Spot-Fixing Doesn't Happen in Football, Does it?

The spot-fixing scandal in Pakistan's cricket team has displaced the floods as a top news story (below).  Surely this sort of thing wouldn't happen in English top league football?  Guess again.

Financial Times on IPCC

The Financial Times strikes exactly the right note on the IPCC (and its chairman).  Here is an excerpt:

Restoring public confidence in the IPCC is essential, because it is the main intermediary between scientists and politicians who have to decide on climate policies that could cost the global economy hundreds of billions of dollars. Given that most scientists believe in the need to tackle global warming, the IPCC cannot hope to satisfy the most extreme “climate sceptics”. But it must never again undermine its own credibility by sloppily repeating unsubstantiated statements that exaggerate the risk of climate change, such as the notorious claim that Himalayan glaciers could disappear by 2035.

At its plenary meeting in South Korea next month, the 194 national governments that control the IPCC must push through a thorough overhaul of management and procedures. The IPCC needs stronger leadership to maintain credibility, including a new executive committee (with at least one member who is not a climate scientist) and a chief executive rather than a relatively powerless secretary. Although Rajendra Pachauri, IPCC chairman since 2002, has been unfairly vilified in some quarters, his recent performance under pressure has not helped the cause of climate science; the time has come for him to move on.

A rejuvenated IPCC leadership could tackle the deficiencies in its review process. This should become more inclusive, welcoming alternative views where these are scientifically valid, and at the same time more exclusive, rejecting unsubstantiated claims of dramatic change. The many uncertainties need recognition, with IPCC assessments talking more about risks and probabilities than they have in the past. Then the debate can get back to the real issues posed by climate change.

Reminder: EPL Picks Due by Next Week

Get your picks in by next Friday on this comment thread.

BIDU

BIDU Weekly Trend Model

BIDU is one of the stocks that is followed in my private email subscription service.  The above Weekly Trend Model is why.  It reversed LONG the first week in March, 2009 @ 17.26 and is up 356% in 18 months.  As the chart suggests, a weekly close below 73.50 will reverse the model to SHORT.  A weekly close below 73.50 will also break the double bottom formation put in over the past two weeks at 76.00.

BIDU is also worth watching as a bellwether for NASDAQ, the Technology sector and China.  In other words, this is one to keep an eye on for lots of good reasons. 

Past performance is not a guarantee of future results.

What is a Conflict of Interest?

Several conversations that I have had off-blog suggest to me that the notion of "conflict of interest" with respect to scientific advisory panels is not well understood.  The IPCC does not presently have any COI policies so it is impossible to judge whether its chairman, or anyone else, has a conflict.  However, under the application of COI policies of other bodies, such as the UN, WMO and NAS, it is indisputable that the IPCC chairman has conflicts of interest.  This is so patently obvious that is not really worth debating.  Whether the IPCC will implement similar policies , and if they do, whether its current chair will be ruled exempt from them are entirely different questions.

Here is how the US National Academy of Sciences defines the concept with respect to financial interests (PDF):

It is essential that the work of committees of the institution used in the development of reports not be compromised by any significant conflict of interest. For this purpose, the term "conflict of interest" means any financial or other interest which conflicts with the service of the individual because it (1) could significantly impair the individual's objectivity or (2) could create an unfair competitive advantage for any person or organization. Except for those situations in which the institution determines that a conflict of interest is unavoidable and promptly and publicly discloses the conflict of interest, no individual can be appointed to serve (or continue to serve) on a committee of the institution used in the development of reports if the individual has a conflict of interest that is relevant to the functions to be performed.

General Principles

The term "conflict of interest" means something more than individual bias. There must be an interest, ordinarily financial, that could be directly affected by the work of the committee. Conflict of interest requirements are objective and prophylactic. They are not an assessment of one's actual behavior or character, one's ability to act objectively despite the conflicting interest, or one's relative insensitivity to particular dollar amounts of specific assets because of one's personal wealth. Conflict of interest requirements are objective standards designed to eliminate certain specific, potentially compromising situations from arising, and thereby to protect the individual, the other members of the committee, the institution, and the public interest. The individual, the committee, and the institution should not be placed in a situation where others could reasonably question, and perhaps discount or dismiss, the work of the committee simply because of the existence of such conflicting interests.

The term "conflict of interest" applies only to current interests. It does not apply to past interests that have expired, no longer exist, and cannot reasonably affect current behavior. Nor does it apply to possible interests that may arise in the future but do not currently exist, because such future interests are inherently speculative and uncertain. For example, a pending formal or informal application for a particular job is a current interest, but the mere possibility that one might apply for such a job in the future is not a current interest.

The term "conflict of interest" applies not only to the personal financial interests of the individual but also to the interests of others with whom the individual has substantial common financial interests if these interests are relevant to the functions to be performed. Thus, in assessing an individual's potential conflicts of interest, consideration must be given not only to the interests of the individual but also to the interests of the individual's spouse and minor children, the individual's employer, the individual's business partners, and others with whom the individual has substantial common financial interests. Consideration must also be given to the interests of those for whom one is acting in a fiduciary or similar capacity (e.g., being an officer or director of a corporation, whether profit or nonprofit, or serving as a trustee).

Financial Interests

The term "conflict of interest" as used herein ordinarily refers to financial conflicts of interest. In assessing potential conflicts of interest in connection with an individual's service on a committee of the institution used in the development of reports for sponsors, particular attention will be given to the following kinds of financial interests if they are relevant to the functions to be performed: employment relationships (including private and public sector employment and self-employment); consulting relationships (including commercial and professional consulting and service arrangements, scientific and technical advisory board memberships, and serving as an expert witness in litigation); stocks, bonds, and other financial instruments and investments including partnerships; real estate investments; patents, copyrights, and other intellectual property interests; commercial business ownership and investment interests; services provided in exchange for honorariums and travel expense reimbursements; research funding and other forms
of research support.

UPDATE:  A colleague remind me of this useful definition, posted long ago on Prometheus:

“A conflict of interest is a set of conditions in which professional judgment concerning a primary interest (such as a patient’s welfare or the validity of research) tends to be unduly influenced by a secondary influence (such as financial gain)… The secondary interest is usually not illegitimate in itself, and indeed it may even be a necessary and desirable part of professional practice. Only its relative weight in professional decisions is problematic. The aim is not to eliminate or necessarily to reduce financial gain or other secondary interests (such as preference for family and friends or the desire for prestige and power). It is rather to prevent these secondary factors from dominating or appearing to dominate the relevant primary interest in the making of professional decisions.”

Reference: Thompson D. F., 1993. Understanding Financial Conflicts of Interest. The New England Journal of Medicine, 329:573-576.

Units of evidence

We often encounter the question whether a proposition, P, is true or false. The probability that it is true is "p". Various arguments - logical inference - may exist to determine our subjective value of "p". In particular, Bayesian inference multiples the probabilities "p" and "1-p" by the probability that the respective hypotheses give the result that agrees with the newest observation.

Some of the arguments may be K-sigma deviations of the measurements from the prediction of a null hypothesis. The value of "K" may be translated to "p" through the conventional error function: for example, a 3-sigma deviation translates to the 0.3% probability that P is true (99.7% that it is false).

It could be helpful to define another function of "p" or "K", called "AE", that kind of interpolates between "p" and "K". The letters "AE" stand for "amount of evidence". It is a dimensionless quantity but you may still use the term "unit of evidence" or "UE" for the unit. "AE" is defined as

AE = ln(p/(1-p))
AE = ln(1/(1-p)-1)

---

p = 1/(1+exp(-AE))

For your convenience, I have also written down the formula for "AE=AE(p)" where "p" only appears once, as well as the inverse relationship where "AE" appears once. If "AE" is positive, the evidence supporting the proposition P is stronger than the evidence going in the opposite direction.

