It's good that he is upfront about it, but this surely shouldn't be taken as a general advice, since everybody has his own preferences. So this really shouldn't be a blogpost, but rather a "Contributing Guidelines" section in whatever projects he maintains.
I firmly believe the author's stance should be the default policy of just about every open source project. I don't even write my own code anymore, I sure as hell don't want to deal with your code.
Give me ideas. Report bugs. Request features. I never wanted your code in the first place.
You believe. So it applies to projects you maintain. It doesn't mean it applies to project I maintain, or anybody else maintains. So this shouldn't be any more default than any other mode. And probably less default, since people generally developed other conceptions about "defaults" of etiquette in open source projects over the last 15 years.
I'm not exactly disagreeing with you. I appreciate the author's stance, and I appreciate the blog post making it to HN. I think the author's stance should be widely adopted. If they had simply stuck their blog post into CONTRIBUTING.md in their repo, no one would have seen it. Now it's being more widely disseminated, and in a longer form with good reasoning attached.
Not sure if it's true. I mean, I do agree with the core of it, but how do you even do PRs and resolve conflicts, if there are no branches and a developer cannot efficiently update his code against the last (remote) version of master branch?
Trunk based development has every developer in the company committing straight to main - no PRs, supposedly no merge conflicts (but reality is that main moves fast and if someone else is working in the same files as someone else, there will be merge conflicts)
A middle ground is small PRs where people are constantly rebasing to the tip of main to keep conflicts to a minimum
It's not about being costly or not, this is completely irrelevant to the point being made. eml is just some abstract function, that maps ℝ² to ℝ. Same as every other mathematical function it is only really defined by the infinite set of correspondences from one value to some other value. It is NOT exp(x) - ln(y), same as exp is not a series (as you wrongfully stated in another comment). exp can be expressed (and/or defined) as a series to a mathematician familiar with a notion of series, and eml can be expressed as exp(y) - ln(y) to a mathematician familiar with exp and ln. They can also be expressed/defined multiple other ways.
I am not claiming this is better than 1/(x-y) in any way (I have no idea, maybe it isn't if you look closely enough), but you are simply arguing against the wrong thing. Author didn't claim eml to be computationally efficient (it even feels weird to say that, since computational efficiency is not a trait of a mathematical function, but of a computer architecture implementing some program) or anything else, only that (eml, 1) are enough to produce every number and function that (admittedly, somewhat vaguely defined) a scientific calculator can produce.
However, I want to point out that it's weird 1/(x-y) didn't appear on that graph in Figure 1, since if it's as powerful as eml, it should have all the same connections as eml, and it's a pity Odrzywołek's paper misses it.
Oh, glad you are still here. Because I kept wondering about 1/(x-y), and came to the conclusion it actually cannot do nearly as much as eml. So maybe you could confirm if I understood your assumptions correctly and help me to sort it out overall.
In your original post you were kinda hand-wavy about what we have except for x # y := 1/(x-y), but your examples make it clear you also assume 0 exists. Then it's pretty obvious how to get: identity function, reciprocity, negation, substraction & addition. But I effectively couldn't get anywhere past that. In fact, I got myself convinced that it's provably impossible to define (e.g.) multiplication as a tree of compositions of # and 0.
So here's my interpretation of what you actually meant:
1. I suppose, you assumed we already have ℕ and can sample anything from it. Meaning, you don't need to define 5, you just assume it's there. Well, to level things out, (#, 0, 1) are enough to recover ℤ, so I assume you assumed at least these three. Is that right?
2. Then, I suppose you assumed that since we have addition, multiplication simply follows from here. I mean at this point we clearly have f(x) = 3x, or 4x, or 5x, … so you decided that the multiplication is solved. Because I couldn't find how to express f(x, y) = x⋅y, and as far, as I can tell, it's actually impossible. If I'm wrong, please show me x⋅y defined as a sequence of compositions of (#, 0, 1).
3. This way (assuming №2) we get (ℚ, +, -, ⋅, /). Then, I suppose, you assume we can just define exp(x) as its Taylor series, so we also have all roots, trig functions, etc., and then we obviously have all numbers from ℝ, that are values of such functions acting on ℚ. Exactly as we do in any calculus / real analysis book, with limits and all that jazz.
If that's what you actually meant, I'm afraid you completely missed the point, and 1/(x-y) in fact isn't nearly as good as eml for the purposes of Odrzywołek's paper. Now, I didn't actually verify his results, so I just take them for granted (they are totally believable though, since it's easy to se how), but what he claims is that we can use eml essentially as a gate, like Sheffer stroke in logic, and express "everything else" just as a sequence of such gates and constant 1 (and "everything else" here is what I listed in №3). No words, limits, sets and other familiar mathematical formalism, just one operation and one constant, and "induction" is only used to get all of ℕ, everything else is defined as a finite tree of (eml, 1).
