So, like compulsory jury duty and the draft, this would be directly against the 13th Amendment.
Then again, according to the Supreme Court, even forced, unpaid road duty (chain gangs anyone?) is an inherent power of the government, so maybe this is ok.
> In view of ancient usage and the unanimity of judicial opinion, it must be taken as settled that, unless restrained by some constitutional limitation, a state has inherent power to require every able-bodied man within its jurisdiction to labor for a reasonable time on public roads near his residence without direct compensation.
(spoiler alert: according to the ruling, the US Constitution, including Amendments, does not limit this power; and this is in fact cited as justification for upholding the draft)
Do you have any reason to believe that amendment was ever intended to cover things like mandatory jury duty? Or are you advocating for reading the text verbatim with zero consideration of the context or history? That kind of reading impacts a lot more than this, and not entirely in a good way.
I think there are much better argument for mandatory jury duty, like the fact that it's an inherent and explicit part of the preexisting Constitution, and that was not explicitly repealed nor (as far as I know) considered.
But the Court chose not to use those arguments, perhaps because they are less absolute and don't apply as cleanly to the draft.
Personally, I think that jury duty as it is today (no real pay, sometimes very long trials, "hardship" completely at the discretion of the judge) is actually a substantive violation of the principles of liberty that the 13th Amendment (along with the rest of the Constitution, notably the 5th Amendment) was meant to protect; (though I myself would likely enjoy actually being on a jury, and am fortunate that I can afford it/my work would likely pay).
And I don't think it would've been crazy to require an Amendment to institute a compulsory military draft, or better yet interpret the 13th Amendment to allow the draft (and jury duty) on narrower grounds but use it to better protect soldiers against various abuses inherent in the current military power structure and lack of exit option.
I do think that mandatory road duty is about as direct a violation of the purpose of the 13th Amendment as anything else the state could do. I think the (explicit) argument that the takings and due process clauses protect your money but not your labor is patently ridiculous.
> I do think that mandatory road duty is about as direct a violation of the purpose of the 13th Amendment as anything else the state could do.
Let me make sure I'm getting this right. You're making a serious claim that if the state required you to, say, clean the road by your house every morning, you'd feel like your experience would rival those of 19th-century slaves? You genuinely think that was the kind of thing the amendment was written for and do not see a meaningful distinction between the two?
> Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith.
Obviously the experience wouldn't rival one of a 19th century slave and nobody is making that claim. However, forced labor for no compensation is slavery, by definition.
> Obviously the experience wouldn't rival one of a 19th century slave and nobody is making that claim.
This was literally the comment:
>> I do think that mandatory road duty is about as direct a violation of the purpose of the 13th Amendment as anything else the state could do.
The state could bring back 19th-century-style slavery, too. Wouldn't that be a more direct violation of the purpose of the amendment? Because eliminating that sort of thing was kinda the purpose of the amendment, no? The purpose of the amendment clearly wasn't to prevent the government from requiring you to maintain the road around your home... right?
This isn't my interpretation, I'm reading what you guys are writing as-is. You're trying to add more context and explanation that wasn't there, weakening (and frankly contradicting) their argument.
It's especially ironic given you're both simultaneously trying to read the amendment so blindly and disregarding the context or purpose (the original purpose emphatically was not to prevent you from having to do a bit of upkeep around your neighborhood), yet somehow you don't like it when your own writing is read literally?
Systematic widespread slavery is obviously different from using the threat or application of violence to compel unpaid labor in smaller-scale scenarios, but both are de facto slavery and both are direct violations of the amendment. If you wanna argue that there is a concept of a "lesser violation" and that it makes some forms of slavery OK, be my guest but even children don't buy arguments like that.
It's like trying to argue that a little murder is fine because really, the laws are set up to prevent mass murder.
