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45^2 = 2025

Happy perfect square year, everyone. The previous one was 1936 and the next one will be 2116.


2025:

1) is a square: 45²

2) is the product of two squares: 9² x 5²

3) is the sum of 3-squares: 40²+ 20²+5²

4) is the sum of cubes of all the single digits: 1³+2³+3³+4³+5³+6³+7³+8³+9³


5) sum of the single digits squared: (1+2+3+4+5+6+7+8+9)²


Some more (thanks to chatgpt-o1)

6) sum of the first 45 odd numbers: 1+3+5+...+89

7) is a Harshad number: https://en.m.wikipedia.org/wiki/Harshad_number


6 is kind of cheating. It's a restatement of 45^2.

3^2 is the sum of the first three odd numbers. 4^2 is the sum of the first four odd numbers. 5^2 is the sum of the first five odd numbers.

Edit: sorry, don't mean to be a pill.


I don't consider it cheating, I bet most of these rules have an internal relation.


They do indeed have an internal relation - they all add up to 2025.

Obviously all the formula will be equivalent to each other. They are, by construction, all restatements of each other.


I guess that means that every number is equivalent to a formula? Is there some sort of metric of how many formula produce the same number?


You’d have to at least exclude subtraction and division (and zero) to not have infinitely many formulas for every number.


I would say that a rule is "cheating" iff it is implied by another rule for any arbitrary N.


I think that it is a nice observation. Some people complain that explaining the formation of a rainbow scientifically makes it lose its "aweness" but I think it even deepens it.

Actually, property 5) trivially implies 1) but also 2), as `(1+2+...+n)² = n²(n+1)²/4` and either n or n+1 must be divisible by 2 hence one of the squares divisible by 4 hence it is a product of squares. But also property 4) as `(1+2+...+n)² = 1³+2³+...+n³` (easy to show by induction).


4 and 5 too


How so? I'm too dumb to see it.


The sum of the first n cubes is always the square of the sum of numbers from 1 to n. For example 1³+2³+3³+4³=(1+2+3+4)².

You can prove it by induction; just expand (n(n+1)/2)² – (n(n-1)/2)², the result is n³.


89 isn't 9^2, 81 is.


Huh? 89 is the 45th odd number.


(just reading wikipedia here, I didn't know about Harshad numbers)

There is no such thing as a Harshad number, there is a _Harshad number in a given base_. All integers between zero and n are n-harshad numbers.

Which is a pity, because apparenty it means the `joy-giver`. I think human kind could use a joy giver year


8) the sum of 2024 + 1 also


Oh I like these two.


How do people find these kinds of things out without idly brute forcing things?


Also, (20 + 25)^2 = 2,025! Happy New Year :)


Python:

    [x**2 for x in range(32,100) if x**2 // 100 + x**2 % 100 == x]
    [2025, 3025, 9801]


This decomposition is especially fun!


Great to know that someone else too keeps track of squares.

At the ages of perfect squares is when we all cross or achieve significant milestones in our lives as children, students, (young)adults, spouses, parents, grandparents, senior citizens of society and so on.

This year being a perfect square, I wish that it will be as much or more special as it was for everyone at those ages.


My youngest is fascinated by squares at the moment. Luckily for him, he is 4 years old, his older brother is 9, while I just turned 36. He will be delighted when I tell him that we are entering 45 squared!


Also, if you add your ages together… 7^2

If you multiply your ages… 36^2


This is the most Hacker News comment I’ve seen today. Well played.


Up there with Putnam and Dropbox.


Thank you for the Putnam; I did not know about it. For anyone else that did not understand this reference; https://news.ycombinator.com/item?id=35015. Legendary.


That's an epic thread. Thank you very much for sharing it :)

And now, looking back 17 years later, I'd say he succeeded. It's the tarsnap founder.


Indeed! And it was so much fun when dhouston popped up in the thread :-)


And "Less space than a Nomad"


Putnam? Of math competition fame?


Yep, specifically this comment: https://news.ycombinator.com/item?id=35083


Totally nothing bad happened in the decade following the last perfect square year in 1936. :')


Well things have already been a tad rough around this square, so if we follow the trend, the next square might turn bad even sooner. So maybe around, I dunno, 2101?


