is most likely transcendental. According to Efimov's original paper, the magic value "22.7" (we shall M) is given exactly by e^(pi / |s0|), where s0 is a pure imaginary solution (very close to i) of an equation (9) he derives earlier and is related to the three-body problem (there are an infinite number of real solutions s1,s2...). If you define s0 = i x where x is real, then (by converting from trig to hyperbolic trig) it can be shown that the number M is given by e^(pi / x), where x is the positive real solution to:
0 = (8 / sqrt(3)) sinh( pi * x / 6) - x * cosh( pi * x / 2)
If you copy/paste the right-hand side into the WolframAlpha website, you will see that the curve has exactly two non-zero solutions, approximately (+-) 1.00624.
You can ask for more digits, and it will give you x=1.0062378251027814891..., which means to eight digits, M = 22.694382595...
This equation above is a transcendental equation whose non-zero solutions are neither rational nor algebraic, and very likely M itself is also transcendental. Proving these sorts of things, however is very difficult. The best we can hope for is that the number can be expressed as an infinite expansion whose terms have a nice form which converses rapidly. A few more clicks on Wolfram Alpha and I'm sure someone will work it out.
I was referring to our own work on using neural networks for pattern recognition in images.
The research we were doing was in fact prompted by the well-documented success of neural networks in other nonlinear problems. One of the very first good examples of an applied adaptive neural network was in the standard modem of the time, which used a very small neural network to optimize the equalizer settings on each end.
Neural nets appear to have a lot more success with constructing nonlinear maps from subsets of Rn to Rm with n and m relatively small. Vision is not such a case as the input space n is very large. Once n and m get large you will require an exponentially large number of training samples, with the increased risk of falling into local minima (mitigated by simulated annealing or tunneling). In addition, if there is any inherent linearity in the problem an old-school Kalman filter may be less sexy but more useful.
Many of the success stories of neural nets are really of the "Stone Soup" variety, in which the neural network is the "Stone" and the meat-and-potatoes real work is in how to preprocess the data to reduce the dimensions n and m. One of the most amazing (non-neural) pattern-recognition apps that I have seen recently is the Shazam technology, which can identify a recorded song from 30 seconds of a (noisy) snippet. Their dimension-reducing logic involves hashes of spectrogram peak pairs. No neural nets to be seen, but absolutely brilliant and points to ways that similar things could be done in the visual domain.
Back in 1987 I was working in the Multimission Image Processing Lab at JPL/Nasa, and the whole Neural Network fad was in its second resurgence, after the original "perceptron" work of Minsky and Papert caught some attention in the early 70's. The group that I was in was mostly interesting in mapping, and in particular identifying features (e.g. soil types, vegetation, etc) from both spatial and spectral signatures. As usual, the military was also interested in this, and so Darpa was throwing a lot of loose money around, some of which fell our way.
I spent a lot of time on this project, writing a lot of neural net simulations, supervised and unsupervised learning, back-prop, Hopfield nets, reproducing a lot of Terry Sejnowski's and Grossman's work, taking trips over to Caltech to see what David Van Essen and his crew were doing with their analysis of the visual cortex of Monkey brains, trying to understand how "wetware" neural nets can so quickly identify features in a visual field, resolve 3D information from left-right pairs, and the like. For the most part, all of the neural net models were really programmable dynamical systems, and the big trick was to find ways (steepest descent, simulated annealing, lagrangian analysis) of computing a set of synaptic parameters whose response minimizes an error function. That, and figuring out the "right" error function and training sets (assuming you are doing supervised learning).
Bottom line was, not much came of all this, beyond a few research grants and published papers. The one thing that we do know now is, real biological neural networks do not learn by backward-error propagation. If they did, the learning would be so slow that we would all still be no smarter than trilobites if that. Most learning does appear to be "connectionist" and is stored in the synaptic connections between nodes, and that those connections are strengthened when the nodes that they connect often fire simultaneously. There is some evidence now of "grandmother cells" which are hypothetical cells that fire when, e.g. your grandmother comes into the room. But other than that, most of the real magic of biological vision appears to be in the pre-processing stages of the retinal signals, which are hardcoded layer upon layer of edge-detectors, color mapping, and some really amazing slicing, dicing and discrete FFT transforms of the orginal data into small enough and simple enough pieces that the cognitive part of the brain can make sense of the information.
