Archive for the ‘Hyperspace’ Category

That which we call a pentahedroid

Wednesday, May 1st, 2013

triakis tetrahedronWhen you turn a tetrahedron inside out so that it can contain tetrahedron-shaped standing waves, you get something already known as a triakis tetrahedron.

It is as if you sliced the original tetrahedron into four smaller ones, then put them where the original’s faces would be — but pointing outward instead of inward.

To see this, go here and compare the picture with this one.


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Two Fingers Tapping

Monday, April 22nd, 2013

MattIf I was a Native American, instead of a descendant of immigrants, that would be my name: Two Fingers Tapping.

That’s because I never learned what we used to call “touch typing”.  Now it’s called “keyboarding” and is a required subject in good schools.  But I went to school back in the Dark Ages, when dinosaurs walked the Earth and “typing” and “home economics” (i.e., cooking) were courses that only girls took.  So I never learned to type.  Took wood shop instead. Big mistake.

My father never did either.  He used a keyboard the same way I do, with only a few fingers.  It didn’t stop him from having a career and earning advanced degrees like his Master’s in Nuclear Engineering from MIT.  It didn’t stop him from programming on the Whirlwind I – the first computer with video display terminals that ran in real time.

I’ll never be half the man he was, but like him, I don’t let my primitive keyboarding stop me.  So far I’ve written three unpublished novels, all around 100,000 words, and am now working on the fourth, the conclusion to my Gamers and Gods series.

I’m not certain what I’ll write next.  Those of you who have seen my main website know that I have unfinished business with hypercube loudspeakers.  I need to get out a nonfiction book about that, but I’ve been a bit shy about approaching agents with a book proposal about that.  It’s because I’ve spent a significant part of my life as a voice crying in the wilderness trying to drag humanity kicking and screaming into the Hyperspace Age.

patent drawingAt first this was because we had a patent on the technology (U.S. Patent #4,231,446 granted Nov 4, 1980) and I thought it was going to make us rich. Well, it didn’t; I profoundly underestimated the extent to which credibility depends upon credentials. You see, I hadn’t even graduated from college yet. Imagine, if you will, a college dropout trying to tell NASA he can make a better rocket fuel.  It was kind of like that.  I literally presented to men with PhDs in Audio Engineering — you can imagine the looks on their faces when I tried to push what they considered science fiction at them.

Tom and I tried to promote the technology for years.  We knew darn well that a geometry that affects one kind of wave will affect many others.  For example, parabolic dishes are used to focus sound waves, radio waves, and microwaves.  So the remarkable behavior of sound in our shape (well, Nature’s shape, but like Kepler, we re-discovered it) was something that we knew could transform a lot of devices and industries.  So we tried.  And tried.  We exhausted ourselves and our personal finances trying to get the word out.

We didn’t get rich, of course.  And now the patent is PUBLIC DOMAIN. Can anybody out there hear me?  You can all use it for FREE.  You don’t have to pay us for discovering it.

Eventually I gave up, temporarily, and went back to college and got my Bachelor’s degree in Physics and began a career in computer programming. (It seems I always find myself following in my father’s footsteps in some ways.)  But when the Internet appeared I taught myself HTML and created my website to keep getting the message out.

I’m not finished yet.  I’ve been reading Science Fiction since I was in fourth grade.  Maybe that’s why I tested at the 14th grade reading level when I was in 9th grade.  In any event, it helped prepare me for this weird life of mine.  I have no regrets about it; I wouldn’t trade my life for anyone’s.  I have been uniquely privileged to see she shape of the future.

Now if only it gets here while I am still alive.


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A Hypercube by any other name

Wednesday, July 4th, 2012

Hypercube loudspeaker

Hypercube loudspeaker

Sometimes it’s difficult to see something sitting in plain sight.

This is because there are so many ways of looking at things. Johannes Kepler saw it as an inside-out cube. Geologists saw it as lodestone, garnet, copper, lapis lazuli.

Beekeepers saw it as an efficient use of wax and space. But their honey drawers preserved only the two-dimensional aspect of the lattice — the hexagonal grid.

Rhombic Dodecahedron

Rhombic Dodecahedron

Mathematicians saw it as a minor non-Platonic solid — an alternative form of the dodecahedron.

But we know differently. We see differently. We see that the rhombic Dodecahedron (so-called) is actually the outer envelope of one of the projections of the 4D hypercube onto 3-space.