Unless something equivalent happened in 1849, 1764, 1691... I think we're OK :)


1225: ten years earlier, Magna Carta starting to limit monarchs and the seed of individual freedom

1681: eight years later was glorious revolution with a bill of rights, marking individual freedoms

1764: ten years later, beginning of American Revolution and being free of monarchs

1849: ten years-ish later, start of US civil war; was the time of an attempt by the British to end slavery around the world

1936: ten years later, colonial empires were being dismantled, UN established to attempt global cooperation, US in the ascendancy with a seed of ties being established more by economics than military force, great economic upswing lifting people out of poverty (60% in poverty then, 10% now) while the global population blossoms

2035: Majority of the global population in middle class or better, triumph of individuals over technocrats, bureaucrats, and corporatists :)


I love this! Haha, I was hoping someone would do that. :)


2025 = 515 (palindromic in base 20)



And

    (20+25)^(20/(2*5))
as well.


US President number 45 returns, kind of seems like squaring applies.


Donald = Donald E. Knuth? ;-)


here’s to all be alive and well floating in amniotic liquid living in VR paradise


The algorithm behind this has to be super fun


My guess is that they host a version of the model locally on the iPhone.


Even if they don’t (or if it’s partially networked as some recent rumors suggest), it’ll be rolled into one or both of two predictable costs (to the consumer):

1. The device sale itself, either raising the ASP or offsetting some other cost (to Apple) savings

2. Recurring payments for iCloud (or any rebranding it might undergo along with the feature)

Apple’s pricing model, if not totally predictable, is exceedingly formulaic. If they deviate from these into some sort of nickel and diming on “AI” features alone, that would almost certainly be a clear sign that they’re betting against it as a long term selling point.


This indeed seems to have been a heavy focus of their research team in the past year, eg. "Efficient Large Language Model Inference with Limited Memory" [1] and OpenELM [2]

[1] https://arxiv.org/pdf/2312.11514

[2] https://arxiv.org/pdf/2404.14619 (with 1.1B parameters, this appears to be their attempt at building a lightweight LLM)


Maybe a very cut down version - any of the more recent and capable OpenAI models are surely far too large to put on an iPhone, and far too large to run (in terms of both memory available, and processing power).

This would maybe align with the 'limited abilities are free' approach.


Do you have any examples of your prompts? I've found Opus to be vastly superior to ChatGPT for intricate tasks.


Sure.

---

In the following, Opus bombed hard by ignoring the "when" component, replying with "MemoryStream"; where ChatGPT (I think correctly) said "no":

> In C#, is there some kind of class in the standard library which implements Stream but which lets me precisely control when and what the Read call returns?

---

In the following, Opus bombed hard by inventing `Task.WaitUntilCanceled`, which simply doesn't exist; ChatGPT said "no", which actually isn't true (I could `.ContinueWith` to set a `TaskCancelationSource`, or there's probably a way to do it with an await in a try-catch and a subsequent check for the task's status) but does at least immediately make me think about how to do it rather than going through a loop of trying a wrong answer.

> In C#, can I wait for a Task to become cancelled?

---

In the following exchange, Opus and ChatGPT both bombed (the correct answer turns out to be "this is undefined behaviour under the POSIX standard, and .NET guarantees nothing under those conditions"), but Opus got into a terrible mess whereas ChatGPT did not:

> In .NET, what happens when you read from stdin from a process which has its stdin closed? For example, when it was started with { ./bin/Debug/net7.0/app; } <&-

(both engines reply "the call immediately returns with EOF" or similar)

> I am observing instead the call to Console.Read() hangs. Riddle me that!

ChatGPT replies with basically "I can't explain this" and gives a list of common I/O problems related to file handles; Opus replies with word salad and recommends checking whether stdin has been redirected (which is simply a bad answer: that check has all the false positives in the world).

---

> In Neovim, how might I be able to detect whether the user has opened Neovim by invoking Ctrl+X Ctrl+E from the terminal? Normally I have CHADtree open automatically in Neovim, but when the user has just invoked $EDITOR to edit a command line, I don't want that.

