I used to be absolutely against software patents on those grounds, but I nowadays actually think it's a weak argument.

We don't see people arguing we shouldn't patent physical machines because ultimately each operation is a simple physical movement, so the sum of everything is just a sequence of physical movements.

Yet we see people arguing we shouldn't patent software "machines" because ultimately each operation is a simple mathematical operation, so the sum of everything is just a sequence of mathematical operations.

The argument against the patentability of maths, AFAIK, has always been "maths is naturally inherent and merely discovered by humans". This, to me, is an argument against pure maths especially; but as we get into applied maths I think it's much less arguable that algorithms and data structures are naturally inherent (much like how physical constructions—machines—aren't naturally inherent from the laws of physics).

I still strongly think far too many patents get issued, but I'm less convinced than I used to be software patents are inherently bad, and that patents do need reform in various ways.

All programs are proofs and their results are theorems[1]. If "math is naturally inherent and merely discovered by humans" then so are all programs; programmers are just discoverers and not inventors. Given the proof of Curry-Howard Isomorphism rests on existing maths we can have another discussion about whether mathematical patents should be issued if we don't believe that maths are inherent and are actually invented, but as long as we hold that we can't patent maths then it must also hold that we can't patent programs due to their equivalence. [1]: https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

Programs and proofs are not actually equivalent. The Curry-Howard correspondence is only concerned with the types. If you take a useful program and replace every function with another of the same type, the program is now pointless but still corresponds to the same proof. And unless you're explicitly trying to encode mathematical statements into the type system, that proof is likely to only show something trivial like "there is an integer".

>I still strongly think far too many patents get issued

Then you are against software patents.

If millions of people carried machine shops around in their backpacks, you would be against mechanical engineering patents, because far too many patents would be issued.

At the core of patent law is "presumption of validity", which places the burden of proof on the accused, rather than the accuser. Anything that multiplies the number of patents the PTO has to examine makes that presumption less reasonable. At some point it's arguable that a party accused of patent infringement is not getting due process.

Software patents. Presumption of validity. Due process. Choose any two.

Patents on mp3 and RSA didn’t prevent them from being used everywhere. I guess a patent on FFT (which, by the way, was considered at the time, according to Wikipedia) wouldn’t have stopped its adoption either.

Also, IMO, a formula, which tells you what to compute, is essentially different from an algorithm, which tells you how. FFT would be patentable because it is non-obvious, even when given the formula for doing a Fourier transform.

It still might be non-patentable on other grounds, such as the fact that Gauss apparently described it in 1805 (http://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf), two years before Fourier published his work on what now is known as Fourier series.

Sorry, a formula and an algorithm are not at all different.

A mathematical formula is just a symbolic expression of an abstract concept, with the procedure (algorithm) how to use it being implicit (= obvious to the person skilled in the art).

A computer algorithm can be trivially converted into purely mathematical/logic representation ("formulas" if you want), e.g. using things like lambda calculus. And vice-versa - an abstract mathematical problem formulation can be converted into an algorithm (assuming the solution is known).

If you start patenting algorithms, you are patenting math.

It is true that an algorithm can be converted to a formula, and a formula to an algorithm, but it is unlikely a given useful algorithm could be generated mechanically from a (human-written, useful) formula.

For example, you could write a formula to express the property of order in lists, and maybe with some mechanical procedure (falling under "obvious to the person skilled in the art") you could then generate an algorithm that sorted lists. However, what's the time/space complexity of that algorithm? What are the practical runtime characteristics? For industry applications the practical runtime characteristics matter as much as anything else. That you technically could compute something doesn't matter at all, if that computation might not finish until relevant celestial bodies have phase changes.

I'm not saying Quicksort should be patentable, but I do think it's at least a step and a half removed from pure math.

But you could also argue that algorithms can be expressed through Language by trivially converting them into a purely semantic/logic representation. Is then anything that can be expressed through Language not patentable because it is trivially reduced to words?

With an algorithm implementation, you require integration with a runtime, quick storage, data, a data format. You also maybe need some tests and an SLA. There must be other components I missed.

>Patents on mp3 and RSA didn’t prevent them from being used everywhere

When the people who spread adoption ignore the law, sure patents don't prevent anything, e.g. https://en.wikipedia.org/wiki/MP3#Internet_distribution

If you take a different example, say, improvements to JPEG, it's a lot harder for camera manufacturers to ignore patents. You're at the mercy of the patent holders, whose terms apparently haven't been reasonable enough for anybody to improve the compression in digital photos beyond what we had decades ago.

You have to be careful to avoid cherry picking results. As a counter-example in the same area, arithmetic coding was arguably shut down as commercial technique by IBM patents.

If someone can patent, say, the magsafe connector, then I don't see why someone couldn't patent the FFT.

Whether it's a good thing that patents exist is another matter, though.

I think the idea behind patents was that you can't patent natural phenomena and things that derive from them. Algorithms are just another way of expressing mathematics and logic so that is what gives the rise to the idea that these things shouldn't be patentable. Mathematics and logic describe laws of nature (such as waves in the case of a Fourier transform) which exist without us "inventing" them.

Magsafe connector is an engineering invention that doesn't exist or derive from anything in the nature.

Good luck to define "natural".

A patent on fast Fourier transform would essentially do nothing, as no one appears to be selling the algorithm outright.

A patent on FFT would stop anyone from using it in their products. A patent does not solely mean you can’t sell the patented thing, it means you are prohibited from commercially using the patented thing in any way.

Seems like it would be possible to do something like: produce a freely available device that you provide some kind of supportive or value-added service for.