> Systematic widespread slavery is obviously different from using the threat or application of violence to compel unpaid labor in smaller-scale scenarios,
Eh? Violence? For refusing mandatory upkeep around your home and neighborhood? Are you writing this from North Korea or something? How is fining you such a foreign concept where you live that your government has to resort to violence to get you to do some upkeep as a homeowner?
> but both are de facto slavery and both are direct violations of the amendment. If you wanna argue that there is a concept of a "lesser violation" and that it makes some forms of slavery OK, be my guest but even children don't buy arguments like that.
This was the "strongest plausible interpretation" of what I've been saying this whole time?
Children buy perfectly well the idea that requiring homeowners to do some upkeep around them is not even remotely "slavery". Just like how they understand perfectly well that making them clean their rooms is not "slavery" either. They understand it's not only ridiculous, but outright insulting to human dignity to suggest that these are comparable to slavery. Adults on HN are the ones who somehow struggle with this, not children.
> Eh? Violence? For refusing mandatory upkeep around your home and neighborhood? Are you writing this from North Korea or something? How is fining you such a foreign concept where you live that your government has to resort to violence to get you to do some upkeep as a homeowner?
What happens when you don't pay the fine? What happens when you resist the armed men at your door?
> outright insulting to human dignity to suggest that these are comparable to slavery
What's outright insulting to human dignity is authoritarians justifying slavery on the basis of "other forms are worse".
Garnish your wages? Freeze your bank account? Put a lien on your house? I don't know, I've never been blessed with the urge to die on this hill. They sure as heck have a million options besides injuring you, and they won't injure you unless you do something other than merely refusing labor or payment. "He didn't pay the fine, let's go beat him up till he does" is not how things work in my part of the world.
Ah yes, our wonderful governments won't beat us up if we don't comply, they'll just take our possessions and money so we don't have food, shelter, transportation, or the capacity to generate income. Totally non-violent.
"political power flows from the barrel of a gun" - Mao
The central claim in particular is not proven because a physical theory P need not be able to express statements like "there exists a number G, which, when interpreted as the text of a theory T, essentially states that the theory T itself is unprovable in the broader physical theory P" as an empirical physical fact.
It's also very hard to verify the sources for some claims: I would expect the snag to be that many model theory results we have (Such as Gödel theorems) require quantifying over an infinite set, but that seems plausibly not possible to model in the physical universe. I quickly found this quote from the paper:
> Arithmetic expressiveness; LQG can internally model the natural numbers with
their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits
Here the citations are four entire books. How am I supposed to very that LQG can model N with that?
Here's a dumber argument: suppose you simulate a Newtonian universe in a computer. We do this at a coarse scale all the time. Now, suppose we dedicate a few percentage of solar output to this project and out pops functioning artificial life that can think more or less like we do. Such an "organism" would be able to discover Gödel incompleteness just as well, and thus eventually conclude via the same chain of logic as this paper that the simulation hypothesis is false. While inside a simulation.
Sure, I'm assuming here that nothing Gödel's brain did is fundamentally non-computable, but that's a pretty easy lift I think. Math is hard but it's not that hard.
For what it's worth, while I find this "obvious" as well, given the Church-Turing Thesis etc, Nobel Prize-winning physicist and philosopher Roger Penrose famously does think that human brains require access to non-computable insights to do math.
appear to the a-life Moses with tablets with the non-simulation proof written in Lean. They don't need insights to verify that proof, just a computer running inside the simulation.
Or just start simulating QM on a limited basis, just inside their brains. You might need to run evolution for another few million years until they start taking advantage of whatever Penrosian effects there are.
This is not really necessary tho; it only requires that the mathematical model has a certain arithmetic complexity. The usual demo is Robinson Arithmetic, which is addition, multiplication on the natural numbers, and a successor operation.
Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.
Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).
Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.
But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.
And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.
Godel's proof relies on the self-referential nature of the Godel sentence; without that, his theorem does not apply. Generally you need arithmetic, but also (something equivalently expressive to) universal quantification. Physical theories do not need to include that.
