This Week's Finds in Mathematical Physics (Week 270)
John Baez
October 11, 2008
This Week's Finds in Mathematical Physics (Week 270)
John Baez
Greg Egan has a new novel out, called Incandescence - so I want to
talk about that. Then I'll talk about three of my favorite numbers:
5, 8, and 24. I'll show you how each regular polytope with 5-fold
rotational symmetry has a secret link to a lattice living in twice
as many dimensions. For example, the pentagon is a 2d projection of
a beautiful shape that lives in 4 dimensions. Finally, I'll wrap up
with a simple but surprising property of the number 12.
But first: another picture of Jupiter's moon Io! Now we'll zoom in
much closer. This was taken in 2000 by the Galileo probe:
1) A continuous eruption on Jupiter's moon Io, Astronomy Picture
of the Day, http://apod.nasa.gov/apod/ap000606.html
Here we see a vast plain of sulfur and silicate rock, 250 kilometers
across - and on the left, glowing hot lava! The white dots are
spots so hot that their infrared radiation oversaturated the detection
equipment. This was the first photo of an active lava flow on another
world.
If you like pictures like this, maybe you like science fiction. And
if you like hard science fiction - "diamond-scratching hard", as one
reviewer put it - Greg Egan is your man. His latest novel is one of
the most realistic evocations of the distant future I've ever read:
2) Greg Egan, Incandescence, Night Shade Books, 2008. Website at
http://www.gregegan.net/INCANDESCENCE/Incandescence.html
The story features two parallel plots. One is about a galaxy-spanning
civilization called the Amalgam, and two of its members who go on a
quest to our Galaxy's core, which is home to enigmatic beings that may
be still more advanced: the Aloof. The other is about the inhabitants
of a small world orbiting a black hole. This is where the serious
physics comes in.
I might as well quote Egan himself:
"Incandescence" grew out of the notion that the theory of general
relativity - widely regarded as one of the pinnacles of human
intellectual achievement - could be discovered by a pre-industrial
civilization with no steam engines, no electric lights, no radio
transmitters, and absolutely no tradition of astronomy.
At first glance, this premise might strike you as a little hard
to believe. We humans came to a detailed understanding of gravity
after centuries of painstaking astronomical observations, most
crucially of the motions of the planets across the sky. Johannes
Kepler found that these observations could be explained if the
planets moved around the sun along elliptical orbits, with the
square of the orbital period proportional to the cube of the
length of the longest axis of the ellipse. Newton showed
that just such a motion would arise from a universal attraction
between bodies that was inversely proportional to the square of
the distance between them. That hypothesis was a close enough
approximation to the truth to survive for more than three centuries.
When Newton was finally overthrown by Einstein, the birth of the
new theory owed much less to the astronomical facts it could explain -
such as a puzzling drift in the point where Mercury made its closest
approach to the sun - than to an elegant theory of electromagnetism
that had arisen more or less independently of ideas about gravity.
Electrostatic and magnetic effects had been unified by James Clerk
Maxwell, but Maxwell's equations only offered one value for the speed
of light, however you happened to be moving when you measured it.
Making sense of this fact led Einstein first to special relativity,
in which the geometry of space-time had the unvarying speed of light
built into it, then general relativity, in which the curvature of the
same geometry accounted for the motion of objects free-falling
through space.
So for us, astronomy was crucial even to reach as far as Newton, and
postulating Einstein's theory - let alone validating it to high
precision, with atomic clocks on satellites and observations of
pulsar orbits - depended on a wealth of other ideas and technologies.
How, then, could my alien civilization possibly reach the same
conceptual heights, when they were armed with none of these apparent
prerequisites? The short answer is that they would need to be
living in just the right environment: the accretion disk of a large
black hole.
When SF readers think of the experience of being close to a black
hole, the phenomena that most easily come to mind are those that are
most exotic from our own perspective: time dilation, gravitational
blue-shifts, and massive distortions of the view of the sky. But
those are all a matter of making astronomical observations, or at
least arranging some kind of comparison between the near-black-hole
experience and the experience of other beings who have kept their
distance. My aliens would probably need to be sheltering deep inside
some rocky structure to protect them from the radiation of the
accretion disk - and the glow of the disk itself would also render
astronomy immensely difficult.
Blind to the heavens, how could they come to learn anything at all
about gravity, let alone the subtleties of general relativity? After
all, didn?t Einstein tell us that if we?re free-falling, weightless,
in a windowless elevator, gravity itself becomes impossible to detect?
Not quite! To render its passenger completely oblivious to gravity,
not only does the elevator need to be small, but the passenger's
observations need to be curtailed in time just as surely as they're
limited in space. Given time, gravity makes its mark. Forget about
black holes for a moment: even inside a windowless space station
orbiting the Earth, you could easily prove that you were not just
drifting through interstellar space, light-years from the nearest
planet. How? Put on your space suit, and pump out all the station's
air. Then fill the station with small objects - paper clips, pens,
whatever - being careful to place them initially at rest with respect
to the walls.
Wait, and see what happens.
Most objects will eventually hit the walls; the exact proportion will
depend on the station's spin. But however the station is or isn't
spinning, some objects will undergo a cyclic motion, moving back and
forth, all with the same period.
That period is the orbital period of the space station around the
Earth. The paper clips and pens that are moving back and forth
inside the station are following orbits that are inclined at a very
small angle to the orbit of the station's center of mass. Twice in
every orbit, the two paths cross, and the paper clip passes through
the center of the space station. Then it moves away, reaches the
point of greatest separation of the orbits, then turns around and
comes back.
This minuscule difference in orbits is enough to reveal the fact that
you're not drifting in interstellar space. A sufficiently delicate
spring balance could reveal the tiny "tidal gravitational force"
that is another way of thinking about exactly the same thing, but
unless the orbital period was very long, you could stick with the
technology-free approach and just watch and wait.
A range of simple experiments like this - none of them much harder
than those conducted by Galileo and his contemporaries - were the
solution to my aliens' need to catch up with Newton. But catching
up with Einstein? Surely that was beyond hope?
