> Hyperbole perhaps, but not nonsense.
It's definitely nonsense. Things with corporeal existence are clearly distinguishable from algorithms. It is unambiguously true that a brick is not an algorithm.
> A photograph can be saved as a file on a computer. The file essentially just consists of instructions for displaying the photo. Does that mean photography === mathematical algorithms?
Traditional photography is a chemical process. The shutter opens and the light causes a chemical reaction on the film. Digital photography is an electrical process. Light strikes the sensor causing electrical charges that can be measured and recorded. Both of those are physical processes. Neither of them is an algorithm, although the data either of them produce could be processed by algorithms (e.g. JPEG compression). Moreover, a camera as a product is the sort of thing you could patent. You can tell it isn't an algorithm because you can't load software into a general purpose computer and have the software cause the computer to be able to take photographs without a camera.
> I'm not arguing that he should be able to patent the mechanisms of the game, but not because it's just one big "mathematical algorithm". That's ridiculous; it's a work of art.
That's exactly why it's not patentable. For art you get a copyright, not a patent.
> To use the example from the article, any design must be described with a sequence of words. You can't patent a sequence of words, so all patents should be invalid.
This appears to be the source of the nonsense. You aren't distinguishing between the words (or algorithms) that describe a thing and the thing itself.
> To me, that's not much more of a stretch than saying that all software is simply a collection of mathematical algorithms. Perhaps literally true in a sense, but essentially meaningless.
All software is simply a collection of mathematical algorithms. That isn't meaningless, it's the reason it's impossible for any software to exist that you could load into a computer and cause it to be able to take photographs without a camera.