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I am sorry this post is so late, I have been fairly busy and didn't get
back to my e-mail till today.
While following this thread I forwarded the e-mails to my resident
mathematician, statistician, and a friend that trades Natural Gas and
Crude. These are their comments, I am re-posting them as I suspect that it
might be of interest. It is a fascinating subject area, that unfortunately
(or perhaps fortunately) is beyond the capabilities of Trade Station.
It seems that we are using developed math theorems to track the market. But
the market is not like the physical world where all cause and effect events
are physically real even though their descriptions might use the abstract
realities of mathematics. The trick of doing this is the analogical
assignment of market variables to logical and digital representations in
advance math formulations that utilize unreal numerical values to track and
then probability forecast the behavior of real physical values. This is
the world of advanced math that physicist use in nuclear, genetical,
astronomical, etc. studies. I think the developers of Juno are doing this,
not with the market, but with net management.
Mathematically, dots and lines are unreal non-dimensional representations,
and scalars, vectors and tensors are unreal dimensional valued
representations. The positive number line is real and its mirrored twin is
imaginative; but both are abstract. Just as our world exist in the
universe, mathematical systems must be determinate to work for the
physicist. (Undeterminate mathematical systems can reveal the discoveries
of abstract realities but not of the physical world). For physical
realities require determinate number theory, for its values such as the
decimal vs. hexadecimal vs. binary systems.. Physical reality also requires
space fixation in a coordinate system such as used in various kinds of map
making. The two most common are Cartesian (x,y,z) and polar (angles,)
coordinate systems. Tensors are used to transfer from one coordinate
system to another and/or to merge one coordinate system into another.
Scalars quantify things like apples , vector size, etc. Vectors have
directional and directional change values.. Newton discovered calculus --
speed is a scalar and thus is fixed. A change in speed is a vector and at
an instant in time us also fixed ( accelerating or decelerating) A change
in acceleration is a derivative ( another vector) For example a turning
motorcycle has to be described in 4 dimensions of time, x-direction and y-
direction . If the cycle is doing jumps, its description requires a fifth
dimension of z-direction. The human person can only represent pictorially 3
dimensions, but the computer handles matrices of any dimension.
My statistician had this to say;
I guess people "get lost" in their abstract theory of reality which
deprives the theorist to use common sense to describe the practicality of
everyday events. IE; can't see the forest because the trees are blocking
the view! Just remember every probability model must include "room for
error", formally called "Confidence Intervals". For example, I'm 95%
confident that Clinton will not be impeached because such and such
variables are behaving in this manner. However, I'm also 5% confident that
Clinton will be impeached. Thus, I'm never wrong nor my statistical model
invalid!!! Every statistician must predict both opposite future events.
Another thing to remember is that Advanced math is really a guessing game
of estimates. For example a circle is an infinite set of straight tangent
lines that barely touch the surface of the circle. Likewise no matter how
curvy the line that is the description of the mathematical formula with all
of it's bumps and dips; a small enough interval can always be chosen that
converts it into a straight line within that interval.. Consequently the
slope-intercept linear equation taught in high school will accurately
describe that abstract doctorate theoretical model within that tiny
interval. Remember Y = MX + B where B is the y-intercept, but in this case
is in reality a numerical fudge factor to adjust the vertical position of
the line to more accurately describe the model it's a mirror image of.
Furthermore, B itself can be a value within a predetermined range of
numbers. So the fudge factor itself can also be fudged........all due to
the 95% confident probability model! The probability of all this is called
extrapolation where you graph past events then adjust a "linear fit" to the
small interval to predict future events. Notice that when the interval
changes, so does the behavior which forces one to start the "fitting
process all over again".
Another trader that trades hundreds of crude and natural gas contracts at a
time had this to say:
Isn't all this you are talking about really called "fuzzy logic"?
Determining a behavior (represented mathematically) based on
probabilities? I know that in my industry there is this concept of
VAR, or value at risk, and all it means is that within a confidence
level, with such and such position, the current market exposure is
"X". The problem or tweaking of the numbers, comes into play to
address issues not always adequately represented in the model, such as
liquidity, and the real chance that a 1 standard deviation move will
more likely result in a 2 or 3 standard deviation move...or better
yet, nonperformance of contracting parties...I get a newsletter called
Financial Engineering...I'll see if I can get you a copy and forward
it to you..
To which my mathematician had this to say;
Yes it is fuzzy logic by fuzzy wuzzy engineers but I think such must go on
to facilitate progress. IBM had several fuzzy projects before they
perfected virtual memories. This is too rich for most traders to apply but
not for others.
Happy trading,
John Hayden
http://sente.net
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