> A consequence of that is the potential does not drop to zero as you go further away. Unlike what is the case for the 3d case.
The integral of const/r^2 doesn't drop to zero as r gets larger, but approaches some constant. Unlike const/r, which is unbounded as r gets larger. So potential is bounded in R3, but not in R2.
I should have said that it rises to zero, assuming standard sign conventions.
The gravitational potential infinity of a point mass at the origin is defined to be zero.
Could you expand on why you think it approaches a constant, presumably a non-zero constant. In any case absolute values do not matter, only the potential difference matters, but am still interested in your thought.
> Could you expand on why you think it approaches a constant, presumably a non-zero constant
Because the gravitational potential between two massive objects is equal to the amount of energy it would take to separate them (from touching) out to their current distances, and equal to the amount of kinetic energy they'd have when they impacted if they started from rest and eventually came together. This is not zero for any two massive objects that are any distance apart.
If you pulled two objects further and further apart in R3, the force required at each point would drop off proportional to 1/r^2, and the total energy would be the integral of that (let's assume total mass == 1). This integral approaches a constant: for a total mass of 1 and a starting (or "touching") distance of 1 (you can't use 0 or you can't pull them apart), this integral is 1. So no matter how far apart you pull them, potential never exceeds 1. But it must be nonzero, because you could extract energy from releasing them and letting them come together.
In R2, the force required to pull them apart at each point drops off as 1/r, so the integral grows as Ln(r), and so has no upper bound.
I recognize we basically agree on all this, I'm just clarifying why I consider the limit of the potential to be nonzero as distance approaches infinity. You could extract energy from the system with a "water wheel" setup, at least at every finite distance. You could argue "but not at an infinite distance, because they'd never come together, their attraction force is 0, and where would you put the water wheel?" but that problem only comes up at infinity. We're talking about the limit as r approaches infinity, so this problem never actually comes up.
But what's the integral of 1/r^2 from 0 to \infty ...that's the part not that not squaring up.
Newtonian gravitational potential of a point mass at origin of mass M is - GM/r so at r = \infty the potential is zero. Well, partly just by definition.
I believe we are assuming different models and I want to understand yours.
Because everything in the real universe occupies a volume, and therefore no two distinct "things" can be 0 distance apart. The distance between two marbles' center of masses is the sum of their radii. So if you want to measure the potential gravitational energy between the two marbles, you'd take the integral of (GM^2/x^2) dx between x = [sum of radii of marbles] and x = infinity, as an approximation.
Your analogy is way off base. This is how you've framed it:
> Let's say I [the Netherlands] pay [!?] someone [Ukraine] to punch you [Russia] int the face every day. Then one day when you [Russia] punch me [Ukraine] in the face do I have a right to complain?
Ukraine is defending itself, and nobody is paying Ukraine to do that. Russia is the aggressor here. It's weird that I need to point that out. We're talking about Russia sabotaging someone for selling defensive capabilities to Ukraine. So a better analogy is this:
Let's say I punch you in the face every day. Then one day you buy a baseball bat from Gart Sports to defend yourself, so I go in and punch the manager of Gart Sports. Am I in the wrong?
Yes, very obviously, when you frame the analogy correctly, you are in the wrong.
With you up until there. There's nothing defensive about drones. Retributive capabilities certainly, pre-emptive capabilities maybe, but absolutely offensive capabilities, not defensive ones. Attacking Russia back was a line that was definitively crossed in May 2024. You may argue it was justified, but not that it wasn't attacking. In terms of that stupid punching analogy (which wasn't yours to begin with, I know) this is going over to your bully's neighborhood with that baseball bat.
and people who could do those things. Sure. That was a line which was crossed, and everyone knew that - including Ukraine, which is why they didn't do it until two years into the war after getting explicit permission from the governments supplying them with weapons.