Note Godel's proof is mechanically exactly analogous to Turing's proof of the undecidability of the halting problem, because ultimately it's the same thing (Curry-Howard, Prolog, and all that). So you can bypass arithmetic, but you can't really bypass self-reference; just like programming languages need some looping or recursion (or equivalent expressiveness) to be Turing-complete, mathematical theories need universal quantification to be subject to Godel's Incompleteness Theorem.
Of course, you can have a physical theory that _is_ Turing-complete, say the Newtonian billiard ball model (and, y'know, we can build computers); but that doesn't mean the theory will necessarily tell you, as a static, measureable physical fact, whether a particular physical process (say, an n-body system) will ever halt or loop, or go on forever with ever-increasing complexity; so you could (in principle, in Newtonian mechanics) build some (mechanical!) physical system that simulates the Goldbach conjecture, or looks for solutions to an arbitrary Diophantine equation, but if there are no integer solutions you'll never actually be able to show it; the theory is incomplete in the mathematical sense, but just as complete a description of reality's rules.
They have some explicit examples of physics explainable by quantum gravity that resolve but are undecidable, n-body thermalization being one. Of course that’s given a sort of hand wavey understanding of quantum gravity, I guess one that they say should tell us whether a system thermalizes.
EDIT:
I should also mention the idea that reality can tell us if a statement about a theory is true, given that the theory is an accurate description of reality. So if there’s an accurate Turing complete theory of reality, and we see some process that’s supposed to encode a decision on an undecidable statement being resolved (I guess in a non-probabilistic way as well), then we can conclude that reality is deciding undecidable statements in some nontrivial way.
Note that in general, a physical instantiation of an undecidable problem must be specified/realized to _infinite_ precision; that is, for any such system S, and for any eps>0, there is a perturbation p with distance d<eps (eg, move a billiard ball an arbitrarily small amount) that is provable; this is analogous to the fact that existence of solutions to Diophantine equations is undecidable, but the theory of real closed fields is decidable, which means that the only undecidable case is when an equation has solutions _arbitrarily close_ to integers, but never quite an integer. I am not a physicist, but I don't believe any physics actually cares about infinitely-precise setups.
Integers exist in quantum physics (e.g. electron charge, spin), which is why I think quantum gravity is important to this argument. Spacetime ends up being discretizable and we can end up having rational valued physical phenomena.
Mostly as an abstraction on top of a continuous wavefunction/quantum field
> Spacetime ends up being discretizable
As far as I know this is speculative and usually assumed by physicists to be false; it's definitely not a required feature of quantum mechanics per se, and as far as I know not of any other well-accepted theory.
> Integers are fundamental in quantum mechanics, particularly as quantum numbers that define the discrete properties of particles, such as energy levels, angular momentum, and spin.
> Quantum mechanics dictates that certain properties, like energy and angular momentum, are quantized, meaning they can only exist in discrete packets or "quanta".
I'm not an expert/lawyer, but this does seem to indicate that the situation is a bit more complicated than either "pernicious myth" or "probably illegal" in general (but much closer to toast0's understanding); my interpretation is that you can either avoid an 80% threshold of "disparate impact" or you can in theory formally validate that a particular test measures/predicts performance at a particular job; that all sounds compatible with "companies do it in the open, but very few, and you can easily get in trouble for doing it wrong"
https://www.law.cornell.edu/cfr/text/29/1607.15
The comment to which I responded claimed that IQ tests "probably aren't legal in the US", which is false. They aren't more widely used because they don't work well for candidate selection, but they are used by very large companies that are attractive targets for employment discrimination suits, and wouldn't be if they were legally risky. There are well-known tech companies that up until a few years ago gave IQ tests to candidates!
Empirical observation trumps axiomatic derivation in this case.
I read this paper some 10 years ago, and have always wondered whether these ideas are implemented in industry. I know people use Denotational Semantics in academia, but eg I want an actual language that can encode the language-independent "meaning" of both a c++ template library and a Python program in a composable way, and also express and prove refinement relations between different specifications and implementations.
