A patent on a computer running an algorithm explicitly does not cover performing the algorithm in your head, on a pad of paper, inherently when you do some other function, etc. It is quite distinguishable.
What is the significant difference between evaluating an algorithm in your head, and doing the same thing with computer assistance, which would justify a patent? What is the novel, non-obvious change in the state of the art which such a patent would document? We agree that it's not the algorithm, or the computer; what's left?
More specifically, what is it about "evaluate this algorithm with a computer" which would make it patentable, which would not also apply to "evaluate this algorithm with pencil and paper"?
I can invent a new automobile transmission, and the fact that I wasn't the one who invented the automobile is irrelevant. You've created a new rule whereby each industry gets one patent by the founder of that industry, and any improvements in that industry are forever unpatentable because they incorporate something not invented by the applicant.
This is an obvious straw-man argument. There is no new rule prohibiting patents which build on prior patents. The only rule being applied here, which is hardly new, is that the patent must add something to the state of the art which is both novel and non-obvious. The automobile in your example is not novel, but your transmission is presumably both novel and non-obvious. The patent would cover just the transmission, not the automobile.
On the other hand, if you tried to get a patent on combining an existing transmission with an existing automobile design, I would expect such an application to be summarily rejected unless there was something both novel and non-obvious about the concept or method of combining the two. This is where software patents fail. You have two pre-existing components, the algorithm and the general-purpose computer. The patent application only covers combining these two existing elements together in the most obvious way possible, as running algorithms is the sole purpose of a computer.
Can you do the same and show that the software industry has stagnated because of patent disputes?
Actually, yes. For one obvious example, just look at the areas where interoperability has suffered due to Microsoft's FAT filesystem patents, or patents on media codecs, or lossless compression algorithms, or rendering techniques. Software patents are also inherently incompatible with free and open-source software; any license fee whatsoever will block legal free software development in that area. Driving people to reinvent the wheel, often in an inferior way, isn't progress. Start-ups and other small for-profit organizations have a similar problem; they don't have the portfolio necessary to enter into the standard cross-licensing agreements, or the financial resources for drawn-out patent fights in the courts. Their only real option is to settle for being bought out (under duress) by an larger incumbent.
It's obvious that patents, and especially software patents, impose costs and place roadblocks in the way of innovation. It is hoped, but not proven (and not for lack of trying), that the incentive of a state-backed monopoly is enough to compensate for this. What we lack is an alternate world to compare against, one with the same initial conditions but without patents.
If Google Glasses makes it to market, then you can publicly post a retraction statement that patents don't stifle innovation. Sounds good? ... Of course you won't agree to that...
Exactly, because no retraction would be justified. That a particular product eventually makes it to market does not imply that patents do not stifle innovation—which is not the same as saying that no innovation can occur, only that the patents impede innovation rather than contributing to it. To decide that we would need a parallel world without patents to compare against, and we unfortunately do not have access to such a world. All we have are guesses regarding the relative costs and benefits, the costs being much concrete.
We know how much is spend on patent litigation, and about some things which are avoided due to patent concerns. There is more we don't know about specifically which was never created because the cost of dealing with the patents was deemed too high. On the other side, it is rare to be able to claim even that something was invented which would probably not exist were it not for the patent, much less that it certainly would not have been invented.
I'm saying that software patents require hardware, and as such, innovations in software-using hardware indicate that software patents are not stifling innovation, as many claim.
So... you're saying that patents on software (with or without a computer involved; it makes no difference) do not stifle innovation in hardware? I might have to give you that one, though one could argue that lack of software interoperability due to software patents stifles demand for innovative hardware. The effect is likely to be small, though. What you should be arguing, though you'll have a hard time of it, is that software patents drive hardware innovation. If the effect isn't positive then there's no justification for the patents. It's not enough to argue that they aren't particularly harmful. The algorithms covered by software patents generally run just fine on existing computers, so it's not like software patents drive demand for faster or more efficient computers, either.