Hurricane Parties and Hypercubes


Well, Hurricane Irene has begun hammering the coast, but it slipped by me down here in Florida. I live way out in the boonies on the “Nature Coast” of Florida aka the Gulf Coast aka the West Coast. So far out on the edge that Irene didn’t even tickle us here.

It’s late now, nearly 2AM EST and I sit here, as usual, in front of the computer that is most of my life, reflecting on past and imaginary glories. There is a story I want to tell, something I wanted to tell long ago. It was a long time ago when I actually thought I had something important to tell the world, but without resources and mass media it was damned hard to get the word out. Now that the Internet is here I have a chance to reach more people. If you are a physicist like me, or a musician like me, or are interested in hyperspace like me, you might find it interesting. And yes, it is a true story, the story of U.S. Patent #4,231,446.

Once upon a time, two nobodys in backwoods Florida created the tesseract loudspeaker. How do I know this, since most don’t? That’s easy. I was one of those nobodys: my name is on the patent as the co-inventor.

hyperspace I had just returned to Florida after spending two years at the Naval Academy at Annapolis, Maryland studying Engineering Physics.  My father was a career naval aviator who retired to Florida; he had five sons and three of us tried to follow in his footsteps. NUmber 1 (William) graduated from USNA and served on nuclear submarines. Number 4 (David) graduated from USNA and became a back-seater (radar intercept officer or “RIO”) in F-14 Tomcats.

I was the only one in the family to apply, receive a Presidential appointment, attend USNA and then NOT graduate. It was because I saw the handwriting on the wall: unlike my father, I wear glasses and would never have qualified for Aviation. Unlike my older brother, I wan’t making the grades to qualify for Nuclear Power school. I faced the fact that I was surviving the hazing but would never have a career like my father’s.


So I resigned and left. Was it because I couldn’t take the pressure? No, I had already made it through the hardest year (Plebe year) and another year besides. But I just didn’t see myself sitting on a destroyer or cruiser for 20 years of boating. So I left. It should have been obvious where I was going: I had the university of Florida (Gainesville) send me a catalog of courses. I figured my future was in Physics, not Floating.

Enrolling in UF continuing my major in Physics, I ran into a friend from my home town who was there as a Business major (back then you had to be a Business major to take programming courses; the IT degrees did not exist). We resumed discussions we had begun years earlier, about things like Hypercubes (tesseracts), Moebius Strips, and Klein Bottles.

tesseractOne day I decided to construct a cardboard model of one of the projections of the 4-dimensional hypercube onto our 3-space. This surface is usually drawn by drawing a little cube centered inside a larger cube, with the corners connected. Well, drawings are nice, but I wanted to hold it; I wanted something tangible.



inside-out tesseract modelI quickly saw that I could make six pyramids with their tops cut off (like the pyramids of Mexico and so on) into square faces; shove them together and the six square tops of the truncated pyramids would form the little cube inside the bigger cube. So I started cutting and taping pieces of posterboard.


inside-out tesseract modelOnly I put it together inside out. While I was taping it I realized that there were two ways to put the pieces together. I already knew how the one way would look, so I taped them together the other way, taping the bases of the pyramids together so that the tops of the pyramids faced outwards in the up, down, left, right, forward, and backward directions.

When my friend saw it he was amazed; neither of us had seen anything like it before. He made some models himself, with complete pyramids, not chopped off at the top, so that it looked like a cube with pointy pyramids sticking out from each face (see above for the tiny wood model I am holding).


While we were holding the cardboard models of these inside-out projected tesseract shapes and we noticed something; they seemed to be pretty resonant.  Hollow objects are like bells or organ pipes: they vibrate strongly at their natural resonant frequency determined by size, and much less at other frequencies. But these durn models seemed to be resonating to all of the frequencies. I told myself it was probably because the cardboard wasn’t thick enough. But it was weird: we could feel the music, all of it, when we held the hypercubes.

When he went home for the summer my friend showed the model to his father and suggested it might make a cool shape for a loudspeaker enclosure. His father, who had actually built loudspeakers as a hobby when he was younger, told my friend that the idea was ridiculous.


Never tell a genius he is full of baloney! Tom went straight to his room, pulled down a couple of his paintings, scraped the paint off them, cut up the masonite with a sabre saw, and created the world’s first tesseract loudspeaker enclosure. He fastened a little speaker to it and went to go show his dad a thing or two. When they turned it on, they were floored. The little 3-inch woofer was putting out more bass than it had any right to…and all the other frequencies too!  And there seemed to be less distortion! AND it was omnidirectional — putting music out in all directions. AND it had an amazing transient response — which MLSSA testing shows as an easily-seen difference in the “spectral decay” or “waterfall” plot of the regular vs. hypercube speakers.

