Re: Bobby Fischer's Conquest of Everest..
- From: thumbody <master@xxxxxxxxxxxxxx>
- Date: Thu, 14 Aug 2008 04:11:27 +1000
thumbody wrote:
.
help bot wrote:
Obviously, you know nothing about physics--
I'm aware I know nothing bot which paradoxically adds up to something, a
concept which has exercised the minds of the great & good these many
long years..
Here is a nice little lecture which thumbody was quite pleased with
apart from the good Profs. unfortunate use of the execrable 'paradigm'
word..
MUCH ADO ABOUT NOTHING
Professor John D Barrow
Today we?re going to hear lots about nothing, I fear. Those of you who
attended Robin Wilson?s talk a few months ago about zero in mathematics
will have heard about that side of the story and so I won?t talk in very
much detail about that. If you want to go and learn more than you ever
wanted to know about that aspect of nothing, then you should take a look
at my book from a few years ago which was called The Book of Nothing!
The curious thing about nothing is that it is one of those ideas that
induces feelings of nausea and panic and boredom simultaneously. It?s
something of a pivotal idea in all sorts of different areas of human
thinking, and I?m going to try today to touch on some of those areas to
show you how the idea of nothing is rather more subtle and was rather
more important and pivotal in all sorts of ways of thinking about the
world. Philosophers tied themselves in knots thousands of years ago
wondering how it could be that nothing could be something, and in the
West at least, that was a considerable impediment to developing a
coherent idea about nothing, developing mathematics which included a
zero. In physics and mathematics, the situation is more predictable, but
literature, art and music, all have facets of nothingness. Theologians
were always worried about trying to create the world out of nothing, or
not, and cosmologists, well, they?re interested in whether the world
might disappear back in to nothing.
Let?s start with the mathematical side of things. If you were to write
down 3 strokes ? 111 ? and you were to talk to a Roman centurion, they
would imagine that this was the number 3, but if you talk to somebody
here, 111 means a hundred and eleven. But if you talk to the wrong sort
of computer scientist, who works in binary, 111 means something
different altogether, so it means one, plus two to the one, plus two
squared times one. So if you use a base two arithmetic, 111 means
something different to what it means if you use base 10. This idea of
the position of a numeral having a meaning was something that was
introduced originally by the Sumerians and the Babylonians. It?s a
rather sophisticated idea. It wasn?t used by the Egyptians, it wasn?t
used by the Ancient Greeks, it wasn?t used by the Romans. But once you
start to record numbers, like the Babylonians did, you have a stylus of
a particular shape; you can represent it vertically, horizontally, and
the position of the marks you make carries some meaning. The Babylonians
used a system which combined a base 10 with a base 60, so instead of
having hundreds, they had multiples of 60 times 60; instead of having
tens, they would have multiples of 60, and then they would have the
rest.
For a long period of time, they simply left a space on the tablet, but
that could create an ambiguity. It wasn?t too clear what the number was.
So inclined marks of the stylus were used to indicate an empty slot in
the register, what we would call a zero. All this may sound rather
remote, but on the other hand, what we?ve derived from the Babylonian
system is our measure of keeping time ? 60 seconds to the minute, 60
minutes to the hour ? and of angular measure ? degrees, minutes and
seconds of arc. Their way of representing numbers was almost like us
thinking in terms of degrees, minutes and seconds of arc.
The Babylonians weren?t the only people to think of zero. The other
culture that developed a system that needed to use a zero, a great
culture, but very mysterious, was the Mayans. I had the great privilege
to go the Mayan Riviera, as you might call it, into Mexico, in November
for a couple of weeks, and was able to see some of the Mayan glyphs and
old cities there ? an extraordinary culture that developed mathematics
to a relatively sophisticated level, but never invented the wheel. What
the Mayans did was to produce images of numbers, in rows. In the first
row, you would keep track of what we would call units, and then they had
a base 20 system rather than 10, so they counted the number of digits
feet and their fingers originally. So the number 400 would be denoted by
the dot, two dots, and a strange shell-like symbol, which represented
zero. At the top you would see lots of pictures from different glyphs.
What they would then do was to add a number alongside a rather exotic
picture of a creature, which was representing the number being shown.
What?s curious ? they have a place value system in a sense, so they sat
in particular positions, so when they created the artistic work on the
glyph, if they didn?t have a symbol for zero, they had a gap in the
ornamentation. And so zero was in effect invented for aesthetic reasons
to complete the picture, as it were.
Babylonians finally got round to introducing their explicit zero around
500BC. The Mayans, as you know, just before William the Conqueror came
along, were dying out. Nobody seems to quite know why they did; they
weren?t necessarily conquered completely by the Spaniards in any way.
