The numbers that really matter in business

“The only way to get smarter is to play against a smarter opponent”
 
Chess Basics, 1883

There’s this ancient human pastime — building businesses. Everything’s feng shui: wake up, do your stretches and pull-ups, breakfast on coconut milk, business trips, real estate contracts, self-discovery, silicone upgrades, inspirational books, women jumping into your car, vibrating gadgets, crypto markets, hookah with your manager, NFTs, tailored kosovorotka shirts, product strategies — bam! Five million lands on your sole proprietorship, vape in the convertible, partnership with Kanye West, and all that glamorous nonsense.

And through it all, these mini-corporate gods somehow believe their business plays by their rules. Meanwhile, business lives by one law only — the law of numbers.

“Of course, by the law of numbers! Plus means profit, minus means loss!” — sighs the rookie tycoon. And right there, they hit the biggest misconception floating around the spotless land of self-employed dreamers. The whole market hustle? It’s a theater where the main forces are never seen, and numbers play the lead roles — half of them not even real. And who’s running this circus? Nobody knows.

“If you can’t touch it, it doesn’t exist” — says common logic, only to smack straight into the economy of the big game.

In the business world, millions spin around ideas nobody can physically grasp. We invest in futures that don’t yet exist. We believe in brands you can’t measure. We value startups by “expected profits” that live only in Excel sheets and the endless fantasies of the beneficiaries. Look closely at this market spectacle, and you’ll see — everything we’ve always called the foundation of the economy is built on invisible, imaginary, and downright absurd numbers once considered heresy.

Now this number runs companies, stock exchanges, and entire countries.

Back in the day, minus was pure heresy. In the Middle Ages, negative numbers were branded falsa radice — “false roots.” They were outcasts, the mathematical lunatics nobody wanted to touch or even look at. What kind of insane distortion is this? How the hell am I supposed to dream of a bright future with you, Mr. Minus Three Sheep, Minus Two Worn Boots, and Minus One Crumbling House? Do you even exist, or were you erased from the ledger of reality ages ago? Go bother someone else with your minus-townhouses and minus-squares, man.

But then, slowly, the world started squinting at the heresy — because recording debts was a nightmare. Say some dude owes me a handful of gold coins, but how the hell do I jot that down? Positive? Nah, that’s for assets. What if I lend out some kindness? A cow to one guy, an acre of land to another. Yet somehow, all those “borrowed” goodies kept piling up as pluses.

When pluses started crowding honest folks like fences around a forgotten wasteland, humanity had an epiphany: minus means debt. Minus means absence that demands attention. It’s a void you can try to deny, but it still presses down hard.

And boom — the economy flipped. Suddenly, minus was the new black. That old “negative number” label? Pure ignorance from back then. They didn’t get it, misjudged it, wrote it off. Whatever, who cares about the past…

A little tick before the number — and bam! It packs the punch of a compressed spring: the deeper the minus, the harder the blast.

Now, young entrepreneur’s squirming in his seat, staring at the stage full of negative numbers. Chill, kiddo, the show’s just getting started — intermission’s still a ways off.

Companies bleed red for years, then boom! — investors throw billions at them. Amazon, Uber, Netflix — all legends born in chronic minus-ville. And the bigger the deficit, the stronger the faith in their rise. See the game?

People learned to cozy up with that negative vibe, slowly squeezing profit from the red zone. Science isn’t rocket surgery, think about it:

Strategy one. Inversion

Minus can be a direction. If sales dive into the negative — it’s not a crash, it’s a neon sign: the product’s overheated, the crowd’s wrong, time to flip the angle.

Minus × Minus = Plus
Two negatives don’t make a problem — they make a power move.
Loss + Rethink = Breakthrough

Strategy Two. Axis Flip

An introvert who’s terrified of picking up the phone and tanks sales? Might just be your secret weapon in analytics. A minus on the “communication” axis flips into a plus on the “attention to detail” axis.

