Archive for February, 2012

The Graduate: Sowing My Wild OATL

Monday, February 27th, 2012

hypercubeOur story thus far:

On December 19, 1981 I was cast out from Academia into the outer darkness of the Real World, emerging from my ivory tower cocoon at UCF with my B.S. degree and little else. Seven years had passed since my graduation from Crystal River High School; I had spent five of them in college learning known Physics and two of them trying to introduce Hypercube loudspeakers and their not-previously-known physics to the world with Tom Weiss, who built the first functioning Tesseract Loudspeaker prototype and formed the corporation Tesserax with me to profit from our discovery. When we spent ourselves broke and it looked like this might take longer than we had expected, I went back to school at UCF and finished my bacherlor’s degree in physics. But now what?

Starving inventors need to eat. I moved from my dorm room back to my parents’ house in Crystal River and began spewing resumes out to employers.

I won’t say I didn’t get any interviews because I did. I was contacted by a headhunter at the Optics Applied Technology Laboratory (OATL) at West Palm Beach, a fairly well-known research center owned by United Technologies. They were interested in talking to me, and so I drove over across the Florida peninsula to see what was on their mind. West Palm beach is a rich neighborhood. As I pulled into the hotel parking lot and took in the manicured lawns, the upscale shops and the herds of BMWs, I said to myself, this is a lifestyle I could get used to.

The next morning I went out to OATL. United Technologies is an American multinational conglomerate that owns Otis (elevators), Pratt & Whitney (makers of aircraft and rocket engines), Sikorsky (maker of helicopters), and various other business centers involved in defense and energy research and manufacture. They were interested in talking to me, it turned out, because I had mentioned our patented Resonating Chamber geometry on my resume, and lasers are optical resonators, just as bells and organ pipes are acoustical resonators.

It would have been pretty wonderful if they had hired me. I would have gotten to work with laser physicists and gotten a good start on a sexy resume. But it wasn’t meant to be. When they realized that the patent was for a loudspeaker cabinet geometry and my experience with lasers was not extensive enough, they paid my hotel bill and bid me a fond farewell. Lasers, especially military and industrial lasers, tend to be essentially one-dimensional cylinders with a beam coming out one end; rather than try funky new resonator geometries, they were far more interested in doing useful things with the beam like holography, remote sensing, and range-finding for distant targets. I was an interesting but essentially ephemeral distraction from their actual focus. With regrets, they passed.

So I drove back to Crystal River, home to mullet fishermen, nuclear power reactor employees, and the Hypercube Speaker. As the months begin to pass with no serious job offers I began to worry. To hedge my bets I applied and was admitted to Florida State University (FSU) in Tallahassee as a Physics graduate student. When no offers came in, I moved to Tallahassee in the late Summer of 1982.

Next: The Year of Living Theoretically (learning never ends for an apprentice Wizard or a growing Mad Scientist).

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And Pass the Word Along

Friday, February 24th, 2012

And so we dance our time and then we die
but do you wonder why we have this life?
Is there a point to strife? To struggle on?
To see another dawn? To multiply
before we die, and see the torch is passed?
I know we came before our time
no time to climb careers to gain respect;
our task direct: to pass along the key –
of many questions, answer. Hidden, lost,
and at great cost recovered for you all
before we fall. So hearken to my tale;
we shall not fail. And pass the Word along
Untie the wave and turn it inside out
that it may shout; and all the rules reverse
that this small universe, this tesseract
be seen as fact — as it has always been
sound goes within and wraps itself around
this lack-of-boundary; at last, be whole!

And by my soul,
we shall see all these secrets known
in crystals grown and by bees made
now see revealed and manifest
acoustic best; and other waves delight
from slowest sound to sharpest light


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Back to School; Simulations and Laser Crystals

Wednesday, February 22nd, 2012

UCFIt had been almost as decade  since I looked this way in 1970; now it was late 1979. I had interrupted my pursuit for a Physics degree to try to get into business constructing and selling hypercube loudspeakers. When our trip to NY didn’t turn out as well as we had hoped, we were broke again; the corporation more or less went dormant, waiting for the eventual issuance of the patent which happened 12 months later in Nov 4, 1980 as Reagan was being elected President.

