Maths Lingo

[sjastro]

Anyone care to decipher this?

In mathematics (http://en.wikipedia.org/wiki/Mathematics), the monster Lie algebra is an infinite dimensional generalized Kac-Moody algebra (http://en.wikipedia.org/wiki/Generalized_Kac-Moody_algebra) acted on by the monster group (http://en.wikipedia.org/wiki/Monster_group), which was used to prove the monstrous moonshine (http://en.wikipedia.org/wiki/Monstrous_moonshine) conjectures.

Yes folks this is the stuff that makes it's way into theoretical physics and gives us a greater understanding of the Universe.;)

Regards

Steven

[renormalised]

Translation = " mathematicians sniffing too much glue":P:P:D:D

"Kac-Moody superalgebra" = what they were feeling after sniffing too much glue:P:P:D:D

Monster Group = What they were hallucinating whilst sniffing the glue. Mainly the likes of chupacabras, imps, succubi and trolls:P:P:D:D

Happy Family = Only after intense intervention by psychologists:P:P:D:D

Monstrous Moonshine = Very large illegal still they had out in the forest:P:P:D:D

Monster Lie algebra = maths the politicians pretend to use when running the economy, so it's a lie upon a lie:P:P:D:D

[sjastro]

I think there is a simpler definition.

These pure mathematicians have their heads stuck up their backsides for too long during a day.:P

Steven

[renormalised]

It's probably the reason why physics has been stuck in a rut for so long...too much maths, not enough imagination. No "gedankenexperiment" anymore. Just abstract, symbolic claptrap.

[sjastro]

The problem is made worse as physics is so "mathematicized" that the mathematics is beyond the scope of many physicists.

As a result much of the theoretical work is "contracted" out to pure mathematicians so it will only get worse.

Ed Witten is one of the very few physicists that is able to bridge the gap between pure mathematics and theoretical physics.

Steven

[renormalised]

Ed Witten is one of those lucky few who can not only think in terms of numbers but he can also think intuitively, which is where he can connect between the two. He bridges the theory and the experimentation...the methodical logician and the insightful experimentalist.

[sjastro]

The man is a genius.

Whereas many mathematicians have gone on to win Nobel Prizes in Physics and Economics, Witten is the only physicist to win the Fields Medal in pure mathematics, which is the maths version of the Nobel Prizes.

Steven

[Robh]

I can see where you're coming from. Pure mathematics can appear to be so removed from physical reality that one can only wonder at the amount of time being wasted on some of these studies.
All the sciences and indeed a great majority of careers rely on varying levels of mathematical understanding and usage, whether it be all-encompassing as in physics and engineering or as an occasional acquaintance in social work in the form of statistics.
However, there is always a fuzzy area between pure and applied mathematics. Once considered pure and "useless" mathematics can all of a sudden find a revolutionary application in the real world e.g. complex analysis and electronics. It begs the question whether things are only to be only studied for their practical application or is there reason to research it for its esoteric value. For example, Goldbach's conjecture (unproven) states that every even number greater than two can be expressed as the sum of two prime numbers (4=2+2, 6=3+3, 8=3+5, 10=3+7 or 5+5 etc). Pretty much useless but a lovely problem nonetheless. There are many other things which have no real practical use but are valued and appreciated by the human mind e.g. art, music, a good novel.
I can't comment on the monstrous moonshine conjectures other than to wonder how many mathematicians would be familiar with them. Perhaps, there is a present or future application in the real world, perhaps not. Perhaps, there are some revolutionary lines of thinking that might inspire other areas of mathematics.
So, I guess in the final analysis it comes down to how many areas of pure mathematics have diverged and progressed along specialised lines of study that are pretty much isolated from mainstream mathematicians.
It is to be hoped that mathematics does not evolve and separate into a myriad of isolated studies that to all intents and purposes form a random pile of unintelligible and useless conjectures. After all, one can invent and formulate theorems around any structured set of axioms.

Interesting topic for debate.

Regards, Rob.

[AlexN]

Was it not Einstein who said the biggest hindrance to his understanding of physics was his math education (more a accurately, his lack of math education..)

It is perhaps a bit of a shame that mathematics weighs so heavily upon a physics, and mathematics practically being theoretical physics.. It makes it hard for the average person to input.. Physics, and experimenting in physics is as much about imagination and intuitive thinking as it is the math. but, both however are not mutually exclusive. without the imagination and intuitive thought to dream up the ideas and the experiments, the math is without meaning and vice versa.. without out one, the other is somewhat moot.

I somewhat dislike math. However its just something I have to put up with...

[sjastro]

I did 3 years of Pure Maths as an undergraduate before moving over to Applied Maths. My senior lecturers who also researched Pure Maths considered themselves artists rather than mathematicians. Their "art" was based on creativity, simplicity and logic.

One can argue that theoretical physics is based on the same principles.
Physics however is first and foremost an experimental science hence apart from creativity, simplicity and logic, there is also reality to consider. The reality component is expressed through experiment and observation.

When pure mathematicians start taking on the role of theoretical physicists the reality component can go missing.

This is highlighted by String Theory. String Theory is not verifiable through experiment or observation.