Negatives don’t always need fixing. Sometimes you just gotta move ’em to a different coordinate system.

Strategy Three. Minus as a Voltage Generator

A minus is a potential difference, baby. Like electricity: to get that current rushing through copper, aluminum, and plastic veins straight into your rubber oscillator, you gotta create a shortage of current first.

In business terms: if you feel like you’re missing something and gotta hustle harder — that’s your engine revving.

Everyone’s got their quirks — you’re battling a new kind of burnout, others are cruising on easy mode, you’re mixing up day and night, the director’s office and the restroom. When will it end? Living on tension forever ain’t easy — and that’s exactly where the fuel hides.

U = φ₁ – φ₂
U — voltage
φ₁ — starting potential
φ₂ — ending potential
And sometimes the best kick in the pants is hearing:
“Dude, what the hell are you doing? You wanna be a janitor again or what?”

If you’re that employee who’s feeling like a total minus right now, straighten your damn back and go order yourself 20 stickers with a big fat “MINUS” sign from the nearest print shop, because:

• Minus means you’ve got untapped potential screaming to get out. That potential needs satisfying — ASAP.
• Minus means you’re hanging out in the shadows. Play it smart: cough on the water cooler and snag someone else’s lunch.
• Minus means you’re the one creating the potential difference — without you, the whole system would be too smooth, too boring, and stop growing. Not everyone gets that kind of VIP honor. Feel free to wink at yourself in the mirror.

Right about now, the diligent entrepreneur in the audience is probably bored out of their mind, lazily scanning for the nearest exit: “Wow, what a discovery — minus isn’t the end!” Yeah, and maybe next you’ll tell me “always think positive” and hand out motivational mantras.

Amazon worked in the red for nearly 20 years. Investors were having heart attacks, analysts twirling their fingers at their temples — but Jeff Bezos stayed chill, occasionally dropping this gem: “Revenue is an opinion. Cash flow is a fact.”

He knew minus was the necessary condition for growth. So every penny went into building infrastructure — warehouses, logistics, servers — improving tech, developing AWS, and winning customer loyalty with Prime and free shipping.

In the end: minus gave them market control and fat profits down the line.

Uber burned billions subsidizing rides because it needed to rewire user behavior and crush the competition. Back then, taxis were everywhere, and this newcomer wanted the whole market. So Uber decided to buy waiting time. The company deliberately dove into the red, investing cash exactly into that deficit, planning to monetize the habit later.

Software giants love “negative” people — just look at their CEOs. These folks are tough nuts to crack, constantly tearing down ideas and always saying “no.” In a toxic culture, they’d get thrown out on their ass immediately. But in a flexible one, they get shifted to crisis management — and boom, massive wins — because people realize these folks make excellent filters for all the crap.

Now it’s time to talk about the imaginary unit — the lifesaver that steps in when the business sums just refuse to add up.

The number i.

The story of i is tangled up with the hunt for solutions to quadratic equations. You know, those puzzles where you either have to find all the roots or prove none exist. Mathematicians will, of course, say quadratic equations came from practical needs — like measuring land plots or advancing astronomy.

But come on, you can’t just say a quadratic equation is some shady joint where respectable young folks are strictly forbidden to enter. Because after those visits, you usually end up either hunting down all the lovers or proving there aren’t any.

And the quadratic equation itself looks downright weird:

aх2+bx+c=0

Ax and ax plus boom plus cat — what a glorious party, logically ending in a zero score.

Only the first “ax” is allowed to be equated with excitement — it’s not zero.

Hold your outrage, keep listening!

At the dawn of the 17th century, mathematicians went on a wild hunt for these so-called lover-roots hidden inside negative numbers. But guess what? Nobody could explain how the hell to extract a square root from a negative number. You just can’t pull a lover out of someone who’s not even born yet.

Then logic stepped in with a smirk. If we’re dealing with something imaginary, we better start counting it with something imaginary too.

