text:
## Wednesday, August 31, 2005 ... /////

### Warped Passages out

The U.S. edition of Lisa Randall's book called

is finally out, about three months after the British edition. More precisely, you should see it everywhere by tomorrow. I greatly recommend the book especially to those who have already been interested in particle physics for some time.

This is a book in which you not only learn what is a dimension and how various laws depend on the spacetime dimensionality etc., but you will also see what the one-brane and two-brane Randall-Sundrum models are, even what locally localized gravity is, how the branes got started in string theory, what are the different scenarios by which the branes are included in string-theoretical and string-inspired models of reality, and how the extra dimensions may solve problems of particle physics such as the hierarchy problem or the flavor-changing neutral currents.

These are just examples. On page 152, you will even learn how a famous Russian communist was wrong in his argument with a Czech anti-communist, an argument that was focusing on the structure of the electron. :-) Was Lenin wrong? That's what the first female tenured physics professor (or at least theoretical physics, in one case) at MIT, Princeton, and Harvard who wrote the book says.

### Entanglement entropy

One of the most interesting papers 24 hours ago was a paper by three authors from Santa Barbara, Israel, and Michigan claiming that the black hole entropy in all known examples in string theory may be entirely interpreted as

It is certainly true that not everyone has believed and believes that the whole entropy equals the entanglement entropy; others viewed entanglement entropy merely as one of the contributions. The total number of microstates of the interior counts the total entropy; but it is not necessarily true that each of them is entangled with a different state of the exterior degrees of freedom. The entanglement entropy could therefore be smaller. I am curious to hear comments from others.

Also,

offers a new proof of the CSW rules for the tree amplitudes based on the maximally helicity violating vertices. If someone can explain in what sense the proof is more direct than the BCFW proof, it may be interesting.

### Katrina Relief

The hurricane Katrina has not only killed 100 people or more but it may also have become the costliest natural disaster in the U.S. history - with the damage counted in tens of billions of dollars. While America always helps others, it seems unlikely that others share the same standards of compassion. Well, this is one of the reasons why the U.S. is special in the world today. But you may be different:

The money will help those who became homeless to satisfy the basic life necessities. Next time it may be better not to build new huge and fascinating cities like New Orleans below the sea level. Be ready that the oil price is gonna hit \$80 per barrel in the short term and gasoline will surpass \$3 per gallon.

## Tuesday, August 30, 2005 ... /////

### Short world news

General and politics:

• According to a Flemish participant, the most impressive speech during the recent regional meeting of the prestigious Mont Pelerin Society was the speech of the Czech president Václav Klaus who warned against Europeanism, NGOism, and other -isms that are starting to replace socialism; see also Klaus's completely new article in the Financial Times (without fees)...
• The hurricane Katrin will cost the insurers and others something between 10 and 25 billions of dollars; if the higher number is true, it will be the most expensive hurricane on record. Also, the oil price has tried the $70 level because of the weather. Katrin is manifested here in Massachusetts as a rather pleasant and peaceful summer rain... • Wearing sandals and sunglasses, Allan Adams, a Harvard physicist specializing in "string theory," looks like he would be at home sipping espresso in a Greenwich Village coffeehouse: "Gliding isn't macho-type activity. There's no adrenaline rush" :-)... • The TIME magazine has escalated the worries that the upgef*cked terrorists are planning something significant against our good old Europe. Al-Zarqawi, the Jordanian head of the "Al Qaeda in Mesopotamia, the land of two rivers", is apparently organizing lectures of European languages so that their task becomes easier to solve; Balkans (especially Albania) may become their "golden gate" to Europe... ## Monday, August 29, 2005 ... ///// ### Anthony's review erased Just a small comment. Two days after Anthony Kirmis received his$13.08 grand prize for his review of McCutcheon's book, the review has been erased and the average rating of "The Final Theory" returned to 5 stars. All 1-star and 2-star reviews posted before the challenge as well as after it started are gone. Crackpots may often be perfectionists. ;-)

Joe Marsano has told me about something he has heard from Josh Lapan: if you look for the author "Marc McCutcheon" (with "c" which may mean that it is a different guy than the author of "The Final Theory", namely Mark McCutcheon), you will find the following book:

The book explains that you don't have to have any degree or knowledge, and explains you how should you promote your book. In other words, it is the complete guide how books like "The Final Theory" may be written. Incidentally, this book also has around 35 reviews and the average rating is 5 stars. Do you think it is the same M. McCutcheon?

## Sunday, August 28, 2005 ... /////

### BBC: sensitive IQ tests

The attitude presented in the following paragraph is a joke, of course.

BBC has apparently abused the freedom of speech in England. They were not afraid and ashamed to publish the outrageous results of IQ tests designed to measure "general cognitive (spatial and verbal) ability" that two British researchers (Paul Irwing and Richard Lynn in British Journal of Psychology) gave to 80,000 people plus 20,000 extra students; well they summarized some previous tests but it does not really matter. What a crummy article.

• Below 14 years: no measurable difference between boys and girls
• Above 14 years: IQs differ by 5 points
• IQ 125 and above: 2 vs. 1 ratio
• IQ 155 and above: 5.5 vs. 1 ratio

Their story immediately became the most discussed news story in the blogosphere. To balance the viewpoint, an alternative research with the opposite result was performed by Barry Sheerman, a British MP: women are cleverer than men, he said.

The word "research" used for Sheerman's statements was another joke, of course.

Now: most IQ tests are not terribly deep (and one can train herself or himself to get better results) - and one can't really deduce anything certain from one silly number. Nevertheless, if a question should be studied rationally, something like that had to be done anyway and the correlations between the resulting IQ and other things will exist. As far as I know, they (mostly?) used the Raven Standard Progressive Matrices which is respected as a good test of the pure intelligence factor g.

## Saturday, August 27, 2005 ... /////

### Let us build the ILC

The purpose of this page is not to explain things like which two European countries shared the LEP collider. Incidentally it is either South Africa and Nigeria, or France and the Supersymmetric Republic of Switzerland, or Australia and New Zealand, or Peru and Chile.

JoAnne Hewett has encouraged everyone to promote the ILC, the "Imaginary Linear Collider", as our phenomenological friends call it. It is a pleasure to follow her instructions. My comments are primarily addressed to the true American patriots who, I hope, are well represented among the readers. :-)

