Re: More on Quantum vectors...

[Julian Assange]

Frank Atanassow <[EMAIL PROTECTED]> writes:

> I would not be surprised to find this article appearing in the next Scientific
> American.
> 
> Consider these gems:
> 
>   "Finger-Length Ratios and Sexual Orientation," Terrance J. Williams,
> 
>   "Why are Toads Right-Handed?" Nature, T. Naitoh and R.J. Wassersug,
> 
>   "Effect of Ale, Garlic, and Soured Cream on the Appetite of Leeches," Anders
>
>   "Bed Rest: A Potentially Harmful Treatment Needing More Careful Evaluation,"
> 
>   "Pigeons' Discrimination of Paintings by Monet and Picasso," Shigeru
> 
> So, no matter what your problem, rest assured that, sometime, somewhere,
> somewhy, a scientist has probably already reported on it.
> 
> [These citations are courtesy of the Annals of Improbable Research,
> http://www.improbable.com.]

The Annals have gone down hill over time, three* of these papers were excellent.

*No, I'm not telling you which three :)

Cheers,
Julian.

Re: More on Quantum vectors...

[Jan Skibinski]

In a second round I have made several improvements
to the formalism of QuantumVector module. Module
Momenta is also adjusted to match the changes.

The most notable improvement is related to tensor
products of vector spaces. Previous definition was
not good enough; although it could deal with many
subsystems but they had to be of the same type. 
This restriction has been now removed.

It does not sound like much, but in fact this
is a significant leap forward. I have few interesting
examples in mind which I intend to demonstrate
later. 

On Tue, 6 Jun 2000, Frank Atanassow wrote:

> I am aware of the many books on QM. However, I would not expect a
> CS person to read a whole book just to read a paper which has
> to do with QM.

I do not see a single principle of physics employed
in module QuantumVector. This is all preparatory work
based solely on some mathematics. There is some
physics in module Momenta though, and I provided
some summary of few laws a reader should know.

> 
> Sure, it's a rehash of material available elsewhere, but it only needs to
> touch the points which are relevant for your paper.

Section 6 of QuantumVector is devoted to linear
operators and is mainly a rehash of known definitions,
to quote you.
You can find some documentation there. This was not
a main goal though; I was trying to demonstrate that
all known definitions of operators, such as inverse,
adjoint, unitary and hermitian, are valid -- even
though we deal here with strongly typed language and
have to assure that we do not compare apples to oranges.
Operators, as I view them here, are not just tables
of unnamed numbers; in many cases they map one distinct
type to another.

Jan

Re: More on Quantum vectors...

[Frank Atanassow]

I cannot resist replying to this remark:

Jan Skibinski writes:
 >  Now, someone, somewhere could have written a paper
 >  "Isolation properties of sandwiched materials", but
 >  how on earth he/she would ever invented something
 >  of this sort in the first place or - granted that -
 >  how could he/she ever appreciate an importance
 >  of this little problem?

I would not be surprised to find this article appearing in the next Scientific
American.

Consider these gems:

  "Finger-Length Ratios and Sexual Orientation," Terrance J. Williams,
  Michelle E.  Pepitone, Scott E. Christensen, Bradley M. Cooke, Andrew
  D. Huberman, Nicholas J.  Breedlove, Tessa J. Breedlove, Cynthia L. Jordan,
  and S. Marc Breedlove, Nature, vol.  404, no. 6777, March 30, 2000,
  pp. 455-6. [This yielded what the authors call "some surprising
  information." From it they concluded that, statistically, it is possible to
  ascertain people's sexual orientation simply by knowing the ratio of each
  individual's finger lengths.]

  "Why are Toads Right-Handed?" Nature, T. Naitoh and R.J. Wassersug,
  vol. 380, 1996, pp. 30-1. [Sims, Andrews, and Young explore the method by
  which certain fish "remove noxious material from the stomach." Called "full
  gastric eversion," this consists of turning the stomach inside out and
  draping it through the mouth. Wassersug explains that, "for the record, the
  serious scientific answer is that frogs have to do this task of stomach
  wiping with their right hand simply because the upchucked stomach always
  hangs out of the right side of the mouth."]

  "Effect of Ale, Garlic, and Soured Cream on the Appetite of Leeches," Anders
  Barheim and Hogne Sandvik, "British Medical Journal," vol. 309, Dec 24-31,
  1994, p. 1689. [This article won the Ig Nobel Prize.]