Claude invents `if v:progname != '-e'`; ChatGPT (I think correctly) says "you can't do that, try setting env vars in your shell to detect this condition instead"


Now I come to think of it, maybe the problem is that I only ask these engines questions whose answers are "what you ask is impossible", and ChatGPT copes well with that condition but Opus does not.


(Nope, this hypothesis doesn't seem to be it. Maybe it just confidently doesn't know anything about Neovim?)


Do you have an example implementation of reimplementing the core of these?


It's literally what I did at work last week, which is why I found this submission timely. I'd have to check with my employer if it can be made public. I don't see any reason why not, there's not much to it.


What did you use to implement the regularization of the trend breakpoints? Prophet by default uses a regular grid and thins them out with STAN. I couldn't find a quick regularization replacement in numpy/scipy/statsmodels with equivalent performance. (I don't want to drag in another huge dependency with Torch or TF).


Do you have any examples?


https://proceedings.neurips.cc/paper_files/paper/2018/file/9...

For the relationship between concentration of the measure and this: the main theorems of concentration generalise the CLT beyond the additive case, for any lipschitz operator over iid vars, the first i can even be relaxed.

You can find online, works by eg. Gromov and his students for a deeper understanding.


Reddit is very bizarre right now.

Most of the active users are non-power users who are flummoxed at why mods have shut down their favorite subreddits. They are complaining in droves. Lots of long-winded Facebook boomer-style rants about how they read the subreddit with their kids and they need it back up to entertain them.

Some subs are protesting the spez moderator removal threat by changing the topic of the sub entirely.

Meanwhile, most of the content producers seem to have fled the site and latest high quality serious content is a week old at this point.

I don’t see how Reddit recovers from this without losing a great deal of value for their shareholders. I’m expecting Huffman to resign based on how much he has damaged their monetization potential with advertisers.


Loss of the primary content creators is serious, more than I think most realize. Without active serious creators you end up with nothing but an endless feed of endlessly recycled memes. Reddit was already trending that direction anyway with repost bots posting almost as much as real users, and creators leaving will only accelerate the process.


> Without active serious creators you end up with nothing but an endless feed of endlessly recycled memes.

This is what drives the most eyeballs to ads though. Reddit simply wants to be like Instagram with memes, not an actual text-based discussion forum.


A lot of their messaging to advertisers revolves around discussing the value proposition of subs like /r/buyitforlife which has 1.5 million users who are likely actively considering a purchase at the moment of viewership, are willing to be convinced to spend more money, and are relatively affluent. Klaje (Reddit’s rev executive) loves talking about trust and positivity of the user base. I’m not sure how that messaging survives if the site moves away from quality content.


But now their serious competition is 9gag not quora or some other site. Most of my regular friends started using Reddit not just for the memes but the text based ones (like AITA, BORU) and local subs. Good luck making them look good with a large fraction of creators and good mods leaving.


I don't understand why people talk about the current mods as "good." They were literally chosen the same way future mods would be chosen, by volunteerism. There is no reason to believe future mods would be any less good than current mods. And I should amend my previous statement, text based subs that generate drama also generate ad impressions, ie AITA or BORU. I'm talking about how Reddit is moving away from niche text based communities since those do not generate nearly the same amount of ad impressions.


Maybe they can replace mods with new volunteers, but Reddit Admins have also just explicitly shown that mods with valid complaints will get no support, may be libeled, and potentially have an admin-led coup done against them if they don't comply.

This is likely to dissuade folks who are in it for the right reasons and want to do a good job with good tooling and proper care and power hungry weirdos who now know that if they disagree with the Admins, the Admins have shown they can weather any storm and don't care if any user, even powerful mods, disagree with them.

I'm not sure why anyone would decide to be a mod at this point. Before this month, it was a chance to run your own corner of the internet, for better or worse. Now it's been made very clear who actually runs the show, and that those people could not care any less about you.


No, the current mods were picked by 15 years of natural selection, where mods that don't care about their role have had the potential to get bored and leave or have their community migrate to a different subreddit that more matches what that community wants.