Steven

[Robh]

You are quite right here. The role of mathematicians, real or applied, should be to help physicists construct models that explain observations. The problem arises when a model can't be constructed to explain all the current observations. It is here that all and sundry start fictionalizing the real world in a haphazard attempt to fluke upon a solution. Quite often these quasi-worlds are just way off the mark. I don't know whether String Theory will improve our understanding of the real world or just end up being a red herring.

Regards, Rob

[xelasnave]

I would like a push model please.
I enjoyed this thread very much as I get a slight insite into the wonderful world of math folk.
I find it strange that "string theory" can be called a theory because there is no evidence as far as I know via observation or experiment ... it is an idea or a hypothisis I would think..given that is the reality I find it extrodinary it seems to be held up as somesort of major step forward... it ceratinly has its place and stuff may flow but the elevation to the class of theory seems inappropriate.
I dont know enough about conventions whatever surrounding theory but it seems string theory is string idea to be fair.
alex

[Robh]

Hello Alex,

You need to make a distinction between what constitutes proof in mathematics and what constitutes proof in science.
In mathematics, number and geometry can exist independently of the real world. For example, I can count 1, 2, 3, ... without actually counting out physical objects. I can create different geometries apart from the everyday Euclidean geometry we are familiar with. The establishment of a theorem in mathematics runs something like this: I observe a pattern or relationship and formulate a conjecture. Using existing self-evident axioms, I derive a step by step proof which shows my conjecture to be true. The conjecture becomes a theorem. This theorem is watertight and timeless i.e. does not depend on any future observations of our environment.

In science, the process is analogous but not final. I observe a pattern or relationship in nature, perform measurements and then formulate an hypothesis. Over time, if further observations support the hypothesis, it may then become a theory. At any stage, a mathematical model may be produced to represent the hypothesis or theory. If the model itself makes predictions that can be observed to be true, it gives further credence to the validity of the hypothesis or theory. If, however, one observation does not support the theory it can then become invalid. Attempts may be made to modify the model to make the theory become palatable again. Thus, a scientific theory is not timeless. It is dependent on observations in the real world and may be proved false at any time. For example, in the Big Bang theory, inflation was invoked to explain the isotropic homogeneous nature of the Universe. Dark matter was proposed to explain anomalies in the speed of stars in the outer part of galaxies. Dark energy was created to explain accelerated expansion. Thus, our model or theory is rather kinetic and changes with differing observations.

String theory, with its roots in physics, has evolved primarily as a logically consistent mathematical model or set of models in an attempt to explain our Universe. In its support, one of these models represents the standard model of particle physics. String theory is the first attempt at the theory of everything, linking all known forces. It is hard to know where the pure mathematical consistency merges with physical reality. The theory's flexibility is also its weakness- which model (or models) represents the real Universe? A major criticism is that experimental confirmation of its predictions are not practicable (at least not yet). But like all theories, it depends on continued support from new observations.

Regards, Rob

[xelasnave]

Thank you Rob for such a well considered post I found it most helpful.
alex

[xelasnave]

mmmmm so that means that General Relativity must have started life as a math theory (as there were no observations or experiments at the prize stage) and later with observation became a science theory but now is dealt with as math which is really the way of physics a branch of science... I think
alex

[Ian Robinson]

Sorry folks , having studied physics at 200 and 300 level at uni , it is obvious that the science is very heavily mathematically involved.

Unlike some other sciences (chemistry, geology) which while having some cross over with physics and mathematics are also big memory jobs , I remember studying 200 and 300 level chemistry and having to memorize special reactions and structures .... :sadeyes:

If you can't understand the maths, you wont understand the physics simple as that , and no it's not the mathematicians are too anal or off in la la land.

Being hard to come to grips with and understand is not a bad thing.

If it was an easy science to study and learn , then everyone would do it.

[Robh]

Remember there is a difference between a mathematical theorem and a scientific theory. A theorem is essentially absolute whilst a theory is relative (dependent on new observations).
Initially, GR would have been a model developed from special relativity and Newton's laws of gravitation. It has its roots in physics and was not just pure imagination. However, as a developed mathematical model of gravitation, it was transformed from an hypothesis by Einstein into a theory. In fact, Einstein had to wait many years before predictions made by the theory were and continue to be confirmed. These confirmations lend more credence to GR. However, again, if GR is found to be inconsistent with new observations then the theory would have to be modified.

Rob

[Geoff45]

I think I detect a theme here: "I can't do it, so it must be crap"

[sjastro]

Not at all. With regards to the first post it's a dig at the colourful terminology used by pure mathematicians.

Theoretical physicists are aware of "monstrous moonshine" in bosonic string theory. But try explaining it at a science conference.....

[renormalised]

Very easy....they had to have a few (dozen) swigs of the "monstrous moonshine" in order to understand the string theory in question:P:P:D:D

[Nesti]

Dunno about "a theme", but I have a quote...

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
Nikola Tesla

[renormalised]

Tesla hit the nail right on the head.

[xelasnave]

for me its...

