1,377 karma · joined November 29, 2017
Glancing at the artist's [article on Wikipedia](https://en.wikipedia.org/wiki/Roy_Lichtenstein ), it looks like some folks really liked his work and would pay a lot of money for it..? But, why?
Doesn't seem like a serious article about math so much as a feel-good story.
I mean, Wikipedia shows a better proof in [this section titled "proof using similar triangles"](https://en.wikipedia.org/wiki/Pythagorean_theorem#Proof_usin...), which kinda starts the same way, but it's a lot shorter and doesn't require the Law-of-Sines nor infinite-series.
If anyone wants to design further "trigonometric" proofs, they can just start from what's on Wikipedia and add in steps that rely on trigonometry.
From their summary:
> [...] these results support a neuro-metabolic model in which glutamate accumulation triggers a regulation mechanism that makes [lateral prefrontal cortex (lPFC)] activation more costly, explaining why cognitive control is harder to mobilize after a strenuous workday.
Because, if a device has all of the information needed to connect to a network on it, then.. well, it has all of the information needed to connect to a network on it. Could be passwords, hashes, or whatever -- doesn't really matter.
In what way is it a scam? For example, is it a pyramid-scheme, pump-and-dump, pretext to trick people into downloading malware, etc.?
[That story (2022-04-06)](https://www.technologyreview.com/2022/04/06/1048981/worldcoi... ) did offer one major concern:
> Others took issue with the company’s purported focus on fairness given that 20% of the coins had already been allocated: 10% to Worldcoin’s full-time employees, and another 10% to investors, like Andreessen Horowitz.
20% of coins being in the hands of a few does sound potentially pretty corrupting -- at least, if it's a system like Bitcoin, where there's a cap on the total such that, if mass-adopted, that small group of people would end up controlling 20% of the total wealth. But does it work like that?
Beyond that, it sounds like the article's suggesting that it's a scam to get iris-scans:
> Meanwhile, those who fear that the whole thing may have been a scam want to know what they’ve lost. “50 KS is not enough to give an eyeball away,” says Okach, the university student in Nairobi that spent a weekend recruiting others to Worldcoin. “That’s manipulation, taking advantage of students without clear clarification about what it is they are doing or what they want.”
But the idea of a scam to get folks' iris-scans, especially iris-scans of people in less-developed areas, sounds a bit strange.
I mean, if someone has a database of folks' pictures, DNA, or fingerprints, then that database might help track folks without their knowledge or consent -- plus DNA might also reveal things about a person that they'd rather have kept private.
But what might scammers do with iris-scans that might potentially justify the trouble of collecting them like that?
Then it's also great to see that they seem to be pretty open about stuff, [including their hardware](https://worldcoin.org/blog/engineering/opening-orb-look-insi... ).
That said.. it's hard to see terms like "coin", "wallet", "Web3", "NFT", etc., without a bit of concern -- even if, admittedly, such terms might be appropriate and justifiable in this sort of application.
Is there a page that shows their overall economic model, perhaps with flow-charts and such? This is, where are the cash/token/hardware/etc. in-flows and out-flows?
And is there an early-adopter incentive? And if so, is it significant, or is the system designed to be fair to folks whenever they might join?
Asking in part because the classic pyramid-scam thing, where early-adopters end up collecting huge rewards at the expense of late-adopters, seems like a major hallmark of dubious projects. Projects without such asymmetries would seem more credible, both in terms of not being yet another pyramid-scam and long-term viability.
I mean, surely anyone who knows anything about blockchains would be aware that the long-term plans, even among traditionalists, would involve an ecosystem of interacting chains. And then presumably folks with some level of technical understanding realize that even a singular ecosystem's overly naive. I doubt few people actually believe in Bitcoin-maximalism, outside of memetic-humor. ...right?