I constructed "AE" as a simple function of the odds - the ratio of probabilities of "P" and "non P", i.e. as a simple function of "p/(1-p)". The precise definition of "AE" has the obvious property that if you negate P i.e. if you exchange "p" and "1-p", the value of "AE" simply switches the sign.

Moreover, when you evaluate independent pieces of evidence by Bayesian inference, "AE" simply behaves additively. Note that if the less likely answer is very small, 10^{-n}, then the amount of evidence "AE" is approximately "2.3 n" (with the correct sign - plus means probably yes, minus means probably no) where "2.3" should be the natural logarithm of ten.




If the evidence against P takes the form of a K-sigma deviation of the observations from the null hypothesis, "AE" additively shifts by "K^2/2" in the obvious direction. Moreover, it should always be understood that the amount of evidence is always determined with some inevitable error margin, something like +-1 or +-2. So the amount of evidence whose absolute value is smaller than 1 or 2 should be discarded as "no evidence".

If you want the equivalent of "one in two million" confidence level, i.e. a discovery in the particle physics sense, it's approximately "AE=+14" or "AE=-14" coming from "ln(1 or 2 million)". Because "5^2/2=12.5", you need a slightly more than 5-sigma to achieve "AE=14". But it's OK to give some automatic punishment - for cherry-picking - if your evidence is based on a K-sigma deviation.

The exact formula would contribute slightly more than "K^2/2" to "AE" (by an asymptotically universal additive constant) but because you may have cherry-picked for the "bumps", it's OK to say "K^2/2". Depending on the context, the punishment of "AE" for the possible cherry-picking of your argument could be calculated more accurately.

You may write all the rules-of-thumb that you need to use "AE" efficiently in many sorts of situations. It may be pretty useful if you could just say that "some argument provides us just with 1 or 2 units of evidence" while "another argument is potentially 6 or 7 units of evidence". The value of "AE" could be written with some error margins, too.

See also exponential percentages for a closely related proposed logarithmic terminology.

For people with congestive heart failure, a hot dog can trigger a trip to the hospital due to excessive salt

The average daily salt intake in America is one and 1/2 teaspoon a day. This is 3,400 milligrams of sodium a day, or 1,100 milligrams more then the recommended maximum.

For people with congestive heart failure, a salty hot dog can trigger a trip to the hospital.

The experts say the new target for sodium intake should be set at 1,500 milligrams daily.

In a previous study, reducing dietary salt by 3 gm per day (1200 mg of sodium per day) was projected to reduce the annual number of new cases of coronary heart disease by 60,000 to 120,000, stroke by 32,000 to 66,000, and myocardial infarction by 54,000 to 99,000 and to reduce the annual number of deaths from any cause by 44,000 to 92,000. Such an intervention would be more cost-effective than using medications to lower blood pressure in all persons with hypertension.

77% of the salt in the American diet comes from processed food. Only 6% is shaken out at the table, and only 5% is sprinkled during cooking.

Once people cut back on salt -- whether or not they know they are doing it -- they begin to prefer less salt in their food. This happens in a matter of weeks.

For example, alarmed by high death rates from strokes, Portugal plans to decrease salt in bread, blamed for high blood pressure. Portugal has one of the highest mortality rates from strokes in Europe - double that in Spain and 3 times that in France. http://is.gd/ndNv

The daily salt intake in Portugal is a staggering 12.3 grams (ranging from 5.2 to 24.8 gm) http://is.gd/ndQq

References:
Americans Need Help Shaking The Salt Habit - Shots - NPR Health News Blog.

"Cutting Salt as Good as Quitting Smoking"

3-gram reduction in daily salt intake would decrease coronary heart disease, stroke, and death

Image source: Wikipedia, GNU Free Documentation License.

Math Workbox: Estimation

I'm creating a series of 3x5" math task cards. I print them on cardstock and organize them in a recipe holder to rotate through our Math Workbox.

Today, I begin with cards on Estimation, using Bruce Goldstone's awesome books, Great Estimations and Greater Estimations. (Please see my book reviews and read an email from the author.)

I made 3 task cards that I will rotate through a Math Box along with Goldstone's books. In one activity, for example, the Math Box will include a baggie of 1/2 cup of popcorn. My student will count out 10 kernels, then 100 kernels, and use that information to estimate the total number of kernels, modeled after the visuals in Goldstone's books. Another task card includes a link to the author's website where students may estimate using the "Estimatron."

The cards are available in pdf format as a free download. Grab your own and print them on cardstock. Please enjoy the activity and leave me a comment to let me know what you think!

P.S. I'm sorry the tea towel (right) is wrinkled. I don't take time to iron. I take time to create math activities! ;)

I invite you to link to a Workbox post on math. Please link to posts that emphasize Living Books, games, and hands-on activities as opposed to worksheets and drills.

Why complex numbers are fundamental in physics

I have written about similar issues in articles such as Wick rotation, The unbreakable postulates of quantum mechanics, and Zeta-function regularization, among others.

But now I would like to promote the complex numbers themselves to the central players of the story.

History of complex numbers in mathematics

Around 1545, Girolamo Cardano (see the picture) was able to find his solution to the cubic equation. He already noticed the quadratic equation "x^2+1=0" as well. But even negative numbers were demonized at that time ;-) so it was impossible to seriously investigate complex numbers.

Cardano was able to additively shift "x" by "a/3" ("a" is the quadratic coefficient of the original equation) to get rid of the quadratic coefficient. Without a loss of generality, he was therefore solving the equations of the type

x³ + bx + c = 0

that only depends on two numbers, "b, c". Cardano was aware of one of the three solutions to the equation; it was co-co-communicated to him by Tartaglia (The Stammerer), also known as Niccolo Fontana. It is equal to

x₁ = cbrt[-c/2 + sqrt(c²/4+b³/27)] +
 + cbrt[-c/2 - sqrt(c²/4+b³/27)]

Here, cbrt is the cubic root. You can check it is a solution if you substitute it to the original equation. Now, using the modern technologies, it is possible to divide the cubic polynomial by "(x - x_1)" to obtain a quadratic polynomial which produces the remaining two solutions once it is solved. Let's assume that the cubic polynomial has 3 real solutions.




The shocking revelation came in 1572 when Rafael Bambelli was able to find real solutions using the complex numbers as tools in the intermediate calculations. This is an event that shows that the new tool was bringing you something useful: it wasn't just a piece of unnecessary garbage for which the costs are equal the expenses and that should be cut away by Occam's razor: it actually helps you to solve your old problems.

Consider the equation

x³ - 15x - 4 = 0.

Just to be sure where we're going, compute the three roots by Mathematica or anything else. They're equal to

x_1,2,3 = {4, -2-sqrt(3), -2+sqrt(3)}

The coefficient "b=-15" is too big and negative, so the square root in Cardano's formula is the square root of "(-15)^3/27 + 4^2/4" which is a square root of "-125+4" or "-121". You can't do anything about that: it is negative. The argument could have been positive for other cubic polynomials if the coefficient "b" were positive or closer to zero, instead of "-15", but with "-15", it's just negative.

Bombelli realized the bombshell that one can simply work with the "sqrt(-121)" as if it were an actual number; we don't have to give up once we encounter the first unusual expression. Note that it is being added to a real number and a cube root is computed out of it. Using the modern language, "sqrt(-121)" is "11i" or "-11i". The cube roots are general complex numbers but if you add two of them, the imaginary parts cancel. Only the real parts survive.

Bombelli was able to indirectly do this calculation and show that

x₁ = cbrt(2+11i) + cbrt(2-11i) = (2+i) + (2-i) = 4

which matches the simplest root. That was fascinating! Please feel free to verify that (2+i)^3 is equal to "8+12i-6-i = 2+11i" and imagine that the historical characters would write "sqrt(-1)" instead of "i". By the way, it is trivial to calculate the other two roots "x_2, x_3" if you simply multiply the two cubic roots, cbrt, which were equal to "(2+-i)", by the two opposite non-real cubic roots of unity, "exp(+-2.pi.i/3) = -1/2+-i.sqrt(3)/2".

