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| Square-Truncation Hypercube |
In 1977, towards the end of my Senior year (CLEPed-out Freshman year & Calculus), my friend Matt Kennedy and I created a resonant chamber in the shape of the parallel projection of a four-dimensional hypercube onto 3-space (a rhombic dodecahedron) with a corner truncated and a speaker mounted on the plane of truncation. This projected longitudinal compression waves (sound waves) both away from the chamber (front wave) and into the chamber (back wave).
Sound waves can interact profoundly with other sound waves in addition to reflecting off of solid objects, as long as the sound waves have the correct phase relationship with each other. The sound waves projected into the chamber reflected off of the walls of the chamber and also interacted with each other, forming a standing-wave structure in the shape of an actual right four-dimensional hypercube.
Well, it turned out that when connected to a high-fidelity stereo amplifier instead of a frequency/waveform generator, they reproduced music insanely well. Of course, we both immediately got get-rich-fever, dropped out of college, got a utility patent (4,231,446), and formed our own corporation - Tesserax, Inc.
The Hypercube Speaker never got off the ground - I got a real lesson (actually, an entire curriculum) in the school of hard knocks when I tried to start a manufacturing company on a $20K (1977 dollars) shoe string (you can stop laughing any time now...).
The sheer volume of State and Federal regulations that must be navigated through when starting up a manufacturing enterprise are a red-rimmed nightmare.
Besides the expenses involved with the regulatory mountain range, It turned out that making them out of wood (1/8" gum plywood) by hand costs too much to allow a reasonable retail price (especially when one insists that the finish be of a quality sufficient to enable one to take at least a little smidgen of pride in the result of one's labor).
The best way, in both the long-term economic and functional senses, was to make them out of a highly rigid and very thin glass composite plastic like DuPont Rynite 545.
Unfortunately, that required a seriously high capacity injection molding set-up - and manufacturing a speaker enclosure large enough to accommodate a 10 inch speaker using a maximum of two pieces (more than that, you get buzz, buzz, rattle, rattle) involved turning 2½ tons of nickel steel on a 25 inch lathe to make the die (the volume of a rhombic dodecahedron increases much more quickly than that of a cube as the length if its edge increases) - serious capital requirements - and I had no source of additional venture capital. Worse, I didn't know how to get one.
We tried to license the patent under very reasonable terms to established high fidelity speaker manufacturers (including JBL), but ran into the "Not Invented Here" syndrome.
Not only that, but their audio engineers refused to even listen to the speakers, just said they had "too many corners" and did not fit the Thiele-Small equations for loudspeaker enclosures.
Their actual basic problem was that the only system of equations they knew how to use had at its root the implicit assumption that the enclosure had the shape of a rectangular prism - with one wall parallel with the baffle plate.
A 13-sided polyhedron having no wall parallel with the baffle plate rendered their precious little system of equations utterly irrelevant - and they couldn't really do mathmatics themselves, all they could do was to crank numbers through equations handed to them by someone else, like mindless little organ-grinder monkeys.
We were pretty clueless when it came to raising venture capital - I freely admit that I was truly pathetic at being a businessman - all we really wanted to do was to work in the lab, exploring new frontiers of knowledge.
We had about 50 little things on the drawing board that played fast and loose with various aspects of the space-time continuum - the business was supposed to fund that research, not eat up all of our time performing as catamites for gubmitt bureaucrats.
Frankly, the whole experience left me with a deep amazement that anything gets invented and produced these days.
We ran out of capital and folded before we could really make anywhere near enough Hypercube Speakers to start feeding retail distribution chains.
Hey, live and learn, no excuses, other than I was young & dumb.
Not to get too nuts on you, but during our experience building and testing Hypercube Speakers of different sizes and power ranges we observed a disturbing phenomenon.
Remember, the whole point of that enclosure is to take the back-wave coming from the rear of the speaker (and 180 degrees out of phase with the front-wave) and fold it into an actual right hypercube made of sound - a four dimensional object made of a four dimensional material (the fourth dimension, time, maps to phase in three dimensional space). In four dimensions you can have rotation about a plane (analogous to rotation about a line in 3-space).
The back-wave rotates about the planes of the enclosure's surfaces, rotating its phase by 180 degrees as it does so, emerging in 3-space in phase with the front-wave in perfect constructive reenforcement of it. This effectively doubles the speakers efficiency and power output as measured in decibels with the added benefit of making it an omni-directional sound radiator.
When I say that the power output was doubled as measured in decibels, I mean that the measured power of the sound output by the Hypercube Speaker averaged three decibels higher at all frequencies when compared to the measured output of the stock JBL L40 - same drivers, cross-over, and amplifier.
