Why I’m Solving Puzzles Right Now

When I was a kid (well, a teenager) I’d read puzzle books for pure enjoyment. I’d gotten started with Martin Gardner’s mathematical recreation books, but the ones I really liked were Raymond Smullyan’s books of logic puzzles. I’d go to Wendy’s on my lunch break at Francis Produce, with a little notepad and a book, and chew my way through a few puzzles. I’ll admit I often skipped ahead if they got too hard, but I did my best most of the time.

I read more of these as an adult, moving back to the Martin Gardner books. But sometime, about twenty-five years ago (when I was in the thick of grad school) my reading needs completely overwhelmed my reading ability. I’d always carried huge stacks of books home from the library, never finishing all of them, frequently paying late fees, but there was one book in particular – The Emotions by Nico Frijda – which I finished but never followed up on.

Over the intervening years, I did finish books, but read most of them scattershot, picking up what I needed for my creative writing or scientific research. Eventually I started using the tiny little notetabs you see in some books to mark the stuff that I’d written, a “levels of processing” trick to ensure that I was mindfully reading what I wrote.

A few years ago, I admitted that wasn’t enough, and consciously  began trying to read ahead of what I needed to for work. I chewed through C++ manuals and planning books and was always rewarded a few months later when I’d already read what I needed to to solve my problems. I began focusing on fewer books in depth, finishing more books than I had in years.

Even that wasn’t enough, and I began – at last – the re-reading project I’d hoped to do with The Emotions. Recently I did that with Dedekind’s Essays on the Theory of Numbers, but now I’m doing it with the Deep Learning. But some of that math is frickin’ beyond where I am now, man. Maybe one day I’ll get it, but sometimes I’ve spent weeks tackling a problem I just couldn’t get.

Enter puzzles. As it turns out, it’s really useful for a scientist to also be a science fiction writer who writes stories about a teenaged mathematical genius! I’ve had to simulate Cinnamon Frost’s staggering intellect for the purpose of writing the Dakota Frost stories, but the further I go, the more I want her to be doing real math. How did I get into math? Puzzles!

So I gave her puzzles. And I decided to return to my old puzzle books, some of the ones I got later but never fully finished, and to give them the deep reading treatment. It’s going much slower than I like – I find myself falling victim to the “rule of threes” (you can do a third of what you want to do, often in three times as much time as you expect) – but then I noticed something interesting.

Some of Smullyan’s books in particular are thinly disguised math books. In some parts, they’re even the same math I have to tackle in my own work. But unlike the other books, these problems are designed to be solved, rather than a reflection of some chunk of reality which may be stubborn; and unlike the other books, these have solutions along with each problem.

So, I’ve been solving puzzles … with careful note of how I have been failing to solve puzzles. I’ve hinted at this before, but understanding how you, personally, usually fail is a powerful technique for debugging your own stuck points. I get sloppy, I drop terms from equations, I misunderstand conditions, I overcomplicate solutions, I grind against problems where I should ask for help, I rabbithole on analytical exploration, and I always underestimate the time it will take for me to make the most basic progress.

Know your weaknesses. Then you can work those weak mental muscles, or work around them to build complementary strengths – the way Richard Feynman would always check over an equation when he was done, looking for those places where he had flipped a sign.

Back to work!

-the Centaur

Pictured: my “stack” at a typical lunch. I’ll usually get to one out of three of the things I bring for myself to do. Never can predict which one though.

Nailed It (Sorta)

Here’s what was in the rabbit hole from last time (I had been almost there):

I had way too much data to exploit, so I started to think about culling it out, using the length of the “mumbers” to cut off all the items too big to care about. That led to the key missing insight: my method of mapping mumbers mapped the first digit of each item to the same position – that is, 9, 90, 900, 9000 all had the same angle, just further out. This distance was already a logarithm of the number, but once I dropped my resistance to taking the logarithm twice…

… then I could create a transition plot function which worked for almost any mumber in the sets of mumbers I was playing with …

Then I could easily visualize the small set of transitions – “mumbers” with 3 digits – that yielded the graph above; for reference these are:

The actual samples I wanted to play with were larger, like this up to 4 digits:

This yields a still visible graph:

And this, while it doesn’t let me visualize the whole space that I wanted, does provide the insight I wanted. The “mumbers” up to 10000 do indeed “produce” most of the space of the smaller “mumbers” (not surprising, as the “mumber” rule 2XYZ produces XYZ, and 52XY produces XYXY … meaning most numbers in the first 10,000 will be produced by one in that first set). But this shows that sequences of 52 rule transitions on the left produce a few very, very large mumbers – probably because 552552 produces 552552552552 which produces 552552552552552552552552552552552552 which quickly zooms away to the “mumberOverflow” value at the top of my chart.

And now the next lesson: finishing up this insight, which more or less closes out what I wanted to explore here, took 45 minutes. I had 15 allotted to do various computer tasks before leaving Aqui, and I’m already 30 minutes over that … which suggests again that you be careful going down rabbit holes; unlike leprechaun trails, there isn’t likely to be a pot of gold down there, and who knows how far down it can go?

