Science > Physics > This Week's Finds in Mathematical Physics (Week 212)
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"John Baez" |
| Date: |
27 Mar 2005 01:07:56 AM |
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This Week's Finds in Mathematical Physics (Week 212) |
Also available at http://math.ucr.edu/home/baez/week212.html
March 26, 2005
This Week's Finds in Mathematical Physics - Week 212
John Baez
As you may know, theoretical particle physics is highly enamored of
"supersymmetry" these days. This is not because there's a shred of
experimental evidence for it - there's not - but just because it's such
a cool idea from a mathematical point of view. Mathematicians should
have gotten this idea and run with it first, but physicists did - and
maybe it's turned them into mathematicians.
The unarguable central core of this idea is that everything is made of
bosons and fermions. In the Standard Model, most bosons are "force
carriers", like photons, which carry the electromagnetic force. Fermions
are more like what we'd normally call "matter": leptons and quarks, for
example. The one big exception is the Higgs boson, which gives elementary
particles their mass and... umm... hasn't been seen yet!
But, at a more fundamental level, the really important thing is that
bosons commute:
xy = yx
while fermions anticommute:
xy = -yx
Also, in case you're wondering, bosons commute with fermions.
But already, most mathematicians reading this will be confused and unhappy.
What does it mean for two particles to commute, much less anticommute?
Does an apple commute with a grape? Here in the suburbs of Los Angeles
almost everyone commutes, but that's not what we're talking about.
The whole idea of particles commuting or anticommuting only occurred to
people after they invented quantum theory, where the state of any
system is described by a unit vector in some Hilbert space. In quantum
theory, if you have a system in some state x, and you check to see if
it's in the state y, your experiment gives you the answer "yes" with
probability
|<x,y>|^2
the square of the absolute value of the inner product of x and y.
There! Now you know quantum theory.
Given this setup, when you have a system consisting of two particles, the
first in some state x and the second in some state y, it's natural to
write the state of the whole system as a kind of product xy. But
then you have to figure out what rules you want this product to satisfy!
If you require it to be commutative:
xy = yx
you're saying that there's no difference between the FIRST particle
being in state x and the SECOND particle being in state y, and the
other way around. In other words, the particles don't have little
name tags on them saying who they are.
This seems reasonable, and particles satisfying this rule are called
"bosons". But, there's another popular option, called "fermions":
xy = -yx
Here again, the particles don't have name tags, since if we put
the whole system in the state xy and check to see if it's in the
state yx, we get the same answer as when we check to see if it's
in the state xy! See:
|<xy,yx>|^2 = |<xy,-xy>|^2
= |<xy,xy>|^2
thanks to the absolute value. This means that the states xy and
yx are indistinguishable.
Reading what I just said, you'd be forgiven for wondering what's the
big difference between fermions and bosons! After all, that absolute
value in the formula probabilities just ignores minus signs.
One difference is the "Pauli exclusion principle". Take a pair of
fermions and check to see if they're both in the state x. The
probability is always zero, since
xx = -xx
so xx = 0. So, fermions are antisocial: that's why the electrons
in an atom form "shells" with different electrons in different states,
instead of all hanging out at the lowest energy state.
Bosons, by contrast, are gregarious: when a store clerk uses a laser
scanner to ring up your purchases, that beam of red light is a bunch of
photons all in the same state! A laser is a quintessentially quantum-
theoretic gadget - we live in a marvelous world, where such things are
taken for granted.
After getting used to these ideas for a while - Bose and Einstein worked
out the idea of bosons in 1924, Pauli came up with his exclusion principle
in 1925, and Dirac systematized the whole business in 1926 - physicists
eventually started looking for symmetries that relate bosons and fermions.
Supersymmetries! They're not seen in nature, but physicists were looking
to see if they're mathematically possible. They turn out not only to
be possible, but fascinating.
Formulating supersymmetries in a slick way requires that we take
everything we knew about linear algebra and generalize it by letting
all our vector spaces have both an "even" or "bosonic" part and an
"odd" or "fermionic" part. Mathematically this just amounts to writing
our vector space as a direct sum
V = V_0 + V_1
where V_0 is the "even part" and V_1 is the "odd part". Such a thing
is called a "Z/2-graded vector space", or "super vector space".
So far this is pathetically simple. But then - and this is the really
crucial part! - whenever we multiply things, we have to follow this rule:
even odd
----------------
even| even odd
odd | odd even
It's a little confusing, since this isn't what happens when you
multiply even and odd numbers - it's what happens when you ADD them.
