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I followed Start Bodyweight for a while, seemed pretty good. The emphasis on being able to manipulate one's own bodyweight appealed to me, and end goals of the progressions like one-armed pushups/chinups/etc are pretty cool. Minimal equipment required, mostly just access to a bar for pullups/chinups and somewhere to do inverted rows and dips, though it's usually advised that you add deadlifts. 30mins 3 days per week is about what's required.

The Bodyweight Fitness subreddit provides similar routines, as well.

http://www.startbodyweight.com/

https://www.reddit.com/r/bodyweightfitness/

There are also a lot of resources on youtube if you want video demonstrations/walkthroughs. Calimove was pretty useful for me.

https://www.youtube.com/@calimove

That said, I was probably in the best shape of my life back when I used to do indoor rock climbing three days a week. It incorporates a satisfying combination of technique/problem-solving and physical strength/endurance.

I didn't interpret you as saying that the F-35B should be cancelled. I'm more bringing context that it's not solely a US Marines toy, and not solely a baby-carrier plane.

I don't think that adding catobar support for modern fighter platforms is viable for all of these small carriers that are incorporating the F-35B. Admittedly my understanding of the situation is very shaky, but by all accounts I've heard, the catapults and arrestor gear place very significant strain on even the US supercarriers. More countries used to operate catobar carriers in the past (such as my home country of Australia, up until the retirement of the Melbourne and a decision to discontinue fixed-wing carrier ops), which I suspect has to do with the operation of lighter aircraft from the carriers at the time. (~7t max takeoff weight for a Sea Venom, ~11t for a Skyhawk; compare to ~30t for a Super Hornet or an F-35C.) Maybe the situation has gotten better with EMALS cats, but we're yet to see this technology used to make baby catobar carriers a thing, so who knows?

The countries in question would likely need to upgrade from their ~25000t LHDs to something with at least the displacement of the 40000t Charles de Gaulle. (Not to mention that most such carriers use nuclear power for both propulsion and to power the cats and traps.) Such vessels would come at great expense, and likely also have significantly larger crewing requirements, which tends to be a pain point for middle-power navies. I also don't think a lot of these vessels would've been built bigger in anticipation of catobar requirements, as they were largely originally specced for helicopter deck and amphibious roles. The F-35B really seems like an opportunity which all of these countries have siezed upon after seeing it come to fruition.

Again, it seems like you have a case with the Queen Elizabeths, though it seems like the UK balked at the cost of fitting catobar, if that's any indication.

As to whether the costs would've been offset by savings in the development of the F-35B, I don't even think we're talking about costs on the same magnitude here. For reference, total R&D costs for the F-35 as of 2019 were $71.9billion in 2012 dollars. Building and sustaining big boy carriers for middle-power countries would've cost the JSF partners hundreds of billions of dollars, easily.

It's about a combination of stealth and the sensor/avionics package -- the ability to detect and identify SAM radar systems and launchers, and chart a path which minimizes likelihood of detection, aided by the aircraft's low radar signature, while enabling strike operations to take place. If you're arguing that the F-35 is not invisible, then you're attacking a strawman.

The F-117 was central to SEAD operations during Desert Storm, and the F-35 is regarded as the most credible SEAD platform in the USAF inventory today.

There are 12 catobar carriers in existence at the moment, 11 operated by the US Navy. (Soon to be 13 with the Chinese Fujian carrier entering the mix.) Maybe the UK would've gotten their act together and fitted catobar on the Queen Elizabeths if the F-35B didn't exist, but for the most part I think this is indicative of the challenge of putting together the hardware to launch/recover modern fighter aircraft at sea.

The F-35B may have started as a Marines ask, but it seems to have become an export success with countries that aren't really up to footing the costs for catobar-capable flat-tops for modern fighter aircraft during peacetime, e.g. the UK, Japan, Italy, Korea, potentially Spain.

The Marines have also been exploring the F-35B in austere basing, EABO conops, airborne amphibious ops, etc., so it's not just carrier ops.

It has been a lead weight on the JSF development project, for sure, but the F-35B does seem to provide an intriguing capability now that it's a thing. I'm also not convinced that a dedicated STOVL project would've given a more suitable plane -- it really seems like you would want the whole stealth + advanced sensor/avionics package on your jump jet to meet needs like naval LHD-borne fixed-wing AEW/air interceptor/task group anti-air range extender, airborne amphibious ops CAS, etc. Owing to the difficulties encountered by the JSF in supporting the F-35B, I doubt it's going to be succeeded by another platform for a very long time.