I thought it might be, until I sat down and did some detailed
calculations. It turned out that, close to a black hole, the
differences between Newton's and Einstein's predictions would easily
be big enough for anyone to spot without sophisticated instrumentation.
What about sophisticated mathematics? The geometry of general
relativity isn't trivial, but much of its difficulty, for us,
revolves around the need to dispose of our preconceptions. By
putting my aliens in a world of curved and twisted tunnels, rather
than the flat, almost Euclidean landscape of a patch of planetary
surface, they came better prepared for the need to cope with a
space-time geometry that also twisted and curved.
The result was an alternative, low-tech path into some of the most
beautiful truths we've yet discovered about the universe. To add
to the drama, though, there needed to be a sense of urgency; the
intellectual progress of the aliens had to be a matter of life and
death. But having already put them beside a black hole, danger was
never going to be far behind.
As you can tell, this is a novel of ideas. You have to be willing to
work through these ideas to enjoy it. It's also not what I'd call
a feel-good novel. As with "Diaspora" and "Schild's Ladder", the
main characters seem to become more and more isolated and focused on
their work as they delve deeper into the mysteries they are pursuing.
By the time the mysteries are unraveled, there's almost nobody to talk
to. It's a problem many mathematicians will recognize. Indeed, near the
end of "Diaspora" we read: "In the end, there was only mathematics."
In fact, I was carrying "Incandescence" with me when in mid-September I
left the scorched and smoggy sprawl of southern California for the cool,
wet, beautiful old city of Glasgow. I spent a lovely week there talking
math with Tom Leinster, Eugenia Cheng, Bruce Bartlett and Simon Willerton.
I'd been invited to the University of Glasgow to give a series of talks
called the 2008 Rankin Lectures. I spoke about my three favorite numbers,
and you can see the slides here:
3) John Baez, My favorite numbers, available at
http://math.ucr.edu/home/baez/numbers/
I wanted to explain how different numbers have different personalities
that radiate like force fields through diverse areas of mathematics and
interact with each other in surprising ways. I've been exploring
this theme for many years here. So, it was nice to polish some things
I've written and present them in a more organized way. These lectures
were sponsored by the trust that runs the Glasgow Mathematical Journal,
so I'll eventually publish them there. I plan to add a lot of detail
that didn't fit in the talks.
I began with the number 5, since the golden ratio and the five-fold
symmetry of the dodecahedron lead quickly to a wealth of easily enjoyed
phenomena: from Penrose tilings and quasicrystals, to Hurwitz's theorem on
approximating numbers by fractions, to the 120-cell and the Poincare
homology sphere.
After giving the first talk I discovered the head of the math department,
Peter Kropholler, is a big fan of Rubik's cubes. I'd never been attracted
to them myself. But his enthusiasm was contagious, especially when he
started pulling out the unusual variants that he collects, eagerly
explaining their subtleties. My favorite was the Rubik's dodecahedron,
or "Megaminx":
4) Wikipedia, Megaminx, http://en.wikipedia.org/wiki/Megaminx
Then I got to thinking: it would be even better to have a Rubik's
icosahedron, since its symmetries would then include M12, the smallest
Mathieu group. And it turns out that such a gadget exists! It's
called "Dogic":
5) Wikipedia, Dogic, http://en.wikipedia.org/wiki/Dogic
The Mathieu group M12 is the smallest of the sporadic finite simple
groups. Someday I'd like to understand the Monster, which is the
biggest of the lot. But if the Monster is the Mount Everest of finite
group theory, M12 is like a small foothill. A good place to start.
Way back in "week20", I gave a cute description of M12 lifted from
Conway and Sloane's classic book. If you get 12 equal-sized balls
to touch a central one of the same size, and arrange them to lie at
the corners of a regular icosahedron, they don't touch their neighbors.
There's even room to roll them around in interesting ways! For
example, you can twist 5 of them around clockwise so that this
arrangement:
1
5 2
6
4 3
becomes this:
5
4 1
6
3 2
We can generate lots of permutations of the 12 outer balls using
twists of this sort - in fact, all even permutations. But suppose
we only use moves where we first twist 5 balls around clockwise and
then twist 5 others counterclockwise. These generate a smaller group:
the Mathieu group M12.
Since we can do twists like this in the Dogic puzzle, I believe M12
sits inside the symmetry group of this puzzle! In a way it's not
surprising: the Dogic puzzle has a vast group of symmetries, while M12
has a measly
8 x 9 x 10 x 11 x 12 = 95040
elements. But it'd still be cool to have a toy where you can explore
the Mathieu group M12 with your own hands!
The math department lounge at the University of Glasgow has some old
books in the shelves waiting for someone to pick them up and read them
and love them. They're sort of like dogs at the pound, sadly waiting
for somebody to take them home. I took one that explains how Mathieu
groups arise as symmetries of "Steiner systems":
6) Thomas Beth, Dieter Jungnickel, and Hanfried Lenz, Design Theory,
Cambridge U. Press, Cambridge, 1986.
Here's how they get M12. Take a 12-point set and think of it as
the "projective line over F11" - in other words, the integers mod
11 together with a point called infinity. Among the integers mod 11,
six are perfect squares:
{0,1,3,4,5,9}
Call this set a "block". From this, get a bunch more blocks
by applying fractional linear transformations:
z |-> (az + b)/(cz + d)
where the matrix
(a b)
(c d)
has determinant 1. These blocks then form a "Steiner (5,6,12) system".
In other words: there are 12 points, 6 points in each block, and any
set of 5 points lies in a unique block.
The group M12 is then the group of all transformations of the
projective line that map points to points and blocks to blocks!
If I make more progress on understanding this stuff I'll let you
know. It would be fun to find deep mathematics lurking in mutant
Rubik's cubes.
Anyway, in my second talk I turned to the number 8. This gave me a
great excuse to tell the story of how Graves discovered the octonions,
and then talk about sphere packings and the marvelous E8 lattice,
whose points can also be seen as "integer octonions". I also sketched
the basic ideas behind Bott periodicity, triality, and the role of
division algebras in superstring theory.