When additions to these insights were made by John Wallis in 1673 and later by Euler, Cauchy, Gauss, and others, complex numbers took pretty much their modern form and mathematicians have already known more about them than the average TRF readers - sorry. ;-)

Fundamental theorem of algebra

Complex numbers have many cool properties. For example, every N-th order algebraic (polynomial) equation with real (or complex) coefficients has exactly "n" complex solutions (some of them may coincide, producing multiple roots).

How do you prove this statement? Using powerful modern TRF techniques, it's trivial. At a sufficiently big circle in the complex plane, the N-th order polynomial qualitatively behaves like a multiple of "x^N". In particular, the complex phase of the value of this polynomial "winds" around the zero in the complex plane N times. Or the logarithm of the polynomial jumps by 2.pi.i.N, if you wish.

You may divide the big circle into an arbitrarily fine grid and the N units of winding have to come from some particular "little squares" in the grid: the jump of the logarithm over the circle is the sum of jumps of the logarithm over the round trips around the little squares that constitute the big circle. The little squares around which the winding is nonzero have to have the polynomial equal to zero inside (otherwise the polynomial would be pretty much constant and nonzero inside, which would mean no winding) - so the roots are located in these grids. If the winding around a small square is greater than one, there is a multiple root over there. In this way, you can easily find the roots and their number is equal to the degree of the polynomial.

Fine. People have learned lots of things about the calculus - and functions of complex variables. They were mathematically interesting, to say the least. Complex numbers are really "new" because they can't be reduced to real diagonal matrices. That wouldn't be true e.g. for "U-complex" numbers "a+bU" where "U^2=+1": you could represent "U" by "sigma_3", the Pauli matrix, which is both real and diagonal.

Complex numbers have unified geometry and algebra. The exponential of an imaginary number produces sines and cosines - and knows everything about the angles and rotations (multiplication by a complex constant is a rotation together with magnification). The behavior of many functions in the complex plane - e.g. the Riemann zeta function - has been linked to number theory (distribution of primes) and other previously separate mathematical disciplines. There's no doubt that complex numbers are essential in mathematics.

Going to physics

In classical physics, complex numbers would be used as bookkeeping devices to remember the two coordinates of a two-dimensional vector; the complex numbers also knew something about the length of two-dimensional vectors. But this usage of the complex numbers was not really fundamental. In particular, the multiplication of two complex numbers never directly entered physics.

This totally changed when quantum mechanics was born. The waves in quantum mechanics had to be complex, "exp(ikx)", for the waves to remember the momentum as well as the direction of motion. And when you multiply operators or state vectors, you actually have to multiply complex numbers (the matrix elements) according to the rules of complex multiplication.

Now, we need to emphasize that it doesn't matter whether you write the number as "exp(ikx)", "cos(kx)+i.sin(kx)", "cos(kx)+j.sin(kx)", or "(cos kx, sin kx)" with an extra structure defining the product of two 2-component vectors. It doesn't matter whether you call the complex numbers "complex numbers", "Bambelli's spaghetti", "Euler's toilets", or "Feynman's silly arrows". All these things are mathematically equivalent. What matters is that they have two inseparable components and a specific rule how to multiply them.

The commutator of "x" and "p" equals "xp-px" which is, for two Hermitean (real-eigenvalue-boasting) operators, an anti-Hermitean operator i.e. "i" times a Hermitean operator (because its Hermitean conjugate is "px-xp", the opposite thing). You can't do anything about it: if it is a c-number, it has to be a pure imaginary c-number that we call "i.hbar". The uncertainty principle forces the complex numbers upon us.

So the imaginary unit is not a "trick" that randomly appeared in one application of some bizarre quantum mechanics problem - and something that you may humiliate. The imaginary unit is guaranteed to occur in any system that reduces to classical physics in a limit but is not a case of classical physics exactly.

Completely universally, the commutator of Hermitean operators - that are "deduced" from real classical observables - have commutators that involve an "i". That means that their definitions in any representation that you may find have to include some "i" factors as well. Once "i" enters some fundamental formulae of physics, including Schrödinger's (or Heisenberg's) equation, it's clear that it penetrates to pretty much all of physics. In particular:

In quantum mechanics, probabilities are the only thing we can compute about the outcomes of any experiments or phenomena. And the last steps of such calculations always include the squaring of absolute values of complex probability amplitudes. Complex numbers are fundamental for all predictions in modern science.

Thermal quantum mechanics

One of the places where imaginary quantities occur is the calcuation of thermal physics. In classical (or quantum) physics, you may calculate the probability that a particle occupies an energy-E state at a thermal equilibrium. Because the physical system can probe all the states with the same energy (and other conserved quantities), the probability can only depend on the energy (and other conserved quantities).

By maximizing the total number of microstates (and entropy) and by using Stirling's approximation etc., you may derive that the probabilities go like "exp(-E/kT)" for the energy-E states. Here, "T" is called the temperature and Boltzmann's constant "k" is only inserted because people began to use stupidly different units for temperature than they used for energy. This exponential gives rise to the Maxwell-Boltzmann and other distributions in thermodynamics.

The exponential had to occur here because it converts addition to multiplication. If you consider two independent subsystems of a physical system (see Locality and additivity of energy), their total energy "E" is just the sum "E1+E2". And the value of "exp(-E/kT)" is simply the product of "exp(-E1/kT)" and "exp(-E2/kT)".

This product is exactly what you want because the probability of two independent conditions is the product of the two separate probabilities. The exponential has to be everywhere in thermodynamics.

Fine. When you do the analogous reasoning in quantum thermodynamics, you will still find that the exponential matters. But the classical energy "E" in the exponent will be replaced by the Hamiltonian "H", of course: it's the quantum counterpart of the classical energy. The operator "exp(-H/kT)" will be the right density matrix (after you normalize it) that contains all the information about the temperature-T equilibrium.

There is one more place where the Hamiltonian occurs in the exponent: the evolution operator "exp(H.t/i.hbar)". The evolution operator is also an exponential because you may get it as a composition of the evolution by infinitesimal intervals of time. Each of these infinitesimal evolutions may be calculated from Schrödinger's equation and

[1 + H.t/(i.hbar.N)]^N = exp(H.t/i.hbar)

in the large "N" limit: we divided the interval "t" to "N" equal parts. If you don't want to use any infinitesimal numbers, note that the derivative of the exponential is an exponential again, so it is the right operator that solves the Schrödinger-like equation. So fine, the exponentials of multiples of the Hamiltonian appear both in the thermal density matrix as well as in the evolution operator. The main "qualitative" difference is that there is an "i" in the evolution operator. In the evolution operator, the coefficient in front of "H" is imaginary while it is real in the thermal density matrix.

But you may erase this difference if you consider an imaginary temperature or, on the contrary, you consider the evolution operator by an imaginary time "t = i.hbar/k.T". Because the evolution may be calculated in many other ways and additional tools are available, it's the latter perspective that is more useful. The evolution by an imaginary time calculates thermal properties of the system.

Now, is it a trick that you should dismiss as an irrelevant curiosity? Again, it's not. This map between thermal properties and imaginary evolution applies to the thermodynamics of all quantum systems. And because everything in our world is quantum at the fundamental level, this evolution by imaginary time is directly relevant for the thermodynamics of anything and everything in this world. Any trash talk about this map is a sign of ignorance.

Can we actually wait for an imaginary time? As Gordon asked, can such imaginary waiting be helpful to explain why we're late for a date with a woman (or a man, to be really politically correct if a bit disgusting)?

Well, when people were just animals, Nature told us to behave and to live our lives in the real time only. However, theoretical physicists have no problem to live their lives in the imaginary or complex time, too. At least they can calculate what will happen in their lives. The results satisfy most of the physical consistency conditions you expect except for the reality conditions and the preservation of the total probabilities. ;-)

Frankly speaking, you don't want to live in the imaginary time but you should certainly be keen on calculating with the imaginary time!