-the Centaur

P.S. I am not suggesting this time spent was not worthwhile; I’m just trying to understand the option cost of various different problem solving strategies so I can become more efficient.

Don’t Fall Into Rabbit Holes

SO! There I was, trying to solve the mysteries of the universe, learn about deep learning, and teach myself enough puzzle logic to create credible puzzles for the Cinnamon Frost books, and I find myself debugging the fine details of a visualization system I’ve developed in Mathematica to analyze the distribution of problems in an odd middle chapter of Raymond Smullyan’s The Lady or the Tiger.

I meant well! Really I did. I was going to write a post about how finding a solution is just a little bit harder than you normally think, and how insight sometimes comes after letting things sit.

But the tools I was creating didn’t do what I wanted, so I went deeper and deeper down the rabbit hole trying to visualize them.

The short answer seems to be that there’s no “there” there and that further pursuit of this sub-problem will take me further and further away from the real problem: writing great puzzles!

I learned a lot – about numbers, about how things could combinatorially explode, about Ulam Spirals and how to code them algorithmically. I even learned something about how I, particularly, fail in these cases.

But it didn’t provide the insights I wanted. Feynman warned about this: he called it “the computer disease”, worrying about the formatting of the printout so much you forget about the answer you’re trying to produce, and it can strike anyone in my line of work.

Back to that work.

-the Centaur

75K

I was going to write “And from his labors, he rested” but that’s entirely to uncomfortably Messianic for me, so here’s the scoop: on the last day of Nano, I have stopped at 75,282 words.

This somehow all magically happened because I never lost my momentum after the Night of Writing Dangerously, oh, and because this is Cinnamon Frost, and she’s awesome!

This is the most I’ve ever written in Nano, by a long shot – almost 10,000 words more. Not quite, and I’m not super motivated to make it exactly 10,000 words more. If I think of more words tonight, eh maybe.

Oh yes, the traditional excerpt:

The first challenge was easy—spirit. Awareness. Being aware of faerie.

The second challenge was harder—mind. Intellect. Learnin’ the logic of faerie.

The third challenge was the hardest of all. Body. Emotion. Feeling faerie in your bones.

A huge cacklin’ thing bursts out of the water. Its head is as big as Krishna’s, a huge green dripping thing under a mass of hair, its wide smooth but mottled nose remindin’ me of a diseased muppet. We can’t see the thing’s eyes, but its arms loom around us. Ben and Surrey screams.

Do you care?” it screams, openin’ a maw filled with giant teeth the size of playing cards. I think it could swallow any of us whole. “Do you care if you diieie?”

“Aaaah!” Benjamin and Surrey screams. “We care! We care!”

The thing looms further forward. “Then flee, mortals, or you may perish here!

“Don’t flee,” I murmurs. “Or you may perish elsewhere—”

“We—we will not flee,” Surrey cries.

“For we may perish elsewhere,” Benjamin says with sudden insight. Did he hear me?

But stay here, and death will be certain, mortals!” the thing cries, loomin’ over them.

“Stay anywhere, and death is certain, for mortals!” Benjamin cries.

“And you don’t care if you die,” I murmurs into Surrey’s ear.

“And we don’t care if we die,” Surrey says. “What? Ci—”

“Surely death comes to all mortals,” Benjamin says. “Why should we care?”

I could make death hurt,” the thing cries, stretchin’ its arms out like a giant Muppet.

“Or we could die in our sleep,” I murmurs. “But I can make death hurt him more.”

I actually have practically finished BOT NET,  so next up is Cinnamon Frost #3, ROOT USER! Oh, and editing Dakota Frost #4, SPECTRAL IRON! Due in about 4-5 months. Aaaaaaa!

Onward!

-the Centaur

Ludicrous Speed

If I keep up the pace that I’ve been keeping …

I won’t just beat my best record ever (which I already have) …

… I’ll hit the somewhat ludicrous amount of 75,000 words in a month, beyond the 70,000 I’ve already hit.

4,648 words to hit that goal … less than I did yesterday or even today. Let’s get cracking.

-the Centaur

Nanowrimo, Challenge Mode

If I write 11,293 words by the end of the month …

~2900 words a day, not counting today …

I will beat my all time Nanowrimo record of 65,995 words:

Sounds like a worthier goal than spending the same words responding to everyone who’s wrong on the Internet.

Onward!

-the Centaur

Viiictory, Nineteen Times

So, I just succeeded the 19th time at National Novel Writing Month!

This year, I was working on BOT NET, the second Cinnamon Frost novel. I’m writing these three books in one huge manuscript, which I successfully took from 179591 to 229911 words as of today!

This year, the combination of participating in the Night of Writing Dangerously, plus having the luxury of taking off the week of Thanksgiving to write, really pushed me over the edge:

Interesting, the hole at Thanksgiving. I wonder if that’s true every year? That’s not something you can readily see when you look at the yearly charts since it moves (stay tuned, these charts are going to come back later):

There was a time when almost every post about Nanowrimo I’d include an excerpt. Frankly, that’s gotten harder to do as I’ve switched from doing Nano once per year to three times per year; the Nano material has become more inchoate as I blaze new paths out into story space, requiring more work to turn it into final material. But, occasionally, I can indeed include some material that gives you a flavor …

“I … I gotta be honest here. I needs help.”