But, one quickly adapts.
Also, when we generalize equations involving multiplication, we must
remember to stick in an extra minus sign whenever we switch two odd
vectors.
So, for example, the usual concept of an algebra gets replaced
by that of a "superalgebra". This is a super vector space A
equipped with an associative product and unit such that when we
multiply even and/or odd vectors, the rules in the above table hold.
We say a superalgebra is "supercommutative" if
xy = yx
when at least one of x,y lives in the even part A_0, while
xy = -yx
when both x and y live in A_1.
Similarly we can define super Lie algebras, super Lie groups,
supermanifolds, and so on....
People have done a lot of work on this stuff: it would take me days to
explain it all - even longer if I actually knew something about it.
But right now, I just want to zoom in the direction of super division
algebras. These are not the most important aspect of "superalgebra" -
but they're pretty cool, and Todd Trimble has been explaining them to
me lately. Everything interesting I'm about to say is due to him.
As you know, I'm inordinately fond of the normed division algebras:
the real numbers, complex numbers, quaternions and octonions. They're
so beautiful, it's a little sad at times that there are only four!
Could superalgebra allow for more?
YES! And, they turn out to be related to Bott periodicity.
Nobody seems to have pondered *nonassociative* super division algebras
yet, but Deligne has a nice article about the associative ones, which
I mentioned in "week211". I'll give more references later.
So, what's the idea?
I've already told you what a superalgebra is. We say it's a "super
division algebra" if every nonzero element that's purely even or
purely odd is invertible.
That's pretty easy. What are they like?
Well, I don't completely understand all the options yet, so I'll
just list the "central" super division algebras over the real numbers,
namely those where the elements that supercommute with everything
form a copy of the real numbers. There turn out to be 8, and their
beautiful patterns are best displayed in a circular layout:
R
0
R[e] mod e^2 - 1 7 1 R[e] mod e^2 + 1
C[e] mod e^2 - 1, ei + ie 6 2 C[e] mod e^2 + 1, ei + ie
H[e] mod e^2 + 1 5 3 H[e] mod e^2 - 1
4
H
What does this notation mean? Well, as usual R, C, and H stand for
the reals, complex numbers, and quaternions. In all but two cases,
we start with one of those algebras and throw in an odd element "e"
satisfying the relations listed: e is either a square root of +1 or
of -1, and in the complex cases it anticommutes with i.
So, for example, super division algebra number 1:
R[e] mod e^2 + 1
is just the real numbers with an odd element thrown in that satisfies
e^2 + 1 = 0. In other words, it's just the complex numbers made into
a superalgebra in such a way that i is *odd*.
The real reason I've arranged these guys in a circle numbered from
0 to 7 is to remind you of the Clifford algebra clock in "week210",
where I discussed the super Brauer group of the real numbers, and
said it was Z/8.
Indeed, the central super division algebras are a complete set of
representatives for this super Brauer group! In particular, the
Clifford algebra C_n is super Morita equivalent to the nth algebra
on this circle:
C_0 = R ~ R
C_1 = C ~ R[e] mod e^2 + 1
C_2 = H ~ C[e] mod e^2 + 1, ei + ie
C_3 = H + H ~ H[e] mod e^2 - 1
C_4 = H(2) ~ H
C_5 = C(4) ~ H[e] mod e^2 + 1
C_6 = R(8) ~ C[e] mod e^2 - 1, ei + ie
C_7 = R(8) + R(8) ~ R[e] mod e^2 - 1
where ~ means "super Morita equivalent".
I think this is cool. I'm not quite sure what to do with it yet,
though. How much of what people ordinarily do with division algebras
can be done with super division algebras? For example, can we define
projective spaces over super division algebras? (See "week106" and
"week145" for why that would be interesting.)
To read more about this, try:
1) Pierre Deligne, Notes on spinors, in Quantum Fields and Strings:
A Course For Mathematicians, volume 1, American Mathematical Society,
Providence, 1999. Also available at
http://www.math.ias.edu/QFT/fall/spinors.ps
A lot of the ideas go back to here:
2) C. T. C. Wall, Graded Brauer groups, J. Reine Angew. Math. 213
(1963/1964), 187-199.
and here's another good reference:
3) Peter Donovan and Max Karoubi, Graded Brauer groups and K-theory
with local coefficients, Publications Math. IHES 38 (1970), 5-25.