Sorry, I'm still confused about junk like flat-Earthers. I mean, I've known flat-Earthers who were straight-up committed trolls; they were committed to the bit and would actingly-angrily denounce the round-Earth conspiracy, but they most definitely didn't actually believe that Earth was flat. But.. other folks.. it was harder to tell; were they even more committed, or did they actually believe that Earth was flat? Anyway, a lot of blockchain-stuff's similar -- I get that a lot of folks are trolling, but are there really true-believers who're legitimately sincere?
I mean, an NFT would tend to exist on a particular blockchain. If that blockchain forks (e.g., [as Bitcoin's done a number of times](https://www.investopedia.com/tech/history-bitcoin-hard-forks... )), then it's not unique, but rather exists multiple times -- potentially with different copies being owned by different folks. Plus folks could create duplicate NFT's of the same (by simply minting new ones), presumably on the same blockchain or/and others. And then, if an NFT is reliant on external-resources (like links to a host-server), as I've heard that most are, then presumably those could break and even if someone continues to "own" an NFT on some particular blockchain, the NFT itself would seem decontextualized and essentially meaningless.
Then, durability isn't ensured even on a continuous blockchain, as blockchains can elect to remove stuff (e.g., through forks or filter-protocols). Presumably blockchains would ultimately want to truncate historical stuff; it'd seem strange to assume that an NFT would necessarily be carried through such a process.
Then there's the non-optimality of primitive blockchains. This is, when there're innovations, we'd presumably expect folks to create new blockchains that may displace older ones, retiring prior-NFT's in the process.
Then if we're talking long-term, historic value, then we'd probably consider stuff like advances in cryptography mooting the original signatures, and just generally how ancient blockchains would seem to be of little interest to those in the future. Plus, I'd imagine that advanced AI artists would render the concept of trivial art being in any way non-arbitrary obsolete.
Long rant short, it's just weird to hear non-technical folks seemingly believing that blockchains confer "uniqueness" outside of more limited, subjective contexts.
As for polymer-concrete's history (https://www.sciencedirect.com/science/article/pii/B978184569... ):
> The history of the research and development of polymer concrete is relatively short compared with that of conventional cement concrete. The early research and development of the polymer concrete was done mainly in the Soviet Union (currently, Russia),1 the United States,2 Germany3 and Japan4 in the late 1950s to the early 1960s.
The idea of making polymer-concrete with recycled-plastic has also been around. For a random review article (https://www.sciencedirect.com/science/article/pii/B978085709...):
> Abstract: [...] The volume of polymeric wastes such as tyre rubber and polyethylene terephthalate (PET) bottles is increasing at a fast rate. [...] The majority is just landfilled. This chapter reviews research published on the performance of concrete containing tyre rubber and PET wastes. Furthermore it discusses the effect of waste treatments, the size of waste particles and the waste replacement volume on the fresh and hardened properties of concrete.
[It's been around since at least the 1950's](https://www.sciencedirect.com/science/article/pii/B978184569... ).
For example:
public class A
{
// If a programmer writes this:
public void DoSomething(int x) { /* ... */ }
// ...then C# sees this:
public static void DoSomething(A this, int x)
{
if (this == null) { throw new NullArgumentException(); }
/* ... */
}
}
C# even lets programmers write methods that can be called on an instance OR as `static`: [extension methods](https://docs.microsoft.com/en-us/dotnet/csharp/programming-g... ).
Then there's a difference between C# and Java: in C#, non-static methods can be `virtual` if marked as such, whereas in Java, all non-static methods are automatically `virtual`.
---
Anyway, my point about the perspective from [this comment](https://news.ycombinator.com/item?id=31383483 ),
> If you’re writing code calling static methods on instances of classes, you deserve to have that code broken.
, was that that's basically what C# does by-default, ignoring syntactic-sugar.
Because, in C#, methods aren't `virtual` by-default, so when C#-programmers call a default method on an instance, they're calling it non-virtually, much like a Java-`static` method -- it may look a little different in C# due to the syntactic-sugar, but it's basically the same thing.
To demonstrate that same-ness, I took the Java code that used `static` from [this comment](https://news.ycombinator.com/item?id=31379783 ), then showed the same without `static` in C# in [this comment](https://news.ycombinator.com/item?id=31385859 ).
