Are You Dividing By Zero?

Some people approach their money thoughtfully, having considered what they want to prioritize and acting accordingly. Other people approach money by choosing to divide by zero. For the laypeople here, that means doing what is not only nonsensical, but upends the very foundations and logic an entire discipline is built on. It means stretching back thousands of years and involving famous historical figures like Alexander the Great and Isaac Newton, only to make their work crumble under your heinous acts of sacrilege akin to blasphemy or conspiracy. It could hold the power to destroy civilization as we know it, sending us to some obscene Dark Age while cackling demons circle overhead in search of new blood to spill on the weeping battlegrounds below.

I got very dramatic there, I’ll admit. I promise no literal demons are coming if you divide by zero. No, dividing by zero with your finances will leave you so out-of-sorts that you won’t need demons to come at all. You’ve already created your own.

What Happens When You Divide By Zero?

Before I go on, let’s have a math lesson with Darcy to explain how dividing by zero works. Well, more like doesn’t work. You might get hand-wavey explanations of either “can’t be done so don’t worry about it” or “it’s undefined/approaches infinity/blah blah insert jargon the average person doesn’t grok”. They’re not wrong, but there’s a very easy way to understand why dividing by zero doesn’t make sense. Here it is: attempting to divide by zero destroys everything you know about basic mathematics.

The reason behind this is because zero doesn’t act like other numbers, having super special properties no other digit embodies on the infinite number line. I didn’t realize this until I read this fascinating book about the history of zero, which also taught my what dividing by zero does in the world of numbers.

https://www.instagram.com/p/CTsfUm3vRj8/

If we wanted to treat it as any other number that can be divided, we’ll find ourselves with more fallacies than a televised political debate. Let’s look at some easy math to see what I mean.

Here’s a dead simple “solve for X” kind of math problem.

X * 4 = 12

If you don’t already know what X is, it’s easy to figure out if you divide both sides by 4.

X * 4 = 12

(X * 4)/4 = (12)/4

The 4 on the left cancels out, and 12, when you divide by 4, turns out to be 3. This leaves you with a straightforward, easy answer of X=3.

X = 12 / 4

X = 3

If you wanted to get back to 12, you’d just have to redo the multiplication and multiply by 4.

3 * 4 = 12

Now that the basics are out of the way…

Now we’ll do something more interesting and add zero to the mix. We know already that multiplying anything by zero would result in zero. One times zero is zero. Pi times zero is zero. Two googol times zero is zero (yes, googol is an actual numerical unit). No matter what, X times zero is always going to result in zero.

Combine that with what we’ve just done with undoing multiplication by division. The rules of math show us you can undo division you’ve done with multiplication. Getting to 3 from 12 means dividing by 4; getting back to 12 means multiplying by 4.

This logic, when it includes zero, provides some very wonky results. Say you’re looking at the below equation:

0 * 2 = X

Obviously the result is zero. Getting to 0 from 2 means multiplying by 0. But if we want to get back to 2, according to our established rules, we’d want to divide by 0. Here’s what happens if we do that:

0 * 2 = 0

(0 * 2)/0 = (0)/0

The 0 on the left cancels out. If 0 times 0 is 0, then 0 divided by 0 should also be 0. Therefore, we can assume that:

2 = 0

is the ultimate truth.

Mathematics at work!!

This is why you don’t divide by zero. There are many fancy graphs, tomes, and centuries of debate that will give you much more in-depth explanations for the problems in dividing by zero, but you get the idea here.

No one is honestly going to look at two avocados and say there are zero avocados. But how can you say that when we can prove, mathematically, that 2 equals zero?

And why stop there? Using this same logic I can argue 2 actually equals 1 and 250,000 is equal to one million (hey look, I’m now financially independent!) Everything to do with mathematics would break down. No one would be able to agree on how much money something cost or how many products they were looking at. You couldn’t measure anything, whether that’s a child’s growth spurts or the material needed for home construction. To keep the peace, we need to make the number zero play by different rules.

Applying This to the World of Finance

This unequal treatment works because zero doesn’t act like other numbers. It’s not a negative or a positive; it’s a void that was once so terrifying, Western philosophy and religion went out of its way to avoid it for a thousand-plus years. It was still scary even when Isaac Newton used it to finally form calculus (and advance all the enraging high school math classes we have today). Zero is also scary all by itself in finance. You might like zero if there’s a lot of them after a certain number, like five zeroes after a one or two. You might also like zero if it’s showing how much you spent on some budget category in a given month. Otherwise, you don’t want “zero” to describe your savings, investments, bank account, house equity, or job raises. Zero sucks so bad in personal finance.

There is only one thing worse than zero in personal finance. And that’s when people try to divide by zero with their money. By “dividing by zero,” they’re going to get results that inherently make no sense at all… but they either don’t know better or haven’t tried to fix it. This might leave them with an “answer,” but it’s one that is flagrantly wrong.

Who’s Trying to Divide by Zero?

The way I see it, there are at least four groups of people who are continuously dividing by zero:

• The “high-earning poor,” or those living paycheck-to-paycheck on a bloated salary.
• The low-income poor, scraping by, at best, with little financial education/opportunity for advancement,
• The confused, who genuinely don’t understand what having a budget means, and
• The big spenders who never think about money… until it’s no longer there to use

They all have different reasons for trying to divide by zero in their financial circumstances – the low-income individual is trying to divide by zero to make their unlivable wage stretch enough to earn them (expensive) housing, (expensive) transit, and groceries (with prices rising rapidly). That big spender is trying to divide by zero too: forsaking wealth preservation or the pursuit of true wealth in favor of flashy toys in an attempt to influence others or keep up with the elusive Joneses. Dividing by zero, in any of these cases, is illogical – unfortunately for the former, flamboyantly for the latter.

It’s the ones with more money than sense that really grind my gears here. They might genuinely believe dividing by zero works for them. Just as I can “prove” to you that 2 equals 0, they can “prove” having little investment diversification is fine because Shitcoin is going TO THE MOON, DARCY, JUST YOU WAIT. Or that having no investments at all is a fine choice because YOLO. Or “I’ve got time to save/invest later”. I’ve also heard whining about how it’s not their fault they can’t save with a higher-than-average salary, and what’s the big deal when not saving anything isn’t a criminal offense?

The big deal is: you’re hurting yourself in the long run with this nonsense. You can’t build anything you’re proud of on this illogical road.

Get Better Rules

Just as not every number adheres to the same rules (lest there be chaos) you’re not able to find a financial plan that applies equally to everyone (lest there be chaos). You’ll need to forge a game plan tailored to your unique circumstances (affected by your salary, expenses, investment choices, debt payments, dependents, and other financial obligations).

With that said, your game plan has to make sense. What’s the ultimate goal or dream your financial plan is in place to reach? How do you plan to improve your financial situation, or at least maintain some kind of stability? What will you do if shit hits the fan and becomes an emergency? These don’t come with easy answers. If you try to ignore it or half-ass your plan, you’re setting yourself up for vulnerability and failure.

It was Ben Franklin who first said

If you fail to plan, you are planning to fail.

You can replace the second half of that phrase with “might as well divide by zero”. You’ve shown a disregard to the positive advancements humanity’s made already. Do yourself a favor and get your money situation straightened out. That way you’ll save yourself from following a path that is going to hurt you and make you look like a fool. We’ve got better numbers to play with and a kinder future to reach.

Cover image credit: Hans-Peter Gauster via Unsplash