I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man? Is the number of linearly independent units a property of the nature, or can we use any number we like? If it truly is a property of nature, what is the number? -five? can we prove that there not is more?
In the answers please do not consider cgs units, as extensions really is needed to cover all phenomenon. - or atomic units where units only disappear out of convenience. - or SI units where e.g. the mole for substance amount is just as crazy as say some invented unit to measure amount of money.
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$^1$length, time, mass, electric charge, and temperature (or/and other linear independent units spanning the same space).$^1$length, time, mass, electric charge, and temperature (or/and other linearly independent units spanning the same space).