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.
-
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.