I don't think you understand the kinds (and volumes) of SAM firepower a Soviet hangover can leave you with. Ukrainian skies are the most dangerous skies in the world right now, for both sides.

Are you claiming that the Pentagon is secretly acquiring F-35 airframes for far higher prices than other JSF program partners or foreign sales customers, in order to cook the books?

These are some weird takes. Saying that the F-35 is built for ground strike roles doesn't mean that there's no need for ground forces or infantry, or that other capabilities won't ever be more suitable for certain strike operations, or that people have WWII-era strategic bombing campaigns in mind.

fwiw, if you're looking for a particular kind of strike target, the F-35 is widely regarded as the USAF's most credible SEAD/DEAD platform. It's suitable for a wide range of other roles, but SEAD really sets it apart.

> We keep saying missiles are great and dogfighting is over, and we keep being proven wrong.

My understanding is that the "dogfighting is over" rhetoric stopped being proven wrong during the Iran-Iraq war, when Iraqi fighters started mysteriously exploding in the sky during operations.

> Pretty much all buyers of the F-35 have been offered different sorts of kick-back deals, where they get to produce parts of the plane or handle maintenance, so the deal props up the national arms industry in some way or another.

What? This is pretty much standard practice across the board in military procurements. For example, as part of SAAB's Gripen bid for Canada, they would arrange for the aircraft to be produced, assembled, and maintained in Canada if the Gripen were selected. Countries do this for a variety of reasons -- yes, to bolster local industry, but also to give them a leg-up on sovereign sustainment of the platform, and so that they can ramp up manufacture to meet their own needs in the event of a war.

You might want to track down the information they release from multinational training exercises like Red Flag. Reportedly the F-35 has put in multiple dominant showings at Red Flag since its debut. I'm not sure how complete the information they release from these exercises is, though, and some of the aircraft involved (most notably the F-22) are notoriously restrained to keep the true capabilities of the platform secret.

Small, high-GDP countries like the nordics are also likely to rear a small amount of the high-quality pilots required for operating fighter jets. Maximizing those pilots by putting them in exquisite, high-end aircraft, with strong interoperability with aircraft operated by close allies (in this case most of the rest of NATO), makes a lot of sense.

Yeah, this. Smaller countries can easily wind up holding the bag with less-widely adopted defence procurements, and without a wider community of users investing in the platform and its parts ecosystem it can become a sustainment nightmare.

For example, Australia became the sole operator of the F-111 from when the USAF retired it in 1998, until the RAAF retired it in 2010. The Australian Army also found itself in the position of sole operator of the ARH variant of the Eurocopter Tiger, a situation which lead to severe sustainment issues and exorbitant per-hour flight costs (estimates of up to AU$34k), and eventually lead to the 2021 decision to replace them with Apache Guardians.

The four colour theorem does generalize to infinite planar graphs, in the sense that if an infinite graph can be embedded in the plane without overlaps, then a four-colouring is possible. It's a straightforward consequence of the compactness theorem for propositional logic, which I set as an exercise for my students when I teach the topic.

Don't worry, they probably just want to fill out requirements documents with "Agile" written on them.

Really the best usage of all the computation models we're discussing here is using them in mathematical reasoning. If you're looking to "create real working programs," then a better basis is probably going to be some combination of actual industry-grade programming languages and actual CPU architectures.

This response might come off as a little facetious, but seriously, I think the idea of "founding" industrial computing languages/platforms upon theoretical research models of computation misunderstands the relationship between theory and practice. There is a relationship for sure, the research on these models usually does want to translate into real-world implications somehow, but your functional programming language is not the literal lambda calculus.

This whole debate is always so bewildering. Programming paradigm fanboys get into heated arguments about which model is the "best" one, but actual computer science research uses myriad different models of computation, usually endeavoring to select the one that is most convenient for the given purpose.

Sometimes that could mean using the lambda calculus, particularly in study of language theory and type systems. Other times that could mean some sort of black box model, such as when proving lower bounds for solving problems using specific operations (see e.g. the sorting lower bound). Yet other times, like when establishing the ground-zero of some new variety of computational hardness, I can't think of many more suitable models to cut up into pieces and embed into the substrate of some other problem than those based upon Turing machines.

When you mentioned infinite structures, I thought you'd bring up the idea that our goal to automate often pits us against problems defined as collections of infinitary instances. I don't think the potential infinity of tapes and running times poses as much of a concern by comparison.

Maybe computer science is about giving, to borrow a little bit from Hilbert, finitary representation to infinitary structures. (Finitary representation with other properties of interest, such as tractability and whatnot, of course.)

