🚧 Work in Progress 🚧 Some parts are not yet functional or lacking content 🚧
background
MAKE GOOD USE OF THIS UMBRELLA   •
A Day Plotted Logarithmically

A Day Plotted Logarithmically

Part 5: Logarithm



After the owner announces the closure, a brief silence ensues.
37: Really?
Medicine Pocket: Closing down? What do you mean "closing down"?
Shopkeeper: Uh, I mean, I'm going out of business. I can't keep this shop afloat.
Medicine Pocket: Of course, I know what "closing down" means. Ugh ... Do you really think I need you to explain THAT to me?
The questioner rudely interrupts.
Medicine Pocket: Don't tell me that this means I have to go back to Clever Cones? Their Carbuncle servers always sneak bites from my order! When I complained, they said it was within "normal loss allowance"!
37: So, we won't be able to have this ice cream anymore?
The girl who was about to leave stops in her tracks.
37: That beautiful, regular dodecagram, and its magical, refreshing, and rich flavor ... The next time I come here, I won't be able to taste it?
37: Happy, beautiful things, never to be seen again. What terrible news.
37 thinks for a moment.
37: I must admit, I don't know much of anything about economics. But if this shop sells such beautiful ice cream, yet it's closing down. There must be something wrong.
37: How about this? I'll help you solve your problem.
It appears their farewell was premature.
37: So, then I believe this is the problem.
After subjecting the shopkeeper to a dizzying series of questions, the little nascent consultant consumes another free ice cream as she announces her solution.
37: This chart illustrates the gap between your shop's data and that of other shops. Apparently, your foot traffic and average transaction value are significantly lower—that is the issue.
37: So, we only need to increase these two numbers, and your troubles will be over.
Shopkeeper: Really? Uh, which ones did you say?
The owner leans over the charts, attempting to decipher the many points and lines, growing more and more confused.
Medicine Pocket: Are you serious? I feel like I've walked onto the set of some boring sitcom.
Medicine Pocket: This is my private lab—a place for ideas of consequence! Now you've barged in here with your kitschy number name and festooned my brainstorming board with profit-loss analyses for a two-bit ice cream stand!
Mesmer Jr.: Correction: This is not your private lab. But I admit, I am questioning why we're still here, too.
X: Come on, friends. We all know why. We're having a good time, aren't we?
Medicine Pocket: You wouldn't know fun if it came up to you and sat on your head.
Medicine Pocket: "Let's all sit around having 'fun' while we discuss how an ice cream shop owned by some idiot that doesn't even understand business is failing ... Duhhh!"—the answer's obvious.
Medicine Pocket: How can you expect to help someone who, when asked, "How much product do you need to restock daily," answers, "I don't know exactly, but it feels like a lot"?
Shopkeeper: Hey! I've put up with your insults long enough! I can hear you, you know?!
Shopkeeper: You're the one who's always making unreasonable requests, like asking for refills when you've eaten all the ice cream off your cone. To think I actually topped you up, and now you're making fun of me?!
Medicine Pocket: I'm just stating the facts. People can excel at some things but suck at others.
Medicine Pocket: Your ice cream is to die for, but your business is a mess. Why don't you just sell your recipe?
The shopkeeper is speechless, her face slowly reddening.
Medicine Pocket: You can't be serious.
Shopkeeper: Fine, I admit it! This is my dream! To own an ice cream shop—it's always been my dream, and I don't want to give it up!
The owner turns away from Medicine Pocket's rolling eyes and faces her would-be savior.
Shopkeeper: I was ready to give up, but then you appeared out of nowhere. Do you think you can really help me, little girl? What was it that you said I need to increase?
37: Average transaction value and foot traffic. Look, your average transaction is about a third of other shops.
37: And your foot traffic is only 63 people a day, which is just not enough. That's why you're losing money: your revenue is too low.
Shopkeeper: I thought 63 people was a lot! Think about it—over sixty people!
Medicine Pocket: That's some scary level of obliviousness, lady. Look at the other stores around you! They've got lines of people queuing up at Clever Cones' ice cream truck every day! That's hundreds and hundreds of ice creams daily!
Medicine Pocket: You should thank Ezra for not using the museum store to make a buck, or you'd be losing even more. He lacks business sense, like someone else I know.
Shopkeeper: Okay, okay! You're right.
The shopkeeper surrenders to their tirade, reexamining the chart 37 drew.
Then, she does something almost unheard of at the Laplace Scientific Computing Center: She questions 37's conclusion.
Shopkeeper: But I sell ice cream, and the others sell souvenirs, so of course their average transaction value is higher.
Shopkeeper: I can't price my ice cream to match their average transactions. I know it tastes great, but honestly, I don't think people will pay that much.
37: You mean this ice cream isn't worth a higher price? Even with such a beautiful regular dodecagram shape?
The mathematician, unfamiliar with prices, is momentarily stunned, then humbly accepts this correction.
