Fridger's Unicorn & "warped extra dimensions"

General physics and astronomy discussions not directly related to Celestia
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Post #21by t00fri » 03.09.2003, 00:04

jamarsa wrote:After reading the NYT article, I have a strange idea rounding my mind...

The article says that it could be possible, in time, that the 'warped' six remaining dimensions would unwarp in time, as result of the loss of energy. It could be that the Big-Bang would be, in fact, the expansion of the first four (and actual) dimensions? Or perhaps they unfolded one at a time (being the first the 'time' one, of course :wink: ), thus converting from an one-dimension to 2-dim, 3-dim and so on?

Wild idea, don't you think?


I wonder how my wife would look like in 10 dimensions;-)
I guess, it's time to go to bed now...

Bye Fridger

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Post #22by t00fri » 03.09.2003, 00:17

Oh yes, and just before I go to bed:

I have meanwhile read the article "The New Cosmology" by Wendy Freedman and Michael Turner in the October issue of Sky & Telescope.

I can highly recommend it to anyone with an interest in these exciting new developments!

I know Mike Turner personally since many years. He is a most knowledgable, charismatic Professor at Chicago University, working since decades at the interface between cosmology and particle physics.

So the article is well worth investing a few bucks at the nearest news stand...

Bye Fridger

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Post #23by don » 03.09.2003, 06:01

--------
Sorry this is belated. We had a nasty thunderstorm go over us this afternoon and I shut everything down in the middle of my reply. Just now getting back to the PC (11 pm)...
--------

Howdy Fridger,

I'll bet you were a GREAT teacher as you worked your way up, yes? :D Thank you very much for chatting with us "armchair physicists", as you have time. It is *VERY* mentally stimulating! I have one heck of a headache, but for once in many years, it's for a positive reason <grin>.


t00fri wrote:Clearly, I can hardly anymore go explicitly though all of your questions and comments ...
Agreed. I had considered breaking the questions/sub-topics up into individual post topics, but it got too late this morning <frown>. It might still be a good idea to do this when you reply to one of the items on the list you created. That way we can keep the individual sub-topics separate, instead of having this thread become a 1,000 message monster. Personally, I wouldn't worry about who asked what question, since anyone reading this thread is more than likely interested in most all of it. :)


t00fri wrote:--again what is a warped space-time geometry?
When you reply to this one ... The NY Times article mentioned above (which is pretty good - thanks guys!) related the six "invisible" dimensions as being like the small loops in a carpet (with the carpet being our observable universe). This made sense to me.

When I see the word "warped", I think of a piece of untreated, cut lumber that has been sitting outside in the rain and sun for several months. It gets "warped" in both directions, length-wise and width-wise.

However, might "warped" dimensions be better described as "curved" or "bent", like bending a piece of sheetmetal to form a "U"? Or, warped in some other, complex geometrical manner?

The bottom line on this sub-topic is not so much to describe *what* warped means, but why these extra dimensions are supposed to be (theoretical), or are (verified), "warped, and what you and your team are actually doing (looking into, theorizing, etc.) along the lines of "warped extra dimensions" :)


--------< Thunderstorm Break -- several hours later .... >----------


t00fri wrote:-- meaning and relations of: dark energy, cosmological constant, vacuum energy, zero point energy
--purpose of extra dimensions (for theoretical physicists)?
--why are six dimensions fashionable?
--Hawking's state of health
--why we hope to produce little black holes at the next generation of particle accelerators?
--good reviewer names for "strings, branes, extra dimensions, new cosmology..."

If I forgot anything crucial, please let me know, while I am thinking how to present these things in a non-tech and most intuitive manner....

I think that pretty much covers all the questions I had.

It would be interesting to find out how we might, or are, interacting with (directly or indirectly) these warped extra dimensions (WEDs). Such as, what kind of measurements can we take (temp, density, composition, etc.?), how would they be, or are they performed, and what are we "expecting" to see / find in these measurements?

Can we currently create WEDs, or only "non-warped" extra dimensions? Or are *all* extra dimensions "warped" by definition?

Are they observable?

If we can create millimeter size extra dimensions, can we create even bigger ones? Or are we simply "coaxing" existing microscopic extra dimensions to become "large", meaning one millimeter, in a specific area we define?

Thank you once again Fridger, for this most enlightening conversation! :) :D 8O

-Don G.

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Post #24by don » 03.09.2003, 06:12

selden wrote:Perhaps I wasn't clear enough, although you may be writing about possibilities, while I was writing about current events.