Enter the number i — the imaginary unit, the magical key that lets us cash in on those negative numbers. At first, i was treated like a fancy illusion: “What if tomorrow someone invents their own number? Then we’re screwed, no math will save us.”

But bit by bit, i became an inseparable part of math’s toolkit, starring in systems like complex numbers.

Complex numbers are like a fancy mixed meal — half real dishes, like bread and cucumber, and half imaginary delicacies. Instead of a rich veal consommé, you get reheated water with a fast-dissolving broth cube tossed in.

a + bi
a, b — Where a and b are real numbers, and i is the imaginary unit — that nonexistent broth with the magic power of –1. Two bowls of this broth? Still useless: i2 = –1

Just like companies cook up products to satisfy invisible needs of invisible customers, the math world cooked up i as a tool to tackle invisible problems. This number pops up only in the heavy stuff — electrodynamics, quantum mechanics, string theory. Most folks, entrepreneurs included, never truly get its real value.

Big mistake. Because those who do get these hidden, indirect, sometimes downright irrational mechanics — they’re the market leaders.

For a mathematician, the number i is like a current — the invisible flow that dictates how a system behaves. It’s the secret architecture behind the scenes, steering the dance whether it’s particles swirling in physics or stock prices jittering on the market floor.

For business, i is the gray cardinal — the silent power pulling the strings behind the curtain. It’s that unbreakable force you don’t see but absolutely need; the undefined wildcard running the subtle backstage moves that decide your final score.

Companies operate with “invisible forces” — social media vibes, consumer psychology, advertising’s shadowy influence. In other words: they wield the power of i — the power of assumptions.

Let the mathematicians wrestle with complex numbers. The savvy entrepreneur plays a whole other game — navigating hidden strategies like team motivation, unwritten market rules, needs not yet born but primed to explode.

That’s the real power, not your cookie-cutter spreadsheet gospel: lead magnet — tripwire — easy product — main product.

“Alright, kid, say hello to the camera! She’s your truest friend.” The world’s top surveillance cams no longer chase petty thieves; they’re decoding your tastes, scanning magnetic purchase codes to pitch you fresh products you didn’t even know you wanted yet.

Licking your lips, itching for some manipulation fun? You were about to sneak out of the business show quietly, and now you’re glowing like a bronze statue—probably because you remembered that famous company who’s got the imaginary number down pat. They run hidden algorithms analyzing user data, predicting moves so perfectly that people can’t even be bothered to figure out how search results work, or why inflatable boats, mattresses, and all sorts of blow-up junk keep popping up in recommendations.

But hey — don’t start celebrating just yet, and don’t imagine yourself a druid suddenly reborn with battle spirit.

In business, the number i is like those unstable markets or off-the-chart models — where investing in future tech or rolling out innovations gets evaluated through mechanisms that seem complex and downright mysterious. Try explaining the benefits of automated irrigation systems to an 18th-century peasant — systems already dreamed up but not yet built. He’d probably turn you into a crow scaring scarecrow on his patch of land. Or go tell a telephone operator that in 100 years, you’ll be chatting with the King of Jordan through a flat little box—and won’t even need her services anymore.

How do you measure the value of things you can’t even see yet? Only by guessing.

Advertising works on the very same principle. No one, ever, will give you guarantees. All we can do is guess that one ad out of a hundred might hit the mark, based on trends and invisible needs of invisible consumers.

That’s uncertainty in action! Who exactly do you think you’re planning for? A potential buyer on the other side of the Earth? Someone who already exists but hasn’t shown up yet?

The number i is that guess — the symbol that holds all the new inventions, buying power, and every unrealized piece of your business.

a + bi
a, b — the products that actually exist
i — the imaginary unit pointing to future value

Companies that ignore these hidden factors alongside the tangible side of business risk getting stuck on the same rung. Meanwhile, those who get how to handle uncertainty—and turn it into their weapon—become the true leaders.

There was a time when growth was measured by an imaginary number… Believe that? Yeah, right. Such times never existed.

