Replying to LO23899 --
Dear Organlearners,
Fred Nickols <nickols@worldnet.att.net> writes:
>By stating the obvious (i.e., pointing out that the symbol
>has a small end and a large end -- something that would
>elude only an innumerate like me) I have a hunch I will be
>able to pick up speed from now on.
Greetings Fred,
I eluded me also for a couple of years. This was one of the reasons why I
myself feared working with the < or >. I had to make out from the text
whether < meant "is maller than" or "is larger than". But in most cases I
the context was new to me so that it took me a lot of time to figure it
out. Then one day I realised my fallacy -- do not try to use the unknown
(context) to explain the unknown (<). Find something in the symbol "<"
itself to suggest what it means.
>>I will continue the "painting rich picture" in a following one.
>>Perhaps you can already intuitively see where I am steering
>>to. Is it
>> /_\E = 0
>> /_\S > 0
>>
>>Who cares to paint too?
>
>I don't know what you're getting at, At, but I'll give it a shot.
>
> /_\E = 0
> /_\S > 0
> /_\S > /_\E
> /_\E < /_\S
> 0 < /_\S
>
>Hmm. Doesn't look like "painting" to me. Looks more like
>childish scribbling. I have no idea what the symbols represent;
>all I've done is shove them around by applying a few rudimentary
>rules.
Fred, my granddaughter Jessica drew last year (her first year in school)
once again a picture of me. But, rather unusual, she made me promise that
I will not show it to anybody else. So I promised. I am now partially
breaking that promise. She drew me with a flower coming out of my ear. So
I asked her what it meant. She said: "Oupa, you listen also and not only
look." There was nothing wrong with it -- she could not have given me a
better gift.
The two lines
> /_\S > /_\E
> /_\E < /_\S
is like a flower coming from the ear. It is mathematically
as sound as can be.
Let us write
3 appels > 2 pumpkins
It is sound as can be when we think of the NUMERICAL FORM involved.
It is somewhat daring to do so when it involves the masses of the 3 apples
and the 2 pumpkins. Farmers can grow very large pumpkins.
One of the "biggest secrets" in science is that when a symbol expresses a
physical quantity like E for energy or S for entropy, it expresses the
VALUE of that quantity. The VALUE is made up by two things -- the
MAGNITUDE (which is a number) and the UNIT (which is a unique value) Thus,
when we have to give E a value
E = 7
will not do. The seven is only the magnitude. Where is the unit which will
relativise the value? Thus it has to be an expression like
E = 7 joule
The two energy values "7 joule" and "7 erg" have exactly the
same magnitude. But we cannot, for this reason, write
7 joule = 7 erg
Why? The unit "joule" is 10 milllion times as large as the unit
"erg". Knowing this, we have to write
7 joule > 7 erg
A "joule" is a million times as large as the unit "microjoule".
Thus we may also write
7 microjoule > 7 erg
But since the factor of difference between them is now only
10, we may also write
7 microjoule = 70 erg
We were able to play with the "<" and "=" relationships on
the units joule, microjoule and erg BECAUSE they are ALL
units of energy.
When we write something like
3 meter = 3 kilogram
we compare 3 meter (a value of length) with 3 kilogram (a
value of mass). In the case of
3 meter < 2 second
we compare 3 meter (a value of length) with 2 second (a
value of time). By seeing the units in each of these
relations, we are able to question the phsyical sense of
such a comparison. Such comparisons will make physical
sense only when we have a FUNCTIONALISED apparatus
or TESTED theory to compare the two sides.
For
3 meter = 3 kilogram
we have at present neither an apparatus nor a theory to help
us making physical sense of the relationship. But for
3 meter < 2 second
we now have Einstein's TESTED theory of relativity. Time can
be thought of as the fourth dimension of space-time. Thus we
can transform 2 seconds into distance by using the velocity
of light -- 3 billion meters per second. Thus the order relation
3 meter < 2 second
can be written as
3 meter < 6 billion meter
which has sense. This is why astronomists use a "light year"
(the distance travelled by light in one year) to measure
distances in the galaxy.
When we want to compare energy E and entropy S with each other, we must
also first take their units into consideration. However, NOTHING IN BOTH
THE SYMBOLS FOR energy AND entropy TELLS US ABOUT THEIR UNITS. In fact,
this is TRUE of the symbols of ALL PHYSICAL quantities. In other words,
the units of the quantities are TACITLY implied in the symbols. Since you
do not know about this TACIT knowledge involved, you do not know that the
units of energy and entropy are from different dimensions. Thus you do not
know that they cannot be compared by a functionalised apparatus.
Fred, I find it most extraordinary that you who, of all fellow learners,
come back time and again to TACIT knowledge, have now to be confronted
about this TACIT dimension of symbolised physical quantities. Is it not
most exciting! I myself began investigating this TACIT dimension of
symbolised physical quantities in 1969. The more I uncovered the more my
peers said "You are wasting your time and our time". What a funny world we
live in. Today more and more thinkers begin to take notice of the tacit
dimension of knowledge. Perhaps more people are now wasting their time ;-)
It is indeed possible to relate energy E with entropy S for any system by
a TESTED theory. That theory is the brilliant master piece of J W Gibbs
and involves the concept of the "free energy F" of the system.
Wow, I like your becoming. I wish you are my student. We are not so very
far off to see how Ilya Prigogine managed to explicate the irreversible
increase /_\S in the entropy of a system in terms of tension-flow pairs
for discrete changes, or force-flux pairs for continuous changes. Keep
track of this topic and I hope to lead you right into it.
With care and best wishes
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
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