But that leaves us back where we started doesn't it? If it's fair game to attack civilian infrastructure which was used or could be used to make the weapons you are getting hit with - then why should it make a difference if it's in the Netherlands? Or in China for that matter? I'm pretty sure that if Russian weapons were made in a state technically not in the conflict (say Belarus), that wouldn't stop Ukraine from sabotaging them.
I'm not denying that Russia was the initial aggressor. I am saying enough lines have been crossed that we really can't fault Russia if they wanted to sabotage weapons production in the west.
> Is that because we're engaged in large scale human rights violations against our own population and enabling defacto slavery for profit generation?
Yes, that is absolutely correct: the United States is engaged in large-scale human rights violations against our own population and enabling slavery for profit generation. You nailed it. It's not even "de-facto" slavery, it's de-jure slavery on the actual books. Slavery is not (fully) illegal in the United States.
> I think it's something similar with China
China also commits wholesale human rights violations against its own people, although the scale is much worse. I strongly doubt the U.S. actually has more prisoners than China, it's just that we actually count them all.
> They've had major problems with separatist movements and terrorism from the Xinjiang/Uyghur region and are similarly awkwardly trying to resolve it
This is assuming good faith to the point way beyond naivete. The Chinese government is not "trying to resolve terrorism", they are committing mass murder and ethnic genocide.
> extremely easy to frame as being the greatest crime against humanity since Justin Bieber
Are we doing Whataboutism here? Let criticisms stand. I can say "it's wrong to round up ethnic minorities and put them in concentration camps" without it having to be the greatest crime against humanity ever. Are we really going to be forgiving all actions because someone in history did something worse?
> It's all just geopolitical poo flinging
Not everything is always the same. While criticisms can be levied against every country, scale and impact matter. I'm sure someone could come in and point out problems with the government of The Netherlands, and those problems should matter to the Dutch people and they should call them out and work on fixing them. But that doesn't mean it's the same as what China is doing or what for-profit prisons in the U.S. are doing, nor would it be hypocritical or "geopolitical poo flinging" for The Netherlands to be critical of those practices.
> A lot of messaging is much more propaganda than reality.
Yeah, I'm so tired of people moaning about how huge swaths of Earth's ecosystem are being destroyed and rendered uninhabitable to humans, how secret police are murdering Americans in the streets, how the president is a child rapist who openly accepts bribes, how unfettered capitalism is destroying tens of millions of lives, how the United States is rapidly falling into facism, how civil rights are being systematically destroyed, consumer and environmental protections are being gutted, and entire generations are being intentionally cut out of the possibility of economic prosperity. YAWN! Give it a rest!
Man, the people who want to just get away with open corruption sure love you.
Hyperpolitics is one term for this. There was an article in NYT about the concept. Attention economy for political info causing burnout possibly same phenomenon as Gen Alpha surrealism and viral adoption, but no institutionalization to preserve the lessons.
It's not necessarily clear that this statement requires infinity, if you're willing to treat "... =" as a shorthand. You might prefer something like "1 + 1/2 + 1/4 + 1/8 ... -> 2" if it's more clear, where "->" means something like "gets as close as you like without ever getting further away than that", but really the "=" sign is already overloaded in all sorts of subtly different ways anyway, so there's not really any trouble using it here. Almost any rigorous definition you can write down of exactly what that statement means would not rely on the use of infinity.
If you allow infinite recursion, you soon get to Godel and undecidable problems.
Finite deterministic systems are decidable, because you can in principle enumerate all the states. The halting problem is decidable for deterministic systems with finite memory. It may be exponentially hard for some programs, but that's quite different from being undecidable.
(This is too long a subject to discuss here, and I haven't worked on constructive mathematics in many years. It's more practical than it was decades ago. You need power tools, which we now have.)
Really trying to assume good faith here, but it's hard ...
We have record high levels of people needing support at the same time we have record high levels of spending on that support? What an outrage! Obviously nothing is working and government bad!
Of course the spending on support services goes up as more people need that support. We're supposed to assume that's some sort of failure?
> Government intervention and welfare is proven not to solve the things it tries to.