Analytic continuation

The thermal-evolution map was an example showing that it is damn useful to extrapolate real arguments into complex values if you want to learn important things. However, thermodynamics is not the only application where this powerful weapon shows its muscles. More precisely, you surely don't have to be at equilibrium to see that the continuations of quantities to complex values will bring you important insights that can't be obtained by inequivalent yet equally general methods.

The continuation into imaginary values of time is linked to thermodynamics, the Wick rotation, or the Hartle-Hawking wave function. Each of these three applications - and a few others - would deserve a similar discussion to the case of the "thermodynamics as imaginary evolution in time". I don't want to describe all of conceptual physics in this text, so let me keep the thermodynamic comments as the only representative.

Continuation in energy and momentum

However, it's equally if not more important to analytically continue in quantities such as the energy. Let us immediately say that special relativity downgrades energy to the time component of a more comprehensive vector in spacetime, the energy-momentum vector. So once we will realize that it's important to analytically continue various objects to complex energies, relativity makes it equally important to continue analogous objects to complex values of the momentum - and various functions of momenta such as "k^2".

Fine. So we are left with the question: Why should we ever analytically continue things into the complex values of the energy?

A typical laymen who doesn't like maths too much thinks that this is a contrived, unnatural operation. Why would he do it? A person who likes to compute things with the complex numbers asks whether we can calculate it. The answer is Yes, we can. ;-) And when we do it, we inevitably obtain some crucial information about the physical system.

A way to see why such things are useful is to imagine that the Fourier transform of a step function, "theta(t)" (zero for negative "t", one for positive "t"), is something like "1/(E-i.epsilon)". If you add some decreasing "exp(-ct)" factor to the step function, you may replace the infinitesimal "epsilon" by a finite constant.

Anyway, if you perturb the system at "t=0", various responses will only exist for positive values of "t". Many of them may exponentially decrease - like in oscillators with friction. All the information about the response at a finite time can be obtained by continuing the Fourier transform of various functions into complex values of the energy.

Because many physical processes will depend "nicely" or "analytically" on the energy, the continuation will nicely work. You will find out that in the complex plane, there can be non-analyticities - such as poles - and one can show that these singular points or cuts always have a physical meaning. For example, they are identified with possible bound states, their continua, or resonances (metastable states).

The information about all possible resonances etc. is encoded in the continuation of various "spectral functions" - calculable from the evolution - to complex values of the energy. Unitarity (preservation of the total probabilities) can be shown to restrict the character of discontinuities at the poles and branch cuts. Some properties of these non-analyticities are also related to the locality and other things.

There are many links over here for many chapters of a book.

However, I want to emphasize the universal, "philosophical" message. These are not just "tricks" that happen to work as a solution to one particular, contrived problem. These are absolutely universal - and therefore fundamental - roles that the complex values of time or energy play in quantum physics.

Regardless of the physical system you consider (and its Hamiltonian), its thermal behavior will be encoded in its evolution over an imaginary time. If Hartle and Hawking are right, then regardless of the physical system, as long as it includes quantum gravity, the initial conditions of its cosmological evolution are encoded in the dynamics of the Euclidean spacetime (which contains an imaginary time instead of the real time from the Minkowski spacetime). Regardless of the physical system, the poles of various scattering amplitudes etc. (as functions of complexified energy-momentum vectors) tell you about the spectrum of states - including bound states and resonances.

Before one studies physics, we don't have any intuition for such things. That's why it's so important to develop an intuition for them. These things are very real and very important. Everyone who thinks it should be taboo - and it should be humiliated - if someone extrapolates quantities into complex values of the (originally real) physical arguments is mistaken and is automatically avoiding a proper understanding of a big portion of the wisdom about the real world.

Most complex numbers are not "real" numbers in the technical sense. ;-) But their importance for the functioning of the "real" world and for the unified explanation of various features of the reality is damn "real".

And that's the memo.

Should Rajendra Pachauri Resign?

If you want people to take action, then you obviously would make the arguments that require a certain set of actions.

Rajendra Pachauri, August 2010, Wall Street Journal

I spoke with a lot of reporters today in the US and UK about the IAC IPCC Review report.  An overwhelming focus of their interest was on Rajendra Pachauri and his future with the IPCC.  The speculation comes from the following statements in the IAC report (PDF, p. 41):

 A 12-year appointment (two terms) is too long for a field as dynamic and contested as climate change. . .

Recommendation: The term of the IPCC Chair should be limited to the time frame of one assessment.

When asked for a specific comment about Pachauri by Seth Borenstein of the AP I said:

"It's hard to see how the United Nations can both follow the advice of this committee and keep Rajendra Pachauri on board as head"

I followed this statement by emphasizing that the reforms of the IPCC go well beyond one individual.  Removing Pachauri and doing nothing else would do little to fix the IPCC.  Conversely, doing everything else recommended by the IAC and leaving Pachauri in place would go a long way to improving the organization.  So in many respects I see the focus on Pachauri as a distraction. (Somehow those comments did not find a place in the AP story!)

That said, as I've detailed before (e.g., here and here and here), Pachauri has many issues of potential conflict of interest.  He would all but certainly be found to have conflicts of interest under the WMO and UN guidelines that the IPCC is exempt from following.   The IAC Review finds the fact that the IPCC has no such guidelines to be unacceptable, recommending:

The IPCC should develop and adopt a rigorous conflict of interest policy that applies to all individuals directly involved in the preparation of IPCC reports, including senior IPCC leadership . . .

Should Pachauri be deemed exempt from the recommended one-term term limit (as some have suggested) then it would not only make a mockery of the report, but also set the stage for a damaging battle over developing conflict of interest guidelines and how those should be applied to existing IPCC officials.  The IPCC could of course decide that Pachauri's conflicts do not disqualify him from the position.  Any such efforts to circumvent the IAC recommendations would risk further damaging the IPCC.

The bottom line?  The IAC Review has unambiguously recommended that the IPCC Chairman serve only one term.  Rajendra Pachauri has now served more than one term.  On this basis alone he should go.  However, even if an exception were made for him, he faces significant issues of conflict of interest that would result in his potential disqualification as the IPCC chair (should the IPCC implement policies anything like those of the WMO or UN or NRC).

If the IAC Review recommendations are to have any meaning at all then Pachauri should go.  Talk of retroactive application and grandfathering of the rules are a slippery slope back to the same sort of ad hocracy that got the IPCC into trouble in the first place.

As Expected: Cuccinelli Quashed

Exactly as expected, a Virginia judge ruled against (PDF) Attorney General Kenneth Cuccinelli's fishing expedition at the University of Virginia.  The Washington Post reports:

Judge Paul M. Peatross Jr. ruled that Cuccinelli can investigate whether fraud has occurred in university grants, as the attorney general had contended, but ruled that Cuccinelli's subpoena failed to state a "reason to believe" that Mann had committed fraud.

The ruling is a major blow for Cuccinelli, a global warming skeptic who had maintained that he was investigating whether Mann committed fraud in seeking government money for research that showed that the earth has experienced a rapid, recent warming. Mann, now at Penn State University, worked at U-Va. until 2005.

According to Peatross, the Virginia Fraud Against Taxpayers Act, under which the civil investigative demand was issued, requires that the attorney general include an "objective basis" to believe that fraud has been committed. Peatross indicates that the attorney general must state the reason so that it can be reviewed by a court, which Cuccinelli failed to do.

For his part AG Cuccinelli says he is going to pursue the effort based on the guidelines of the ruling:

Cuccinelli said in a statement that he will send a new CID to UVa to continue his hunt for proof that Mann defrauded Virginia’s taxpayers in obtaining grants that funded his climate change research.

“While this was not an outright ruling in our favor, I am pleased that the judge has agreed with my office on several key legal points and has given us a framework for issuing a new civil investigative demand to get the information necessary to continue our investigation into whether or not fraud has been committed against the commonwealth,” Cuccinelli said.

