathematics and physics as living somehow in symbiosis.

Mathematics as far as I know was historically developed not just for "fun". I think it proved to be a powerful language in which we can accurately and quantiatively express many things that we face in nature. Similary I think science itself has developed, from various faith, opinions into a more systematic method of learning. Because clearly there is an utility in "how to learn", and make sure this method converges to something we can be confident in, rather than just "another opinion".

So from the point of view of philosophy of scienece, I see many interesting similarities between different fields of science. And the most interesting connection is to compare it's structure of method an utilities.

Certainly there is an utility in mathematics? And maybe one can imagine that mathematics with little or no utility (in any field) would be more unlikely to be developed.

What would physics be today without math altogether? And what would math be without any applications (utility) whatsoever?

Would it have been equally well developed just out of plain curiousity? I think not.

/Fredrik

 

[Fra]

The main issue is learning what words mean before you use them.

Maybe I am pulling this scentence out of it's original context, but in the light of the original topic (comparing math and physics, what can be loosely thought of as comparing language with what is beeing communicated), I thikn this is interesting.

A philosophical question is howto defined the meaning of words, when detaching them from it's environment of use?

I think development often develops new languages in the course of trying to something, and it may be a bit of a chicken vs egg situation. What comes first? Langauge or context? Do I start to speak because I learned howto, or do I develop the ability of speaking because I need it? I like to think that they go hand in hand.

So while it is silly to use a language you don't understand, it's equally to take the language out of context.

In a way I think mathematicians, does study the language out of context, but not quite. There is still an utility in this in the overall picture. Mathematics research would hardly be funded if it developed a language that had no utility.

So I think that the apparent isolation of pure mathematics and say physics is only apparent. At a deeper level of scientific development I think there is a connection.

/Fredrik

 

[Focus]

I think the reason why maths and physics is similar is due to the fact that physics is maths with added axioms. You need to draw these axiom from real life (such as continuous time, free fall acceleration, etc..). It is often that these axioms are wrong or incomplete or do not represent real life accurately. I think if there is an analogy to Godels incompleteness in the physics world, it is Heisenberg's uncertainty principal. They almost say the exact same things about the fields, that you can't know everything.

In my view, what logic is to maths, is what maths is to physics. It is a tool to use.

 

[HallsofIvy]

No, physics is NOT "maths with added axioms"! We do use mathematics in physics, just like we do in many other things- but there is no closer connection.

 

[CRGreathouse]

No, physics is NOT "maths with added axioms"!

Although that *does* sound like a good working definition for mathematical physics.

 

[Focus]

No, physics is NOT "maths with added axioms"! We do use mathematics in physics, just like we do in many other things- but there is no closer connection.

Ouch, I think I hit a physicist nerve there. Is there any physics theorem that is not expressible in mathematical formulae?

 

[Ygggdrasil]

Mathematicians invent self-consistent mathematical structures. Physicists attempt to describe natural phenomena with these mathematical schema. The science part comes in where you are determining which mathematical frameworks describe your physical system best.

 

[evagelos]

I think if there is an analogy to Godels incompleteness in the physics world, it is Heisenberg's uncertainty principal. They almost say the exact same things about the fields, that you can't know everything.

I am glad that someone finally saw an analogy-similaririty in mathematics and physics. Finally someone saw a boundary in these fields. A boundary that coexists. I have the sense that many other similirities-boundaries exist between these fields.

 

[evagelos]

We do use mathematics in physics, just like we do in many other things- but there is no closer connection.

Well, indeed we use mathematics like a tool to describe physics laws. Mathematics in another point of view is an expression-language that physics has. However mathematics do have limits. The limits of mathematics depend on the axioms that are set in the beginning.
The main limit of mathematic is not to have contradictions. Because in this case anything falls to pieces. You have not a step to stand. Mathematics can describe many univerces, however in all these universes the well known godel theorem says that always will be a truth statement (physic law or any other physics meaning) that can not be prooved.

