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Comment by B-Con | Hacker News Reader

In this type of scenario (be it bitcoin hashes, serial numbers elsewhere, etc), the real question is how many possible "vanity" hashes exist. The odds of this specific one are not interesting, it's the space of all of them that is.

It's pretty much always infeasible to enumerate that space, but generally speaking there are a looooot of things that could qualify as special-looking enough to be included. All forms of english, foreign languages, language abbreviations, leet-speak, slang, pop-culture-inspired references, etc.

The odds of randomly tripping across something "special" eventually are pretty good. And bonus points if eventually one of those special coincidences is vaguely time-correlated with a real-world version of itself (eg, the number happens to be in the news, the slang word was recently used by a celebrity, etc).

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My kids used to celebrate "holimoments" (after the pattern of "holiday"). These were occasions when they'd look at the digital clock on the microwave and see something that didn't quite look random, like "10:01" or "12:34". They had a little ceremony when they saw one of these, pretending to take pictures with an invisible camera and doing a dance which involved wiggling their butts (because butts are always funny). There are a lot of events which deserve a holimoment dance and nothing more.

Hah! That is incredibly endearing. I've also had friends remark (more joking than serious) that if you happen to glance at a clock that reads 11:11 to make a wish because it's lucky.

I have obsessive compulsive disorder, so unfortunately these cosmic peccadillos really throw my brain for a loop!

Read this comment, then checked my clock. It was 11:11. This will be a lucky day.

You digital people, you. On analog watch, if two hands (hours and minutes) overlap when you take a look, that means someone is thinking of you!

I checked mine when I read yours. It was 20:30.

I'm reading this at 22:22.

I've seen the 11:11 and 1:11 come up a lot in random people's Facebook posts and memes. Or, driving around, they'll tell you to make a wish.

probably to do with Armistice Day.

This is like a variation of the birthday problem. Finding someone who shares your birthday is difficult, but finding any two people who share birthdays is almost inevitable. Trying to generate one vanity hash is almost impossible, but having a large number of interesting vanity hashes will help you find a few easily.

> The odds of this specific one are not interesting, it's the space of all of them that is.

So what you're saying is basically that there's no way to tell whether it's Jesus or Mohammed or Buddha that might be trying to communicate with us, because any of them might be using any of their magic codewords? /s

https://en.wikipedia.org/wiki/Interesting_number_paradox

That actually has an interesting failure. The first interesting number that's interesting because it's not special works. The second might qualify, the 10008 does not.

How can there be a second one if there isn’t a first one?

Because I constructed a set of otherwise boring numbers. The first otherwise boring number can arguably be interesting, but if you accept numbers are not inherently interesting by being on the number line you need find a reason to remove them from the otherwise boring list.

I think the word “otherwise” is key here, and makes the situation completely different. The paradox arises from a self-referential definition, and that word removes the self-reference.

How can an arrow move if it needs to get halfway to wherever it going first?

Lots of paradoxes you can construct with infinitite recursion or self reference in the absence of time.

In this case, interesting is fundamentally a temporal concept and there is only a paradox if you pretend that it isn't.

Zeno’s Paradox is solved with real numbers and calculus. This paradox is explicitly on the natural numbers, meaning you have a well defined notion of “smallest” for any nonempty set of them.

I don’t think the solution is related to time. Rather, it’s simply a matter of recognizing that it’s ok for something to be well defined that does not exist. The notion of an interesting natural number, such that it’s a binary property and being the smallest natural number, just doesn’t work. Thus we can conclude that there’s no such thing as “interesting” as defined like this. You can fix it by making interestingness a continuous value, or using a definition such that being the smallest number in a set isn’t enough to be interesting.

There are a bunch of ways to solve Zeno's Paradox involving time (and not necessarily involving real numbers and calculus), Wikipedia gives a quick overview of many.

In the interesting number paradox a solution can be related to time (or recursion depth) such that, as the person you were responding to mentioned, the first few otherwise not interesting numbers can be considered interesting without considering all not otherwise listed numbers as interesting. The wikipedia page gives a different example solution involving time.

Absolutely, when I was searching I followed this guide to search for hex words: https://nedbatchelder.com/text/hexwords.html

But there are definitely other 'interesting' numbers people could come up with.

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