I was a bit surprised at Yorda when he/she said that algebra wasn't important. But it really is, and it helps us make more accurate details. One thing you do learn in Algebra for instance is Exponential Rules.

Suppose we had:

z^-a

You would reduce the z^-a as if it where |z^-a| making:

1/z^a

Another major rule of Exponential is working with brackets. Suppose the following:

(yz)^a

reduces simply into:

y^a z^a

and for brackets and division:

(y/z)^a

reduces to y^a/z^a

If you are dividing expressions with the same bases, then a critical change in the powers happen:

a^7/a^4 = a^7-4 = a^3

And if you use the dot as the symbol, then another critical change is found:

a^x . a^y . a^z = a^x+y+z...

This is all just child play, but i just wanted to show a really elementary reason why algebra is really important, to physics especially.

The importance of (simple) algebra is not clearly demonstrated/explained in your example.
The importance of algebra over using specific numbers is that in using letters you define / prove the position for the entire set of real numbers (or whatever else is defined as "a", "b" etc) rather than just any specific case.

E.g. x^2 + y^2 = 2 defines an infinite number of points and defines a complete relationship for all "x" and all "y".
One could say that 1 + 1 = 2, but this only provides worth for this specific example.

Well... I agree.

..why algebra is really important, to physics especially...
The algebra relies on inertial physics, where the particles are colliding mutually without change (the action of them remains additive).

Without inertia no algebra would really exist.

Algebra does not depend on physics.

but i just wanted to show a really elementary reason why algebra is really important, to physics especially.

How have you done this?

Without inertia no algebra would really exist.

Seriously?

I never said it was dependant on physics, but rather it is a well-used tool in physics, and it really needs it for accuracy... big difference.

Where in real life would algebra be highly important?

In describing the universe. I feel, it is a useful tool in describing events with variables, rather than long-numbers. It cut's an equation down to size, and allows us to use them as descriptions of reality.

Mathematics is a language. And languages allow us to represent ideas so that we may communicate them to others and record them for posterity. But more importantly it allows us to think in terms of "what if" and thus deal with and possibly plan for and control the future. Imagine if there were no vocal or sign languages how limited we would be.
The specific sublanguage Algebra deals with shapes, functions and transformations [among other topics]. The example above that x squared plus y squared equals 2 is a precise description of the locus of points the square root of two away from the origin.
A cirlce. In fact all quadratic equations in 2 variables describe one of 4 conic sections;
circle, parabola, ellipse or hyperbola. Higher order polynomials describe more active shapes precisely too.

What is the importance of Algebra ?
It is the exact and elegant language of one subset of our reality.
This is why physicists need it and use it to explain the natural world.
But it would exist even if there were no scientists.

Much like our own description of reality...

... but ALAS... not too many round here seem to grasp this importance.

If you didn't know algebra you couldn't do any calculus problems, physics problems, chemistry problems, economic problems, computer science problems, etc, etc, etc...If you don't think algebra is important you clearly haven't dealt with any of these problems so yes you would be correct in saying that it isn't important for you to know, but that doesn't mean it isn't important at all. If algebra wasn't invented the things you see around you in modern society simply wouldn't exist and life would be much different.

If you study a little algebra, you will learn a good trick: when you break a stick, instead of calling one piece X and the other piece Y, call one piece X and the other piece 1-X.

And the world will suddenly make a new kind of sense.

Yes... well... Quite right.

One of you tough guys care to explain exactly what an algebra actually is? (Beware - there is a multiplicity of algebras out there!)

I don't know how to answer you question. Algebra comes in many forms in physics, such as: Expressions, Linear Equations + Non, Inequalities, Polynomials, Matrices ect ect.

Algebra is just peachy and useful. But the fact that most of us were forced to learn something we can really do without, that's just...poop.

Where in real life would algebra be highly important?Algebra is vitally important in finance. The whole subprime mortgage crisis might not have occurred if more people new the basics of algebra. At some point in the transaction, after mentally deciding how large a monthly payment they could afford, they'd do an order-of-magnitude estimate of the balloon payment and say, "Excuse me sir, you must have made a mistake. This is preposterous."

If you study a little algebra, you will learn a good trick: when you break a stick, instead of calling one piece X and the other piece Y, call one piece X and the other piece 1-X.

And the world will suddenly make a new kind of sense.

Calling one piece X and the other Y is an example of assigning a NAME to the pieces. It would be bad form to name a stick as its length. What about it's other properties? It would be very confusing to say "10 cm is 80 grams" when, instead, I can say "Piece X is 80 grams."

I understand what you MEAN to say, but please make sure you are more clear. Mathematics turns very ugly when you create confusing statements.


And unless I am mistaken, we discussing high school algebra. Can we talk about abstract algebra? That's more fun.

I personally find ''matrices'' more fun.

