skysight-inc/HackerNews huggingface dataset:
>> Quaternions are hypercomplex numbers of the form

>

>I'm gonna guess "hypercomplex" means "involves imaginary numbers" due to the rest of this.

Think it is right.

>>

>> Where w, x, y, and z are real and i^2 = j^2 = k^2 = -1 and ij = k, ji = -k, jk = i, kj = -i, ki = j, ik = -j.

>

>Why even use different letters for i, j, and k, if they're all the same thing? Which thing appears to be i, as in, the square root of -1, that is to say, the most well-known and basic imaginary number, if I'm reading this right.

They are not the same thing. All of these are equal to -1 when squared, but they are different when multiplied by any other of this set and multiplication between them is anti-commutative.

>As for the second part, I can't even begin to unravel the significance. I know it must not be, but it just seems like arbitrary rules added for... some unknown reason.

>

These are not added for unknown reasons. They specify rotations of unitary vectors of a canonical base around one another.

>> Being u = (x, y, z) = xi + yj + zk a unitary vector, it is possible rotate any vector q by an angle theta around u by doing:

>>

>> pqp'

>>

>> where p = cos(theta/2) + sin(theta/2)u and p' = cos(theta/2) - sin(theta/2)u .

>>

>Oooooh kay... 1) Where'd w go?

The coordinate 'w' is the real part. For the vector 'u', such coordinate is 0. For 'p' and 'p'', it is cos(theta/2).

>Is this one of those things where there's a (situationally-defined) constant in the formula but we just pretend it doesn't exist most of the time (until it comes time to actually use the math to, like, do anything real)?

No.

>Would we need to bring it back in to apply the rest of this?

No. Just follow the rules to multiply hypercomplex numbers and the rotation will occur.

>2) "u =" is just defining something, fine, but (x, y, z) doesn't seem to equal the thing after it at all—I suppose this is a shorthand function notation, though it seems really weird to me to use equality to relate that. Am I right, or is this something else?,

The notation '(x, y, z)' is just a shorter notation for "xi + yj + zk". For this problem, the vector 'u' defines the axis of rotation.

>3) A quaternion is... a point, then? Since we're rotating around it?

You can see a quaternion as a point in R^4 since it has 4 coordinates. Actually it describes an axis of rotation, by its imaginary part, and the angle of rotation.

>4) I've got a feeling that theta needs a direction in this hypercomplex space but don't see where it's coming from. Somewhere "off screen", in this explanation? Or is it there but I'm not seeing it?

>

The axis of rotation is actually the vector "u".
The evidence for the expectations model has changed significantly over the past two years or so. Obviously, central banks are going to move slower given that expectations has been the consensus for two decades. But I think academics are realising (about seven years after markets realised) that central banks have a huge role in signalling and the consumers form their expectations about inflation based on the past (note: the last point is compatible with evidence for expectations when inflation is falling...in other words, if inflation was falling over your sample you would be unable to distinguish between an expectations-based theory and a moving average-based theory of inflation).

Also, investors won't start exiting the market if they expect expansion in housing stock. Financial markets trend, they absorb information imperfectly, they overreact, and there is massive volatility as all this occurs. Indeed, there are some investors who base their investment strategy on the inability of markets to react to capital cycles (Marathon Asset Management have written books about this). Investors have different time scales, if the housing stock was going to expand then you would see capital pile into the sectors because people will chase that growth expecting to flip at a higher price at the top.
It'll be trivial for any competent administrator to filter the bogus applications based on the non-unique IPs they were submitted from. Further, user agent is probably going to be identical. Finally, the time they were submitted is going to be another way of filtering them out. Addressing these flaws would make the resume jamming far more effective.

This is not advice, just observation.
> Most products today are less durable and are generally worse than "yesterday", in my opinion.