The other great culture that developed the zero in the form that we know
it is the Indian tradition. The early Indians developed mathematics and
geometry in a sophisticated way using very nice notation. They used the
decimal system, they used the same numerals that we use today, and this
entire way of doing mathematics came to Europe, and ultimately to us, by
way of the Arab cultures in the early Middle Ages. What?s interesting
about the Indian conception is it does something that really the Greeks
were unable to do. The Greeks, because of their philosophical views
about nothing, never had a zero symbol, and nor did the Romans. All
these logical problems about whether it was an illegal move to regard
nothing as something made them very reluctant to introduce the idea of
zero as a formal element in logical argument, because if you introduce
one false element, then everything collapses and you can prove any
statement. The Indians of course, because of their philosophical views,
were much more mystical, much more conversant with the concept of
nothingness and non-being, very comfortable with these ideas, and so
what you find in Indian culture is not just a zero symbol, but the whole
panoply of interconnections of the words for zero with nothingness and
the void and the vacuum that we?re familiar with. For the Babylonians, a
nation of accountants and astronomers, the zero symbol was just a gap in
the register, but for the Indians had basic words which were used for
the void, or for the zero, or for that red dot on the woman?s forehead.
In Indian poetry, you?ll see women?s beauty is extolled in the same
language, rather like mathematics of generating dots and zeros. From
this, you generate all the concepts that we?re now familiar with about
non-existence and the void and things being worthless and having no
value, going all the way down to the more abstract notions about
emptiness, nothing, and the mathematical ideas that if you multiply
something by zero, you get zero, and even if you divide by zero, you get
infinity. All these ideas were present in early Indian arithmetic and
mathematics.
We?re familiar today with the words zero and cipher. In slightly older
English, there?s a usage of the word cipher rather different to how we
use it today. We tend to use it as meaning a code of some sort, but a
cipher was just a nonentity, so if you said that a gentleman was a
cipher in his own household, you meant that he was a zero presence. So
these two terms have come to have slightly different meanings, and we
still see them in language today. The interesting message is the way
that the philosophical climate in India was conducive to the development
of the mathematical idea of zero.
One of the things of a non-mathematical sort that are rather interesting
about European and certainly English culture in the early Middle Ages,
up to the time of Shakespeare or so, was there was a great tradition of
word play and linguistic paradoxes about nothing, hence Much Ado About
Nothing. The whole tradition that there are certain paradoxes about
nothingness and zero began even with some of the early Greeks like Zeno,
and all the paradoxes revolve around the idea that nothing might be
something. There was something of an insurance element in this; there
was a time when, for philosophical and religious reasons, the idea of
nothingness or vacuum was something of a forbidden idea, a heresy, if
you like. In the Jewish tradition, and therefore the early Christian
tradition, nothingness and the void was something that was anathema ?
this was characteristic of the world without God, before the world was
made. This was not something that you wanted to pursue ? quite different
from the Indian tradition. And so if you wanted to talk about nothing,
with these sorts of paradoxes, nothing is what is not, as it were, in
Shakespeare?s terms; it?s a safe way to talk about it, because if
someone challenges you for propagating heretical ideas about nothing and
the vacuum, you can always say that you were merely exhibiting these
linguistic paradoxes to bring the whole idea into disrepute. Countless
writers played this game, so in the early 1500s; you?ll find a whole
literature of this nihil paradox type game.
Shakespeare really did it better than anybody, and if you look through
his plays, you?ll find constant word play and use of this idea of
nothing. If you look through Lear and other plays, you?ll find that he?s
constantly using this idea of nothing being something.
The other ingredient of it, which had a sort of theological element, was
that there was something that we might now in the press regard as the
moral vacuum. So the world of nothingness and the vacuum, was something
without god, it was something where there were no morals, where humanity
wouldn?t go. This whole period of thinking that you could learn
something about nothingness and the vacuum and the void just by playing
games with linguistic paradoxes really went on right up until Galileo
came along. Galileo did away with this whole idea of thinking that just
by studying what people said long ago, by creating linguistic paradoxes,
you might learn something about the vacuum, and he replaced it by real
experiments.
While all sorts of the arts are fascinated by nothingness and the void,
there are countless works of art around the world that look like blank
canvases. There?s something terribly unoriginal about these sort of
works; for some reason they all have a rectangular frame ? you never see
pictures that have an elliptical or asymmetrically shaped frame. And the
musician John Cage, with his 4 minutes and 33 seconds of silence, that?s
273 seconds of silence, the absolute zero of sound. And the other matter
of silence in music, which is more serious, experts can talk to us at
great length, is the whole matter of timing in music, the silences
between the notes, which are absolutely crucial for determining the
structure and the effect.