Of course, I don't mean that they look exactly the same, due to the syntactic-sugar. Just that they're conceptually the same in terms of logical-structuring and behaviorally the same in terms of what they actually do (e.g., how they printed the same responses in those examples).
For example, [this comment](https://news.ycombinator.com/item?id=31379783 ) provided code showing the issue in this branch of the thread using `static` in Java. Here's the same thing in C# without using `static` (except for `Program.Main()`):
public class Program
{
public static void Main()
{
A a = new B();
if (a is B b)
{
a.Print(); // Prints "A".
b.Print(); // Prints "B".
}
}
}
public class A { public void Print() { System.Console.WriteLine("A"); } }
public class B:A { public new void Print() { System.Console.WriteLine("B"); } }
Generally speaking, virtual-methods resolve with dependence on the object they're called on since they consult a [virtual-method table](https://en.wikipedia.org/wiki/Virtual_method_table ). Non-virtual methods can resolve without considering the object they're called on (whether static or not) because they call the method that belongs to the apparent-type.
This is, in C#, all methods are called according to an object's apparent-type, not its actual-type, by default. To get the Java-behavior, a C#-method would need to be declared `virtual` (or `abstract`), and then more-derived methods would need to choose to `override` them (rather than hide them, often via `new`).
Part of the advantage might be performance. This is, methods that go with the apparent-type don't need to do a virtual-lookup-table resolution, which can save some work in method-calls.
Another advantage is that it can help provide more flexibility in class-hierarchies, since more-derived classes can "hide" less-derived classes' methods without overriding them. It's probably not something that folks really need to do too often, but it's nice to have an easy solution when such a case occurs.
For example, you can't generally scale-up a machine by just multiplying all of its dimensions by, say, 2, and expect it to still work the same way. Ditto for organizations.
Scalability would generally be a problem even if you could ensure that the sorts of people involved wouldn't change. But, if you're considering a scenario where the the types of folks involved also change, then that'd probably tend to amplify the effect.
That said, systems can often be scaled-up with due consideration to how they work and ensuring that the fundamentals are kept.
> Our fee structure is different to that of a brokerage or exchange. As a retailer, our expenses are generally higher than a sole crypto trader’s.
So apparently not an "exchange platform", but rather a "retailer".
Presumably they're trying to cater to less-technical folks who'd pay extra for the convenience/ease.
> What you see is what you get! Our advertised rates include ALL fees, and the price agreed upon at the time of purchase is fixed regardless of what happens in the market. Our fees appear slightly higher than exchanges because we have done all the hard work for you – with education and support to help get you started, and no need for you to deal with multiple exchanges or currency conversions.
The title makes it sound more general, e.g. like under-18's couldn't use social-media at all. But instead, it sounds like they don't want under-18's having user-generated content individually targeted at them, or something like that.
I'd guess that the concern would be echo-chamber effects? This is, if users get targeted with content algorithmically selected just for them, then it may tend to silo users' perceptions. And that might be especially concerning for less-experienced users, who may not realize it's happening or see stuff outside of that bubble.
> (b) The social media platform is liable to an individual account holder who received user-generated content through a social media algorithm while the individual account holder was under the age of 18 and was using the individual account holder’s own account, if the social media platform knew or had reason to know that the individual account holder was under the age of 18 and located in Minnesota. [...]
Sounds like they're not requiring unreasonable knowledge of faked ages.
It'd seem like a more direct title might be something like, "An unauthorized party posted using my Twitter account.". Or just, "My Twitter got hacked.".
The related issue of someone-else allegedly posting on the author's Twitter-account would seem more interesting.
I mean, the parent-comment was saying that folks could get the last-word by replying-then-blocking. It sounds like folks on your platform could get the last-word by simply not approving the other-side's response.