Hi Selden,

I appreciate that there are "bad apples" in *every* croud / business / endeavor. But, ZPE is a topic for another thread. :) I just don't want to waste time or space discussing it in this very good thread. Okay? If someone wants to start another thread on ZPE, it will probably end up in Purgatory anyway, since it is *not* "real" physics. Just my two cents. :)

-Don G.

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Post #25by don » 03.09.2003, 06:58

t00fri wrote: "Dark energy, cosmological constant, vacuum energy, zero point energy"

Thus according to the basic credo, theorists would naturally expect the vacuum energy density of gravitation to be of order

O(1)* Lambda_P^4 = O(1) 10^76 GeV^4 !!!

a huuuuuuuuuuuuuuuuuuge value or else exactly zero, e.g. due to some symmetry, like Supersymmetry.
INFINITE (practically) or ZERO, but never anywhere in between, even via any other symmetry or the warping of space-time?


t00fri wrote:... convincing evidence that the

gravitational vacuum energy = dark energy = cosmological constant

is different from zero, but so small that again we have no natural energy scale available that may account for it!
If it is so small, then how is it accelerating the expansion of the entire universe? Because of the massive *amount* (or size) of the gravitational vacuum within the universe?


t00fri wrote:The "hierarchy problem" has an entirely new facet, it is now considerably aggravated!
But of course! :lol: That's the FUN of being a theoretical physicist, right? 8O New twists and turns every other day!


t00fri wrote:... in the expectation of detecting this expected deceleration. What has instead been observed was an acceleration, associated with this non-vanishing dark energy!! Spectacular and most unexpected...

Is the acceleration the same everywhere in the universe, or is it faster and faster the further out (back in time) one looks?

If the vacuum itself, in our universe, and everything contained within it, is being "stretched" like a sheet of rubber (expanding) then what is the force / energy / process causing the stretching itself? Is it self-contained (ie. a "bubble" of force/energy in the vacuum decides to double its size, like cell replication), or is it external (opposing forces all around the edges of the rubber sheet pulling it apart)? If it is internal, where does the extra force/energy come from to make the existing force/energy twice it's size?

Here's a kicker question ... :wink: ... Is *everything* in our universe being expanded / stretched at an accelerated rate, including time? I would assume the answer to be yes, since the other 3 dimensions are being expanded. If so, how could this be computed / observed? And at what rate would it be happening? What effect would we observe over a lifetime (if any)?

Thank you for a very educational thread Fridger!

-Don G.

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Post #26by don » 03.09.2003, 07:08

jamarsa wrote:... thus converting from an one-dimension to 2-dim, 3-dim and so on?

Wild idea, don't you think?

The same thought entered my mind and my wife and I discussed it at dinner tonight, before I turned my PC back on.

Fridger, does string theory tell us that the remaining 6 dimensions will all "unravel" in one instant, or is this "one at a time" unraveling (like the petals of a rosebud) actually a possibility -- when the Cosmic Constant starts to decrease (instead of it's current increase), but has not completely gone to zero?

In my mind, as of tonight anyway, I am viewing the Cosmic Constant as being similar to a "pressure", like in a pressure cooker, or someone's exhaling breath blowing up a balloon. Therefore, the question arises, is it possible that the Cosmic Constant is cyclic? Like the person blowing up the balloon stopping to take a breath, and then continuing to exhale into the balloon.

-Don G.

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Post #27by don » 03.09.2003, 07:14

t00fri wrote:I wonder how my wife would look like in 10 dimensions;-)
Would that be WARPED dimensions, infolded or unraveled? Baked, or boiled? :lol:

Say goodnight Fridger ...


t00fri wrote:I guess, it's time to go to bed now...

Goodnight Fridger. :)

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Post #28by don » 03.09.2003, 07:20

t00fri wrote:... the article "The New Cosmology" by Wendy Freedman and Michael Turner in the October issue of Sky & Telescope.

I can highly recommend it to anyone with an interest in these exciting new developments!
I, for one, have already ordered the back-issue you mentioned earlier, along with one of their pay-per-view articles, and am waiting for the Barnes & Noble book store in the city to get their shipment of the October issue. All they have right now is September. Maybe they should change the name of their magazine to Sky, Telescope and Physics? :P


t00fri wrote:I know Mike Turner personally since many years.

It is always good to have a referral, thanks Fridger! :)

-Don G.