Also available at http://www.math.jussieu.fr/~karoubi/Donavan.K.pdf
I should admit that I have a yearning to classify *nonassociative*
super division algebras. Has anyone ever tried this? It's already
plain to see that we have two 16-dimensional nonassociative super
division algebras:
O[e] mod e^2 + 1
and
O[e] mod e^2 - 1
where e is an odd element that commutes with all the octonions.
(I should have mentioned this before, when talking about H[e]:
even though the quaternions are noncommutative, we assume that
e commutes with all of them.) Maybe one of these algebras
deserves to be called the SUPEROCTONIONS. I bet these or
something awfully similar are lurking around in string theory.
Hmm... next I wanted to write something about the topology of Bott
periodicity and how *that* fits into what I've been discussing,
but I'm running out of energy. Let me say it briefly, in a way
that only experts will understand, just in case I never get
around to a decent explanation.
Two super algebras are super Morita equivalent precisely when
they have equivalent categories of super representations. So,
the super Brauer group really consists of 8 different *categories*:
the categories SuperRep(C_n), where Bott periodicity says
SuperRep(C_{n+8}) ~ SuperRep(C_n)
Moreover these are symmetric monoidal categories, since direct
summing lets us "add" objects in these categories in a nice way.
A long time ago, Graeme Segal figured out how to take a symmetric
monoidal category and get an infinite loop space from it.
I explained this construction in "week199", but for a much more
detailed and intense treatment with lots of references to earlier
work, try:
4) R. W. Thomason, Symmetric categories model all connective
spectra, Theory and Applications of Categories 1 (1995), 78-118.
Available at http://www.tac.mta.ca/tac/volumes/1995/n5/1-05abs.html
If we do this to SuperRep(C_n), I think we get something like
Omega^n(kO)
that is, the n-fold loop space of something called kO, the "connective
K-theory spectrum", which I explained in "week105". The fact that this
repeats with period 8:
Omega^{n+8}(kO) ~ Omega^n(kO)
is the topological version of Bott periodicity - see "week105" for more.
So, we get the topological version of Bott periodicity from the algebraic
version by turning symmetric monoidal categories into infinite loop
spaces!
But, the interesting puzzle here is: what process can we do to SuperRep(C_n)
to get SuperRep(C_{n+1}), which is the algebraic version of looping?
And I think the answer is: "taking super representations of C_1 in it".
You see,
C_1 tensor C_n = C_{n+1}
where I'm using the super tensor product of superalgebras, and this
means that the category of representations of C_1 *in* SuperRep(C_n)
is SuperRep(C_{n+1}).
And, if I were trying to really explain this instead of merely scribbling
notes about it, I would try to say why this is because C_1 is the complex
numbers, and the unit circle in the complex numbers is related to LOOPS.
But, sigh, that will have to wait.
One more thing before I quit for today...
I just saw a cool paper by Dror Bar-Natan, Thang Le and Dylan Thurston
about the "Duflo isomorphism". This is a cousin of the Poincare-Birkhoff-
Witt theorem, which in its best form says that the universal enveloping
algebra UL of a Lie algebra L is isomorphic *as a coalgebra* to the
symmetric algebra SL. You'll often see worse versions of the PBW theorem
in textbooks, and ugly proofs, but James Dolan showed me the nice version
and proof a while back.
The kernel of the idea is this: if L is the Lie algebra of a group G,
UL consists of left-invariant differential operators on G, and there's
a map UL -> SL sending any differential operator to its "symbol".
This is an isomorphism of vector spaces and even of coalgebras, but
not of algebras.
Anyway, there's something vaguely similar relating the invariant
subalgebras of UL and SL. By "invariant" here, I mean that since
L acts as derivations of UL and SL, we can look at the subalgebra of
either one consisting of guys who are killed by these derivations;
such guys are called "invariant". Physicists call invariant elements
of UL "Casimirs", after the first physicist to think about this stuff.
They form commute with everything else in UL. Invariant elements of
SL are like classical Casimirs: there's a Poisson bracket on SL, and
these are the guys whose Poisson bracket with everyone vanishes.
The Duflo map is an *algebra isomorphism* from SL to UL. So, it's
like a very nice way to quantize Casimirs, one that gets along with
multiplication. It's called the "Duflo map" because it was invented by
Harish-Chandra for semisimple Lie algebras and for Kirillov in general.
