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A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this idea occasionally for years without making any progress. When I finally got serious about it, I discovered Planck Units and that seemed to settle the issue.

Now my problem is that Planck Units are so small that they can't be used for "normal" things without huge exponents, most of these being very different depending on the quantity being measured. Solving human-scale equations with these units by computer would thus either be very inaccurate due to floating-point errors (for numbers that are even within range) or very slow due to the need for extended precision. They also go "up" but not "down", which renders almost half of the possibile signed floating-point values as useless.

I considered the idea of creating a new system by raising each Planck Unit with a standard exponent or multiplier, but I think this would bring some into an acceptable range but not others.

So what I want to know is whether a system of natural units exists that uses units that are appropriate for work with technology that humans can interact with, or can be made appropriate without introducing too many arbitrary elements.

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    $\begingroup$ What's wrong with meters, kilometers, and seconds? Or centimeters, grams, and seconds? Also, computers don't care - floating-point specifications mean all they care about is the number of significant figures, not the size of the exponent (unless your exponent is several hundred...). $\endgroup$
    – user10851
    Aug 29, 2013 at 18:07
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    $\begingroup$ I deleted a couple of more-or-less inappropriate comments. $\endgroup$
    – David Z
    Aug 29, 2013 at 23:40
  • $\begingroup$ Don't forget that base 10 is human based and therefore SI exponents like kilo, mega, femto are human based. You would have to make more universal exponents, maybe based on pi, e, 2, ... $\endgroup$
    – Cano64
    Apr 9, 2015 at 18:44

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The problem is that a system of units can be “natural” or it can be human-scale, but not both. As you’ve already seen with the Planck units, human scales are almost always much larger than the smallest meaningful value and much smaller than the largest meaningful value. (For example, the average human height of 1.6 m is $10^{34}$ times longer than the Planck length but $10^{26}$ times smaller than the diameter of the observable universe. I just grabbed the number from Wolfram Alpha, and of course the size and shape of the universe are still up for debate, but you get the idea.) Any system that works out to have nice numbers for human-sized quantities also necessarily has a high degree of arbitrariness.

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