Physics Discussion Thread

Amber G. · Post by **Amber G.** » 28 Jun 2011 08:11

^^ Check out/google for "Tau-Theta puzzle
say Symmetry Destroyed: The Failure of Parity
(While parity is conserved in Strong or EM interactions.. not for weak interactions)

Rahul M · Post by **Rahul M** » 28 Jun 2011 09:05

kasthuri ji, that's what Amber ji referred to last page. I was asking how biological systems do it. there must be a mechanism.

vina · Post by **vina** » 28 Jun 2011 09:14

Amber G. wrote: (who is credited for discovering SOFAR) remained fairly quiet about his later work)

I had no idea that it was called "SOFAR". I just knew it as thermocline channels !

( A few things are still not that well known, outside specialized scientific world) Movie was ho-hum but the book described some parts and techniques of 'sofar' fairly accurately.. (this was almost 10 years before it got unclassified) .. I remember talking some interesting stuff with an US Navy scientist (Physics PhD and a student ) about that movie..

More than the Physics part of it, it is the engineering part of building a good usable sonar that is devilishly complex. It increases in orders of magnitude if you get into littoral and shallow waters, particularly with stuff like multi path reflections (the sea/air surface is a good reflecting boundary) and shadows, scattering , bottom effects and all that kind of stuff, along with the salinity and temperature gradients. Deep water tends to lessen these problems. Add to that it is the low frequency sound that propagates well and with minimal noise in water, but that does not make for very good discrimination (for eg, a sub lying in the bottom motionless or against the side of an underwater hill, it will be very difficult to discriminate with long wave length) and even if you manage to detect (say via a reflected mutlipath signal), it could be extremely difficult to get a firing solution.

vina · Post by **vina** » 28 Jun 2011 09:28

Amber G. wrote:Okay a puzzle...let us see what the gurus think...

It has more to do with down to the earth useful physics..No tensors or higher dimensions are involved..

There was a news paper story about four strong swimmers who drowned. All were young (18-20 years old) and the place where it happened was familiar to them, except at this time their haunt was engrossed with foamy water after a heavy rain. A waterfall close by was the cause of that foam and turbulence. One person slipped on a rock and fell into that water and other friends, one after other, to help, jumped and all died. The expert (police recovered the body) remarked that, that place was known as a "drowning machine"... and even the strongest of the swimmers would not have had any chance..."The laws of physics were against them".. it was remarked...

What laws of physics?

(If you have read the news paper story or heard its analysis .. please give others a chance to guess)

Probably some sort of vortex /circulation gets created at the foot of the waterfall, that tends to draw swimmers underwater ?

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 09:32

Amber G. wrote: I can still tell my left hand from right hand even if I am floating in water

Ask yourself *why* you can do that. I don't doubt that you can.

Anyway I am sure I am missing something deep...

yes, you are. You are ignoring the fact that you are a creature of training. Who trains the embryo? That is the crux.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 09:37

Amber G. wrote:^^ Check out/google for "Tau-Theta puzzle
say Symmetry Destroyed: The Failure of Parity
(While parity is conserved in Strong or EM interactions.. not for weak interactions)

Good example. And quite timely. Ask yourself how the K_long knew left from right as opposed to K_short.

The fact that *you* know it as a human being does not answer the fundamental question.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 09:51

Rahul M wrote:kasthuri ji, that's what Amber ji referred to last page. I was asking how biological systems do it. there must be a mechanism.

exactly. those who are so sure should be able to outline the mechanism/algorithm.

If not, they should fall in line and agree that it is a mystery.

What will it be?

Rahul M · Post by **Rahul M** » 28 Jun 2011 09:54

it's a mystery as long as we are not able to identify the particular mechanism.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 09:59

From Amber's link:

When Lee and Yang's paper appeared in the October 1, 1956 issue of The Physical Review, physicists were not immediately prompted into action. The proposition of parity nonconservation was not unequivocally denied; rather, the possibility appeared so unlikely that experimental proof did not warrant immediate attention. The physicist Freeman Dyson wrote of his reaction to the paper: "A copy of it was sent to me and I read it. I read it twice. I said, `This is very interesting,' or words to that effect. But I had not the imagination to say, `By golly, if this is true it opens up a whole new branch of physics.' And I think other physicists, with very few exceptions, at that time were as unimaginative as I." [6]. Hence, the initial reaction among most physicists to verifying parity conservation was not enthusiastic.