To avoid one side getting a last-word in a feud, it'd seem like you'd need to ensure that both sides could eliminate the entire conversation should they not be satisfied with its ultimate conclusion, such that there'd be no last-words in any feuds as there wouldn't be any (published) feuds. Short of that, it'd seem like one party could end up getting in a last-word.
After "Theorem 2", there's a "Proof" with multiple lines directly equated. Among those lines were
> = 1 - p(h,eb) - p(e,b) + p(he,b)
> = p(h←e,b) - p(h,eb)
1 = p(h←e,b) + p(e,b) - p(he,b)
1 = p(h←e) + p(e) - p(he)
So, "h←e" refers to NOT(e) plus AND(h,e).
So, "h←e" equals OR(NOT(e), AND(h,e)).
So, the evidence "e" implies the hypothesis "h" when both are true, plus also when evidence "e" is false.
---
So, "Theorem 1" claims
p(h←e, e) < p(h←e)
OR(NOT(e), AND(h,e)) when e < OR(NOT(e), AND(h,e))
h when e < OR(NOT(e), AND(h,e))
h when e < NOT(e) + AND(h,e)
h when e < NOT(e) + (h when e) * e
0 < NOT(e) + (h when e) * e - (h when e)
0 < NOT(e) + (h when e) * (e - 1)
0 < (1 - e) + (h when e) * (e - 1)
e - 1 < (h when e) * (e - 1)
1 - e > (h when e) * (1 - e)
1 > h when e
p(h | e) < 1
But to work that out with the sides keeping their values,
h when e < NOT(e) + (h when e) * e
h when e < NOT(e) + (h when e) * (1-NOT(e))
h when e < (h when e) + NOT(e) - (h when e) * NOT(e)
h when e < (h when e) + NOT(e) * (1- (h when e))
h when e < (h when e) + NOT(e) * (NOT(h) when e)
So.. I guess that explains the definitions that they were using.
---
Anyway, what seems odd to me about that is that "Theorem 1" seems like it's meant to be surprising -- like it's meant to show that finding evidence reduces the meaningfulness of the evidence itself, or something?
However, some things seem off. For example, the expression of "h←e" seems weird to me; it'd seem more sensible for it to be like this:
OR(AND(NOT(e), NOT(h)), AND(h,e)) when e < OR(AND(NOT(e), NOT(h)), AND(h,e))
h when e < OR(AND(NOT(e), NOT(h)), AND(h,e))
h when e < (!h when !e) * !e + (h when e) * e
0 < (!h when !e) * !e + (h when e) * (e - 1)
0 < (!h when !e) * (1 - e) - (h when e) * (1 - e)
0 < (!h when !e) - (h when e)
(h when e) < (!h when !e)
Because the second thing that seems off is the notion that this matters -- that the evidence, "e", should be a concern for not just figuring out the probabilities in the model, but also retro-actively adjusting the meta-model, or something?
In short, after tracing their math and such, it's unclear what point they might be trying to make, as this doesn't seem surprising or unexpected.
I'm having trouble figuring out a non-absurd interpretation of that paper.
For example, their Equation-7:
> p(h←e, e) = p((h←e)e, e) = p(he, e) = p(h, e)
, which looks like they're saying that, when there's evidence "e", the probability that a hypothesis "h" is true is equal to the probability that "e" proved it.
For example, say we consider the hypothesis, "h", that there aren't 10-armed spider-monkeys that like jazz-music currently on Earth. Then based on that hypothesis, we make the prediction that we won't see a 10-armed spider-monkey listening to jazz-music in the next room. Then, let's say we check that room, and there's not such a 10-armed spider-monkey listening to jazz-music, such that there's "e".
Did our test prove the hypothesis? Wouldn't seem like it.. I mean, even if there were 10-armed spider-monkeys, it'd seem like they could just be in places other than in the other-room. So, "p(h←e, e)" would seem pretty close to zero.
However, it still seems like the hypothesis that such spider-monkeys don't currently exist on Earth would seem fairly probable. So, "p(h, e)" would seem fairly close to one.
So, "p(h←e, e) = p(h, e)" wouldn't seem to hold, even approximately.
