[time-nuts] SI Unit Problems

Brooke Clarke brooke at pacific.net
Tue Apr 5 17:39:34 UTC 2011


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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