In their paper, Lee and Yang stated, "To decide unequivocally whether parity is conserved in weak interactions, one must perform an experiment to determine whether weak interactions differentiate the right from the left." [7]. And they proposed several experiments. One of the simplest experiments (conceptually) invovled measurements on the beta decay of cobalt-60. The idea involved orienting cobalt nuclei with a strong magnetic field so that their spins are aligned in the same direction. Beta rays (electrons) are emitted at the poles of the nuclei. A mirror image of the system would also show beta rays being emitted from the poles of the mirror cobalt nuclei, the only difference being that the north and south poles of the mirror nuclei would be reversed since they spin in opposite direction of their real counterparts. Hence parity conservation demands that the emitted beta rays be equally distributed between the two poles. If more beta particles emerged from one pole than the other, it would be possible to distinguish the mirror image nuclei from their counterparts. Thus an anisotropy in the emitted beta rays would be tantamount to parity violation.

This is an early example of symmetry violation.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 10:00

Rahul M wrote:it's a mystery as long as we are not able to identify the particular mechanism.

Bingo!!

kasthuri · Post by **kasthuri** » 28 Jun 2011 16:59

GuruPrabhu wrote:
Rahul M wrote:it's a mystery as long as we are not able to identify the particular mechanism.
Bingo!!

GuruPrabhu ji,

I don't deny that it is a mystery. But I don't understand why is this obsession in explaining everything that we know of into the language of math that we know - be it symmetric groups or Symplectic geometry. The math in its current form is simply inadequate to explain several things. A new kind of math (with different rules of deduction) needs to be developed from scratch. This is not an immensely difficult task. All we need to do is move away from classical logic to other logics which don't just hold on to modus ponens and modus tollens like anything. The incompleteness of first order logic is costing us a lot. Even a very simple axiomatic system such as the natural numbers with addition and multiplication is incomplete, meaning there are questions in the system which cannot be answered within the system. This is my contention.

brihaspati · Post by **brihaspati** » 28 Jun 2011 17:07

Maybe - symmetry is broken as soon as the embryo develops a head and a tail. Any thing that starts to elongate around that head-tail line [even if it is curved - it is still topologically equivalent to a line segment] as an axis will have rotational equivalent of different directions. If cells are programmed to grow out of the central stem and develop in contiguity - the initial "break in symmetry" [along the rim of the initial circular cross section] orientation could matter, and be a matter of encoded programming. Just a hypothesis.

kasthuri · Post by **kasthuri** » 28 Jun 2011 17:18

Why all this enthusiasm with symmetry, btw?

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 18:35

kasthuri wrote:I don't deny that it is a mystery. But I don't understand why is this obsession in explaining everything that we know of into the language of math that we know -

The operative word above was "mechanism". It doesn't need to be mathematical - use the language of your choice to explain it.

Amber G. · Post by **Amber G.** » 28 Jun 2011 19:10

GuruPrabhu wrote:
Amber G. wrote: I can still tell my left hand from right hand even if I am floating in water
Ask yourself *why* you can do that. I don't doubt that you can.

First there was just an .. assumption that I could not tell my left from right (when I was a kid)

Now question of *why* is being pondered upon ... Let me just quote Feynman..

On Causality

You see, when you ask why something happens, how does a person answer why something happens?

For example, Aunt Minnie is in the hospital. Why? Because she went out on the ice and slipped and broke her hip. That satisfies people. But it wouldn't satisfy someone who came from another planet and knew nothing about things... When you explain a why, you have to be in some framework that you've allowed something to be true. Otherwise you're perpetually asking why... You go deeper and deeper in various directions.

Why did she slip on the ice? Well, ice is slippery. Everybody knows that-no problem. But you ask why the ice is slippery... And then you're involved with something, because there aren't many things slippery as ice... A solid that's so slippery?

Because it is in the case of ice that when you stand on it, they say, momentarily the pressure melts the ice a little bit so that you've got an instantaneous water surface on which you're slipping. Why on ice and not on other things? Because water expands when it freezes. So the pressure tries to undo the expansion and melts it...

I'm not answering your question, but I'm telling you how difficult a why question is. You have to know what it is permitted to understand... and what it is you're not.
....

. You are ignoring the fact that you are a creature of training. Who trains the embryo? That is the crux.