So what can we do? In this case physics comes and introduce the experience of life.
I hope that nobody will say that other thing is life and other is physics?
The hypervasis of these limits is the life.The limits continue to exist. But the knowledge and cosmos seem a little more magical. I am happy that godel theorem exist. I would n't like to be in position to have the posibillity of having all the truth statements in my pocket. And this is validated by godel's theorem as CONTRADICTION.

 

[D H]

Ouch, I think I hit a physicist nerve there.

Before you make any more bright statements you should check Halls' profile. Click on his name ...

Is there any physics theorem that is not expressible in mathematical formulae?

How many times do you need to be told? Science has theories, mathematics has theorems. Mathematics and science follow different sets of rules.

Suppose that in 1910 a refinement of the Michelson-Morley experiment had shown a relation between the speed of light and the speed of the source/observer did exist. That experiment would have scientifically invalidated Einstein's axiom regarding the constancy of the speed of light: The end of relativity as we know it. On the other hand, those observations would not have invalidated that axiom mathematically. All of the neat mathematics that resulted from the axiom would have remained mathematically valid.

 

[evagelos]

Before you make any more bright statements you should check Halls' profile. Click on his name ...

What do you mean by that? i did not tell anything about hall's profile, however, i really do not like when people get blind from another human's profile. Just do not do that. It is not good respect for your shelf.

 

[evagelos]

Before you make any more bright statements you should check Halls' profile. Click on his name ...

How many times do you need to be told?

You sound as professor to a student. Have you got an idea for what i am talking? No..you painted them as bright?
There is axiomatic physics, think only the classical mechanic and the 3 Newton's law. How all the rest came (theorems)? By these 3 laws we sent human to the moon. These are mathetic axioms. However there was a truth, the quantum mechanic that could not come fom these axioms...new axioms a priori should be added.

You make a distinction between theory and theorems. Well, do you know what theory is? Theory is our opinion on how world works, but it can be exrpessed by axioms and THEOREMS. In fact any theory is constituted by AXIOMS and THEOREMS.

Thanks for your understanding

 

[D H]

What do you mean by that?

You made a stupid remark about hitting a physicist's nerve. Halls is a mathematician, not a physicist.

think only the classical mechanic and the 3 Newton's law. How all the rest came (theorems)? By these 3 laws we sent human to the moon. These are mathetic axioms.

Newton did develop new mathematics (the calculus) and then used it in the course of developing his laws of physics. There is, however, no new mathematics in any of those three laws. F=dp/dt is not new mathematics and is not a mathematical axiom. It is merely a mathematical expression using existing mathematics.

 

[Fra]

the reason why maths and physics is similar is due to the fact that physics is maths with added axioms.

There was already objections on this, but I also reacted a bit on this description, although I must confess it is what one might express when a pure mathematician takes on physics, but then he might not be interested in the physics itself.

You need to draw these axiom from real life (such as continuous time, free fall acceleration, etc..). It is often that these axioms are wrong or incomplete or do not represent real life accurately.

If we for a second consider that you insist of this view, that knowledge of the natural physical world (physics), is best accomplished by "finding" the axioms/postulates, from which everything else should supposedly follow by deduction, then you are decomposed the problem into a two parts.

And clearly the difficult part here is finding the right axioms or "fundamental principles" from which all else follows from deduction.

This traditionally leads us into a version of the philosophical problem of induction - howto soundly infer the future from that past. Hume's critics is that such deductive inferences is impossible, and while it might not be possible to prove, I agree with his inductive skeptisism.

Karl Popper who one might see as one of the founders of the modern falsification/hypothesis generation style of the scientific method tried to solve by bypassing the induction, and instead come up with the idea of putting hypothesis to tests, where one risks falsfying a theory by deduction. However Popper doesn't solve the whole problem deductively.

One question is the logic of hypothesis generation, in case the previous hypothesis was falsified. Clearly this is hardly a deductive process.

