I woke up from a dream a little too early this morning. I dreamt that I had died and gone to a cliché. That’s right, I was standing before the Pearly Gates…only they weren’t so pearly, and St. Peter wasn’t exactly nice.
I was standing on a grey field of cold clay that stretched endlessly around me, and I was in the midst of a muttering mob of grey people. In the distance I could see a high white wall girdling some kind of city, and standing before its gate was a monstrous creature, 30 feet tall at least, in the traditional white robes and carrying a colossal flaming sword. Its back bristled with an impractically large number of wings, and its head was ringed with eyes. It was nightmarishly biblical. And then it howled a bone-shaking roar, and I staggered back.
“Don’t worry,” said a grey man next to me, “it’s just asking a question.”
“What’s the question?”
“We don’t know,” he said, “apparently you have to be right at its feet to sort out the harmonics.”
“Why doesn’t someone go find out what it wants?”
“Watch.”
And then I saw that people would pop into existence all over the plain, and some would see the city and the gates and the hideous angel and rush towards it.
“Those are the devout. They’re sure they know the answer that will get them into the city.”
We watched one person stride up to the angel, who looked down and howled his Godzilla howl, and yes, I could detect a querying note to it. The person replied — at his distance I couldn’t tell what they said — and then the flaming sword swooshed down, and the person turned into a faint cloud of smoky vapor and wafted into nothingness.
Others were hanging back, like the people I was with. “Whoa,” I said, “I can see why you’re afraid to go over there.”
“We’re not afraid. We’re philosophers. We’re going to think about it.”
I didn’t have to think. I’m an atheist. I wasn’t supposed to be here in the first place, so getting annihilated by a flaming sword seemed like a more grandiose exit than I’d ever considered. So I just walked up to the giant expecting prompt dissolution.
It looked down at me with all those eyes, and then hit me with a sonic assault — it had a voice of brass, for sure, and it also contained notes so deep I couldn’t hear them, but felt in my bones, if I’d had them, and squeals so high they’d have shattered my capillaries, if my ghost had those, and would have left me bleeding out in a jellied heap, if I’d been alive. It was a question, or layers of questions, all imbedded in one complex roar.
“WHAT DID YOU LEARN? WHAT WAS YOUR PURPOSE? WHAT WILL YOU DO NOW?”
Oh, it was an easy question.
“dx/dt,” I replied.
“Excellent,” he said as he turned into Isaac Newton, “although I don’t approve of your notation, that’s the correct answer.” Then he took me by the elbow and led me through the gates, which in a feat of glorious geological transformation, rose rockily as the pillars of Hercules, and we walked on, not into a city, but out on the surface of a great ocean.
“So much to see, but every voyage has to begin at home,” said Newton, and suddenly we were knee deep in a gently flowing river, in what looked like the English countryside. “No, not here, not for you. Everyone has their own river.”
And then I was alone, in a different place, still knee-deep in a river. I felt a familiar silt beneath my toes, smelled the pleasant cleanness of a recent rain, saw the shadows of a salmon run flitting by and the ropy tangles of the blackberry bushes on the banks, and felt so at home. It was the Green. I knew exactly where I was. There by the side of the river was my bike.
I hadn’t thought of it in years. When I was a teenager, my father got a bike for me at a yard sale. It was cheap, because it was totally unsuitable for the terrain. It was an English Racer (it said so right on the frame: “ENGLISH RACER”), and it was tremendously stripped down. The tires were skinny little tubes, like rubber razors; the seat was like a narrow bit of railing covered with an unpadded scrap of leather. And no dérailleur, none of that fancy nonsense of changing gears. It had one gear, at a painfully high gear ratio, and you’d better like it.
I loved it. You didn’t want to begin pedaling from a cold stop — I’d usually get going by running alongside it, and then leaping on board — and the only way to deal with hills was to charge at them at maximum speed and hope momentum was enough to carry you over the top. But on the flats or going down the hills, it was like riding a freakin’ lightning bolt. If my parents had known about the breakneck way I drove that skinny scrap of tubing, they would have confiscated it. Best they didn’t know.
What else was I to do? I picked the bike up (it had no kickstand, another of its charms) and started running down the road. Then the familiar maneuver: in mid-stride, place the left foot on the pedal (Ah! That sharp, spiky cleat, like an old friend…), simultaneously swinging my right leg back and over to end up straddling that slender leather-clad seat. I’d kill myself if I tried to do that in real life now, but the muscle memory is still there, and it still works in my dreams, in which I was already dead anyhow.