What is the crux? That I am ignoring some fact?

kasthuri · Post by **kasthuri** » 28 Jun 2011 19:22

GuruPrabhu wrote: The operative word above was "mechanism". It doesn't need to be mathematical - use the language of your choice to explain it.

I don't know. I don't have the language to explain it. You haven't answered my question - Why this enthusiasm with symmetry, btw? Or anti-symmetry for that matter.

Added later: Should be rephrased in the light of the above post - What is this enthusiasm with symmetry/anti-symmetry.

Amber G. · Post by **Amber G.** » 28 Jun 2011 19:29

On parity .. I remember one of Lee's (Lee of CN Yang and TD Lee) popular lecture.. It went something like ..

Imagine there are two cars, side by side on identical roads.. both cars are also almost identical except one is American version (with drivers seat on left) and the other is Japanese (with driver's seat on right)..they are symmetrical...If there is a small dust particle floating in the right corner of the one car's tank ..there is an identical dust particle floating at the right corner .. ityadi ...Now both cars accelerators are pressed exactly the same amount..Will the cars go at the same speed?

The audience replied "yes"..

Lee continued .. "That's what every one thought before.. my work ended up in a noble prize for doubting that this is not the case in all the situations..

Then he continued to explain parity violation in laymen's terms ..

Wish more scientists gave more popular lectures these days....

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 19:32

Amber G. wrote:
. You are ignoring the fact that you are a creature of training. Who trains the embryo? That is the crux.
What is the crux? That I am ignoring some fact?

No, the crux is that the embryo is not trained. It is not such a difficult point.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 19:36

kasthuri wrote:
GuruPrabhu wrote: The operative word above was "mechanism". It doesn't need to be mathematical - use the language of your choice to explain it.
I don't know. I don't have the language to explain it. You haven't answered my question - Why this enthusiasm with symmetry, btw? Or anti-symmetry for that matter.

Added later: Should be rephrased in the light of the above post - What is this enthusiasm with symmetry/anti-symmetry.

Because all of modern physics relies on formulation of symmetry. All conserved quantities arise from a symmetry. To name a few:

energy = time translation symmetry
momentum = space translation symm
angular momentum = rotational invariance symm
charge = U(1) phase change symm

ityadi.

mass is not a conserved quantity, but it is proposed that it arises from a spontaneously broken symmetry.

the difference between matter and radiation is sought to be erased by introduction of a theory of supersymmetry.

The enthusiasm for symmetry is based on overwhelming success of symmetry groups in physics.

kasthuri · Post by **kasthuri** » 28 Jun 2011 19:45

GuruPrabhu wrote: Because all of modern physics relies on formulation of symmetry. All conserved quantities arise from a symmetry. To name a few:...

This is precisely what is called "physics envy"...

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 19:51

^^^ what does that mean?

Rahul M · Post by **Rahul M** » 28 Jun 2011 20:00

the point is that discovering this mechanism (unless it has been done already) would very likely to improve our understanding of biological systems by a huge margin.
and when a parallel framework is readily available in physics and it seems such a waste not to try to apply it at least to similar phenomena. I don't see why this has to be a source of angst against physics.

the framework of modern chaos theory owes much to research on weather phenomena, yet that doesn't stop physicists, biologists, chemists, economists and even bankers to shun the framework due to "meteorological envy"

Amber G. · Post by **Amber G.** » 28 Jun 2011 20:04

GuruPrabhu wrote:
kasthuri wrote: I don't know. I don't have the language to explain it. You haven't answered my question - Why this enthusiasm with symmetry, btw? Or anti-symmetry for that matter.

Added later: Should be rephrased in the light of the above post - What is this enthusiasm with symmetry/anti-symmetry.
Because all of modern physics relies on formulation of symmetry. All conserved quantities arise from a symmetry. To name a few:

energy = time translation symmetry
momentum = space translation symm
angular momentum = rotational invariance symm
charge = U(1) phase change symm

ityadi.

mass is not a conserved quantity, but it is proposed that it arises from a spontaneously broken symmetry.

the difference between matter and radiation is sought to be erased by introduction of a theory of supersymmetry.

The enthusiasm for symmetry is based on overwhelming success of symmetry groups in physics.