Shakespeare might have said that that which we call a hypercube, by any other name would smell as sweet. But there is something in a name if you want to get attention. Calling this shape “one of the crystalline forms of garnet” misses the point and relegates it to obscurity.

tesseract loudspeaker

tesseract loudspeaker

Perhaps ancient describers were trapped by their 3-dimensional outlook. The Hypercube is best appreciated not as a static form but as a geometry embedded in four-dimensional spacetime. This would seem obvious in retrospect, but was not fully realized until the advent of the audio industry at the beginning of the 20th century. For the first time moving 4-dimensional sound wavefronts were being produced under controlled conditions.

When we regard the rhombic dodecahedron as a geometry embedded in spacetime affecting the propagation and movement of energy in spacetime, then we begin to see more of its possibilities.

The rhombic dodecahedron form of the hypercube excels as a wave trap. In the Middle Ages people believed that a pentagram could somehow trap a demon. Nowadays we see quantum dots trapping electrons. The RD can support cube-shaped standing waves at a wide spectrum of frequencies. Since the tapering pyramidal points crowd sound waves into turning around without hitting a solid wall, this geometry supports resonance across the spectrum. The favoritism of old-style speaker cabinets that boomed some notes and stifled others is now obsolete forever. This harnessed resonance is a result simply of altering the boundary geometry of the air inside the speaker cabinet.

It is no accident that the “rhombic dodecahedron” turns out to have acoustic advantages as a resonator; changing the shape changes the boundary, which changes the air flow, which changes the performance.

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Than Serve in Heaven: Walkabout, part II

Monday, March 12th, 2012

sisyphusOur story thus far:

Having co-invented the Hypercube resonating chamber with Thomas Weiss and after receiving U.S. Patent #4,231,446 for its application to loudspeakers, our first attempt at soliciting investors for the project failed. With family money, what little there was, we tried to manufacture them ourselves on a shoestring budget. When that effort was not crowned with success, I went back to school and got my B.S. in Physics and then did a year of graduate school.

It was while in grad school at FSU that I met and mingled my fortunes with Shirley Malone, a gifted prescriptive/diagnostic learning facilitator in private practice who saw immediately the value of hypercube resonators when she witnessed them the first time. When she moved back up north I elected to go with her, beginning an association that was to last for 18 years (until she logged out of the game in late 2000). After a couple of years of living poor in a trailer in Delaware making doughnuts and teaching at Wesley College, I found a job in Baltimore at National Training Systems teaching electronics and programming. Thus did I fall from the True Path of Physics into the outer darkness of a career in programming, what is now called Software Development.

I was asked to leave NTS in 1990 after I conferred with co-workers about suspected financial irregularities at NTS. (I later heard that the state of Maryland closed them down shortly thereafter, leaving several optimistic instructors who believed their paychecks would stop bouncing lost and twisting in the wind.) After struggling myself, I accepted a minimum-wage job at a Wendy’s near our apartment and survived long enough to find a new job at decent pay working for a company in Columbia MD called Sylvan KEE.

Instead of flipping burgers, I was programming again. Some wanted our title to be Educational Technicians, but I was dead against that; as far as I was concerned, we were Courseware Programmers. We used source code in a proprietary programming language called Veritas, (with custom modifications by a diligent staff of in-house C coders) to create “Courseware” — software that taught people how to use popular productivity tools such as MS PowerPoint, Lotus 123, WordPerfect, and so on. Using screen captures and commands to display boxes of text directions and receive mouse and keyboard input, the lessons guided user through the arcane arts of word processors, databases, and spreadsheets and followed up with unit tests and a final exam. It was a clever technology that let corporations train their employees cheaply; we sent them a stack of 3.5 inch diskettes with the courseware PKZipped across the diskettes, and all they had to do was pop them one by one into a PC’s 3.5 drive and install the courseware and let their employees have at it.

Although I was making no progress with Hypercubes, I was pretty happy with my work at KEE because I was making software that helped people. I stayed with KEE when Sylvan sold the division to SHL SystemHouse, “Canada’s IBM”. The company was renamed from KEE to SHL KEE and moved us to a new building. While I remained there I got to travel to work on a product for Canada’s Department of Transportation. I discovered that it was possible back then to cross the US/Canada border without a passport as long as I had some kind of government photo ID. I also learned that Canadians are Americans too: “America” is the continent on which the countries of Canada, the United States, Mexico, etc. all exist. North, Central, or South, it’s all America no matter which national borders you find yourself within. It’s the same in Europe, where French , Germans, Italians, and so on are all Europeans.