The frequency response curve of the Hypercube Speaker looked like a hand-drawn ideal (bugged the Hell out of the acoustic engineer we hired to do a certified test - and of course the other acoustic engineers refused to believe it was real, despite the engineer's seal on the report), while the JBL's frequency response curve looked like the Andes Mountain Chain in comparison.
Well, it turned out that when connected to a high-fidelity stereo amplifier instead of a frequency/waveform generator, they reproduced music insanely well. Of course, we both immediately got get-rich-fever, dropped out of college, got a utility patent (4,231,446), and formed our own corporation - Tesserax, Inc.
The Hypercube Speaker never got off the ground - I got a real lesson (actually, an entire curriculum) in the school of hard knocks when I tried to start a manufacturing company on a $20K (1977 dollars) shoe string (you can stop laughing any time now...).
The sheer volume of State and Federal regulations that must be navigated through when starting up a manufacturing enterprise are a red-rimmed nightmare.
Besides the expenses involved with the regulatory mountain range, It turned out that making them out of wood (1/8" gum plywood) by hand costs too much to allow a reasonable retail price (especially when one insists that the finish be of a quality sufficient to enable one to take at least a little smidgen of pride in the result of one's labor).
The best way, in both the long-term economic and functional senses, was to make them out of a highly rigid and very thin glass composite plastic like DuPont Rynite 545.
Unfortunately, that required a seriously high capacity injection molding set-up - and manufacturing a speaker enclosure large enough to accommodate a 10 inch speaker using a maximum of two pieces (more than that, you get buzz, buzz, rattle, rattle) involved turning 2½ tons of nickel steel on a 25 inch lathe to make the die (the volume of a rhombic dodecahedron increases much more quickly than that of a cube as the length if its edge increases) - serious capital requirements - and I had no source of additional venture capital. Worse, I didn't know how to get one.
We tried to license the patent under very reasonable terms to established high fidelity speaker manufacturers (including JBL), but ran into the "Not Invented Here" syndrome.
Not only that, but their audio engineers refused to even listen to the speakers, just said they had "too many corners" and did not fit the Thiele-Small equations for loudspeaker enclosures.
Their actual basic problem was that the only system of equations they knew how to use had at its root the implicit assumption that the enclosure had the shape of a rectangular prism - with one wall parallel with the baffle plate.
A 13-sided polyhedron having no wall parallel with the baffle plate rendered their precious little system of equations utterly irrelevant - and they couldn't really do mathmatics themselves, all they could do was to crank numbers through equations handed to them by someone else, like mindless little organ-grinder monkeys.
We were pretty clueless when it came to raising venture capital - I freely admit that I was truly pathetic at being a businessman - all we really wanted to do was to work in the lab, exploring new frontiers of knowledge.
We had about 50 little things on the drawing board that played fast and loose with various aspects of the space-time continuum - the business was supposed to fund that research, not eat up all of our time performing as catamites for gubmitt bureaucrats.
Frankly, the whole experience left me with a deep amazement that anything gets invented and produced these days.
We ran out of capital and folded before we could really make anywhere near enough Hypercube Speakers to start feeding retail distribution chains.
Hey, live and learn, no excuses, other than I was young & dumb.
Not to get too nuts on you, but during our experience building and testing Hypercube Speakers of different sizes and power ranges we observed a disturbing phenomenon.
Remember, the whole point of that enclosure is to take the back-wave coming from the rear of the speaker (and 180 degrees out of phase with the front-wave) and fold it into an actual right hypercube made of sound - a four dimensional object made of a four dimensional material (the fourth dimension, time, maps to phase in three dimensional space). In four dimensions you can have rotation about a plane (analogous to rotation about a line in 3-space).
The back-wave rotates about the planes of the enclosure's surfaces, rotating its phase by 180 degrees as it does so, emerging in 3-space in phase with the front-wave in perfect constructive reenforcement of it. This effectively doubles the speakers efficiency and power output as measured in decibels with the added benefit of making it an omni-directional sound radiator.
When I say that the power output was doubled as measured in decibels, I mean that the measured power of the sound output by the Hypercube Speaker averaged three decibels higher at all frequencies when compared to the measured output of the stock JBL L40 - same drivers, cross-over, and amplifier.
The frequency response curve of the Hypercube Speaker looked like a hand-drawn ideal (bugged the Hell out of the acoustic engineer we hired to do a certified test - and of course the other acoustic engineers refused to believe it was real, despite the engineer's seal on the report), while the JBL's frequency response curve looked like the Andes Mountain Chain in comparison.
The transient response of the woofer and mid-range drivers asymptotically approached measurable perfection during this "burn-in" period, and this was reflected in the quality of the reproduced music - we could just about hear the fingerprint ridges of a guitar player as they played, and the bass response was unprecedented, tight and oh so crisp (none of that "flubby" quality you hear from those fiberglass-stuffed rectangular boxes). The output sound power level in decibels remained the same.