Kirillov conjectured that it was always an isomorphism; what Duflo
did is prove it:
5) Michel Duflo, Operateurs differentiels bi-invariants sur un groupe
de Lie, Ann. Sci. Ecole Norm. Sup. 10 (1977), 265-288.
Apparently all known proofs are sort of hard! According to Bar-Natan,
Le and Thurston:
In the book of Dixmier, the proof is given only in the last chapter
and it utilizes most of the results developed in the whole book,
including many classification results (a situation Godement called
"scandalous"). As discussed below, there have been several recent
proofs that do not use classification results, but they all use tools
from well outside the natural domain of the problem.
The proof by Bar-Natan, Le and Thurston uses the connection between
knot theory and Lie algebras - namely, the theory of Vassiliev
invariants. I think there's still something slightly scandalous about
this, but it's awfully interesting. Anyway, take a look:
6) Dror Bar-Natan, Thang T. Q. Le and Dylan P. Thurston, Two
applications of elementary knot theory to Lie algebras and Vassiliev
invariants, Geometry and Topology 7 (2003), 1-31. Available at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.html and also
as math.QG/0204311.
For more, try Thurston's thesis:
7) Dylan P. Thurston, Wheeling: a diagrammatic analogue of the Duflo
isomorphism, math.QG/0006083.
and, just for fun, Deligne's handwritten letter to Bar-Natan:
8) Pierre Deligne, letter to Dror Bar-Natan about the Duflo map,
available at http://www.math.toronto.edu/~drorbn/Deligne/
-----------------------------------------------------------------------
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/twf.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
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 02:04:36 AM |
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From Osher Doctorow
Your first page is excellent, and I'm turning to page two next. I
still have to type something else and my bedtime is approaching. I'll
try to get to page 2 first thing tomorrow morning, hopefully.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 02:16:48 AM |
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From Osher Doctorow
Page 2 is excellent, and so is page 3.
Now I have to type something else and go to sleep. Come to think of
it, what are the dimensions of "sleeping on it," when one finds a
solution to a problem during sleep? Does the universe sleep? Hmmm....
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 11:58:11 AM |
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From Osher Doctorow
Well, I followed up my "sleep" ideas on my Cantor TOE thread this
morning.
Your page 4 is technically fine, but now you start losing what started
out as an interdisciplinary-looking orientation. I don't think that
you concentrate on interdisciplinary in the sense of "think snow" or
"follow the money". It's more for you like "think algebra in physics"
as well as "just think algebra". I start seeing also why your paper
emphasizes supersymmetry and symmetry -it's the algebraists' "only
breakthrough almost" and it really didn't come from algebra or
algebraic physics although Emmy Noether made it look like it did but
from Einstein and even earlier geometers. Prof. Hestenes of Arizona
State U. (ASU) is so far ahead of you that I'm embarrassed to discuss
it, and he emphasizes the geometric side of Clifford "algebra" in terms
of Spacetime Physics/Spacetime Calculus. Nevertheless, you get points
for technical expertise and for trying on page 4. I'll look at page 5
next. I'm sure that you have allies on Clifford algebras since much
of the British and Canadian Clifford algebra schools, unlike the
Hestenes school which is "infinitely" better, is bogged down on
algebraic gobbledygook.
I do appreciate your effort to communicate with us "lower mortals",
which is "infinitely ahead of Uncle Al", and I look forward to teaching
you how far ahead of you some of us are. Happy Passover and Happy
Easter or Happy Atheists Day, whichever you choose if any.
Osher Doctorow
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| User: "Jan Panteltje" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 12:04:33 PM |
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On a sunny day (27 Mar 2005 09:58:11 -0800) it happened "OsherD"
<mdoctorow@comcast.net> wrote in
<1111946291.520025.193000@f14g2000cwb.googlegroups.com>:
From Osher Doctorow
Well, I followed up my "sleep" ideas on my Cantor TOE thread this
morning.
Are you a new incarnation of Sarafatti?
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| User: "hanson" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 03:01:28 PM |
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"Jan Panteltje" <pNaonStpealmtje@yahoo.com> wrote in message
news:1111946683.d0afa00137ee6dff59eb359f1aa7f106@teranews...
On a sunny day (27 Mar 2005 09:58:11 -0800) it happened "OsherD"
<mdoctorow@comcast.net> wrote in
<1111946291.520025.193000@f14g2000cwb.googlegroups.com>:
From Osher Doctorow
Well, I followed up my "sleep" ideas on my Cantor TOE
thread this morning.