At this time my brother James (2 of 5) and me (3 of 5) were experiencing the joys of a summer job as Graveyard Shift “Custodial Hosts” at Walt Disney World.  James got to polish the brass and I got to mop floors and wash monorail windows, knowing kiddie fingerprints would be all over them ten minutes after the park opened the next morning.

Tom could have kept his discovery for himself. He didn’t. He insisted that my name should be on the patent too, since he had gotten the idea from my inside-out hypercube model.  So we worked on the patent application together. Here is the first page. We decided to avoid a lot of hassles by referring to the geometry by its traditional name: the Rhombic Dodecahedron. There were a lot of ways to use the geometry; we needed a lot of expensive drawings to cover all of the feasible variations. Drawings1. Drawings2. Drawings3.

Yes, we had dollar signs in our eyes. Wealth was just around the corner. All we had to do was get a manufacturer to license the design and pay us royalties, and we’d be on our way to wealth and security and fame.

Ever hear of the “Not Invented Here” syndrome? People who make their living doing something are rarely happy when something new comes up that makes previous designs obsolete — unless of course they invented it. We ran into this problem quite a bit over the years.

The problem was, Tom and I didn’t invent the field of Audio Engineering, and it had existed long enough, its experts concluded, to have learned all about how loudspeakers work. What we had discovered simply didn’t fit into the paradigm. Loudspeaker enclosures are considered a known science, with well-known problems and equally well-known products designed and engineered to overcome said problems. Maybe I would have agreed with the experts, except (a) I didn’t have any degree yet and (b) I have ears.

If we had had the resources to just swing into full production and show them up in the marketplace, history might have been different. But we didn’t, so we made the mistake of wasting a lot of time and family funds trying to convince the experts. So we began constructing, demonstrating, and testing prototype after prototype, being naiive enough to think that working models would be enough to show we were not crazy. No one argues with a working model, right?

hyperspace So we bought conventional loudspeakers and converted them. Sometimes we converted both the left and right units; sometimes we converted one and left the other in its original enclosure. We found we could do this with plywood, sheet metal, plastic…the shape didn’t care, as long as it was the right shape. (Geometry is powerful; a parabolic dish works just as well in tin or aluminum as it does made of solid gold.)

Along the way, we picked up bits of audio engineering to help us explain the differences, and worked on a mathematical theory to explain why the shape was such an improvement. You see, traditional woofers are dipole radiators — they shout “out” of the box but the back of the woofer shouts INTO the box. And that interior energy is the problem; if you confine it and try to muffle it with stuffing, you get a less efficient speaker (and distortion). If you cut a vent to make a “ported” loudspeaker, the “backwave” (which is 18o degrees out of phase with the “frontwave”) interferes with the frontwave at most frequencies, making a boomy box that performs unevenly, though it is more efficient than the sealed or “acoustic suspension” design because you arent throwing away half of the energy by keeping it inside the box.

The problem is, those were and still are the two main loudpseaker designs. A couple of rascals with PhDs in audio engineering called Thiele and Small codified it in their theory, which attempts to predict how loudspeakers behave based upon the “Thiele-Small Parameters” of a particular design, which you plug into an equation to predict the frequency response curve.

So when experts asked us what our Thiele-Small parameters were, we looked dumb. So what if our tesseract loudspeakers outperformed their conventional ones? At least THEY had a mathematical theory that other people believed. “You made our speaker omnidirectional? Nonsense!”

After we failed to interest anyone in using this fantastic technology, spending ourselves broke, I grew discouraged and enrolled in the University of Central Florda (Orlando) to finish my degree in Physics.  The patent was granted on 11/4/1980 and my B.S.Physics degree was awarded on 12/19/1981.

Thinking maybe it was just a matter of degrees, I applied and was accepted into physics grad school at Florida State University (Tallahassee — where the hanging chads fall where they may). At this point I was still ignored like a crackpot — but a crackpot who was in a doctoral program! Maybe when I was Dr. Kennedy they experts would at least listen to a demonstration….

Grad school was boring compared to what I already knew. And the math was, well intense.  I was trying to wrap my mind around elliptic integrals and Hermite polynomials, while I took quantum mechanics and classical (Lagrangian) mechanics. But I didn’t seem to be getting the traction I needed.  I moved north to Delaware, where I was a night adjunct at Wesley College teaching evening calculus-based physics classes. After that I moved to Maryland and got programming jobs, eventually doing ASP Web development for Sylvan, Walter Reed Army Medical Center and Agile Access Control. I built more tesseract loudspeakers over the years, demonstrating their power and purity for Pier Six Pavilion in the inner Harbor in Baltimore and many others.