If by "proven" you mean "kinda maybe arguable if you intentionally misrepresent correlational studies", sure.
These exemptions are not granted based on logic or precedent. "Less dirty" has nothing to do with it. They're entirely based on open bribery. This will be granted to any industry that bribes the administration enough. What's the good news again?
> 2) resist the urge to impart correlations into the generation
I think the opposite. The more dimensions you have, the more "invalid space" there should be. Otherwise you end up with giant dinosaurs with tiny feet and fairy wings. You end up with a yellow kitchen with a barrel full of arrows next to a blue dungeon with a giant dresser. You end up with nothing making sense, and everything feeling random in the same way. Trying to spot the differences between 100100111101011110110001001011101 and 1101101110111010000100111001011101 is exactly the "bowl of oatmeal" problem. The vast majority of possible combinations of values should be invalid and impossible, otherwise the choices actually don't matter.
Yes, and it's a problem procedural space games have in particular. Because the planets usually don't interact at all in any meaningful way - what's on one planet (or indeed in one zone on a planet) has no impact outside it. Maybe you can get random quests on planet A to find some landmark on planet B, but it doesn't feel like that was because anything on planet A had anything to do with what was on planet B. For all its improvements over the years (and they are many, and OK in their own way) this is a thing which has not changed in No Man's Sky.
This I think is a core challenge with procedural generation. You can have procgen countries with procgen cities with procgen citizens, but if none of those citizens have an aunt in another city - who you can actually visit, in a new world from the same seed, and learn that she has a nephew in the first city - then it feels empty, fake.
Hierarchial procgen is easy. But you need cross-interactions like that to make it feel alive, and that's hard.
Agreed. Elsewhere in this conversation people mention simple games that procgen well: Spelunky, Terraria, Dwarf Fortress, Dungeon Crawl Stone Soup
These are games painting with a 16 color palette while the technology exists for any shade in RGB. The more variations, the less likely things will be coherent (let alone brilliant)
I mean, almost no games have that many meaningful dimensions in the first place. It's more likely that the correlations you add just reduce the potential for interesting combinations to arise in the first place.
> Lightspeed intelligence ... biology might also be able to evolve computation at the speed of light
I feel like this is dramatically missing the point. It is trivial to come up with a communication system where signals travel at the speed of light. In fact, anything visual meets this criteria: sign language, semaphores, clicking your flashlight on and off. Radio waves travel at the speed of light. All of humanity became a giant "lightspeed-intelligent" brain when radio was first invented.
It really does matter what you're doing with those signals, how much information each contains, how many you're sending, how much power it takes to send and receive them, how they're encoded, etc. Focusing on the fact that they travel at the speed of light is silly.
> The advantage of this over biological computation is clear: Biological computation happens at max 100m/s, 6 orders of magnitude less than the speed of light
You are trying to compare computation power by measuring distances. You are basically saying "one biological computation" is a million times slower than "one silicon computation" because of how fast signals travel, completely ignoring what is actually happening in those extremely different computations. It's still not clear that brains can be compared to computers at all, but if you try to simplify it down to FLOPS (a much better measure of computation speed than "how fast do some signals go"), our best estimates are that one brain has the computational equivalent of somewhere between 1,000 and 100,000 modern GPUs.
> All of humanity became a giant "lightspeed-intelligent" brain when radio was first invented.
That is a good example of another very very probable pattern. If an alien civilization at the other end of this universe exists, it is very, very probable that they also have communication networks that operate close or near the speed of light.
> It really does matter what you're doing with those signals, how much information each contains, how many you're sending, how much power it takes to send and receive them, how they're encoded, etc. Focusing on the fact that they travel at the speed of light is silly.
You're correct that the speed of the signals isn't the only aspect that is important. It is however not silly to focus on it, because it represents a fundamental, physical, upper bound on a key aspect of the maximum 'performance' of signals/information transfer. The amount of information that can be encoded in electromagnetic radiation would be another.
