Infinity makes me question precision and measurement

There is something deeply unsettling to be about the concept of infinity. I’ll just talk about it in the concept of numbers, not in terms of space, because that’s its own thing, even if it’s related.

When conducting interviews for junior candidates, I often give a Body Mass Index(BMI) challenge. It’s not a particularly hard thing to program, nor is BMI that great of a measure health for various reasons, but sometimes it leads into an interesting place.

The BMI Range

The BMI range is as follows:

• less than 18.5 is underweight
• 18.5 to 25 is ideal
• greater than 25 and less than 30 is overweight
• 30 and over is overweight … mostly. You see, in most of the scales, the values published use tenths of a number, and they have gaps. For instance, this is what the CDC publishes:
• less than 18.5 is underweight
• 18.5 to 24.9 is ideal
• 25 to 29.9 is overweight
• 30 and over is obese This looks harmless and reasonable, right? Let me now mess with you.

The gaps

So, here it is, while you can say that the distance between 24.9 and 25 is one tenth numerically, in terms of the values that can take place between those two points is infinite. There is infinite precision to be measured between these points, even if we lack the instruments to make the measurements. If you have 24.9, with the 9s repeating millions of times, there’s still an infinite range or precision between that last 9 and the next whole number of 25.

That’s it. In the physical world, it seems that everything is an approximation, because actually being able to measure to infinite precision is impossible.