- #1
oldman
- 633
- 5
About the meaning of words like "is" and "are"
My dictionary defines them as "exist, be present", which is not nearly good enough for mathematics and physics. Perhaps folk here can clarify the meaning of such common words in such a context.
A musical note is usually not pure, in the sense that it is said to consist of a fundamental note and various harmonics. To some extent our ears can detect a note's composite nature, and we easily distinguish between the same note played on different instruments because they have different sets of harmonics.
Physics uses the logical language of mathematics to do this job quantitatively. For instance a "square wave" sound note may mathematically be Fourier-analysed into an infinite series of odd harmonics whose amplitudes diminish in proportion to the inverse of the odd numbers.
Alternatively, the "presence" of these harmonics may be demonstrated by listening to their "beats" with waves of frequencies close to these harmonics, when these are mixed with the square wave.
Now the question arises: do such harmonics "exist"? or "are" they simply artifacts of the way our sense of hearing processes sounds, and of the mathematical dialect we use to describe and analyse a square wave? "Is" not the reality just jerky alterations in the average speeds of air molecules? Or "is" a harmonic several things at the same time? because we can devise different descriptions of what "is"?
My dictionary defines them as "exist, be present", which is not nearly good enough for mathematics and physics. Perhaps folk here can clarify the meaning of such common words in such a context.
A musical note is usually not pure, in the sense that it is said to consist of a fundamental note and various harmonics. To some extent our ears can detect a note's composite nature, and we easily distinguish between the same note played on different instruments because they have different sets of harmonics.
Physics uses the logical language of mathematics to do this job quantitatively. For instance a "square wave" sound note may mathematically be Fourier-analysed into an infinite series of odd harmonics whose amplitudes diminish in proportion to the inverse of the odd numbers.
Alternatively, the "presence" of these harmonics may be demonstrated by listening to their "beats" with waves of frequencies close to these harmonics, when these are mixed with the square wave.
Now the question arises: do such harmonics "exist"? or "are" they simply artifacts of the way our sense of hearing processes sounds, and of the mathematical dialect we use to describe and analyse a square wave? "Is" not the reality just jerky alterations in the average speeds of air molecules? Or "is" a harmonic several things at the same time? because we can devise different descriptions of what "is"?