It's pretty easy to train a small back-prop net to "spot" a silhouette of a cat and distinguish it from a triangle and a doughnut. It is not so easy to write a network simulation that can pick out a small cat in a busy urban scene, curled up beneath a dumpster, batting at a mouse....
Check out spaceweather.com. It has been around for some time, and has some excellent aurora galleries. Besides summarized ACE data, this website also features the techie-cool far side views of the sun from SOHO, computed using helioseismic holography.
For the truly worried, they offer for-fee email solar-flare alert services, which also come in handy if you just want to know when to go out to look for auroras. Anyway, most of the site is non-subscription, and it's worth a look.
There's your problem right there. An EOL (End Of Line) control character in the middle of
the data stream interrupted the listing of the species after they had only gotten
through the first 30,000 animals. Good thing their website wasn't named EOT.org or
they would have been logged out of the Internet completely...
This result is not only well known, it is classical. I'm sure there must
be some new twist to the analysis to make it publishable, but I can't find it.
The article made me search my bookshelves for an old textbook I used for teaching a class in
Applied Mathematics back in the 80's (in my starving professor phase of life):
Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow Richard Haberman, Author Prentice Hall, published 1977.
It has a very nice development of the math behind traffic flow, which also turn
out to be the 2D equations for a compressible fluid. And in a compressible fluid
the speed of flow decreases with density, causing the characteristic lines
(the direction of wave propagation) to cross, causing a classic shock wave to
form. The shock wave in traffic flow is the traffic jam. The section on Traffic
Flow is about 140 pages of the book. Select chapters names include:
Flow Equals Density Times Velocity
Conservation of the Number of Cars
Experimental Observations
Traffic Density Waves
After a Traffic Light Turns Green
Wave Propagation of Auto Brake Lights
Stationary Shock Waves
Effect of Red LIght or an Accident
and so on. It made for an interesting class (and the only math class where
I ever assigned a paper!). I recommend the book.
If only we could train people to behave in traffic as if they were an
incompressible fluid, we would never have traffic jams; but to do
that, you'd need to be trained to speed up when traffic got heavy.
Assuming a civilization was advanced enough to be able to travel
and communicate galactic distances, they would also have long ago
realized what we only recently learned, which is that the Andromeda
galaxy is due to collide with our own in about two billion years.
Probably not much they could do about that, so they charted
out another more hospitable galaxy and took off.
So long and thanks for all the fish.
The defacto purpose of the ISS is to justify the existence of the space shuttle.
The defacto purpose of the shuttle is to build the ISS, (and to give fidgety astronauts
something to do with their hands).
Science has nothing to do with it.
When I first came to work at JPL in 1987, folks were already gearing up for what they called their
"Third Annual Galileo Pre-Launch Picnic",
to be held out in the nearby Oak Grove Park (which by the way, has one of the best frisbee golf
courses on the planet--but I digress). It might have been the Fourth, but I lost count.
Those who worked on the mission would joke about this, but you could always tell that
there was some ironic bitterness in their voices. Galileo was neither the first nor the
last of the victims of the politically-inspired space shuttle, but for many at the 'lab it became the
iconic poster-child for the sacrifice that science has paid on the altar of politics and
the almost religious cult of man-in-space hero worship.
This Galileo Page barely scratches the surface of the number of ways
in which real scientists, engineers, and mathematicians had to wrack their brains trying
to fix, work-around, and ultimately solve technical problems that arose on Galileo --
problems which were entirely avoidable, and were either directly or indirectly caused
by the resources that were pulled from the unmanned science missions of JPL, Goddard,
and the like.
Galileo was originally supposed to be launched on an unmanned rocket like its esteemed
predecessors Voyagers I and II, but JPL was forced to reconfigure the probe to be
launched from the shuttle instead, again (like the IIS) to give some justification
for building the shuttle. After the Challenger disaster, the cargo bay was redesigned
and so again the probe had to be reconfigured. It has never been proved, but was suspected
that the reason that the high-gain attenna "umbrella" jammed was due to the loss of
lubricant over the many years of storage prior to its final launch. And so it went...