[Jan]
Are you a new incarnation of Jack Sarafatti?
[hanson]
.... ahahaha.... No, I don't think so. Osher doesn't have Sarfatti's
intellectual acumen nor Jack's caliber, but he could be the
Jewish version-incarnate of George Hammond, who proselytized
his g_uv = God, and now Oshi trumps and out-does Ge/orgi
with his own Cantor TOE... even in his sleep!....
Quite an advanced accomplishment!.. wouldn't you say so?...
Let's hear it for Oshi, the rarefied septuagenarian... ahahaha...
ahaha... ahahanson
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 03:11:47 PM |
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From Osher Doctorow
Hanson said:
[hanson]
ahahaha.... No, I don't think so. Osher doesn't have Sarfatti's
intellectual acumen nor Jack's caliber, but he could be the
Jewish version-incarnate of George Hammond, who proselytized
his g_uv = God, and now Oshi trumps and out-does Ge/orgi
with his own Cantor TOE... even in his sleep!....
Quite an advanced accomplishment!.. wouldn't you say so?...
Let's hear it for Oshi, the rarefied septuagenarian... ahahaha...
ahaha... ahahanson
Hey Hanson, how can they hear it if you're laughing all the time?
As for "intellectual acumen" and analogies with proselytizing, do I
detect a defrocked priest and a person who is over-impressed by long
words and long-winded "explanations" that Jack Sarfatti specialized in?
(My guess is that Jack has returned to some hole for Easter and will
pipe up afterwards in a random location like a drive-by although he
indicates that he doesn't get probability - but neither does Hanson.)
Osher Doctorow
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| User: "hanson" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
28 Mar 2005 02:17:21 PM |
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"OsherD" <mdoctorow@comcast.net> wrote in message
news:1111957907.820203.226070@l41g2000cwc.googlegroups.com...
[hanson to Ian Pantelje]
ahahaha.... No, I don't think so. Osher doesn't have Sarfatti's
intellectual acumen nor Jack's caliber, but he could be the
Jewish version-incarnate of George Hammond, who proselytized
his g_uv = God, and now Oshi trumps and out-does Ge/orgi
with his own Cantor TOE... even in his sleep!....
Quite an advanced accomplishment!.. wouldn't you say so?...
Let's hear it for Oshi, the rarefied septuagenarian... ahahaha...
ahaha... ahahanson
[Osher Doctorow]
Hey Hanson, how can they hear it if you're laughing all the time?
[hanson]
Does me laughing about/at/cuz of you, crank you, Oshi?... ahahaha...
... and "they" could hear it well alright, as is seen by the Rare
example that YOU have given by responding as "a they" my post
since it was directed to Ian and not you... ahahahaha....
[Oshi, the Rare]
As for "intellectual acumen" and analogies with proselytizing, do I
detect a defrocked priest and a person who is over-impressed by long
words and long-winded "explanations" that Jack Sarfatti specialized in?
(My guess is that Jack has returned to some hole for Easter and will
pipe up afterwards in a random location like a drive-by although he
indicates that he doesn't get probability - but neither does Hanson.)
Osher Doctorow
[hanson]
You should not get so flustered, nor discombobulated, nor pissed or
cranked like you did here, Oshi, and especially not let your Rarity
get the better of you. You should learn, even this late in your life,
to take my constructive evaluation and/or commentary with class
and humor and retort with style.... ahahaha...
Or are these qualities too rare in/with you, Oshi?... ahahahaha...
ahahaha... ahahanson
PS: How is your emerging cyber-relationship with Tom Pinko-Potter,
the Pottler, developing? It should not be a rare event for you to
re-educate Pottler since he has never shown any class, nor humor
& lacks pizzazz. Can you do it, Oshi, or will your collective, Rare history
repeat itself, with/by and thru current and future dominance of such
Pottler types over you?
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 12:57:40 PM |
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From Osher Doctorow
Jan Panteltje said:
Are you a new incarnation of Sarafatti?
Ach Liebe Gott, on Easter you ask such a question? Sarfatti appears
to be in temporary suspension and hates me; no, make that he regards me
in my opinion as an insect. This is nixt normale to quote the Swiss
(an old woman Swiss biker trailing a Swiss biker gang actually). I
never got along with Sarfatti. I'm not even sure that Sarfatti really
exists or ever existed. The only reason that I know anything about
Sarfatti is that he is interested in Consciousness, but more in the
sense of S. Hameroff of Arizona U. or Arizona State U. which is a
shackled Consciousness (shackled by Conformity to his/their theories)
in my opinion.
