I agree with the author, we need better primitives, if you need functionality now:
Major tools that exist today for partial structure traversal and focused manipulation:
- Optics (Lenses, Prisms, Traversals)
Elegant, composable ways to zoom into, modify, and rebuild structures.
Examples: Haskell's `lens`, Scala's Monocle, Clojure's Specter.
Think of these as programmable accessors and updaters.
- Zippers
Data structures with a "focused cursor" that allow local edits without manually traversing the whole structure.
Examples: Huet’s original Zipper (1997), Haskell’s `Data.Tree.Zipper`, Clojure’s built-in zippers.
- Query Languages (for semantic traversal and deep search)
When paths aren't enough and you need semantic conditionals:
- SPARQL (semantic web graph querying)
- Datalog (logic programming and query over facts)
- Cypher (graph traversal in Neo4j)
- Prolog (pure logic exploration)
These approaches let you declaratively state what you want instead of manually specifying traversal steps.
In case anyone is wondering, "when would I EVER use this (in hand-written code)?", it's a trick that makes DSL (domain specific language) and small language implementation much easier. A great reference for this is Peter Norvig's Paradigms of Artificial Intelligence Programming, when he implements a subset of Prolog and bolsters the functionality using CPS[1].
The second, although more
obscure, is that you can use it in languages that do not have "non-local exits" to terminate a deeply nested computation early or return to an earlier point in the call stack. For example, Clojure does not have nonlocal exits, as only the final form of the function is returned. However, using CPS, you can terminate the expression early and return to the original caller without executing the rest of the function. You probably only want to use this in specialized cases though or it may upset your team, they are tricky to debug.
Lastly and probably most controversially, you can make an extensible "if" statement using CPS if you are in a dynamic language and you have no other tools to do so. Admittedly I do sometimes use this in ClojureScript. This allows you to write "append only" code without continually growing the "cond". Again, most teams don't like this, so it depends on the circumstances, but might be
nice to have in your back pocket if you need it.
Tao's notes seem to be based on the book Linear Algebra by Friedberg, Insel and Spence. I found it to be one of the best books on Linear Algebra, better than even Hoffman/Kunze. The proofs are extremely clear, it has examples like PageRank, Markov Chains, PCA and the solutions to just about every exercise is available on Quizlet.
Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineering feat of the tunnel of Eupalinos.
Iamblichus’s “life of Pythagoras” [1] is worth a read as he had access to all the old sources now lost. The relationship between math and spirituality was very strong back then!
There are lots of fun stories that may be true but no one will ever know. In Diogenes Laertius’ “Lives of the Philosophers,” it is claimed that when Pythagoras made his discovery of what we call the Pythagorean theorem, he sacrificed 100 oxen (a hecatomb) [1]. As noted by Charles Dodgson (Lewis Carrol), “that would produce an inconvenient supply of meat” [3], especially for a vegetarian. Iamblichus, on the other hand, claims it was a single ox — and made of flour!
[1] Guthrie, K. S., & Fideler, D. R. (Eds.). (1987). The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Red Wheel/Weiser.
[2] “he sacrificed a hecatomb, when he had discovered that the square of the hypotenuse of a right-angled triangle was equal to the squares of the sides containing the right angle.” DL, found in [1]
[3] Maor, E. (2019). The Pythagorean theorem: a 4,000-year history. Princeton University Press.
I got excited when I saw something about helicopters. There are hardly ever any articles about helicopters on HN. I have a commercial helicopter license and almost 900 hours of combined helicopter and airplane flight time. If any extra rich people in the bay area or Sacramento want to buy a heli I will be your personal pilot available 24/7. Helis can go almost anywhere. I love to fly but it is hard to fly them unless you have a lot of money. You can get a used Robinson R-44 4 seater for about $500k. Maintenance and insurance are expensive but no insurance is required if you pay cash. Let me know.