  "Bed Rest: A Potentially Harmful Treatment Needing More Careful Evaluation,"
  Chris Allen, Paul Glaszious, and Chris Del Mar, The Lancet, vol. 354,
  October 9 1999, p. 1229. [The authors conclude that bed rest by itself
  doesn't necessarily help you get well, especially if you are ill.]

  "Pigeons' Discrimination of Paintings by Monet and Picasso," Shigeru
  Watanabe, Junko Sakamoto, and Masumi Wakita, "Journal of the Experimental
  Analysis of Behavior," vol. 63, 1995, pp. 165-174. [Another Ig Nobel Prize
  winner, "for their success in training pigeons to discriminate between the
  paintings of Picasso and those of Monet."]

So, no matter what your problem, rest assured that, sometime, somewhere,
somewhy, a scientist has probably already reported on it.

[These citations are courtesy of the Annals of Improbable Research,
http://www.improbable.com.]

-- 
Frank Atanassow, Dept. of Computer Science, Utrecht University
Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands
Tel +31 (030) 253-1012, Fax +31 (030) 251-3791

Re: More on Quantum vectors...

[Frank Atanassow]

Jan Skibinski writes:
 >  Well, Frank, there are zillions of papers and books on 
 >  mathematical background of QM and I certainly would not add
 >  anything of a consequence here. A theoretical foundation of
 >  Quantum Mechanics is the Hilbert space. Dirac's formalism
 >  is a neat notation for that space and the physicists like it,
 >  but you could use any other notation for that matter.

I am aware of the many books on QM. However, I would not expect a CS person to
read a whole book just to read a paper which has to do with QM.

Sure, it's a rehash of material available elsewhere, but it only needs to
touch the points which are relevant for your paper.

Conversely, if I were going to write a paper to do with lambda-calculus but
which is aimed at an audience of physicists, I would include a little
background in the paper rather than just refer them to Barendregt's book. (Of
course, a solid bibliography is also necessary.)

 >  If you are asking for a paper on application of
 >  QM that's again uncountable a task.

No, I'm not.

 >  But if you are asking for a paper on QM vs. FP - that's
 >  another story. Jerzy sent one pointer in his last post.
 >  I hope more papers of this kind will appear in the future.

I'm asking for (er, rather, trying to encourage you to write) a paper on your
QM modules, and your perspective on QM vs. FP as well. (I'm going to look at
Jerzy's paper next.)

-- 
Frank Atanassow, Dept. of Computer Science, Utrecht University
Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands
Tel +31 (030) 253-1012, Fax +31 (030) 251-3791

Re: More on Quantum vectors...

[Ronald J. Legere]

Hey, I am reading this thread to , it is pretty interesting :)
Sometime I hope to have time to look at the package in detail, but
the idea is of course very interesting. 

 
+
Ron Legere  -- http://www.its.caltech.edu/~legere
Caltech Quantum Optics
MC 12-33
Pasadena CA 91125
626-395-8343
FAX: 626-793-9506
+



On Mon, 5 Jun 2000, Frank Atanassow wrote:

> Jerzy Karczmarczuk writes:
>  > ...although apparently there are exactly two readers/writers
>  > of this thread on this list. Oh, well, it is as boring as any 
>  > other subject.
> 
> I'm reading it. I think this field of application could be very

Re: More on Quantum vectors...

[Jan Skibinski]

On Mon, 5 Jun 2000, Frank Atanassow wrote:

> Jerzy Karczmarczuk writes:
>  > ...although apparently there are exactly two readers/writers
>  > of this thread on this list. Oh, well, it is as boring as any 
>  > other subject.
> 
> I'm reading it. I think this field of application could be very
> interesting. Jan, could you write up a paper on it, with enough of the
> mathematical background for non-physicist CS people to grok it?

Well, Frank, there are zillions of papers and books on 
mathematical background of QM and I certainly would not add
anything of a consequence here. A theoretical foundation of
Quantum Mechanics is the Hilbert space. Dirac's formalism
is a neat notation for that space and the physicists like it,
but you could use any other notation for that matter.

If you are asking for a paper on application of
QM that's again uncountable a task.

But if you are asking for a paper on QM vs. FP - that's
another story. Jerzy sent one pointer in his last post.
I hope more papers of this kind will appear in the future.