All of these are standard fare in abstract algebra classes, and I didn’t care to write it all out. Once you have the “inverse” operations - and reciprocal, the entire structure follows, for a large set of objects, whether N or Q or R or C or finite fields or division rings, and a host of other structures. So I only wrote - and 1/x
Then, subtraction is (x#y)#0 = x-y. Reciprocal is x#0 = 1/x. Addition follows from x+y=x-((x-x)-y). This used the additive identity 0.
Multiplication follows from
x^2= x-1/(1/x + 1/(1-x)), so we can square things. Then -2xy = (x-y)^2 -x^2 - y^2 is constructible. Then we can divide by -2 via x/-2 = 1/((0-1/x)-1/x), and there’s multiplication. In terms of #, this expression only needed the constant 1, which is the multiplicative identity.
Now mult and reciprocal give x * 1/y = x/y, division.
Any nontrivial ring needs additive and multiplicative identities 1!=0, which are the only constants needed above. If you assume this is Q or R or C, it may be possible to derive one from the other, not sure. But if you’re in these fields, you know 0 and 1 exist.
Then any element of Q is a finite set of ops. R can be constructed in whatever way you want: Dedekind cuts, Cauchy sequences, whatever usual constructions. Or assume R exists, and compute in it via the f(x,y).
This also works over finite fields (eml does not), division rings, even infinite fields of positive characteristic, function fields (think elements are ratio of polynomials), basically any algebraic object with the 4 ops.
Not sure why this is "hilarious", but it's very nice. I almost wish I was keeping this history too, even though I never really even had a "PC" as this separate major thing, I just have a bunch of various devices that serve different purposes, and most my desk "PCs" are just laptops.
> using EML trees as trainable circuits ..., I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4
That's awesome. I always wondered if there is some way to do this.
Is it exclusively football or do they try to fight piracy this way for some other major streaming events? I am just curious, because it's just comical to go this far over some dumb ball-game.
This tragism and pathos of it is almost comical. A wounded Twitter warrior heavily sitting in his chair, wiping sweat from his forehead with a sleeve of his blood-stained shirt. "I'll keep fighting. Just Not on X", he mutters bravely. The wound being that, apparently, nobody reads his posts anymore.
I mean, seriously, if whatever they posted on Twitter actually helped anyone (I'd be surprised, but what do I know), then obviously they'd want to deliver it through every channel available to as many people as they can. If not, and they just want to show their protest by quitting — well, at least they could have tried to get themselves banned on Twitter and whine about it later everywhere else. But this — it's just pathetic.
So, anyway, how do we make sure that our phones don't turn into a pumpkin on a set date? I suppose it's all shit long term, but at the very least I don't want to be forced to look for a solution before I need a new phone. So, what do you do? Can you just disable android updates somehow and it will solve the issue? Or it is already a ticking bomb that will be activated on the set date no matter what?
I remember the story of it being made, and I seem to even remember there was some very generous bounty attached, but I never got the point of it. I mean, honestly, ISBN is a pretty problematic thing on its own, especially today, when self-publishing is common, and especially for a web-library that is collecting scans of everything somewhat notable that ever was out there. But even accepting it as a main entity, because that's what we've got right now, what does this visualization achieve? What does it show? You cannot really find a book using it, I mean, any more specifically than "some random book probably in a given language". I was kinda surprised when this visualization was declared a winner of that particular bounty/contest.
There's a bit of an issue with the linked deployment (in my opinion). In the most zoomed out view you should see the first layer of blocks - very big blocks titled "English language", "French language", "German language". See https://phiresky.github.io/isbn-visualization/ maybe. That makes it a bit easier to read.
The point of the visualization is showing different attributes of books in the space of ISBNs. ISBNs correlate with country, publisher, and release date, that's why using it as a space is useful. You can clearly see the history of when blocks were created, which blocks are rarer than others (present in fewer libraries), and (on the AA hosting) which blocks are more present in AA vs not.
In any case though, yes ISBNs as spatial data are clearly not perfect. Do you have any suggestions that would order the 100 million data points better?
exactly, that map looks like a mess of random blocks...
big blocks are registration groups (countries) and squares inside are registrants (publishers). like a hierarchy.
this visualisation helped me to put pieces together - https://vectree.io/c/isbn
