While reading a WayBack Machine archived Wikipedia article about probability density, I noticed that the article’s implied context was entirely in the world of mathematics (i.e. abstract logical objects) and not in the world of physical phenomena.

(Which is more fundamental: mathematics or physics?)

The Wikipedia article contained a passage which supports what is communicated in the yellow highlighted paragraph:

“In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample…”

I was thinking about how my next assignment should be to make a probability application which defines purely mathematics notions of probability for a beginner level’s audience (i.e. people in middle school up to community college level)

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