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PS I had a boss who was originally an electrical engineer and used that expression "orthogonal" all the time in any kind of situation, not just technical, so Pardonnez-Moi for not thinnin' to splain it.

"In mathematics, orthogonality is the relation of two lines at right angles to one another (perpendicularity), and the generalization of this relation into n dimensions; and to a variety of mathematical relations thought of as describing non-overlapping, uncorrelated, or independent objects of some kind." From a different Wiki article. Now that explanation actually leads to a glimmer of intuitive understanding. Well, at least a little bit. And with shit like this, every little bit helps.

One thing for sure Thailand in general terms is far safer then Brazil. You walk 2 streets off Copacabana and no telling what will happen . And ATM withdrawals are always dangerous. This never happens in Thailand . That said for multi trip visitors , they know what to do and not to do and for first time visitors there is plenty of information here about how to limit the chance of any bad experiences.

The bombing was an isolated incident and I don't think it will stop tourism for the long term. I have spoken to at least 20 people there now and all feel perfectly safe. I had 2 friends from USA in Thailand when the bombing happened and they felt safe as well. Things like this can happen anywhere in the world and most people know this. Thailand does not have the reputation for violence against foreigners. That said, I do think this Junta has hurt tourism and will make it much worst before it gets better.

Computing by Brain - Los AlamosWalking around the hastily built wooden barracks that housed the soul of the atomic bomb project in 1943 and 1944, a scientist would see dozens of men laboring over computation. Everyone calculated. The theoretical department was home to some of the world's masters of mental arithmetic, a martial art shortly to go the way of jiujitsu. Any morning might find men such as Bethe, Fermi, and John von Neumann together in a single small room where they would spit out numbers in a rapid-fire calculation of pressure waves. Bethe's deputy, Weisskopf, specialized in a particularly oracular sort of guesswork; his office became known as the Cave of the Hot Winds, producing, on demand, unjustifiably accurate cross sections (shorthand for the characteristic probabilities of particle collisions in various substances and circumstances). The scientists computed everything from the shapes of explosions to the potency of Oppenheimer's cocktails, first' with rough guesses and then, when necessary, with a precision that might take weeks. ... When he (Feynman) started managing groups of people who handled laborious computation. he developed a reputation for glancing over people's shoulders and stabbing his finger at each error: "That's wrong." His staff would ask why he was putting them to such labor if he already knew the answers. He told them he could spot wrong results even when he had no idea what was right something about the smoothness of the numbers or the relationships between them. Yet unconscious estimating was not really his style. He liked to know what he was doing. He would rummage through his toolbox for an analytical gimmick, the right key or lock pick to slip open a complicated integral. Or he would try various simplifying assumptions: Suppose we treat some quantity as infinitesimal. He would allow an error and then measure the bounds of the error precisely. ... When Bethe and Feynman went up against each other in games of calculating, they competed with special pleasure. Onlookers were often surprised, and not because the upstart Feynman bested his famous elder. On the contrary, more often the slow-speaking Bethe tended to outcompute Feynman. Early in the project they were working together on a formula that required the square of 48. Feymnan reached across his desk for