If you look at my slides you'll also see an appendix that describes two
ways to get the E8 lattice starting from the dodecahedron. This is a
nice interaction between the magic powers of the number 5 and those of
the number 8. After my talk, Christian Korff from the University of
Glasgow showed me a paper that fits this relation into a bigger pattern:
7) Andreas Fring and Christian Korff, Non-crystallographic reduction
of Calogero-Moser models, Jour. Phys. A 39 (2006), 1115-1131. Also
available as hep-th/0509152.
They set up a nice correspondence between some non-crystallographic
Coxeter groups and some crystallographic ones:
the H2 Coxeter group and the A4 Coxeter group,
the H3 Coxeter group and the D6 Coxeter group,
the H4 Coxeter group and the E8 Coxeter group.
A Coxeter group is a finite group of linear transformations of
R^n that's generated by reflections. We say such a group is
"non-crystallographic" if it's not the symmetries of any lattice.
The ones listed above are closely tied to the number 5:
H2 is the symmetry group of a regular pentagon.
H3 is the symmetry group of a regular dodecahedron.
H4 is the symmetry group of a regular 120-cell.
Note these live in 2d, 3d and 4d space. Only in these dimensions
are there regular polytopes with 5-fold rotational symmetry! Their
symmetry groups are non-crystallographic, because no lattice can
have 5-fold rotational symmetry.
A Coxeter group is "crystallographic", or a "Weyl group", if it
*is* symmetries of a lattice. In particular:
A4 is the symmetry group of a 4-dimensional lattice also called A4.
D6 is the symmetry group of a 6-dimensional lattice also called D6.
E8 is the symmetry group of an 8-dimensional lattice also called E8.
You can see precise descriptions of these lattices in "week65" -
they're pretty simple.
Both crystallographic and noncrystallographic Coxeter groups are
described by Coxeter diagrams, as explained back in "week62". The
H2, H3 and H4 Coxeter diagrams look like this:
5
o---o
5
o---o---o
5
o---o---o---o
The A4, A6 and E8 Coxeter diagrams (usually called Dynkin diagrams)
have twice as many dots as their smaller partners H2, H3 and H4:
o---o---o---o
o
|
o---o---o---o---o
o
|
o
|
o---o---o---o---o---o
I've drawn these in a slightly unorthodox way to show how they "grow".
In every case, each dot in the diagram corresponds to one of the
reflections that generates the Coxeter group. The edges in the
diagram describe relations - you can read how in "week62".
All this is well-known stuff. But Fring and Korff investigate
something more esoteric. Each dot in the big diagram corresponds to
2 dots in its smaller partner:
5
o---o o---o---o---o
A B B' A" B" A'
o C"
5 |
o---o---o o---o---o---o---o
A B C C' B' A" B" A'
o D"
|
o C"
5 |
o---o---o---o o---o---o---o---o---o
A B C D D' C' B' A" B" A'
If we map each generator of the smaller group (say, the generator
D in H5) to the product of the two corresponding generators in
the bigger one (say, D'D" in E8), we get a group homomorphism.
In fact, we get an *inclusion* of the smaller group in the bigger
one!
This is just the starting point of Fring and Korff's work. Their
real goal is to show how certain exactly solvable physics problems
associated to crystallographic Coxeter groups can be generalized to
these three noncrystallographic ones. For this, they must develop
more detailed connections than those I've described. But I'm already
happy just pondering this small piece of their paper.
For example, what does the inclusion of H2 in A4 really look like?
It's actually quite beautiful. H2 is the symmetry group of a
regular pentagon, including rotations and reflections. A4 happens
to be the symmetry group of a 4-simplex. If you draw a 4-simplex
in the plane, it looks like a pentagram! So, any symmetry of the
pentagon gives a symmetry of the 4-simplex. So, we get an inclusion
of H2 in A4.
People often say that Penrose tilings arise from lattices in 4d space.
Maybe I'm finally starting to understand how! The A4 lattice has a
bunch of 4-simplices in it - but when we project these onto the plane
correctly, they give pentagrams. I'd be very happy if this were
the key.
What about the inclusion of H3 in D6?
Here James Dolan helped me make a guess. H3 is the symmetry group
of a regular dodecahedron, including rotations and reflections.
D6 consists of all linear transformations of R^6 generated by
permuting the 6 coordinate axes and switching the signs of an even
number of coordinates. But a dodecahedron has 6 "axes" going between
opposite pentagons! If we arbitrarily orient all these axes, I believe
any rotation or reflection of the dodecahedron gives an element of D6.
So, we get an inclusion of H3 in D6.
And finally, what about the inclusion of H4 in E8?
H4 is the symmetry group of the 120-cell, including rotations and
reflections. In 8 dimensions, you can get 240 equal-sized balls to
touch a central ball of the same size. E8 acts as symmetries of
this arrangement. There's a clever trick for grouping the 240 balls
into 120 ordered pairs, which is explained by Fring and Korff and also
by Conway's "icosian" construction of E8 described at the end of my talk
on the number 8. Each element of H4 gives a permutation of the
120 faces of the 120-cell - and thanks to that clever trick, this gives
a permutation of the 240 balls. This permutation actually comes from
an element of E8. So, we get an inclusion of H4 in E8.
My last talk was on the number 24. Here I explained Euler's crazy
"proof" that
1 + 2 + 3 + ... = -1/12
and how this makes bosonic strings happy when they have 24 transverse
directions to wiggle around in. I also touched on the 24-dimensional
Leech lattice and how this gives a version of bosonic string theory
whose symmetry group is the Monster: the largest sporadic finite simple
group.
A lot of the special properties of the number 24 are really properties
of the number 12 - and most of these come from the period-12 behavior
of modular forms. I explained this back in "week125". I recently ran
into these papers describing yet another curious property of the number
12, also related to modular forms, but very easy to state:
8) Bjorn Poonen and Fernando Rodriguez-Villegas, Lattice polygons
and the number 12. Available at
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.2555
9) John M. Burns and David O'Keeffe, Lattice polygons in the plane
and the number 12, Irish Math. Soc. Bulletin 57 (2006), 65-68.
Also available at http://www.maths.tcd.ie/pub/ims/bull57/M5700.pdf
Consider the lattice in the plane consisting of points with integer
coordinates. Draw a convex polygon whose vertices lie on this lattice.
