Concept

Why are digit changes at base-10 boundaries only an illusion of significance?

Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1

"But if you had been writing these numbers out as base-10 representations, like you’re used to doing, you might have thought differently. You’d have gone from: (A) 8 to (B) 9 to (C) 10 When going from B to C, your “odometer” wrapped around. You had to go from a one-digit number to a two-digit number, simply because you ran out of room in one digit. This can lead to the illusion that something fundamentally different happens when you go from B to C. This is completely an illusion. Nothing different happens to the number just because the way we write it down changes. Human beings have a curious habit of thinking that odometer changes are significant. When the temperature breaks 100, it suddenly feels “more hotter” than it did when it merely rose from 98 to 99. When the Dow Jones Industrial Average first reached 10,000, and when Pete Rose eclipsed 4,000 career hits, and when the year 2000 dawned, we tended to think that something truly important had taken place. But as we’ll see, the point at which these milestones occur is utterly and even laughably aribitrary: it simply has to do with what number we’ve chosen as our base. And we quite honestly could have chosen any number at all."

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Why are digit changes at base-10 boundaries only an illusion of significance? | Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk | Bifalgorithm | Bifalgorithm