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Post by hydrophilic on Jan 13, 2016 5:49:28 GMT
This is mainly a fun question for physics professors!! (God knows I wish I were still in college to drop this bomb on them...) If you are smart enough (dumb enough) to employ dimensional analysis, then you might conclude this question is complete Boulderdash. However, I am serious... what is the answer? There is an answer inside SAM. I don't know what his answer means... hence this post for discussion! |
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Post by gsteemso on Jan 13, 2016 13:48:54 GMT
Writing out the problem gives you {0.0096 s – (2200 s^–1)}. The units are of differing powers and thus algebraically immiscible. Of course common sense would tell us that by inspection, but now it’s presented formally! Woo.
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Post by nonefornow on Jan 14, 2016 1:19:53 GMT
The question as posed cannot really be answered only with physics nor algebra, but also it requires a logical (philosophical) element.
Given that 1Hz is defined as a cycle per second 2.2 kHz are equal to 2,200,000 milliseconds.
Subtracted by 9.6 milliseconds gives (2,199,990.40).
These concepts are vastly used in alchemy for studying transformation of matter. In particular the above may become helpful in determining the chromatic characteristics of the Thuringian Rose, which is not a chemical color but alchemical.
Sadly such color is missing in the c128 palette.
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Post by hydrophilic on Jan 14, 2016 23:52:20 GMT
I agree, gsteemso, the algebraic units are immiscible... but SAM does this calculation anyway (and many more like it), and gets good results. Wow, nonefornow, you really through me for a loop! I guess I need to research the chromatic properties of Thuringian Rose... but I agree it is missing from the C128 palette  My theory is SAM is using a simple short-cut... to avoid a more complex algebraic equation. SAM's computation works well over a vast range of variables, but I am still baffled as to its meaning... all I know for sure is the result is a time period (milliseconds, etc.) which eventually is realized as wavelength (1/frequency). |
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Post by gsteemso on Jan 16, 2016 17:04:13 GMT
Given that 1Hz is defined as a cycle per second 2.2 kHz are equal to 2,200,000 milliseconds.
Subtracted by 9.6 milliseconds gives (2,199,990.40). Uh… Say what? That doesn’t even pretend to make sense. 2.2 kHz is equal to (2200 cycles) divided by (1 second), which is a fraction with the seconds on the bottom. 9.6 ms is equal to (9.6 seconds) divided by (1000), which is a fraction with the seconds on the top. It should be obvious even to an upper-grade elementary school student that you can’t do any addition or subtraction between such incompatible fractions. |
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Post by nonefornow on Jan 18, 2016 2:33:50 GMT
Uh… Say what? That doesn’t even pretend to make sense. 2.2 kHz is equal to (2200 cycles) divided by (1 second), which is a fraction with the seconds on the bottom. Say that!! Because you are applying the generally accepted notion of Hz frequency. Instead think of a process performed in sequential terms philosophically. 1Hz = 1 cycle = 1 second.; Then 2Hz = 2 cycles = 2seconds. Thus 2200 Hz = 2200 cycles = 2200 seconds. 2200 seconds = 2,200,000 milliseconds. 9.6 ms is equal to (9.6 seconds) divided by (1000), which is a fraction with the seconds on the top. It should be obvious even to an upper-grade elementary school student that you can’t do any addition or subtraction between such incompatible fractions.
Hence the solution is not in algebra The logical solution is to make the 2 fractions compatible.
Alchemy is the notion that defines an inexplicable or mysterious transformation.
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Post by gsteemso on Jan 18, 2016 20:30:47 GMT
Because you are applying the generally accepted notion of Hz frequency. Yeeees, that would be because that is how it is DEFINED. There is no other meaning. By this reasoning, driving to the corner store always takes 30 hours (50 in metric-using countries), and going somewhere on a freeway always takes at least 60 hours. Call me old-fashioned if you like, but somehow I just can’t buy that one. …You are saying you want to want to make two fractions compatible, but not mathematically? (Algebra involves variables. Pretty sure this stuff is plain old arithmetic.) Good luck with that one! Well, I think you’re on the right track to match that definition. I can’t figure out how your proposed method seems internally consistent to you. |
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Post by 8bitheaven on Jan 19, 2016 18:20:55 GMT
Assuming the 9.6ms is the period of a frequency Then convert the 2.2KHz to its period. The period of 2.2kHz is 1/2200= .4545454545ms.
Therefor 9.6ms-.4545454545ms=9.145454545ms
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Post by hydrophilic on Jan 21, 2016 1:06:38 GMT
Good answer, 8bitheaven! I like to think *conceptually* that is what happens inside SAM. But in *reality*, SAM literally calculates X milliseconds - Y Hertz = Q milliseconds. It is just plain wrong from pure physics (dimensional analysis)... yet it works quite well  |
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