Dear Organlearners,
Glen <VoxDeis@aol.com> writes:
>I was reading some of the contributions and I noticed a concept
>on a few occasions. That concept was the idea of time being
>non-linear.
>
>How can a measurement instrument that is used as a "standard"
>be non-linear? I compare it to thinking in the standard of weight
>and attempting to formulate a construction where a kilo, or some
>other system of weight measurement, would be non-linear given
>the environmental variables are constant. Such measurement
>devices only have their value in the precise nature of creating
>ratios and standards which can be used and shared where all
>who then refer to the standard maintain a similar mental model.
>Wouldn't the concept of time lose the purpose it is then used for
>- -- the associated reference forwhich to measure the sequence of
>events.
Greetings Glen,
Your comment concerns a very important question: "Is linearity necessary
to standardise the measuring instrument for any physical quantity?" Please
notice that we assumed that what applies to all physical quanties will
apply to time also as one of them. It is very important to question this
assumption at some stage. I will not do it in this contribution.
When we standardise any measuring instrument for any physical
quantity, we have to meet the follwing two main requirements:
1. A unit for the quantity equal to a unique value of that quantity
called the international unit.
2. A scale of values of which each value can be expressed in terms of
the unit value in an regular fashion.
Historically, a linear, decimal scale of values was selected for each
physical quanity. Super-divisions (and sub-divisions in a like manner) of
the scale were standardised by the following scheme (regular fashion):
1=1
1=1, 1+1 = 2
(1=1)=1, 2+1 = 3
(1=1)=(1=1), 2+2=4
(1=1)=(1=1)=1, 2+2+1=5
(1=1=1=1=1)=1, 5+1=6
....7, 6, 9, 10, 11, ....
It is the same sheme as the one which we still use to determine the change
in a money transaction.
Now observe in this scheme that establishing any number of identical units
comes before combining them into different values. This "establishing of
any number of identical units" has nothing to do with linearity, but all
with categorical identity. The linearity arises when these (any number)
identical units are combined to form a value different form the unit
value. In the scheme above the combination is a linear one. But nothing
prevented us form making non-linear combinations. Here is such a scheme
(regular fashion):
1=1
1=1, 1+1 = 2
1=(1=1), 1+2 = 3
(1=1)=(1=1=1), 2+3=5
(1=1=1)=(1=1=1=1=1), 3+5=8
...., 13, 21, 34, ....
This scheme is better known as the Fibonacci series, already discovered
during the Middle Age. Successive Fibonnaci numbers often occurs in the
morphology of living entities. For example, the number of spirals of
flowers in any composite flower of any species in the family Compositae
are related to the Fibonacci numbers. The ratio of any Fibonacci number to
its preceding one approaches the golden number 1.618034... as the series
approach infinity. This golden number was already discovered by the
ancient Greeks. They used it carefully in the composition of most of their
artistic creations to give a very pleasing appearance.
Using a nonlinear scale for every possible physical quantity will come as
a shock to us who are used to linear scales. There is no doubt about it.
Ask any student in chemistry who have learnt to work with the pH scale
which measures the concentration of H3O+ acid in a non-linear manner.
Their first encounters with the pH scale usually ended up in confusion!
But even us, who are used to linear scales, accept the need for non-linear
scales without realising it! Prefixes such as mega=1000000, kilo=1000,
milli=.001 and micro=.000001 are nothing else than factors to transform
our originally linear scale to a non-linear one. Thus, for example, the
change from 2 meter to 3 meter differs very much from the change from 2
kilometer to 3 kilometer. It is important to observe in the previous
sentence the role of "change". We do not become aware of our need for a
non-linear scale until we compare changes (and not absolute values) with
each other.
>The measurement variable of time doesn't change however the
>cognitive strategy did. Whatever the process that one engages
>in, the standard of time remains constant. The "realitivity" or the
>cognitive/emotional introspection of personal experience can vary
>greatly...but does the linear nature of our construction of time?
