Extrapolating Polynomials, for ABC's LOST!
CoreyWhite
we do a little numerology and add them all together we get 108. And
that is the time it takes on the show for the countdown to D-Day, on
the island. If they don't punch the numbers into the computer by then,
there is no hope. But we know the numbers must have a deeper mystry,
and I have found a pattern in them, by extrapolating a polynomial
function out of the numbers.
Here is the master equation
y = -0.225x^5 + 4.25*x^4 -29.375*x^3 + 91.75*x^2 -122.4*x + 60
Just plug in x, and it looks like this
x=1, y=4
x=2, y=8
x=3, y=15
x=4, y=16
x=5, y=23
x=6, y=42
next in the series
x=7 y=46
.. But after that part of the series, everything just starts going
negative! So it looks like whatever formula is creating this formula
isn't sustainable and will eventually self distruct after exactly 7
steps.
boson boss
Many years ago there was a special section of a magazine (sort of a new
year special) with super small letters of printed C code for solving
"which number comes next in line" kind of problems. I had some doubts,
nevermind not understanding the code. It was long and had to be typed
for a long time. Finally I took one actual problem with line of numbers
that was from another magazine. The problem seemed very very
impossible, like -22, 100, 35, -3, 0.125... It was invented for some
quiz with an award by a guy named approximately or not at all
Andrabindranat Pradhahmabadaganesh. In conclusion I didn't get the
result. The solution was inconvenient in the fact that there was a
simple manipulation with digits involved in computing the next number.
I can only guess that program could not estimate not even remotely
something so unpredictable.
CoreyWhite
To solve this problem we created the formula
f(y)=a(x^5)+b(x^4)+c(x^3)+d(x^2)+e(x)+f
Then we solved simotaneous equations with calculus for a,b,c,d,e,f
Using the points: (1,4) (2,8) (3,15) (4,16) (5,23) (6,42)
Impossilbe to do by hand, but even the free math software Octave can do
it. Which is what we used. And what is interesting about this formula
is as long as they are an ordered sequence spaced evenly appart, then
this prediction should be accuracte. The arangement in the order of
1,2,3,4,5,6 is arbitrary.
boson boss
Interesting but why would you think there exists such a differentiable
function with all those properties so that you can make a next in line
solution or whatever? I mean polynomials are interesting for all those
neat hand made procedures, dividing polynomials and such. Some nice
polynomial could be factorized to (x-a)(x-b)(x-c)()()()()()=0. But you
are looking for a, b, c... in maybe a function, maybe whole algorithm.
You would have to create whole formulas upon formulas without end! The
set to which this is mapped to is maybe not integer like your arbitrary
choice and the resulting set could be ordered and have that next
number. Then if all those formulas could be factorized you would have
the droplets of reality that had impact on each other. I just seem to
believe in auspicious factoring without particular ending.
CoreyWhite
We can do another example.
If we take the english alphabet, a-z. And then we are to order them
1-26, correct? Then if we create a code, and replace the english
alphabet with other characters we can find a map very directly using
this formula. But years ago I did another experiment, and I took the
entire bible, and replaced each character with representations of those
characters using 'leet speak. For example we take the letter e, and we
can replace it with either e, E, 3, or perhaps even another character.
So then the code became not only the alphabet, but it became all of the
'leet speak characters. So using this formula I was able to hide a
message inside of the bible. Because I created a 1 to 1 translation
using a polynomial function from 1-26, and a-z, and all of the leet
speak characters. So the leet speak translated back into my hidden
message, but you could still read it as the bible. This seems nearly
impossible, unless you have a computer figure it out in this way. But
it worked because there was a direct sequence to the leet speak
characters, and there is also a direct sequence to the english
alphabet. Extrapolating polynomials, automaticlly determined what
function would map both of those sequences, to both the bible and to my
hidden message.
Interesting yes?
CoreyWhite
I will show you a simple way to do it.