Antagonizing a large swathe of your volunteer-base of active mods all at once and then replacing them with new mods who seem fine with that antagonistic behavior is not going to select for the same group of people.


> Meanwhile, most of the content producers seem to have fled the site and latest high quality serious content is a week old at this point.

I highly doubt this, most content producers explicitly can't post their content because their subs are restricted or private, eg AskHistorians.

> I don’t see how Reddit recovers from this without losing a great deal of value for their shareholders. I’m expecting Huffman to resign based on how much he has damaged their monetization potential with advertisers.

No, this is great for shareholders as it explicitly removes users using apps that are not able to show Reddit ads.


I’m an avid Redditor and have been for a decade. I just stopped using it since the blackout. Turns out life is fine without it. Occasionally I go into it when I have a specific question or something but that’s it. Screw that site and these myopic CEOs who think they’re Elon Musk 2.0. I doubt I’m the only big contributor to do this. Whether the subs come back or not, I give Reddit a mere 50% chance of being able to survive this long term. Eat this shareholders, for leaving an idiot on as CEO.


Again, shareholders explicitly love this action by the CEO. As for survival rate, it depends on your definition of longterm but every social network eventually dies. Most people simply don't care about the internal politics of a company whose social network they're using. For all of Facebook's scandals, they still have 3 billion monthly active users.


Maybe myopic share holders sure. There’s no way a logical person would think this is going to increase their returns on this company. Alienating your top creators is not a great strategy.

As for your Facebook analogy, I don’t buy it. Every young person I know (less than 45 yo) both in US and India maybe logs into FB once a month to see if someone in their extended life got married or bit the bullet. That’s it. The 3 billion number seems to be some clever accounting to me. I agree that between instagram and WhatsApp they have covered most people however, but not by just Facebook. And I’d argue that’s not necessarily because they alienated their users actively anyway. Not like Reddit is doing now.


Users being mad at mods that think that they own communities that aren't theirs? Shocking! What a bunch of boomers, they should just let the mods get their powertrip! It's not like they are volunteers that could just... Go away if they dont want to moderate the community anymore.

(Again, moderators do not own the subreddits, they can't unilaterally close it. I mean, they can, but they can't be surprised if they lose mod rights. The funny thing is that they are all reopening now that they might actually lose their little fiefdom. Random readers being affected didn't matter to them, but once there was even a hint that they could lose their online janitor status they quickly caved in. Very very selfless)


> Users being mad at mods that think that they own communities that aren't theirs?

This is one of these places where the concept of "ownership" falls apart, at least in the monolithic ownership. A community consists of users, mods, and the platform operator. As soon as one of these components defects, the community is destroyed. So really the community as an entity can only exist when all three sides cooperate, which makes the question of who owns it somewhere between unhelpful and nonsensical.


Shows solidarity without threatening anyone’s livelihoods. You can’t get fired for simply taking a lunch break.


But also shows you’re not willing to take any risk for your principles. Probably a strategic error.


Could you explain more? Sounds like a fun problem.


I'll do my best! Dodging proprietary bits (and bad term usage) along the way :D

First, some background: we had to pivot from one NFS instance to another. Assume the data was already consistent.

The goal being to minimize observable disruption to the guests. We can pause time, but can't restart the instances -- the services involved should be unaware.

Processes hold onto files they have open. This is pretty well understood - many have heard of file descriptors

These are very sticky -- particularly for things with mounted filesystems. This is where my path to glory appeared

The thinking was... as long as that path was there when the VM process was resumed, we'd be fine...

In reality, we weren't! The kernel isn't really concerned with the fully qualified path.

From the example above, /somepath is really just like "mount ID 2" to the kernel.

In the end we had to renew those file descriptors, consequently picking up the new mount IDs

We ended up pausing the instances, saving the memory state locally, swapping the mounts, and then resuming the VMs.

Time only briefly skipped, and we successfully moved thousands of instances from one NFS 'host' to another


American baby boomers are worth, on average, something like $1.2M depending on your source. That's a lot of retirement capital that will be leaving various markets and chasing goods and services over the next few decades.


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