" i cant do it..oh crap"
alex:):):)

[KenGee]

Chemist and biologist are just glorified accounts it is all physic's in the end. :-)

[sjastro]

Tesla was unaware of phenomenlogical theories.

Here is an example.
http://en.wikipedia.org/wiki/Particle_physics_phenomenology

Steven

[renormalised]

That's true, but he was still right. Phenomenology is nothing more than an attempt to bridge that gulf between the physics "fantasy" and the real world. It's only as successful as those who can understand how to make that bridge, in which case it's the "egg heads" trying to help the "hands on" guys to get the jist of their brand of hieroglyphics:D

[sjastro]

In particle physics the "hands on guys" or experimental physicists are very much guided by the theory. The theory not only predicts an outcome but also how an experiment needs to be devised in order to achieve the outcome. That's where phenomenology comes into the picture.

The LHC is a good example. Although the Standard Model does not accurately predict the mass of the Higgs Boson we know the minimum energy required to perform the test. Also the theory predicts how the Higgs boson will decay which will help the hands on guys "where to look".

Steven

[Zaps]

Math is everything and everything is math. Like it or not.

[xelasnave]

Yes indeed but can you eat it?:D

alex:):):)

[renormalised]

Make sure you get your daily serve of integers and derivatives, but watch out for those square roots...they can give you indigestion:P:D:D

[Nesti]

oh P_L_E_A_S_E !!! :lol:

[sjastro]

And wash it down with monstrous moonshine.

[renormalised]

All in moderation, of course:P:D:D

[marki]

Physics like maths are only tools to serve useful sciences like chemistry, biology and geology. Without our work physics would not have any funding to come up with half the crap it does. Pure fantasy, no more no less. The way I see it is Albert and friends opened up a can of worms letting the theory mad maths geeks loose in science. They have been giving physicists a right butt kicking for years and all they can do is hop around holding their bottoms.

Mark

[snas]

As a veterinarian, I wear a number of different hats:
1. Physician; I diagnose and treat illness
2. Surgeon; I physically remove disease, repair fractures etc
3. Anaesthetist
4. Pathologist
etc etc
You get the idea.
The science at the base of all that I do is biology. So, as a veterinarian, I am perhaps best regarded as being something of a specialised biologist.

But what IS biology? When we get down to the question of what actually makes biology tick, it is the chemistry of life, or biochemistry. That anaesthetic drug I inject works because it blocks various receptors in the brain. My patient gets sick because the virus in its gut caused abnormal biochemical reactions to occur leading to vomiting, diarrhoea, loss of vrious electrolytes which in turn has other effects in other parts of my patient's body.

So it appears that biology comes down to being the result of a massive complex of chemical reactions that come together to prodcue life and all that goes with life.

So perhaps I am a biochemist.

But then again, what is chemistry? What is it that makes all of those chemical reactions occur, whether that be occurring in the body of my patient or in a beaker of acid to which I have placed a piece of metal (not because that has anything to do with biology, but just because I wanted to see what happened)? Why does one atom of this react with 2 atoms of that? why does one sodium ion like to get together with one chloride ion to produce table salt? What makes the NaCl molecule stay together as a molecule and not fly off as two separate ions? Or why does it fly off as two separate ions?

Physics! The electromagnetic force between the two ions, the strong and weak nuclear forces. As for gravity, I'm nt sure how much of a role that has to play in biology. But the thing is that it's physics that makes the chemistry happen which makes the life happen which gives me a patient to treat.

As far as I can tell the maths comes in as a way of describing the physics, it's the story (equation) of how and why the physics works the way that it does. But then, what would I know, I'm just a vet! :D

So, in reply to Zaps comment of "maths is everything and everything is maths", I have been known to say the same thing about physics. Not going to argue about which, if either, of those statements is correct.:)

Stuart

[sjastro]

The 1963 Nobel Prize for physics winner Eugene Wigner summarized maths and physics as follows:

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_M athematics_in_the_Natural_Sciences

On the other hand for non-physical sciences, maths is seen differently.

http://en.wikipedia.org/wiki/Unreasonable_Ineffectiveness_of_Mat hematics

[Nesti]

How would Richard Feynman reply to something like that....
Let's ask him??? http://www.youtube.com/watch?v=iMDTcMD6pOw :rofl:
(http://www.youtube.com/watch?v=iMDTcMD6pOw)

[sjastro]

A shame it's truncated.

However there is enough of it for certain individuals to take note!

Steven

[Nesti]

Actually Steven, what I really wanted to post was the link to Feynman's lecture introduction on 'The Relationship Between Physics and Mathematics'...it's roll on the floor material, but I can't find it.

Would have been the perfect follow-up to your post...Doh!

[marki]

Ah yes. I see you have it all worked out :rofl::rofl::rofl::rofl::rofl:.

Just like the last time, I guess I should steer my students away from physics as there is obviously no need for further research let alone asking the question "have we got it wrong"? :P.

Steven I do understand the importance of mathematics in scientific models (believe it or not chemists have been known to use it on the odd occasion;)) but I also have a very healthy sceptisim towards what are essentially radical ideas some of which cannot be tested with any rigour. Show me the empirical evidence and I will become a true believer.

Mark