Episode Details

You go up 50%. Then you go down 50%. You should be back where you started, right? You're not. You just lost 25%. The math we all learned in school is quietly, systematically deceiving us.

In this episode, we tear apart the hidden mechanics of relative change — the simple formula behind every percentage you've ever read in a headline, a bank statement, or a sales pitch. We start with why absolute change fails (a $100 price hike means riots at a coffee shop and a shrug at a car dealership), then expose how marketers reverse-engineer the reference value in a percentage to make their numbers say whatever they want.

From there, things get worse. We walk through the "percentages of percentages" trap that makes a 1-percentage-point rate increase sound negligible when it's actually a 33% jump, the total collapse of the formula when your starting value hits zero or goes negative (the math will tell you it's getting colder when it's physically getting warmer), and why dropping the absolute value brackets in a physics lab could mean you just broke Einstein's theory of relativity.

Then we meet the fix that almost nobody uses: logarithmic change. Log points are perfectly additive, perfectly symmetrical, and they don't compound errors no matter how many times the market bounces. They're mathematically superior in every way. So why does the entire financial world still cling to broken classical percentages? The answer says more about human psychology — and institutional incentives — than it does about math.