Obviously, the *differences* of successive vertices also lie on the
lattice. We can create a new convex polygon with these differences as
vertices. This is called the "dual" polygon.
Say our original polygon is so small that the only lattice point in its
interior is (0,0). Then the same is true of its dual! Furthermore,
the dual of the dual is the original polygon!
But now for the cool part. Take a polygon of this sort, and add up the
number of lattice points on its boundary and the number of lattice
points on the boundary of its dual. The total is 12.
You can see an example in Figure 1 of the paper by Poonen and
Rodriguez-Villegas. I like how their paper uses this theorem as a
springboard for discussing a big question: what does it mean to "explain"
the appearance of the number 12 here? They write:
Our reason for selecting this particular statement, besides the
intriguing appearance of the number 12, is that its proofs display
a surprisingly rich variety of methods, and at least some of them
are symptomatic of connections between branches of mathematics that
on the surface appear to have little to do with one another. The
theorem (implicitly) and proofs 2 and 3 sketched below appear in
Fulton's book on toric varieties. We will give our new proof 4,
which uses modular forms instead, in full.
-----------------------------------------------------------------------
Quote of the Week:
When the blind beetle crawls over the surface of a globe, he doesn't
realize that the track he has covered is curved. I was lucky enough
to have spotted it. - Albert Einstein
-----------------------------------------------------------------------
Addenda: I thank Adam Glesser and David Speyer for catching mistakes.
The only noncrystallographic Coxeter groups are the symmetry
groups of the 120-cell (H4), the dodecahedron (H3), and the regular
n-gons where n = 5,7,8,9,... The last list of groups is usually called
I_n - or better, I_2(n), so that the subscript denotes the number of
dots in the Dynkin diagram, as usual. But Fring and Korff use "H2" as
a special name for I_2(5), and that's nice if you're focused on 5-fold
symmetry, because then H2 forms a little series together with H3 and H4.
If you examine Poonen and Rodriguez-Villegas' picture carefully, you'll
see a subtlety concerning the claim that the dual of the dual is the
original polygon. Apparently you need to count every boundary point
as a vertex! Read the papers for more precise details.
For more discussion visit the n-Category Cafe:
http://golem.ph.utexas.edu/category/2008/10/this_weeks_finds_in_mathematic_31.html
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twfcontents.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
Uncle Al
>
> Also available as http://math.ucr.edu/home/baez/week270.html
>
> October 11, 2008
> This Week's Finds in Mathematical Physics (Week 270)
> John Baez
> Blind to the heavens, how could they come to learn anything at all
> about gravity, let alone the subtleties of general relativity? After
> all, didn?t Einstein tell us that if we?re free-falling, weightless,
> in a windowless elevator, gravity itself becomes impossible to detect?
>
> Not quite! To render its passenger completely oblivious to gravity,
> not only does the elevator need to be small, but the passenger's
> observations need to be curtailed in time just as surely as they're
> limited in space.
Einsteins's elevator postulates isotropic vacuum. A chiral
pseudoscalar vacuum backround whose interaction is confined to the
massed sector is 100% consistent with all observations of "isotropic
vacuum" to date. However, it divergently interacts with small
emergent scale opposite parity atomic mass distributions such as
single crystals of enantiomorphic space groups P3(1)21 and P3(2)21
quartz (cinnabar, selenium, tellurium, berlinite and analogues;
organic chemical benzil, etc.). A left foot is nothing special to
socks or to left shoes. A right shoe interacts very differently.
A chiral pseudoscalar vacuum background strongly selects matter over
antimatter, powers post-Big Bang inflation (freezing in matter while
the background dilutes to contemporary values), sources the
left-handed Weak interaction, and selects biological homochirality.
Somebody should run a parity Eotvos experiment contrasting single
crystals of space groups P3(1)21 and P3(2)21 quartz. Theory predicts
what observation tells it to predict.
A massed sector chiral vacuum background is a crazy idea! Just one
crazy idea, not 10^1000. Testable on a benchtop in existing apparatus
using commercial materials. Testable in a regime boasting 400+ years
of net null outputs. When perfect failure is the gold standard, how
much incremental aversive risk is success?
http://www.mazepath.com/uncleal/qz4.pdf
There is *not* only mathematics - there is observation.
[snip]
> -----------------------------------------------------------------------
> Previous issues of "This Week's Finds" and other expository articles on
> mathematics and physics, as well as some of my research papers, can be
> obtained at
>
> http://math.ucr.edu/home/baez/
>
> For a table of contents of all the issues of This Week's Finds, try
>
> http://math.ucr.edu/home/baez/twfcontents.html
>
> A simple jumping-off point to the old issues is available at
>
> http://math.ucr.edu/home/baez/twfshort.html
>
> If you just want the latest issue, go to
>
> http://math.ucr.edu/home/baez/this.week.html
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Traveler
<Uncl...@hate.spam.net> has elevated ass kissing to a new level of
perfection:
>Einsteins's elevator postulates isotropic vacuum. A chiral
>pseudoscalar vacuum backround whose interaction is confined to the
>massed sector is 100% consistent with all observations of "isotropic
>vacuum" to date. However, it divergently interacts with small
>emergent scale opposite parity atomic mass distributions such as
>single crystals of enantiomorphic space groups P3(1)21 and P3(2)21
>quartz (cinnabar, selenium, tellurium, berlinite and analogues;
>organic chemical benzil, etc.). A left foot is nothing special to
>socks or to left shoes. A right shoe interacts very differently.
>
>A chiral pseudoscalar vacuum background strongly selects matter over
>antimatter, powers post-Big Bang inflation (freezing in matter while
>the background dilutes to contemporary values), sources the
>left-handed Weak interaction, and selects biological homochirality.
>Somebody should run a parity Eotvos experiment contrasting single
>crystals of space groups P3(1)21 and P3(2)21 quartz. Theory predicts
>what observation tells it to predict.
