From: smullins@cidmac.ecn.purdue.edu (Scott H Mullins)
Subject: Re: The Holden number
Organization: Purdue University Engineering Computer Network
Date: Mon, 6 Apr 1992 15:19:37 GMT

In article <4402@sheol.UUCP> throopw@sheol.UUCP (Wayne Throop) writes:
>Scott H Mullins has been asking about the derivation of the formula
>for the infamous Holden Number:
>
>> smullins@cidmac.ecn.purdue.edu (Scott H Mullins)
>> Message-ID: <1992Mar26.142843.26018@noose.ecn.purdue.edu>
>> It looks to me like you just made
>> this up off the top of your head. Why is the 2/3 power significant? 
>
>> smullins@cidmac.ecn.purdue.edu (Scott H Mullins)
>> Message-ID: <1992Mar30.222851.10369@noose.ecn.purdue.edu>
>> I will ask again: Where did the 2/3 power come from? I think you made this
>> up to match your own assertions.
>
>It turns out that Ted actually more-or less answered this in the "still
>waiting for answers" thread.  Here's an excerpt from what Ted has to
>say:

My &$%!#! news reader keeps throwing away bushels of posts every weekend.
I do not usually get a chance to read it over the weekend and by the time
Monday rolls around a lot of good ones are gone. That is my problem to deal
with and I apologize if I have posted in error due to this difficulty.

On with this show...

>> news@fedfil.UUCP (news) (Ted Holden)
>> Message-ID: <2696@fedfil.UUCP>
>>>  I don't understand, could you clarify this for me please?
>> You lose power-to-weight ratio as you get bigger...  weight goes up in 
>> proportion to volume, which is a cubed figure.  Strength and every other 
>> measure of efficiency go up only in proportion to various squared figures.
>> Strength in particular is proportional to cross-section of bones and muscles.
>> Two-thirds power of body weight is a kind of a general average of body
>> cross-section, and for this reason is the natural scaling factor for lifting
>> events.  

The 2/3 scaling rule only applies to similar structures. In other words the
flat-iron building can not be scaled up to the size of the Sear's tower
but this does not prove that the Sear's tower can not be built.

Actually Wayne explains this idea much more effectively than I can, so I
will leave his words intact.

>Ted doesn't mention it explicitly, but volume (assuming constant
>density) is proportional to mass, which in turn (assuming constant
>gravitational acceleration) is proportional to weight.  Thus, the
>two-thirds power is simply the square-cube scaling factor.  The units of
>the Holden Number (far from being "dimensionless" as Ted has incorrectly
>claimed several times in the past), are therefore force over area. 
>
>What Ted absolutely refuses to believe (but which is nevertheless the
>case) is that square-cube scaling of the simple sort he is doing only
>applies to animals of uniform density and shape.  Since human
>weightlifters (all being human) are indeed very roughly all the same
>density and shape, the square-cube scaling factor applies to them quite
>well. 
>
>The problem is that Ted claims this "generalized cross section"
>nonsense, which is demonstrably not true.  His calculation of "about 27"
>as the Holden Limit is flawed, because he doesn't take account of
>quadruped vs biped differences, limb leverage differences, and the
>inaccuracy of the "squat" weightlifting events as a model. 
>
>These things have all been pointed out to Ted for more than four years,
>and he has yet to understand and agree to these simple facts.  I don't
>expect him to start now. 

Well, in my naivete I had assumed that this was a novel argument by the great
Holdenator. I was therefore trying to guide him to the fact that his
"Holden number" is completely meaningless. I suffer extreme humiliation and
embarrassment in the face of being shown that the arguments have been made
before and are already being ignored by HTE (His Totalitarian Exchequier?).

>
>PS: Recently, Ted claimed that Ultrasaurus' weight by volume
>measurements was 360000 lbs, and that the weight given in the Guiness
>Book of Records was (probably) from footprint depths, and thus
>underestimated because of his also-infamous lessened Felt Effect of
>Gravity.  Thus, the lighter weight measured by the GBR (of 100-140 tons)
>is what accounts for the Ultrasaurus' existance.  Ted apparently didn't
>do his arithmetic: this has the Ultrasaurus, even in Ted's Antedeluvian
>Wonderland, having a Holden Number somewhere between 40 and 55. 
>
>This is not too surprising.  The last time Ted proposed this solution
>to the discrepency of his weights to forces derived from track
>depths and the like, he didn't do his arithmetic about the volume
>of the Seismosaurus, confusing diplodocids and brachiosaurids
>as he is wont to do.
>--
>Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw

Thanks for taking this off my hands Wayne. I was just getting started in 
checking the weights of animals to see if there is a violation of the
mythical number. Wait! did I just say that the "Holden number" is a myth!?
That must mean it is true! :-)

Again, pardon me for thinking that HTE would respond to a factual
argument.

Scott