Anthony Karmis (undergrad: UIUC, grad: UC Santa Barbara) has become the winner of our grand prize - $13.08 - for his first 1-star amazon.com review of McCutcheon's book. We have explained the little scandal over here and some of the initial developments here. The money has been transferred to his paypal.com account. Anthony's prize is a deserved one. He remains the only person whose 1-star review survived for one week - and the only one that remained on the web until the present. Tens of unwelcome review posted before Anthony's review as well as after it have been erased. The latter category includes, for example, Quix from Columbus, Ohio. There seem to be many witnesses who may confirm that Brian Powell was right and something was wrong - and most likely something is still wrong. ## Thursday, August 25, 2005 ... ///// ### Sidneyfest videos The web page of Sidneyfest now includes 13 videos - virtually all talks from the conference. QuickTime 7 or QuickTime Alternative needed. Enjoy! ### Trackbacks and arXiv Paul Ginsparg has introduced a new experimental service - trackbacks; most likely, Jacques Distler was the driving force behind this new feature. See Paul's explanation here. This service allows the visitors of arXiv.org, at least in principle, to see the list of blog articles that are describing a given paper. For example, look at the paper You will see "1 trackback" at the bottom of the page. Actually, there are 2 trackbacks; their new system has some minor bugs so far, for example it cannot count properly. If you click at this "1 trackback", you will see two blog articles about the paper, namely Jacques' and mine. ### Marcos Mariňo's book  Figure 1: Marcos Mariňo likes similar T-shirts except that he admires the opposite side than the soldier on the picture - namely Gentlemen like Fidel Castro, Karl Marx, Che Guevara, Mao-Tse Tung, and the ideals of communism and general copulation. ;-) This did not prevent him from becoming a smart mathematical physicist. Because I helped Peter Woit to promote his book, it may also be useful to mention that Marcos Mariňo has written another book that is probably much more meaningful, namely a book on Chern-Simons theory, matrix models, and topological strings: It should be released in November or so (which means that it is already out). The previous book is about topological quantum field theory on four-manifolds: In the new book, one should be able to learn all the relations between the matrix models, Chern-Simons theory in 3 dimensions and its "holographic" duality with topological string theory; and the implications for knot theory and the Gromov-Witten invariants. ## Wednesday, August 24, 2005 ... ///// ### Verizon I forgot to include an elementary introduction to the black holes in string theory before the black hole posting in the morning, so here it is: The Verizon customers already know the powerful stuff. When will the readers of Not Even Wrong join them? ## Tuesday, August 23, 2005 ... ///// ### Book that is Not Even Wrong Let's start with my first public review of this book. Bitter emotions and obsolete understanding of high-energy physics (1 star) Peter Woit is the owner of a well-known blog that provides high-energy theoretical physics with the same service as William Dembski's ID blog offers to evolutionary biology: it is designed to misinterpret and obscure virtually every event in physics and transform it into poison - and to invent his own fantasies to hurt science. This makes Woit's blog highly popular among the crackpots, for example some of the reviewers of this book. The book is not identical to the author's blog but it is not too different either. Parts of this book are fun to read, although they will be too difficult for outsiders. But the text is definitely not a trustworthy source of knowledge about physics. The book can basically be divided into two parts. The first part of the book describes physics from the early 20th century to the 1970s or so. This part covers some standard material as well as some points that have not yet appeared in the popular literature. The early chapters also honestly explain that the author has not done any important work in high-energy physics himself and that he has been isolated from research (and researchers) for the last 20 years. Because of these reasons, I originally rated the book by two stars. ### Hagedorn, black holes, and Brownian motion Most of us seem to agree that the most interesting hep-th paper today is one by It's true that no one seems to be able to say exactly what is the new stuff - probably because no one has read the paper in detail so far - but there is a lot of interesting material in it anyway. Let me describe some of the crucial ideas for this business. They study the behavior of strings near the Hagedorn transition. As you know, the partition sum diverges above this critical temperature because the number of excited string states at a certain level increases faster than what the Maxwell-Boltzmann exponential factor is able to suppress; alternatively, the partition sum diverges because a thermal scalar emerges - it is a tachyonic winding string wrapped on the thermal (Euclidean periodic time) circle in spacetime; its winding number equals one. These two pictures are related by the modular transformation on the worldsheet (tau goes to -1/tau). Kruczenski and Lawrence insist on the traditional Atick-Witten rules of the game and don't try to believe some recent "Hagedorn revolution" papers that we discussed a short time ago. When the tachyon dominates, the partition sum may be calculated using the path integral over the histories of this particular field in spacetime; these are the random walks or, equivalently, the Brownian motion. I believe it's a well-known fact that the highly excited strings - which are inevitably long (more precisely, one long string with a gas of small strings is the typical configuration) - are a dual description of the thermal scalar near the Hagedorn temperature. Albion and Martin focus on the typical size of these chaotic strings and random walks and they argue that the characteristic radius goes like the square root of the energy in string units (recall the basic rules of the Brownian motion pointed by Einstein 100 years ago). Then they make a jump to the long strings in the AdS space and argue that there exists a transition to the black hole - something that has been advocated by various authors. We will only see the new argument once we look at the paper in detail. You know, there exists a nice paradigm that a black hole may be thought of as a condensate of the thermal scalar. This is most clearly manifested in the work by Adams et al. In their case, a circle in spacetime with antiperiodic boundary conditions for the fermions carries a scalar field that becomes tachyonic if the radius shrinks below a critical value; the final state of the condensation of this scalar is a spacetime with a different topology in which the handle is cut into two pieces and the closed strings are banned from the region that used to connect the two sides. This picture can also be interpreted in the case when the circle is viewed as the thermal circle: the condensation of the thermal scalar then produces a black hole. Note that it is not true that you get the black hole "immediately"; you must roll over the configuration space and increase the condensate to actually change the topology of the spacetime, and this fact makes many connections between these two pictures difficult to calculate. Together with Allan, we also tried to interpolate between the tachyonic perturbative instability and the Witten's non-perturbative instability of the Kaluza-Klein compactification but it is pretty hard to extract any quantitative checks from such a nice picture especially because the Witten bubble is a "large" condensate of the tachyon. Albion and Martin also study the excited strings in the anti de Sitter space and advocate their connection with the anti de Sitter black holes. One of the paradigms that their work seems to support - or at least paradigms that they independently believe to be relevant - have been summarized in various intriguing papers by Lenny Susskind around 1994, for example in this work by Uglum+Susskind. They argued that the black hole entropy can be explained using a long string that is chaotically wound around the black hole horizon. I also believe that these ideas must be morally correct - well, I've rediscovered them independently, too. It is even plausible that this picture, once it's put on firm ground, will confirm Samir Mathur's ideas that the black hole interior is very different than we thought. But no one seems to have a clear picture yet. ### Disengagement is mistake The Israeli-Arab conflict is a very sensitive issue. Let me start with the following points: ## Monday, August 22, 2005 ... ///// ### Becker Schwarz Becker Becker Schwarz Becker. That's not a description of a tennis duel in Germany but a rumor about a possible new string theory textbook that is being prepared. Anyone knows more? This rumor came from the blog of CapitalistImperialistPig. ### Stanford supports Newton The Stanford experimental group around Alan Kapitulnik has found no deviations from the Newtonian gravitational law. They have improved their limits on a new force at 20 microns - a force that they parameterize as a Yukawa force - and published a paper about it, namely hep-ph/0508204. According to the newest rumors, the Washington group will also confirm a negative result. The results so far are consistent with Newton's theory much like the new Intelligent Falling theory. ;-) It is not hard to summarize all hep-th papers today. Raman Sundrum offers his TASI lectures on the fifth dimension. Alexander Vilenkin reviews the cosmic strings and confirms that the Hubble decision about the CSL-1 galaxies (Cosmic String Lensing?) should appear by early 2006. One abstract paper speculates about the Immirzi parameter and torsion. There is shockingly one more paper about the Immirzi parameter: a new value of it is proposed. Although many people would be happy if someone else referred to their (my) work often, I am personally very confused what all these guys want to do and why they think it's interesting; see the quasinormal story on quasinormal modes. Christian Saemann studies a certain cousin of the twistor space for three-dimensional gravity - in fact it is N=8 supergravity. Agarwal and Ferretti study integrability of spin chains; they show that a new, "higher" conserved charge in the su(2|3) sector of N=4 Yang-Mills is determined algebraically. Similar questions in a different, su(1|1) sector of the same theory is studied by Alday, Arutyunov, and Frolov in relation with the free fermions. Frey, Mazumdar, and Myers argue that stringy effects can leave imprints on the CMB radiation through inflation and reheating in multi-throat cosmologies; a new, long-string era plays role in their picture. Two Sorokas argue that they can construct a multiplet in the Minkowski space with different masses in it, marginally contradicting the Coleman-Mandula theorem. Finally, Kopper tries to make some facts about renormalization flows (in the context of the Euclidean lambda.phi^4 theory) more rigorous. ## Saturday, August 20, 2005 ... ///// ### Franziska Michor: math of cancer Beauty of math vs cancer Picture: Alois Endl This is the first one from a planned series of occasional interviews of The Reference Frame with some of the most distinguished very young scientists (below 30 or so). It is likely that many of the interviewed people are going to be Harvard Junior Fellows; however, you may suggest your own candidates. Update: See also Esquire about Franziska Michor Q: We will start with Franziska Michor, who is a Harvard Junior Fellow working on mathematical models of cancer. Franziska, can you quickly describe how you got here? A: I did my undergraduate in molecular biology and mathematics at the University of Vienna, during which I spent half a year in Italy studying medical biotechnology. After that I started my PhD at Harvard University with a sabbatical at the IAS in Princeton. I got my PhD from Harvard in 2005, and now I'm a Junior Fellow. Q: When you study cancer, do your results apply to all types of cancer or is there a difference between colon cancer, lung cancer, or leukemia, among other examples? A: Some of my work is concerned with genetic alterations that occur in all kinds of cancers. For example, tumor suppressor genes are genes that contribute to cancer progression if both copies are inactivated or lost from the cell. There are many different tumor suppressors that are involved in different types of cancer, but they all function similarly inasmuch as they need to be inactivated in both copies for tumorigenesis. Therefore, an interesting question for most types of cancers is how long it takes to inactivate a tumor suppressor gene in a population of N cells. The answer represents an important step towards a quantitative understanding of cancer genetics. Another such example is the role of genetic instability in tumorigenesis. Other projects, however, are concerned with mutations or treatment strategies that are specific to one kind of cancer. ### Diversity sinkhole The only serious journal analysis of the so-called and those$50 million for the so-called "diversity" efforts appeared in City Journal. Heather Mac Donald concludes in

that Harvard is throwing away more than just the money. The title of this blog article has been borrowed from The Washington Times. Of course, the bad news from Harvard has also been celebrated by conservative Yalies.

A few months ago, I would not have the courage to make this posting. Today, after a change of personal policy, I am once again absolutely certain that this posting is completely legal according to all existing laws and codified regulations, and I have the right - and not only the right - to endorse Mac Donald's reasoning. On the other hand, the advocates of the only "correct" opinions don't have the right to impose it on others.

For all who have also been pacified, neutralized, and psychologically tortured by the recent PC craziness, let me mention that unlike the case of Czechoslovakia in 1968 i.e. exactly 37 years ago, there are no PC tanks in the streets of Cambridge, and this should make a difference. Let's just stop the bad era; it has been enough indeed. Let's regain our human dignity and never allow the enemies of independent and rational thinking to manipulate with us again. Thank you.

Dictionary:

50 million USD: the total value of all physics Nobel prizes roughly since the war (or the beginning); the total money needed to run a new large physics institute, such as the Perimeter Institute, in the medium term; the amount of money that can be easily thrown away for an attempt to engineer evidence supporting wild hypotheses that cognitive skills are independent of physical parameters

diversity efforts: efforts to make the life very difficult for everyone, especially for diverse large groups of people - such as the conservatives, libertarians, moderates, meritocrats, and eventually also all white males - by creating a large body of new and intimidating bureaucracy, restrictions, regulations, and discrimination

## Friday, August 19, 2005 ... /////

### Common crackpots' errors

Everyone knows John Baez's Crackpot Index that allows you to calculate how obvious crackpot the author of a given article is. While I agree with the general philosophy, let me offer a complementary description of some features that, according to my vast experience and uncountable encounters with most of the crackpots living on this planet, distinguish scientists and those who are viewed as crackpots by the scientific community.

In the most optimistic case, it will help someone to find a more rational approach to the scientific questions and avoid some common mistakes - even mistakes that are usually not emphasized. In the more realistic case, it will at least lead some readers to ask new questions. No doubt, many of the points below overlap with each other but I decided to divide the discussion into these paragraphs anyway. It is also clear that many important points are missing.

Poor estimates of certainty and uncertainty

The crackpots are typically unable to estimate the amount of uncertainty associated with any particular insight. Such an intellectual exercise should often be pretty simple: one should look how many papers or inventions or industries seem to depend on a particular conjecture or theory. And if numerous papers or inventions seem to work, one should be more careful before he questions or replaces the very basic features of the underlying theory. The crackpots may fall on both sides of this divide. There are crackpots who have no problems to question insights that have been tested billions of times; there are also crackpots who seem to be completely certain about a statement that is totally uncertain (or incorrect). Usually these two groups heavily overlap.

Crackpots see no difficulties in assuming that every single statement or equation in every book by the most famous scientists, as accepted and checked by thousands of their readers, is based on a new logical error. Common sense is always less important than the revolutionary message of the crackpot.