>
>A massed sector chiral vacuum background is a crazy idea! Just one
>crazy idea, not 10^1000. Testable on a benchtop in existing apparatus
>using commercial materials. Testable in a regime boasting 400+ years
>of net null outputs. When perfect failure is the gold standard, how
>much incremental aversive risk is success?
ahahaha... I have said it before, nobody kisses ass like Uncle Al
Shwartz. Question is, is John Baez's ass worth all this effort? Does
Baez give a shit about Uncle Al's crap? Or is John Baez more concerned
with kissing bigger asses than his own? ahahaha... AHAHAHA...
ahahaha...
Ladies and gentlemen, the laughable crap above is a prime example of
what Thomas Kuhn warned us all about. Peer review (ass kissing) is an
incestuous mechanism that engenders hideous monstrosities. Only a
revolution can free us from this madness.
ahahaha...
Louis Savain
Rebel Science News:
http://rebelscience.blogspot.com/
John Baez
this. -P.H.]
Also available as http://math.ucr.edu/home/baez/week270.html
October 11, 2008
This Week's Finds in Mathematical Physics (Week 270)
John Baez
Greg Egan has a new novel out, called Incandescence - so I want to
Blind to the heavens, how could they come to learn anything at all
about gravity, let alone the subtleties of general relativity? After
all, didn?t Einstein tell us that if we?re free-falling, weightless,
in a windowless elevator, gravity itself becomes impossible to detect?
Not quite! To render its passenger completely oblivious to gravity,
not only does the elevator need to be small, but the passenger's
observations need to be curtailed in time just as surely as they're
1
5 2
6
4 3
becomes this:
5
4 1
6
3 2
{0,1,3,4,5,9}
where the matrix
(a b)
(c d)
5
o---o
5
o---o---o
5
o---o---o---o
o---o---o---o
o
|
o---o---o---o---o
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Quote of the Week:
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http://golem.ph.utexas.edu/category/2008/10/this_weeks_finds_in_mathematic_31.h
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Traveler
<ba...@math.removethis.ucr.andthis.edu> wrote:
>[Moderator's note: Some (but not all) readers might have already seen
>this. -P.H.]
>
>Also available as http://math.ucr.edu/home/baez/week270.html
[This is a repost. I just thought Baez's fan club would love to read
this. ahahaha...]
The Many "Nows" and Many "Is" Hypothesis of Dr. John Baez
Dr. John Baez of UC Riverside, who loves to point out that he
regularly flies to conferences around the world (he's a proud
jet-setting physicist), is the well-known usenet crackpot and math
puzzle fanatic who once wrote this wonderful gem:
I would prefer to say that there are infinitely many "nows", but no
one "now" that is any better than the rest. In special or general
relativity, we can define a "now" to be a spacelike hypersurface -
or more technically, a Cauchy surface. In one "now", I am typing
this article while sitting at my desk on a hot summer morning in
Riverside. In another, I am asleep on an airplane flying to
Portugal. In most of them, I don't exist. Since we can describe
the state of the universe by giving the values of fields at any
given "now", all these "nows" give isomorphic descriptions of the
universe. The isomorphism between them is what we call "the
passage of time".
ahahaha... Wait, it gets even better. In response to the following
mesmerizing nugget of wisdom by fellow crackpot, Mark William Hopkins:
In reality, there is no "I". It's all an illusion based entirely
on the abovementioned misperception. Once you begin to perceive
yourself as you actually are (i.e., part of a 4-dimensional
web-like structure) then the "I" part just disappears.
Baez brilliantly replies with the refined aplomb of a professional
academic crank:
I wouldn't say there is no "I". I would instead say there are
many.
ahahaha... I am not making this shit up, I swear. This shit is forever
recorded in the annals of sci.physics.research, one of Baez's favorite
censored hangout.
http://www.lns.cornell.edu/spr/1999-07/msg0016990.html
The only other academic crackpot (that I know of) that may surpass Dr.
John Baez in crackpottery is Dr. David Deutsch of quantum computing
fame. Deutsch wrote the book on voodoo physics. ahahaha... Having said
that, I must add that the little con artist in the wheelchair is not
too far behind. Ah, the wonderful farce of physics. Insane nerds
having fun with the little games they love to play. I love it.
ahahaha... AHAHAHA... ahahaha...
hanson
------------- AHAHAHAHAHAHA -------------
>
Louis Savain "Traveler" <noassk...@nowhere.net> wrote
in message news:of87f4hojjbf1grvu...@4ax.com...
http://www.lns.cornell.edu/spr/1999-07/msg0016990.html
ahahaha... AHAHAHA... ahahaha...
Louis Savain
-------------------- ----------------- ---------------------
>
hanson wrote:
Hey old chum, I haven't heard from you in a long while:
Great post and good to have you back . Not much new
here, except I have acquired a mentally challenged
slightly touched cyber mutt by name of Andro. He loves
me and follows me around and barks in great awe at me
He just can't help himself... ahahaha... He is funny tough!...
Watch him cruse by shortly... ahahahaha... AHAHAHA...
>
Anyway,
re: the 2 blessed gentlemen above. Baez and Hopkins
aka Rock Brentwood, you must give credit to though,
because it's no mean feat to be in the public eye and
admit to have a split personality... ahahahaha... ahahaha...
But then , nothing escapes the lattice, n'est pas!
>
Listen, on your own work on that subject did I read/get
you right by stating:
-- Newton saw nature as an interplay of masses &
energy in Space AND Time.
-- Einstein et. al complicate the game into abstract
schemes by conjuring up space-time as a single
enmtity that plays games with mass & energy.
-- Savain, equally radical, goes the other way and
does away with space and time and constructs
a Lattice/Matrix that absorbs and incorporates
the properties of space and time into itself.
>
Is that what you did?... Have you seen any possibilities
yet about possible experiments arising out of it?
>
Other subject: Since you are interested in ancient
cultures, get the Nov 2008 Discover Magazine and
read about Sam Osmanagich, the pyramid hunter.
In Bosnia he looked at a hill, decreed that it was the
biggest and oldest pyramid in the world and he
started a thriving pyramid-tourism business, so
lucrative that he even got big governments grants to
do the digging... for artifacts he claims to be 12KY old.
>
Check it out & do something similar with your "Lattice"...
