Some Kind of Motivation - A Math Blog

Del apuro solo queda el cansancio

2005-06-14T19:14:00.000-03:00

Learn

2005-06-12T10:07:00.000-03:00

LAO-TZEc.604 - c.521 BC

Chinese Philosopher
Lao-tze is the reputed author of the'Tao Te Ching' and founder of the Taoist religion in China. His name means 'Old Master' and 'Tao' means the 'Way'. The 'Tao Te Ching' teaches a nonagressive approach to life and a stoical indifference to the powers of the world. It called for a return to an imaginary simple way of the past and for a style of life in harmony with the universe. It says that man must imitate the universe, which endures because it does not live for itself. Lao-tze worked as a librarian at the court of Chou. When the kingdom showed signs of decay, Lao-tze left and was never heard of again.
Legend says that Lao-tze, saddened by the evil of men, set off into the desert on a water buffalo leaving civilization behind. When he arrived at the final gate at the great wall protecting the kingdom, the gatekeeper persuaded him to record the principles of his philosophy for posterity. The result was the eighty-one sayings of the 'TaoTe Ching.'

Baseball Education

2005-06-11T02:16:00.000-03:00

The always Big Leaguer Andres "El Gato" Galarraga retires (in a way) from professional baseball only to restart to teach baseball to children in Venezuela.

Bravo!

More Leibniz

2005-06-02T17:18:00.000-03:00

I have rediscovered Leibniz by rediscovering Chaitin who also rediscovered Leibniz (but I don't know by rediscovering who, sorry, hmh, probably Goedel) , anyway, Leibniz dixit

"Every mind has a horizon in respect to its present intellectual capacity
but not in respect to its future intellectual capacity."

Then I read this essay by Chaitin and then he says:

The simpler the theory, the better you understand
something. A very
complex
theory means something is wrong.

No more also-reads

2005-06-02T16:47:00.000-03:00

in the adsabs.harvard.edu, why?

Not swinging yet

2005-06-02T16:22:00.000-03:00

http://arxiv.org/abs/math.DG/0505634

The paper has been withdrawn by the author due to the inappropriate formulation
of the main theorem used in the paper. We do hope the gap can be fulfilled in
the near future.

I read some and it *would* be really nice to fill that gap.

Some Also-Read articles

2005-06-01T15:32:00.000-03:00

1
2004math.....12125A
141.000
12/2004
A X U
Alayon-Solarz, Daniel
On Some Modifications of the Fueter Operator
2
2004math.ph..12013A
31.000
12/2004
A X U
Alayon-Solarz, Daniel
A Very Brief Note on Some Commutative Algebraic Properties of a Dirac-Fueter Modified Equation
3
2005astro.ph..3200C
16.000
03/2005
A X C U H
Chapline, G.
Dark Energy Stars
4
2005hep.th....4078W
11.000
04/2005
A X U H
Witten, Edward
Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
5
2005math......3081T
11.000
03/2005
A X U
Thurston, William P.
Mathematical Education
6
2005hep.th....3249F
9.000
03/2005
A X U H
Fox, P. J.; Kaplan, D. E.; Katz, E.; Poppitz, E.; Sanz, V.; Schmaltz, M.; Schwartz, M. D.; Weiner, N.
Supersplit Supersymmetry
7
2005gr.qc.....3097S
9.000
03/2005
A X C U H
Susskind, Leonard
Wormholes and Time Travel? Not Likely

The (scientific) world swings again (??)

2005-06-01T15:01:00.000-03:00

I think that if Leibniz was alive today he would be certainly reading this paper:

http://arxiv.org/abs/math.DG/0412316

Look to this beautiful simple idea: S^6 is contained on the imaginary octonions and then he somehow evades the old non-integrability stuff.

Questions:

1) Exotic diphemorphism in S^6 are expressed with the use of quaternionic exponential, a function is defintely ruled by the Class II. What is the relationship between this complex estructrure and the exotic diphemorphisms? I guess there is something here having to do with the riemann manifold that result as the analytical continuation of the Class II. The dimension is also 6.