I want to complete what one might say about mathematics by telling you
about something that developed after the ordinary idea of zero and
counting. By the time we got to the 19 th Century, mathematicians
realised that there wasn?t one mathematics ? counting, geometry and so
on ? and these were the thoughts of god and this was the way the world
worked, as even Galileo believed, but mathematics was made of all sorts
of mathematical systems, collections of axioms. There were different
geometries ? non-Euclidian ones, Euclidian ones - different arithmetics,
lots of different mathematical systems. You specify what the objects are
? whether they?re lines or points or symbols - and you specify the rules
of the game, rather like chess or drafts, and all the possible games of
chess are like all the truths and theorems that can be proved using that
system. What this means is that each system has its own zero, and
although the word might be the same for each system, the idea is
completely different. So if your zero is something that you do to the
objects in your system which doesn?t change them, then if you have a
collection of symbols and just the operation of addition, then you have
what we denote by our zero symbol, but if you had a system where only
multiplication is defined, then the symbol that doesn?t change your A,
which is what we normally call one. Every system of logic and
mathematics has an operation, if you wish, that corresponds to zero, but
they?re different, so there is an infinite number of zeros or versions
of that concept.
The nearest to the original idea of zero in mathematics is something
that?s known to mathematicians as the empty set. A set?s just a
collection of things, a collection of cars in your garage, in the toy
box, and the empty set is the set that doesn?t have any members. This is
quite different from the numerical zero, which is defined as part of
arithmetic. So this is the set that has no members, and out of that set,
you can define all the numbers of arithmetic. Out of nothing, you can
generate everything. How do you do that? Well, you define what we
normally call zero just to be the empty set, and you?ll define by the
number one the set which has got a single member, and you?ll define two
to be the set that contains the object zero, and one as members. So the
number two is defined to be the empty set and the set which contains the
empty set, and so on with three. The number three is defined to be the
set that has these members; the empty set, the set containing the empty
set, and the set containing the empty set, and the set that contains the
empty set, and so on forever. So you can define all the numbers just in
terms of the empty set.
Well, I warned you that it was Galileo who really taught us about taking
the vacuum seriously experimentally. The idea of a physical vacuum is
something that had been a tortuous question, particularly for early
Greek philosophers, for medieval scientists and philosophers, and there
were two rather crucial examples that played a role for thousands of
years. The first was a Greek object ? sometimes it?s called the Water
Catcher. This would be made out of metal, had a tube, then lots of holes
were made in it. You can imagine what happens if you put this in water.
So if you immerse it in water, with your finger off the top so it fills
up, and then you put your finger over the top and you pull it out of the
water, then the water doesn?t come out of the holes, but if you take
your finger off the top, the water will all come out of the holes. If
you take it empty, and you put your finger on the top and you immerse it
in the water, the water won?t come in, but if you take your finger off,
the water will. This understanding of why the object behaved in this way
was a problem that took thousands of years to solve, and there were all
sorts of extraordinary ideas about why this object behaved as it did.
The other great paradigm that began really with Lucretius was the idea
of just having two plates, maybe of metal, later of glass. You put them
very close together, and then you ask when you separate them, does a
vacuum form instantaneously or not? Why is that interesting? Well,
ancient philosophers had all sorts of great ideas about the vacuum on
which an awful lot rested because they were pivotal ideas in great
philosophical systems. For Plato, the whole idea of a vacuum, of having
nothing, was inconceivable, because for Plato, what we saw around us
were just expressions of the abstract forms in some other world of
ideas, so even if there was nothing here, there still had to be a form
corresponding to that, so there is no possibility of there being nothing
at all. Aristotle believed it was impossible to create a physical
vacuum, so it was not possible to make a vacuum in the world. And this
became bound up with the whole idea that it was not possible for nothing
to be something, for nothing to be part of the whole story and
argumentation about the world. What Aristotle and his followers for
thousands of years would have argued is that you cannot create nor have
what they called intra-cosmic void. You can?t make a void, a complete
vacuum, anywhere in the world, or in the visible universe, but it might
be possible to have what they called extra-cosmic void. So if you
imagine that the world is some great finite ball, then beyond it, there
might be a void, a complete vacuum. But that?s another story.