Glen, I tried to illustrate above that even the construction of standard
time (which happened historically to be linear) is loaded with cognition.
I want to stress that we cannot escape our need for non-linear standard
time as soon as it involves time intervals (changes in time). For example,
when we work paleontologically (history of all kinds of life), we use time
intervals of MILLIONS of years. When we work anthropologically (history of
humankind) we use time intervals of THOUSANDS of years. When we work with
our own lives, we use time intervals of individual years which happens to
correspond to the linear scale based on the unit "year".
However, the time unit "year" has already introduced a non-linear scale
into time. The fundamental unit of time in the physical sciences is the
second. Have you ever tried to use the "second" consistently in a linear
fashion? If you do, then you will have to say "I will meet you seven two
zero zero seconds from now" rather than "I will meet you two hours from
now". And on your birthday you will have to say "My next birthday
anniversary will be three one five three six zero zero zero seconds from
now" rather than "My next birthday anniversary will be one year from now".
Let us carefully think about the question "Is linearity necessary to
standardise the measuring instrument for any physical quantity?" We have
determined that neither is linearity necessary, nor is it wise to insist
on linearity. So why did we ask the question at all? Again I want to
stress how important is the tacit knowledge of each of us to us. What
tacit knowledge made us articulate this question in the first place -- an
articulation which we have determined to be not appropiate? The way to
reach into our tacit knowledge (data mining they would say in KM), is to
ask question upon question related to our inappropiate question. For
example, "What property other than linearity is necessary to standardise
the measuring instrument for any physical quantity?" Or, "Is it not the
case that no property at all, including linearity, is necessary to
standardise the measuring instrument for any physical quantity?"
Look again at the two main requirements for standardisation. I have moved
them as far as possible to the front of this contribution. My strategy was
to let you recognise your tacit knowledge in their articulation without
any further questioning. Then I employed two schemes (regular fashions) to
show to you that both linear and non-linear scales can be constructed --
nothing to confront you with your tacit knowledge. But now I am
confronting you with your tacit knowledge by insisting that you have to
articulate it. What property have I refered to in these two requirements?
The property of REGULARITY!! So let us articulate our tacit knowledge
again with the question "Is regularity necessary to standardise the
measuring instrument for any physical quantity?"
I do not know about you learners, but I get the gooseflesh once again.
What is regularity? One dictionary writes that it means "the state,
quality, character or property of being regular". What is regular? The
same dictionary writes, among other things that it means "made according
to rule" or "acting orderly". It gives ten other synonymous meanings and
advises the reader to consult "system" for other synonyms. Going to
system, the dictionary writes that it means "orderly combination or
connection of parts into a whole" as well as giving eight other synonymous
meanings.
Have you noticed it? Within a few sentences we have landed from head to
heels into concepts like system, order, wholeness, fruitfulness
(connection), etc. To measure all values for any physical quantity, we
need a way (method, rule) to order all possible values of that quantity.
We call this emerging order of values the scale of measurement. It is not
linearity which is essential to measure in a standardised manner, but
regularity or order. However, I have stressed in many contributions that
order itself is not just "something which is out there". Order is
something which has to emerge from chaos. Since both chaos and order are
manifestations of entropy production, it shows once again how entropy
production (irreversibility) is essential to the measurement of any
physical quantity.
The measurement of the time as one of the phsyical quantities poses unique
problems. The reason is the intimate relationship between time and
entropy. The emminent cosmologist Sir Arthur Eddington described this
relationship as "entropy is the arrow of time". No other physical quantity
can serve as the arrow of time. Thus, if we want to learn about time
without learning about entropy we will not learn anything worthwhile about
time. This is why Prigogine dared to say that time is the almost forgotten
dimension of physics.
What do clocks, our instruments for measuring time, measure? The formal
answer is to say that they measure time. It is such an obvious answer that
we do not think a second time about it. But what does your tacit knowledge
say? Look at your wrist watch. We have learnt from other people that it
ticks second after second away. But is it what the watch is actually
doing? What regularity is actually operating here?
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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