No... It's "I accuse you of a crime and provide sufficient evidence that you have committed the crime - the URL of your page with my copyrighted photo, and my sworn statement of ownership of that photo. You get punished for that crime unless you assert that you're innocent, at which point your site returns and we can fight it out in court. And if you can prove I was lying in my sworn statement, you can get lots of money in damages."

There's nothing unconstitutional about that. This isn't criminal, it's civil... there's no requirement for a jury to find you guilty first.
And consider, if I accuse you of stealing, or drug trafficking, or whatnot, you can get arrested and held, potentially without bail, until trial. Isn't that "punishing" you? And yet, it's certainly constitutional.

You're confusing two different things here. When a patent claims "[super novel and non-obvious technique] performed by a computer," it's not saying that the computer is the point of novelty... and there's also nothing that requires every element of a claim to be independently novel and nonobvious. Hell, if that were true, you could never claim an improvement: "A better mousetrap, comprising..." and someone would jump up and say "mousetraps aren't new!" Similarly, you could create a brand new chemical composition or drug, never before seen in nature, and someone would jump up and say "that's just made of basic elements like hydrogen! It's not new!"

Additionally, you're also confusing two different statutes. 35 USC 102 and 103 are the ones that say patents have to be novel and nonobvious. 35 USC 101 - what we're talking about - is the one that says that even a novel, nonobvious idea is unpatentable if it's not directed to patent-eligible subject matter.

Again, there's two different requirements here. The computer makes it patent-eligible. The novel, nonobvious algorithm makes it, well, novel and nonobvious.

And now you've moved the goalposts back - the computer. Because it's tied to a computer, it's patent-eligible. The pencil and paper version is not patent-eligible, even if it's the most novel and non-obvious algorithm ever invented.

Then why did you bring up this: "The general-purpose computer was not invented by the applicant" (emphasis in original). I agree with your new statement here - there is no rule that that's a requirement, so it's irrelevant that the computer was not invented by the applicant.

Exactly.

Depends on the claim. It could also cover an automobile including the transmission.

Agreed.

Except that the algorithm is not necessarily pre-existing. If it is, you can find prior art showing it. If you can't, then you can't simply wave your hands and say "but it's software, all software is pre-existing." Rejecting a patent as being obvious requires evidence.

It's true. My FAT-formatted USB stick won't run at all on my Mac. And I still have to view everything in vector graphics since rendering techniques are patented.

Sorry, do you have any concrete examples of this?

I fail to see how that's an argument for or against them - they're incompatible with the idea that all software should be free, but so what? I don't necessarily buy into that argument.

On the contrary, the greater variety of wheels we have - wheels that will enter the public domain in a relatively short time - greatly increases the rate of progress.

And you think abolishing patents would change any of that?

Not entirely true... we can look at countries that haven't had patent laws until very recently, such as Vietnam, China, Brazil, or India, and see if they're starting to innovate more now. "But wait," you say, "those are all poor countries." That's okay - we can also look at Switzerland, which intentionally didn't have a functioning patent system until relatively recently. How much innovation was coming out of Switzerland? None... that's why they didn't grant patent rights. How about now? Actually, quite a bit. There are many Swiss companies doing amazing work in pharma and bioinformatics.

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.

Then, lacking such an alternate world, we defer to our elected legislators, who felt that "patents" were better than "no patents". If we wish to go the other way, we should elect new legislators.

It's true, patent licensing and litigation is expensive. You know what's also expensive - product liability. Or medical malpractice. In fact, any time someone loses a lawsuit, it's expensive... and that money could be spent creating new ideas instead. Clearly, what we need to do is abolish the entire court system, right?

They're video compression algorithms. I thought we were talking about patents.

So you agree that the base ideas would be patentable if they were embodied in a hardware chip? Then how is that different from embodied in software and executed by a hardware chip?

I'm sorry, I came here for an argument, not abuse.

As a pro-tip, if you want people to debate you, you have to first not come off as a jackass.

But, as you note, there's a physical device involved. It's not just a mathematical algorithm. You could not possibly infringe that claim with a pad of paper and a pen or by doing math in your own head.

Do you have a patent number we can look at?

Claim 1: "1. A 3-D graphics method performed by a computer for real-time rendering of shadows in 3-D scenes to be displayed on a computer monitor..."

The claim explicitly requires a computer and a monitor. That's not pure mathematics. The pure mathematical algorithm is outside of the claims - if you did it in your head, by definition, you could not possibly infringe the patent.

On the contrary, if the patent claims require a computing device, then you cannot, by definition, do it in your head. You could perform the same algorithm, but you wouldn't infringe the patent - hence the patent isn't claiming the algorithm.

Claims must be read in light of the specification as it would be understood by one of ordinary skill in the art. The "broadest possible reading" of a term applies during prosecution, but in litigation, the claims must be interpreted more narrowly based on the spec. In this case, the claims recite correspondents, which the spec describes as including a random number generator and performing computing functions. While it's possible to read these as humans, I think a more reasonable reading is that they're computers.

That one's even easier. Claim 1 recites a cryptosystem, which is illustrated in FIG. 2 including an ALU and RAM.

Claim 1: "1. A method of generating in a digital data processor..."

There you go. In all cases, pure math - or performing the steps in your head or on a pad of paper - would not be covered by the patent claims. Therefore, they can't be claiming pure math.