Exponential Logarithms
When Flops gifts The Stoat a math joke t-shirt about floating point errors, he discovers the speed of delivery via "Salazon", the power of math, and ultimately the fragility of floating point systems. The Stoat takes pride in his newfound t-shirt, and the statement printed on it quickly makes others laugh too.
A: TV-PG Pre-Intro Segment
Dook and Flops' House — Morning.
Flops lounges on the couch, thumb flicking through Salazon listings. Dook waters a fern with the precision of someone defusing a time-sensitive device.
Flops (reading aloud): "My Code Compiles: Lowering Standards Since 1991." Heh. (Scrolls.) "There Are 10 Types of People..." Overdone. (Scrolls.) Oh wait—
Dook (not looking up): Your pupils dilated. Discovery imminent.
Flops (grinning): "log(exp(n)) makes IEEE 754 sad." That's... that's perfect.
Dook (finally turning): Context?
Flops (leaning back): The Stoat. Remember last week? He was complaining about his calculator giving him 12.999999 when it should've been exactly 13?
Dook (thoughtful): Ah. The existential despair of floating-point approximation. A shared trauma by many.
Flops (tapping screen): And it's got a skiing moose on the size chart. That's gotta be a sign!
Dook (inspecting his potted fern): Moose indicate quality craftsmanship, possibly Canadianness. Proceed.
Flops hits "Buy Now." PING-THWIP! A parcel slides through the door slot and lands upright like it trained for this exact moment the whole week.
Flops (blinking): That was... too fast.
Dook (matter-of-fact): Duh, it's Salazon. They send it before you even know you're about to buy it. Their predictive algorithm is frighteningly competent.
Flops (picking up the box, suspicious): You think they're reading our minds?
Dook (deadpan): No. Just our browsing history, purchase patterns, ambient conversations, and the subtle electromagnetic shifts when we contemplate clicking. Possibly every other dream.
Flops (shrugging): Fair enough.
Theme sting.
B: TV-PG Intro Segment
Montage: Flops doing gift-wrapping gymnastics; Dook holding tape like a surgical nurse calling out measurements; a roll of glossy wrapping paper with skiing moose pattern spins like a candy-cane helix. Dook snips a piece of ribbon with laboratory precision. The package ends in a perfect bow with an accidental sprig of fern tucked under it.
Dook (admiring the bow): Festive moose increase comedic bandwidth by approximately 23.000000001%.
Flops (grinning): It'll remind him of home, eh.
Dook (tucking in a card): Card reads: "From your decimal-place-adjacent friends."
Flops (laughing): Perfect!
C: TV-PG Story Segment — Part 1
Ext. Kiosk Next to the Bank.
The bell jingles. The Stoat is mid-lean on the counter, pretending to read Canadian Convenience Store Quarterly.
Flops (presenting the gift): For you, eh... uh, in your dialect.
The Stoat (eyes lighting up): Aw geez, buds, you didn't hafta.
He rips it open; the tee unfurls.
The Stoat (reading, then wheezing): "log... exp... n..."—(Beat. Processing.)—"makes IEEE 754 sad"—buddy, that's a weapon-grade chuckle, eh!
He collapses behind the counter, laughing gasps. A package of beef jerky tumbles off a nearby shelf.
Dook (peering over): Oxygen levels nominal. Comedy levels spiking. Jerky casualty: one.
The Stoat (popping back up, already tugging the shirt on over his vest): Best day ever, eh!? (He smooths it like it's formalwear.) This right here—(taps the text)—this is my lived experience, buds.
Flops (curious): Oh yeah?
The Stoat (leaning in conspiratorially): Last month, right? I'm doing inventory. Calculator says I got 47 boxes of maple cookies. System says 47. But when I do the formula—cost divided by wholesale times markup, then reverse it—I get 46.9999998. Nearly had a breakdown, eh.
Dook (nodding sagely): The rounding errors accumulate. Like snow on a roof. Eventually: collapse.
The Stoat (emphatic): Exactly! Spent two hours recounting. Thought I was losin' it. Turns out it was just the calculator being sad.
Bell jingles again. Odie Yotie strides in, portfolio under one arm, scanning shelves with the intensity of someone who alphabetizes their files by font weight.
Odie (businesslike, then distracted): Morning. Do you still stock the subpoena letterstock—the Canadian kind with the watermark of the... maple leaf that looks judgmental?
The Stoat (thumbing toward the premium rack): Top shelf, next to the legal pads with the tiny moose in the margins. Corner spot, can't miss it, eh.
Odie reaches up, then freezes mid-grab. His eyes land on The Stoat's chest.
Odie (reading slowly, voice dropping): "log... open paren... exp of n... close paren... makes IEEE seven fifty-four sad."
He sets the paper down carefully. Then collapses in a dignified heap, one paw clutching his chest.
Dook (to Flops): That's two. Statistically significant response.