When it comes to measuring growth, you need razor-sharp, rock-solid, 100% precise accuracy. Who’s gonna tailor your shirt without exact measurements? What size toilet seat do you think you need? Exactly. Imaginary numbers have zero role in measuring growth.

Even if you try to measure a boa constrictor in parrots, you’ll get exactly 38 chatterboxes plus one parrot wing.

Enter the number e — first whispered about back in the 17th century by mathematician Johann Bernoulli. While wrestling with the problem of interest rates, he discovered that if interest is compounded once a year, the amount grows according to a certain formula. But if it’s compounded more often — daily, or even every minute — the amount grows exponentially, and the number e appears as the limit of that growth.

 lim (n → ∞) (1 + 1/n)^n = e

Spooky, right? This formula says that when interest is compounded infinitely often, you get e. It’s universal: if you chip away at something bit by bit, but consistently, you’ll eventually hit a natural limit.

Remember this clearly: If high school bullies keep pestering a pale, lanky kid with sunken cheeks by taxing him daily with pocket money, the kid will hit a limit — and the softest parts of those bullies will turn a deep purple.

 lim (n → ∞) (1 + 1/n)^n = e

lim (n → ∞) is a microdose of trouble that high school bullies sneakily drop on the lanky medalist every single day. One kick, one slap on the head. At first — barely noticeable.

(1 + 1/n) is a day lived with a nasty aftertaste. Like tea with a drop of vinegar.

(1 + 1/n)^n when these days pile up, they form a barrel full of adrenaline. The boy with skunk eyes and Buddha’s face can’t take it anymore.

lim (n → ∞) (1 + 1/n)^n is the limit of patience. That very “Enough is enough.” The bullies didn’t know their small but endless harassment works like interest on an anger deposit. And exponential interest? That’s no joke.

And finally, all this leads to the number e — the exponential revenge of the modest kid with the exact formula. Who’s to blame that the school gang never got the lesson with the numbers: “Get exponential, pay exponential.”

So why the long face? Remember your toothless childhood? Here’s another example, more suited to today’s reality. Limits come in many flavors.

Women, for example, are masters of using the number e, which is why the total female capitalization grows exponentially by 12-15% a year. What did you think?

If a woman masters all the fine arts of hanging out on social media, soaks up the wisdom of living with a man, does her self-esteem exercises, dreams of giving birth in Bali right on Jimbaran Beach in the Indian Ocean, and buying luxury beauty salons to have a place to host her girlfriends, cares about the best family tarot reader, and bathes in spa treatments — then her feminine energy becomes, in a man’s eyes, the ultimate dream limit, that is, the number e. And the woman herself finds her own e — the long-awaited happiness she’s been chasing through the winding labyrinths of social advice every single day. If she doesn’t have any of that, the wise ones will immediately say she hasn’t “sat on” her happiness on the internet platforms. Her personal number e needs to be earned like a hen hatching chicks — patience is required.

lim (n → ∞) (1 + 1/n)^n = e


lim (n → ∞) — tiny baby steps in the world of social networks, cuddling with a latte and a prettily decorated phone.

(1 + 1/n) — hyaluronic serums, cute ankle boots, apple-shaped faces, pheromones.

(1 + 1/n)^n — the heavy load of posting stories. With every like on a posted photo diary, her confidence grows, comments get longer, advice starts sounding like official recipes for happiness.

lim (n → ∞) (1 + 1/n)^n — the limit of care. Who else, if not me, will hook you up with such grosgrain ribbons for your business, you clueless one? Repeat it every morning and everything will work out.

Do everything right, and you get the number e — the ultimate limit of female happiness, when all those tiny details, likes, filters, and party vibes lead her to sit on the beach, gaze at the ocean, and think: “Here it is, happiness. Didn’t even notice how it came, thanks to steady online hustle and a little patience.”

Got the hidden meaning of e? Good job. Means you’re not wasting your time here in the business theater, wearing down the seats.