I agree with the sentiment, but I've actually come to consider "computer science" to be a great name for our field.

Turing's universal machine is the original dependency inversion of our field: instead of specifically studying the programs that can be written for any particular hardware device, we largely study phenomena that are regarded as computation as defined by the Church-Turing thesis, and require that the hardware vendors supply suitable universal machines which can instantiate the phenomena of our study. Or field is the science of computers -- every program is a blueprint for a computational device -- but we choose to simulate most of our blueprints using universal machines, so that we don't have to send each one off to the silicon fab separately.

I think the point being made here, is that it is difficult to gain recognition for counterfactuals.

> Even in the much cleaner world of mathematics, basically all interesting work is done within the realm of formally provable statements.

More-or-less this. I'm going to take this as an opportunity to drop one of my favourite quotes, because I can't help it:

"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles."

-- Alan Turing, Computing Machinery and Intelligence

I was expecting a book about mathematical modelling of games from the Street Fighter fighting game series.

I wrote a basic response, but it got longer than I thought it would and HN complained about it being too long, so here's a pastebin: https://pastebin.com/zTJA4bJh

If the time bound is being put in place in the hopes of being able to automatically analyze the behaviour of the code, then no.

I singled out "outputting 0" on every input because it's among the simplest possible specs you could try try to check with the kind of "very powerful semantic analysis" tool the top-level post was hoping for. In practice you probably want to check a more complex spec -- you want your code to solve a specific problem on whatever input it receives -- but if the "always output 0" spec is impossible to automatically check, then what hope do more relevant specs have?

> call the time bound N

Call the time bound c|x|^k, where x is the input and c and k are constants.

I see what point you're making, and I agree that you get yourself a nice, merely coNP-complete problem if you're willing to cut off the space of inputs at a point by enforcing a constant time bound or whatever. More than anything, this kind of argument makes me shudder at just how hard the very worst stuff in NP must be.

This is kinda part of the promise of regular expressions, context-free grammars, relational algebra, map-reduce and other stream/pipeline-based programming models, and maybe to some extent P-complete things like convex optimizers and programming models based on horn clauses like datalog.

Each of these things aims to allow the user to specify a task in a restricted model of computation. In turn, it tends to be possible for the engineer writing the solver to build an engine capable of very radical transformations, optimizations, and analyses, that generally can't be matched by compilers and interpreters for Turing-complete programming languages.

This might get you away from the literal statement of Rice's theorem, but we tend to ask questions about our programs' behaviour across all possible inputs, and these questions tend to remain impossible to solve in general.

For example, finding out whether a time-bounded Turing machine outputs 0 all inputs is still undecidable. (coRE-complete, in fact. That's better in some sense than the Pi_2-completeness of the same problem for Turing machines without the time bound, but since neither admits a solution in the form of a computer program, a lot of people would consider the difference an academic curiosity only.)

> (hypothetically, bugs aside)

This is the problem. Interesting computing is some impossibly complex (undecidable, in fact) subset of all computing, that you try to get inside of via the practice of software engineering. Turing's theory of computation provides reasoning tools which allow us to bring rigor to the idea that building correct software that does useful things is generally difficult.

> Designing a computing model that only covers what's useful while also making it convenient appears to be a long standing open problem.

Per the above point, depending on how you characterize this goal, it's probably impossible to accomplish.

I don't think this discussion thread is giving the writer's concern enough credit. Universality on its own obviously doesn't allow the instance to take over its host, but it can enable the bulk of the malicious payload to be encoded as legitimate instances of whatever P-hard optimization problem the cloud service solves, so that it need not be injected directly via the actual vulnerability that the malicious actor uses to take over the host.

> TC isn't quite the actual top! There are ways to make problems that, even with an oracle for solving Halting, are still hard [0].

I'm not sure why you're raising the subject of the degrees here. Malicious software doesn't need to have hypercomputational powers to be a threat.

Fair. The topic is often taught to students without broaching the topic of Turing machines.

I think we agree that as a matter of actually building the topic of NP-completeness, nailing down a concrete model of computation for the verifiers which can itself be operated upon constructively is vital.

I don't think you need to reach for Turing machines to specify P or NP, but I think it's fair to say that Turing machines* play a key role in establishing NP-completeness. (And other completeness phenomena.) Computational hardness is computational universality turned on its head, e.g. a problem X is NP-hard because someone has been able to figure out how to smuggle full-blown time-bounded nondeterministic Turing machines into instances of X.

*Or some other simple model of computation that's polynomially invariant wrt Turing machines, but at this point I don't think "you don't need Turing machines" remains as salient.