About the only good thing that came out of the decision to launch Galileo from the shuttle was that it forced us to look
at new data compression algorithms, so that we could store more data on the mag tape
for later broadcast over the low-gain antenna. But, given the choice, I think the
unanimous consensus was that if we had to do it all over again, we'd have told
Johnson and Kennedy to stuff it, thank you very much, and we'll stick to our plans
and launch the damn thing from a nice, reliable, unsexy but technologically sound
unmanned rocket.
Few IT people, even those who understand Patterns methodology,
have ever read the original works by the architect
Christopher Alexander.
His book A Timeless Way of Building is a masterpiece of design philosophy, that
describes the Way of building anything,
from a single chair, to a house, a neighborhood, a city, a program,
a world, or even a life. Shut down your browser, skip a couple
of RSS feeds, and take the time to read this charming little
book. My two cents.
The replies to my note are quite correct. I tracked down my old copy of "The Inventions of Daedalus",
and in the chapter on the xenon tank David Jones notes that the critical density of
xenon is 1154 kg / m^3 at 16.6 degrees C and (important point) 58 atmospheres of pressure. This is very likely not suitable for human use. He also notes that regular saline can
dissolve enough oxygen at 5 atmospheres to breath, and that some fluorocarbon liquids can
hold enough oxygen at one atmoshere. Still a cool idea!
In "The Inventions of Daedalus", scientist and author David E. Jones points out that
Xenon is a noble gas with a density greater than water. If you
combine Xenon with oxygen and put it in a really big tank, you will have a breathable gas in a tank, in which human being can float. By combining xenon with appropriate amounts of nitrogen, you can get the density close to that of humans, and it will be similar to weightlessness. Wikipedia points out that Xenon has some anaesthetic effects, which would come in handy for those bruising scrimmages...
Given that kids will soon be in the adult world,
occasionally going to bars and socializing, it is
of course important to get them aclimated as soon
as possible to mixed drinks. Certainly by the
sixth grade they should be able to distinguish
good tequila from bad (important), and by high school they should really know whether they
like their martinis with a twist or dirty.
Anything more addictive and IQ-reducing, such as
crystal meth or laptops, should be shielded from
kids until they can prove they can handle the
less destructive stuff.
The folks in Vail have obviously not read
this slashdot article about the correlation
between computer usage in the classroom and a degradation of academic performance.
Axel, et al are firmly in the predominant "Shape"
theory camp regarding smell. There is also a small
but resilient camp that wonder why certain substances
(e.g hydrogen cynanide and bitter almonds) smell very similar
but have no common molecular structure. There is no doubt that the huge genetic pool discovered by Axel produce a large variety of receptors that do *something*, and thanks to their work the pathways to the brain are now known, but exactly *what* is being detected is not well understood.
Luca Turin is the current proponent of the theory
that olfaction is at least influenced not only by
molecular shape, but also by the vibrational modes
and spectra of the molecule. Recent double-blind
experiments in March '04 put doubt on this theory, but had no absolute proof of the "shape" theory
either. Clouding the whole scientific controversy is the cult-following Turing has acquired following
the publication of Chandler Burr's book about Turin, "The Emperor of Scent".
You can find discussions of this and other
theories of smell here.
If you actually go to adobe's website and
RTFM,you will see that Adobe did the Right Thing (TM):
A DNG-format file is fully compliant with the
TIFF 6.0 Specification Standard and the ISO
TIFF-EP codification of that spec,
which was designed from day one as a fully extensible raw, processed, or whatever
image / metadata annotation spec.
BTW, TIFF was originally designed for offset printing folks, and in the 6.0 standard already
supports a huge number of colorspace models besides RGB, and has an extensible mechanism
for specifying color-data encoding and
compression schemes (you can even store JPEG
encoding in TIFF).
When I worked at the ground-data processing
section of the Jet Propulsion labs, TIFF was
occasionally used to store and transmit raw
multispectral satellite data, which consisted
of over 256 separate color-spectra bands from
far infrared to ultraviolet, stored spatially
in separate tiles.
Working together with Spot Image and other
satellite providers, NASA also helped develop
the GeoTIFF extension to TIFF, which annotates
an image with exact georeferencing information.
It looks like Adobe went the route of using
SubIFD's to define the extended data. A little
bit unfortunate, since that data will not show
up in a "tiffdump" listing of the file, but in
any case I have no doubt that folks are already
taking the spec and writing "libtiff" extensions
to parse the stuff.