Even so, I'd guess that this is the last we'll hear from Cuccinelli on this subject.

Math Boxes

Today I begin a new series of posts on Math Boxes. The lessons will highlight Living Books, games, and hands-on activities that would be great for any school setting, but are especially good for Workboxes.

When I post, I will often invite others to link to Workbox posts on math. I encourage bloggers to link to posts that emphasize children's books/Living Books, games, and hands-on activities as opposed to worksheets and drills.

Let the fun begin!

US Dollar - UUP

I continue to like the US Dollar trending models and in particular, the UUP Daily Trend Model:

UUP Daily Trend Model

I'm not going to even pretend to know what global financial currents affect currency trends, but I can recognize a well trending trading vehicle when I see it and this one speaks for itself.  Looking at the recent historical performance of this trading model, it appears that about 2 out of 3 trend signals work for gains of between 5-10%, while the losers drop maybe 2% before getting stopped and reversed.  

For what it is worth Prechter is very bullish on the US Dollar, suggesting a surge higher in the coming months.  The above trend model isn't so prescient, suggesting only that the trend is up and that should be good enough for now.  

It is.

A

Report of the IAC Review of the IPCC

The InterAcademy Council Review of the IPCC has been released. The report is remarkably hard hitting with constructive and far-reaching consequences.  In the report's own words:

If adopted in their entirety, the measures recommended in this report would fundamentally reform IPCC’s management structure while enhancing its ability to conduct an authoritative assessment.

It is an excellent, thoughtful report.  While the report focuses on procedural questions and does not address any questions of scientific content, its recommendations have far-reaching substantive implications, such as for how to deal with uncertainty.  The report also directly addresses difficult subjects such as conflict of interest, policy advocacy and tenure of the IPCC chairman.

This post is simply a summary of the report's recommendations, and I will soon follow it with a bit more analysis.  Here then are the report's "key recommendations" that are highlighted in the Executive Summary, follwed further below by the recommendations found in the body of the text:

Governance and Management

The IPCC should establish an Executive Committee to act on its behalf between Plenary sessions. The membership of the Committee should include the IPCC Chair, the Working Group Co-chairs, the senior member of the Secretariat, and 3 independent members, including some from outside of the climate community. Members would be elected by the Plenary and serve until their successors are in place.

The IPCC should elect an Executive Director to lead the Secretariat and handle day-to-day operations of the organization. The term of this senior scientist should be limited to the timeframe of one assessment.

Review Process

The IPCC should encourage Review Editors to fully exercise their authority to ensure that reviewers’ comments are adequately considered by the authors and that genuine controversies are adequately reflected in the report.

The IPCC should adopt a more targeted and effective process for responding to reviewer comments. In such a process, Review Editors would prepare a written summary of the most significant issues raised by reviewers shortly after review comments have been received. Authors would be required to provide detailed written responses to the most significant review issues identified by the Review Editors, abbreviated responses to all non-editorial comments, and no written responses to editorial comments.

Characterizing and Communicating Uncertainty

All Working Groups should use the qualitative level-of-understanding scale in their Summary for Policy Makers and Technical Summary, as suggested in IPCC’s uncertainty guidance for the Fourth Assessment Report. This scale may be supplemented by a quantitative probability scale, if appropriate.

Quantitative probabilities (as in the likelihood scale) should be used to describe the probability of well-defined outcomes only when there is sufficient evidence. Authors should indicate the basis for assigning a probability to an outcome or event (e.g., based on measurement, expert judgment, and/or model runs).

Communications

The IPCC should complete and implement a communications strategy that emphasizes transparency, rapid and thoughtful responses, and relevance to stakeholders, and which includes guidelines about who can speak on behalf of IPCC and how to represent the organization appropriately.

Here are additional recommendations found in the body of the report:

The IPCC should make the process and criteria for selecting participants for scoping meetings more transparent.
The IPCC should establish a formal set of criteria and processes for selecting Coordinating Lead Authors and Lead Authors.

The IPCC should make every effort to engage local experts on the author teams of the regional chapters of the Working Group II report, but should also engage experts from countries outside of the region when they can provide an essential contribution to the assessment.

The IPCC should strengthen and enforce its procedure for the use of unpublished and non-peer-reviewed literature, including providing more specific guidance on how to evaluate such information, adding guidelines on what types of literature are unacceptable, and ensuring that unpublished and non-peer-reviewed literature is appropriately flagged in the report.

Lead Authors should explicitly document that a range of scientific viewpoints has been considered, and Coordinating Lead Authors and Review Editors should satisfy themselves that due consideration was given to properly documented alternative views.

The IPCC should adopt a more targeted and effective process for responding to reviewer comments. In such a process, Review Editors would prepare a written summary of the most significant issues raised by reviewers shortly after review comments have been received. Authors would be required to provide detailed written responses to the most significant review issues identified by the Review Editors, abbreviated responses to all non-editorial comments, and no written responses to editorial comments.

The IPCC should encourage Review Editors to fully exercise their authority to ensure that reviewers’ comments are adequately considered by the authors and that genuine controversies are adequately reflected in the report.

The IPCC should revise its process for the approval of the Summary for Policy Makers so that governments provide written comments prior to the Plenary.

All Working Groups should use the qualitative level-of-understanding scale in their Summary for Policy Makers and Technical Summary, as suggested in IPCC’s uncertainty guidance for the Fourth Assessment Report. This scale may be supplemented by a quantitative probability scale, if appropriate.

Chapter Lead Authors should provide a traceable account of how they arrived at their ratings for level of scientific understanding and likelihood that an outcome will occur.

Quantitative probabilities (as in the likelihood scale) should be used to describe the probability of well-defined outcomes only when there is sufficient evidence. Authors should indicate the basis for assigning a probability to an outcome or event (e.g., based on measurement, expert judgment, and/or model runs).

The confidence scale should not be used to assign subjective probabilities to ill-defined outcomes.

The likelihood scale should be stated in terms of probabilities (numbers) in addition to words to improve understanding of uncertainty.

Where practical, formal expert elicitation procedures should be used to obtain subjective probabilities for key results.

The IPCC should establish an Executive Committee to act on its behalf between Plenary sessions. The membership of the Committee should include the IPCC Chair, the Working Group Co-chairs, the senior member of the Secretariat, and 3 independent members, including some from outside of the climate community. Members would be elected by the Plenary and serve until their successors are in place.

The term of the IPCC Chair should be limited to the timeframe of one assessment.

The IPCC should develop and adopt formal qualifications and formally articulate the roles and responsibilities for all Bureau members, including the IPCC Chair, to ensure that they have both the highest scholarly qualifications and proven leadership skills.

The terms of the Working Group Co-chairs should be limited to the timeframe of one assessment.

The IPCC should redefine the responsibilities of key Secretariat positions both to improve efficiency and to allow for any future senior appointments.

The IPCC should elect an Executive Director to lead the Secretariat and handle day-to-day operations of the organization. The term of this senior scientist should be limited to the timeframe of one assessment.

The IPCC should develop and adopt a rigorous conflict of interest policy that applies to all individuals directly involved in the preparation of IPCC reports, including senior IPCC leadership (IPCC Chair and Vice Chairs), authors with responsibilities for report content (i.e., Working Group Co-chairs, Coordinating Lead Authors, and Lead Authors), Review Editors, and technical staff directly involved in report preparation (e.g., staff of Technical Support Units and the IPCC Secretariat).

The IPCC should complete and implement a communications strategy that emphasizes transparency, rapid and thoughtful responses, and relevance to stakeholders, and which includes guidelines about who can speak on behalf of IPCC and how to represent the organization appropriately.

Hurricane Earl in Historical Context

The image above is from the ICAT Damage Estimator and shows the current position of Hurricane Earl, along with the tracks of all historical storms that passed within 50 miles of that position.  The histogram on the left shows the historical normalized damage in 2010 values for those 12 historical storms, which had a median damage of about $3 billion.