There are so many things that mathmatics has helped me to understand! Exponentials is just the tip of the iceberg! I wish I had taking it to the last levels. But I am not dead...there is still time!!!

Another major rule of Exponential is working with brackets. Suppose the following:
(yz)^a
reduces simply into:
y^a z^a
and for brackets and division:
(y/z)^a
reduces to y^a/z^aThis is only true for positive numbers y, z or integers a. It's not true in general or if you're not careful.
en.wikipedia.org/wiki/Exponentiation#Powers_of_complex_numbers

For instance

1 = (1)^{\frac{1}{2}} = (1 \times 1)^{\frac{1}{2}} = \sqrt{1 \times 1} = \sqrt{-1 \times -1} = \sqrt{-1} \times \sqrt{-1} = i \times i = -1

For complex numbers you need to be careful.
I personally find ''matrices'' more fun.Feel free to be specific, NeoNo.1....

What makes you think i would honor you in any way, mmm?

As usual, rather than explain your comments, you resort to dodging. We've established you don't grasp group theory or Lie algebras/groups. You don't understand various essential parts of matrix theory which relate to particle physics. So what about matrices do you find particularly 'fun'? You claimed to have looked into string theory research but how can you have when you don't grasp what an SO(8) transverse polarisation Lie group symmetry is? Or how SU(4) doesn't contain a singlet but SU(3) does, thus leading to Calabi Yau compactifications?

And you are a pompous swine.

Don't tell me of what i know and do not, because you know not of me.

And besides... if this is why you came here, then please do not commune with me.

.......thus leading to Calabi Yau compactifications?
The question is, why somebody, who is really interested about physics should know about some Calabi Yau compactifications, if the string theorists know already, just the concept of CY compactification has lead the string theory into unphysical predictions (the cosmological constant (http://motls.blogspot.com/2008/02/free-fermionic-heterotic-models.html), for example)? This renders whole concept of CY compactification as an unphysical BS, despite of its complexity.

It's like some member of Holly Church would tell Galileo before years:

"How is it possible, you troll, you're trying to talk about physics - while you don't know about epicycles at all"?

Algebra does not depend on physics.

Without particle concept (inertial particles in particular) you'll never have nothing to add or to compute with. For example, the ripples at the water surface cannot be counted and their interractions aren't additive.

http://www1.istockphoto.com/file_thumbview_approve/2283807/2/istockphoto_2283807_water_ripples_background.jpg

Does it means, these ripples are less real by such way? The formalists are so naive.

Don't tell me of what i know and do not, because you know not of me.I know you can never justify your claims of understanding any part of physics you talk about.

Feel free to prove me wrong.
And besides... if this is why you came here, then please do not commune with me.As usual, you think the world revolves around you (you and Kaneda have that in common). Feel free to search my posts here and notice that the vast majority have nothing to do with you and relate to topics you know nothing about.
The question is, why somebody, who is really interested about physics should know about some Calabi Yau compactifications, if the string theorists know already, just the concept of CY compactification has lead the string theory into unphysical predictions (the cosmological constant, for example)? This renders whole concept of CY compactification as an unphysical BS, despite of its complexity.I love how you link to a post about aether and then say how it results in unphysical predictions! :roflmao:

The cosmlogical constant is an open problem. It actually is the expectation of the potential due to the Kahler function and the super potential, ie <V> (equation 2.1 :arxiv.org/pdf/hep-th/0603129, though that doesn't include fermionic contributions but the point in the same).

A considerable amount of research is put into finding <V>=0 solutions with DW != 0 (ie supersymmetry is broken in the vacuum). <V> is then soft broken to a tiny non-zero value.

As usual, you fail to both to learn anything about string theory but think you understand it.
you'll never have nothing to add or to compute withJust like you have nothing to compute with in AWT! ;)

Justify? To you? And you think the world in my eyes revolves around me... Lol...

...how you link to a post about aether and then say how it results in unphysical predictions..
OK, link corrected.

...just like you have nothing to compute with in AWT...
The string theory cannot explain anything and it's formal predictions are wrong. The AWT can explain at least something - in fact, it's quite good & predicative theory, if we consider, how little IQ, time & money is really behind such concept till now - with compare to forty years old string theory, which reformulated every few years.

Besides... face it... string theory is dying.. if it's not dead, and not sooner it should have been.

..besides... face it... string theory is dying.. if it's not dead, and not sooner it should have been.

Don't be too naive - the string theory is feeding too much theorists, who cannot do nothing else to die very soon. The string theorists succeded in magical trick - to develop "rigorous theory", which has no fixed postulate list defined at all. Such stuff is better then the Lapis philosophorumm indeed - you can change such "theory" from scratch and continue without public feedback in it's development like alchemists of medieval era - until the money are going.

The contemporary string theory has nothing to do with theory of the same name before thirty years - in fact it's whole large bunch of mutually incompatible quantum field theories without any common predictability. Note how the string theorists are avoiding to illustrate their theory by any way to prohibit the public control and to enable the publicity to understand, what they're really trying to model.