Good post. Very clearly written. Thanks.

kasthuri · Post by **kasthuri** » 28 Jun 2011 20:07

Guru Prabhuji,

By saying "physics envy" I assumed that you are treating a biological phenomena as a *conserved quantity*. Why do we need to put biology into the ambit of the physics that we know? Please ignore this if my assumption is wrong.

kasthuri · Post by **kasthuri** » 28 Jun 2011 20:15

Rahul M wrote:I don't see why this has to be a source of angst against physics.

I would like to make it clear that in no way I am against physics. Physics is as beautiful as it is. I am just against the non-trivial reductionism.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 20:23

kasthuri wrote:By saying "physics envy" I assumed that you are treating a biological phenomena as a *conserved quantity*. Why do we need to put biology into the ambit of the physics that we know? Please ignore this if my assumption is wrong.

Yes, physicists can be blamed for thinking that all physical phenomena are based on universal laws. Biological processes are also considered to be physical processes.

Everyone is free to make up their mind regarding this. Some may invoke things like spirituality or God to explain life forces. Others may formulate biological principles that are outside the realm of physical principals. It is all cool.

I belong to the school of though that believes in cosmology as the history of the universe and evolution as the history of life on earth. If better explanations are made available I will gladly change my mind.

This may be termed as envy or whatever - it is just a statement of a set of beliefs. Ultimately, there is no absolute proof for this choice.

I don't think that physicists are causing any harm to anyone by pursuing research within this set of axioms. It should be easy to ignore this minute fraction of the world's population.

Since this is the physics dhagaa it seems appropriate to discuss physics here. Surely, there are other venues for discussing envy.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 20:34

kasthuri wrote:I would like to make it clear that in no way I am against physics. Physics is as beautiful as it is. I am just against the non-trivial reductionism.

IMO, the reductionism in biology has been achieved by biologists themselves.

First, it was claimed that all known species arose from single cell organisms and evolved over 100s of millions of years. This has the effect of reducing the rich diversity on planet earth to amoeba.

Second, it was claimed that basic proteins are the most fundamental life form.

Now, it is believed that the fundamentals of life actually reside in DNA code. Isn't this reducing biology to abstractions?

So, why is physics doing the reduction? All physics is saying is "hey, now that you have reduced the problem to a level we can understand, we can get into the game of explaining it also"

kasthuri · Post by **kasthuri** » 28 Jun 2011 20:46

GuruPrabhu wrote:Biological processes are also considered to be physical processes.

Guru Prabhu ji,

Don't get me wrong. It is not my intention to keep the forum discussing topics away from physics or talking philosophy. This is a wonderful forum and I want to keep the spirit of it going. I am simply failing to understand why biological process are considered as a physical process. Is it because everything is ultimately made up of atoms? I am a lay person enquiring and just hoping to get your reasoning behind this assumption. Again, it is not a debate, but a attempt to understand how physicists think about biology. Being relatively new to biology, I see a wide difference between the worlds. I only wish things were more connected, logic forming the foundation.

Thanks.

Amber G. · Post by **Amber G.** » 28 Jun 2011 20:48

GuruPrabhu wrote:No, the crux is that the embryo is not trained. It is not such a difficult point.

But sir ji - How do you know that embryo is not trained? What is the definition of training? Do we need a power point presentation before it can be called a proper training? Can DNA/gene "instructions".. be a part of the training?
Just thinking out loud..no need to answer

To me there are two separate aspects. a) There is enough data (embryo is not an ideal symmetric sphere) that a embryo can (theoretical possible) find its 'left' from its 'right' ..b) How exactly it does that may be more interesting etc but it does not violate the present understanding of left/rightness ityadi...

kasthuri · Post by **kasthuri** » 28 Jun 2011 20:53

GuruPrabhu wrote:First, it was claimed that all known species arose from single cell organisms and evolved over 100s of millions of years. This has the effect of reducing the rich diversity on planet earth to amoeba.

Second, it was claimed that basic proteins are the most fundamental life form.

You are absolutely right. There is no consensus in biology as we have in physics. That's the fun of it...isn't it?

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 21:01

kasthuri wrote:I am simply failing to understand why biological process are considered as a physical process. Is it because everything is ultimately made up of atoms? I am a lay person enquiring and just hoping to get your reasoning behind this assumption. Again, it is not a debate, but a attempt to understand how physicists think about biology. Being relatively new to biology, I see a wide difference between the worlds. I only wish things were more connected, logic forming the foundation.

