It's not clear to me why such a hard distinction is drawn between software and hardware patents.

The usual argument for this separation is that "software patents are just math", but then aren't hardware patents are just physics (which, ultimately, is also just math)?

It feels like there's no clear line here, and whatever benefits, if any, are to be derived from patents, they apply equally to either side of it. Basically, either it's a net benefit to society, and then both kinds are valid; or it's a net drain on society, and then we should just get rid of them altogether. Or maybe set the bar for what is patentable much higher wrt to novelty and value (but, again whether it's hardware or software feels irrelevant).

I think I covered one major distinction well. Copy software has 0 cost, copying matter has some. This is just a re-wording and perspective change on "software patents are just math" angle.

Some people feel that since there is no copying cost, software favors the little guy more than with physical goods, so normal patent protection doesn't provide an benefit. These people claim that a big big evil corporation could start making a million of their widget per month and out compete them, but with software this cannot happen per their arguments. I think these people acknowledge that both physical and software patents get abused and are imperfect but feel that physical patents provide enough gain to offset their downsides.

I disagree with those people completely. I am unaware of ANY actual evidence that patents help.

Your distinction doesn't make any sense. Besides, you can patent a gadget without ever building one. In other words you can patent a CAD diagram. Then you could use your gadget patent to prevent anyone from legally building your gadget (in the US assuming a US patent)

I am aware of actual evidence that patents help, if enabling small companies to withstand pressure from behemoth companies is considered help.

Could you share this evidence? Because I haven't seen it.

They are currently necessary for the payment structure in the medical industry. I'm not saying they couldn't be replaced for that somehow, but simply removing patents without having something in place would be very disruptive there.

they are already far more disruptive everywhere else

I agree. Even "hardware" patents are too hard to defend to really be worth it most of the time (ex: fidget cube and other chinese kickstarter clones). You can't rely on patents to ensure defensibility to your business model, so they really just end up being money-sinks.

Not sure about how the Chinese patent system works but isn't it the case that these companies having U.S. patents doesn't really matter in China?

It matters if they want to sell to consumers in the US

A US Patent has jurisdiction in the US. You can bar foreign companies from legally importing your patented inventions. US customs will seize such goods at the port or elsewhere if they are aware of them.

That isn't a real solution. Searches are imperfect and this forfeits the entire foreign market. I think Musk has the right idea on novel inventions, the only way to keep them secret is to actually keep them secret.

An honest patent forces a description good enough to duplicate. Better to keep your secret sauce secret.

Just a nitpick, by definition what does not have protection is not IP.

Trade secrets.

As long as they remain secret they have protection, but the very act of outing them makes them not secret. I am aware of very few successful suits defending trade secrets.

Plenty of trade secrets are defended successfully.

Trade secrets cases are lost when the owner is claiming something is a trade secret when it doesn't meet the legal definition of a trade secret.

Trade secrets are useful for long-lived secrets like the formula for Coca-cola. But if someone independently develops the same thing you are trying to keep secret too bad.

Also, if the secret accidentally gets out (w/o theft) the trade secret enters the public domain.

Hmm. Sounds like a choice of definition but to my mind some IP that lapses in to public ownership (and so is not protected) doesn't cease to be IP, some IPR cease to exist but I'd still consider that work/invention/mark/design/database to be intellectual property just it's now owned by the public.

It probably doesn't matter at all.