I was optimistically excited when I heard of the upcoming merger between SHL Systemhouse, our parent company, and MCI. I was certain it would bring new resources and opportunities and help my resume. I was wrong. This was the first time I was to fall victim of a corporate merger. For those of you who have never experienced a merger, here is a clue: a merger is a time in which you usually find unexpected staff reductions. Having spent money to make it happen, the companies involved usually announce that there will be “no major changes” just before they prune their payrolls. I was weighed and found wanting, and laid off with a severance package two weeks before Christmas after nearly five years of service. I had been hired in February, so I failed to reach the five-year mark for inclusion in the company’s pension plan.

Unexpected unemployed again, I was surprised by the unexpected pleasure of a visit from my old friend Tom Weiss, who had been doing Y2K and other programming consulting in the U.S., France, Germany, Israel, and Canada. Tom was southbound, returning to Florida because his father was losing his battle with cancer. I was sorry to hear that, but glad that Tom was still alive and employed. Tom wanted to pass control of Tesserax over to me so that I could continue efforts at promoting the technology while he was distracted by this family tragedy. He had had no more success than I had, and since there were several years left on the patent, which would expire in 1997, he wanted to let me give it another try.

I accepted his offer, bought a little voting stock to bring my portion over 50% so that we could act without having to consult Tom first, and considered my options.

Tesserax card circa 1978

Tesserax card circa 1978

It had been so many years that Tesserax had been trying and failing to make progress; I decided that it might be time to make a fresh start without all that history and baggage, so that I would not have to explain to potential investors or manufacturers why we had not been able to make it a successful product up to now. Shirley and I therefore incorporated in Delaware as Alternity and executed an agreement between Tesserax and Alternity transferring ownership of the patent to Alternity in return for sharing revenues from it with Tesserax. I considered that in this fashion I could avoid discussing past failed efforts to promote it, while keeping faith with Tesserax investors and having them share in any moneys we were finally able to make from the technology.

Alternity then began to arrange for loudspeaker testing, and to begin planning production runs to demonstrate the feasibility of manufacturing this geometry.  –MRK

Next: Getting Serious:  CAD/CAM, Not WebCam

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Building Rhombic Dodecahedra Resonators

Friday, March 2nd, 2012

hypercubeBuilding this shape can be challenging if you do not know the right geometry.

In conventional language, the shape is a truncated rhombic dodecahedron. It is made of 8 rhombuses (rhombi), 4 triangles, and 1 square.

The basic rhombus can be made from joining four triangles together. Each triangle has sides proportional to one, the square root of two, and the square root of three. Put simply, the small angles of the rhombus are both approximately 70.5 degrees and the large angles are both about 109.5 degrees.

rhombusIf you want more accuracy, the angles are 70.5287 degrees and 109.4712 degrees. This is generally accurate enough for most CAD/CAM systems.


trianglesThe triangles (whose bases meet the square where you cut a whole for the woofer) are actually half-rhombi — that is, they come from slicing the rhombus down the middle of the two big angles, making two triangles whose angles are 70.5287 degrees and 54.73565 degrees and 54.73565 degrees.
trianglesThe easiest way to proceed is to take three rhombi, lay them outer-face-up and tape them together like so.

Repeat this process to get two groups of 3 panels taped together (tripanels). Now apply a strip of tape to close up each tripanel and flip them over so you are looking at the insides or concave view.

Putting a rubber glove on your hand, get some glue on the end of your gloved index finger and trace down the Y of the three internal seams so that they are glued. Do the same for the other tripanel, and then set them to dry for an hour.

Now take these two tripanels and tape them together to make a pyramidal point corner like this. Glue the seams on the inside as before. Looking at this “hexpanel” assembly, you will see two spaces for rhombi. Tape and glue rhombi into these spaces and you will see where to add the four triangles and the square.


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Driving to Manhattan; the Need for Validation

Monday, February 20th, 2012

Tesserax logo stickerOur story thus far:

A funny thing happened to me on the way to my Bachelor’s degree. I had spent my first two years as an Engineering Physics major at the United States Naval Academy, seemingly trying to turn myself into another copy of my career-Navy father. When I decided my path lay elsewhere, I resigned and entered the University of Florida at Gainesville, majoring in Physics. It was there that I met up with Tom and Rob Weiss, whom I had known back at Crystal River High School. After catching up and endless discussion about hyperspace and hypercubes, I decided to make a cardboard model. But I put it together inside out, producing a shape neither of us had ever seen before. Tom made better models than mine and we found they they resonated amazingly strongly to all the music we were listening to. When Summer break came and my brother James and I went off to Orlando to earn a little money as graveyard shift janitors (”Custodial Hosts” in Disney-speak), Tom went home and told his father he had found a great shape for loudspeaker cabinets. His father was dubious, so Tom scraped off some of his paintings, cut out pieces, and made the first functioning Hypercube speaker. it worked even better than he had hoped, and we applied for a U.S. utility patent and began making plans to build and sell this great new technology. At first we tried using a radial arm saw, then we decided it would be more practical to get cabinet makers to cut the pieces for us.