Unfocused understanding of scientific terms

Scientific terminology is often a complicated enterprise. It also involves a lot of misnomers that got stuck because of purely historical reasons. But scientists always prefer compact terminology when it leads to no misunderstandings. This implies that more or less every piece of a scientific term plays some role for the whole term; it just can't be omitted. Some crackpots avoid scientific terminology altogether and this paragraph is not about those guys. This paragraph is about the crackpots who like to use scientific terms but they do not understand them. The most typical manifestation of this problem is that a crackpot uses a long scientific term as a compact black box that should not be analyzed or deconstructed. Such a crackpot sees no problem to talk about "twisted sector closed string tachyons" and conjecture that it is the same thing as the "Higgs boson". Of course, for two expressions to be equivalent, all of their features must match. But a crackpot typically does not ask "Why does the word 'twisted' appear in the expression and what it means?" He or she simply uses the whole expression as a single black box and he believes that it is never important to "look inside" in order to verify his ideas.

### Incan string theory

Some people complain that string theory is an invention of the Western civilization and it does not apply elsewhere. We're happy to inform you that according to the newest computer analysis, string theory was developed in the Andean empire roughly 1500 A.D:

It seems likely that the local bureaucrats were actually using some version of level-truncated string field theory with different levels computed by different officers:
• "Local accountants would forward information on accomplished tasks upward through the hierarchy, with information at each successive level representing the summation of accounts from the levels below," Urton says.
New Scientist does not explain whether some non-perturbative effects were known to the Inca bean counters.

## Thursday, August 18, 2005 ... /////

### Matt Strassler and LHC olympics

You should know that Matthew Strassler, the master of cascades and N=1 AdS/CFT duals, and his collaborators Steve Ellis and Matt Bowen - turned out to be ones of the main heroes of the LHC olympics. So far it's only them who had the courage to make some analysis of the data created by Gordon Kane etc. to figure out that there was always a full correlation between the flavor and the charge of the two leptons in the final di-lepton states. The organizers confirmed this observation to be correct. This observation means that the initial state was an excitation of a real field and many other things.

We worried that only one person would be interested in the data that will be produced by a collider for 1.5 billion USD, but at least we were assured that there is a whole subcommunity that is ready to analyze similar data and that did not participate in the LHC olympics because they're doing similar things every day anyway. At any rate, our pheno friends seem to share the opinion that it will take years before the new physics is identified from the LHC data. The heavy A_0 (CP-odd) Higgs and/or gluinos could be the fastest ones to be found.

### Crackpot grand prize raised

The Reference Frame decided to raise the grand prize from $3 to$13.08. It is the prize for the first person who will be able to submit a 1-star review under McCutcheon's book "The Final Theory" as explained in

We mentioned some early attempts to submit a non-5-star review here. Some recent reviews had survived for two days or so. However, Josh Lapan has pointed out that they disappeared once again and the average rating of the crackpot's book - one that even denies the existence of the universal gravitational force that operates both terrestrially as well as celestially - returned to 5 stars. One week seems unbeatable so far despite tens of attempts and several complaints that physics professors from many universities have sent to amazon.com.

If the first 1-star review survives one week provably as a result of an article about the scandal or another influence, the reader of this blog who initiated the article will share the prize with the first reviewer. If no winner appears for a few more weeks, we will increase the grand prize significantly and ask sponsors for their support. If you want to raise the prize immediately, please choose an amount of the format ??.?8 USD (eight cents modulo ten cents), for a better identification, and use this button:

Don't be afraid to click the button; the payment only occurs after one more window where you must fill your paypal.com username and password. Please don't contribute less than $2 or more than$20 at this moment. Thanks, Tobias Sander, for the first donation.

### A compromise with Lenny Susskind

After roughly six e-mails we exchanged with Lenny Susskind who started the debate with this sentence:

• LS: Dear Motl, I heard that you have some strong opinions that differ from my own. You are a smart guy so I thought I better understand your point. (...)
the following words of Lenny about the status of the anthropic reasoning could have been more or less subscribed by both of us although they don't contain some of the most novel points in our debate. Lenny wants me to post it on the blog which is what I'm gonna do right now:
• LS (+LM): Let me propose a formulation that I think is honest, non ideological, and combines what I think are the best of each side.
• First of all, the evidence for inflation suggests a very large universe which may not be everywhere the same. We can't be sure.
• The existence of a cc just at the predicted value (Weinberg) is completely mysterious from any known framework other than the "populated landscape."
• There are strong signs of a very large landscape of string theory.
• ...
• BUT
• ...
• the landscape is far from a mathematical fact at this point.
• the math behind eternal inflation is still shaky.
• It is not impossible that there are unknown mathematical ingredients of string theory (or some other theory) that might surprise us.
• Finally, I think it is fair to say that there is no other concrete competing proposal to the "populated landscape." There is also no theorem (actually there is --Weinberg's theorem about the cc) that forbids another explanation. [LM objected to the inconsistency of the second sentence and the historical character of the first sentence.]
• ...
• The conclusion that should be drawn from this is that
• YES, IT IS PREMATURE TO STOP LOOKING FOR "RATIONAL" EXPLANATIONS OF THE FINE TUNINGS.
• But NO, IT IS NOT PREMATURE TO SERIOUSLY CONSIDER THE ENVIRONMENTAL OPTION.

It is conceivable that the following exchange - a standard example how senior left-wing people are talking to their right-wing junior colleagues in Academia - should be added to this file, too:

• LS: Lastly, I should say that some people have tried to get a lock on the use of the word "rational" in the same way that George Bush tries to monopoly on "compassionate." As far as I can tell, at the present time, the only rational explanation of the cc is the A.P. Unless you have another.

LM: Your comparison of your attitude to Bush's attitude may be an apt one. That's not an insult - as you know, I usually like Bush. ;-)

• LS: Now, on another point--bush? Motl, you are either dumber than I thought, sicker than I thought, or about as mischievous as I thought. Which is it? You can tell me. I won't tell anyone else.

Note added to the blog only: Lenny won't, but I will. You may think that I am used to this kind of comments from the communist times. However, surprisingly, I am not. I don't remember a single communist whose opinion about the U.S. president (probably Reagan at that time) or even his moderate supporters would be formulated in such strong and humiliating terms.

## Tuesday, August 16, 2005 ... /////

### Topological blog

Those who are interested in mathematical aspects of string theory and the newest twists and turns in topological string theory in particular should look at the KITP weblogs, especially

written by Andy Neitzke. Andy is one of the coolest bigshots among recent graduates, and because he is also a clear expositor (recall, for example, his and Cumrun's review of topological strings), you should try to look at his comments.

## Monday, August 15, 2005 ... /////

### What string theory forbids

In this article, I would like to collect some of your examples of phenomena or situations that are completely compatible with low-energy effective field theory but do not arise from any known - and perhaps not even any unknown - stringy compactication. In other words, predictions of string theory that are independent of the vacuum selection mechanisms.

For example, pure N=2 supergravity is anomaly free and OK as an effective field theory, but string theory always predicts new multiplets, does not it? Also, the U(1)^{496} supersymmetric Yang-Mills theory coupled to type I supergravity in ten dimensions is anomaly free and nice, but it does not seem to describe any stringy background.

There are other similar properties related to the axion decay constants and the strength of various gauge couplings that apparently can't be anything you want; work in progress. However, I would love to hear some completely different examples of universal predictions of string/M-theory. Thanks.

## Sunday, August 14, 2005 ... /////

### Terrorism and Prague?

Because the Greek plane that killed all 121 Cypriots on board was en route to Prague, it is a natural context to mention the likelihood that the Central and Eastern European cities such as Prague could be attacked.

Yesterday, the Czech daily Právo ("Law/right" which used to be called "Rudé právo" i.e. "The Red Law" and it was the leading communist daily) published several scenarios how (and why) Prague could be attacked by the terrorists.

Today, the Czech BIS (the FBI and CIA combined) seems to deny all the speculations, claiming that they have heard no credible signals and it would be strange if such complicated algorithms were used for a country that is not viewed as the primary target. Pavel Blažek, the author of the article, insists that his account is trustworthy.

Let me admit that the article in Právo looks more realistic to me than the completely cool reaction of the BIS. Although it is not clear what is the true origin of their information, they speculate about the following possibilities:

• ultralight airplanes with 160 kilograms of explosives piloted by suicide pilots or remotely could explode at/near the Old Town Square; hundreds of casualties would be expected
• the subway could be flooded by a massive explosion in the train while it is going under the Vltava river; the entrances to the subway are less secure than in London
• an explosion in the Sazka aréna, the most modern multipurpose arena in the world, could kill hundreds of visitors
• attacks against the Old-New Synagogue and/or the Jewish cemetery would sound natural, too

What are the potential reasons behind such an attack? For example, what is the Czech attitude towards the Palestinian issue? Around 1949, Czechoslovakia was very helpful in establishing the state of Israel. However, by the end of the communist era it was Arafat and other comrades who were painted as the closest friends of Czechoslovakia in the region.

### New visual TeX: MicroIMP

Some time ago, we announced the Wolfram Publicon, a Mathematica-like graphic interface for TeX. There is a new competitor for Publicon and LyX that may be even more revolutionary. It's called

It's primarily created for Windows XP; it could run under Windows 2000 or Linux's VMWare or Wine. LaTeX is a higher layer of the program; there is some XML running inside. You may control the program much like other WYSIWYG editors but the subtle combination of the physical and logical formattings allows you many new things - such as changing the layout of your document by a single click. All features of TeX are available together with spellcheck and other things.

Some of you should check this program. You may download it after you register at the MicroIMP forums. Micropress Incorporated has done a lot of work to make TeX visual - e.g. VTeX - and you may look at their website, too. Even if you don't speak Czech, you may find this article useful because of the screenshots.

## Saturday, August 13, 2005 ... /////

### Poems from the heaven

Let me change the topic dramatically for a while to something very serious, sad, philosophical, and human: death and poems. I guess that you are thrilled by this change; the main focus will be on a guy whose nickname was Thriller.

