This article (and entire book) actually posits that US will remain the primary producer and consumer of copium worldwide and thus the #1

Maybe I'm really dumb, but it should be obvious that replacing a section of rope in one knot with another, is intuitively not going to simply "add the unknotting numbers"

And yet it almost always works. There were no known counterexamples where it failed until this was published.

Yup. I've had lots of intuitions for things, only to discover there was a very non-intuitive theorem conclusively proving my intuition wrong.

So much of math and physics is discovering these beautiful, surprisingly non-intuitive things.

And this fits right in that pattern -- it seems intuitive that it wouldn't be true, but nobody's been able to find a counterexample. So it's yet another counterintuitive result that math is built on. Not proven, but statistically robust.

Which is what makes it great when somebody does ten years of work in simulating knots so a counterexample can be found.

Which doesn't even confirm the original intuition, because there are still so many cases where the rule holds. Whereas our intuition would have assumed a counterexample would have been easy to find, and it wasn't.

I'm with the OP on this one. Intuitively (to me, anyway) I wouldn't expect it to work in general.

I'm surprised it took so long to find a counterexample, but it doesn't surprise me at all to hear it doesn't work.

Mine too, but this is not very interesting, although our intuition was right, it was almost certainly right for the wrong reasons.

Agreed, this is the real takeaway for those who think it’s unsurprising: they simply haven’t understood why it is surprising.

Definitely!

My understanding of knot theory is limited to having watched a few YouTube videos and reading the first introductory chapters of a book. A neat topic, but not one I'm going to dig too deeply into.

If that is the case the counterexample is the sort of thing a stubborn cynical and amateur mathematician (and programmer) may have found.

May I humbly request you to join the dwitter.net community?

You're the second person to mention dwitter.net, now I feel like I have to... Got a busy week coming up but when I have more downtime I'll join and share!

This is why Stallman is so vehement on GPLv3

Commercial entities will always exploit your work - you need to force them to give back, they will never do the positive sum game by default

What everyone secretly knows but won't say because it has funding

Wow - I cant think anyone would spend such a long time on how everyone but themselves is wrong.

It started out interesting, but was simply a long rambling text where there seems to be no point

Wow the silver bullet is finally here. Rewrite everything with AI :D

Disagree totally....

The whole point is to be able to convert JS data structures (or often plain JSON) into HTML via JSX

Data and representation are different. I may be using the same array to display different components

Remember "The Zen of Code Optimization" by Michael Abrash in the 90s?

This word count challenge was the first one he described. The table driven approach was discussed, but was not necessarily the fastest due to the large cache overflowing (on 90s processors) table needed.

I used the same example in a chapter I wrote for a C++ book

Try lazydocker as well