> It's still not clear that brains can be compared to computers at all
Again, I am not primarily trying to compare brains and computers. Lightspeed intelligence could technically be biological. I am also not saying that current artificial neural networks do as much with their signals as our brains.
The fundamental point was and is that an intelligence with signals that propagate at the speed of light will emerge and become dominant.
There are a bunch of secondary points that can be made as to why biology has a much harder time than brains in developing lightspeed intelligence (evolving something like glass fiber, the limitations of brain size, cooling issues, etc.), but those are not as important as the fundamental point.
This is a great illustration of why most database designs are so bad. Hear me out.
I think you can imagine a situation where you end up with a table named "Salad" (or "Salads", or maybe even "SALADS" if you're nasty). Perhaps you're building a database application for a restaurant or grocery store, or some sort of meal planner or nutrition tracker.
Salads are obviously Distinctly Different Things than Meats, Dairy, and Drinks, so those are separate tables. Except, invariably, you run into the exact pointless arguments being made in this article: you cannot actually define the boundaries of a salad, because, like almost every noun, "salad" is an address in conceptual space. It's a way of summoning a group of ideas into a conversation so that you can communicate, not a way of Doing Exact Math as CSMastermind eloquently pointed out in another comment. You can start at this address and adjust it with modifiers like "fruit" or "Caesar". You can move arbitrarily far: "I had a fruit salad for dinner, except the fruit was all fermented and smooshed up into a bottle. It was wine. I had wine for dinner."
So you end up with records that are kinda-salads and you don't know what table to put them in, and you also end up with wanting to say a whole bunch of the same things about Salads that you want to say about Pizzas and Sodas too. So you end up with both poor cohesion and high duplication. Your tables mostly share the same 12 columns and you don't know where to look for things.
"But I would never make a 'Salads' table," you say, "that's far too specific!". But you do: you make an Employee table, or a PcrTest table, or an ElectricalSubstation table. Or perhaps those should be more general: "Meal", or "Person", or "Analysis", or "Facility"! But now your SELECT results look like a checkerboard of NULLS and real values as the sub-definitions show up anyway. And even then, you still run into cases that somehow don't fit: we're making a lot of these kinds of Facilities, so we want it in the Facility table, but it's not a real facility, it's a template facility! You've weakened your definitions for not much gain.
And all of this is assuming you already know everything about the domain, but you don't! You're exploring, discovering, iterating, beta testing, pivoting. You make database tables by identifying the nouns that your SMEs use when the SMEs themselves can't fully define them, and then you get annoyed at the inalienable property of language that it is resistant to strict definitions, and briefly wonder whether we'd all be better off speaking Lojban. Then you wonder about abandoning this restrictive idea of "schema" and go NoSQL or key/value, until you realize that you still have a schema, it's just now no longer enforced or supported, and you go back to relational SQL with a few remaining key/value pair systems still jammed in here and there.
So you start from faulty assumptions, make choices you don't need to be making, develop an inflexible design, and end up having pointless arguments like the one in this article -- except instead of being recreational lunchtime arguments, they are ones that determine the failure or success of your business.
Stop defining tables based on the first nouns you encounter. Nouns do not work that way. You will never be able to define them. Instead, define tables based on statements you want to make about your entities. Every time you come across something you want to write down -- a person's name, a place's address, nutritional information, a SKU -- find a table for that. Keep things cohesive: Full Name and Address don't belong together, because many things have one but not the other. Stop trying to decide whether a given entity is a "Person" or an "Employee" or a "Salad" or a "Facility": you don't need to care! All you need to know is what you want to say about it.
This has a ton of design implications that could easily fill a textbook, but it does work. You can actually have a flexible database design that isn't full of NULL checkboards and the same 12 columns in every table. But you do have relegate these pointless Salad Theory-type arguments to the lunch hour, because you'll instead find yourself talking about actual useful things during design meetings.
The integral of const/r^2 doesn't drop to zero as r gets larger, but approaches some constant. Unlike const/r, which is unbounded as r gets larger. So potential is bounded in R3, but not in R2.
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