Well, the reasoning is quite simple really. Physics believes that the universe arose as described by big-bang cosmlogy.

This event happened about 14 billion years ago, and the universe then evolved according to the laws of physics. No one will claim that *all* laws are known - the claim is that there were *some* set of laws that governed the evolution of the universe.

No one also claims that they know *how* these laws came into being.

Now, the main point. Biology/life was not present in the universe at that time. Even planet earth was not present at that time.

So, when life did emerge on planet earth, billions of years later, it makes sense to believe that the same laws that were governing the universe until that point of time were also responsible for life creation.

Why would one believe that some new laws/principles came into being specifically for planet earth and created life?

[well, we all know that creationists believe precisely this.]

Hence, it is logical to believe that Biology just emerged from the original set of laws. All physics wants to do is understand these laws.

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 21:08

Amber G. wrote: To me there are two separate aspects. a) There is enough data (embryo is not an ideal symmetric sphere) that a embryo can (theoretical possible) find its 'left' from its 'right' ..b) How exactly it does that may be more interesting etc but it does not violate the present understanding of left/rightness ityadi...

Let me try a thought experiment on you.

Suppose I put you in a pitch dark room and give you 10 balls. I give you a pen and ask you to put an "x" on each ball.

Now, if the balls were all identical white balls, I can always rotate them so that all the "x"s line up.

However, if the balls were one hemisphere while and one hemisphere yellow, you will see two kinds of balls -- with x in white or x in yellow.

The equator breaks the symmetry - no problem. But, the x can go either way.

In the case of the embryo, it manages to put the x always on the white side.

The embryo floating in a womb is analogous to you in the dark.

Can DNA/gene "instructions".. be a part of the training?
Just thinking out loud..no need to answer

Yes, that is the point of how this thread started. DNA breaks "handedness" in its helix. So, it seems likely that it breaks parity in the embryo evolution also.

Or, it could be just a coincidence

kasthuri · Post by **kasthuri** » 28 Jun 2011 21:30

^^^ Thanks. All I can say is that if biologists are struggling to find any law, physics has a long way to go! Creation is one aspect of biology which may be due to physical laws at the beginning of evolution. Sustenance of life is completely different ball game altogether. Just to think about routine DNA duplication and programmed cell death drives me nuts! Also, to bring the entire bio process to physical process based on few events looks unfair. May be it is a starter - and the only option that we may have...

Amber G. · Post by **Amber G.** » 28 Jun 2011 22:06

vina wrote: Probably some sort of vortex /circulation gets created at the foot of the waterfall, that tends to draw swimmers underwater ?

Slightly different thought was from Brihaspatyiji regarding buoyancy being reduced by air/gas bubbles... What people think may be the main point?

GuruPrabhu · Post by **GuruPrabhu** » 28 Jun 2011 23:57

kasthuri wrote:^^^ Thanks. All I can say is that if biologists are struggling to find any law, physics has a long way to go!

Both biologists and physicists are human beings with different skill sets and tools. This is not a competition but a human endeavor.

Most of the research work being done involves teams that have not only biologists and physicists, but also chemists, material scientists, technologists and what not. Breakthroughs will come, hopefully sooner than later.

Amber G. · Post by **Amber G.** » 29 Jun 2011 00:24

..Because all of modern physics relies on formulation of symmetry. All conserved quantities arise from a symmetry....

Sorry can not resist ... an old limerick..

As Noether most keenly observed
(And for which much acclaim is deserved),
We can easily see
That for each symmetry,
A quantity must be conserved.

Vayutuvan · Post by **Vayutuvan** » 29 Jun 2011 01:11

kasthuri wrote:Unless someone comes up proving P=NP, in which case we can hope to have non-deterministic polynomial algorithms have polynomial solutions. That would be one of the greatest break through (almost equivalent to solving Riemann hypothesis), but yet COD will still be an issue. Even the simplest n-body problem which is O(N^2) complexity would take years on a HPC for 10 million bodies!

Kasthuri garu

Right on. One my committee members used to say that as far as numerical analysis algorithms go, anything complexity worse than O(n) is already too bad. Greengard's algorithm (not linear as claimed in his original paper) works reasonably well on real life problems. There are other algorithms that are provably O(n^{1+\epsilon}) and O(n) for regular geometry, but with large constants.