People forget how (relatively) expensive products used to be. Example: my family had a very early VHS video recorder. I believe it cost ~$1000 in the early 1980s. I may be misremembering. But that was a lot of money then. So of course it was worth repairing. Labour was considerably less expensive in terms of percentage of outlay costs. That's why it was justified.

Computers came along and you had a bunch of chips on a board, some of which were worth replacing. But each interconnect costs money. Each external package costs money. We've seen the rise of complicated SoC chips that basically do everything in one chip. These are overall cheaper to fab (compared to 2+ chips) and have lower build, integration and interconnection costs.

The downside? If it stops working, you just throw it away (or at least replace the entire SoC). And if the SoC is relatively cheap, it's not worth paying someone to order a replacement and replace it (with or without soldering).

So really what you're missing is tech being very expensive. Personally I prefer what we have now.

There are other downsides to modern tech (eg Internet-connected TVs to insert advertising) but durability just isn't one of them.
I was turned off by that too, but I'm actually the kind of person who makes a point of reading things written by intelligent people with whom I ideologically diverge. I also acknowledge that I lack the authoritative knowledge of history to evaluate whether assertion that the 1619 project is rewriting history is true or not.

I rather like the 1619 project and its narratives, so perhaps I'll add some books to my list for the coming year to be able to call bullshit on that or not.

In general my promotion of things that increase skepticism in statements made by authority (such as the NYT) outweighs my disdain for the brawlers in the current US culture war.
You have to remember that the first amendment was written to protect people like the founders - wealthy, bourgeois, powerful men. It was never intended to create a press that challenges state power.
I bet you're wrong, and it looks like a very small majority agree with me. Want to stake some internet points on that position?

https://www.metaculus.com/questions/7977/inflation-above-3-i...
You know, I wasn't entirely sure, but after researching it, the "let" form in Clojure is a monad.

Monads are something that I keep trying to learn, but for whatever reason, the info just won't stick. After decades of doing this, my brain automatically seeks out the laziest way of doing things (while still being deterministic, testable, automatable, etc). Monads seem to be a very "hands on" way of doing FP programming, which to me defeats the whole purpose. I would probably only use them in an emergency, or to port existing functionality from an imperative language, like I mentioned.

These are the first 3 links that popped up for my Google context:

https://github.com/khinsen/monads-in-clojure/blob/master/PAR...

https://cuddly-octo-palm-tree.com/posts/2021-10-03-monads-cl...

https://functionalhuman.medium.com/functional-programing-wit...

Aspects of this do look eerily similar to async (promises/futures), like maybe monads could be implemented via nullable/optional values. I think of promises as polling a nonblocking stream result until the point in the code where the result is needed, and then blocking until the promise is fulfilled. Which is basically fork/join of threads of execution, with different syntax.

The articles mention that Haskell has syntactic support (I assume sugar) for monads. I'm nearly always against syntactic sugar and domain-specific languages (DSL) though, because they obfuscate what's really going on and double the mental load by creating two or more ways of doing the same thing. It would be fine if languages let us instantly reformat the code by transpiling with various languages features toggled (like Go's gofmt but more than just whitespace) so we could see what the syntactic sugar is doing. But nobody does anything like that, which is why I'm skeptical.

I feel like monads are one way of approaching mutability, but there are others. I'm curious how shadowing variables and even stuff like Rust's borrow checker plays into this. Like why couldn't we have a pure FP language with only immutable data and no borrow checker? That executes in its entirety when new data arrives on a queue like STDIN or a queue like STDOUT has a slot available, otherwise it blocks? I guess fundamentally, I don't understand why a spreadsheet needs scripting (written in mutable languages of all things!) or FP needs monads.

Another insight is that a monad isn't really an optional value, it's a way of executing multiple potential branches of logic. Which is similar to electrical circuits or switching at railway stations. This happens in shaders when both sides of a branch are executed, but only the outcome that matches the result of the branch is kept:

https://fsharpforfunandprofit.com/rop/

https://vimeo.com/113707214
Mary, Queen of Scots ‘locked’ final letter using paper-folding, research finds
Trailer: https://www.youtube.com/watch?v=sgNj2Sf_mgo
sure but they could easily scrape Zillow in 2020 and compare the numbers to 2021. Those numbers would show a ~17% increase. If they are unable to adapt their model to modern data sets then the model is pretty much useless.