That said, the author didn't clearly specify exactly what they meant, so maybe they meant something else? But I'm not seeing an obvious, non-absurd interpretation of their claims.
Why would their algorithm do this?
Like, whether that's a bug or intended, how could their algorithm have ended up suggesting that "annoyed" was non-inclusive?
Exponential-growth occurs when each unit of the growing-thing grows at a continuous rate. For example, if Alice invests $100 in a continuously-compounding bond, then keep re-investing the yields into more of the same bonds, then that'ld tend to be an exponential-growth process.
Linear-growth occurs when the growing-thing is produced at a regular rate. For example, if Bob keep making widgets, then the growth-rate of Bob's widget-pile would tend to be linear.
Anyway, apparently [this paper (2020) [PDF]](https://web.stanford.edu/~chadj/IdeaPF.pdf ) had its Equation-(1) basically parse to:
> dA/dt / A = alpha * S
, where "A" would be "ideas" (which seems vaguely defined), "t" is time, "alpha" is a constant-proportionality-factor, and "S" is an amount-of-scientists (who presumably generate the "ideas").
This equation is for an exponential-growth model. For example, if we reduce it to "dA/dt = k * A" (where "k" is a constant for alpha*S, to make this easier on WolframAlpha), then [the solution is an exponential-function](https://www.wolframalpha.com/input?i=dA%2Fdt+%3D+k+*+A ).
By contrast, it'd have been a linear-function if the authors instead assumed
> dA/dt = alpha * S
... this is, no "/ A" on the left-hand-side.
Anyway, a lot of comments on this thread seem to claim that any (first-order continuously-differential) function is approximately linear if we zoom in enough. Which, yup! -- we can look at both the linear-function and exponential-function as linear-functions by zooming in. So let's do that!
Basically, we can compare:
1. dA/dt = alpha * S (the linear-case)
2. dA/dt = alpha * S * A (the exponential-case)
where "dA/dt" is basically the rate at which "ideas" are generated, and then the right-hand-side of both equations is the marginal-rate (or instantaneous-rate), which is basically the slope of the linear-function that we'd see if we zoomed in enough on both functions such that they both appear (at least approximately) linear.
Practically speaking, we can ignore "alpha". It's basically just a fit-constant to be solved for. Then both equations also have "S", which is basically the amount of scientists who're working.
The big difference is that the exponential-case (which the 2020-paper linked above assumed) also includes a factor of "A" -- this is, the ideas. So, does it follow that "ideas" multiply how fast scientists produce more "ideas"? For example, if a scientist is working in a society that has 100 times more "ideas", then would that scientist produce new "ideas" 100 times faster?
If YES, then the exponential-form would seem appropriate. But if NO, then the linear-form would seem appropriate.
---
EDIT: Skimming a few more sources, it looks like various folks may be trying to use the same equations/data/terminology, possibly for different things?
In the above-comment, I was mostly trying to comment on the basic-model that seemed to be presented in [this paper (2020) [PDF]](https://web.stanford.edu/~chadj/IdeaPF.pdf ), which the linked-article seems to be in-response-to.
However, it's unclear if the definitions cited, including of the variable "A", were necessarily representative of their usage elsewhere.
That said, [the linked-article's paper [PDF]](https://pages.stern.nyu.edu/~tphilipp/papers/AddGrowth_macro... ) starts its Section-5, "Conclusion", with:
> TFP growth is not exponential. New ideas add to our stock of knowledge; they do not multiply it.
, which seems to be in-line with the above-comment's interpretation from the other-paper.
Looks like they link a lot of stuff from the past month.
Examples of links in the article from within the last month:
1. https://arxiv.org/abs/2203.15930
2. https://davidgerard.co.uk/blockchain/2022/04/04/if-you-want-...
3. https://datafinnovation.medium.com/the-consequences-of-scala...
4. https://web3isgoinggreat.com/?id=2022-04-05-0
5. https://ethresear.ch/t/np-completeness-of-a-strong-form-of-s...