In the Spring of 1979 Tesserax was in communication with an advertising corporation named, I believe, Omnimedia (I do not know if they still exist.) We were still wondering how we could make a splash in the market and get the technology the attention it deserved without detailed test reports. We had vague ideas about them making an infomercial or something for us. And then one day we were reading Stereo Review magazine, and had an idea that might work. If we could get our speakers reviewed by the prestigious Julian Hirsch of Hirsch-Houk Laboratories, well known for independent audio equipment testing, that could be our big break that would finally get us some traction in the marketplace. Through Omnimedia, we got in touch with Larry Klein, the Technical Editor, and from our conversations it appeared that if we got some hypercube speakers to Stereo Review’s office in New York, NY he would give them a listen and forward them to Hirsch-Houk Labs for serious testing and review.

hypercube speakerThe speakers we had been trying to sell up to that point were car speakers, but we wanted SR to see something more substantial. So we decided to go all out and design a new speaker model. This time we would even make a custom grille mounting. Normally, loudspeaker are rectangular boxes and the woofers are protected by a rectangle of acoustically transparent foam or just grille cloth. We had no time to learn how to mold acoustically transparent foam so we went with grille cloth stretched over a wooden frame.

3D speaker grilleIn another flash of brilliance, Tom suggested that since ordinary speakers have square or rectangular 2D grilles, our hypercube speakers should have 3D grilles. That way the grille would be one dimension higher than the usual too. It would be a hypercube speaker with a seemingly cubical grille.

And so it was. The grilles for these speakers would be a labor of love and an exercise in solid geometry. I didn’t make them, but they were made.

uncovered speaker Our car speakers had employed a single 4 inch cone driver from Pioneer. For small speakers, a single cone means no crossover needed and simple mounting. For Stereo Review, however, we would need more. Using my father’s VISA card we ordered the large woofers, cone midranges, and horn tweeters from SpeakerLab in Seattle. We went with the triangular truncation baffle plate and mounted the midrange (with its own separate hypercube sub-enclosure inside the main cabinet) and horn tweeter on the adjacent panels.

After the pieces for the cabinet we assembled, stained, and oiled we had to get them to the Big Apple. But who would we entrust them to? We would get only one shot at this; if damaged loudspeakers arrived in new York we would look incompetent.

We decided to deliver them ourselves. So Tom, his father, and me carefully boxed them up and placed them in a van. We drove that van from our warehouse-factory all the way from Florida to NY. We carried them in personally, got back in the van, and drove home to Florida, full of hope that we would finally get attention.

broken speakerWeeks passed with no word. Finally we received word to pick up our speakers at the airport. When we opened the boxes, we were aghast. The baffle plates were cracked and the woofers, wider than the holes they had been mounted on, were somehow inside the cabinets lying on the bottom but still connected by wires. When we contacted Stereo Review for an update, we were told that they were “okay speakers” but that there would be no test report or review.

When we asked how the speakers had become damaged, we were first told that they had arrived damaged. When we protested that we had personally delivered them to their offices, our contact speculated that the damage must have resulted from some jolt that happened when the plane landed at Tampa.

A suspicious person might speculate that the woofers had been pried off the cabinets to learn what was inside to make them so good. Since we had attached the woofer with a strong bead of silicone rubber, attempting to pry off the woofers would have cracked the baffle plates; the wood was considerably thinner than the 1/2 - 1″ thick particle board usually used by speaker makers.

It is also possible that rough handling by loaders or an unusually hard landing just might have caused the damage; the woofers were heavy. But not having been there when it happened, we will never know exactly what happened. In any event, it was over. Stereo Review had decided that we weren’t worth the trouble.

The pictures you see in this post were taken today, 2/20/2012. The speakers are still in my parents’ living room here in Crystal River, FL. I have left them unchanged since 1979 to remind me of the importance of safe packaging.

Next: Back to School; Numerical Integration = Simulation


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