[time-nuts] SI Unit Problems

Max Robinson max at maxsmusicplace.com
Wed Apr 6 00:52:57 UTC 2011 

I used to tell my students upon the introduction of angular frequency that 
if the math of AC analysis had come along a little earlier that our radio 
dials would be calibrated in radians per second instead of cycles per second 
(Hz).

Regards.

Max.  K 4 O D S.

Email: max at maxsmusicplace.com

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----- Original Message ----- 
From: "Brooke Clarke" <brooke at pacific.net>
To: "Discussion of precise time and frequency measurement" 
<time-nuts at febo.com>
Sent: Tuesday, April 05, 2011 12:39 PM
Subject: Re: [time-nuts] SI Unit Problems


> Hi Arnold:
>
> The web site contains a lot of unit related computations, see:
> http://futureboy.us/fsp/frink.fsp
> and it's author has spent quite a lot of time in understanding units.
> In school when I learned this it was called dimensional analysis.
>
> Here is the section dealing with Hertz:
> -----------------------------------
>
> hertz :=               s^-1        // frequency
> Hz :=                  hertz
> //
> // Alan's Editorializing:  Here is YET ANOTHER place where the SI made a
> // really stupid definition.  Let's follow their chain of definitions, 
> shall
> // we, and see how it leads to absolutely ridiculous results.
>
> // The Hz is currently defined simply as inverse seconds. (1/s).
> //  See: http://physics.nist.gov/cuu/Units/units.html
> //
> // The base unit of frequency in the SI *used* to be "cycles per second".
> // This was fine and good.  However, in 1960, the BIPM made the
> // change to make the made the fundamental unit of frequency to
> // be "Hz" which they defined as inverse seconds (without qualification.)
> //
> // Then, in 1974, they changed the radian from its own base unit in the SI
> // to be a dimensionless number, which it indeed is (it's a length divided 
> by
> // a length.)  That change was correct and good in itself.
> //
> // However, the definition of the Hz was *not* corrected at the same
> // time that the radian was changed.  Thus, we have the conflicting SI
> // definition of the radian as the dimensionless number 1 (without
> // qualification) and Hz as 1/s.  (Without qualification.)
> //
> // This means that, if you follow the rules of the SI,
> // 1 Hz = 1/s = 1 radian/s which is simply inconsistent and violates basic
> // ideas of sinusoidal motion, and is simply a stupid definition.
> // The entire rest of the world, up until that point, knew that 1 Hz needs 
> to
> // be equal to *2 pi* radians/s or be changed to mean *cycles/second* for
> // these to be reconcilable.  If you use "Hz" to mean cycles/second, say,
> // in sinusoidal motion, as the world has done for a century, know that 
> the SI
> // made all your calculations wrong.  A couple of times, in different 
> ways.
> //
> // This gives the wonderful situation that the SI's Hz-vs-radian/s 
> definitions
> // have meant completely different things in the timeperiods:
> //
> // * pre-1960
> // * 1960 to 1974
> // * post-1974
> //
> //
> // Thus, anyone trying to mix the SI definitions for Hz and angular
> // frequencies (e.g. radians/s) will get utterly wrong answers that don't
> // match basic mathematical reality, nor match any way that Hz was ever 
> used
> // for describing, say, sinusoidal motion.
> //
> // Beware the SI's broken definition
> // of Hz.  You should treat the radian as being correct, as a fundamental
> // dimensionless property of the universe that falls out of pure math like
> // the Taylor series for sin[x], and you should treat the Hz as being a
> // fundamental property of incompetence by committee.
> //
> // One could consider the CGPM in 1960 to have made the original mistake,
> // re-defining Hz in a way that did not reflect its meaning up to that 
> point,
> // or the CGPM in 1974 to have made the absolutely huge mistake that made