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Post #29by t00fri » 03.09.2003, 19:28

jamarsa wrote:After reading the NYT article, I have a strange idea rounding my mind...

The article says that it could be possible, in time, that the 'warped' six remaining dimensions would unwarp in time, as result of the loss of energy. It could be that the Big-Bang would be, in fact, the expansion of the first four (and actual) dimensions? Or perhaps they unfolded one at a time (being the first the 'time' one, of course :wink: ), thus converting from an one-dimension to 2-dim, 3-dim and so on?

Wild idea, don't you think?


Javier,

indeed such an "anti-compactification" sounds odd and honestly, I have never heard of it either...

On the one hand, it might indeed be not forbidden, but I feel it would be most unprobable.

Here is a perhaps better known analogue from thermodynamics: The 2nd principal theorem of thermodynamics is basically an "empirical theorem", stating the impossibility of a "perpetuum mobile of the second kind"! Of course, it refers to irreversible processes, that are allowed by energy conservation etc.

What does that mean in practice? Here comes an example:

According to the conservation law of the total energy and the first principal theorem of thermodynamics the following would be possible:

A brick that fell down from a roof might in principle jump back onto it, by drawing the required kinetic energy out of its heat energy content by cooling off. Such reversed processes have never been observed;-). This is precisely expressed by the 2nd theorem...

Back to "anti-compactification". I am quite certain that also here, there is intrinsic irreversibility at work...

Bye Fridger
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Post #30by t00fri » 03.09.2003, 19:59

don wrote:
t00fri wrote:--again what is a warped space-time geometry?
...
When you reply to this one ... The NY Times article mentioned above (which is pretty good - thanks guys!) related the six "invisible" dimensions as being like the small loops in a carpet (with the carpet being our observable universe). This made sense to me.


This is an excellent comparison!

I had elaborated a bit on the process of compactification in string theory earlier in the original Unicorn thread.
A short reminder: String theory can be consistently formulated only in 10 (or 11) dimensions. In other dimensions there would be tachyons that would destroy causality etc... ("unkissed mothers;-)"..). So a mechanism is needed to "get rid" of the extra six dimensions somehow. The idea is that these "curl up" so to speak into tiny little 6d spheres in each 4d space-time point during some kind of "dimensional collapse" <=> "compactification". Unfortunately, there are many different kinds of geometries possible and lots of uncertainties arise at this (necessary) step string theory has to undergo! There is the possibility of warped geometries but other simpler /and/ much more contrived scenarios are also thinkable.

Back to

warped extra dimensions

Consider again the cylinder as an intuitive example of a non-warped geometry wrto the extra dimension (the circle around which our "2d" model world is wrapped (the cylinder's surface).

In this case, the metric on the surface of the cylinder is always the same, no matter at which point of the circle (extra dimension) I am looking.

Mathematically the cylinder geometry is said to factorize into the 2d surface sheet and the circle.

But suppose I decide to sew the upper half and the lower half circle together ( i.e. identify it), then mathematicians would call the resulting geometrical object an "orbifold". This horrible thing would be a warped geometry, for example!

Got at least a feeling what this is up to?


Bye Fridger

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Reading

Post #31by t00fri » 03.09.2003, 21:06

Reading

Since the Celestia forum always provides the latest and hottest access to the frontiers of science;-), here are a few links from one of our biggest conferences that took place this year at Fermi National Lab in Batavia/Illinois barely 2 weeks ago. It may be just fine for people living 50 miles away from the nearest news stand;-)...

Normally, I would also have attended it, but this time I was simply too busy...

Here are some interesting talks (transparencies) that you may either just browse or download. You may also switch to live video performance of all speakers if you prefer...

The URL with the whole (clickable) programme is here, for you to browse...and click according to taste/interest:

http://conferences.fnal.gov/lp2003/program/index.html#S9

These talks might be of particular interest in our context:

1) Cosmic Microwave Background Experiments (Wmap, latest!)
http://conferences.fnal.gov/lp2003/program/S9/verde_s09.pdf

2) Dark Matter & Energy:
http://conferences.fnal.gov/lp2003/program/S9/kirshner_s09_updated.pdf

3) Dark Matter experiments:

http://conferences.fnal.gov/lp2003/program/S10/dejesus_s10_ungarbled.pdf

4) Conference Summary:

http://conferences.fnal.gov/lp2003/program/S17/murayama_s17.pdf

Of course it is difficult for me to anticipate people's background in these matters. But judging from the kind of (clever) questions that were posed here, I feel the level of these talks would not be too much advanced (mostly). They are usually kept quite general and non-technical, since also many of the >1000 delegates from all over the world have substantially varying backgrounds. Of course, all of them are physicists...