So I pedaled. I felt the ache. My speed was rising. I pedaled harder. Trees whipped by in a blur. Sustained the effort. dx/dt. Constant acceleration. I was flying. Faster. I was light, I was a photon, I was motion and change. I was gone.
Then I woke up. Someday, I promise I won’t.
Nice. I’m afraid I had to google dx/dt and suspect I’m not the only one. Not sure if that’s a problem with the story or if it carries the theme over ingeniously: probably the latter. Very nice indeed.
@ Sastra
d —-> “delta” = (incremental) change
X —–> distance/length (measured along x axis)
t ——> time
“Incremental change in x per increment of time”. The basis of Calculus. It appears hard, but really isn’t. (Though calculus can get extremely difficult, we have machines to do all the heavy lifting for us.)
You’re just fishing for outraged comments :P
Sounds like it would be a lovely dream, though.
PZ:
Geez, VD is pestering you in your dreams now?
Even better than dx/dt. d²x/dt², man!
Pure click bait.
And upon his forehead was a name written, Enlightenment, Newton The Great, the Father of calculus and the motions of the planets.
[Link]
Newton was too into mystical woo. I’d prefer finding Isaac Asimov at the gates. But, great little story!
{pedantry:} One of the first things my calculus teacher taught, was the difference between ‘delta’ and ‘d’ [lowercase Greek delta, not the Anglo-Saxon lowercase D] and that is: the ‘d’ is an infinitesimal difference, while ‘delta’ is a small but significant difference. { /pedantry}
Back to the dream: He asked 3 questions, and PZ supplied 1 answer. And he accepted that?
“dx/dt” is just a mathemagical way to say, “Change”. “Everything is in a state of change”.
the take-home message is god is not a creationist.
Clearly this is all God telling you to repent for the mortal sin of feeding and housing a cat.
(No, I’m not kidding: providing food and shelter to one of the perfidious felines is a mortal sin: it ranks somewhere between genocide and inviting one of the Walton heirs to the restaurant)
I’d prefer to meet Newton, alchemy and all. At least he wouldn’t be likely to get handsy like Asimov was known to.
I got dx/dt right away but failed to see how it answers “What will you do now?”
… the flaming sword swooshed down, and the person turned into a faint cloud of smoky vapor …
Don’t flub your calculus, kids: like Saint Pete, the sainted PZ is a tough grader.
Huh. I always find descriptions of people’s dreams to be odd, because I haven’t got any. Not to remember, anyway.
@ Numenaster @12 –
re – Asimov’s ‘handy-ness’. It was a different time even though it is certainly within my memory. Mostly it was a joking riff on his ‘dirty old man’ stchick and he was a gentleman about it. The times I witnessed it and experienced it, if he saw it was making someone uncomfortable he *stopped*. For all you know, Newton would have expected you to lay down for him if he thought you belonged to a certain social class that didn’t count as having finer feelings.
All three questions have he same answer!
Gwynnyd
As far as anyone is aware, Isaac Newton had no sexual interest in women whatsoever (it’s not clear that he had any interest in men either; he may well have been asexual), and there’s no indication that he ever expected (or wanted) anyone to lay down for him.
Damn. That’s a good story.
Hurts so much when we lose things, but – everything is changing all the time.
this post and a previous one about Dad have a little bit of fall in them. A time of realization that things are passing and do so continuously.
Nice story well told, personal and reflective, hope to read more some day.
I do not know why it took me to realize that the great song The Rivers of March (Águas de Março) was about the fall. so many thing passing but the music so openly joyous
https://www.youtube.com/watch?v=QF_Ekf6nHj8
uncle frogy
got lost in listening and forgot to type “so long” above
uncle frogy
Wow! That is one beautiful dream. I’m envious. Much of it so vivid, the visuals, the audio, the olfactory, the kinesthetic, the prostate. You don’t often get all that in a single dream. It if were my dream, I could have fun with it for weeks.
Since you have it written down an interesting thing to do is in a couple of days or a week from now, without looking write the dream down again then check to see whats missing. Play with the missing parts, see where they take you.
Pardon my suggestions if you already do mess around with your dreams, if so you already know that paying attention to them may inhibit your remembering them for a while.
Dreams want you to know whats going on down there but they don’t want to make it too easy.
“The tires were skinny little tubes, like rubber razors; the seat was like a narrow bit of railing covered with an unpadded scrap of leather. And no dérailleur, none of that fancy nonsense of changing gears. It had one gear, at a painfully high gear ratio”
Wow! That sounds just like my Claude Butler: fixed wheel (gears are for sissies); Campag alloy hubs and pedals. It weighed about 14lbs (back in the 60’s that wasn’t bad).
Happy days!!