Edit: General response to the responses. I am not advocating for Zillow to be a source of truth, I was responding to the parent comment of my post and their mention of Zillow. What I am saying is that we are not limited to using methodologies of the past, there are vast datasets and modern data collection methods available to us now that can be used.
Gargantext might be of interest: https://iscpif.fr/gargantext/
> Congratulations

Please don't be snarky. It's rude and it also makes it more difficult for others to follow your train of thought. I'm not part of the original thread and I don't understand what argument you're making here.
> We've just witnessed a large transfer of wealth to the lower and middle classes, and the economy is booming.

Nonsense. The wealthy have a diversified portfolio of assets, not just money in a bank account. Most of these assets are at least hedged against inflation, if not appreciating over time. The lower and middle classes then take debt to buy some of these assets from the rich.
I use https://paddle.com/ for a paid Chrome extension (https://www.checkbot.io/).

The major reason I use Paddle over Stripe is Paddle deal with all EU VAT and other country specific tax + admin for you which Stripe still don't (as far as I know). If you're a small team or solo, you really don't want to be burdened with the extra work here and the scope for complicated and scary tax related mistakes.

Each month Paddle send me a single payment and I record those as business income - that's it, done.

Edit: Pricing is 5% + $0.50 per transaction. As far as I know, Fastspring is more expensive and Gumroad is cheaper, and both take care of tax for you the same as Paddle.
>lots of new money (currency) leads to inflation

I thought that in 2008 but we had a decade of low inflation.
Thank you for taking the time to share your thoughts. There is a lot to unpack in what you wrote.
if "laws" cannot protect one man, why bother with the sham that is "democracy"? its not just in the US but rest of the countries as well. when "pride" of a democracy is greater than the life of a human, it is no better than china or north korea. there at least you have the expectation of their intentions, that you are on your own. "democracies" are supposed to protect the little guy regardless of the adversary. as the other commenter said, this sets the precedent for the rest of the world. now india can go ahead and do the same to its dissenters because america could do it.
> At the same time, we need to acknowledge that doc tests were pioneered elsewhere and have existed in many other languages for a long time.

I agree. I understand that a lot of people talk about Rust as if everything it does is novel, when it is really a culmination and execution of a lot of good ideas (Which tbf is what most good things are anyway).

And the fact that many people's introduction to Rust come from books written by the developers means that even beginners will be exposed to these features early on
> You could say the same thing about the whole spectrum of ethically questionable jobs. I think we can all agree that there is at least some point on that spectrum where "Well, I needed a job" is an unacceptable excuse.

Sure, but "ethically questionable jobs" is a pretty massive spectrum, and I'm not sure that I would agree that "making cereal during a labor dispute" meets the line of "to unethical for me" for the majority of people.

> So, if you have to take a job, there are currently plenty out there that keep your hands clean of strike-busting.

So is strike-busting the only place you draw the line? What about having to take a job at Hobby-Lobby? Or Chick-fil-a? Amazon has some some pretty sleezy stuff, so you don't want to support them. Walmart employees often depend on food stamps, and you should keep your hands clean of supporting a company that treats it's employees so poorly.

There are tons of jobs that you could take in order to keep food on your table that aren't Kellogg, or Hobby-Lobby, or Chick-fil-a, or Amazon, or Walmart.

If you keep digging, you'll quickly run out of "non-questionable" jobs. You are definitely welcome to blame the employer for their actions, policies, and decisions, but it's not fair to say "Well Jonny over there once worked at a company that I have an objection to, so he should never be allowed to have a job again!"
> After 2016, i went from getting "oh you radical crazy commie" looks wearing a wikileaks shirt to immediately "oh you're a republican, let me guess you listen to alex jones and joe rogan?"