All these little experiments with the water catcher and the two strips
all revolved around the question of whether it was really possible to
make an intra-cosmic void. Some people were arguing that if you put two
slabs together perfectly, then there?s nothing between. When you pull
them apart, air rushes in, but there must be a fleeting moment before
the air gets in when there?s a vacuum. And if you look at the whole
medieval argument about this, it?s really quite sophisticated and very
interesting. The next stage, people say, no, you can never have
perfectly smooth surfaces, so actually there isn?t a perfect vacuum to
start with, and so you don?t have to wait for the air to rush in. And
then Blasius of Parma pointed out, well, it?s worse than that; if they
were perfectly smooth, you wouldn?t be able to separate them. And then
other people pointed out, you don?t need two slabs at all; just take one
slab, drop it on the floor, and at the moment when it?s in contact
before it bounces, it?s in perfect contact, and when it bounces off,
that?s the same process of a vacuum being replaced after a finite time
by air rushing in. Other people said, the air rushes in at exactly the
right rate never to allow the vacuum to form, because there?s a sort of
celestial agent, as William Burley called it, rather like Roger
Penrose?s cosmic sensor that wants to stop naked singularities forming
in the universe ? exactly the same sort of philosophy. The celestial
agent stops a vacuum ever forming in the world. And so there was a great
argument then about whether the laws of nature really could have
negative aspects, whether there could be a law of nature that says no
vacuum ever forms. The trouble with that was, when you looked at your
water catcher, the celestial agent could stop a vacuum forming in all
sorts of ways, in that when you took your finger off, it could fill it
up with water, but it could also have made the metal collapse and squash
everything out. Why did it choose to do one thing rather than another?
The celestial agent didn?t really tell you enough.
All these arguments about whether it was possible to make a vacuum or
not went on pretty much unabated until the famous event in 1277, the
Paris condemnations, Albert the Great, when there were theological
statements for the first time trying to place no restrictions on the
actions of God. It wasn?t possible for you to say, for example, that
there couldn?t be infinities in the world because this was somehow a
challenge to the operation of God?s actions. So this whole story about
the physical vacuum had an interesting experimental, philosophical
background.
This was all changed in the early 1600s by Galileo and Torrichelly, his
student. As he wandered the country, Galileo had noticed rather
interesting things when farmers were pumping water in their fields. He
noticed that nobody could pump water higher than a particular height,
about 10.5 metres in our units, and he obviously had a strong idea why
this was so. He talked to his student and secretary, Torrichelly, who
became a great scientist and mathematician himself, and Torrichelly
picked a different, much denser, material than water, the densest liquid
there is, mercury, to demonstrate this effect and then understand what
was going on. He created the manometer, or the barometer that we know
today. You take a long tube, longer than 76 centimetres in length, you
fill it up with mercury, and then you invert it in a little jug of
mercury and watch what happens. The level of the mercury in the tube
drops, and you get a height of 76 centimetres, what we call atmospheric
pressure. This was very mysterious, philosophically, theologically. You
see, when the tube started, it was completely full, there was nothing in
it, and nothing?s been allowed to get in it, but when it was stood up
vertically, what happened was that a vacuum appeared. It doesn?t matter
what shape the tube is, the mercury will always rise to the same level,
and so the issue was, what was that? Torrichelly maintained this is a
perfect vacuum ? I have created a vacuum here before you in the
laboratory. If you?re a physicist, the way you work out the height, you
work out the weight of the mercury that?s pressing down, which is its
density times its volume times acceleration due to gravity, and that?s
equal to the force exerted by the pressure of air, which is just the
pressure times the area over which the pressure is acting. You notice
the areas cancel out. It doesn?t matter what the cross-sectional shape
of your tube is. The height of the mercury is given by air pressure,
divided by the density of mercury, and the acceleration due to gravity.
As Galileo and Torrichelly appreciated, if you did this experiment in
different places, at different heights above the Earth?s surface, you
get a slightly different rise. But this created a whole sea change in
attitude, so you see what I meant by saying Galileo did away with the
old way of thinking about nothing and vacuum and the void. Suddenly,
it?s an experimental issue, and you don?t discuss the vacuum by
linguistic paradoxes, but you make a vacuum and you try to do things to
it.
In this country, Robert Boyle, not very far away, carried out all sorts
of exotic experiments ? putting canaries in tanks, and evacuating the
air and watching the canary become unconscious, then putting the air
back in again and it comes back to life; seeing if magnetic fields were
propagated, as it were, across a vacuum, and noting that chemical
reactions came to a halt if you took all the air out of a chamber. So
there began an early experimental phase of investigating the vacuum.
