Chaitin's constant does not count? Depends on your definition of constructed, but contrary to "easy" normal numbers such as Champernowne's constant, it's not defined by its sequence of digits.
You can design a number. Just take all finite digit strings in order of length and numerical order: 0.123456789 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 ... 99 000 001 002 ... 999 0000 0001 ...
obviously it contains every finite digit string in base 10. I can't prove the digits are uniformly distributed in every base - you'd have to be more clever but you see the idea.
But pi is also "constructed", in the sense that you can write down a constructive definition for it, for example \sqrt{6 \times \sum_{k=1}^\infty \frac{1}{k^2}}.
So I suppose maybe OP meant we haven't proven any number to be normal (or not) that is not designed to be normal (or not) ?
Before your muscle memory is updated, all you need to remember is how to “quality check” the knot when you’re done. If the loops are perpendicular, it’s wrong, they should be aligned with the laces.
If it landed up perpendicular, start over (i.e. the part before you make the loops) with doing the opposite of what you did before e.g. right-over-left rather than left-over-right.
For me it was very easy to fix the pre-loop stage, trying to change the loop stage seemed way harder to me as I was already so practiced at it.
I do a similar quality check when tying a square knot (right over left, left over right but without the bows - probably the default knot for something you don't intend to ever untie and don't have a Scout's encyclopedic knowledge of more specialized knots) - since it doesn't have the bows, the quality check is that it should have a line of symmetry whereas if you repeat the same direction twice the finished knot is more of a spiral, having no line of symmetry.
>(perhaps guide them how they can use them professionally)
If that's anything like how they guided me to use programming languages professionally...
In my workplace I find systems and policies move too slowly to keep up with how rapidly the LLM world is changing. Colleges are even more glacial. They've barely adapted to video conferencing.
Yes, meanwhile, Claude Cowork was only released this past January. And that was amazing. But I don't know about anyone else but I've already moved on to just using Codex for just about everything (except some Kagi use). Schools work on timescales of years, AI is advancing on the timescale of weeks and months.
Until that situation stabilizes I think the only institution capable of teaching about it is the family -- parents.
I'm not sure parents have the right tools either. Microsoft is about to ship OpenClaw as part of windows (talked about at BUILD) and they're acting like it's production ready and they've solved the security issues.
I don't believe them for one second, it's far from a solved problem yet these companies are selling this tech as if it's been around for decades and thoroughly battle tested instead of highly experimental and unstable.
> In my workplace I find systems and policies move too slowly to keep up with how rapidly the LLM world is changing. Colleges are even more glacial.
Perhaps this is rather a sign that you currently shouldn't jump on the LLM hype train, but rather attempt to get a good foundation on the basics. When the whole LLM area becomes much more "stabilized" (I see signs that this is currently happening, if only for the reason that training state of the art models has become more and more expensive), you can still get into LLMs if you want.
I partly agree, depending on what you count as the basics. I don't think there's much value in learning the quirks of LLMs today: they will just change, your value-add becomes part of the model or harness.
On the other hand I think there are real development gains in jumping on the train today. To my career's detriment.
Traditionally, moving slow with policies was fine with new tech because, outside of the PC revolution it wasn't all that impactful, and things used to rightly be labeled as experimental so you could safely ignore it for a while as a big enterprise and be just fine until thinks shook out.
LLMs were, IMO, pushed out too early and without that clear "this is experimental tech" label. Full public access from day 1, no invite only betas, no research previews for a select few pilot customers/orgs, etc. I've been in IT for a little over 18 years now and I haven't seen anything move this fast before.
I mean, I never though I'd see Microsoft go on stage at BUILD and and announce freaking OpenClaw for Enterprise, and then make it available the same day. This is highly unstable tech and what I'd consider still experimental, being sold to F500s as production ready.
I think it's incredible how much those ancient brains can successfully adapt to technology. Some people can sit in highly-strung sports cars and use them at the absolute limit of their performance like they're just an extension of our own limbs and senses.
I love this book. Before anything else it's a pleasure to read: it's funny, touching, and the constant referring to the poem at its core forces literary engagement - even if it's only to notice where Kinbote is bending the truth. It also scratches a metafictional itch that has now become a huge trend in modern media...
Spoilers below
...but I find it suffers in criticism for a different trend: that everything has a 'gotcha'. While I accept that there is no sensible reading where the narrator is entirely reliable, I reject that there is an evocative reading using the Shadean theory referenced in footnote 2.
Sometimes this is given as 'Shade wrote the whole book'. I have no time for that. You don't need a character who writes Pale Fire on index cards: that's just Nabokov. And what would it mean if this Shade writes a heartfelt canto about his own loss, then the interpretation that cruelly misses the topic?
Sometimes it's given that Kinbote is a dissociative identity of Shade. I see this as an interpretation that minimised the impact of the text to maximise the self-satisfaction of the reader. Read through the book with it in mind and you find yourself asking what's the point of it all. In line 62's explanation, Kinbote reads 'hal.....s' as 'hallucinations'. If Kinbote is a real character within the story, that's a joke between Nabokov and the reader. With this theory it's nothing. Kinbote's writings make up the bulk of what you read. It's much more interesting to do so if you choose believe there's a point to them.
Spoilers done
I had a similar experience reading interpretations of Lolita, with the added problem of takes that over-correct and signal against the subject and wider public perception.
I went into it blind and the first thought ( which is probably very common ) is that this experience would greatly benefit from a hypertext implementation.
There's a neutral interpretation here.
https://www.tundrasquid.com/palefireindex.htm
I think jumping back and forth via hypertext would be a bad reading experience; what you ideally want is two panes scrolling in parallel. (I read it keeping two copies of the book open on my kindle and phone but if I reread it I'll probably use split windows on a laptop instead)
Counter-anecdote: I've played a game where the developer included a bug that gave other players arbitrary code execution on my PC and left it online while fixing the bug. I've never launched it since and had owned it less than 48 hours. Steam rejected my refund.
This project makes clear the counter-argument: the input that gets you the file out of π is a badly compressed version of the file.
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