The flip side of this is that we're apparently focusing on the wrong things.

Assange was prosecuted under Trump, now he's being prosecuted under Biden. Who were we realistically supposed to vote for in order to make this stop? If this is the only front then we lost before there was even a vote.
This is an annualization of the change over the course of November. So the baseline is October 2021.
Video showing the technique: https://youtu.be/U3lGlmRPMKw
> It would be nice to see the EU commission competing against GitHub for Open Source hosting

Why would you want them to get into that? It doesn't seem like it's something appropriate for a government to get into.
Magnus Carlsen defends his World Chess Championship crown
Read receipts make me not even want to talk to people. I want to be able to walk away and go do my own thing and not possibly offend someone that it took me hours to reply or didn't reply at all. It feels so invasive to me and my time.
Human interactions. People tend to socialize less and "digitize" more. Even when sitting together, people constantly scroll through Instagram. This shouldn't be what the new generation defines as "socializing".
I'm not sure why they don't just hire voice actors and ask them to naturally respond to the situation while watching the video, with a set of target phrases.

"Say something to the effect of this, when this thing happens on screen, but phrase it however you like."

Visually stunning, but no matter how realistic it is, you're killing the chance of enjoying it because you go "Nobody would say that", and it also doesn't sound natural.

This is why I enjoyed the Fallout games so much. Even the earlier ones like 3 and New Vegas that weren't realistic looking had fantastic, believable dialogue.
Disclaimer: I'm not a dark-mage-of-the-smith-chart - I'm just a dude who had to take a course in EM once. Honestly, I'm pretty ignorant and you should take all of this with a grain of salt.

My understanding is that the noise model is very different - that LTE/ofdm are very good at getting around radio noise by-frequency - ie a bunch of interference at a particular frequency. But 3G/umts/cdma was very good at dealing with multi-path distortion because of the whole chip-code-orthogonality property and the fact that the radio would have multiple time-shifted taps on the antenna. That would mean that in theory LTE would be better at dealing with persistent environmental noise, but 3G would be better in a city where the phone is receiving that same signal but reflected against buildings and slightly time-shifted.

I doubt this makes any difference in your case - it's probably just that 3G is typically on 850MHz and that LTE is probably on a higher frequency like 2300MHz which wouldn't propagate as well.
Whatever many of these problems may be, I see pretty much all of my non-tech friends completely helpless in handling them.

They're so fucked and don't have a chance.
Show HN: Generate Sublime Text syntax definitions for a context-free grammar
> Maybe not advertising completely but at least targeted advertising.

Non-targeted advertising is still distracting.

Why not ban it completely? Or perhaps allow dedicated advertising places, so everybody can be happy.
Do you mean in the word "affective"? It's a perfectly cromulent word.

It's the adjectival form of the word "affect" in its noun sense, meaning "mood" or "feeling". This form is pronounced differently: A-fect (emphasis on the first syllable, with the vowel like in "rat").

"Affective polarization" is "people being polarized in how they feel about each other", i.e. animosity towards people in the other party. It's a technical term used by sociologists and not in common use, but it's not a typo.
Yes but credit should not be given for their mistakes.
We had enough folks reach out to us that we put together a blog post about this CVE: https://fusionauth.io/blog/2021/12/10/log4j-fusionauth/

You can also read the full CVE description here: https://nvd.nist.gov/vuln/detail/CVE-2021-44228
This is correct. They keep a low profile.
If it's super important to me, I'll actively look for it.

Opt-in advertising is another option, I have no problem receiving advertising I've specifically agreed to receive.
I don't think repeatedly hitting F5 on a webpage is illegal.
Norway’s Magnus Carlsen wins FIDE world chess championship
Governed advertising and education channels would be an answer to this
Ok, so factually we are more wealthy than we have ever been as a society across the entire wealth distribution and yet we have an obesity epidemic. An obesity epidemic is very much a rich country problem. Our terrible food has nothing to do with it being too expensive (Although listening to the FDA back when they advocated 10+ servings of grains a day probably didn't help).