The well-known people who recently died in the U.S. and in the Czech Republic seem to be "nicer" than the average; one could almost be afraid that the world is becoming a worse place to live in. Pavel Dostál, the Czech minister of culture (for the Czech Social Democratic Party), died of cancer. In comparison with some of his colleagues, he was a good man of culture and a former dissident. The Czech actor Jiří Kodet was a good guy, too (incidentally, he was a friend of the president Klaus and that's apparently enough for Kodet's daughter to be disciminated by various groups of Czech artists and bureaucrats in the culture). Finally, Miss Ellie Ewing who died of lung cancer was one of the better members of the Ewing family, too (although I don't know what was the actress like in the real life). I could continue for a while.

But what I really want is to look 10 years into the past. How did the internet look like in August 1995? While the first web pages started to appear on the servers of Academia (with many discussions whether the commercial sector was gonna be allowed to join the Internet; you can see my oldest March 1995 web page here), there were no blogs, so what the hell were the people like me doing instead of blogging?

Well, as a student in Prague, I was spending hundreds of hours of free time with BBSes (Bulletin Board Services), especially the Liane BBS located in the Bohemian city of Liberec. We used to connect to the server using telnet. Most of the discussions were in Czech (this includes most discussions in which I participated); the sysop MadGeorge (Jiří Randus) always planned to internationalize his BBS but these plans were never quite successful. Some of my postings could have been about string theory but the overall structure of the topics was more primitive (for example, neverending debates about science vs. paranormal phenomena and postmodernism but also some Czech poetry).

The most successful English board was Poetry. And the most impressive contributor to that board was nicknamed Thriller, a very gentle and talented guy. How did his moral standard differ from others? For example, he was one of the four candidates for the first ChatOp, or a chat moderator. Later it was revealed that three of these four candidates, including me, have voted for themselves. Only Thriller had voted for someone else (namely me). In real life, I only met Thriller once: during the first BBS session in Liberec.

In August 1995, Thriller's plans to commit suicide were completed. Everyone could read them on the board in advance. At that time, I really did not care about English poetry much although I knew he was pretty good. Among many other poems, Thriller had submitted six parts of his "Invisible scar"

What do you think about these poems?

Well, after he submitted these poems, he joined the family of those who had jumped from the Nusle bridge. Exactly ten years later, I find it amazing that no one could have stopped him even though his plans had been known in detail for a month or so. Why did he do it? The answer should not be unexpected: the main reason was a girl. He obviously loved her a lot and she did not seem to care.

Thriller's was a very delicate mind. On the other hand, I would guess that the girl from his dreams became an average, superficial, aging woman. However, while she is not presented as the ultimate hero, she is probably alive. The message is that if you care about the 2015 articles about you at The Reference Frame more than you care about your life, you should love others more than they love you, and you should write deep poems about it (and about other issues).

Incidentally, the rating of nuclear physicists among their randomly chosen girlfriends is just a little bit better than the rating of poets like Thriller as shown in a story that Feynman liked to say:

• One of the men who discovered this [how stars burn] was out with his girlfriend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said "Look at how pretty the stars shine!" He said "Yes, and right now I am the only man in the world who knows why they shine." She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well it is sad to be alone, but that is the way it is in this world.

Incidentally, did you see the Perseids yesterday?

As far as I know, Thriller probably believed neither in the heaven nor in reincarnation, and neither do I. The best hope I can offer is a duality transformation based on string theory that transforms your degrees of freedom before you die into a new kind of matter. But don't forget: it is just a hope. ;-) Incidentally, have you ever wondered whether there is any chance to survive the scary journey into the black hole singularity? Can you T-dualize yourself and appear elsewhere? Can there be a new dual description "after" the space-like singularity of the Schwarzschild? We (with Mukund) have not found the answer when we discussed it in Berkeley but I personally find it very unlikely.

### Common sense and science

Not all New York Times contributors read The Reference Frame or other blogs about physics. One of those who apparently don't is John Horgan, the author of the controversial book The End of Science - as Peter Woit pointed out - and whom I originally confused with the enlightened professor of pure consciousness John Hagelin who has worked for Maharishi Mahesh Yogi. (Did you know that in Cincinnati, Ohio, a vedic approach to military defense based on Hagelin's insights about consciousness may earn you a PhD?)

Thanks to a reader for explaining me the difference between Horgan and Hagelin and please accept my apologies for this error.

In his book The End of Science, Horgan argued that all important discoveries in science had been made and science had switched to a postmodern speculative mode - something that Horgan called "ironic science". Even if there were something true about this general, vague, slightly arrogant, and discouraging thesis, it cannot justify the absurd details; and Horgan offers many crazy details, indeed.

In his new op-ed piece

he argues that science is compatible with the common sense and those who argue that they are incompatible are misled. Much like others, I would say that the validity of this assertion depends on your particular definition of "common sense". My definition of "common sense" is such that Horgan's statement is incorrect. Any "sense" that is supposed to be called "common sense" should be "common" which means that many (or most) people should have it.

It is obvious that most people have lived in the world where relativity, quantum mechanics, or even quantum gravity play no material role. This fact implies that most people's intuition is based on the ideas and expectations that were later mathematically embodied in classical, non-relativistic physics. In other words, quantum physics and relativity are not parts of the natural instincts of the majority of the world's population. Most of us "feel" neither relativity nor quantum mechanics. The more we work with these concepts and the relevant theories and experiments, the more natural and essential they look to us. Quantum mechanics and relativity have been included in the instincts of most theoretical physicists (and many experimental physicists) - and those intelligent people who have been exposed to theoretical physics for a sufficient amount of time.

One of the criteria to measure the depth of ideas is their ability to challenge the beliefs and intuition of most people, including the smartest ones; in particular, deep ideas often challenge common sense. No doubt, both relativity and quantum mechanics satisfy this criterion. We have emphasized many times that even thousands of philosophers working for thousands of years would not be able to invent a valid theory of the Universe that is as weird as quantum mechanics by pure thought; that's essentially a statement by Sidney Coleman whose original author may be Richard Feynman, as David Goss has pointed out to me.