<random ramblings>
As you know, It is generally believed that P != NP. So, there is little scope for any breakthrough for solving quickly combinatorial and non-linear, non-convex optimization problems. The trick is to recognize that there are no random problems - there is always structure and approximations involved and those should be taken advantage of while designing algorithms for physical problems.

As to the question whether Physics is more funda or math, one should go back to the great master of both, Courant. Initial parts of his book "What is Mathematics" is quite an interesting read. The distinction between pure and applied math is a recent artificial division (paraphrasing Courant). IIRC, he also says that Mathematics by itself cannot stand - it was invented to solve Physics (and originally Geometry) problems. Another basic text would be "Introduction to logic" by Tarski where he talks about models etc. Of course, in a logician's world view everything becomes a language problem and is completely divorced from physical reality.

If, on the other hand as Bade saar says, everything is counting based, then it should be possible to axiomatize Physics entirely in (the question whether it has really failed is still open, IMHO) Peano Arithmetic (i.e. axioms of Physics are reducible to axioms of PA). This is highly improbable, IMHO. Any speculations are well above my pay grade.
</random ramblings>

kasthuri · Post by **kasthuri** » 29 Jun 2011 02:14

matrimc wrote: Right on. One my committee members used to say that as far as numerical analysis algorithms go, anything complexity worse than O(n) is already too bad. Greengard's algorithm (not linear as claimed in his original paper) works reasonably well on real life problems. There are other algorithms that are provably O(n^{1+\epsilon}) and O(n) for regular geometry, but with large constants.

Barnes-Hut type schemes with O(N*logN) works fine and its more easier than translations introduced by Greengard. Either way O(N^2) is simply not acceptable. Apparently, my doctoral thesis happens to be an extension of Greengard's work for Lennard-Jones potential (plus other things)!

The trick is to recognize that there are no random problems - there is always structure and approximations involved and those should be taken advantage of while designing algorithms for physical problems.

Approximation algorithms, dynamic programming approaches and combinatorial optimization are our hope - although they don't provide optimal solution, we have to take it to their maximum advantage if we assume P != NP

As to the question whether Physics is more funda or math, one should go back to the great master of both, Courant. Initial parts of his book "What is Mathematics" is quite an interesting read. The distinction between pure and applied math is a recent artificial division (paraphrasing Courant). IIRC, he also says that Mathematics by itself cannot stand - it was invented to solve Physics (and originally Geometry) problems. Another basic text would be "Introduction to logic" by Tarski where he talks about models etc. Of course, in a logician's world view everything becomes a language problem and is completely divorced from physical reality.

Thank you for suggesting nice books. I have to read them. As far as I can recall, G.H. Hardy in his "A Mathematician's Apology" makes this distinction clear. However, I am unable to reconcile the division, having found physics as beautiful as math. IMHO both has to co-exist as almost all legends have contributed to either fields. When it comes to logic, I don't believe logicians are completely divorced from physical reality. The below link shows logicians are trying to formulate relativity in the context of first-order logic. This will be an interesting pursuit if it goes somewhere.

http://arxiv.org/abs/gr-qc/0604041

If, on the other hand as Bade saar says, everything is counting based, then it should be possible to axiomatize Physics entirely in (the question whether it has really failed is still open, IMHO) Peano Arithmetic (i.e. axioms of Physics are reducible to axioms of PA). This is highly improbable, IMHO.

True. Although Peano's arithmetic is quite sophisticated, as a first order theory, it lacks sufficient power to express the least upper bound property which is fundamental to define real numbers. I don't know how physics can sustain without real numbers. IMHO, any axiomatization of physics would need at least a second order theory. But of course, there are always non-standard models.

Any speculations are well above my pay grade.

Amber G. · Post by **Amber G.** » 29 Jun 2011 03:13

Most of the research work being done involves teams that have not only biologists and physicists, but also chemists,

...
From what I heard ...

Biologists want to be Chemists..
Chemists want to be Physicists..
Physicists want to be God
And God wants to be a Mathematician...

kasthuri · Post by **kasthuri** » 29 Jun 2011 04:10

Amber G. wrote:
Most of the research work being done involves teams that have not only biologists and physicists, but also chemists,
...
From what I heard ...

Biologists want to be Chemists..
Chemists want to be Physicists..
Physicists want to be God
And God wants to be a Mathematician...

And mathematicians want to be decently paid!