2) Why Ed Witten wouldn't answer my emails about his paper?:

http://arxiv.org/abs/hep-th/0504078

named: Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects

In my case the perturbation comes after his silence. What do people have email for? Can't they just have courtesy and say: "I am busy, sorry" or "I don't care/ I am not interested" or "your mirror operator and my mirror operator are very alike, maybe there is some sort of bridge here". I am afraid this smoke signal of blogging will supercede private non-communication.

Quaternions and phenomenology

2005-05-19T14:02:00.000-03:00

A New Family Symmetry: Discrete Quaternion Group

by Michele Frigerio

Animations II

2005-05-16T18:10:00.000-03:00

Peter Woit landscapbashes with dexterity this 16 may.

Lubos Motl shows us some amazing plugin that will change the way he writes his own blog. Install it now!

I am unemployed and enjoying. Looking for a jobb, you know. Here you all have a warpy, is twistie that has more to do with logarithms than anything else.

Animation

2005-05-12T16:03:00.000-03:00

Far from Wrong

2005-05-12T16:01:00.000-03:00

I have enjoyed quite a lot the latest posts of Peter Woit. Somehow I like this much more than the landscape bashing series. They were fun too.

The Mirror operator

2005-05-06T10:20:00.000-03:00

Consider the complex case first. take f any complex function that satisfies cauchy-riemann and note that H(f)(z):= Conj(f(conj(z)) is not necesarily the same function as f(z) but it will satisfiy cauchy-riemann. more explicitly: we split any complex function f as g + ih were g and h are complex analytical functions that are expressable with real coefficients power series.

Doing the same trick with the class II and one obtains that

The Cullen quaternionic form of the functional H defines uniquely a ring isomorphism between the left and right Class II. The Class III is invariant under H.

naturally this is not a surprise as anybody can see the left and right class are isomorphic. The nice thing is that there exists a bigger, underlying algebraic-closed EC space consisting of all the finite sums and products of left and right class II fellows. So there exists a space where the left and right class live together. This is conceptually richer than a merely left-right theory. Seems to be something elemental to the quiral swing.

More twisting surfaces

2005-04-20T00:26:00.000-03:00

Integrals

2005-04-13T20:32:00.000-03:00

Yesterday I checked out that a Cullen lemma is valid in general for Class II functions, that means that is possible to discuss integrals.

The Butterfly

2005-04-06T06:04:00.000-03:00

In the quest for self-similarity

2005-04-05T22:21:00.000-03:00

this one results a good candidate. Isn't it?

Mathematica Notebook on Quaternions

2005-04-05T15:59:00.000-03:00

Mathematica Notebook by Robert Piziak and Danny W. Turner here.

Idea for a Geometric Mandelbrot

2005-04-02T12:13:00.000-03:00

I am going to write an article on this, the idea is to start with the seed for a Julia set:

f(z)= z^2 + c

where c = x + iy

and consider instead:

f(p) = p^2 + /rho(x,y,z)

where p is a quaternion and rho(x,y,z) = arctan(x/y) + i arctanh(z/Sqrt(x^2+y^2+z^2)).

A commentary by I. Singer on education

2005-04-01T18:03:00.000-03:00

"I observe a trend towards early specialization driven by economic considerations. You must show early promise to get good letters of recommendations to get good first jobs. You can't afford to branch out until you have established yourself and have a secure position. The realities of life force a narrowness in perspective that is not inherent to mathematics. We can counter too much specialization with new resources that would give young people more freedom than they presently have, freedom to explore mathematics more broadly, or to explore connections with other subjects, like biology these day where there is lots to be discovered.When I was young the job market was good. It was important to be at a major university but you could still prosper at a smaller one. I am distressed by the coercive effect of today's job market. Young mathematicians should have the freedom of choice we had when we were young."