Also expecting people to apologize for their social station is tacky as hell. You play the hand you're dealt to the best of your ability. Anyone who claims otherwise has an agenda. Why would your critique of spoken like someone who has never been poor have any merit whatsoever?
Just because our leaders are democratically elected doesn't mean that they always make decisions in the best interests of our country or its people. Indeed, it's incumbent on every citizen to oppose policies they disagree with. For that reason, it's never correct to say that someone is against democracy just because they oppose the government or its policies.
Your method doesn't control for shrinkflation[0] if only looking at your debit card statements.

[0] https://www.mouseprint.org/category/downsiz/

Edit:

Humans aren't robots folks, if there's consistently some excess food being disposed of it could simply mean there's slightly less going into the wastebin.

And regarding TP, I don't know about you, but I tend to be wasteful with TP when the roll is fresh and increasingly frugal as the roll approaches empty.

This is all highly subjective but the fact is people tend to be inconsistent and wasteful.

You need to track normalized unit costs for such data to be reliable. Package sizes are constantly being manipulated, period.
Will raising interest rates solve supply chain issues? Will it decrease demand for goods and increase demand for services to pre-pandemic levels? It seems to me there are causes of inflation outside of the Fed's control.
There’s nothing wrong with write offs, about half of my income is paid to the government. I will always do everything I can to minimize my tax liability, and it’s natural to do so.
I am confused. Are you saying that the quality of the iron makes them shit swords, or that guns are better than swords?
Serverless Storage for Serverless Cloud
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> I also remember a "cup holder" app which was advertised as a free cup holder. It had a button which when clicked opened the CD drive.

I remember a Coca-Cola branded version of that app. I had way too much fun giving it to friends. :)
Just creating money doesn't necessarily mean much:

> But this is what so much of the money supply represents – money that has been issued and is just sitting around unused. Why is this useful? It’s like calculating your weight changes by counting how much food you have in your refrigerator. No. That’s potential calories consumed and potential weight gain. The amount of food in your fridge tells you little about your future weight changes just like the amount of money in the economy tells us little about the actual price changes in the economy.

* https://www.pragcap.com/three-things-i-think-i-think-i-see-d...

It actually has to be used, which it generally has not been:

* https://econbrowser.com/archives/2021/11/so-you-want-to-be-a...

* https://fred.stlouisfed.org/series/M2V
I can just see some salivating HN startup candidate pitching, "We'll use AI to automate creating personalized products!"
Technologists' cliché lack of social skills is a major ethical hazard in the world of technological innovation. We have engineers designing systems to interact with humans, but those engineers don't understand the relevant interpersonal forces and dynamics. If you want more ethical systems, raise conscious and sociable children who become engineers.
I bought a new TV about the time this article came out. I think I’ve watched maybe a dozen shows on it via the tuner. Every single other thing has been either optical media, gaming, or streaming.

The replacement I bought this year will probably never have anything connected to its coax jack.
I always talked about ideas since I was a kid and got lots of applauses, but no one ever bothered to actually take my hand and try to explore with me. I didn't simply get bored, I ended up in complete social isolation. In my personal case, neglection actually runs deeper and beyond the educative system, but if you fail to "get people on board", any other metric will be irrelevant.
https://www.apartmentlist.com/research/rent-estimate-methodo...
Yes all forms of advertising should be banned. But, it will never happen. So, better not to get too excited with the idea.
An interesting study would be to compare quality of public education in a given country, as well as the prevalence of conspiracy theories, or the breakdown of trust in verifiably correct information. How does the spread and proliferation of nonsense in Norway compare to somewhere like Germany? To American and Canada? This could give some interesting insight on what exactly we can tune up in a given system to improve critical analysis skills.