Mathematics will always be only a model of what occurs in the implementation. A physical device patent may also include a configuration of materials, treatments, dimensions, operating conditions, and other characteristics that contribute to the device operating as the mathematical model intends it to. In this way it is an implementation that can be considered non-trivial and innovative and much more than pure mathematics.

Software patents are largely math because the implementation in a device is carried out in the digital domain. I almost want to capitalize digital domain because it is very special. It is a contract that the analog reality of a computing system can be abstracted to transact purely in digital, generally binary, computations that will always give the intended digital output. Software is math because it must be according to the digital domain contract. Any computing system that fails to fully abstract the reality of the implementation into a purely digital construction is operating in error.

The only software patent that I see as worthy is RSA. But even there I think that it is the signing protocol that is innovative and I could be persuaded otherwise. The asymmetric computations that make it viable are too close to pure math to be patentable IMHO. RSA is tremendously valuable and it is difficult to imagine another way to do it. That makes a 20 year patent unpleasant but that alone is no reason not to grant the patent. The cotton gin seemed difficult to implement otherwise and very useful and it was certainly worthy of patent, though that patent was promptly ignored. In both cases the world probably benefitted from the public disclosure of the workings as described in full detail in the patent.

They go hand in hand. It would be hard to get the Hubble Space Telescope into orbit without a space program and its technology. Hubble provided data that informed scientific theory.

This morning I was waiting for the ferry on a barge-dock. The barge was rocking a bit in the bay. Two ripples were playing across a puddle on that barge but at two different frequencies. They passed through each other with virtually no interaction. Speaking as a non practicing EE - I thought about how much more there is to do at the gate level with solid state physics.

3-d, efficiency (power density, not volume density), photonics and plasmonics for non-interfering signals, its all at its infancy. Plasmonics in particular has huge potential because it gets many of the benefits of photonics while staying within more traditional solid state physics.

The Soviets used powdered bismuth on that reactor to kill it. Bismuth does not turn radioactive and is also a decent coolant as it transitions from solid to liquid to gas. Liquid to gas alone is ~750kJ/kg. It also has one of a the lowest thermal coefficients among metals. I can't find anything about it slowing down nuclear reactions but at worst it is neutral. I think the concrete went over the bismuth and that more or less killed the thing.

GPS sats are too high for current gen Chinese ASATs but that may well change at some point. GPS is WELL above LEO.

I think every grunt has a GPS these days - so they would ALL have to have flat batteries. And mil-spec GPS that can't take jungle humidity? laugh... again, one of the units would work. Orienteering should still be taught but it isn't as critical as it once was. Too bad, the world feels awful small when you can't get lost in it.

The military is working on inertial systems that take advantage of the fact that one or both boots of a soldier is normally on the ground. Networking a platoons boot heels turns out to be a very decent way of figuring location from the last available absolute position fix. It's great inside concrete structures where GPS signals can fail to penetrate. Firefighters are a likely civilian beneficiary.

Not really.

GPS satellites orbit at 20,000 km and are therefore VERY hard to take out. We have bigger problems if that happens.

Jammers that are strong enough to disrupt aircraft are strong enough to locate and destroy (AGM-88 HARM). Perhaps the trickiest situation would be small jammers in dense, civilian locations. In that case use them as a beacon a la Skyhook.

The crew could take a Soyuz down.

It seems like the shuttle would make meaningful addition to the usable to the ISS with its arm, cargo bay and pressurized quarters. What a shame to deorbit all that useful stuff and mothball it in a museum.

Quicklaunch doesn't get nearly enough attention.

The heavy, durable stuff should be shot out of a gas cannon and only the squishy humans should ride the rockets.

http://www.newscientist.com/article/dn17931-blasted-into-space-from-a-giant-air-gun.html

http://www.youtube.com/watch?v=1IXYsDdPvbo

Third is that they are not naturally suited to being pressurized like cylinders. Flying wing cargo planes make tons of sense on the first two points, though I think most cargo is pressurized.

You would need a very special camera to catch such high-speed toggling of the LED. Normal video 24-30 frames per second. That's well below the 300 baud of even early modems and you need at least twice the switching frequency to get the data (Nyquist). At 3MB/s they would need to be encoding a lot of bits per switch to get in range of a video camera. Some specialized sensors can do 1 million frames per second but their buffers can only handle 100 frames at a time.

Most of the time players find the daily double while running through categories they know REALLY well. Then they only bet ~$2k out of their $12k stash.

Even if they get the daily double right they will have to risk losing in final jeopardy b/c they haven't doubled the second place player's score. The smart play is to "make it a true daily double" and lap your opponents on a category you know well. Daily double questions are no harder than final jeopardy and I generally find them much easier. That's the time to risk it all. You not only increase your probability of winning but also your cash winnings.

Imagine you are up 80% on your opponent and the final jeopardy category comes up as something you know NOTHING about. That's the time when you wish you bet more on that daily double.

Easy to drop that freezing point with additives and/or keep the fuel warm. Worst case you go dual fuel where you start up on gas then switch to butanol that has thawed out on the engine heat.

They won't have backlash but they will have a certain amount of compliance. High speed low torque situation would be perfect for magnetic gears but traction situations? not so much. I think dozens of people have had the idea of magnetic gears - I know I did. Isn't it a children's toy already?

I hope this isn't worthy of a patent b/c anyone who has seen a Halbach array will immediately appreciate patterns of poles can generate interesting fields. Halbach arrays Manufacturing of the magnets is non-trivial and a bit more worthy of IP.

Bronze is under appreciated. It is really hard but can be brittle. My recollection is that it is as hard as carbon steel, though no where near as ductile.

You have to remember that iron back then wasn't steel, it was wrought iron or pig iron. A bronze ax is a totally decent tool and largely the equal of an iron one. I wouldn't want a long bladed bronze sword b/c it would snap easily but you could field a lot of shorter bronze swords for the effort of one iron one.