For more information on TIFF, see my old, clunky
website that is chock full of invalid links,but
still has a few useful things to say:
While commercial developers may somehow be more
"serious" about the product, they are also
encumbered by business requirements to be able
to dominate the market. One strategy that MS,
for example, takes to do this is to tightly couple
components (e.g. kernel and browser) that have no
business being coupled.
The consequences for this at the security level are
a ready-made back door to root privileges.
Decoupling does not guarantee security, but it helps. It is also in conflict with many business
requirements of those aiming to take over the
marketplace.
hey... if they could embed a permanent static electric
charge in the fiber, it would repel dirt; then you
could make a suit out of it that would never wear
out and never need washing:
SIDNEY [Alex Guinness to Joan Greenwood]: Do you know what a long chain molecule is ?....
This appears to be another case of a growing
trend to create bogus agenda-laden "Institutes"
and using the names of famous thinkers to put
unearned legitimacy on highly questionable ideas.
I just did a random google on ${FamousPerson} Institute and came up with some doozies.
Slashdot Mirror
is most likely transcendental. According to Efimov's original paper, the magic value "22.7" (we shall M) is given exactly by e^(pi / |s0|), where s0 is a pure imaginary solution (very close to i) of an equation (9) he derives earlier and is related to the three-body problem (there are an infinite number of real solutions s1,s2...). If you define s0 = i x where x is real, then (by converting from trig to hyperbolic trig) it can be shown that the number M is given by e^(pi / x), where x is the positive real solution to:
0 = (8 / sqrt(3)) sinh( pi * x / 6) - x * cosh( pi * x / 2)
If you copy/paste the right-hand side into the WolframAlpha website, you will see that the curve has exactly two non-zero solutions, approximately (+-) 1.00624. You can ask for more digits, and it will give you x=1.0062378251027814891..., which means to eight digits, M = 22.694382595... This equation above is a transcendental equation whose non-zero solutions are neither rational nor algebraic, and very likely M itself is also transcendental. Proving these sorts of things, however is very difficult. The best we can hope for is that the number can be expressed as an infinite expansion whose terms have a nice form which converses rapidly. A few more clicks on Wolfram Alpha and I'm sure someone will work it out.
What happened to volumes four through seventy three ?
I was referring to our own work on using neural networks for pattern recognition in images.
The research we were doing was in fact prompted by the well-documented success of neural networks in other nonlinear problems. One of the very first good examples of an applied adaptive neural network was in the standard modem of the time, which used a very small neural network to optimize the equalizer settings on each end.
Neural nets appear to have a lot more success with constructing nonlinear maps from subsets of Rn to Rm with n and m relatively small. Vision is not such a case as the input space n is very large. Once n and m get large you will require an exponentially large number of training samples, with the increased risk of falling into local minima (mitigated by simulated annealing or tunneling). In addition, if there is any inherent linearity in the problem an old-school Kalman filter may be less sexy but more useful.
Many of the success stories of neural nets are really of the "Stone Soup" variety, in which the neural network is the "Stone" and the meat-and-potatoes real work is in how to preprocess the data to reduce the dimensions n and m. One of the most amazing (non-neural) pattern-recognition apps that I have seen recently is the Shazam technology, which can identify a recorded song from 30 seconds of a (noisy) snippet. Their dimension-reducing logic involves hashes of spectrogram peak pairs. No neural nets to be seen, but absolutely brilliant and points to ways that similar things could be done in the visual domain.
I spent a lot of time on this project, writing a lot of neural net simulations, supervised and unsupervised learning, back-prop, Hopfield nets, reproducing a lot of Terry Sejnowski's and Grossman's work, taking trips over to Caltech to see what David Van Essen and his crew were doing with their analysis of the visual cortex of Monkey brains, trying to understand how "wetware" neural nets can so quickly identify features in a visual field, resolve 3D information from left-right pairs, and the like. For the most part, all of the neural net models were really programmable dynamical systems, and the big trick was to find ways (steepest descent, simulated annealing, lagrangian analysis) of computing a set of synaptic parameters whose response minimizes an error function. That, and figuring out the "right" error function and training sets (assuming you are doing supervised learning).