Below is a map produced by the ICAT Damage Estimator of the current National Hurricane Center 5-day forecast cone, showing that the storm is forecast to remain offshore.  If the storm were forecast to make landfall, then you could use to ICAT Damage Estimator to compare normalized damage from analogous historical storms under 2010 conditions.

 The graph below shows the individual forecast model predictions for the track of Earl, illustrating a high degree of agreement across the models.

The ICAT Damage Estimator does not make predictions, but it is very useful for putting official predictions into a historical context.  Have a look.

Stay tuned, Fiona, the next storm in line could be interesting.

Doctors blends cardiology and country music

Listen to the Doctor: Cleve Francis, cardiologist and country singer.

Dr. Francis, who recently turned 65, is a genteel singer of country and pop songs. He favors vintage ballads.

A man inching up the line in a walker can't believe it. "You want his autograph? I get it on a prescription every three weeks," he says.



References:

Listen to the Doctor: Cleve Francis, cardiologist and country singer. Washington Post.
Dr. Wes: Working the Backup Plan

IAC verdict on IPCC: leadership shouldn't work on 2nd report

During the press conference at 10 a.m. New York Summer Time, the IAC panel has recommended all 8 top IPCC leaders to work on 1 report only, among other things to increase transparency and impartiality. The IAC reviewers have also recommended a new external board of overseers to supervise the IPCC. The IPCC has been successful but fundamental changes are needed, they say. Shapiro said that the GlacierGate and others have unequivocally dented the trust of the IPCC. Trust is something one has to earn again and again.

BBC: IPCC needs reforms, IAC review recommends

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RTT News: Review recommends major overhaul of UN climate body

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Irish Times: Report criticises climate change body

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Reason: IPCC processes critiqued

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Earth Times: Probe urges deep reforms in the IPCC

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Daily Mail: Body needs overhaul

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Fox News: Independent audit slaps U.N. climate panel

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Others at Google News

Rajendra Pachauri was elected in 2002 and re-elected for his second term in 2008. However, when asked whether the one-term IAC recommendation also implies that Pachauri should resign, Princeton's ex-president Prof Shapiro answered that it was too difficult a logical problem for him to solve so he has to leave the "interpretation" to others.

Well, that's how the Tuesday son puzzle would end up if I allowed the solution to be open to "interpretations" instead of logic, too.

When Shapiro discussed the IPCC errors such as GlacierGate that are dedicated some chapters in the IAC review, a lady from Al Jazeera asked whether he was not afraid that it could be interpreted as that he thinks that the IPCC has made some errors. Her eyes hinted that her Islamist and leftist friends could perform a terrorist attack against the IAC. But Shapiro didn't quite collapse although he clearly tried to appease the PC lady a bit.

In the IAC panel's opinion, the errors occurred because the IPCC did not obey its own guidelines - so the guidelines might be enough in their opinion.

Completely different words sounded an hour later

At 11 a.m. New York Summer Time, Pachauri has glorified himself, making catastrophic climate science look more worshiped than ever. He has read some comment from a jerk or two who has worship him. When Pachauri was asked whether he would respect the IAC recommendation and resign, he said that his interpretation was that it was forward-looking and for Pachauri personally, it's a mission he can't leave so "we will see". ;-)

Another IPCC apparatchik said that the IAC review - that has previously claimed that the scandals have dented the credibility of the IPCC has - shown that the IPCC's credibility is stronger than ever. :-) That's the "interpretation" by the IPCC logic.

Key fresh links (explanation below):

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► U.N. webcast (with Dijkgraaf, Shapiro, and others): LIVE; began at 10 a.m. New York Summer Time; continues from 11 a.m. (with Pachauri et al.)
► IAC report website
► IAC: web page about & before the release
► IAC: web page about & after the release

Older text written before the press conference

In March, Prof Robbert Dijkgraaf, a boss of the InterAcademy Council (IAC), was asked to investigate the methods underlying the work of the IPCC.

Robbert Dijkgraaf will review the IPCC

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Robbert Dijkgraaf: ClimateGate unrelated to the IPCC

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Princeton ex-president chairs the meta-IPCC panel

So he and his colleagues have chosen a meta-panel that has been reviewing the work of the IPCC for six months. Many of us have expected and expect that this IAC meta-review would be just another whitewash. But we couldn't really know for sure. We will learn the truth today.

BBC: UN climate change panel to face Himalaya error verdict

Ban Ki-moon will receive the IAC report, apparently focusing on the GlacierGate as key evidence of the IPCC's malfunctioning (well, the whole "juicy" portion of the IPCC report is made out of similar "material"), today in New York.




The following title used by Australia's ABC unequivocally answers the question whether the United Nations themselves were intending to build an impartial panel that would find the right answer about the IPCC's work whatever it is:

UN hopes science review eases climate scepticism

As you can see, there is no glimpse of honesty in the work of the United Nations. By the way, an Indian Wall Street Journal blog includes the IAC report among the two most important events of week, together with the new Indian GDP figures:

The Week Ahead: Report on IPCC, GDP Figures

The Hindustan Times propagate rumors that the report will not even call for the resignation of the IPCC's most famous scammer and liar, Rajendra Pachauri:

Pachauri likely to get away with mild rap

It would be just like the Nuremberg trials that would be evaluating the Nazi era but that wouldn't tell Adolf Hitler to resign.

Gauge theory in 12 dimensions?

The highest dimensionality in which a non-gravitational supersymmetric effective field theory is understood is 10 - or 9+1 - dimensions. And the theory is nothing else than the 9+1-dimensional Yang-Mills theory.

It is non-renormalizable but it may emerge either as the effective description of non-gravitational parts of the 10-dimensional N=1 supersymmetric string vacua or it can be compactified to 3+1 dimensions or lower to produce extremely important (not only for Matrix theory and AdS/CFT) renormalizable supersymmetric gauge theories.

The reason why 9+1 dimensions is the maximum dimensionality for supersymmetry is rather simple.

Particles may be invariant at most under 1/2 of the supersymmetry. Because the remaining broken supercharges act as ladder operators within the supermultiplet and because we want the spin to be at most 1 (3/2 is already too much because the only consistent spin-3/2 massless fields are gravitinos), there can be at most 4 raising and 4 lowering generators "broken" by a particle - to get us from -1 to +1 by the 1/2-steps that supercharges offer.

However, that means that there can be at most 8 supercharges broken by a particle that preserves 1/2 of supercharges - and at most 16 supercharges in total. The maximum dimensionality where spinor representations with 16 real components exist is 9+1 dimensions. The corresponding theory has a spin-1/2 field with 16 real components (a Majorana-Weyl spinor) all of which turn out to be physical - which is inevitable for the Dirac spinors and their reductions. These 16 fields may be Fourier-transformed into 8 creation and 8 annihilation operators for fermions in the momentum space. That's great because the 8 fermionic polarizations match the 10-2 physical bosonic polarizations of a gauge field in 10 dimensions.

Two times and higher dimensions

That's fine but can't we go slightly above 10 dimensions? Isn't there a more fundamental reality in a dimensionality that slightly exceeds 10? After all, we've seen examples that this must be true to some extent. M-theory provided us with a more fundamental, 11-dimensional platform to discuss type IIA and heterotic E8 x E8 string vacua in 10 dimensions. And F-theory brought us a geometric, 12-dimensional perspective on type IIB vacua with the variable dilaton-axion field.




Itzhak Bars has been studying and promoting theories with two time coordinates for decades. And today, he and his collaborator reveal their construction of a 12-dimensional supersymmetric gauge theory:

Super Yang-Mills theory in 10+2 dimensions, the 2T-physics source for N=4 SYM and M(atrix) theory

As you see, the signature is 10+2. Such a theory has two times. It's clear that the conventional physical interpretation of dynamical theories is impossible if there are two time coordinates. After all, if there were at least two large time coordinates, there would exist a two-dimensional "Euclidean" plane with purely time-like directions.