Matthew Nobes is currently the front-runner for the $3.00 "grand" prize because of his 1-star review. However, it must survive for one more week for Matthew to become the official winner. Unless there will be some complaints, I will forgive Matthew that his review is below those 200 words. ## Friday, August 12, 2005 ... ///// ### Josephson disproving the landscape? I feel that in order to compensate the revelation that Prof. Josephson believes ESP - and tries to unify Mind, Matter, and Music into his own version of M-theory :-) - we should write something nice and hot related to him. The cosmological constant is surprisingly small. The zero point fluctuations associated with various fields are examples of terms that are expected to contribute much more; a currently fashionable explanation of the smallness is that the contributions cancel by chance and this chance is justified and "explained" by the required existence of life (or galaxies). However, one may imagine that there is an ultraviolet frequency cutoff that simply removes the high frequencies. I was writing about these issues when the concept of fat gravitons was discussed together with the rumors about the observed deviations from the Newton's law. Incidentally, the newest rumors (via A.S. of Stanford) say that the anomaly has disappeared once again. Back and Mackey argued that the required frequency is about 1700 GHz; above this frequency, the vacuum fluctuations could disappear if a "natural" explanation of the dark energy operates in our Universe. If Back and Mackey are right (which is a very non-trivial "if", as argued later), such a disappearance could be measured using the Josephson junction that plays an important role for superconductivity; in fact, the critical frequency lies just behind the corner and should be accessible to our technology in the very near future. Today, Paul Frampton - whom I send greetings - argues why such an unexpected cutoff would have dramatic consequences. For example, it could nuke out the landscape. As Frampton points out in a provocative but legitimate way, if the landscape is an inevitable mechanism implied by string theory, the observed cutoff would falsify not only the landscape but also string theory. Would not it be fun if an obscure condensed matter phenomenon that was once believed to lead to a new generation of computers - but whose author eventually became an advocate of telekinesis and ghosts - would serve as a tool to show that the smallness of dark energy has a rational, non-religious explanation? Unfortunately, nature does not necessarily choose scenarios that maximize fun. What's the problem? The main problem is probably the statement by Jetzer and Straumann that the noise measurements of the Josephson junctions cannot determine the vacuum energy contributions; their line of argument is obvious. In any non-gravitational experiment (such as those proposed by Back and Mackey), only the energy differences matter. ### Amazon.COM controlled by crackpots? Josh Lapan has informed me about the following incident. Brian Powell, a physics student from Buffalo whom Josh met at TASI 2005, has repeatedly tried to submit a review of the following book sold at amazon.com: As I explain below, the book does not deserve anything else than one star (and my guess is that the readers, even those who sometimes like to argue with me, will agree). The short story is that the staff at amazon.com has repeatedly prevented the reviews by Brian Powell from appearing on their website. Arguably, the last reviews are absolutely legitimate and polite. Brian Powell was kind of frustrated that the opinion of a dumb crackpot about theoretical physics is obviously more important than the opinion of a graduate student of theoretical physics. And he summarized his story here. ## Tuesday, August 09, 2005 ... ///// ### Interpretation of QM and progress One of the recorded discussions in Toronto was between Lee Smolin and Martin Roček. They debated the achievements of the research focusing on the interpretational issues of quantum mechanics. Martin Roček argued that almost no progress occured in this field while Lee Smolin claimed that quantum computing is one of the counterexamples. I tend to agree with Martin. Quantum mechanics looks weird. As Sidney Coleman once said, if thousands of philosophers were trying to find the weirdest possible thing for thousands of years, they would have never come up with something as strange as quantum mechanics. But quantum mechanics is true and successfully tested. All those great physicists who could not swallow it and who were proposing various "completions" were wrong. This list includes de Broglie, Schrödinger, Einstein, Podolsky, Rosen, Bohm, Bell, and many others. We should certainly admit that the questions raised by these Gentlemen were instrumental in deepening our understanding of quantum mechanics. The physicists have understood the EPR effect, entanglement, quantum teleportation, and some mechanisms useful for quantum computing. But it is even more important to say that their opinion that quantum mechanics had to be modified has been falsified as much as you can get. There have been some unsatisfactory features of the Copenhagen interpretation - such as its unjustified separation of the world into the microscopic and macroscopic realm - but these features do not really affect the predictions for any experiment that has been done (or even realistically planned). Moreover, these features have been more or less clarified by the concept of decoherence from the 1980s that has become a part of satisfactory, modern neo-Copenhagen interpretations of quantum mechanics such as the Consistent Histories. There also remain several open questions about the interpretation of quantum mechanics in the context of cosmology and quantum gravity (what are the right observables near the Big Bang?), but these questions can hardly be answered before we properly understand dynamics of quantum gravity. Traditionally, dynamics and interpretation are two separated parts of the intellectual structure called quantum theory, and it is only dynamics with which most serious physicists may be spending hundreds of hours and about which they can write quantitative papers. While it is fair to say that quantum gravity has the capacity to smear the boundaries between dynamics and interpretation, it is not fair to say that the people who are simply questioning the foundations of quantum mechanics are contributing to the research of quantum gravity. Concerning quantum computing, I believe that one of the important boosts for its development came from the 1982 article by Richard Feynman about simulating the quantum world by computers. And Feynman was no philosopher who would like to think about subtle philosophical principles and feel unsatisfied with a working theory of physics because of some abstract prejudices. On the contrary, Feynman thought that the philosophers were politely speaking dopes, and his favorite interpretation of quantum mechanics was summarized by the dictum "Shut up and calculate!". ### Uniqueness of quantum gravity One of Steve Shenker's recent deep ideas - and inexhaustible sources of frustration - is the following observation: • Holography seems to associate a (d+1)-dimensional theory of quantum gravity with any d-dimensional quantum field theory (or quantum mechanics). This implies that theories of quantum gravity do not seem unique anymore. Start with any QFT, and you obtain a theory of quantum gravity. Consequently, Maldacena and holography may be able to bring us as much desperation as they have offered excitement. In other words, we must ask: Is every quantum field theory a theory of quantum gravity? Well, I would emphasize that the dual gravitational theories are typically strongly curved (and they have large gradients of fields like the dilaton) and they cannot be described as a small perturbation of a well-defined smooth geometry. This fact itself makes it inappropriate to call these backgrounds "quantum gravity" because the QFT description is always more controllable than the geometric one - and only the field theoretical description is potentially weakly coupled. Even our intuition should be enough for us not to call the Hydrogen atom or loop quantum gravity a "theory of quantum gravity" because they don't describe a nearly flat space on which wiggles can nevertheless propagate. A spin foam, for example, is rather a piece of dirty and unpredictable material that threatens the crews of space shuttles. Fortunately, a piece of spin foam has been removed from the Discovery space shuttle and its crew safely landed in California today. (Well, I guess that this piece would fly away even if the astronaut did nothing, but it is sometimes better to be safer than sorry.) The exceptions are the "large N" theories whose dual geometry becomes weakly curved. In these cases, one of the well-known examples of local gravitational physics emerges (eleven-dimensional supergravity, type IIA, IIB, or SO(32) or E8 x E8 type I ten-dimensional supergravity). There may be many quantum field theories whose large N limits give the same theory of gravity in the flat space; that's one of the examples of universality of string theory or examples of the famous rule • All roads lead to string theory. For example, both conformal field theories dual to "AdS4 x S7" and "AdS7 x S4" locally lead to 11-dimensional physics of M-theory in the large N limit. At any rate, the rules of uniqueness have to be clarified a bit; feel free to disagree and identify errors: • The only consistent theory (description of local dynamics) of quantum gravity in 11 dimensions with curvature much smaller than the 11D Planck scale is M-theory. Below 11 large dimensions, the number of possible theories is larger but all of them may be described as generalized compactifications of the same string/M-theory. The information which compactifications are possible is encoded in a deep enough analysis of string/M-theory backgrounds in the highest dimensions. Note that this new formulation accepts the observation that our theories have to be more unique if the number of large dimensions is large, and the degeneracy arises as the number of large dimensions decreases; all of these possibilities must be interpreted as compactifications of the same theory; of course, the word "compactification" is not the naive field-theoretical one as it may contain branes and other stringy phenomena. In particular, 11 is the upper limit for the number of spacetime dimensions that may be more or less flat and the complexity of the lower-dimensional vacua is bounded from above because there is a limited number of compactifications. The colleagues who believe that string theory predicts equally good vacua above 11 dimensions (e.g. in 18 dimensions) that can also be arranged to be essentially flat will have to modify these rules. I have no idea whether these people believe in uniqueness of quantum gravity in any sense, and if they do, what is exactly their sense. If someone believes that there is a well-defined supercritical M-theory in 2003 dimensions (I chose the dimensionality to be 3 modulo 8, to agree with M-theory), it is likely that the possible number of her compactifications down to 4 dimensions will form a pretty large landscape. Because the set of ridiculous numbers like 2003 is infinite, their landscape is more or less guaranteed to be infinite. I choose to believe that these supercritical theories have to be inconsistent (or at least irrelevant for anything we would like to call physics) because their existence has not been established with the standards usual for the supersymmetric backgrounds, and because the assumption of their existence would render string theory meaningless in my understand of the word "meaning". Even though the number of compactifications down to lower dimensions may be large, it is limited and all of them may furthermore share some general properties. For example, string theory will probably never generate a pure N=2 supergravity in 6 dimensions although this theory seems to be perfectly valid as an effective field theory of "something". Those who share my belief that the only consistent quantum gravitational background with 11 flat or nearly flat dimensions is M-theory may ask many other questions, for example: • Can we define rules - rules independent of string/M-theory - what such a theory should look like whose unique solution is M-theory in 11 dimensions? In other words, is string/M-theory a unique solution to some general bootstrap conditions of self-consistency? What are exactly those rules, and how do we prove (at least partially) that the solution is unique? ## Monday, August 08, 2005 ... ///// ### String Theory, Book 1: Voyager Congratulations to Jeffrey Lang. His new book is going back to the publisher for a second printing. A very simplified abstract: • Captain Janeway's crew encounters a species that should not exist according to the known physical laws: the Monorhans. Technology from Voyager (TM) offers the required stringy corrections to save them from extinction. However, an unexpected shock wave catapults Voyager into a place beyond the fabric of space and time. Voyager struggles to prevail on an extradimensional battleground. The excerpts make it clear that it is no easy reading, at least for me; Polchinski, Zwiebach, as well as Green+Schwarz+Witten seemed more accessible. Nevertheless, I wish you happy reading if you purchase the paperback. ;-) ## Saturday, August 06, 2005 ... ///// ### Non-critical M-theory Petr Hořava and Cynthia Keeler promote their so-called non-critical M-theory in 2+1 dimensions. It is related to non-critical type 0A in 1+1 dimensions in the same Kaluza-Klein way in which the usual critical 10+1-dimensional M-theory is related to type IIA in 9+1 dimensions: the KK modes of M-theory are represented by some D0-branes in both cases. All dimensionalities are reduced by 8 spatial dimensions; spacetime supersymmetry is sacrificed; the transverse oscillators of the strings and membranes disappear because of the low dimension. They define the non-critical M-theory as a double scaling limit of non-relativistic fermions in 2+1 dimensions much like the usual M-theory may be defined using the large N limit of a non-relativistic description of D0-branes in type IIA. Petr and Cynthia only have the description in terms of fermions, not the matrix model itself. The off-diagonal elements of such a hypothetical matrix model should be pure gauge anyway, I think. They also show that noncritical type 0A and 0B theories appear as "hydrodynamic" solutions of their noncritical M-theory. You may think that this work is another variation on the topic of extending the well-known dualities to uncontrollable non-supersymmetric cases. But there's a difference: in two spacetime dimensions, string theory becomes stable and the "tachyon" becomes a misnomer: the stringy "tachyon" actually becomes massless. The same thing morally holds for their non-critical M-theory in 2+1 dimensions. Because of this special feature, the system is actually exactly solvable - unlike the duality between type 0A in 10 dimensions and M-theory on the Scherk-Schwarz circle, for example. A general comment about this situation is that we know two important classes of exactly solvable systems, namely those with ### Anthropic principle lacks confidence It is somewhat surprising to obtain the hottest news about the opinions in the string theory community from leading U.S. newspapers. But that's exactly what Dennis Overbye has achieved in his highly penetrating article The Reference Frame has predicted in May that the panel discussion about the next superstring revolution would be one of the most interesting moments of the Strings 2005 conference. (However, let's admit that the causal relation between the prediction and the NYT article may be slightly different than you think.) What did various people say during the panel discussion in Toronto four weeks ago? Andy Strominger was very upbeat; something that Joe Marsano has been explaining to me, too. He criticized those of us who spread the atmosphere of pessimism. He informed everyone that soon or later, the string theorists will find the right explanations and all of them will be celebrated as heroes; there are no obstacles in principle to solve all of our current problems. Not everyone has to join the efforts to complete string theory; for example, the stupid people and the people focusing on other parts of physics won't do it. ;-) ## Friday, August 05, 2005 ... ///// ### Flight I just arrived to the Boston area, after stops in Prague, Amsterdam, and Newark and more than 28 hours in transit. If you want to make a purchase in July of an air ticket for early August, and you want to pay less than$2000, it is often necessary to buy such an awkward ticket. Unless you're much more skillful with these matters than I am.

During the flight, I could also read most of the new Czech book by Mr. Pavel Houser "Before a Thylacine Comes" (Czech: "Než přijde vakovlk") - interviews with 14 Czech scientists about various current issues in science. It starts with cosmology "chronologically" (an interview with a Czech physics assistant professor at Harvard); continues with paleoclimate, evolution of dinosaurs and other ancient animal species, old civilizations and their culture, DNA sequencing and then it turns to the future topics. The previous long sentence makes it clear that I know how this book was created - and I am very impressed by the breadth of Houser's knowledge penetrating all of science. He was asking pretty good questions that reveal that for a non-professional, he knows a lot about cosmology and perhaps even high energy physics, and the remaining 13 interviews prove that he may have even a deeper knowledge about the other fields.

Incidentally, only Boston and London offered an easily available wireless connection at the airport, as long as you wish to pay \$10 for a day or so. (I was checking them with the MA111 Wireless USB external card bought from ubid.com and sent via FedEx, one of the U.S. companies I hate.) There is no wireless network whatsoever at the Prague airport (although Ruzyne seems to have the most available power outlets) and the networks in Amsterdam and Newark can't be easily connected to.