Enjoy,

Bye Fridger

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Post #32by don » 04.09.2003, 07:30

NYT Article wrote:The hitch, in each case, was that the acceleration would be only temporary. It might last an extremely long time, but eventually the dark energy of the cosmological constant would melt away, decaying just in time to avoid the problems of permanent acceleration that string theorists have worried about. The universe would then coast for the rest of eternity.

The work followed on previous work by Dr. Kachru with Dr. Joseph Polchinski of the Santa Barbara Institute and Dr. Steven Giddings of the University of California at Santa Barbara, and by Dr. Polchinski and Dr. Raphael Bousso of the University of California at Berkeley.

Part of the reason dark energy decays, explained Dr. Linde of Stanford, is that these solutions describe the four-dimensional universe we observe around us — three dimensions of space and one of time — with the other six curled up so tightly that they cannot provide closet space. But it takes energy to keep the extra dimensions confined.

"In the long run," he said, "the universe doesn't want to be four-dimensional. It wants to be 10 dimensions."

So sooner or later, the loops will unravel like a tangle of rubber bands, passing through a succession of configurations that take less and less energy to maintain, until finally the other dimensions expand and the cosmological constant is gone.

The decay of the cosmological constant will be fatal, astronomers agree. At that moment a bubble of 10-dimensional space will sweep out at the speed of light, rearranging physics and the prospects of atoms and planets, not to mention biological creatures.

"What it leaves behind," Dr. Susskind said, "it's hard to say. Almost certainly not a livable universe."
jamarsa wrote:The article says that it could be possible, in time, that the 'warped' six remaining dimensions would unwarp in time, as result of the loss of energy. [quoted above]
t00fri wrote:On the one hand, it might indeed be not forbidden, but I feel it would be most unprobable.

In case you have not had time to read the article Fridger, I pulled out the quote that Javier was referring to and placed it above.

What you write makes sense. What the string theory supposes (10 or 11 dimensions with 6 or 7 collapsed, leaving our 4) makes sense. But what the folks in this article appear to be saying is that the process *might* reverse. This brings to mind our prior thoughts of our expanding universe one day slowing down and eventually reversing, beginning to collapse.

All part of the scientific process. Theories remain theories until proven (verified) or dis-proven (mathematically or otherwise), right? :)

-Don G.

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Post #33by don » 04.09.2003, 07:53

t00fri wrote:Mathematically the cylinder geometry is said to factorize into the 2d surface sheet and the circle.

But suppose I decide to sew the upper half and the lower half circle together ( i.e. identify it), then mathematicians would call the resulting geometrical object an "orbifold". This horrible thing would be a warped geometry, for example!

Got at least a feeling what this is up to?

Great example Fridger. Yes, that truly would be "warped".

Now, as usual, there are questions :D ...

Are the sheet (our 4 dimensions) and the circle (warped dimension) physically connected or attached to each other? If so, that would mean our four dimensions should also be warped, which they do not appear to be, at least to us. Or, a better term would be "combined", as half of our universe would be combined with the other half, as the circle was folded into 1/2 it's original size.

Thus, I would assume that our dimensions are *not* attached to the warped dimension.

But, if they are *not* connected, then why would our universe want to wrap itself around the shape of the circle? Or did the circle initially shape itself to the interior of the cylinder (our universe)?

Thank you Fridger!

-Don G.

PS. Does the name James Stadelmann (Physicist) ring any bells, from the years past? He is a somewhat short, German fellow, who used to work at an accelerator in Illinois (operations), back in the 60's or 70's I think.

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Re: Reading

Post #34by don » 04.09.2003, 08:42

t00fri wrote: Reading

Howdy Fridger,

Thank you for this weeks reading assignment! :D

It will keep me busy for a while.

-Don G.

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Re: Reading

Post #35by don » 04.09.2003, 10:29

t00fri wrote:1) Cosmic Microwave Background Experiments (Wmap, latest!)
http://conferences.fnal.gov/lp2003/program/S9/verde_s09.pdf
Oooooooo, nice graphics! :P

Actually, when viewing their "Cosmic History" slide, my mind immediately thought of a coal-fired power plant furnace, whereby finely ground coal powder is injected and ignited at a very high temperature, towards the top of the furnace, just below the water boilers, releasing all kinds of radiation (primarily heat), gasses, etc. with the resulting particles "spent" fuel (ash) falling downwards to the residue collectors.