Flashback vignette: Odie in a courtroom, laser pointer at a projection screen. Graph shows n = log(exp(n)) wobbling between 13.0000000 and 12.9999999 across multiple calculations.
Odie (voice-over, measured): And that, your honor, is why we do not reconstruct damages using naïve transforms on float fields. The plaintiff claims thirteen thousand dollars. Their spreadsheet, due to compounded rounding, shows twelve thousand, nine hundred ninety-nine, dollars, and... (sighs)... ninety-nine cents.
Judge (squinting at screen): So which is it, counselor?
Odie (with the weariness of experience): Thirteen thousand. The spreadsheet is experiencing what we call "floating-point sadness."
Opposing Counsel (smirking): Objection, your honor. "Sadness" isn't a technical term.
Odie (without missing a beat): Then I'll rephrase: systemic precision degradation, your honor.
Judge (rubbing temples): Sustained. And someone get me an abacus.
Back to the kiosk: Odie rises, composing himself, wiping his eyes.
Odie (to The Stoat, respectfully): That shirt. That is a thesis printed on cotton.
The Stoat (beaming): Just got it, eh! Present from the awesome buds over there.(Points to Flops then Dook)
Odie (turning to Flops and Dook): Gentlebeasts, you have gifted this fine stoat with truth. (Back to The Stoat.) I'll take two packs of the judgmental maple leaf, three legal pads, and—(gestures)—where did you acquire that masterpiece?
The Stoat (pointing to Flops): Salazon. They got a whole section, eh. Math jokes, code jokes, jokes about jokes.
Odie (pulling out his phone, tapping notes): Bookmarked. Thank you. (He taps his card on the reader.) Fifty-seven, ninety-five approved, taxes and existential validation included.
Odie (pocketing receipt, nodding to all): Gentlebeasts. (Exits, still grinning.)
The Stoat (to Flops and Dook): Worth the instant shipping?
Flops (grinning): Worth your whole week.
The Stoat (looking down at his shirt, voice soft): Worth way more than that, buds.
D: TV-E/I Educational Segment
Back at Dook & Flops' living room. Dook stirs cocoa; Flops perches with a whiteboard and a surprisingly enthusiastic energy.
Dook (placing two mugs, ceremonial): Imagine marshmallows as digits. Cocoa is the real numbers—warm, continuous, infinite.
Flops (drawing on the board): In perfect math-land, exp and log are inverses, that means opposites. So log(exp(n)) = n. They cancel each other out! Clean. Simple. Beautiful.
Dook (drops marshmallows into mugs; a couple bounce off the rim): But our mugs—computers—are finite. They use IEEE 754, the floating-point standard. Limited digits. Limited precision.
Flops (writing): So when I exp a number, it can swell huge. Like, n = 1000? exp(1000) is a number with 435 digits. Way too big for a float.
Dook (points to marshmallows on the table): Overflow. The mug says "infinity" and gives up.
Flops (nodding): Then I log it to shrink it back. But log(infinity) = infinity. I don't get my n back. I get... sadness.
Dook (sips cocoa thoughtfully): Conversely: very negative n. Like n = -1000. exp(-1000) is microscopically tiny. Underflow. The mug rounds to zero.
Flops (writing): And log(0)? Undefined. Or negative infinity, depending on who you ask. Either way: not n.
Dook (dropping one more marshmallow in): Even moderate n—say, n = 50—you pour out to the big pot, pour back in, and a few decimal marshmallows go missing. You get ≈ n, not = n.
Flops (tapping the board): In conclusion, when numbers get extreme or tiny, IEEE 754 gets a little... sad. Use higher precision—like double instead of float—or stable formulas that skip the risky transformations.
Dook (raising his mug): Also, cocoa helps.
Flops (laughs, raises his mug): Cocoa helps everything.
E: TV-PG Story Segment — Part 2
Ext. Kiosk — Afternoon. Golden light. The Stoat is serving customers, but keeps sneaking admiring glances at his shirt in the convex security mirror.
The Stoat (to a tourist with a fanny pack): You want the scratch-off with the moose or the loonie, eh?
Tourist (squinting at options): Uh... which one wins more?
The Stoat (leaning in, confidential): Statistically? Same odds. Emotionally? Always the moose.
Tourist (nodding, convinced): ..Moose it is!
The Stoat rings it up, then adjusts his shirt collar in the mirror.
Flops (from the corner, munching a chocolate bar): You've checked your reflection, like, eight times.
The Stoat (unapologetic): It's a good shirt, bud! Makes me feel seen. Like someone out there gets the frustration of inconsistent decimals, eh?
Bell jingles. A harried-looking Raccoon in a lab coat rushes in, clutching a tablet.
Raccoon (frantic): Do you have AAA batteries? I need 'em, like, now.
The Stoat (pointing): Aisle two, next to the energy drinks and regret flavored mints, eh.