Well, despite the years of being slightly transformed by the New World, this is the first early August that I spend in the U.S. The air is obviously more humid here and maybe even hotter than in Central Europe, but you probably know it anyway. Petr Čížek, who was for an unfortunately short period my Czech friend and late mathematician from Rutgers (where we first met, even though we apparently shared an office in Prague in the previous year) who died in a car accident in 1999 or so (with his Russian female friend who was driving and who obviously thought that the road under construction in Minnesota was quite empty so that they could drive in the left lane - it was empty except for the truck; I could not go to their trip because of the qualifying exams), was always describing these hot and humid American summers. This is the first real one for me, a survivor.

Some of the first interesting discussions here were about Strings 2005 and different topics at various conferences (and TASI) - and the Douglas-Kazakov phase transition in the q-deformed two-dimensional Yang-Mills on sphere (it's there, Joe Marsano informed me); equally interesting and probably even the most objective description by Paul Frampton of the early days of string theory in the classical 1968-1974 period (we may write something about this topic later if all permissions work etc.); some work with the Sidneyfest videos (we're still missing Summers' and Steinhardt's talks!); bureaucracy with the Rutgers transcripts that the Harvard International Office needs because otherwise they can't know whether I studied at Rutgers as a physicist or a gender studies expert (imagine how many combinations of the IRS, INS, HIO, CIA, FBI, Rutgers, Harvard you may compose, and each of these combinations seems to require a specific document or three to be developed or copied and sent). :-) I've sent a mail about my opinions whether and how the blogs are transforming the world of physics and physicists' lives; to be discussed later at this website.

At 4:00 pm, I must serve as a committee member during Alex Wissner-Gross' oral exam (greetings to you, if you read it). He seems to be an extremely smart guy (or geek) focusing on various things related to nanotechnology and IT, and therefore his talk could be a lot of fun. Well, I don't want to share various personal and "apartment-related" stories because the expectation is that no one is interested in it. Aren't you also bored by the blogs that describe the size of every piece of waste of the blog owner's cat, for example?

Moving back to the U.S. also means a change in the food rhythm. My typical Czech food, such as a sophisticated variation on the Italian concept of the so-called PIZZA (with names such as Hawaii, Alabama, Al Capone), is replaced by a typical U.S. food such as Chinese cuisine and Mexican burritos. The fortune cookie from the Chinese restaurant that I just opened says:

• You will finally solve a difficult problem that means much to you. Lucky numbers: 20 994 472 770 550 672 476 591 949 725 720
The Chinese cooks have apparently done some research how important it is to find the most fundamental degrees of freedom in string/M-theory or, more precisely, how to generate the rules that allow them to emerge in certain ways and not others, together with the "Hamiltonian" or the "action". Maybe they even know something about the N=2 strings and the del Pezzo surfaces. Sometimes I should write about this approach to TOE and some of my previous detailed errors that have been identified by a closer scrutiny.

But maybe one should not consider the authors of the fortune cookies as terribly trustworthy: they are cooks after all. When you read the cookie message, you must ask: what lucky numbers? The number is the total number of sl(3) representations in AE_3 up to the level 56. But what should I do with it? Count the states in the decomposition of E_{10} or E_{11} to obtain the black hole entropy counting? If the Chinese can't be more specific, why don't they write a message that is almost always correct, for example
• You are the most charming person in the world. Lucky numbers: 7 7 31 12 2005.
After all, 40 percent of Americans believe that they will be among the richest 1 percent of the U.S. citizens at the end of their lives. Well, roughly 39 percent of Americans are misled about an important question. But belief can make many of them happier.

## Monday, August 01, 2005 ... /////

### Iron curtain

Update for German visitors: this blog does not contain and will not contain any nude pictures of Angela Merkel. You must go elsewhere.

Last weekend, which is also the last weekend before I fly back to Boston on Thursday (with stops in Amsterdam and New York - no better air ticket could have been bought so quickly), we made a bike trip to Šumava ("Bohemian Forest" in German), the mountains in the Southwestern Bohemia (Czech Republic) that we share with Bavaria (Germany).

Figure 1: Preparations after a small training on Friday.

The main goal was to conquer the Great Maple peak ("Gross Arber" in German, "Velký Javor" in Czech) at 1456 meters above the sea level, the highest peak of Šumava. Those who know me in person realize that your humble correspondent is no exceptional athlete or at least not a person who would like to picture himself as an athlete ;-) and therefore he can be quietly proud that he was probably the only person in our team and possibly in the world who got to the very top using the mere power of pedals (well, except for 20 vertical meters or so) on that Saturday.

Figure 2: Bikes near the peak. As a kid, my theory was that the spheres were most likely Pershings that Germany wanted to use for an attack against the Soviet bloc. The teachers did not protest against my theory and I don't remember anyone said the word "observatories".


text:
# d'Alembertian and wave equation.

by yungman
Tags: dalembertian, equation, wave
 P: 3,830 I am studying Coulomb and Lorentz gauge. Lorentz gauge help produce wave equation: $$\nabla^2 V-\mu_0\epsilon_0\frac{\partial^2V}{\partial t^2}=-\frac{\rho}{\epsilon_0},\;and\;\nabla^2 \vec A-\mu_0\epsilon_0\frac{\partial^2\vec A}{\partial t^2}=-\mu_0\vec J$$ Where the 4 dimensional d'Alembertian operator: $$\square^2=\nabla^2-\mu_0\epsilon_0\frac{\partial^2}{\partial t^2}$$ $$\Rightarrow\;\square^2V=-\frac{\rho}{\epsilon_0},\; and\;\square^2\vec A=-\mu_0\vec J$$ So the wave equations are really 4 dimensional d'Alembertian equations?
 Sci Advisor Thanks P: 2,104 Your equations hold for Lorenz (NOT Lorentz!) gauge but not for Coulomb gauge. Otherwise it's indeed the d'Alembert operator. Note further that $1/(\epsilon_0 \mu_0)=c^2$ is the speed of light squared which is (contrary to the conversion factors $\epsilon_0$ and $\mu_0$) a fundamental constant of nature.
P: 3,830
 Quote by vanhees71 Your equations hold for Lorenz (NOT Lorentz!) gauge but not for Coulomb gauge. Otherwise it's indeed the d'Alembert operator. Note further that $1/(\epsilon_0 \mu_0)=c^2$ is the speed of light squared which is (contrary to the conversion factors $\epsilon_0$ and $\mu_0$) a fundamental constant of nature.
Thanks for the reply. I am reading Griffiths p422. It specified Lorentz gauge( that's how Griffiths spell it) put the two in the same footing. Actually Griffiths said Coulomb gauge using ##\nabla\cdot\vec A=0## to simplify ##\nabla^2V=-\frac{\rho}{\epsilon_0}## but make it more complicate for the vector potential ##\vec A##. That's the reason EM use Lorentz Gauge. This is all in p421 to 422 of Griffiths.

You cannot combine Coulomb and Lorentz Gauge together as

Coulomb ##\Rightarrow\;\nabla\cdot\vec A=0##

Lorentz ##\Rightarrow\;\nabla\cdot\vec A=\mu_0\epsilon_0\frac{\partial V}{\partial t}##

C. Spirit

format: plain


text:
Mechanics Homework 29-1 340 - Equilibrium of Parallel Force System Name_______________ Mr. Haynes Date_______________

Problem 29-1 For the system of pulleys shown in Fig. P-340 , determine the ratio of W to P to maintain equilibrium. Neglect axle friction and the weights of the pulleys.

$$W/P = 9$$


text:
# 281: Two Photon Interference - The Creation of an Entangled Superposition

In this experiment a down converter, DC, converts an incident photon into two lower energy photons. One photon takes the upper path and the other the lower path. The results of this experiment are that both photons are detected at either A or B. One photon is never detected at A while the other is detected at B. A quantum mechanical analysis of this phenomena is provided below.

After the down converter the initial photon leaving the source has evolved into a state which is an entangled linear superposition.

$| Source \rangle \frac{[ |up \rangle_1 |down \rangle_2 + |down \rangle_1 |up \rangle_2 ]}{ 2^{ \frac{1}{2}}} \label{eq1}$

This is an entangled state (non-factorable) because it acknowledges that it is unknown which photon takes which path. It also incorporates the fact that photons are bosons and consequently the state function must be symmetric with respect to interchange of the coordinates (paths) of the photons. If photons were fermions, |Source> would have to be antisymmetric with respect interchange of coordinates and the positive sign in Equation \ref{eq.1} would be replaced with a negative sign.

A photon that takes the upper path has a 50% chance of being detected at A or B. To reach A it must be reflected at the beam splitter and to reach B is must be transmitted. Conservation of energy requires a 90 degree phase difference between transmission and reflection, and by convention this phase difference is assigned to reflection. To reach detector A the upper photon must undergo a reflection at the beam splitter and its phase shift is recorded by multiplying |A> by i [(-1)1/2]. Thus in terms of the detector states |A> and |B> the photon taking the upper path evolves into the state shown in Equation \ref{eq2}.

$| up \rangle \frac{[ i |A \rangle + | B \rangle ]}{ 2^{ \frac{1}{2}}} \label{eq2}$

Similar arguments show that the photon taking the lower path will evolve to the state given by Equation \ref{eq3}.