Let me be the purser and CFO of that enterprise...
ahahahaha... ahahahanson
Traveler
>
[cut]
>hanson wrote:
>Hey old chum, I haven't heard from you in a long while:
>Great post and good to have you back . Not much new
>here, except I have acquired a mentally challenged
>slightly touched cyber mutt by name of Andro. He loves
>me and follows me around and barks in great awe at me
>He just can't help himself... ahahaha... He is funny tough!...
>Watch him cruse by shortly... ahahahaha... AHAHAHA...
Androcles is a nut (this from another nut, ahahaha). I picture him
jumping up and down, foaming at the mouth and tearing his hair out
every time somebody disagrees with him. ahahaha... One day, the funny
looking people will come after him with a straight jacket and a
leather gag. But then again, most of the folks who spend their entire
waking lives posting and arguing on usenet are a little on the cuckoo
side, if you know what I mean. Many amongst them are retired and
senile. ahahaha... I wonder how old Andro is.
>Anyway,
>re: the 2 blessed gentlemen above. Baez and Hopkins
>aka Rock Brentwood, you must give credit to though,
>because it's no mean feat to be in the public eye and
>admit to have a split personality... ahahahaha... ahahaha...
>But then , nothing escapes the lattice, n'est pas!
Wait a minute. Hopkins also posts as Rock Brentwood? Or are Hopkins
and Baez one and the same?
>Listen, on your own work on that subject did I read/get
>you right by stating:
>-- Newton saw nature as an interplay of masses &
> energy in Space AND Time.
>-- Einstein et. al complicate the game into abstract
> schemes by conjuring up space-time as a single
> enmtity that plays games with mass & energy.
>-- Savain, equally radical, goes the other way and
> does away with space and time and constructs
> a Lattice/Matrix that absorbs and incorporates
> the properties of space and time into itself.
>>
>Is that what you did?...
Sorta.
> Have you seen any possibilities
>yet about possible experiments arising out of it?
I am conducting some experiments right now but don't wish me luck. If
I am right, I don't know whether it'll be a blessing or a curse. This
shit is down right scary. Right now, the world is having a cow over
energy scarcity but we are immersed in an ocean of energy, many orders
of magnitude more energy than we can detect from the visible universe.
The era of free energy and free transportation is almost upon us. No
CO2 or any kind of emission! That'll make the tree huggers happy but
the global warmers won't like it because it will kill their money
skimming operations. OPEC won't be pleased either. ahahaha... Every
form of transportation and energy generation technology will become
obsolete. It's frightening just to think about it.
And one more thing. Neither the atheists, the Big Bangers, nor the
religionists will like it. The atheists, in particular, will have a
fit.
>Other subject: Since you are interested in ancient
>cultures, get the Nov 2008 Discover Magazine and
>read about Sam Osmanagich, the pyramid hunter.
>In Bosnia he looked at a hill, decreed that it was the
>biggest and oldest pyramid in the world and he
>started a thriving pyramid-tourism business, so
>lucrative that he even got big governments grants to
>do the digging... for artifacts he claims to be 12KY old.
>>
>Check it out & do something similar with your "Lattice"...
>Let me be the purser and CFO of that enterprise...
>ahahahaha... ahahahanson
Osmanagich is a crackpot and a con artist. But you gotta hand it to
him. He's a good business man and good entertainer, and I kinda like
his Indianna Jones hat. More than I can say for the little black hole
guy in the wheelchair and the diapers, that's for sure. ahahaha...
hanson
news:47j7f4pkjvlmd80ru...@4ax.com...
>
"hanson" <han...@quick.net> wrote:
>>Hey old chum, I haven't heard from you in a long while:
>>Great post and good to have you back . Not much new
>>here, except I have acquired a mentally challenged
>>slightly touched cyber mutt by name of Andro. He loves
>>me and follows me around and barks in great awe at me
>>He just can't help himself... ahahaha... He is funny tough!...
>>Watch him cruse by shortly... ahahahaha... AHAHAHA...
>
> Androcles is a nut (this from another nut, ahahaha). I picture him
> jumping up and down, foaming at the mouth and tearing his hair out
> every time somebody disagrees with him. ahahaha... One day, the funny
> looking people will come after him with a straight jacket and a
> leather gag. But then again, most of the folks who spend their entire
> waking lives posting and arguing on usenet are a little on the cuckoo
> side, if you know what I mean. Many amongst them are retired and
>
hanson wrote:
>>Anyway,
>>re: the 2 blessed gentlemen above. Baez and Hopkins
>>aka Rock Brentwood, you must give credit to though,
>>because it's no mean feat to be in the public eye and
>>admit to have a split personality... ahahahaha... ahahaha...
>>But then , nothing escapes the lattice, n'est pas!
>
> Wait a minute. Hopkins also posts as Rock Brentwood?
> Or are Hopkins and Baez one and the same?
>
No, they are at different *.edus. But "Rock Brentwood" =
"Einstead" aka "Mark Hopkins" is diversified... ahaha...
>
hanson wrote
>>Listen, on your own work on that subject did I read/get
>>you right by stating:
>>-- Newton saw nature as an interplay of masses &
>> energy in Space AND Time.
>>-- Einstein et. al complicate the game into abstract
>> schemes by conjuring up space-time as a single
>> enmtity that plays games with mass & energy.
>>-- Savain, equally radical, goes the other way and
>> does away with space and time and constructs
>> a Lattice/Matrix that absorbs and incorporates
>> the properties of space and time into itself.
>>Is that what you did?...
>
> Sorta.
>
hanson wrote:
I think your approach is elegant & unique. Keep at it.
Now there is another fundamental possibility still.
As can be seen, SR/GR space-time, 3L+T, with all
its frames and frame dragging sports as its most
obvious property it's "empirical" ability to incite
vicious arguments between its own ED-specialists.
>
Now, this rather entertaining situation could be
vastly improved by additionally incorporating mass
& energy into their space-time and call it ... ahaha...
********** MASSIVE SPACE TIME ***************
Using MST as a story basis to describe nature will
now bring all quarrels to a stop because everybody
will always be right, no matter what, where and when.
ahahahaha... AHAHAHA... It's like uncle rect-Al often
says: "Some one should look"...ahahahaha... ahaha..