Raccoon (grabbing a pack, rushing back): Thanks. My sensor array just died mid-experiment and—(notices the shirt, freezes)—wait..
Raccoon (reading, then laughing in a slightly unhinged way): "Log exp n makes IEEE sad"—oh my stars, that's my entire thesis in one sentence!
The Stoat (perking up): You do floats too, eh!
Raccoon (leaning on the counter, suddenly exhausted): I'm calibrating temperature sensors for a greenhouse study. The raw data comes in, I convert it using exp for some thermodynamic nonsense, then log it back to normalize. Except now my tomatoes are apparently growing at 24.9999999 degrees instead of 25.
Dook (from the corner): The tomatoes do not care about the missing 0.0000001.
Raccoon (pointing at Dook): Exactly! But my grant reviewers do!
The Stoat (sympathetic): Decimals, eh.. They get ya.
Raccoon (paying, taking batteries): I need that shirt. Where'd you get it?
The Stoat (jerking a thumb at Flops): Salazon. Bud got it for me. Highly recommended, eh.
Raccoon (typing into phone): Ordered. (Looks up.) If it arrives before my next grant review, I'm wearing it under my suit!
The Raccoon rushes out. The bell jingles like applause.
Flops (to The Stoat): You've started a movement.
The Stoat (grinning): Sometimes the world just needs a good math joke, eh.
The bell jingles again; a delivery drone zips past the window. A new parcel rockets through the kiosk's mail slot, lands upright. The label reads: "Pre-Order Fulfilled Before Thought Completed."
The Stoat (opening it, deadpan): It's... more legal pads. With extra judgmental maple leaves. Replacing the ones Odie bought, eh? ..Speedy, didn’t even order 'em yet! ..Beauty!
Dook (to Flops): Salazon upgraded their prediction engine to MooseBoost.
Flops (mock-suspicious): Is that... a gradient descent joke?
Dook (innocently): It slopes. Efficiently. So, yes?
F: TV-PG Story Segment — Part 3
Back home at Dook and Flops' House, Twilight. Flops is once again on the couch scrolling Salazon: "Topology: I Bent My Coffee Mug and It Still Holds Coffee", "Never Trust a Float You Haven't Rounded Yourself", "Cache Me If You Can", "My Other Algorithm is O(1)".
Flops (snorting): Okay, "Never Trust a Float You Haven't Rounded Yourself" is pretty strong.
Dook (emerging from kitchen with a fresh tray cocoa): Cocoa time. With extra marshmallow... tolerance.
Flops (takes his mug): You know, we should make our own line. "Dreamland-Grade Tees: Precisely Approximate."
Dook (thoughtful): Each shirt includes one free decimal place.
Flops (raising an eyebrow): Just one?
Dook (sincere): Generosity scales. Additional precision available via subscription.
Flops (laughs): You're joking, but someone would actually buy that.
Dook (sips cocoa): Market research suggests: yes.
Flops (scrolling more): Oh, look—"Heisenberg Might Have Slept Here." (Beat.): I don't know if I'll get that one.
Dook (without hesitation): Uncertainty principle. You can know the bed's position or the sleep's momentum, but not both precisely.
Flops (nodding slowly): ...I'm ordering it.
Dook (approving): Quantum humor. A growth market.
They clink mugs.
Flops (leaning back): You think The Stoat's actually happy? Like, not just "haha funny shirt" happy, but... y'know. Happy happy.
Dook (considering): He experienced recognition with arbitrary precision. Someone acknowledged his specific frustration and turned it into wearable solidarity. That is... non-trivial.
Flops (smiling): Yeah... Good!
G: TV-PG Story Segment — Part 4
Ext. Kiosk — Evening, closing time. The Stoat flips the sign to "Closed, eh" and starts counting the register.
The Stoat (muttering to himself): Okay, forty-seven fifty in fives, twenty-two in ones, eighteen seventy-five in change...
He taps it into his calculator. Pauses. Looks at the readout: 88.9999998.
The Stoat (to himself, grinning): There it is. The floating sadness.
Instead of panicking, he looks down at his shirt, pats it affectionately.
The Stoat (to the shirt): I see you, IEEE 754. I know your ways now, eh!
He manually rounds to 89.00, writes it in his ledger, and closes the register with a satisfied cha-ching.
The Stoat (stretching and grinning wide): Best day ever, thanks buds.
H: Credits Segment
Credits roll over a looping shot of the skiing moose gift wrap unspooling across a table, the pattern forming a playful sine wave. Occasionally a marshmallow bounces across the frame.
I: TV-PG After-Credit Segment
Kiosk — Night. The Stoat locks up, looks at his reflection in the door glass. He wraps his arms around himself and his new shirt.
The Stoat (whispering, content): C'mere, buddy. (He gives himself a squeeze.) You and me against the floats, eh.
Lights out.
Final frame: A delivery drone zips past in the distance, carrying a box labeled "Quantum Humor — Handle With Uncertainty, do not measure."
End.