the Marchant mechanical calculator Bethe said, "It's twenty-three hundred." Feynman started to punch the keys anyway. "You want to know exactly?" Bethe said. "It's twenty-three hundred and four. Don't you know how to take squares of numbers near fifty?" He explained the trick. Fifty squared is 2,500 (no thinking needed). For numbers a few more or less than 50, the approximate square is that many hundreds more or less than 2,500. Because 48 is 2 less than 50, 48 squared is 200 less than 2,500-thus 2,300. To make a final tiny correction to the precise answer, just take that difference again-2-and square it. Thus 2,304. Feymnan had internalized an apparatus for handling far more difficult calculations. But Bethe impressed him with a mastery of mental arithmetic that showed he had built up a huge repertoire of these easy tricks, enough to cover the whole landscape of small numbers. An intricate web of knowledge underlay the techniques. Bethe knew instinctively, as did Feynman, that the difference between two successive squares is always an odd number, the sum of the numbers being squared. That fact, and the fact that 50 is half of 100, gave rise to the squares-near-fifty trick. A few minutes later they needed the cube root of 2 1/2. The mechanical calculators could not handle cube roots directly, but there was a look-up chart to help. Feynman barely had time to open the drawer and reach for the chart before he heard Bethe say, "Thats 1.35. " Like an alcoholic who plants bottles within arm's reach of every chair in the house, Bethe had stored away. a device for anywhere he landed in the realm of numbers. He knew tables of logarithms and he could interpolate with unerring accuracy. Feynman's own mastery of calculating had taken a different path. He knew how to compute series and derive trigonometric functions, and how to visualize the relationships between them. He had mastered mental tricks covering the deeper landscape of algebraic analysis-differentiating and integrating equations of the kind that lurk dragonlike in the last chapters of calculus texts. He was continually put to the test. The theoretical division sometimes seemed like the information desk at a slightly exotic library. The phone would ring and a voice would ask, "What is the sum of the series 1 + (1/2)4 + (1/3)4 + (1/4)4 + . . . ?" "How accurate do you want it?" Feymnan replied. "One percent will be fine." "Okay," Feymnan said. "One point oh eight." He had simply added the first four terms in his head-that was enough for two decimal places. Now the voice asked for an exact answer. "You don't need the exact answer," Feynman said. "Yeah, but I know it can be done." So Feynman told him. "All right. It's pi to the fourth over ninety." He and Bethe both saw their talents as labor-saving devices. It was also a form of jousting. At lunch one day, feeling even more ebullient than usual, he challenged the table to a competition. He bet that he could solve any problem within sixty seconds, to within ten percent accuracy, that could be stated in ten seconds. Ten percent was a broad margin, and choosing a suitable problem was hard. Under pressure, his friends found themselves unable to stump him. The most challenging problem anyone could produce was: Find the tenth binomial coefficient in the expansion of (1 + X)20. Feynman solved that just before the clock ran out. Then Paul Olum spoke up. He had jousted with Feynman before, and this time he was ready. He demanded the tangent of ten to the hundredth. The competition was over. Feynman would essentially have had to divide one by pi and throw out the first one hundred digits of the result-which would mean knowing the one-hundredth decimal digit of pi. Even Feymnan could not produce that on short notice. Reproduced (scanned) from: GENIUS. Richard Feynman and modern physics. J Gleik. First Published in Great Britain in 1992 by Little Brown and Company (1992). Chapter 4 (Los Alamos). http://www.precisioninfo.com/index.php?doc_id=64