“Cinnamon,” Nri says gently. “I know that. I’ve had many, many students before.”

“Another damn teacher,” I rollin’ my eyes. Then I realizes—“Did I say that out loud?

“Yes, you did,” Nri says, smiling sardonically. “I don’t even think that was Tourette’s.”

“It-it wasn’t,” I says. “I’m sorry, sir, but …” I grimaces. I genuinely don’t know what tone to set here. Act like Mom’s world, use Southern politeness, act like the werekindred, use growls and barks … or, maybe, just be me? Who’s that then? “I, uh, don’t, ah, know how to say this but I wasn’t tryin’ to insult you before or to butter you up now but we gots a real situation and if we leaves it up to my Mom there’s a very good chance that the D of the W. A. will spirit my boyfriend and my alt-crush off to the wilds of nowhevers, and if the elders of the werehold finds out where they are they may go and do somethin’ stupid right on the doorsteps of people totally prepared to do somethin’ stupid, so I’m guessin’ the smart thing is for the people who are smart and wizardly to do somethin’ smart and wizardly, but I can’t do this alone, because I am, like, thirteen, and why in godsname does everybody think I can do everythin?”

Nri stares, blinks, shakes his head, like he’s comin’ out of a trance.

“God, I’d wish I’d timed that,” he says. “I think you talk faster than JFK—”

“Who?” I asks.

“Nevermind,” Nri says. “I’m sold.”

Ah, Cinnamon, you and your wacky hijinks. Thanks for coming into my writing life, wherever the hell you came from.

And now, on to all the things I’ve been putting off blogging while I’ve been working on Nano, including … how to succeed at Nano! (I hope you’ll agree I have some credentials in that area).

Onward, fellow adventurers!

-the Centaur

200,000 Words of Cinnamon Frost

Milestones are coming. And the first of these is catching up on my wordcount for my Nanowrimo project this November, BOT NET!

Winning at Nano always feels like climbing a hill, but for me in particular it almost always feels like I start out sliding back down, Sisyphus-like, as I struggle to get a handle on the story.

But then there comes that magic point where I need to write 1,666 words in a  day and I. Got. Nothing.  Then I’m forced to be creative, and the real fun stuff happens, an event I call “going off the rails”. Hey, let’s try to embed a tweet!

So now things are back on track for the month, and I’m smack in the middle of where I normally am this time of Nano … Actually, it appears I’m ahead. Checking the stats … yep. At this point, I’m normally just shy of 6,000 words behind ( -5,984, though that estimate is numerically precise, it is not likely to be meaningfully accurate ) but today I am 169 words ahead of the Nano wordcount:

I’m one more thing too: 200,000 words into the Cinnamon Frost trilogy.

There are 3 published Dakota Frost novels: FROST MOON, BLOOD ROCK and LIQUID FIRE, and three more finished rough drafts: SPECTRAL IRON, PHANTOM SILVER, and SPIRITUAL GOLD. By my count, I’ve written about 900,000 words about Dakota Frost, Skindancer, the woman who can bring her tattoos to life. But in one sense, that’s expected: I planned Dakota. I wanted to write a character that other people who can relate to.

Cinnamon Frost, as I’ve said before, is a character I never expected. She shoved her way into the Dakota Frost universe, in one of those “step off into space moments”, and she shows no signs of leaving.

Cinnamon might say 200,000 seems significant because of how humans process patterns – how we love all those zeroes – but it’s just a number: 2*10*10*10*10*10. But somehow, it feels right to take it this far, and I look forward to writing the next 100,000 to 150,000 words that will finish her trilogy and give her a chance to live her own literary life.

Time to get back to it.

-the Centaur

P. S. I said milestones are coming. If you’ve read closely in this post, you’ll realize another milestone is coming soon. Stay tuned …

10,000 words into Nano

So, the good news: I just crossed the 10,000 word mark in Nanowrimo 2017!

The bad news: I need to be at 13,333 words by today!

The good-bad news is, normally I’m closer to 4500 words behind at this point of Nano, so I am ahead of where I am normally behind:

What can I. say? “Don’t get cocky, kid.” Back to it …

-the Centaur

Timeline 10(ab)”’

No progress on BOT NET for Nanowrimo yet today … yesterday I got my daily word count, but today I needed to core dump some ideas I’d been brewing about a Jeremiah Willstone novella, “Crypt of the Burning Scarab”.  I had a brain flash about how to make the plot work out, involving a twisty time travel paradox I haven’t seen before, and wanted to make sure I read up enough physics and math to make sure the idea made sense, then wrote it all down before I dove back into Cinnamon’s world of mathematical magic.

But you know your plot is complicated when you non-ironically need a timeline point 10(ab)”’ – that’s point 10, timelines A&B, variant 3 (prime prime prime).

Happy writing …

-the Centaur

Pictured: A few of the math/physics books I’ve been reading on this idea, plus the “GBC” (Goodfellow, Bengio and Courville) Deep Learning book which I’m (re)reading for work.