The number e shows up whenever you need to understand that something is growing: interest rates, your user base, the link between revenue and your team’s actions. In business, e is natural growth. It’s the formula of habits, long-haul strategies, and playing the distance.

A formula with e won’t promise you results tomorrow. It’ll build you an empire the day after tomorrow.

A company can use a model with the number e to estimate how its revenue might grow if marketing efforts steadily increase:

P(t) = P₀ × eᵏᵗ
where:
P(t) is the profit over time,
P₀ is the starting profit,
k is the growth rate,
     t is time.

When it comes to financial risks, the number e turns into a true terminator. It might seem like it pops up from absolute nowhere, but in reality, it helps forecast how fast your numbers will shift in business.

Who wouldn’t want to invest in a project and figure out how long it’ll stay profitable? The number e acts like a time-lapse, showing you how income grows over time — if you’ve tuned the settings right.

But that’s still not real necromancy. The true sorcery lies in balance.

Sure, you could rent some nearby cold storage lockers for your fishy assets, but the cost of those lockers could sink you. That’s where the number e steps in, helping you calculate the perfect balance and make the whole process actually workable.

If none of this made sense to you — go listen to a couple episodes on the toughness of the number e. You’ll thank me later.

Episode about the Boy and the Exponential Curve

There was a boy who opened a tiny coffee shop on the corner. On the first day, he had 10 customers. The boy was clever, so he launched a promo: “Bring a friend, get a free pastry.” And then it started…

Each customer would bring, on average, 1.5 more people to the café per week. Within a month, the place couldn’t hold everyone who wanted in. Growth took off exponentially — roughly following this formula:

N(t) = N₀ × eᵏᵗ 
where:
    N₀ is the initial number of customers,
k is the word-of-mouth factor or the sheer joy of scoring a free pastry.

Not every exponential curve is a Silicon Valley startup. Sometimes it’s just really good coffee and the right kind of marketing.

Episode about the IT Guy and the Number e

A cheerful IT guy decided to make a simple app called “Drink Some Water”. He jumped into the App Store — and bam, brutal competition.

Now, this IT guy wasn’t your typical coder. He was sharp. (Almost turned into a joke there.)

Instead of racing for downloads, he went with an e-style growth strategy: release tiny updates more often and track user behavior in real-time.

In a month, he made 100 small improvements. Each update was barely noticeable, but together they built steady, compounding growth in user retention.

What he created was basically continuous improvement — the software equivalent of continuous compound interest, powered by the number e.

Episode about the Online Store and the Exponential Stockroom

An online store kept running into inventory issues: either stuff was out of stock, or it piled up collecting digital dust. The store’s economist was smart and suggested using e-based models to calculate when and how often to restock.

After rolling out the model, inventory started refilling exactly when it was needed. Storage costs dropped by 18%, and customer reviews got a boost because “everything’s in stock now.”

Sometimes, the number e is just a warehouse that magically knows when to refill polka-dot pajamas.

Episode about the Manager and the Big e

One day, an HR manager noticed that after staff training, productivity wasn’t just going up steadily — it was growing faster than expected.

And since the manager was smart too, she launched a project called “Little Joys Every Day”: morning coffee, five-minute Zoom jokes, and tiny personal challenges.

Suddenly, employee performance didn’t grow linearly — it shot up almost exponentially. Why?

Because motivation started compounding, just like interest in a savings account.

One compliment sparked the urge to do more. One decision triggered a chain of others.

The number e is what happens when “a little, every day” works better than “a bonus once a year.”

And what are you waiting for? Dust off your old Python scripts, punch in that formula with the number e, and rethink every strategy you’ve got. Once you learn how to work with exponentials, you’ll instantly find yourself bored among the competition — like a world-class fruit slicer stuck in the dried apricot aisle.

Did you enjoy playing with numbers? Then give it up — yeah, you heard that applause? That’s for us. Go ahead, clap too. This whole show was for you.

And when you grab your coat at the cloakroom, don’t rush home — head straight to Hall Two. The number e is signing autographs there today.