Tuesday, September 20, 2016

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Julia - Gödel 3


3

So let's go over the two glitches that we have. One is the longitudinal glitch. We're do you start longitude? In one case it simple - 0°. but that only works when you know where zero is. Where you have nothing, then that is zero. But what about the case where you don't have nothing? Let me explain. Look at the world, and tell me where nothing is. There is not a point on the globe, which you can point to, which has “nothing”. You have to just pick on arbitrary point, which in the case of the world is 0° Greenwich Mean Time. But that only was true, universally, from 1884. for the time though there were conventions, and the most common of which was GMT, there were other points that could be used. And of course, because this was a fight between capitals, everyone had a different angle. Some wanted Greenwich, others preferred Washington, Paris was common, and so was St. Petersburg.

What this led to was a series of prizes, 1567 Philip the II of Spain offered a prize, and Philip the III of Spain increased it 1598. Holland offered a prize in 1636. then Louis XIV offered a prize in 1666. only in 1714 was written entered in to establishing a prize. Note that these were on the Atlantic seaboard. There is reason for this, which does not take any time to figure out. Countries on the Atlantic seaboard were going to be the ones who would benefit the most from longitude.

What everyone figured out, was the relationship between time and longitude. In this period they were not treating numbers as a kind of clock, that would be a different insight. That cards would be a kind of time didn't enter in to anyone's equations. And we will get to reading of cards in the next chapter with Pascal. So what everyone was thinking had to do with a round sphere, and which point on it is Zero Meridian. And as you can see from the prizes, offered by Spain, Holland, France, and finally Great Britain, was there was intense interest in this. They weren't competing for a theoretical prize that was of no value, they were competing for an intensely practical problems. Longitude had real meaning, as the real disaster in 22 October, in 1707, off of Sicily show. Their were 1400 Mariners who lost their lives. Now realize that in 1707 roughly, an I mean very roughly because different experts quote different numbers on this, about 750 million people had been born. As opposed to 7 billion.

So by one estimate, there are nine times as many people on the globe. Think about disaster larger than 9/11, or Pearl Harbor. Think about the disaster as large as the rape of Nanjing. There are disasters worse, but until this moment, you probably haven't heard of 1707 before. Where has you have heard of several disasters much smaller in scale. As with 9/11, four ships were lost. There is no accurate count of the dead, estimates range between 1400, and 2000. but adjusted for the time, that is larger than any year disaster, any fleet disaster, and only assumes it's appropriate scale among the massacres of the time. And as I said, you probably haven't heard of it until this moment.

That was the terror of longitude. It would wipe clean, by the wrath of God, said Raiders of Lost Ark, an entire fleet. Thus it was mandatory that a prize be awarded to finding out what latitude the ships have, because that was what people understood was the problem. It wasn't the real problem from a relational database management, it was the problem as they understood it. They began to work on the longitudinal problem, as they understood it. And that meant breaking out how far from a line fixed in space a ship was.

There were two routes to go, one was a Galileo route, that is of tracking the moons of Jupiter, and figuring out where they were. The other method was to calculate and internal distance of latitude, and compared with what would be known were they standing on the prime Meridian. This actually involves two calculations. One is how far east or west you are, and the other one is our you along the Prime Meridian, or along the reverse side. Because remember there are two lines drawn, one is the Prime Meridian, and the other one could be said to be the Counter-prime Meridian.

These two calculations are not easy, and people as only that there calculation be good enough. As we know from time, good enough means not really good enough. If you don't think that this is important today, think about the disaster which engulfed MH370, who was lost by a different means, but the same ends. It to was lost by a line of longitude. Ignore such things as the US Army did it, and look at the details. It slipped off the radar, and cruised for eight hours. Most of the time everyone was dead. In other words, the problem of longitude has been not been solved, it is solved well enough for current purposes.

What people wanted him to 17th and 18th centuries was to find the location of a very slow moving ship. And they want to know where the shoals were, that was good enough for them. Thus they didn't want to know enough to realize that longitudinal problem is also the card problem. Though they worked on both problems, they did not understand that they were the same.

So through the 1700s people worked on the two solutions to longitudinal problem: and they came up with solutions to both. For fixed calculations on land, the way to go was to calculate the moons, because moons are fixed and you can go over the calculations and tell the are correct. On the sea, however, you only have one chance, and you had best make it count. In that form, you place a great deal of faith in the calculations, rather than the siting of moons, because you only have an instant to do the siding, and many hours to do the calculations. In other words, though it seems there is one problem, there are two roads to go, and each one of them has a different solution. If you have plenty of time to the calculations, but not much time to cite - you quickly find the way to cite quickly and to the calculations. Where as if you have plenty of time to cite, then oftentimes you will carefully cite. And this is what happened here: if you have only one moment to get right, you take a very quick citation, and work out the details. This is what John Harrison did. While he had some help, it was his vision that made a timepiece which was sufficient alone to do the work.

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On the other side of the problem, this is glicth #2. that being of chance and cards, a man by the name of Blaise Pascal realized that chance was only the result of a theoretical hand, and that all hands were different in the exact same degree. It is humans that want particular hands, in a particular order. And thus he described Pascal triangle. Of course it had been studying before, but Pascal noted that they were binomial coefficients of Pascal's rule, which is expanded to n-dimensions by Pascal's simplex.

What Pascale was not the first person to realized was that every hand was derived from the two numbers above it. This was very old, Pingala, or one of his disciples, knew in the second century BC. What he did realize was that the properties of several sets is contained within the triangle. This leads to other places that we do not have time to discuss, such as Sierpinski triangle, or a grid of knights moving on a Plinko game board. What we are interested in is how random becomes order, because we're interested in a relational database management system, which seeks order rather than randomness.

Pascal realized that he could do calculations, and proceeded to show that a Pascal calculator could do important work. For example he showed that addition did not mean the calculator could do multiplication, which is later to be shown to be important. But what was regarded as important was his work with Pierre de Fermat on probability theory, and is refutation of Aristotle's dictum that nature abhors a vacuum.

Now if I were gazing at Pascal, I would have no trouble in talking about the amazing things that he did. But I'm not. Instead, I am going to talk about what is missing. And one thing that is missing is Pascaline is a demonstration that multiplication is not simply repeat subtraction. It comes close to this, but though the principal is there, no one, not even Pascal, notices it. But someone will notice it and form the correct conclusion. That is, he will notice that addition and subtraction, without multiplication, are different. Addition and subtraction without multiplication are simple, multiplication is complex. That addition is not the same as subtraction is difficult to understand, and in time I will have to explain.

As for Pascal, he was dying, and knew this: saying “Sickness is the natural state of Christians.” and disorder is a natural state of orderly things. He died at only 39. But he glance at a vision, which would be made and remade, for one, by Cantor. This vision is that there is an infinitude of points, and they are different from the infinitude of lines. The sheer size of this revelation would occupy mathematical thinking, even to this day.



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