When the speaker was turned off and then turned back on at a later date, the effect took up where it left off - no "burn in" required. If the speaker was moved to a different location in space, then the "burn in" again became necessary before the effect could be observed.
Hypothesis:
To produce a sound wave of a given amplitude, the moving surface that alternately compresses the air in front of it and then pulls a slight vacuum as it reverses direction, thus generating the sound wave can do one of two things.
The mass of the woofer was unchanged. The input energy (voltage & amperage or current) was the same. The inductance was unchanged. The effect was not observed in a stock unmodified JBL L40 speaker unit (the enclosure was the typical rectangular prism lined with glass wool to absorb the energy of the back-wave, and the woofer looked like it was trying to jump out of the box at low frequencies no matter how long it was played) operated as an experimental control next to a hypercube speaker using the identical (within manufacturing specs, anyway) drivers and cross-over. Both were on the same amplifier, which was set to operate in monophonic mode.
The only way we could explain these observations given these base conditions was that somehow the instantaneous acceleration of the woofer cone rapidly increased to a very high level.
Given equal mass and equal energy we could only hypothesize (with apologies to Newton & Einstein) that the either:
The rate at which time passes in the vicinity of the enclosure differed over a radius from the center of the enclosure (which could potentially do interesting things to the speed of light's status as an inviolable constant).
The material of the woofer cone lost its inertia but not its mass(weight = mass in a 1G field). (and Newton spins in his grave with relativistic radial velocity).
Integration of these two alternatives implies that inertia is primarily a property not of mass but of time - that inertia appears to be a mass property only under the condition of a constant time rate in much the same way as mass appears to equal weight only under the condition of a 1G field.
Both of these alternatives, never mind their integration, directly contradict just about all theoretical physics done from Newton on - and no high-spectrum autistic paragon of Academe is going to peer-review the work of a couple of college drop-outs who have made a serendipitous discovery.
That was a classic example of Hobson's Choice (the only real choice available was a hopelessly quixotic life-consuming battle against all of Academe), and Occam's Razor was no help at all.
A] It can move through a large distance slowly, or:
B] It can move through a small distance quickly.
The only way we could explain these observations given these base conditions was that somehow the instantaneous acceleration of the woofer cone rapidly increased to a very high level.
Given equal mass and equal energy we could only hypothesize (with apologies to Newton & Einstein) that the either:
The rate at which time passes in the vicinity of the enclosure differed over a radius from the center of the enclosure (which could potentially do interesting things to the speed of light's status as an inviolable constant).
- OR -
The material of the woofer cone lost its inertia but not its mass(weight = mass in a 1G field). (and Newton spins in his grave with relativistic radial velocity).
Integration of these two alternatives implies that inertia is primarily a property not of mass but of time - that inertia appears to be a mass property only under the condition of a constant time rate in much the same way as mass appears to equal weight only under the condition of a 1G field.
Both of these alternatives, never mind their integration, directly contradict just about all theoretical physics done from Newton on - and no high-spectrum autistic paragon of Academe is going to peer-review the work of a couple of college drop-outs who have made a serendipitous discovery.
That was a classic example of Hobson's Choice (the only real choice available was a hopelessly quixotic life-consuming battle against all of Academe), and Occam's Razor was no help at all.
Yea, I know - it was pretty tough for us to swallow that one too. In order to establish this effect unequivocally, we needed at least two atomic laboratory reference clocks and laser interferometry equipment to quantitatively measure the instantaneous acceleration of the driver cone and to see if the two (preferably at least five at progressive intervals) lab clocks differed after awhile. We also needed a laboratory light-scale to verify that the mass remained unchanged.
Again, major capital requirements and no venture capital.
The utility patent has long since expired (they were only good for 17 years then, 20 years now, and in any case they are really just a license to sue and put some lawyer's kids through multiple Ivy League colleges after buying them all braces anyway - patents do not have statutory protection like a copyright does).
The patent is now in the public domain, so please - feel free to experiment with no problems from our end.
They do reproduce music astoundingly well (if I do say so myself).
There has been a lot of progress in materials technology during the last 30 years - things like Neodymium magnets, Graphene, and Carbon Nanotubes are making a lot of things possible that weren't before.
The primary design criteria for a Hypercube Speaker enclosure is that the material used must be as thin and rigid as possible. Remember, it acts as a four-dimensional axle. You don't want a rubber axle. You don't want the axle to have a larger diameter than the "wheel" it is spinning, either. Ideally, the planes of the enclosure should be thinner than the wavelength of the highest frequency sound put into it, and they should be infinitely rigid.
Have fun!
