Email exchange, also archived to Syn-L, one typo fixed.
Return to An Introduction to Quadrays
Date: Wed, 22 Jul 1998 14:11:30 -1000 From: "D. Lloyd Jarmusch"
To: email@example.com Subject: Quadrays and Nuclear Fusion I was astonished to find your web pages on the quadray system. A month or so ago I had no idea that anyone besides myself had ever conceived the system, much less developed it to the point you have. Your work is brilliant and well presented, and you are to be congratulated for your contributions to the advancement of knowledge. I developed the system myself, independently, back in 1981, and at the time I also called it the quadray system (lately I had been calling it a quadraxial Cartesian system, I notice you call it a NeoCartesian system). I was somewhat surprised that our systems are so similar, right down to the notation for coordinates and the fact that every point has a unique address where at least one of the coordinates is zero and all the others are non negative. In retrospect I should not have been surprised since the system is so natural that it was inevitable that others would come up with it as well. I though you might be interested to know that when I conceived the system myself in 1981 I immediately thought that, since it seemed more "natural" than the rectangular Cartesian system it would be useful in solving some of the problems that physics is struggling to solve using the rectangular system. The first problem of physics I thought to address was the confinement of plasmas in nuclear fusion. It seemed to me that the quadray system revealed a fundamental aspect of nature, that is that space is what I call "four-directional". It seemed to me that the problem of magnetic confinement might be better addressed if physicists were to concentrate on confining the movement of the plasma in any of the four directions, thus forming the plasma into a tetrahedral shape. The problem of magnetic confinement is very complex, and I was merely a freshman studying philosophy, and none of the physicists I talked to were interested in my new coordinate system, so I gave up the problem after a short while. Suddenly in 1993 it occurred to me that fusion might be achieved by colliding beams of hydrogen from the four directions indicated by the quadray system. I investigated the problem of fusion again and became convinced that my design for a nuclear fusion reactor had merit and ought to be developed further. I set out to patent and fund the reactor, and after several years of effort I am finally getting the patent. I just paid the issue fee for the patent last week. I have been trying to develop support for the concept that space is four-directional, especially in the usenet newsgroup sci.physics.fusion. A reader of the group emailed me a paper by you about the quadray system. I was very pleased to read the paper and to visit your excellent webpages on the subject. I cannot express to you how happy I am that you have developed the system so well, and have presented it in such a beautiful and well thought-out format. I will refer to your webpages often. Thank you so much for your surperb work. Aloha, D. Lloyd Jarmusch P.O. Box 677 Kilauea, Hawaii 96754 ======= Date: Wed, 22 Jul 1998 17:45:14 -0700 To: "D. Lloyd Jarmusch" From: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Thanks for your email re quadrays sir! The essential ideas came to my awareness thanks to David Chako, who shared them on Synergetics-L, a listserv re Bucky Fuller's philosophical geometry which I administer. In the 'For further reading' section of http://www.teleport.com/~pdx4d/quadrays.html you'll find a hyperlink to a verbatim excerpt from the Syn-L archives showing where David first introduced his idea (along with some of our initial feedback) ["Genesis on Synergetics-L"]. Josef Hasslberger was likewise entertaining similar notions, minus a formalized notation, and you'll find my link to his web-page on the concept at quadcolors.html (a collaborative work based on his ideas regarding quadrays and color). He calls them Tetra Space Co-ordinates. My contribution to the literature involved coming up with a distance formula and formalizing an XYZ<->quadrays conversion convention (quadxyz.html) that makes this apparatus especially useful for converging with Fuller's synergetics (the main focus of my website, 'Synergetics on the Web'). I also developed source code for outputting polyhedra saved in quadray coordinates, to Povray for ray tracing (some of the renderings need to be redone -- aspect ratio off, giving a slightly 'quashed' appearance). FoxPro Advisor, a computer magazine, has recently solicited an article on my use of VFP to do this kind of geometry work (a novel usage from the point of view of your average bread and butter xBase programmer). I give you all this by way of background and orientation vis-a-vis my viewpoint. That you came up with this same apparatus independently in 1981 (when I was just beginning to get interested in Fuller) is very interesting to me and no doubt your long term consideration of this system in tandem with physics challenges will open up some new vistas, at least from our point of view on Synergetics-L. I should also mention that David Chako has called them 'tetrays' and further elaborated the system, using the equivalence of all (n,n,n,n) from a spatial point of view to introduce a temporal index. His coordinate system increases with frequency through time and vectors come out as probability calculations (ala Pascal's triangle/ tetrahedron) relating to pathways from the origin to a terminus. But I leave the details for him to explain -- I don't pretend competence vis-a-vis his 'tetray' apparatus. As you note, I'm basically using quadrays as a close analog of XYZ, call it NeoCartesian for this reason, and use it in philosophical circles to do Wittgensteinian-type investigations of low-level math concepts e.g. "dimension" and "linear independence" (quadphil.html). Aloha, Kirby PS: with your permission, I'd like to forward your email, and this response, to Synergetics-L for sharing/archiving. I'd also like to save this exchange from a hyperlink at quadrays.html to better include your trajectory and give us a jumping-off point for future developments (both colla- borative and solo). Thanks again for getting in touch. As I'm sure you know, it's not unusual for ideas to occur to lots of folks, unbeknownst to one another -- usually indicative of something in the wind (zeitgeist and all that). === Date: Wed, 22 Jul 1998 16:06:10 -1000 From: "D. Lloyd Jarmusch" To: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Kirby Urner wrote: > Thanks for your email re quadrays sir! You are more than welcome. Thank you for the additional info in your last email. > > > ... with your permission, I'd like to forward your email, > and this response, to Synergetics-L for sharing/archiving. > I'd also like to save this exchange from a hyperlink at > quadrays.html to better include your trajectory and give > us a jumping-off point for future developments I would be flattered to have you forward my email or post it where ever you like. Thank you and aloha for now, D. Lloyd Jarmusch ===== Date: Wed, 22 Jul 1998 22:04:05 -0700 To: "D. Lloyd Jarmusch" From: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Cc: firstname.lastname@example.org >I would be flattered to have you forward my email or post it where ever >you like. > >Thank you and aloha for now, > >D. Lloyd Jarmusch > Our email exchange (sharing genesis of quadrays in our respective scenarios) is now linked from the 'For Further Reading' section of 'An Introduction to Quadrays' (www.teleport.com/~pdx4d/quadrays.html). Lets keep in touch. Your intuition that "space is four-directional" is likewise what Bucky Fuller was communicating when saying space is "four dimensional" (cite www.teleport.com/~pdx4d/terms.html#4d). Ciao, Kirby 4D Solutions