In such a plane, you could draw a smooth circle. That would inevitably be a closed time-like circle (CTC), something that prevents you to organize physics in terms of initial and final conditions because it allows you to kill your grandfather before he had his first intimate contact with your grandmother, thus making your personal existence logically inconsistent. ;-)

To make things simpler, there would be no universal "after" and "before": the future light cones and the past light cones would be connected through the second time coordinate.

I think that Itzhak Bars is aware of this issue. His two-time constructions have always been less "physical" in this sense: he always meant the higher-dimensional two-time starting point to be a more symmetric "master theory" that sheds more light on the unity between the lower-dimensional theories and that makes many of their symmetries and properties manifest.

In my opinion, this is a beautiful template for a very serious and potentially important research. Except that I think that in the examples that Bars has studied, such a program - or working hypothesis - hasn't been successful yet.

In the new paper, the authors construct a 12-dimensional theory that may be reduced to the 9+1-dimensional gauge theory and others. But the actual reduction is not the familiar dimensional reduction. After all, they don't find any Kaluza-Klein modes etc. That means that even the counting of the physical degrees of freedom in the higher-dimensional, 10+2-dimensional theory has to be altered.

If you study their Lagrangian (1.1) for a while, you will see that they actually believe that there could be a gravitational theory in 12 large dimensions. That's an even stronger statement but let us follow their newest paper and focus on the non-gravitational truncation.

This theory has a gauge field, the "F_{mu nu}", with the familiar "F mu nu F mu nu term". It's multiplied by a power of the "dilaton" Omega (taken from the gravitational sector that we try to decouple now) and by other things. All the terms are also multiplied by a volume factor that depends on W, another scalar field, and by some undetermined extra factor K etc.

The overall normalization of the action looks truly strange with so many scalar factors - a hint that the 12-dimensional geometry is not "real".

But what is the key novelty is the terms for the fermions. Normally, in 9+1 dimensions or lower, you have a kinetic term and the coupling to the gauge field that combine into a gauge-invariant combination. However, in their case, they make this gauge-invariant term more complicated, namely

lambda Vslash D lambda.

The covariant derivative is also multiplied by Vslash which is the vector V contracted with the gamma matrices. And the vector V is the gradient of the scalar W (over two). So if you were imagining the scalar field W to be constant so far, well, then you see that the fermion terms would vanish.

In general, you don't want this term to identically vanish. That means that the non-constancy of W has to be crucial for the theory to be physically non-trivial. I feel that the variations of the fields in the direction along the gradient of W (and one more?) are kind of (identically) unphysical which makes the whole construction less meaningful and important.

However, there is some similarity with the Bagger-Lambert-Gustavsson (BLG) theory in 3 dimensions that sparked the "membrane minirevolution" but that was more or less found out to be a new fancy description of the 2+1-dimensional theory. It made the SO(8) symmetry of its conformal limit - which is so important for the Matrix theory of type IIB string theory - manifest - but otherwise you could a posteriori dismiss the whole BLG theory as a new notation for old physics. However, the BLG theory did lead to a class of new theories - the ABJM theories - that were directly inspired by the BLG construction.

If something like that were possible in the Bars-Kuo construction, it would already deserve your attention. However, I am not sure whether it's the case. So far, the extra two dimensions you may find in the 10+2-dimensional theory look very artificial to me. They just don't seem "real" in any way. They don't seem to "explain" any known property of the gauge theories that was previously unexplained (or unexplained in a manifest way).

We may see later.

Kid-Scheduled Workboxes

As I mentioned, I never thought I'd try workboxes. And *try* is still a key word here. I'm going to try them.

Why workboxes?

*I am organizationally challenged. I hope this will encourage me (and my children) to keep things in their place and have things ready for each new school day. No excuses.

*With several workbox tweaks (described below), I want to foster my children's independence.

*My preschooler. At four, he desperately wants to "do school." He has a couple boxes in which I'll stash some hands-on activities and books.

*I have a LOT of school materials around here; I'm hoping this encourages me to use some that I've forgotten about.

Here's my plan...

I want my son to continue to schedule his day. I love the way this gives him a sense of responsibility. It's also beneficial for our parent-teacher-child-student relationship. *I* am not telling him what to do. The schedule--which he created--is telling him what to do. Don't get me wrong. I have no problem telling my children what to do (or I wouldn't have had FIVE); however, I do think that one of the challenges in homeschooling is the ever increasing amount of directives coming from adult to child. For homeschoolers it's not just parent-child directives, but also teacher-student.

I prepared* the schedule cards for this year as follows. (*I prefer to have the child create the cards, but in this instance I needed to figure things out as I worked. Tweaking, always tweaking.)

When my son wakes up in the morning, the chart will look like the one to the left. The orange/yellow cards indicate landmarks that I schedule: breakfast, lunch, rest time, outside play time, my exercise time, etc.

His first job in the morning will be to schedule his day using blue subject cards. Each card has a number in the lower right corner indicating approximately how many minutes of school time need to be reserved. I will set out the cards needed that day; each card will have a corresponding workbox, already filled and ready to go.

Blue cards include subjects:

• science 
• math calendar
• reader/history (Sonlight Core 3)
• journal
• art
• math 
• writing workshop
• violin
• foreign language
• Bible (Sonlight Core 3)
• read aloud/history (Sonlight Core 3)
• history (Sonlight Core 3)
• cursive writing
• "extra" (catch-all box)

And a few daily jobs:

• pick up house
• pick up room

(Remember, the subjects aren't all done every day. I will give him the cards he needs each day.)

Each subject card has a labeled box. (Or at least the ones that use school materials do. Things like "violin" are just part of the schedule and not boxed. I don't have violin-sized boxes! ;)

A few boxes are double labeled like the one at left; we will do art and science on an alternate schedule. A few boxes have an additional sticker. The MOMMY sticker.  This sticker indicates how many minutes Mommy needs to help. For a few subjects, it's the entire time. For most, it's a smaller length of time, designed to introduce a subject (teacher/student), followed by some time to do some independent practice work (student).

Each box includes all materials needed to complete the task. In the "read aloud" (Core 3) box at right, for example, the box contains the book as well as the iTouch containing the CD with the poems read aloud.

When he finishes a subject, he empties the box into a large "I'm done" box and turns over the related blue card.

No moving discs or worrying about velcro. And he still will set his own schedule. The biggest benefit to me is that I am accountable for having his entire school day ready to go the night before. As I told a friend, it's your basic "lay out your clothes the night before" routine. Just for school.

I never was good about laying my clothes out the night before. Hope I can do this. Although we're on Sonlight Core 3, week 9, and have been doing it all summer, we "officially" start school on September 7th. I'll report on my workbox progress then.

Two of my focus boxes on this blog will be preschool math and living math books/related activities. Check back!

Far away from now

Won't you look down upon me, Jesus
You've got to help me make a stand
You've just got to see me through another day
My body's aching and my time is at hand
And I won't make it any other way

I've seen fire and I've seen rain
I've seen sunny days that I thought would never end
I've seen lonely times when I could not find a friend
But I always thought that I'd see you again

Funny, isn't it?  Looking back at all of the people that have crossed paths with us in our lifetimes, how many of them disappeared from our lives entirely, never to see them again? At the time we last were together, neither one of us knew that it was the last time.  The last time we would catch each others eyes,  the last time we would be sharing even a sliver of each other, a time, place and memory forever fixed, so final, finished, the closing chapter of a book too brief, a narrative so fleeting and it was gone before we could grieve.

A lover, an ex, a best friend, a parent, it doesn't really matter, does it?  Time closes all that we have been, whoever we were and whatever life we were living.  Relentless, dogged, unforgiving.

I went dancing last night.  My partner held me close and though the small dance floor was elbow to elbow and tush to tush, we stood alone, caught in an embrace that will live with us forever.  When will this one pass?  When will paths divert, our lives move on, or now, in these years, just end?