UCFI returned to school by entering the University of Central Florida in Orlando (UCF) majoring in Physics. On the way to my BS Physics degree I was gluttonous and took electives like Medical Physics, Numerical Integration Methods (Physics simulations using FORTRAN to calculate trajectories and orbits), Quantum Physics, The Physics of Science Fiction, Electronics, and Laser Physics (a Graduate-level course using Amnon Yariv’s Quantum Electronics as the text).
The FORTRAN simulations turned out to be fun once I discovered that I didn’t have to punch a deck of Hollerith cards. There were a small number of terminals accessing the university computer which allowed FORTRAN files to be entered at video terminals line by line and then executed to generate output. This was more fun than punching cards to make a program.
But the coolest course was the graduate level course in Laser Physics. I learned for the first time that crystals have arcane uses in laser optics. For example, there are the ’simple’ frequency doubling crystals, which under the proper conditions can change red input laser light into blue output light. Then there are the Magneto-Optic effect crystals, which can use an applied magnetic field to rotate the axis of polarization of the laser beam passing through the crystal. The ability to manipulate the polarization of the laser photons, in combination with an external polarizer, enables the beam to be modulated by magneto-optically varying the angle between the beam polarization and the external polarizer. This turns out to have important applications in fiber optic data transmission and Bell’s hypothesis quantum inseparability experiments.

On 11/4/1980 we received U.S. patent #4,231,446. On 12/19/1981 I received my bachelor’s degree.


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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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Of Möbius strips and Klein bottles; a Brief Digression

Thursday, February 16th, 2012

Klein bottleAnd now for something slightly different. For a while now I have obsessed on rectilinear geometry. When I think of measuring area, 3-volume, or 4-volume I think of square feet, cubic feet and hypercubic feet, so when I think of hypersolids, surfaces in 3+ space, I think of hypercubes with straight lines and sharp edges.

The rectilinear surfaces are comforting because their simple symmetry and orientability result from their straight lines.

But there are more geometries than simple  Cartesian or Spherical geometry. We have yet to speak of the non-orientable surfaces.

mobius strip

This is the a simple diagram showing the orientation problem of the Möbius strip when it is embedded in 3D space.
(from You can make one with a strip of paper and a piece of tape by twisting the ends of the paper before you tape them together.

At first it might seem there is no problem; every single point on the surface of the Möbius strip is a point in the 3-dimensional space shown by the transparent box around the surface. If it’s all inside the box, what is the problem with orienting it?

Look at the Möbius strip again and imagine you are a person standing on it at the point between the ends of the red lines. Your head is pointing up in the 3-space, that is, along the +z axis.

Now walk down the center line of the strip in either direction. The road will curve, but if there is gravity holding you to the road you can keep walking around the strip. If you do, you will be surprised to discover that after one time around you are not back where you started. Your feet are still glued to the surface of the strip, but you are on the “other side” of it — your head is now pointing down instead of up, along the -z axis.

If you keep going in the same direction one more time around, after 2 times around you will be back where you started, exactly.

The disturbing thing about this it that this means the Möbius strip only has one side. This means that there are two different opposite directions for the normal to the surface at every point, making geometrically valid orientation problematical. Also surface integrals tend to cancel themselves out, which makes analysis frustrating.

The Möbius strip is an example of a twisted embedding. It is a 2-D object (the original rectangular strip of paper) that has had its “ends” twisted with respect to each other and then fastened to make the two sides into one side. There is also only one edge or 1-surface.

Klein bottleI like to symbolize this as   2  @ 3 –> 1 surface.

The next higher version of a twisted embedding is 3  @  4  –> 2. it is a 3-D object that has had its “ends” twisted with respect to each other in 4-space and attached to make a surface which joins the inside and the outside into one continuous 3-surface with one 2-surface edge or border to it. This surface is called a Klein bottle. (from )


It is hard to see in this graphic image, but if you go inside the Klein bottle and follow the tube around you find yourself walking on the  outside until you go around another 360 degrees again. As before, this is a non-orientable surface because of the double contradictory (antiparallel) normal vectors; there is only one surface (only one side to this object), and you can be standing on it with your head pointing “inward” or “outward” and change from one to the other merely by walking around on the surface.


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Blue Skies and Radial Arm Saws

Thursday, February 16th, 2012

hypercube The teeth that do not smile bite through
to leave their mark upon the cloven wood.
And scorch in haste what Time had grown in years
to carve a dozen capstones.
In 1978 the first attempt to mass-manufacture hypercubes began with the purchase of a Sears Craftsman 12 inch radial arm saw. For those who do not know, this is a tool that consists of a sturdy table and a powerful saw that is mounted on an arm that can be swung parallel to the ground and set to desired angles and bevels.