1. Ephemeral Astroturfing Attacks: The Case of Fake Twitter Trends
A good start! It makes relatively limited claims (they aren't trying to assert whole elections are being distorted by Twitter bots) and is indeed higher quality than the ones I've been citing. It actually makes its data available, which is a step forward. But it's had limited impact (28 citations), and it's also not particularly useful. All they're doing is revealing that there is ordinary spam, hijacking and SEO on Turkish Twitter, which was never in doubt. All social media sites have these problems and the authors were tipped off by some amateur third party that highlights these campaigns. Most of what they find is plain commercial spam, there's also some politics in there related to local Turkish issues like cab drivers protesting against Uber but there's no evidence presented that this is actually having a real impact on politics.
The main question here is why are universities spending grant money on subsidizing Twitter? The only people who can do anything with this paper are Twitter's spam team, there isn't generalizable new scientific knowledge coming out of it.
2. Political Astroturfing on Twitter: How to Coordinate a Disinformation Campaign
This one starts with a big claim, so it can at least say it's doing important research. But I really wonder why you suggested it because it actually agrees with us and even destroys the underlying premise of the entire field! A pretty useful paper that might be worth citing in future articles on the topic, in fact.
Firstly, their conclusion is that "if even a powerful and well-financed organization like the South Korean secret service cannot instigate a successful disinformation campaign, then this may be more difficult than often assumed in public debates". In other words, the supposed problem motivating this entire field of >10,000 papers doesn't actually exist: even government agencies fail to have impact when they try to sway opinions with Twitter.
Secondly, they accept that our criticisms of the field are correct. "We argue that past research’s predominant focus on automated accounts, famously known as “social bots” ... misses its target since reports on recent astroturfing campaigns suggest that they are often at least partially run by actual humans" and "Because a ground truth is rarely available, systematic research into astroturfing campaigns is lacking".
They also dunk on ML models on page three, and admit that "these studies still largely focus on anecdotes and lack a theory-driven framework" i.e. are more like blog posts than scientific research. These were all points being made by Gallwitz, Kreil and myself years ago.
The paper does have issues! Still, they should get some cred for being honest about their findings, albeit on the penultimate page of a 25 page study. The first sentence of the paper is phrased in a misleading way: they assert that astroturfing on Twitter has the potential to influence politics, but their conclusion is that it actually doesn't. That's a problem that you see a lot when reading papers in some fields.
Paper 3. QAnon Propaganda on Twitter as Information Warfare.
Note that this paper also isn't about bots. It's a complaint about the behavior of real American people. Where is the actual science? Why are you picking this as an example of high quality research? It's not only blatantly partisan, reading more like a Guardian op-ed than a research paper, it starts by citing paper (2), the one that wrecks the whole premise of the field! They are happy to cite it as evidence that they should look for astroturfing instead of bots, but forget to mention that it shows that even an intelligence agency was unable to have any impact on politics by running Twitter campaigns. Yet that doesn't stop them asserting that their line of research is important due to the "innovative misuse of social media towards undermining democratic processes by promotion of magical thinking".
This sort of problem is rampant in published research. I've seen it so often that a paper cites another paper which directly undermines the conclusions of the first, yet the authors don't address or even mention it. This sort of thing is just deceptive. If they want to cite paper (2) then they need to tackle its conclusion.
The rest of it is just US Democratic Russiagate talking points. Getting into the accuracy of that is a book-sized job and and not about science, so I won't do that here, there are many such debates on the internet.
So that's your three papers. One is OK but not very valuable, one ends up (unintentionally?) wrecking the premise of the other ~10,000+ papers and one isn't even scientific research. It's unclear how they were picked but if these are really the best examples of high quality research from the field then, indeed, who really cares if Musk cuts it all off.
Major tools that exist today for partial structure traversal and focused manipulation:
- Optics (Lenses, Prisms, Traversals)
- Zippers - Query Languages (for semantic traversal and deep search)