People will get mad at me for saying this but... this isn't that deep. As with most things in academic CS, this is just a formalization of stuff that is very common practical engineering.
> academia, but eg I want an actual language that can encode the language-independent "meaning" of both a c++ template library and a Python program
The name of the paper is "data types as lattices" so data not programs as such and denotational semantics is about programs. So I'll say:
1. A language independent representation of a data type is just a protobuf (or whatever your favorite serialization/deserialization framework is);
2. The language of lattices is very common in eg compilers (eg grep for lattice in LLVM) but again it's cart before the horse kind of stuff because there's not much there to be exploited in representing your unions and intersections as meet and join;
3. A language independent representation of operations is an IR and indeed you can inductively derive certain facts about some language level features (across multiple languages) by analyzing the IR. Again cf LLVM
I realize the paper is from 1976 so someone will pop up and say "the paper inspired these things" but it's just not true; people generally follow their nose when implementing and then someone comes along and says "let's name it a lattice".
This isn't a hot-take or something, it's just experience from being on both sides of the fence.
I think you are not doing this line of work justice.
Lattices like intervals or sets of values or zero/nonzero are typical and natural even without studying lots of theory.
I believe this paper is about how you can use the concept of a particular kind of lattice to give a rigorous mathematical semantics to possibly non terminating computations such as the untyped lambda calculus. This was not at all obvious before Scott. I don't feel qualified to comment much beyond that.
I suppose this is related to the simpler examples of lattices, but it's quite a feat.
I didn't recognize the name but then I went to the paper and realized this is one of the papers that establishes a model (as in model theory) for untyped lambda calculus. I knew about the result but not the author's name (nor the name of the paper). Ok I retract some of my cynicism. Still not very overwhelmed though by the gravity of the result. I'm not one of those people that worships Church ie I'm aware of all of the stuff people manage to prove with lambda calculi but I've yet to see any practical value (so we arrive at an actually negative answer to op's question).
You can implement the "nonstandard arithmetic" suggestion using bignum integers backed by an infinite tape (subject to availability of said infinite tape). Finite integers have a Halt symbol, non-finite ones simply don't. Arithmetic on non-finite integers is not computable, but individual digits generally are. Any finite integer is computably less than any non-finite integer. "Less than" between two non-finite integers is not generally computable, therefore not defined. "Not equals" is semidecidable, so generally all "not equals" statements between two non-finite integers are defined, but "equals" mostly isn't. printf on a non-finite integer will simply print out infinite digits one by one.
You can also define and generate non-finite integers from any computable sequence of integers.
size(void*) can be defined as eg 1111111... (Repeating forever, in an arbitrary base).
If you demand that you can always computably do arithmetic on size_t's, allow storing arbitrary arithmetic or even logical expressions in your bignum integers, and call those bignum as well. Define "less than" on infinite integers based on "alphabetical" order. Then the only thing that is non-computable is (in)equality between two expressions for which non-finite-ness is unprovable under First order logic. Given Godel's Completeness (note, not Incompleteness) Theorem, that should probably meet the definition of a C implementation, though I haven't read the standard.
Have you tried a 1-d kd tree, that at each subinterval keeps track of the largest gap? Should be fairly simple to keep this updated and effectively match/generalize your "coalescing" logic.
Then again, according to the Supreme Court, even forced, unpaid road duty (chain gangs anyone?) is an inherent power of the government, so maybe this is ok.
> In view of ancient usage and the unanimity of judicial opinion, it must be taken as settled that, unless restrained by some constitutional limitation, a state has inherent power to require every able-bodied man within its jurisdiction to labor for a reasonable time on public roads near his residence without direct compensation.
https://supreme.justia.com/cases/federal/us/240/328/
(spoiler alert: according to the ruling, the US Constitution, including Amendments, does not limit this power; and this is in fact cited as justification for upholding the draft)