If that was a dream, then you have dreams in big screen 3 D with 16-track Dolby stereo and should probably hire yourself out to people who are bored with shark movies!
I really do hope that, on the off chance that there is any form of god and afterlife out there, that it cares more about curiosity and exploration than of dogma, toadying, cataracts and bullying.
I would have picked 42 as the answer.
Vox Day was in your dream too?
Beautifully written. Although I’m not ungrateful for your ongoing contributions to the developmental biology of zebrafish, I can’t help wondering whether you’ve missed your true calling. Echoes of Douglas Adams. I can’t wait until the novelized version comes out.
Never understood why it’s called ‘dx by dt’.
I’d have to eat some really moldy cheese to get a dream like that.
thecalmone @27:
Because it’s the limit as Δt goes to zero of dividing Δx by Δt.
The “change in x divided by the change in t” (limit blah blah continuous blah blah blah instantaneous blah infinite blah &c).
Rob Grigjanis@29. “Because it’s the limit as Δt goes to zero of dividing Δx by Δt.”
Yes, of course. I suppose I always looked at it and thought “that’s dx over dt, not dx by dt.” Thanks.
(Sheesh… 4 years of engineering maths and I never figured that out…)
Beautiful imagery, PZ.
P. Z. Myers, I know you already have all of the intelligent design inanity that you can handle, but here is a real doozy about my own favorite subject of protein folding: http://www.evolutionnews.org/2014/10/protein_folding090541.html.
Short version: a review article appears summarizing years of elegant work on how proteins solve the “large search space problem” and quickly find their correct native structure. In response, intelligent design clowns conclude that proteins can’t solve the search problem and are therefore “a materialists nightmare”. Intelligent folding!
Is f'(t) acceptable?
Yeah, not to pile on Newton, but in a more realistic dream, he’d have taken you on a prosaic tour of that city’s largest temple, going on and on about how its sacred dimensions perfectly matched the one described in Kings. I’d have asked for the flaming sword at that point…
#35
dx/dt is the differential operator applied to a variable x, f'(t) is notation for the differential operator applied to an arbitrary function of t – should it be f'(x) ? (and in some notations, you use a dot to show its a time derivative, the dash means a spacial derivative d). Assuming Newton knew what the notation meant, that seems more specific than the other answer. I’m guessing you’d get extra credit for mentioning ‘fluxions’ (I read the entire Baroque cycle, might as well use it).
(If this doesn’t make much sense, I initially confused dx/dt and the differential operator d/dt).
no-genius
athorist: Yeah, Newton would have used the dot notation for time derivatives, as many physicists still do.
ẋ ≡ x′(t) ≡ dx/dt
Very economical.
That’s what you get for not coming over to the cool side of the street: Physics. You and your “j” and stuff. :P
∫dx/dt is simply velocity. Move!
∫dv/dt is acceleration (gravity, yay!)
I much prefer PZ’s version and nominate it to immediately replace the drug-induced rubbish that is Revelations.
Usernames:
I’m guessing you mean for the square root of -1. Yeah, that is weird.
#36
My calculus chops probably aren’t adequate for this thread but I was thinking of a function that relates x to t noted as f(t)=x and then acceleration would be found by the derivative of f(t) labelled f'(t). Note my calculus knowledge begins and ends in highschool. so.. yeah
Spill the wine, take that pearl…
@39 Rob Grigjanis
I’ve always tried not to think too much about imaginary numbers. That’s an epiphany of weirdness that strikes engineering students around the age of 18. Some of us never recover. As engineers, however (although I’m a teacher now), we eventually realise that it’s just used because it works and there’s no point trying to understand it on some deep philosophical level.
Speed is the answer? Were you watching “breaking bad” before bedtime?
thecalmone @42: There’s nothing weird about complex numbers if you think of them as 2×2 matrices.
x + iy corresponds to a matrix with top row x, -y, and bottom row y,x. So i is just the matrix M with top row 0,-1 and bottom row 1,0. This is the matrix which transforms any vector (x,y) to (-y,x). In other words, a rotation of π/2. And M² = -I, where I is the 2×2 identity matrix.
I think this is how students should be introduced to complex numbers. Makes it less ‘weird’. But requires matrix manipulations, etc.
Totally meant v not a there, my bad
PZ, this sounds like an NDE. This is entirely too realistic and too “cultural” (notice how this is explicitly loadedwith modern “Christian” mythology, e.g., “Peter” at a literal set of pearly gates). Are you sure you didn’t come close to death?
Also, what does happen to the ones who got stabberated by Mr. No-Indoor-Voice? Are they actually dead or did they go to your dream version of Hell?