37: Then we only have foot traffic left to work with. We will have to increase that number.
37: Just raise this number to 2.56 times the original, and we can break even.
37: Although I don't particularly like this variable—2.56 isn't an exact number; it's merely a decimal approximation.
Shopkeeper: 2.56? Uh, multiplying that by the 63 people entering the store, that would be ... uh ...
37: You see, this is the downside of using approximations. You'll get 161.28, but the number we're discussing is actually 161.
37: And that's a bit counterintuitive. 161 is a deficient number; its proper divisors add up to less than itself.
37: I think once you reach the goal of 161, you might pursue better numbers, like its next palindrome, 171. Then 181, 191, 202 ...
Shopkeeper: Wait, wait! Please, just stop for a moment.
Although she doesn't understand the girl's calculations, the owner notices the numbers are getting bigger.
Shopkeeper: Let's start with our first goal. You want me to sell 161 ice creams a day? Is that even possible?
Shopkeeper: That's a whole lot of people! How can I serve that many customers every day?
37: There's no need to worry. Your business hours are from ten in the morning to six in the evening, so you only need to sell one ice cream cone every 2.98, or rounding up, every 3 minutes.
37: I didn't time you when you served us, but I simulated the process, and if everything goes smoothly, I think you can do it within 30 seconds.
37: It should certainly be possible.
The shopkeeper's eyes drift into the distance, imagining all the customers.
Shopkeeper: I-I don't know. Maybe I can try?
She's convinced. But then—
She asks the crucial question.
Shopkeeper: But, how do I get these 2.56 times more people to come to my store?
37: Let me think ... Hmm ... hmm ...
The talented mathematician opens her mouth, then closes it.
After a while, she finally tries to give an answer.
37: Multiply by 2.56, then subtract 0.28?
Shopkeeper: Huh?
Medicine Pocket: Haha! What did I say? You can't just say "increase the number."
The long-silent onlooker seizes the opportunity to spit a little venom.
Medicine Pocket: Welcome to the real world, Number Brain.
X: This might be quite sudden, but I think it's time for a drastic reappraisal of our understanding of mathematics.
X: Many people find the world of mathematics to be too abstract and difficult to comprehend, and so they're afraid of it.
X: You can't blame them. Think about an apple, a person, an event, a success, or a failure. These concepts are easy to grasp.
X: But when numbers first detached from their counted objects, when "1" became "1"—and just "1," mathematics departed from the material world we are all familiar with.
X: Bound by our physical forms, we can only chase those numbers in abstract. We study and research mathematics, using those numbers to borrow power from that transcendent world.
X: In that world, "nothing" boldly appears as 0, negative numbers stand on the opposite end of "existence," and even "infinity" can be included in formulas ...
X: In the world of mathematics, we can do anything—at least, theoretically. Our minds are free, no longer constrained by reality.
X: Only a few understand this freedom's charm, and fewer still wield true omnipotence in mathematics. Like our delightful new friend here.
X: But there's just one small problem.
Mesmer Jr.: ...
The silent audience stares at the eloquent researcher, then coldly looks away.
Most people would feel awkward and stop talking, but this unknown number is no ordinary digit.
X: Do me a favor, will you? Ask me, "What problem?"
Mesmer Jr.: ...
Merciless silence.
X: The problem is, mathematics has the power to do anything in the abstract, but to make it work in reality? For that, we need to follow three steps.
X: First, we need to abstract our real-world problem into a mathematical one.
X: Second, we need to solve this problem within the mathematical world.
X: And third, we need to find a way to bring that abstract answer back to reality.
Mesmer Jr.: You mean ...
His audience understands. Mesmer Jr. looks outside.
37: Past data shows an average of 9,837 visitors per day during this quarter over an eight-hour operational period, so after three hours, about 3,689 people should have entered.
Medicine Pocket: Hey, you know visitor numbers vary by time of day, right? There's a "peak period" ... I thought that was just common sense.
37: Even so, the gap is too big. Only 457 people reached an area where they could see the shop's sign.
37: People aren't coming to the refreshments area where the ice cream shop is located. That's the root of our problem!
Shopkeeper: Huh? Four hundred people sounds like a whole lot!
Medicine Pocket: You ever hear of an entry rate? Not all four hundred of them are hungry, so they don't all walk in! And only twenty that do will buy anything!
Medicine Pocket: So only about 12% of visitors come through this refreshments area. I have to admit, that's lower than I expected.
Medicine Pocket: No wonder I like sitting here. There are hardly ever any annoying people around to bother me.
37: But why don't people come this way? I don't understand. Wait, this map ...
The brain that solved the computing center's year-long sales problem in seconds is now buried in a small puzzle about ice cream and visitors.
Mesmer Jr.: She's on the third step.
Returning to reality.
37: I've got it!