Last week I stumbled over Dimensional Analysis which is not only useful for applied fields (physics, biology, economics), but also for math (Why did no one tell me that you can almost always think of df/dx as having "the type of f"/"the type of x"? The fact that exponents always have to be unit-less etc.? It had never occurred to me to make this distinction. In my mind, f(x)=x went from the reals to the reals, just like <span>e^x</span> did.
One example of a question that before I would have had to think slowly about:
What is the type of the standard deviation of a distribution? What is the type of the z-score of a sample?
Answer
The standard deviation has the unit of the random variable X, while the z-score is unitless <span>z=frac{X-mu}{sigma}</span>
If you found the above interesting, I recommend reading (or skimming) [...]
First published:
May 21st, 2025
Source:
https://www.lesswrong.com/posts/jCDa9pwLRe69LcSdJ/units-have-more-depth-than-i-thought)
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Narrated by TYPE III AUDIO).
