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0 pointsjacobolus2y ago0 comments

The logarithmic base for an angle is something like "degrees", "radians" or "turns".

This is analogous to the way a scalar logarithm can have a base of "octaves" (doublings), "decibels", or "powers of the golden ratio" (as found in the Zometool construction toy). Or pick your favorite other logarithmic system.

Both are "units" in a certain sense, but neither one is quite the same kind of "unit" as light years or foot–pounds or amperes.

> 1 meter divided by 2 meters is 0.5 as a number. But it is only 0.5 radians under (1ish) specific arrangements of those lengths in a particular metric space

Just as 1 meter straight ahead divided by 2 meters straight ahead is the unitless scalar number 0.5, we can likewise treat angles (i.e. rotations) as ratios: 1 meter straight ahead divided by 1 meter to the right has the unitless bivector-valued ratio i, oriented like the ground you are standing on. You can multiply this bivector by some other coplanar vector to rotate it a quarter turn. For example, you can multiply it by the vector «3 inches due North» to get the new vector «3 inches due West»; notice how the units do not change because our bivector i is unitless.

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Misdicorl2y ago

I understand your analogy, but I reject it's validity. Degrees/radians/turns map to meters/feet/angstrom. Decibels and octaves are true "number" multipliers. You could for instance talk about degrees in octaves or in dB if you like. It's just not particularly useful for the domain

Edit: another example difference. I can't measure an octave or dB. I can measure a degree

Edit2: we've reached reply limit but I concede you can measure a decibel. Point about dB degrees still stands though

jacobolusOP2y ago

You absolutely can measure an octave or decibel. It's just a relative quantity, in just the same way any quantification of orientation is relative.

(For example, you can measure an octave by marking out a particular fret on your guitar; it will make an octave change whichever particular note you start with.)

You can feel free to "reject" whatever you want. You'll just be wrong/confused. ;-) (But you'll be in good company. Most working engineers, scientists, and mathematicians don't have or need a particularly clear philosophical understanding of angles.)

Misdicorl2y ago

I think this will devolve at this point. But you should consider that you are perhaps far too confident in your position here. My last attempt is due you to consider what happens when you

A) multiply two degrees together

B) multiply two dBm values together

The output "units" in A change but do not in B. dB and angles are very different.

Edit: the units in B do change, but the dB part doesn't. Tired.

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0 pointsjacobolus2y ago0 comments

The logarithmic base for an angle is something like "degrees", "radians" or "turns".

Both are "units" in a certain sense, but neither one is quite the same kind of "unit" as light years or foot–pounds or amperes.

> 1 meter divided by 2 meters is 0.5 as a number. But it is only 0.5 radians under (1ish) specific arrangements of those lengths in a particular metric space

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Misdicorl2y ago

Edit: another example difference. I can't measure an octave or dB. I can measure a degree

Edit2: we've reached reply limit but I concede you can measure a decibel. Point about dB degrees still stands though

jacobolusOP2y ago

You absolutely can measure an octave or decibel. It's just a relative quantity, in just the same way any quantification of orientation is relative.

(For example, you can measure an octave by marking out a particular fret on your guitar; it will make an octave change whichever particular note you start with.)

Misdicorl2y ago

I think this will devolve at this point. But you should consider that you are perhaps far too confident in your position here. My last attempt is due you to consider what happens when you

A) multiply two degrees together

B) multiply two dBm values together

The output "units" in A change but do not in B. dB and angles are very different.

Edit: the units in B do change, but the dB part doesn't. Tired.

1 more reply

j / k navigate · click thread line to collapse