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I recently read this relatively old article, which argues that humans, along with most animals, have an innate intuition for logarithms, and tend to imagine numbers in a logarithmic, rather than linear way.

This seems to imply that children need to "un-learn" their intuition for logarithms when being taught standard base counting. So, my question is:

As an alternative to the linear "base-10" counting system, is there a numeral system capable of representing the real numbers on a logarithmic scale (possibly using different symbols), that may be more intuitive for humans to understand?

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    $\begingroup$ It's called a slide rule $\endgroup$ – steven gregory Jul 14 '17 at 13:53
  • $\begingroup$ @Zack, You had deleted an interesting question I had intended to answer. I'd rather you repost it than make my own repost. We can discuss it in SE chat in this gallery room. A mod or I will delete this comment for being off-topic soon. $\endgroup$ – Mark S. Oct 14 '17 at 13:22
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Interesting question. The article suggests that the logarithmic perception built into the nervous system is for the intensity of a stimulus. But the numbers we write down are for counting things - and they are usually small numbers.

When scientists need to grapple with numbers that cover a large range (near $0$ to very large) they use scientific notation, which is in effect logarithmic.

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Is the current system really "linear", though?

The length of a number (when written down) is actually approximatelly the logarithm (base $10$) of the number, which is why in a way, $10000$ is closer to $100000$ than it is to $100$...

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  • $\begingroup$ When I originally thought about this, I was considering a system where you would have individual symbols for powers of ten, and representing non-powers of ten would involve something equivalent to a radix (decimal) point. I would argue that base ten isn't really logarithmic, because counting numbers (as in 1, 2, 3, 4, etc) is linear. $\endgroup$ – ZKG Jul 14 '17 at 14:13
  • $\begingroup$ @Zack What you are considering is scientific notation, with some invented symbols. $\endgroup$ – Ethan Bolker Jul 14 '17 at 14:32

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