I would like to elaborate a bit more on what was already
said on applications of QM. There are tonnes of riches
of QM worth exploring. Some mathematicians have done it in
the past and some do it today. Some do not have a clue
what's there and that's a pity. This is what I have learned
from my days as a consultant in an engineering field:
a real life brings more interesting puzzles that I could
have ever invented by sitting at my desk and scratching
my head. (*)

Open any book on Quantum Mechanics and flip the pages
at random -- there is high probability that wherever
your finger points there are still some unresolved
problems waiting for you to compute.

Jan

(*) 

P.S.

Speaking of real life inspirations...
 
One apparently silly example: At a top of a high class
office bulding there is a running track for afficionados
of exercising. Runners cause track vibrations. Vibrations
cause noise. Noise propagates few stories down and annoy
the VIP. The VIP wants the problem fixed. The building
is new and noise/vibration consultants had been involved
in the project from the start. But they obviously missed
something.

Well, the track is isolated by sandwiched layers of
rubber and other isolation. Stress waves reflect and
refract in the sandwich, which happens to have some
undesirable coefficients of refractions. As a result
the standing waves build up to extremely high levels.

Now, someone, somewhere could have written a paper
"Isolation properties of sandwiched materials", but
how on earth he/she would ever invented something
of this sort in the first place or - granted that -
how could he/she ever appreciate an importance
of this little problem?

Yesterday my friend posed a question about a concentric
cable whose 1 mm diameter conduit is welded to the base
of a printed circuit board. All of this sits on some
tower in Texas and is exposed to extreme temperature
changes. That causes high stress concentrations on
the contact surface between wire and the weld. The weld
breaks. But that's another unbelievable story...







  


 
 

Re: More on Quantum vectors...

[Gabor Greif]

On Mon, Jun 5, 2000 14:57 Uhr, Frank Atanassow 
wrote:
>Jerzy Karczmarczuk writes:
> > ...although apparently there are exactly two readers/writers
> > of this thread on this list. Oh, well, it is as boring as any 
> > other subject.
>
>I'm reading it. I think this field of application could be very
>interesting. Jan, could you write up a paper on it, with enough of the
>mathematical background for non-physicist CS people to grok it?
>
>And maybe Jerzy could write up something which elaborates this remark:

[snip]

I found this rather interesting, but OTOH I had some of it in uni.
The closure operator |. >< .. | gave me the intuition for deforestation of
intermediate structures in functional languages. So at least for me QM and
FP have some synergy effect.

Gabor

Re: More on Quantum vectors...

[Jerzy Karczmarczuk]

Frank Atanassow wrote:

> ... maybe Jerzy could write up something which elaborates this remark:
> 
>  > I confess that I became interested in Haskell *because* of its possible
>  > applications to scientific computing, and *in particular* to quantum
>  > physics. (And some statistical physics; the underlying math is very
>  > similar, and this is not accidental).
>  >
>  >
>  > Mind you, this is a domain where you see immediately the necessity of
>  > computing using higher-order functions!
>  >
>  > Your states are functions. Your mathematical objects are functions. Your
>  > physical quantities (observables) are functions acting on states.

etc. 

Well, try to have a look here:

http://www.info.unicaen.fr/~karczma/arpap/quantfun.pdf


Concretely: section 3, page 6. This is an introduction to *such* 
applications of FP. The beginning of this paper is an elementary
introduction to FP you won't probably need...

Anyway, thank you *very* much for your interest. 

==


Jerzy Karczmarczuk
Caen, France

RE: More on Quantum vectors...

[STOUT, Mike]

I'm reading it too. Fascinating stuff.
I'm comfortable with Haskell code but struggle with Dirac's book. Expressing
this stuff in Haskell makes it crystal clear (at least to me).
Look forward to reading more.
Mike Stout