>
hanson wrote:
>> Have you seen any possibilities yet about
>
Louis Savain wrote:
> I am conducting some experiments right now but don't wish me luck. If
> I am right, I don't know whether it'll be a blessing or a curse. This
> shit is down right scary. Right now, the world is having a cow over
> energy scarcity but we are immersed in an ocean of energy, many orders
> of magnitude more energy than we can detect from the visible universe.
> The era of free energy and free transportation is almost upon us. No
> CO2 or any kind of emission! That'll make the tree huggers happy but
> the global warmers won't like it because it will kill their money
> skimming operations. OPEC won't be pleased either. ahahaha... Every
> form of transportation and energy generation technology will become
> obsolete. It's frightening just to think about it.
>
> And one more thing. Neither the atheists, the Big Bangers, nor the
> religionists will like it. The atheists, in particular, will have a fit
>
Well of course, I wish you luck. Any and all tools invented
by humankind, throughout its ascent, were "double edged".
AFA your unhappy cultists, that leaves practically only the
agnostics and the non religious people who you'll be happy.
That's a scant 10% of human kind... .... Well, lucky me!
ahahahaha... ahahahaha.... BTW, tell Andro that your ocean
of energy is called **Oeanus Aetherii**... ahahahaha...
>.
hanson wrote:
>>Other subject: Since you are interested in ancient
>>cultures, get the Nov 2008 Discover Magazine and
>>read about Sam Osmanagich, the pyramid hunter.
>>In Bosnia he looked at a hill, decreed that it was the
>>biggest and oldest pyramid in the world and he
>>started a thriving pyramid-tourism business, so
>>lucrative that he even got big governments grants to
>>do the digging... for artifacts he claims to be 12KY old.
>>>
>>Check it out & do something similar with your "Lattice"...
>>Let me be the purser and CFO of that enterprise...
>>ahahahaha... ahahahanson
>
Archimedes Plutonium
> Also available as http://math.ucr.edu/home/baez/week270.html
> October 11, 2008
> This Week's Finds in Mathematical Physics (Week 270)
> John Baez
TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
by Archimedes Plutonium
Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. In this endeavor to make physics super easy, I have made the writing such that you will see core ideas in all capital letters as single sentences as a educational tool. And I have made this textbook chapter writing follow a logical pattern of both algebra and geometry concepts, throughout. The utmost importance of logic in physics needs to be seen and understood. For I have never seen a physics book, prior to this one that is logical. Every Old Physics textbook I have seen is scatter-brained in topics and in writing. I use as template book of Halliday & Resnick because a edition of H&R was one I was taught physics at University of Cincinnati in 1969. And in 1969, I had a choice of majors, do I major in geology, or mathematics, or in physics, for I will graduate from UC in 1972. For me, geology was too easy, but physics was too tough, so I ended up majoring in mathematics. If I had been taught in 1969 using this textbook that I have written, I would have ended up majoring in physics, my first love. For physics is not hard, not hard at all, once you clear out the mistakes and the obnoxious worthless mathematics that clutters up Old Physics, and the illogic that smothers much of Old Physics.
Maybe it was good that I had those impressions of physics education of poor education, which still exists throughout physics today. Because maybe I am forced to write this book, because of that awful experience of learning physics in 1969. Without that awful experience, maybe this textbook would have never been written by me.
Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.
The world needs a new standard in physics education since Feynman set the standard in 1960s with his "Lectures on Physics" that lasted until about 1990 and then AP's Atom Totality theory caused Feynman's Lectures to be completely outdated. And so much has changed in physics since 1960s that AP now sets the new world standard in physics education with this series of textbooks.
To be a Master of physics or Calculus or Mathematics, has to be seen in "signs and signals". Can you correct the mistakes and errors of Old Physics, of Old Calculus, of Old Math? If you cannot clean up the fakery of Old Physics, of Old Calculus, of Old Math, you have no business, no reason to write a physics, calculus or math textbook. There is an old legend in England about King Arthur, and the legend goes, that the King is the one who pulls Excalibur out of the iron anvil. Pulling the sword out of the anvil is a metaphor for Cleaning up all the mistakes and errors of Old Physics, of Old Calculus, of Old Math. You have to clean up and clear out the mistakes and errors of the past, for Physics to move forward.
Should you write a textbook on Calculus, if you cannot see that the slant cut in a cone is a oval, never the ellipse? Of course not. Should you write a Calculus textbook if you cannot do a geometry proof of Fundamental Theorem of Calculus? Of course not. Should you write a physics textbook if you cannot ask the question, which is the atom's real true electron, is it the muon or the 0.5MeV particle that AP says is the Dirac magnetic monopole.
Feynman was the prior King of Physics before AP showed up. Feynman wrote the last textbook in 1960s to guide physics forward, and although Feynman did not clean up much of Old Physics, he did direct the way forward in that Electricity and Magnetism in his Quantum Electrodynamics was the way forward. It would have been nice for Feynman to have found that it is impossible for a 0.5MeV particle to be the atom's electron moving near the speed of light outside the proton of hydrogen and still remain an atom, thus all atoms collapse. It would have been nice for Feynman to say the muon is the real atom's electron and that the 0.5MeV particle was Dirac's magnetic monopole. But it just was not in the fated cards of Feynman's physics. Yet, his textbook served the leadership of physics from 1960 to 1990. Time we have the new replacement of physics textbook.
Now, in 2021, we need a new textbook that carries all of physics forward into the future for the next 100 years, and that is what this textbook is. I predict this textbook will carry physics forward to at least year 2100, and if I am lucky, perhaps my book will last for thousands of years as the standard bearer of Physics education.
I will use Halliday and Resnick textbook as template to garner work exercise problems for 1st year and 2nd year college. For 3rd and senior year college physics I will directly use Feynman's Lectures and QED, quantum electrodynamics. Correcting Feynman and setting the stage that all of physics is-- All is Atom and Atoms are nothing but Electricity and Magnetism.