It's such a non-experimental means, that i justify by saying it is really dead, even though there are those scientists who hold onto the hallucination...

... ...

Justify? To you? And you think the world in my eyes revolves around me... Lol...So much for you proving me wrong. :shrug:
Don't be too naive - the string theory is feeding too much theorists, who cannot do nothing else to die very soon.You'll find that practically every string theorist who has been in the field longer than 10 years has published papers on things like electroweak processes or the framework of QFT. For instance, my supervisor (who has more than a dozen string theory papers published) did PhD work on the electroweak processes of LEP, which was entirely phenomenological. Witten continues to pump out papers on both string theory and the general framework of QFT.

While I went into string theory, I could have easily gone into any other area of theoretical physics. I liked the look of SUSY or GUTs (but not Lattice QCD) and have since heard interesting things about various sections of QFT's framework (like methods which don't use Feynman diagrams but other combinatorial ideas).

I went into string theory not because I thought it would be a free ride. If anything, during my 4th year string theory was my worst topic. I was much better at relativity and group theory! Instead I went into it because it is interesting and the most viable path of research for quantum gravity.

I've explained this to you before but you are doing your usual thing of just ignoring when anyone corrects you and continuing your lies.
The string theorists succeded in magical trick - to develop "rigorous theory", which has no fixed postulate list defined at all.No 'theory in development' is set in stone, that's what 'in development' means. Bohr didn't have a set list of postulates during his initial development of quantum mechanics. Doesn't mean it was nonsense. Developing a theory is about coming up with new structures and seeing what they imply to physical results. Putting in new structures isn't a crime, it's an essential part of development.

String theorists aren't so arrogant as you to think they have the answer immediately.
Note how the string theorists are avoiding to illustrate their theory by any way to prohibit the public control and to enable the publicity to understand, what they're really trying to model.Yeah, all those published papers, textbooks, pop science books, public lectures and TV programs are just a smoke screen! :rolleyes:

How about you, you refuse to derive any result you claim. String theorists publish any derivation they come up with. It's you who is avoding providing answers.
in fact it's whole large bunch of mutually incompatible quantum field theories without any common predictability.Except they are all compatible. F theory is dual to IIB theory. IIB theory is dual to IIA theory. SO(32) and E8xE8 are dual. They are ALL limits of M theory. Your comment is equivalent to saying "Maxwell's theory talks about mutually incompatible notions of magnetism and electricity".
It's such a non-experimental meanYes it does. In sciforums.com/showthread.php?t=73974 someone gave you numerous links showing you're wrong.

Yet more evidence you just spout BS.

So... all of a sudden string theory has become an experimental science|? Has any of these experiments been conducted with accuracy and successfulness?

And what do you want me to prove you wrong on? I'm not here to teach my understanding of physics. I come here to talk about physics... Much more better than what you used to do, by attempting to flout everybody's idea's with the highest impunity.

...It's such a non-experimental means, that i justify by saying it is really dead.....
You're just replacing one belief by another. The strings can be considered as a density fluctuations of the vacuum and such point is nothing wrong even in context of another theories. Currently the string theorists don't understand, what they're trying to describe - neverthelles they're gradually converging towards the string field theory and the free fermionic models. How is it possible? A quite easilly: they're simply choosing one formal model after another and trying, which one is supplying more relevent results, then the others. By such way, they can guess the most correct approach and to claim it as a conceptual victory of string theory at the very end.

Don't forget, what I've said before - just because the string theory is so poorly defined, it's quite flexible...;-)

Mmm... flexible strings... we had a thread on that one time :)

Well, knotted flexible strings....

Yeh... the kind that come in very small packages...

It's like some member of Holly Church would tell Galileo before years:

"How is it possible, you troll, you're trying to talk about physics - while you don't know about epicycles at all"?

But Galileo did know all about epicycles. He was well versed in all the arguments for geocentrism. This is why he was able to argue so well against it. The book that he got in trouble for writing was a ficitional discussion between two people championing the two systems. He didn't get in trouble because the Church thought he was mis-representing their the arguments for geocentrism, but because he used those exact arguments and put them in the mouth of a character who was protrayed as a simpleton. The worst was when he ended the book with this character giving what was the Pope's favorite argument. (That while the heliocentric system might be simpler, God could have created a geocentric universe if he chose to. ) This was seen as mocking the Pope.

Calling one piece X and the other Y is an example of assigning a NAME to the pieces. It would be bad form to name a stick as its length Nothing said about lengh - if you want to use mass, say, or different numbers than "1", more power to you; and the transition from X and Y to X and 1-X is capable of jacking you out of the "name" rut.

That kind of freedom of consideration can be a benefit of algebra, a boost in one's thinking capability that can follow the learning of the little rules and paper manipulations.