MInd, matter, germany unification

2005-04-01T11:01:00.000-03:00

I have discovered this very interesting writing and about how this universe is designed, naturally it is almost trivial when one considers the Clifford Algebra, as is a widely known result that when considered as a split algebra over the field of football-like spinors, then the equations field result in a mental-blow up. Brazilian logic seems to be quite useful when dealing with this concepts, in particular the paralogic statement: "All electrons are liars" can be used, when parametrized under the phase-space of tachyons to explain why whe haven't detected any monopole yet. The reason is that the electron itself rejects the existence of monopoles because as Lacan observed, the electro-weak field is toric almost everywhere, and so the Lacan family parameter of neuroticity is not bounded yet finite. In other words: the electron cannot be conformal because it doesn't conform to the arrow of time.

P.S A certain Uncle Al has discovered this is actually not science. Amazing.

Davenport product

2005-04-01T00:07:00.000-03:00

I have been pondering the following idea:

Take the fueter operator and write it as an diff-operator of a complex z and the conjugate of some complex w, every algebric playaround made with the davenport product (the one with k^2 = 1) over a regular function of a special kind result again in a regular product. as a remarkable case we have that the function z*w^-1 -> S^2, (which is the hopf fibering when interpreted properly) is a regular function.

Rudolf Fueter

2005-03-31T09:04:00.000-03:00

Mathematics, and mathematicians suffer this cliché of absent mindedness and lack of commitment with society's problems. While it's true that many past and present mathematicians feed this point of view there exists one remarkable counterexample, namely (yes, you guessed ir right)

Rudolf Fueter

who actively opposed nazi's influence in Switzerland in the second world war. Read this biographical note.

A blog from a math teacher

2005-03-29T22:16:00.000-03:00

If I lose all of my math-memory and had to choose a highschool math teacher again I'd surely pick one who knows programming. Well, at least remind me I said that just in case.

arXiv

2005-03-29T08:48:00.000-03:00

X. X. Chen, H. Li

The K\"ahler-Ricci flow on K\"ahler manifolds with 2 traceless bisectional curvature operator

No equation and becomes art

2005-03-29T02:44:00.000-03:00

I can't find the seed function for this images and I thought it would be a pitty to delete them anyway.

Twisting surfaces

2005-03-28T10:35:00.000-03:00

This is a graphical representation as an alternative to visualize quiral solutions. This approach should be improved as a lot of information is lost by ignoring the scalar part of the function. Is should try coloring in function of this scalar. it shouldn't be so difficult.

More Pickies

2005-03-28T07:40:00.000-03:00

John Baez This Week 212 elaborates further on topics from Last Week, it has a lot of mentions for periodicity , Superfields, Super Brauer groups. My homework is to learn what Super Brauer groups are.

My friend Peter Arndt, who likes categories and topos very much asked me if I knew about this groups some time ago. On the other side, my friend Pedro Frejlich has pointed out that there is a well developed theory handling with sheaves, and as I understood him this has to do with the concept of branches.

Too many arctan and arctanh has appeared to me lately and I feel I need to know branches in more depth. One strange thing is that the principal branch on quaternions (the one that rules out how you extend the logarithm) is entirely independent of this subordinate branches. As they deal with independent variables to each other. One question: The riemann surface lives in R^3. Here there are not subordinate branches. What is the minimal dimension for the Riemann surface to the Class II such that it contains information about both the principal branch and the subordinate branch. I guess the minimal is 6.

Picks at arXiv

2005-03-28T02:25:00.000-03:00

Nassif Ghoussoub has made available his work on anti-self-duality for hamiltonian and lagrangians, according to the author this has applications to navier-stokes equations and hydrodynamics. That is yet another reason to highlight Olga Rozanova's work about a hydrodynamics approach to quantum mechanics.

Todays Picks at Google

2005-03-24T21:26:00.000-03:00

Here is discussed Fueter regularity and Maxwell equations in readable way.

John Baez This Week offers here some good facts about Bott periodicity and analisis, I like the clock and the symmetries stuff.

An article on hopf fibering, non-commutative rings, diffeomorphisms power series.

Sultan Catto paper about self-dual fields and Quaternions

Watson R.E.S paper on Cauchy-Riemann-Fueter

Mathematical Experiments

2005-03-24T17:26:00.000-03:00

It is raining now so there is no point in going out now. I use code to double check symbolical calculations and I get even theoretical warnings:

General::"spell": "Possible spelling error: new symbol name RFueter\)\" is similar to existing symbol \"\\(LFueter\)\"."