I am the/a Original Nonconformist. Sarfatti is and has been too
Conformist to me. I think that I may have driven him off the internet,
although I only assign a probability of .06 on a 0 to 1.0 scaoe to that
subjectively. David Bohm was also too Conformist for me. Sarfatti is
obsessed with David Bohm and Consciousness. I am only obsessed with
Knowledge, Ethics, and Spirit, mostly in that order from highest to
lowest. Nonconformity, however, is in my opinion a must for such
obsession, because Conformists tend to know little, tend to be
unethical, and tend to have their "little spirits" in their genitals if
not their excretory tracts.
Now let me ask you: are you a new incarnation of the Anti-Sarfattis,
and if so, kindly take your extra "a" out of "Sarafatti" unless you are
building a secret code. Also, if you're an Anti-Sarfattist, where is
your Nonconformity? Did you leave it home? Never leave home without
it - you never know when it may come in handy. And read English more
carefully unless you're skimming like most of the Conformsits.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 01:03:53 PM |
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From Osher Doctorow
I forgot to add: Ach Tu Liebe and Il Nomme Padre Efilio Santo in an
attempt to exorcise Sarfatti (I'm not sure whether forwards or
backwards though).
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 01:15:21 PM |
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From Osher Doctorow
It is time to stop being a nice guy and get back to physics.
On page 5 of John Baez' paper, the "truth is revealed". I quote: "I
wanted to write something about the topology of Bott periodicity....Let
me say it briefly, in a way that only experts will understand, just in
case I never get around to a decent explanation."
This is hilarious! I've heard of Dancing With Wolves, but a man who
Talks With Experts in preference to anything has got to be rare since
there are only a few Experts who could be called Creative Geniuses and
I'm one of them in my opinion. Maybe he's talking with Nathan
Seiberg, or Edward Witten who's still a candidate for Creative Genius
if I ever get around to finishing my own analysis of his contributions
(unofficially, of course). So far, Edward seems too similar to John
von Neumann who had one foot in Creative Genius and one foot in
Ingenious Imitation, though I think that Edward's memory is better than
John's (what this implies is anybody's guess).
Also on Page 5, John Baez reverts to his almost exclusive interest in
abstract algebra, which really is great for Ivory Tower theoretical
physics and mathematical physics branches in Academia (mathematical
physics is the Mathematics Department opposite number of Theoretical
Physics in the Physics Department) but in my current estimate delays
actual progress in both Physics and Mathematics by a century or more.
Perhaps he's a representative of the Galactic Federation who's keeping
the Earth's Violence-Orientation from contaminating the rest of the
galaxy :>)
Osher Doctorow
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| User: "Jan Panteltje" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 212) |
27 Mar 2005 04:04:43 PM |
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On a sunny day (27 Mar 2005 10:57:40 -0800) it happened "OsherD"
<mdoctorow@comcast.net> wrote in
<1111949860.731689.118560@g14g2000cwa.googlegroups.com>:
From Osher Doctorow
Jan Panteltje said:
Are you a new incarnation of Sarafatti?
Ach Liebe Gott,
You are German?, www.heise.de actully wrote about you a couple of weeks ago.
I am the / a original conformist.
Hardly 'the'.
obsession, because Conformists tend to know little, tend to be
I dunno, some know a lot.
Now let me ask you: are you a new incarnation of the Anti-Sarfattis,
Nope, I read Jack's works somtime,s not that I have ever been able to make
sense of it, or even to get to a point where...
He under Alien influence so I have heard, so I remain in control.
and if so, kindly take your extra "a" out of "Sarafatti" unless you are
Yes, this name keeps confusing me with an other that is realy close I know.
building a secret code.
I can do that, but yo ucould not hack it, so why bother?
Also, if you're an Anti-Sarfattist,
I am not anti S, in fact I referenced him - you because both tkae of in a monolog
with themselves.
But Jack never replies directly (but indirectly in his text), you do.
where is
your Nonconformity?
Google 'panteltje' 160000 hits.
Chances are something in there does not conform.
Did you leave it home?
I am home.
Never leave home without
it - you never know when it may come in handy. And read English more
carefully unless you're skimming like most of the Conformsits.
You actually made some typos (you had your finger on the O accidently).
When I substact knowledge in end of your posting from that in beginning,
I find you speak German, but have nothing to say?
Osher Doctorow
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