By different angles, I mean that you can cut at, say, 109.5 degrees or 70.5 degrees instead of 90. By different bevels I mean the saw drive axis can be tilted with respect to the vertical so that you can cut at 30 degrees to the vertical and leave 60 degrees edge on the wood so that two pieces can come together at 120 degrees instead of 90.

There are many kinds of numbers. There are natural counting numbers like 1,2,3… that we use to describe quantities of units such a people or cans of orange juice. There are rational numbers such .250 or 98.6 that lie between the counting numbers (or integers) but are still recognizable as quantities.

And then there are the irrational numbers such a pi and the square root of 3.  These cannot be expressed as finite ratios, yet they are finite numbers. That is, they are finite numbers with an infinite number of decimal places. We know that pi is between three and four. We write it as 3.14159… to indicate that the numbers in it go on forever but are known to express a number larger than 3.14 units and smaller than 3.15 units. Functionally, we could say that pi is the circumference of a sphere or cylinder with a diameter of one unit. In other words, a ball with a radius of 1/2 and a diameter of 1.0 foot has a circumference of 3.14159… feet.

Irrational numbers come up a lot in geometry. The diagonal of a unit square is the square root of 2. The diagonal of a unit cube is the square root of 3. How do we know this? Because a Greek geometer named Pythagoras discovered that if A, B, and C are the lengths of the sides of a right triangle (that is, a triangle that contains a 90 degree angle), and C is the longest side (or hypotenuse), then A2 + B2 = C2 so if you have a 45, 45, 90 triangle such as you get by slicing a square along its diagonal, you have 1 + 1 = C2 or C is the square root of 2.

rhombic dodecahedronWant to make a rhombic dodecahedron? Each of the 12 rhombi that make up the RD is like a square that someone sat on. It has four identical length sides but they are not at 90 degrees. Two of the angles are less than 90 and two are more. But how much more and how much less?

The RD rhombus can be made by putting 4 identical triangles together. They are right triangles and their short sides are A = 1/2 and B = (the square root of 2) / 2.
By the Pythagorean equation we have 1/4 + 2/4 = C2 so we get
C2 = 3/4, or C = (the square root of 3) divided by 2.

Therefore, if we derive the rhombic dodecahedron by turning a 1 x 1 x 1 unit cube inside out all of the 24 edges of the RD are (square root of 3)/2 or approximately .866 units long.

If you have a radial arm saw, you can make rhombi easily.
(1) set the bevel to 30 degrees
(2) set the saw to rip out planks with parallel long sides
(3) set the arm angle to 70.5 degrees at the same bevel and slice across the planks diagonally. Measure the length of the cut edge so that you can cut rhombi with all four sides the same length as this cut edge
(4) keeping the bevel inward (so that each rhombus is like the capstone of an arch on all 4 edges) slice out rhombi from the plank.

If you do this properly, you will make rhombi with 70.5 and 109.5 degree angles and an inward bevel of 30o meaning that 60o of the wood is left and the pieces will come together with a dihedral angle of 120o instead of 90.

This is not the only way or the best way to make rhombic dodecahedra, but it is about the best you can do with the limited accuracy of a radial arm saw. Naturally, the more precisely the material is cut, the easier it is to make all of the pieces fit together. I am not trying to be cruel when I say that more than one experienced cabinet maker has attempted to perfect the process. I do not claim to be a craftsman or even a carpenter. But I do know the correct angles are irrational numbers that cannot ever be reproduced exactly, any more then you can cut a piece of wood exactly pi units long.

This is what we did ourselves, at first. We knew we needed demonstration hypercubes to show people that it could be done. So at first we used the radial arm saw to rip the planks and cut out the rhombi. We made several enclosures this way, but realized quickly that it would be a problem to cut all of the pieces we would need for regular production runs once we were in the business of cranking out hypercube speaker cabinets.

So we found a cabinet maker and explained our needs. In due time he presented us with a box of pieces that did not quite fit together. We grimaced and put them together anyway , sanding as necessary to get the edges to meet etc. while he improved the process and refined his cutting jigs.

At this time we were both essentially college dropouts trying to get into business on a shoestring. We had applied for a patent, so that now we could in good faith put “patent pending” on our business cards and packaging.

Next: Driving to Manhattan; the Need for Validation


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