$| down \rangle \frac{[ i |A \rangle + | B \rangle ]}{ 2^{ \frac{1}{2}}} \label{eq3}$

When Equations \ref{eq2} and \ref{eq3} are substituted into Equation \ref{eq1}, the following final state results (A and B represent the detectors, while 1 and 2 designate the photons):

$|Source \rangle \frac{[i | A \rangle_1 |A \rangle_2 + i^2 | A \rangle_1 B \rangle_2 + |B \rangle_1 |A \rangle_2 + i|B \rangle_1 |B \rangle_2 + i | A \rangle_1 |A \rangle_2 + | A \rangle_1 |B \rangle_2 + i^2 |B \rangle_1 |A \rangle_2 + i|B \rangle_1 |B \rangle_2]}{ 2^{ \frac{3}{2}}}$

Thus there eight final probability amplitudes, and they come in four pairs as can be seen above. However, two of the pairs destructively interfer (see note below) with each other and the final state is,

$| Source \rangle \frac{[ i|A \rangle_1 |A \rangle_2 + i|B \rangle_1 |B \rangle_2]}{ 2^{ \frac{1}{2}}}$

The probability of an outcome is found by taking the square of the absolute magnitude of its probability amplitude. Thus the probability that both photons will be recorded at A or both photons will be recorded at B is calculated as follows:

$P(AA) = \left| \frac{i}{2} ^{ \frac{1}{2}}\right|^2 = \frac{1}{2}$

$P(BB) = \left| \frac{i}{2} ^{ \frac{1}{2}}\right|^2 = \frac{1}{2}$

It was noted earlier that fermions require anti-symmetric state functions. So if this experiment could be performed with fermions Equation \ref{eq1} would become,

$| Source \rangle \frac{[|up \rangle_1 |down \rangle_2 - |down \rangle_1 |up \rangle_2 ]}{ 2^{ \frac{1}{2}}} \label{eq8}$

After substitution of Equations \ref{eq2} and \ref{eq3} into Equation \ref{eq8}, we find

$| Source \rangle \frac{[ B \rangle_1 |A \rangle_2 - |A \rangle_1 |B \rangle_2]}{ 2^{ \frac{1}{2}}}$

In other words the fermions are always detected at different detectors and are never found at the same detector at the same time. In summary, the sociology of bosons and fermions can be briefly stated: bosons are gregarious and enjoy company; fermions are antisocial and prefer solitude.

Note: "The things that interfere in quantum mechanics are not particles. They are probability amplitudes for certain events. It is the fact that probability amplitudes add up like complex numbers that is responsible for all quantum mechanical interferences." Roy J. Glauber, American Journal of Physics, 63(1), 12 (1995).

Reference: Greenberger, D. M.; Horne, M. A.; Zeilinger, A. Physics Today, 1993, 44(8), 22.


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# Compile function for NMinimize

I have a the following script, which essentially minimizes the function $h$ with respect to all the variables $a[\alpha][s][j][n]$, where $\alpha,s\in\lbrace0,1\rbrace$, $j \in \lbrace ,\ldots,\text{nMol}-1\rbrace$ and $n \in \lbrace ,\ldots,\text{nEl}-1\rbrace$.

The minimization is done with additional constraints for the variables $a$.

j1 = 1;
j2 = 1;
Δ = 4;
u = 3;
nMol = 2;
nEl = 2;

h = Sum[-2*j2*Re[Conjugate[a[0][s][j][n]] * a[1][s][j][n]] -
2*j1*Re[Conjugate[a[0][s][j + 1][n]]*a[1][s][j][n] ] +
0.5*(1 + (2*s - 1)*(-1)^j)*Δ*
Sum[Abs[a[α][s][j][n] ]^2, {α, 0, 1}], {s, 0,
1}, {j, 0, nMol - 2}, {n, 0, nEl - 1}] +
u*Sum[(Sum[Abs[a[α][0][j][n]]^2, {n, 0, nEl - 1}])*(Sum[
Abs[a[α][1][j][n]]^2, {n, 0, nEl - 1}]), {j, 0,
nMol - 1}, {α, 0, 1}] +
Sum[-2*j2*
Re[Conjugate[a[0][s][nMol - 1][n]] * a[1][s][nMol - 1][n]] -
2*j1*Re[Conjugate[a[0][s][0][n]]*a[1][s][nMol - 1][n] ] +
0.5*(1 + (2*s - 1)*(-1)^(nMol - 1))*Δ*
Sum[Abs[a[α][s][nMol - 1][n] ]^2, {α, 0, 1}], {s,
0, 1}, {n, 0, nEl - 1}];

con[n_, m_] :=
KroneckerDelta[n, m] ==
Sum[Conjugate[a[α][s][j][n]]*a[α][s][j][m], {α,
0, 1}, {s, 0, 1}, {j, 0, nMol - 1}]
allCon = Table[con[i, j], {i, 0, nEl - 1}, {j, 0, nEl - 1}];
vars = Table[
a[α][s][j][n], {α, 0, 1}, {s, 0, 1}, {j, 0,
nMol - 1}, {n, 0, nEl - 1}] // Flatten;

res = NMinimize[{h, allCon}, vars]

The number of variables $a[\alpha][s][j][n]$ goes as $2\times 2 \times \text{nMol} \times \text{nEl}$, so that for $\text{nMol}=\text{nEl}=20$ one has to deal with $1600$ variables. Of course, this takes long time!

I now want to make this faster. I don't know how much faster this can get, because I lack the experience with mathematica.

I read that one can use the Compile function to gain some speedup. I tried to implement a compiled version of the function $h$ but I failed. Especially, it seems like one has to enter all variable names and their type into the Compile function - which is a rather inconvenient thing to do for 1600 variables.

So my question is basically: How can I make the constrained minimization faster? How do I use the compile function in this context?

I use mathematica 10, if that is a necessary information.

## What I tried:

ceqn = Compile[Evaluate[{#, _Complex} & /@ vars], Evaluate[h],
"RuntimeOptions" -> {"EvaluateSymbolically" -> False}];

NMinimize[{ceqn @@ vars, allCon}, vars]

This, however, is slower than the uncompiled version. What can I do to speed things up?

• Try ceqn @@ vars instead of ceqn. The arguments must be inserted. After that you may want to try reformulating everything in terms of array arithmetic, since your a seems to be a 4-dimensional array. – Szabolcs Oct 7 '16 at 9:15
• Thank you, ceqn @@ vars works! BUT: The compiled function is slower than the uncompiled :/ How do I fix this and how do I rewrite this using arrays? – Merlin1896 Oct 7 '16 at 9:23
• You have a lot of code here and I don't have time to go through all of it and check if array operations would work. It looks like you are doing elementwise operations on arrays and summing along one array index. We can sum along a single array index using the second argument of Total. Element-wise arithmetic works on arrays as normal. The missing piece is getting NMinimize to pass an array into your function. Do this with something like NMinimize[f[x], x \[Element] FullRegion[4]] e.g. for a 4 dimensional array – Szabolcs Oct 7 '16 at 10:18


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# Multivariable integration rules pdf

The book includes some exercises and examples from elementary calculus. This text comprises a threetext series on calculus. Derivation of \ integration by parts from the fundamental theorem and the product rule. A rule exists for integrating products of functions and in the following section we will derive it. Integration by parts can be extended to functions of several variables by applying a version of the fundamental theorem of calculus to an appropriate product rule. Recall that in the previous section, slope was defined as a change in z for a given change in x or y, holding the other variable constant. There exists a lot to cover in the class of multivariable calculus. Double integrals are a way to integrate over a twodimensional area. The simplest region other than a rectangle for reversing the integration order is a triangle.

Methods of integration william gunther june 15, 2011 in this we will go over some of the techniques of integration, and when to apply them. Double, triple and higher integrals using repeated integration. Integrals of a function of two variables over a region in r 2 are called double integrals, and integrals of a function of three variables over a region of r 3 are called triple integrals. We use the sum and constant rules, as well as the power rule which says the derivative of xn is nxn 1. The substitution method for integration corresponds to the chain rule for di. But avoid asking for help, clarification, or responding to other answers.

Integrate can evaluate integrals of rational functions. That is, if f is a function and g is a function, then the chain rule expresses the derivative of the composite function f. Derivation of the formula for integration by parts. Find materials for this course in the pages linked along the left. If this limit does not exist, then the limit of the function does not exist. Thanks for contributing an answer to mathematics stack exchange. Integration definite integral as the limit of a riemann sum. Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies inc,smart board interactive whiteboard. Specify the ranges of integration, and then calculate the definite integral of the function. To reverse the order of integration we use horizontal. Chapter 5 uses the results of the three chapters preceding it to prove the. Sumdi erence r fx gx dx r fxdx r gx dx scalar multiplication r cfx.

However, in multivariable calculus we want to integrate over regions other than boxes, and ensuring that we can do so takes a little work. The second text covers material often taught in calc 2. This will help us to see some of the interconnections between what. Basic integration formulas and the substitution rule 1the second fundamental theorem of integral calculus recall fromthe last lecture the second fundamental theorem ofintegral calculus. Sometimes this is a simple problem, since it will be apparent that the function you wish to integrate is a derivative in some straightforward way. Trigonometric integrals and trigonometric substitutions 26 1. The first documented systematic technique capable of determining integrals is the method of exhaustion of the ancient greek astronomer eudoxus ca. Stephenson, \mathematical methods for science students longman is reasonable introduction, but is short of diagrams. Learn more about variable, integration, matlab, numerical integration. An illustrative guide to multivariable and vector calculus.

A few figures in the pdf and print versions of the book are marked with ap at. Integrals with trigonometric functions z sinaxdx 1 a cosax 63 z sin2 axdx x 2 sin2ax 4a 64 z sinn axdx 1 a cosax 2f 1 1 2. Basic integration formulas and the substitution rule. Definite integral of a multivariate function maple. But if i have some function this is the xy plane, thats the xaxis, thats the yaxis and i have some function. The inner integral goes from the parabola y x2 up to the straight line y 2x. The multiple integral is a definite integral of a function of more than one real variable, for example, fx, y or fx, y, z. Functions that appear at the top of the list are more like to be u, functions at the bottom of the list are more like to be dv.

Volumes for regions constructed by rotating a curve. To understand functions of several variables, start by recalling the ways in which you understand a function f of one variable. Convert the remaining factors to cos x using sin 1 cos22x x. Students should notice that they are obtained from the corresponding formulas for di erentiation. Techniques of integration over the next few sections we examine some techniques that are frequently successful when seeking antiderivatives of functions. Students will integrate functions of the form z fx, y or w fx, y, z. This calculus video tutorial focuses on the integration of rational functions that yield logarithmic functions such as natural logs. If youre seeing this message, it means were having trouble loading external resources on our website. Standard integration techniques note that at many schools all but the substitution rule tend to be taught in a calculus ii class.