"In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. It is a subspace of V." Definition from Wiki. So much clearer with a brief explanation, yes?

Thiago had a day off over this past weekend so I started to look for flights with good times and decent last-minute fares. Montevideo had nothing good. Ditto Foz do Iguacu. The fares to Salvador were higher than to BA. Aerolineas Argentinas had the best prices and times. The drive out to Ezeiza is longer than to Galeao here in Rio. But with the low price of the Argentine peso it was only about US$30.00 each way. I had read some awful trip reports about them over the years but out flight out was only 15 minutes late and the flight back only pushed back five minutes late. Beware that US and Canadian citizens need to get a visa for $160,00 before departure. It is good for ten years. All because of the USA. A reciprocity fee. I spent more than normal for an incredible boutique hotel in Recoleta about 1 block from the cemetery where Evita Duarte Peron can be found. Hotel Mio Buenos Aires. Contempoary design boutique hotel with only thirty rooms and a spa. Very very nice. As to gay life, I really wanted to see the gay tango show. I think Axiom had mentioned something about it being far out of the city. Not at all. In the San Telmo neighborhood. But the show as of now at Le Marshall only takes place on Fridays. We arrived Saturday at 4:30AM and left Monday night at 9:45PM so out of luck. I did some research and found three bar discos to hit. We started at Bar Flux at just after Midnight and the place was dead. It also didn't seem too large. Maybe 10 or 15 guys at that time. So we headed over to Kilometro Zero at about 12:45AM. The place had a nice crowd and only got busier and busier. There was a drag show for ninety minutes and then there were two male and two female strippers and almost everyone dancing. We left at about 4:45am We never got around to what is rated as the #1 spot in B.A. Sitges Bar/Disco Interesting that at KM Zero most everyone ordered bottles of spirits or champagne with mixers. Much less expensive than by the drink. Cover charge was 100 Argentine pesos or about $11.00US. Cheap night relatively speaking. Drinks in Rio are more expensive at a place like 40 Graus in Lapa on Rua Riachuelo. As to sex, well, I had Thiago with me so it wasn't something that concerned me. Thiago and I do agree that Argentines are much better-looking than the "unfortunate" Chileans. We both found the Portenos much more well-mannered than Cariocas. I am a fan of fine leather so that was on my agenda for part of one of the days. On Saturday, we walked and taxied and ended up in Palermo Soho at a Trip Advisor top 50 restaurant, the parilla/steak house La Cabrera, for a large lunch. It was really very good, but with more investigation I probably could have found someplace else just as good, less expensive and not as touristy. We worked off lunch by walking a bit to a three block stretch of outlet leather shops with good prices. Murillo 600 is the address at the start. Near a metro stop as well. If you go to BA, bring Dollars or Euros, as there are two exchange rates in existence. The official was around 9.10 and the street rate used in many shops and restaurants was 15.60, more or less. Sunday was spent visiting various parks in the city including the waterfront where there are a couple of floating museum ships, a schooner and a barquentine. After a nap and fun time, the concierge directed us to a famous late night place with nice food from breakfast through late supper. La Biera, Across the street from the park containing Recoleta Cemetary. On our last afternoon I passed a factory leather store that had some nice things a half block from our hotel. Nice quality. Good service. And they charged my credit card through a bank in Miami so I got the street rate even using a credit card. We spent about three hours at the zoo in Palermo. Really very nice. A bit like Chicago's Lincoln Park Zoo with buildings right on the park, but older and more interesting pavilions architecturally.

I felt totally safe. A city that is a mixture of Madrid and Paris. Much more developed, more educated, certainly more formal. If I had been to Buenos Aires before Rio de Janeiro, I'd probably be living there right now instead of Rio de Janeiro. I'd spend the 4 coldest months back in the States or somewhere else warmer. I also found the city much more survivable than the crowded and hectic São Paulo. I had Thiago with me so I had no interest aim exploring the rent scene. But if I ever other's reports, there are some.houses with boys as well as a large on-line presence of working guys. At Flux and Kilometro Zero, the doormen and the clients we spoke to in either Portuguese or Spanish. Taxis were cheap and with our limited time I didn't want to bother with public transit. Biggest word of advice is before leaving on the plane, fill out and pay for your ten year visa on-line. And either bring lots of Euros or Dollars with you to get the street exchange rate. Or pay asuch as you can before arriving at the better exchange rate and have a way to receive.foreignone while in country. Unless one wants a beach vacation in Brasil(and I for one love the beach culture on Farme de Amoedo) or loves the rent saunas as opposed to call boys, Buenos Aires was great.

I have watched the Rio Times since it started. It was done with a Word Press Theme and initially had all re-written articles from other sources. It has grown a great deal. Please feel free to post any links to any site you feel relevant. It is good information for us all.

Another batch of photos First of the hotel room Two from Evita's family tomb Inside LaBiera this interesting sculpture Pink Flamingos - not the John Waters film Fountain at the entrance to the Palermo Zoo Thiago being swallowed by a tree, not me Santiago Calatrava bridge on the waterfront, old barquentine on the right And terribly sorry, I haven't a clue how to rotate these photos, just posting them took me over an hour.

Here are some photos from the Mio Buenos Aires and La Cabrera parilla