Which means what? Well, it logically follows that the initial singularity from which the big bang happened was definately an infinate mass of some kind (speck of ground coal dust in someone's BIG furnace?). Thus, our physical universe is the residue (mess to be cleaned up and thrown away) of something very useful to someone else -- heat. :lol:

Sorry, I just can't stop my philosopher mind from wandering and trying to relate new data to existing data.

I won't pretend to understand everything presented in these slides, but ...

Now I understand why you (and probably many, many other 'cosmologists') are so excited about the recent CMB measurements from WMAP ... "We have a standard cosmological model: 6 (or 7) parameters fit all." KEWEL!

As to z~17, I've heard "turn the lights on" many times, but to have the newly formed stars re-ionize the entire universe -- that is amazing! Shapiro, et al., have done some great work through the years on describing how it all happened too. Just read a few of their papers (ie. "Photoevaporation of Cosmological Minihalos during Reionization" http://lanl.arxiv.org/PS_cache/astro-ph/pdf/0307/0307266.pdf).

I also learned what CDM and LCDM stands for, ie. "Flat LCDM still fits: 6 parameters fit 1348 points" ... Lambda-Cold Dark Matter, which I had not seen before.

I'll leave the other slides for tomorrow.


t00fri wrote:But judging from the kind of (clever) questions that were posed here, ...

Clever? In what way? I didn't know I had "clever" in me.

Thank you Fridger.

-Don G.

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Post #36by jamarsa » 04.09.2003, 18:23

don wrote:In case you have not had time to read the article Fridger, I pulled out the quote that Javier was referring to and placed it above.


Yes, exactly that!! Thanks for your remark, don. But the current configuration seems to be stable, doesn't it? However, as time is counted as a dimension too, I'm not sure if 'duration' can be seen as a correct measure...

I have some more 'wild' ideas about current dimensions right now (specially the perceived differences between the 'spatial' dimensions and the 'temporal' one), but they need more consideration (and reading the 'homework' proposed :wink: ) before commenting here.

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Post #37by t00fri » 04.09.2003, 19:34

don wrote:
NYT Article wrote:The hitch, in each case, was that the acceleration would be only temporary. It might last an extremely long time, but eventually the dark energy of the cosmological constant would melt away, decaying just in time to avoid the problems of permanent acceleration that string theorists have worried about. The universe would then coast for the rest of eternity.

The work followed on previous work by Dr. Kachru with Dr. Joseph Polchinski of the Santa Barbara Institute and Dr. Steven Giddings of the University of California at Santa Barbara, and by Dr. Polchinski and Dr. Raphael Bousso of the University of California at Berkeley.

Part of the reason dark energy decays, explained Dr. Linde of Stanford, is that these solutions describe the four-dimensional universe we observe around us — three dimensions of space and one of time — with the other six curled up so tightly that they cannot provide closet space. But it takes energy to keep the extra dimensions confined.

"In the long run," he said, "the universe doesn't want to be four-dimensional. It wants to be 10 dimensions."

So sooner or later, the loops will unravel like a tangle of rubber bands, passing through a succession of configurations that take less and less energy to maintain, until finally the other dimensions expand and the cosmological constant is gone.

The decay of the cosmological constant will be fatal, astronomers agree. At that moment a bubble of 10-dimensional space will sweep out at the speed of light, rearranging physics and the prospects of atoms and planets, not to mention biological creatures.

"What it leaves behind," Dr. Susskind said, "it's hard to say. Almost certainly not a livable universe."
jamarsa wrote:The article says that it could be possible, in time, that the 'warped' six remaining dimensions would unwarp in time, as result of the loss of energy. [quoted above]
t00fri wrote:On the one hand, it might indeed be not forbidden, but I feel it would be most unprobable.
In case you have not had time to read the article Fridger, I pulled out the quote that Javier was referring to and placed it above.

What you write makes sense. What the string theory supposes (10 or 11 dimensions with 6 or 7 collapsed, leaving our 4) makes sense. But what the folks in this article appear to be saying is that the process *might* reverse. This brings to mind our prior thoughts of our expanding universe one day slowing down and eventually reversing, beginning to collapse.

All part of the scientific process. Theories remain theories until proven (verified) or dis-proven (mathematically or otherwise), right? :)

-Don G.