> // the whole system inconsistent and wrong, and clearly broke the 
> definition
> // of Hz-vs-radian/s used everywhere in the world, turning it into a 
> broken,
> // self-contradictory mess that it is now.
> //
> // Either way, if I ever develop a time machine, I'm going to go back and
> // knock both groups' heads together.  At a frequency of about 1 Hz.  Or
> // better yet, strap them to a wheel and tell them I'm going to spin one 
> group
> // at a frequency of 1 Hz, and the other at 1 radian/s and let them try to
> // figure out which one of those stupid inconsistent definitions means 
> what.
> // Hint:  It'll depend on which time period I do it in, I guess, thanks to
> // their useless inconsistent definition changes.
> //
> // It's as if this bunch of geniuses took a well-understood term like 
> "day"
> // and redefined it to mean "60 minutes".  It simply breaks every 
> historical
> // use, and present use, and just causes confusion and a blatant source of
> // error.
> //
> // In summary:  Frink grudgingly follows the SI's ridiculous, broken 
> definition
> // of "Hz".  You should not use "Hz".  The SI's definition of Hz should be
> // considered harmful and broken.  Instead, if you're talking about 
> circular
> // or sinusoidal motion, use terms like "cycles/sec" "revolutions/s",
> // "rpm", "circle/min", etc. and Frink will do the right thing because it
> // doesn't involve the stupid SI definition that doesn't match what any
> // human knows about sinusoidal motion.  Use of "Hz" will cause 
> communication
> // problems, errors, and make one party or another look insane in the eyes
> ----------------------------------------
> // of the other.
>
>
> Have Fun,
>
> Brooke Clarke
> http://www.PRC68.com
>
>
> Arnold Tibus wrote:
>> I don't understand what is wrong with 'Hz'.
>> As Time in seconds is a SI unit, Frequency is the reciprocal value of
>> time, f=1/T, Frequency is not a SI base unit but a SI coherent derived
>> unit (in the list with special names and symbols as force, pressure,
>> charge, power, resistance etc.). [11th CGPM, Resolution 12]
>>
>> So Frequency is defined as the measure of the number of occurrences of a
>> repeating event per unit time. To calculate the frequency, the number of
>> occurrences of the event within a fixed time interval are counted, and
>> then it's divided by the length of the time interval.
>>
>> NIST wording: "The rotational frequency n of a rotating body is defined
>> to be the number of revolutions it makes in a time interval divided by
>> that time interval [4: ISO 80000-3]. The SI unit of this quantity is
>> thus the reciprocal second (s-1)".
>>
>> But perhaps I misunderstand your position, could you give an explanation?
>>
>> Arnold
>>
>> Am 05.04.2011 17:54, schrieb Brooke Clarke:
>>
>>> Hi Jim:
>>>
>>> But what you show violates the SI rules, even though it's the correct
>>> calculation.
>>>
>>> Have Fun,
>>>
>>> Brooke Clarke
>>> http://www.PRC68.com
>>>
>>>
>>> Jim Lux wrote:
>>>
>>>> On 4/5/11 8:25 AM, Brooke Clarke wrote:
>>>>
>>>>> Hi:
>>>>>
>>>>> Just reading at:
>>>>> http://futureboy.us/frinkdata/units.txt
>>>>>
>>>>> First about the candela and all it's problems, then what's a Time Nut
>>>>> issue  "Hz ".
>>>>>
>>>>> // This means that, if you follow the rules of the SI,
>>>>> // 1 Hz = 1/s = 1 radian/s which is simply inconsistent and violates
>>>>> basic
>>>>> // ideas of sinusoidal motion, and is simply a stupid definition.
>>>>>
>>>>>
>>>> actually 1/s (= Hz) = 2*pi rad/sec
>>>>
>>>> BTW, if anyone is confused, I have a handy direct reading graph
>>>> published by HP a few decades ago to assist engineers in converting
>>>> from cycles per second to Hertz.  I'll see if I can scan it and attach
>>>> it later.  I know I really should have mentioned this last Friday.
>>>>
>>>>
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