I wrote earlier about the many different ways to measure distance. One way I didn’t include is **unmeasurable distance**.

Sometimes **A** is

- tastier,
- sexier,
- cooler,
- more interesting,
- or otherwise better endowed

than **B** … but it’s impossible to quantify by how much. No problem; just say that **A≻B** but that **|A−B|** is undefined.

It’s still the case that if **A** is sexier than **B** and **B** is sexier than **C**, it must follow that **A** is sexier than **C**.

Symbolically: **A≻B** & **B≻C **⇒** A≻C**.

This concept opens up many parts of **human experience** to the **mathematical imagination**.

I will also express my view on moral rates of **income tax** using **orderings ≻**.

Oh, and if you’re into this kind of thing: using orders **≻** instead of measurable quantities kind of saved the economic concept of “utility”. Kind of saved it. At least instead of talking about 174.27819 hedons, nowadays you can just say **X** is lexicographically preferred **≻ **to **Y**. Ordinal utility instead of cardinal utility.

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Tags: comparable, distance, economics, education, geometry, imagination, math, mathematics, maths, metric, metric spaces, metrics, norm, norms, philosophy, preference, preorder, rank, ranking, size, total order, unmeasurable distance, utility

This entry was posted on January 27, 2011 at 1:38 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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