The most spectacular experiment of all was carried out by Otto von
Guericke, who was the Mayor of Magdeburg. They don?t do experiments like
this anymore. It might be a great Gresham experiment on the day of the
Lord Mayor?s processionI What what Guericke did was to have two enormous
bronze hemispheres made, which he joined together, and then pumped out
the air, and then of course they were locked together, they couldn?t be
separated. He then got two teams of eight horses attached to each side
of the hemispheres, and had the horses revved up, pull in opposite
directions, to try and separate the hemispheres, and they couldn?t do
it. Then he just went along and turned the switch and let the air in,
and the hemispheres just fell apart. You can still see the hemispheres
in the city museum in Munich today. What was remarkable about this
experiment, great showman that he was, he wanted to demonstrate that the
vacuum really was something, that it wasn?t just a vague idea. Worse
than that, Aristotle and early Judeo-Christian philosophy told you that
the vacuum was something that always tried to go away; if you made a
vacuum it was always filled, so it was unstable. But this vacuum didn?t
want you to destroy it, so if you created a vacuum inside the
hemispheres, pull as you might, you couldn?t separate them and destroy
it.
Pascal was another to really complete the story. He played the game of
taking Torrichelly?s type of barometers up to the top of Notre Dame
Cathedral and up into the French countryside, to the highest mountains
that he could find, and of course what he discovered was that the height
of mercury that was raised at the top of the cathedral, on the
mountains, was different, because air pressure varies with altitude, and
even the acceleration due to gravity.
This is an era of demonstration that the vacuum is not just a vague
idea, that it?s part of science, you can manipulate it. In many ways, it
was the mathematicians who, by introducing the idea of zero into Europe,
along with eventually the Indo-Arab system of mathematics, really
smoothed the way for the physicists and other scientists and engineers
to use the idea of the vacuum without huge amounts of persecution and
oppression; so the zero in mathematics was relatively uncontroversial.
It eventually assumed a significant role in accountancy and mathematical
science in Europe, and this gave credence and acceptance to the idea of
nothing as being something.
Moving to the 19 th century, following Newton, and at the time of
Maxwell and others, in physics and astronomy, there grew up a belief
that the whole of the universe was filled with a mysterious fluid, the
so-called ether, and you should imagine us just sitting inside a great
celestial fluid of ether. Physicists took this very seriously. As the
Earth moved in orbit around the Sun, it was moving through this ether.
The challenge was could you identify the ether? Could you measure its
existence?
A famous experiment took place in 1881 by two Americans, Michelson and
Morley, and what they did was to test whether there exists such an ether
by examining what happens to the motion of light in the universe. The
idea, to begin with, is rather like going swimming in a river, so you
think of the ether as flowing past us, rather like a great stream.
Suppose you swim across to the other bank; suppose this is a hundred
metres, and you swim a hundred metres against the flow and a hundred
metres back, and you time yourself on these two swims. Well, if you do
everything exactly the same each time, there?ll be a time difference in
how long it takes you to swim 200 metres by the route where you never go
against the flow, and where you have to against the flow and then with
the flow. You would be able to detect whether there was a flow of the
stream by comparing the round swim times. If there was no current, you
should have exactly the same time to do the two trips. What Michelson
and Morley did was to set up an experiment which timed the travel of
light on two different paths at right angles to each other. This
requires rather fancy technology and very, very high precision
measurement using what?s now become known as interferometer. You can
shine a beam which gets split, you can send light up and back, and you
can allow light to go through and come back. You have the distances
equal, and if the light returning is not coming back at the same moment
and is slightly out of phase, you get interference fringes, which you
can measure with fantastic precision. This great experiment which they
performed, probably the most famous null experiment in modern physics,
discerned no time travel difference for the light in the two paths, and
this, as Einstein predicted, is what you should see if there is no
ether. If there had been ether, you would find a time travel difference.
This experiment pretty much did away with the idea that there was this
extraordinary ethereal fluid that we were moving through. Einstein then
developed the general theory of relativity which contains the idea that
there can be so-called vacuum universes, universes which just contain
waves of gravity; they don?t contain any material at all.
http://www.gresham.ac.uk/event.asp?PageId=4&EventId=258
Aww? - something happened here bot. My 'puter sort of froze up..
especially those areas in which AE goofed up
royally.
You mean something along these lines: Summary
The question whether the speed of light is a true physical limit has no
definite answer yet. It depends on the real structure of the space-time
continuum, which is presently unknown. If absolute time (and a preferred
reference frame) exist, then faster-than-light speeds - and even
faster-than-light travel - are possible, at least in principle. Although
the theory of special relativity states against absolute time and
superluminal phenomena, it does it not by proof, but only by assumption.
If superluminal signals are to be discovered in the future, then the
notion absolute time will surely have to be reintroduced to physics.
Are there indications that absolute time and faster-than-light p
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