Without arguing the benefits/drawbacks of software patents, isn't slide to unlock only a fundamental concept because Apple invented and popularized it? To me, it only seems trivial because it's ubiquitous, whereas that might not have been the case before the iPhone.

Software patents that boil down to "real life action, but we did it on a computer" are just obnoxious. Sliding a bolt to unlock something is something we've been doing for centuries, but suddenly Apple put it on a screen and gets to prevent anybody else from doing it? That makes no sense.

I don't see why this is unique to software. As long as the proof is convoluted enough, how would it differ from making a physical D-pad? Both are made from already discovered axioms/materials, and both are transformed via known ways in a unique order into new tools to accomplish a particular task. If a D-pad patent should be allowed, why not a compression algorithm?

Hardware patents make sense, as it's actually possible to come up with multiple solutions to the same problem. You can create a D-pad multiple different ways, as proven by the many different D-pad patents, as the goal is just to create an interface between electronic inputs and a logical physical shape. How you do it doesn't matter as long as the result is reliable and satisfying for the end-user. The 4-directional shape of the d-pad wasn't the patent, it was how the d-pad worked. Sure some people have preferences to one design or another, but that's where they made the innovation.

But there isn't multiple ways to create Pi. Pi is Pi. Just because you discovered a math equation to define it first doesn't mean you get to claim dibs on it. You could claim that you wrote code that calculates Pi more quickly on a specific computer chip or something, but that's copyright, not a patent. Patents shouldn't be used for things that can be copyrighted, and vice versa.

There's a reason why we have separate systems for copyrights, trademarks, and patents. Copyrights protect creative authorship, ways to express things. Trademarks protect identification, how people recognize you and your creations. Patents protect invention, novel processes to accomplish an action.

Patents are for protecting the processes you develop, not the resulting actions. You can't patent boiling water to create steam, but you can patent the steps you took that led to water boiling and becoming steam.

To bring it back, what process did Apple develop for slide to unlock? Slide to unlock itself is an action, not a unique method of solving a problem. Like patenting the mere action of putting a key into a hole, instead of how the mechanics of the key itself actually opens the lock. They wrote code that interpreted "Box moving from position A to Position B allows access", but that's a copyright. Nobody would argue that they should be able to copy what Apple wrote to make that happen. But why does Apple get to claim that the action of moving a box is something they invented? Because the user can use a human finger on a screen now? Apple didn't invent the capacitive touchscreen, somebody else did, and Apple paid them or a licensor of the tech for using their patent, they didn't invent anything there. So all you're left with is the action, moving a box with a finger, which shouldn't be patentable. And the code that interprets the action, which should be a copyright not a patent.