Bottom line was, not much came of all this, beyond a few research grants and published papers. The one thing that we do know now is, real biological neural networks do not learn by backward-error propagation. If they did, the learning would be so slow that we would all still be no smarter than trilobites if that. Most learning does appear to be "connectionist" and is stored in the synaptic connections between nodes, and that those connections are strengthened when the nodes that they connect often fire simultaneously. There is some evidence now of "grandmother cells" which are hypothetical cells that fire when, e.g. your grandmother comes into the room. But other than that, most of the real magic of biological vision appears to be in the pre-processing stages of the retinal signals, which are hardcoded layer upon layer of edge-detectors, color mapping, and some really amazing slicing, dicing and discrete FFT transforms of the orginal data into small enough and simple enough pieces that the cognitive part of the brain can make sense of the information.
It's pretty easy to train a small back-prop net to "spot" a silhouette of a cat and distinguish it from a triangle and a doughnut. It is not so easy to write a network simulation that can pick out a small cat in a busy urban scene, curled up beneath a dumpster, batting at a mouse....
To do that, you need a dog.
Check out spaceweather.com. It has been around for some time, and has some excellent aurora galleries. Besides summarized ACE data, this website also features the techie-cool far side views of the sun from SOHO, computed using helioseismic holography. For the truly worried, they offer for-fee email solar-flare alert services, which also come in handy if you just want to know when to go out to look for auroras. Anyway, most of the site is non-subscription, and it's worth a look.
There's your problem right there. An EOL (End Of Line) control character in the middle of the data stream interrupted the listing of the species after they had only gotten through the first 30,000 animals. Good thing their website wasn't named EOT.org or they would have been logged out of the Internet completely...
- Flow Equals Density Times Velocity
- Conservation of the Number of Cars
- Experimental Observations
- Traffic Density Waves
- After a Traffic Light Turns Green
- Wave Propagation of Auto Brake Lights
- Stationary Shock Waves
- Effect of Red LIght or an Accident
and so on. It made for an interesting class (and the only math class where I ever assigned a paper!). I recommend the book. If only we could train people to behave in traffic as if they were an incompressible fluid, we would never have traffic jams; but to do that, you'd need to be trained to speed up when traffic got heavy.Assuming a civilization was advanced enough to be able to travel and communicate galactic distances, they would also have long ago realized what we only recently learned, which is that the Andromeda galaxy is due to collide with our own in about two billion years. Probably not much they could do about that, so they charted out another more hospitable galaxy and took off. So long and thanks for all the fish.
- The defacto purpose of the ISS is to justify the existence of the space shuttle.
- The defacto purpose of the shuttle is to build the ISS, (and to give fidgety astronauts
something to do with their hands).
Science has nothing to do with it.When I first came to work at JPL in 1987, folks were already gearing up for what they called their "Third Annual Galileo Pre-Launch Picnic", to be held out in the nearby Oak Grove Park (which by the way, has one of the best frisbee golf courses on the planet--but I digress). It might have been the Fourth, but I lost count. Those who worked on the mission would joke about this, but you could always tell that there was some ironic bitterness in their voices. Galileo was neither the first nor the last of the victims of the politically-inspired space shuttle, but for many at the 'lab it became the iconic poster-child for the sacrifice that science has paid on the altar of politics and the almost religious cult of man-in-space hero worship.
This Galileo Page barely scratches the surface of the number of ways in which real scientists, engineers, and mathematicians had to wrack their brains trying to fix, work-around, and ultimately solve technical problems that arose on Galileo -- problems which were entirely avoidable, and were either directly or indirectly caused by the resources that were pulled from the unmanned science missions of JPL, Goddard, and the like.
Galileo was originally supposed to be launched on an unmanned rocket like its esteemed predecessors Voyagers I and II, but JPL was forced to reconfigure the probe to be launched from the shuttle instead, again (like the IIS) to give some justification for building the shuttle. After the Challenger disaster, the cargo bay was redesigned and so again the probe had to be reconfigured. It has never been proved, but was suspected that the reason that the high-gain attenna "umbrella" jammed was due to the loss of lubricant over the many years of storage prior to its final launch. And so it went...
About the only good thing that came out of the decision to launch Galileo from the shuttle was that it forced us to look at new data compression algorithms, so that we could store more data on the mag tape for later broadcast over the low-gain antenna. But, given the choice, I think the unanimous consensus was that if we had to do it all over again, we'd have told Johnson and Kennedy to stuff it, thank you very much, and we'll stick to our plans and launch the damn thing from a nice, reliable, unsexy but technologically sound unmanned rocket.
