Human height can never be exactly π feet tall, as π is an irrational number and measurements cannot achieve infinite precision. Current scientific models treat reality as a continuum, making accurate predictions without evidence for a fundamental "base unit" of length, such as the Planck length. The prevailing understanding is that all measurements yield rational numbers, reinforcing the idea that there is no universally accepted smallest length. Thus, the notion of a base unit remains speculative and unsupported by empirical evidence.
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Does this mean that the most commonly believed theory of the smallest length is that Planck length is not truly the basic unit? There is no base unit is the most popular belief?PeterDonis said:The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.
Whether this means reality itself has a fundamental "base unit" of length (such as the Planck length) rather than being an actual continuum is a question we have no way of really answering at this point. The best we can do is to say that so far, all of our scientific models treat reality as a continuum and those models make accurate predictions. In other words, we have no evidence for the existence of any "base unit".
batmelon said:Does this mean that the most commonly believed theory of the smallest length is that Planck length is not truly the basic unit?
batmelon said:There is no base unit is the most popular belief?
No. Pi is a very specific value and infinitely beyond our ability to measure anything as vague as human height so precisely.batmelon said:Summary: Are we ever π feet tall?
The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.