Lastly, and I hate to ask this but I’m paranoid, is this a Poe? I will make sure, in case I ever meet Newton, to answer similarly, though mine would be less mathematical: “This is all…not a game, but we’re here to learn. It’s all changing. It’s all about learning and becoming more than we were, dancing with entropy and learning each other and helping one another become what we should be.” Would he accept that, do you think?
@ Usernames! ☞ ♭
Ouch, no. No no no.
∫dx/dt and ∫dv/dt have no meaning. Cannot be evaluated. What variable are you integrating over? Presumably time? If so, one does not simply integrate velocity and obtain velocity. Lose the integrals and you’re golden, as dx/dt is simply velocity, and dv/dt is simply acceleration.
[pedant]
For completeness:
Let x(t) be defined as position (e.g. length unit) as a function of time. Then:
x = x(t) [=] Length
v = v(t) = (d/dt) x(t) [=] Length / Time
a = a(t) = (d/dt) v(t) = (d^2/dt^2) x(t) [=] Length / Time^2
where notation [=] -> has dimensions of.
Then:
x(t) = ∫v(t) dt. For v = v0 (constant), x(t) = x0 + v0*t, where x0 is the initial position
v(t) = ∫a(t) dt. For a = a0 (constant acceleration), v(t) = v0 + a0 * t, where v0 is the initial velocity
And by substition:
x(t) = ∫ [∫a(t) dt] dt is acceleration. For a = a0 and v = v0 (constants), a(t) = x0 + v0*t + a0*t^2, where [see above]
To be completely consistent, those integrals are definite (i.e. bounded) on the interval [t0, t]. Didn’t feel like dealing with further notation. Or sub/superscripts for that matter.
[/pedant]
I Engrish good… make that “substitution”
@ chapwilliams:
That’s pretty common shorthand.
x = f(t)
v = f'(t)
a = f”(t)
Dangerous to use unless you’re doing single-variable crap, as it doesn’t indicate what variable you’re taking the derivative with respect to. But for situations where you only have the one, totally fine.
well that’s years of researching the airspeed velocity of an unladen swallow right out the window.
PatrickG @27: My own contribution to the pedantry;
Seems you wanted to write (note the 1/2 multiplying the a0 term because antiderivative of t is (1/2)t^2)
x(t) = x0 + v0*t + (1/2)a0*t^2
That should be @47, not @27
So, dream-PZ got in with a mathematical formula (or, rather, metaphor), but if he’d pull an Heraclites and talked about the river in which you never bathe twice, that’d be ok too ?
@47: Oh, and missed this very late last night:
No, x(t) is position. Maybe it was very late for you too :)
Boy, you can certainly tell this blog is read by biologists and engineers. I especially liked the ‘dx/dt is far beyond the limits of my calculus’.
Rob @44
Interestingly, I was introduced to imaginary numbers using matrices exactly like you propose, then doing a lot of graphing. So they’ve always seemed a bit weird to me, but never incomprehensible (at least on paper).
Like the story, PZ. This one and your dad post have an extra resonance for me the past week or so, especially yesterday. Thank you.
@ Rob Grigjanis: It was very late. :) Copy/pasta errors, and thanks for catching the 1/2. I just couldn’t let the initial misstatement lie. :)
Whoa. Apparently BRIAN BLESSED is now invading dreams.
Change. :-)
Some people have vivid dreams; and why shouldn’t dreams be at least as cultural as NDEs?
Why do you think such concepts even apply?
I used to haunt an NDE forum on Usenet, & when they learned that I have both vivid & lucid dreams (alas, very rarely — most mornings I wake with no memory of any dreams), they’d say the same thing.
No, it wasn’t real. It was entirely in my head. My spirit did not go a-wandering in supernatural realms.
They’d also tell me to go look up stuff for them in the Akashic Library. That doesn’t exist, either.
That is a weird dream. Really, really vivid. We don’t have any evidence for supernatural realms, but what would count as evidence for that, anyway? In either case, between this and the “most dad thing ever” thread I’m a bit worried about you…are you feeling empty-nest syndrome? :(
Neat dream.
For an old calculus joke:
first derivative – velocity
second derivative – acceleration
third derivative – jerk
fourth derivative – inauguration
That’s right, inauguration is change of jerk. (Most people never deal with the latter two derivatives, but I read old calculus texts. I also had a friend who worked for Otis Elevator and they took the latter two derivatives very seriously. Jerk is that rough feeling when the elevator starts or stops and inauguration can make your stomach lurch. Thanks to old calculus, preserved and transmitted by means of awful jokes, modern elevators operate much more smoothly.)