> Are there any uses or applications for Gödel's theorems (other than their mere implications)?
Theorems are implications, so I'm not quite sure what you mean.
There are practical applications of Gödel's theorems, if that's what you mean.
His incompleteness theorems are useful for determining when to give up on a certain class of approaches toward a problem. I think this is what you meant by "implication", but the importance of this knowledge is difficult to over-state.
His completeness theorems form the groundwork for first-order theorem proving, which has plenty of practical applications.
> you can't heat your home with a heat pump in a place like Wisconsin... Geothermal is better, though I believe you still have problems with saturation in cold climates
Geothermal heat pumps can definitely work in the portions of the upper midwest. I know some people in both MLK and Madison that have heat pumps.
As far as I understand it's hit and miss, though. Depends on the particular piece of property you're living on. And you may need an additional heat source for occasional use (e.g. the super cold winter a couple years back I know one of those folks were super glad they still had gas heating in addition to the heat pump).
> I hadn't even heard of a heat-pump until recently, which makes sense, since they seem to mostly be concentrated in warm, dry areas.
Ironically I'm the other way around. Didn't hear about heat pumps until moving north. Probably because heat pumps don't make as much financial sense in warmer climates where you're not blowing $100+/mo on heat?
German megacorps do just as much manufacturing in developing economies as American megacorps.
The Mittelstand doesn't do the sort of manufacturing that the rust belt did 40 years ago. These smaller firms existing today only because of big disparities in quality between their products and cheaper competitors. They benefit enormously from the German government's investment in applied research.
It even worked for the United States. Protectionism was a major component of our policy approach toward industrialization.
Protectionism as a mechanism for supporting the development of domestic capabilities is, historically, a well-justified policy position.
And if you look to highly protectionist economies today, you'll find mostly developing economies.
> Why not?
1. Most importantly, protectionism as a mechanism for inflating wages and/or spurring job growth in an already developed economy isn't nearly as well-tested an approach as examples of protectionism in America's past. Historic examples of US protectionism had the end goal of boosting domestic labor productivity. Modern protectionism risks doing exactly the opposite.
2. The diffuse benefits of free trade must be weighed against the more localized costs of free trade. It's a difficult calculus, but it shouldn't be ignored. Cheap stuff at Walmart and Amazon benefits a whole ton of people. Perhaps more importantly, access to foreign markets and capital creates a lot of jobs and wealth domstically. A lot of Americans are employed doing high-paying, high-quality work that is exported globally. (Including a lot of software engineers.)
3. The benefits to labor may be short lived if automation wipes out a lot of manufacturing jobs. In which case we've traded access to foreign markets and capital for maybe 10 years of jobs and a false sense of non-urgency in job re-training.
> What I don't understand: the REI market is the one place where Soylent is inarguably better than any other product in its niche, and nobody seems to give a shit about that.
I guess it depends on what you mean by "better".
SAR is a niche within a niche. I can totally understand why Soylent is 1000x better than other options.
But most backpackers are doing it for fun. Reducing weight and space is great, but there are plenty of much more enjoyable meals that are only marginally heavier/bulkier.
At least for me, cooking a good meal before bed is my favorite part of the day. I'll happily carry an extra pound or so to make that happen.
TBF, a lot of purely recreational backpackers care less about the pleasures of life. The type doing 14 hour days and so on. But that's a small market, and all the folks I've met on trails who are doing that sort of thing tend to be pretty price sensitive. Young folks with few savings taking a few months off work don't have three months of Soylent money ;-)
> Isn't that literally what the TSA lock on luggage is?... And with the TSA master keys leaked a couple of years ago all it needs is one malicious airport worker to open your bags and sniff your panties, erm, steal your laptop.
Good point.
> but why do all these arguments against backdoors never mention this?
However, I don't think arguments against back doors should mention TSA luggage locks! It's a bad prior.
You don't want people in the "airport" mindset when you're trying to convince them not to allow the government to snoop.
People who enter airports (or especially customs) basically give up all of their rights to privacy. And most Americans are apparently OK with this. Begrudgingly, perhaps, but ultimately most people accept it and go on with their life.
So, "think about airports" is a really terrible persuasive setting.
Instead, you want people thinking about their bedroom. About their car. About their child's playroom. About the settings where they live 99% of their life. Because that's the setting that government back doors in consumer electronics expose. And that's the setting where people get most uncomfortable about carte blanc government access.
You are correct when you say that writing verifiable/verified code is a separate skill that not many programmers possess.
But crucially, it's a skills gap -- not an intelligence gap -- that stands in their way. For most properties, writing verified code doesn't require that much more intelligence than writing normal code. Different skills, but in most cases not much more intelligence.
But I don't think a skills gap is the most pressing barrier. There is an intrinsic difference in difficulty between stating conjectures and proving theorems. There's no silver bullet here, including either education or raw intelligence. The latter is, intrinsically, more difficult and more time consuming.
You're technically correct, I think -- the actual point isn't to super-charge growth.
But without massive spending cuts, you need supercharged growth to offset lost revenue. The premise of Kansas-style tax policy -- which coincides in spirit with Trump's proposed tax policy -- is that you can avoid massive spending cuts by supercharging growth.
Without that premise, these tax policies would be much more difficult to push through. Because they'd have to admit massive deficit spending, or else come pre-packaged with huge cuts to popular services.
So, the end goal isn't necessarily to supercharge growth, but the promise to supercharge growth is a huge aspect of what makes these tax plans politically viable.
Theorems are implications, so I'm not quite sure what you mean.
There are practical applications of Gödel's theorems, if that's what you mean.
His incompleteness theorems are useful for determining when to give up on a certain class of approaches toward a problem. I think this is what you meant by "implication", but the importance of this knowledge is difficult to over-state.
His completeness theorems form the groundwork for first-order theorem proving, which has plenty of practical applications.