So my own interesting in physics lies at the level of the scientific method.

If you insist on thinking of it like axioms + deductions, then the real problem is how to soundly induce the axioms from experience - this is the scientific problem.

One you have an axiom or hypothesis on the table, for testing, it's easy. The interesting part is what I would like to call "resolving an inconsistency". This is where I possibly
associate to godel. I personally think this becomes more of an issues in the quest for quantum gravity.

I think the basic problem of natural sciences, is howto "infer" from experience and observations the laws of nature, and indirectly infere the future from the past.

So howto do that?

Clearly many questions appear here. And whatever inductive scheme we come up with, how do we konw this can be trusted? IMO we don't. But here is IMO, where three concepts come in, the logic of guessing, the logic of correction, the logic of evolution.

This is my very personal view of things, somewhat in line with many others who think inductive reasoning rather than deduction is the right way to go in physics. And IMO, there is a possible different solution to the problem of induction, that I think might give rise to a "new logic", it would turn the sometimes claim circular argument of induction, into a evolutionary argument. (Ie. the circle is a spiral).

Logic improves, science improves.

/Fredrik

 

[HallsofIvy]

Ouch, I think I hit a physicist nerve there. Is there any physics theorem that is not expressible in mathematical formulae?

That's a lot like saying physics is just English with 'additional axioms' because there is no physics theorem that is not expressible in English!

More to the point, there is NO physics theory (I perfer not to say "theorem") that is exactly expressible in a mathematical formula. All physics involves measurement which is not exact. At best, mathematical formulas can only approximate physics.

And, by the way, I am a mathematician, not a physicist.

 

[Focus]

Before you make any more bright statements you should check Halls' profile. Click on his name ...

How many times do you need to be told? Science has theories, mathematics has theorems. Mathematics and science follow different sets of rules.

Calm down. I didn't realize that people here were so serious. It wasn't ment to be an insulting statement, just a joke. Sheesh.

You are right though, they are theories. Been a while since I last did science. The word theorem kinda gets stuck in my head.

That's a lot like saying physics is just English with 'additional axioms' because there is no physics theorem that is not expressible in English!

More to the point, there is NO physics theory (I perfer not to say "theorem") that is exactly expressible in a mathematical formula. All physics involves measurement which is not exact. At best, mathematical formulas can only approximate physics.

And, by the way, I am a mathematician, not a physicist.

The mathematical formulae are physics. It is physics that constructs them and uses them. Their accuracy is also expressible in formulae. When I talk about physics I do usually refer to theoretical physics. A physicist will say that real life approximates his formulae. Also if you can approximate things than you can use probability and statistics. To me the uncertainty/approximations (and probability stuff for that matter) comes not because nature is that way but because we cannot gather enough information, at best we can guess what happens, thus we say it is distributed this way or that way.

I am glad you are a mathematician, we need more of us in this world!

 

[evagelos]

F=dp/dt is not new mathematics and is not a mathematical axiom.

Well, i am sorry to make you feel sorry but this law, is an axiom of experience. Do not see the big picture? This is axiom too.

And the matematical system that describes the 3 Newton' law, accept that also as axiom.

Axiom is more general idea that the narrow idea of mathematics.

 

[enricfemi]

What is your opinion that every different science, physics, mathematics, phychology are different views of the same thing. For example boundaries in physics speed of light, boundaries in mathematics (godel principle) or in phychology (the unexplained of the personality) exist and try to explain the world from a different prism.

it's determined by what "the same thing" is.
if that is the universe, yes, maybe yes.

 

[evagelos]

it's determined by what "the same thing" is.
if that is the universe, yes, maybe yes.

It means universe , you are right

 

[enricfemi]

then, i don't insist they are different views of the same thing.
i guess they are the same view of the same thing.
maybe, just maybe, there will be one day that philosophy, mathematics, physics, and phychology united into one word "science", or some other things.
because the relationship we haven't clearly find out by now, we identify them temporarily.