So you see, it also thinks this deserves some clarification.

First we have this graphic, which represents the intersection with the plane of the function that makes the determinant go zero for Class III functions, the function is p³:

on the plane one obtains:

for the case p^5, one obtains:

Sci.math years ago

2005-03-24T14:36:00.000-03:00

I have been interested in Usenet again. It is funny to read ones post after a long time. For example this one, where my mild dislexya putted me to invoked the use of the sguare root three times in a road.

Sci.math is still there and I feel that Lounesto would have a lot to say today. There were interesting discussions on quaternions back in 2000, which is precisely when I started to get interested in them although for more modest reasons than Geometric Quantization, in my case exotic spheres. Baez intuition is good, as seen by these posts here. He was close:

Somewhere else I read a nice
definition of analytic functions from the quaternions to the quaternions
that went like this: take your function f: H -> H, think of it as
a function f: R^4 -> R^4, and think of *that* as a 1-form A on R^4 with
its usual Euclidean metric.  (We use the metric to pull this stunt,
of course.)  Now form F = dA and write down the equations F = *F.
These equations supposedly are analogous to the Cauchy-Riemann equations.
They're obviously nice from a physics viewpoint: they're the self-dual 
Maxwell equations on Euclidean spacetime!  But how are they related to
the above stuff?  I don't know yet.  I need to calculate....

I wonder what he calculated...anyway, coming back to present days, perhaps a more modern (read categorical) treatment might be tested. In particular I wonder on what extent it is possible to extract geometric insight from the quiral ring in a methodical way. I can wait until they find a definition for weak n-cathegory. One problem, is that I don't grasp categories, but that should be solvable.

Feriado

2005-03-24T11:42:00.000-03:00

Today is calmer here at Unicamp, and there will be a big Limpieza General . It's rainy too, and birds are clearly audible. There is a lot of birds here, and eventually you see them. There is this marriage of owles, for example, who by night own a little road.

I have been pondering these ideas:

The Integral Counterpart, which is among other things, to include quirality in Cullen's paper.
The When In Doubt, Generalize approach: Go Octonions, parametrize S^6 with euler angles, use this G2 parametrization and/or the exotic diphemorphism, mix and and see what happens with the famous bazillion equations. Maybe you get 1-2-4-8 Calculus, alt. name, Periodicity Calculus after Bott, huh, ok at any case you get math.
The Central path: Develop a way, alt. go find one, to construct functionals like L in a general way. Extending the analytic product to the central regular functions is not well defined until L is modified in way that its kernel is zero.
The Quiral swing: Is there anything between left and right besides the center in the Class II? How to deform a Class? etc...

Utilitarism

2005-03-23T17:20:00.000-03:00

Who said quaternions had no use whatsoever? look

Todays picks at arxiv

2005-03-23T01:10:00.000-03:00

Sergio L. Cazziatori has made available his results on G2, the exceptional Lie algebra. He has found a simple parametrization for it. He has this approach of fibering G2 with fiber SO(2) and base H.

Bill Thurston has made available his essay on Mathematical Education. After reading it one wonders, in this context, if the expression "Creative Student" will ever stop being an oxymoron.

New version of "On Some Modif.." in the arxiv

2005-03-23T00:26:00.000-03:00

I have just sent to the arxiv the latest version, now it looks better.
I have to admit symbolical calculations with quaternions can be boring, and as expected the Mathematica plugin for Quaternions sucks: Who wants to make numerical calculations with quaternions on these days?
I managed to program some stuff on Mathematica in order to double-check explicit solutions.
The quiral left-solutions happen to be prettier than expected:

arctan(x/y) + i arctanh(z/sqrt(x²+y²+z²))

And, to make things even nicer, the conjugate a right-solution! So now it is possible to discuss the other involutions besides the conjugation. BTW, I don't remember when was the last time I used the function arctanh. I am sure any undergrad student knows more about them than I do.