The patent expired in 1997;  it was a little humiliating that none of the major companies (even ones we had contacted about it) bothered to copy it. We couldn’t make money on it, couldn’t even get people to make it for free. It still works. The prototypes still work.

When I was laid off from my telecommuting job I struggled to make ends meet in the relatively expensive northen Virginia. Eventually I was broke, unable to sign a new lease, and moving back to Florida.

Sorry, that was a long story, I guess. But it’s a true story. Not the story of my life, because hopefully I will have a few more chapters before I shuffle off this mortal coil. But the story of the tesseract loudspeaker. The patent exists. The prototypes exist. We have independent tests to prove our design reduces distortion and flattens frequency response. But no one’s listening.

Heh. I bet you thought I’d be trying to sell you something by now. No. I need money, yes, like a lot of people. But this isn’t a landing page or a squeeze page; I’m just trying to share the information, still trying to get it into the ears of someone who can find more applications. I’ve got a few ideas there, but forgive me if I don’t disclose them all without more patents; I’m still ready to tilt at a few more windmills before I retire into even further obscurity.

hyperspace Okay, boo-hoo, I didn’t get rich. Waugh! So what? Life goes on. And there are always new contributions to make. Shapes that affect wave behaviour are amazingly important to technology: look at the Dish network and try to imagine it without parabolic reflectors. The inside-out projected tesseract has, I suspect, a lot more to do for us if we give it a chance. –MRK

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18 Responses to “Hurricane Parties and Hypercubes”

  1. Thanks for reading, Billy. Classes are made of people, so they act the way people act. I wish I was better at controlling other people, but I usually try to reason with them instead and this does not always work. Keep learning and there is no limit to how far you can go in this life. –MRK

  2. Thanks for reading, Tori. I am afraid I am not good at crowd control, so I am probably better at teaching through my writing. It’s an old cliche that a few good students make it all worth the trouble, but in fact this cliche is true. Meeting a few good students who care about what is going on, who want to make their time here count for something is what keeps teachers from giving up. Never stop learning.
    — MRK

  3. billy says:

    dear mr.kennedy:hi
    i am billy i was a student in mrsmuccllands class you are asome and i wish you where my tchear cause you get me and i am your nuber 1 fan and you andyou how the best blog ever and thank you for making it and it teaches me about math and cinda since and you are good at makeing a website
    and teaching pepole facs and detils and math and since and i am so srooy for my class being bad thay all ways doing that to subsutut terchers and did i menchinyou are asom so asomei do not no ho to put it in a sentens i think you are so asome and you have a sweet blog and thank you for bilding it andi love your website

  4. tori says:

    hey love your blog thanks me and olivia think you are a great techer

  5. william says:

    you are so cool at math i wish you where my terhcr

  6. Wow, Jim, you really are a masterful sculptor in wood and not just an ordinary maker of boxes. I love the pictures at and I can only imagine how beautiful the speaker enclosures could be if you ever decide to make some for yourself. Thanks for reading, Jim. Let’s stay in touch. –MRK

  7. Jim says:

    Last name, Small.
    Hurricane, Agnes. Sanibel Island 1972. Swam in her….like diving into concrete. Then the eye passed over, the sun came out, the birds sang, then the wind started in the other direction.
    Enjoying: blog. Found through tetrahedron.

  8. “Wow! Thank you! I always wanted to write in my site something like that. Can I take part of your post to my blog?”

    Yes, feel free to quote me as long as you mention my site or give a link back to it.

  9. Wow! Thank you! I always wanted to write in my site something like that. Can I take part of your post to my blog?

  10. your blog is very good. It was very well authored and easy to understand. Unlike additional blogs I have read which are really not good. I also found your posts very interesting

  11. Bob Johnson says:

    Thanks for an idea, you sparked at thought from a angle I hadn’t given thoguht to yet. Now lets see if I can do something with it.

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  13. Interview Questions and Answers wrote: “I love your blog, you should add an RSS feed feature so I can get automatic notifications of new blogs. If you set one up please email me! i will bookmark you for now. Again Excellent Blog!”

    (ashamed) Thank you, Questions and Answers. I know I have so much to do yet. Yes, need to make the RSS feed easier to find — it is buried in a text link at the bottom and many have complained. I will work on it today if time permits. Thank you for pointing this out. Got distracted last night when @RaveTheWeb and @Familia on Twitter were looking at me.

    But now I have to go exercise before it gets too hot here in Florida . I walk 2.7 miles most mornings. Losing weight, he explained. Never fear, I shall return. –MRK

  14. I love your blog, you should add an RSS feed feature so I can get automatic notifications of new blogs. If you set one up please email me! i will bookmark you for now. Again Excellent Blog!

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