I feel much better now.
Few IT people, even those who understand Patterns methodology, have ever read the original works by the architect Christopher Alexander. His book A Timeless Way of Building is a masterpiece of design philosophy, that describes the Way of building anything, from a single chair, to a house, a neighborhood, a city, a program, a world, or even a life. Shut down your browser, skip a couple of RSS feeds, and take the time to read this charming little book. My two cents.
If they become any kind of threat to Cisco, all Cisco needs to do is to buy the company, and render the issue moot.
The replies to my note are quite correct. I tracked down my old copy of "The Inventions of Daedalus", and in the chapter on the xenon tank David Jones notes that the critical density of xenon is 1154 kg / m^3 at 16.6 degrees C and (important point) 58 atmospheres of pressure. This is very likely not suitable for human use. He also notes that regular saline can dissolve enough oxygen at 5 atmospheres to breath, and that some fluorocarbon liquids can hold enough oxygen at one atmoshere. Still a cool idea!
In "The Inventions of Daedalus", scientist and author David E. Jones points out that Xenon is a noble gas with a density greater than water. If you combine Xenon with oxygen and put it in a really big tank, you will have a breathable gas in a tank, in which human being can float. By combining xenon with appropriate amounts of nitrogen, you can get the density close to that of humans, and it will be similar to weightlessness. Wikipedia points out that Xenon has some anaesthetic effects, which would come in handy for those bruising scrimmages...
Anything more addictive and IQ-reducing, such as crystal meth or laptops, should be shielded from kids until they can prove they can handle the less destructive stuff.
The folks in Vail have obviously not read this slashdot article about the correlation between computer usage in the classroom and a degradation of academic performance.
Luca Turin is the current proponent of the theory that olfaction is at least influenced not only by molecular shape, but also by the vibrational modes and spectra of the molecule. Recent double-blind experiments in March '04 put doubt on this theory, but had no absolute proof of the "shape" theory either. Clouding the whole scientific controversy is the cult-following Turing has acquired following the publication of Chandler Burr's book about Turin, "The Emperor of Scent".
You can find discussions of this and other theories of smell here.
http://www.rathergood.com/independent_woman/
(Flash required)
One of my favorite sites !
A DNG-format file is fully compliant with the TIFF 6.0 Specification Standard and the ISO TIFF-EP codification of that spec, which was designed from day one as a fully extensible raw, processed, or whatever image / metadata annotation spec.
BTW, TIFF was originally designed for offset printing folks, and in the 6.0 standard already supports a huge number of colorspace models besides RGB, and has an extensible mechanism for specifying color-data encoding and compression schemes (you can even store JPEG encoding in TIFF).
When I worked at the ground-data processing section of the Jet Propulsion labs, TIFF was occasionally used to store and transmit raw multispectral satellite data, which consisted of over 256 separate color-spectra bands from far infrared to ultraviolet, stored spatially in separate tiles.
Working together with Spot Image and other satellite providers, NASA also helped develop the GeoTIFF extension to TIFF, which annotates an image with exact georeferencing information.
It looks like Adobe went the route of using SubIFD's to define the extended data. A little bit unfortunate, since that data will not show up in a "tiffdump" listing of the file, but in any case I have no doubt that folks are already taking the spec and writing "libtiff" extensions to parse the stuff.
For more information on TIFF, see my old, clunky website that is chock full of invalid links,but still has a few useful things to say:
http://home.earthlink.net/~ritter/tiff
--Niles (original GeoTIFF and TIFF webpage author)
While commercial developers may somehow be more "serious" about the product, they are also encumbered by business requirements to be able to dominate the market. One strategy that MS, for example, takes to do this is to tightly couple components (e.g. kernel and browser) that have no business being coupled.
The consequences for this at the security level are a ready-made back door to root privileges.
Decoupling does not guarantee security, but it helps. It is also in conflict with many business requirements of those aiming to take over the marketplace.
--I think we're all bozos on this data bus.
hey... if they could embed a permanent static electric charge in the fiber, it would repel dirt; then you could make a suit out of it that would never wear out and never need washing:
SIDNEY [Alex Guinness to Joan Greenwood]: Do you know what a long chain molecule is ?....
Submitted for your Approval:
Pick your own favorite philosopher and google 'em yourself. You'll be amazed at the bizarre ideas attributed to them...