Much and most of 20th century physics was error filled and illogical physics, dead end , stupid paths such as General Relativity, Big Bang, Black holes, gravity waves, etc etc. Dead end stupidity is much of Old Physics of the 20th century. What distinguishes Feynman, is he kept his head above the water by concentrating almost exclusively on Electrodynamics. He remarked words to the effect== "QED is the most precise, most accurate theory in all of physics". And, that is true, given All is Atom, and Atoms are nothing but Electricity and Magnetism.
This textbook is going to set the world standard on college physics education. Because I have reduced the burden of mathematics, reduced it to be almost what I call -- difficult-free-math. I mean, easy-math. Meaning that all functions and equations of math and physics are just polynomials. All functions of math and physics are polynomials. Making calculus super super easy because all you ever do is plug in the Power rules for derivative and integral, so that physics math is able to be taught in High School. In other words, physics with almost no math at all-- so to speak, or what can be called as easy as learning add, subtract, multiply, divide.
What makes both math and physics extremely hard to learn and understand is when mathematics never cleans itself up, and never tries to make itself easy. If all of math can be made as easy as add, subtract, multiply, divide, no one would really complain about math or physics. But because math is overrun by kooks (definition of kook: is a person who cares more about fame and fortune than about truth in science), that math has become a incomprehensible trash pile and the worst of all the sciences, and because the math is so difficult, it carried over into physics, making physics difficult.
And that may sound like a contradiction that AP ended up majoring in mathematics, rather than his first love of physics. But not a contradiction in truth. Because in Old Physics, you have not only a use of the messed up dirty Old Math, but you have use of what I call "idealisms" in Old Physics. Idealisms are "suppose this and that.... " "imagine a ball of mass moving in space....." So Old Physics not only had the tangled mess of kook math of trigonometry everywhere and thousands of silly rules for calculus. But Old Physics had a fakery contraption of "idealism". I ended up majoring in mathematics, although math was a mess, but at least I could still navigate in that mess. But I just could not navigate in physics with their math mess plus, their idealism mess. If you closely examine all Old Physics textbooks, even the latest recent ones, they are all "idealism physics". Idealism is a nice and better term for "fake physics".
You see, one of the greatest omissions of science in the 20th and 21st century was the idea that both math and physics can be reduced to a Simplicity of education. That math need not be hard and difficult. That physics can be made logical, not full of idealisms. Yet no-one in the 20th and 21st century ever had that idea of simplicity, (with the possible exception of Harold Jacobs in mathematics) that math had run out-of-bounds as a science and was more of a science fiction subject for kook mathematicians. Math had become absurdly difficult because of the reason that kooks gain fame and fortune on making math difficult. Mathematicians never thought their job was to make math simple and easy, instead, the kooks of math piled on more trash and garbage to make math a twilight zone of science. The same in physics with idealism run amok. And this is easily proven true about the sociology of math and physics education for it is no secret to anyone in education that college professors are paid not for their teaching so much, no, they are recognized and paid for their research, and this means the simplification of math or physics is secondary, not of first importance. College professor research is of more importance to them, than their failure to make physics or mathematics clear and easy to learn.
When you make all of math be just polynomial equations and functions, you make math the easiest of the major sciences, which then follows up by making physics easy as possible. For there is no longer trigonometry to cloud the mind in everything you do in physics. There is no longer hundreds of calculus rules you must learn just to do Faraday's law or Ampere's law.
So I end up writing this textbook, keeping in mind of AP way back in 1969 in a huge classroom of 1st year college physics, and how AP, the King of Science, especially Physics, would have majored in physics and not mathematics, if physics had been properly taught.
--------------------------
Table of Contents
--------------------------
Part I, Introduction, and about physics.
a) About this textbook and series of Physics textbooks.
b) Brief history lesson of 20th century physics.
c) How we make the mathematics super easy.
d) Horrible error-filled concept of "charge" in Old Physics, and thrown out of New Physics.
e) We increasingly have to use Biology DNA knowledge to unravel the physics of light waves and EM theory.
Part II, 6 Laws of EM theory.
f) The 6 laws of EM, ElectroMagnetic theory and their Units.
g) Matrix of the 6 EM laws.
h) Fixing the horrible mistake of Old Physics units of Magnetic field compared to Electric field.
i) The four differential equations laws of EM theory.
j) Defining the units of Coulomb and Ampere as C = A*seconds; and the Elementary-Coulomb.
k) Faraday Constant Experiment in classroom.
l) Matching the physics Algebra of units with the physics Geometry of units.
m) The EM Spectrum, Electromagnetic Spectrum where electricity is placed between X-rays and gamma rays.
Part III, 1st Law of EM theory.
n) 1st Law of EM theory; law of Magnetic Monopole and units are B = m^2 / A*s^2 = m^2/ C*s.
Part IV, 2nd Law of EM theory.
o) 2nd Law of EM theory; New Ohm's Law V = CBE, the Capacitor-battery law.
p) Short Circuit.
q) Series versus Parallel Circuits connection of closed loop.
r) Review of Geometry volume in 3D and path in 2D.
Part V, 3rd Law of EM theory.
s) 3rd law of EM theory, Faraday's law, C' = (V/(BE))'.
t) Short history lesson of Old Physics, 1860s Maxwell Equations.
u) New Rutherford-Geiger-Marsden Experiment observing Faraday Law.
v) Math Algebra for making one physical concept be perpendicular to another physical concept.
w) EM laws derive the Fundamental Theorem of Calculus.
x) Principle of Maximum Electricity and Torus geometry so essential in Atomic Physics.
Part VI
y) 4th law of EM theory; Ampere-Maxwell law B' = (V/(CE))'.
Part VII
z) 5th law of EM theory; Coulomb-gravity law; E' = (V/(CB))'.
aa) Centripetal versus Centrifugal force explained.
Part VIII
bb) 6th Law of EM theory, Transformer law; differential equation of New Ohm's Law V' = (CBE)'.
cc) Reinventing the Multivariable Calculus.
dd) Atomic bomb physics comes directly out of short circuit of V'=(CBE)', for atoms have no nucleus, just a thrusting muon inside a 840MeV proton torus.
ee) Electric Permittivity and Magnetic Permeability explained.
ff) Two proofs that electricity is not the flow of 0.5MeV particles but is waves between X-rays and gamma rays.