> -Original Message-
> From: Frank Atanassow [SMTP:[EMAIL PROTECTED]]
> Sent: 05 June 2000 13:58
> To:   Jerzy Karczmarczuk
> Cc:   [EMAIL PROTECTED]
> Subject:  More on Quantum vectors...
> 
> Jerzy Karczmarczuk writes:
>  > ...although apparently there are exactly two readers/writers
>  > of this thread on this list. Oh, well, it is as boring as any 
>  > other subject.
> 
> I'm reading it. I think this field of application could be very
> interesting. Jan, could you write up a paper on it, with enough of the
> mathematical background for non-physicist CS people to grok it?
> 
> And maybe Jerzy could write up something which elaborates this remark:
> 
>  > I confess that I became interested in Haskell *because* of its possible
>  > applications to scientific computing, and *in particular* to quantum
>  > physics. (And some statistical physics; the underlying math is very
>  > similar, and this is not accidental).
>  > 
>  > 
>  > Mind you, this is a domain where you see immediately the necessity of
>  > computing using higher-order functions!
>  > 
>  > Your states are functions. Your mathematical objects are functions.
> Your
>  > physical quantities (observables) are functions acting on states.
>  > 
>  > Most problems in QM cannot be solved without using perturbation
> methods.
>  > The perturbation formulae are usually very tedious to implement, unless
> 
>  > one dares to use some lazy coding.
>  > 
>  > Then you can economize a few days of pencil work, and you can spend
> this
>  > time rolling on the ground and laughing at the people who claim that
>  > Haskell is useless for practical computations, because they don't know
>  > how to implement some middle-Chinese chess in it.
> 
> -- 
> Frank Atanassow, Dept. of Computer Science, Utrecht University
> Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands
> Tel +31 (030) 253-1012, Fax +31 (030) 251-3791
> 

More on Quantum vectors...

[Frank Atanassow]

Jerzy Karczmarczuk writes:
 > ...although apparently there are exactly two readers/writers
 > of this thread on this list. Oh, well, it is as boring as any 
 > other subject.

I'm reading it. I think this field of application could be very
interesting. Jan, could you write up a paper on it, with enough of the
mathematical background for non-physicist CS people to grok it?

And maybe Jerzy could write up something which elaborates this remark:

 > I confess that I became interested in Haskell *because* of its possible
 > applications to scientific computing, and *in particular* to quantum
 > physics. (And some statistical physics; the underlying math is very
 > similar, and this is not accidental).
 > 
 > 
 > Mind you, this is a domain where you see immediately the necessity of
 > computing using higher-order functions!
 > 
 > Your states are functions. Your mathematical objects are functions. Your
 > physical quantities (observables) are functions acting on states.
 > 
 > Most problems in QM cannot be solved without using perturbation methods.
 > The perturbation formulae are usually very tedious to implement, unless 
 > one dares to use some lazy coding.
 > 
 > Then you can economize a few days of pencil work, and you can spend this
 > time rolling on the ground and laughing at the people who claim that
 > Haskell is useless for practical computations, because they don't know
 > how to implement some middle-Chinese chess in it.

-- 
Frank Atanassow, Dept. of Computer Science, Utrecht University
Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands
Tel +31 (030) 253-1012, Fax +31 (030) 251-3791

More on Quantum vectors...

[Jerzy Karczmarczuk]

...although apparently there are exactly two readers/writers
of this thread on this list. Oh, well, it is as boring as any 
other subject.

Jan Skibinski comments my observation:

> > ... I assure you that some non-orthogonal
> > bases are of extreme importance in physics, a canonical example
> > being the coherent states in optics.


> I think Jerzy is talking about cases conceptually sketched below.
> 
>   / e2|e2'
>  /|
> / |
>/___   | contravariant basis
>e1  \
>covariant basis  \
>  \ e1'
> 
> e1 * e2' = 0   e1*e1' = 1
> e2 * e1' = 0   e2*e2' = 1
==

Not really. This is not a contra/co geometric problem. In fact, this
begins to be interesting in infinite-dimensional spaces. The coherent
states (eigenstates of the annihilation operator) describe laser beams,
superfluidity, currents in the Josephson junction, and (quasi)
"classical"
distribution within the quantum formalism. They are truly
non-orthogonal,
and redundant (it is an over-complete basis; there are *analytic*
relations
between various basis vectors, which are labeled by complex numbers.
That's why they are called "coherent").


Now, what has all that to do with Haskell?
For most of you probably nothing.

I confess that I became interested in Haskell *because* of its possible
applications to scientific computing, and *in particular* to quantum
physics. (And some statistical physics; the underlying math is very
similar, and this is not accidental).


Mind you, this is a domain where you see immediately the necessity of
computing using higher-order functions!

Your states are functions. Your mathematical objects are functions. Your
physical quantities (observables) are functions acting on states.

Most problems in QM cannot be solved without using perturbation methods.
The perturbation formulae are usually very tedious to implement, unless 
one dares to use some lazy coding.

Then you can economize a few days of pencil work, and you can spend this
time rolling on the ground and laughing at the people who claim that
Haskell is useless for practical computations, because they don't know
how to implement some middle-Chinese chess in it.


Jerzy Karczmarczuk
Caen, France