Who are you missing tonight?  A first friend, first love, first spouse, first wonderful taste of the sweetness that rained down from our first companion in intimacy?

I miss the girl on the dance floor last night.  Though just a few feet down a hallway, I miss the way she was with me last night, buoyed by tequila,  the loud music and crowded dance floor, we found a space and time where we stood alone, a forever moment to be remembered, then missed, one day far away from now.

Math Book Winner

I used random.org to pick a winner of the Living Math Book giveaway. The winner is #22, Brandi! Congratulations and thanks to all who entered.

Workboxes for the Organizationally Challenged

If you're a homeschooler, you've noticed the buzz about "workboxes."  Dead set against doing them (because I couldn't imagine EVER being organized enough to pull it off), I still seemed to keep migrating back to blogs showing photos of the system. Working. Effectively. Even with hopeless organizationally challenge folks like me.

So I'm trying it.

I'll explain my system soon. It's quite different from the velcro tag concept that others are using. I figured out that was too much work last night around 11pm. AFTER I'd already hand-cut and covered 24 number buttons with contact paper. I sat there staring at strips of velcro, wondering how I'd get them to stay on. I went to my email and found that my membership in a workbox forum has been approved. Upon visiting the site, the first post I read: "My velcro won't stay on!!!"

I bailed the velcro ship.

In upcoming weeks, my readers will probably be most interested in two of my workboxes:

• Preschool Math
• K-5 Math--with children's books, games, activities

More to come. Soon. After I find my way out from under all this velcro.

Will the 2013 solar flare return us to the Stone Age?

Fox Business News Channel brought the "top physicist" (right after Al Gore, Lee Smolin, and Joe Romm) Michio Kaku who explained that we're doomed in 3 years:

Every 11 years the [Sun's] north pole and the south pole flip, releasing a burst of radiation. But, every 100 years or so, a monster Tsunami from the Sun emerges which could literally cause trillions in property damage. […]

It could paralyze the economy of the planet Earth. In 1859 we had a gigantic solar storm which knocked out telegraph wires back then, 150 years ago. If that had happened today it would knock out almost all our satellites, knock out power stations, there would be food riots around the country because refrigeration would stop, airplanes would probably crash without radar. […]



And again, this is a once in a century, once in two centuries storm…

We do have them and we have to worry about them. […]

We’d be thrown back 100 years.

Every 100 years, we're thrown back 100 years just by the solar storms, we're told. Because there are dozens of types of similar catastrophes, it is clear that every 100 years, we're thrown back several millennia. ;-)

It sounds scary, doesn't it? One year after the Earth collapses because of the end of the Mayan Calendar in 2012 and after another doomsday prescribed by Nostradamus, we will face yet another Armageddon. Fine. You may buy insurance from me. What is going on?

My friend Olda Klimánek has written some amusing details about the story.



First, some background

The Sun is changing over time. There are approximately 11-year-long cycles of solar activity. The number of sunspots - a sunspot is a little mottle on the Sun that you can see through a telescope - reaches the minimum every 11 years. We have just seen one of the "cleanest" minima in decades a year or two years ago. Almost no sunspots for many long months. But it's over: the Sun shows us some sunspot activity again.

Every 11 years, the Solar magnetic field changes the direction - from South to North, if you wish. Only the absolute value (squared) matters for the number of sunspots. However, because you have a cycle with the "antiperiod" of 11 years, it's not hard to see that the genuine cycle is approximately 22 years long. After 22 years, the magnetic field of the Sun returns to the original state, including the sign.

This periodicity is not perfect, of course: there are also slower cycles (and perhaps also slower aperiodic phenomena) that change the behavior of the Sun every few centuries.

Some Czech media wrote that 2013 will be exceptional because the 11-year and 22-year cycles will reach a point of orgasm at the same moment. This is, as Olda explains, a complete misunderstanding of the cycles. These two cycles are synchronized so in each cycle, they're always in harmony (or disharmony) to the same extent. ;-) Clearly, they wanted to explain the 22-year peak by something else but it is not clear what the something else was.

Usually around the sunspots, the Sun sometimes produces an eruption called solar flare. Lots of radiation and protons with energies up to dozens of MeVs - a third of the speed of light, but usually much less - are ejected. (It's a high speed but the protons at the LHC carry 3,500 GeV at this point so the speed is 99.9999% of the speed of light or so.) Ionosphere of the Earth and long-wave communication is affected when the solar flare reaches our planet. But that's it.

Events: 1859 and 2013

So how did the Michio Kaku apocalypse in 1859 look like?

On September 1–2, 1859, the largest recorded geomagnetic storm occurred. Aurorae were seen around the world, most notably over the Caribbean; also noteworthy were those over the Rocky Mountains that were so bright that their glow awoke gold miners, who began preparing breakfast because they thought it was morning.

Telegraph systems all over Europe and North America failed. Telegraph pylons threw sparks and telegraph paper spontaneously caught fire. Some telegraph systems appeared to continue to send and receive messages despite having been disconnected from their power supplies.

People could see aurorae but they probably caused less trouble than Aurora in the 1917 Saint Petersburg, Russia. ;-) And some miners prepared a breakfast too early. That must have cost trillions of dollars. ;-) But the masterpiece of the story are the telegraphs that turned into perpetuum mobile devices. Clearly, the hungry robots, iPods, and Macs - once disconnected from the power grid - are going to stage an uprising in 2013, being driven directly by the energy from the solar flares. ;-)

I don't claim that all the observations in 1859 were bogus. There surely had to be some telegraphs that failed. But there's a lot of superstition and mythology surrounding such events, too. I personally think that a similarly strong event has occurred several times after 1859 again and almost no one has noticed. (Update: I take this sentence back after some commenters have convinced me that ice core data show an unusually high trace of beryllium-10 from 1859 that may be the highest in 2000 years.)

Why 2013?

Well, it's simple. The Solar Cycle 24 is predicted to reach its maximum in May 2013. And this maximum has to be spectacular, some people said.

In reality, such a maximum occurs every 11 years and just very recently, we thought that the ongoing solar cycle would be one of the least active ones: the sunspot number at the maximum was predicted to be e.g. 90, the lowest peak in 1928, and many people used it to argue that the reduced activity will induce a substantial cooling on Earth. A low activity would also seem to imply a low intensity and frequency of the solar storms and flares.

Nevertheless, two months ago, "NASA" warned of the 2013 apocalypse:

Telegraph, Telegraph video, WUWT, Google News

At least the Telegraph presented it in this way. They may be particularly scared because the 1859 solar storm has crippled a few telegraphs, too (see the picture for a brand new 1859 telegraph) - and telegraphs may sound even more obsolete and vulnerable today. ;-)

(More seriously, I believe that the telegraphs and grids in 1859 were much more shaky and the current electronic devices are much more robust when it comes to their resilience to perturbations.)

You will see that the whole story comes from Richard Fisher, the head of the NASA Heliophysics Division, who promotes his specialized discipline a little bit. But even though he was clearly selected as the advocate of the catchiest scenarios, he's not really saying much - and he's not hiding that what he's suggesting are mostly fantasies.

So I don't really understand why they think that something unusual - at the centennial time scale - should occur in 2013. In fact, I am convinced that this statement is wrong. By the way, Olda K. analyzes some similar statements about related solar events. Around August 3rd, 2010, the media were also writing about a comparably devastating effect of the Sun on our planet that was imminent.

Of course, nothing has happened.

It may be cool to speculate about catastrophes - to imagine that some of the catastrophic movies become reality - but once we entertain ourselves, we should still try to hard to distinguish the reality from the fiction. The reality is that unlikely and infrequent heliophysical (and other) events are unlikely and infrequent which means that unless you have a good reason to expect that they will occur, they will probably not occur anytime soon.

And that's the memo.

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Thanks for the provocation to write it up to: Jaynie B.