Thirty Seven
thirty-seven.org
thirty-seven.org
Don’t get me wrong either, this is still a much much better mobile experience than popover garbage and JS dynamic wank.
Maybe language models will bring back the concept of a “user agent”. One could imagine feeding a GPT the source for this page and receiving mobile-friendly source as output.
I’m looking forward to the day where the AI screens all markup rendered in my browser. (Let’s not think of how power inefficient this would be…)
:p
Since the 90's, desktops went to 1024, 1920 / HD is mainstream now, and 3840 / 4K is on the rise for desktop.
<meta name="viewport" content="width=device-width, initial-scale=1.0">https://www.youtube.com/watch?v=d6iQrh2TK98
Which not only links to this website, but also explains the topic in detail. Can highly recommend the channel anyway — especially for the HN crowd.
Yesterday the traffic on that page exploded. I am sure it's related to the Veritasium movie.
I don't doubt that it crops up a lot when people are asked for a random number between 1 and 100 (especially if, as per the video, you ignore 1, 2, 7, 42, 69, 73, and 77, and sometimes 99 and 100), but it's pretty disappointing for a big channel based around science like Veritasium to not even mention that if you became obsessed with and went hunting for special properties of a different number between 1 and 100 you'd almost certainly find them.
Also, while fooling around with my calculator in school, years ago, I had noticed this pattern:
37 x 3 = 111
37 x 6 = 222
37 x 9 = 333
and so on.
I tried it again just now, all the way up to 37 x 51.
It works perfectly upto 37 x 27 = 999
After that the pattern changes somewhat, but still seems to have some sort of regularity to it.
https://en.m.wikipedia.org/wiki/The_Thirty-Nine_Steps
That was a novel I enjoyed reading around the same time, in college.
The pattern should actually be fine up to 37*54 = (37*3)*18 = 1998; it breaks at 37*57 because that’s (37*3)*19 and 1+9 isn’t less than 10.
Similarly interesting patterns will crop up when multiplying 1111 or 11111 by integers - and similarly in other bases as well (identically, in fact - multiples of 0x111 include 0x1221, 0x1332, etc)
So this sort of reduces to ‘I guess It’s funny that 111 is 37*3’.. but on some level, that’s just how numbers work. Every number has a prime factorization. 1111’s prime factors are 11 and 101. 0x111’s prime factors are 0x3, 0x7 and 0xD; 111’s just happen to be 3 and 37.
That said… it turns out 37 crops up as a prime factor of 111, 111111, 111111111, 111111111111… so there’s something a little more going on here…
Although even that is really just because each of those numbers is 111* a number of the form 1001…001001001 - 1000^0+1000^1+…+1000^n
Every 271st multiple of 41 also forms a nice pattern:
11111
22222
33333
44444
…
But that somehow doesn’t seem as interesting.Like, factorizing numbers of the form 111…111 is a whole thing…
If there’s a composite number of digits in the number, then you can always factor it into a smaller 11…11 number, and a number consisting of 1s separated by repeating 0s - a 100…00100…001 type number.
And you can do the same to that number if it has a composite number of 1s in it (turns out the 1111 case is just a ‘number with a bunch of ones separated by sequences of no zeroes’).
To be concrete:
111111111111 (12 1s)
= 111 * 1001001001 (3 1s, 4 1s)
= 111 * 1001 * 1000001 (3 1s, 2 1s, 2 1s)
Or
= 1111 * 100010001 (4 1s, 3 1s)
= 11 * 101 * 100010001 (2 1s, 2 1s, 3 1s)
And it’s not a coincidence that the numbers of ones in those factors match the prime factors of 12.So numbers in this form tend to have factors like 11, 101, and 111… and of course that means they tend to have 37 as a factor as a result. Like, in the above example, it means 100010001 must have 37 as a factor too.
Lot of weird patterns to be found in here, for sure.
Such a number of puns not intended originally, but noticed and italicized ;)
Okay, will confess, I added one or two puns after the fact, to enhance the result, like the "one" and "complex" at the top, and the words in this sentence.
>That said… it turns out 37 crops up as a prime factor of 111, 111111, 111111111, 111111111111… so there’s something a little more going on here…
There sure is. Paging Ramanujan ... :)
1² = 1
11² = 121
111² = 12321
1111² = 1234321
...
111111111² = 12345678987654321
It works in other number bases too, and once you figure out the math it no longer seems that surprising.Yes, I remember seeing that, though only up to 4 levels or so.
Right, I don't think the number base has much to do with it. These are just properties of numbers. The individual cases may vary per base, that's all.
However none of that matters. What matters is the site is there for all of us to enjoy. It made me smile and I appreciate that.
The Star Trek link is because Trek writer Joe Menosky is a Pomona graduate, and started to include references to the number 47 (and the reverse, 74) in his scripts, starting in TNG season 4, and it started to take off amongst the staff. https://memory-alpha.fandom.com/wiki/Memory_Alpha:Projects/4...
https://uxdesign.cc/odd-vs-even-number-psychology-6307047bf5...
https://www.reddit.com/r/dataisbeautiful/comments/acow6y/ask...
7 is definitely a favorite at least.
I can see the logic behind that, but for the trick in question it’s not like they have a choice (emphasis added):
> Ask your friend to quickly think of a two-digit number between 1 and 100, both digits odd and both digits different from each other.
One thing they don’t mention on the page is that after all the constraints, only a fifth of the original hundred are valid choices: 13, 15, 17, 19, 31, 35, 37, 39, 51, 53, 57, 59, 71, 73, 75, 79, 91, 93, 95, 97. So while on the surface it may seem like you’re guessing one number out of a hundred, you’re guessing one out of twenty.
To a first approximation, at least. As is always the case in math, you can always split finer, and the field of math readers of HN are most familiar with, computation, you can have visible differences in the performance of one identity function versus another. But broadly speaking from a "conventional" mathematical perspective, they're all the same and uninteresting.
If you also want to get all mathy, the argument does depend on the set of numbers being ordered. It breaks down on numbers that aren't, so, for instance, the proof nominally proves that all integers are interesting (since orders on those exist) but it is invalid on real numbers, complex numbers, and a lot of other things that lack orderings, because there is no first "uninteresting real number".
Every number’s sacred
Every number’s great
When a number’s wasted …
Nope, won’t eventuate ...God needs ev'ry number
To enumerate!42 is an obvious choice. Picked at random while gazing through the garden window, so claimed the author, be we all know the truth; there are 42 young tableaux of size 3x3, which represent some of the fundamentals of the universe and everything
lol
Exactly, I feel the same. There is a saying that goes "If you look close enough you start making connections in random coincidences" or something.