Many thanks, Don, for reproducing the relevant protion of the NYT article. Even in my almost "downtown" environment, it is about 5-10 miles to the nearest NYT;-). I usually read the NYT when I am sitting in planes...

Joseph Polchinski , Steven Giddings and Leny Susskind are indeed very well known string theorists. I was not aware of their "latest baby" I must confess. The eventual "melting" of the acceleration caused by the dark energy is very well possible and has been discussed by a number of people. The idea that we might all end up again in 10 dimensions (where we came from;-)) is definitely less convincing to me...I think there is no reversibility.

Bye Fridger

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Post #38by don » 04.09.2003, 20:07

t00fri wrote:Many thanks, Don, for reproducing the relevant protion of the NYT article.
You are welcome.


t00fri wrote:Even in my almost "downtown" environment, it is about 5-10 miles to the nearest NYT ;-) .
As Curly, from the Three Stooges might have said, "Nyuk, nyuk, nyuk. Ohhh, a wise guy!" :lol:

Unlike magazines, many city papers, like the New York Times, are on-line, so all you have to do is "let your fingers do the walking". Here is the entire article "One Cosmic Question, Too Many Answers" in printer friendly format ... http://www.nytimes.com/2003/09/02/science/space/02STRI.html?pagewanted=print&position=


t00fri wrote:The idea that we might all end up again in 10 dimensions (where we came from;-)) is definitely less convincing to me...I think there is no reversibility.

The theory just before this one in the article says that as the energy decreases, our universe would simply continue as-is (no further expansion) for eternity.

That's one of the things that can be enjoyable and positive about living in our 4 dimensions ... we each have our own, individual minds, thoughts, ideas, etc. :) However, like everything else, this too has it's negative side, which can result in war and devastation. :(

Such is life as a human on the third planet from the sun, which keeps spinning, and spinning and spinning ...

-Don G.

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Post #39by jamarsa » 04.09.2003, 20:08

t00fri wrote:Many thanks, Don, for reproducing the relevant protion of the NYT article. Even in my almost "downtown" environment, it is about 5-10 miles to the nearest NYT;-). I usually read the NYT when I am sitting in planes...



Ahem... I was reading the online edition, available even in your downtown environment (and mine). 8)

Here is the article.


Oops!! A little too late..

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Post #40by t00fri » 04.09.2003, 20:28

Let's perhaps do this one next:

Stephen Hawking's state of health

I actually have no first hand info about his latest health status. His story is really sad and phantastic at the same time. Some of it, I know first hand...

As I was told in Cambridge/UK, a long time ago, the story started like this:

On the occasion of his (brilliant) PhD, his parents gave him as a present, a (cultural) trip to Egypt for which he had to be vaccinated, of course. The vaccination in turn was considered the cause for this progressive and extremely rare neuronal infection.

Stephen Hawking is generally believed to have MND - Motor Neurone Disease. If he has, it's a most unusual case, because his has plateaued since he was 27, and that's unique in medical annals. Everyone else who has full-blown MND dies, in about 2- 4 years. Hawking probably has one of the numerous similar but not entirely progresive diseases, pretty much (but not quite) as horrible as MND, a disease which progressively turns off your body, leaving your brain fully active and aware right to the end.

I got to know him personally (and on a daily basis) many years ago, when visiting the Department of Applied Math and Theoretical Physics (DAMTP) in Cambridge's Silver Street as a guest Prof. We all used to meet around 11 am for tea (of course;-)). A little while after having been introduced to him on the first day, I remember, his face turned suddenly red then blue and I was really getting worried! But I seemed to be the only one... He had apparently inhaled some tea into his trachea, and of course was unable to go on breathing normally. During all this, he remained very calm and in serene mood. It was apparently a quite normal event for him.

At the time I could not understand anymore what he was saying, while his friends who took continuously care of him, apparently understood him perfectly well. He used to regularly attend the Theoretical Physics seminars at DAMPT and usually made lots of comments during the talks. Yet only a few were able to understand the "noises" he made and sometimes "insiders" used to translate.

Later as we know, he entirely depended on a voice computer. Also, I remember in his office, there was a most sophisticated machine installed that he used for reading books and journals. While I was in Cambridge he also became 'father' again...

Very frequently, one could see him in his motorized wheelchair in the streets of Cambridge...until a few years later, he was hit by a car and had a very serious accident.

This ends the story of my personal encounter with this ingenious and most unusual human being...

Bye Fridger
Last edited by t00fri on 04.09.2003, 21:10, edited 2 times in total.


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