Treat y as a constant throughout and do the one variable integral with respect to x. In general, if you are evaluating a triple integral of fx,y,z over a volume v, by properly choosing the limits, you can integrate with respect to the. The notes below represent summaries of the lectures as written by professor auroux to the recitation instructors. Emphasizing portability, this book is an ideal complement to other references in the area. Multivariable calculus includes six different generalizations of the familiar onevariable integral of a scalarvalued function over an interval. Equations inequalities system of equations system of inequalities basic operations algebraic properties partial fractions polynomials rational expressions sequences power sums. Stephenson, \mathematical methods for science students longman is. Among other things, they lets us compute the volume under a surface. Free multivariable calculus books download ebooks online. These are all very powerful tools, relevant to almost all realworld. Well learn that integration and di erentiation are inverse operations of each other.

Integral calculus that we are beginning to learn now is called integral calculus. Integrating a multivariate function matlab answers. Lets call that, you know, this is y is equal to some function of x. There are several such pairings possible in multivariate calculus, involving a scalarvalued function u and vectorvalued function vector field v. An examination of the righthand side of the equations in 2.

Multivariable calculus continues the story of calculus. For example, in leibniz notation the chain rule is dy dx dy dt dt dx. In particular, students should have a solid command of single variable calculus including trigonometric and exponential functions, limits and continuity, differentiation, the chain. Partial di erentiation and multiple integrals 6 lectures, 1ma series dr d w murray michaelmas 1994 textbooks most mathematics for engineering books cover the material in these lectures. Definite integral of a multivariate function description calculate the definite integral of a multivariate function. In this page, we give some further examples changing the integration order. For the statement of these three rules, let f and g be two di erentiable functions. Integration of functions of a single variable 87 chapter. Multivariable calculus mississippi state university. Return to top of page the power rule for integration, as we have seen, is the inverse of the power rule used in. The ideas of partial derivatives and multiple integrals are not too di erent from their singlevariable counterparts, but some of the details about manipulating them are not so obvious. You might have learned a formula for computing areas in polar coordinates.

The basic rules of integration, which we will describe below, include the power, constant coefficient or constant multiplier, sum, and difference rules. Changing the order of integration problems and solutions. Examples of changing the order of integration in double. Suppose we have a function y fx 1 where fx is a non linear function. We will use it as a framework for our study of the calculus of several variables. A boundary and area understanding of double integrals. The derivative, rules for finding derivatives, transcendental functions, curve sketching, applications of the derivative, integration, techniques of integration, applications of integration, polar coordinates, parametric equations, sequences and series, vector functions. The integrals of multivariable calculus math insight.

Pdf students understandings of multivariate integrals and how. After successfully completing this course, you will be able to. For indefinite integrals drop the limits of integration. This allows computing the rate of change of a function as its independent variables change along any direction in space, not just along any of the coordinate axes, which in turn allows determination of the. Next, several techniques of integration are discussed. You can download any book for free and can enhance your knowledge. Integration by parts is the reverse of the product rule. Definition in calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. Integrating a multivariate function matlab answers matlab. Learn how tools like the derivative and integral generalize to functions depending on several independent variables, and discover some of the exciting new realms in physics and pure mathematics they unlock. It will be mostly about adding an incremental process to arrive at a \total. The only difference is that we have to decide how to treat the other variable. The rules of partial differentiation follow exactly the same logic as univariate differentiation.

The first part covers material taught in many calc 1 courses. Example 4 reverse the order of integration in solution draw a figure. Pdf prior research has documented several conceptions students have regarding the. Common integrals indefinite integral method of substitution.

It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Listofderivativerules belowisalistofallthederivativeruleswewentoverinclass. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc. The double integrals in the above examples are the easiest types to evaluate because they are examples in which all four limits of integration are constants. Divide the region dinto randomly selected nsubregions. Subsitution 92 special techniques for evaluation 94 derivative of an integral chapter 8. Theorem let fx be a continuous function on the interval a,b. Define, use, and interpret double and triple integrals in terms of. Line integrals, double integrals, triple integrals, surface integrals, etc. It can also evaluate integrals that involve exponential, logarithmic, trigonometric, and inverse trigonometric functions, so long as the result comes out in terms of the same set of functions. First, a list of formulas for integration is given.

You can see how to change the order of integration for a triangle by comparing example 2 with example 2 on the page of double integral examples. It will cover three major aspects of integral calculus. Critical points, in ection points, relative maxima and minima. Multivariable calculus before we tackle the very large subject of calculus of functions of several variables, you should know the applications that motivate this topic. After this is done, the chapter proceeds to two main tools for multivariable integration, fubinis theorem and the change of variable theorem. The chain rule, which generalizes from a product of derivatives to a product of jacobian matrices, using standard matrix multiplication. Demonstrate understanding of the basic notions of multivariable calculus. Multivariable calculus the world is not onedimensional, and calculus doesnt stop with a single independent variable. Integrate can give results in terms of many special functions.

Free books download pdf, free pdf books download in english. There are many ways to extend the idea of integration to multiple dimensions. The value gyi is the area of a cross section of the. Proofs of the product, reciprocal, and quotient rules math. Lecture notes multivariable calculus mathematics mit. Each one lets you add infinitely many infinitely small values, where those values might come from points on a curve, points in an area, points on a surface, etc.

Integrating multivariable functions multivariable calculus. One can integrate functions over onedimensional curves, two dimensional planar regions and surfaces, as well as threedimensional volumes. Chapter 10 is on formulas and techniques of integration. Multivariable calculus with applications to the life sciences. Erdman portland state university version august 1, 20. We will provide some simple examples to demonstrate how these rules work. Integration students will explore double and triple integrals and integrals of vectors. Multivariable calculus that will help us in the analysis of systems like the one in 2.

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text:
# Chapter 18 - For Thought and Discussion - Page 330: 4

The system is not at equilibrium.

#### Work Step by Step

When a reaction cannot be reversed, that means that there is no equilibrium. Since P and V involve equilibrium (for instance, in the equation PV = nRT), it does not make sense to use a PV diagram.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Problem: Provide the structure of the  major product for the following transformation. You may assume any neutral, acidic or basic work up conditions needed.

###### Problem Details

Provide the structure of the  major product for the following transformation. You may assume any neutral, acidic or basic work up conditions needed.


text:
## Cryptology ePrint Archive: Report 2009/233

A strategy for recovering roots of bivariate polynomials modulo a prime

Paula Bustillo and Domingo Gomez and Jaime Gutierrez and Alvar Ibeas

Abstract: Let $p$ be a prime and $\F_p$ the finite field with $p$ elements. We show how, when given an irreducible bivariate polynomial $f \in \F_p[X,Y]$ and approximations to $(v_0,v_1) \in \F_p^2$ such that $f(v_0,v_1)=0$, one can recover $(v_0,v_1)$ efficiently, if the approximations are good enough. This result has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.

Category / Keywords: applications / number theory, lattices and crypto


text:
# [ANN] State estimation with LowLevelParticleFilters.jl

LowLevelParticleFilters.jl is a library for state estimation, that is, given measurements y(t) from a dynamical system with inputs u(t), estimate the state vector x(t). Throughout, we assume discrete-time dynamics on the form

x(t+1) = f(x(t), u(t), p, t, w(t))\\ y(t) = g(x(t), u(t), p, t, e(t))

where p are some form of parameters, t is the time and w,e are disturbances (noise).
The documentation describes how to handle continuous-time ODEs on the form

\dot x(t) = f(x(t), u(t), p, t, w(t))

as well.

The library has existed for a while, but has never really been announced before. I just pushed it over to version 3.0, breaking the previous interface by moving to an interface similar to the SciML ecosystem where many functions accept a parameter vector p. The Documentation has also seen some improvements in the process.

We provide a number of filter types

• KalmanFilter. A standard Kalman filter. Is restricted to linear dynamics (possibly time varying) and Gaussian noise.

• ExtendedKalmanFilter: For nonlinear systems, the EKF runs a regular Kalman filter on linearized dynamics. Uses ForwardDiff.jl for linearization. The noise model must be Gaussian.

• UnscentedKalmanFilter: The Unscented Kalman filter often performs slightly better than the Extended Kalman filter but may be slightly more computationally expensive. The UKF handles nonlinear dynamics and measurement model, but still requires an additive Gaussian noise model and assumes all posterior distributions are Gaussian, i.e., can not handle multi-modal posteriors.

• ParticleFilter: The particle filter is a nonlinear estimator. This filter is simple to use and assumes that both dynamics noise and measurement noise are additive. Particle filters handle multi-modal posteriors.

• AuxiliaryParticleFilter: This filter is identical to ParticleFilter, but uses a slightly different proposal mechanism for new particles.

• AdvancedParticleFilter: This filter gives you more flexibility, at the expense of having to define a few more functions. This filter does not require the noise to be additive and is thus the most flexible filter type.

• DAEUnscentedKalmanFilter: An Unscented Kalman filter for differential-algebraic systems (DAE). Still somewhat experimental.

The code has been written to be reasonably fast and it supports StaticArrays everywhere. For simple systems, we can push about 7k particles per millisecond. We also support particle and Kalman smoothing as well as automatic differentiation through the filters using ForwardDiff.jl, making parameter estimation with the Prediction-Error Method (PEM) relatively easy. We also have a new example of estimating time-varying parameters in ODEs.

Happy filtering
Fredrik

26 Likes

Looks great, thanks for putting it together and writing such nice docs! I was just thinking about trying a DAE+state-space framework thing the other day.

1 Like

Nice work!

How hard would it be to call an external model compiled in C++. The model needs a file(s) that provides the current state, parameters and inputs. I am looking use this model for data assimilation.

Thanks!

As long as you can wrap the c++ model in a Julia function with the signature (x, u, p, t) - >x(t+1) you should be good to go. Wrapping C is generally not that hard, but if you need to go through a file, perhaps performance may suffer slightly.

1 Like

Thanks! I will see what I can do