If we have a binary number, lets say it is 3, in binary it looks like:
11
Now if instead of actually using a 1 or a 0 in ascii to represent 1 and
0, we used the letters I and O, the number 3 in binary would look like:
II
But now instead of this, we were to write it in binary as: ii
or as: Ii
or as: iI
instead of just: II
Now because we are using uppercase to encode this, we have 4 other
numbers we represent, and we only have to decide if 0 or 1 is
represented by upper or lower case numbers.
Now we could take any binary number like 101010, and translate it to
ascii as IOIOIO
Now the question is because we know have 2 new options, for each of
these numbers, and not just one. What patter of 'leet speak, would
best represent the number of our choice?
Well it gets very complicated to do this if we have 2 specific numbers
we want to work with, or even if we have 2 very specific files, which
can be exceptionally long. And it also gets even more complicated if
we have more than just 1's and 0's, or if we have more options than
just I's and O's.
So we can have very sophisticated polynomial functions we are working
with. But the great thing about it is that we only need to take a
small sample of the alphabet to find the right code for the rest of the
alphabet so it is less work. If we were doing this with just abcdefg,
and we wanted to replace abcdefg, with another natural sequence like
gfedcba, that is a very simple function. But even if we give it just 2
points it an extrapolate the rest of the answer. So just solving
simotaneous equations for the points (a,g), and (d,d).. would give us
the whole entire alphabet in code.
It works great for many things. But not random numbers, like Pi, or
the lottery.
CoreyWhite
So what I am trying to say, is that on the TV television show LOST.
The way I have aranged the code of the numbers into a sequence, is only
a guess! 4 8 15 16 23 42, could be coded to other number that we don't
know yet, like 38383, 985873857, 327643874, 384738473, 753762,
92374374. But if we were even given just a small sample of those other
numbers we could extrapolate the entire solution. Because we have no
other numbers to work with, we just have to guess that they are a basic
sequence and go from 1-6, or from 10-16. But with some codes it is far
more complicated.
That's what I'm trying to say. And with the assumptions I am making,
this would be correct, provided it goes in a sequence.
CoreyWhite
extrapolate codes, and functions based on things like codes. If the
sequence 1-6 maps to the numbers from lost, or any other sequence like
20-26 even, then it will discover the code. But if the code were more
complicated and something else mapped to the numbers what I did
wouldn't extrapolate the answers. That's why I used the alphabet as an
example..
Just read about it on wikipedia:
Extrapolation
>From Wikipedia, the free encyclopedia
For the journal of speculative fiction, see Extrapolation (journal).
For the John McLaughlin album, see Extrapolation (album).
In mathematics, extrapolation is the process of constructing new data
points outside a discrete set of known data points. It is similar to
the process of interpolation, which constructs new points between known
points, but its results are often less meaningful, and are subject to
greater uncertainty.
Contents [hide]
1 Extrapolation methods
1.1 Linear extrapolation
1.2 Conic extrapolation
1.3 Polynomial extrapolation
2 Quality of extrapolation
3 Examples of extrapolation error
4 Extrapolation in the complex plane
5 References
6 See also
[edit] Extrapolation methods
[edit] Linear extrapolation
This means creating a tangent line at the end of the known data and
extending it beyond that limit. A linear extrapolation will only
provide good results when used to extend the graph of an approximately
linear function. A linear extrapolation can be done easily with a ruler
on a written graph or with a computer. An example is a trend line.
[edit] Conic extrapolation
A conic section can be created using five points near the end of the
known data. If the conic section created is an ellipse or circle, it
will curve back on itself. A parabolic or hyperbolic curve will not,
but may curve back relative to the X-axis. This type of extrapolation
could be done with a conic sections template on a written graph or with
a computer.
[edit] Polynomial extrapolation
A polynomial curve can be created through the entire known data or just
near the end. The resulting curve can then be extended beyond the end
of the known data. Polynomial extrapolation is typically done by means
of Lagrange interpolation or using Newton's method of finite
differences to create a Newton series that fits the data. The resulting
polynomial may be used to extrapolate the data.
[edit] Quality of extrapolation
Typically, the quality of a particular method of extrapolation is
limited by the assumptions about the function made by the method. If
the method assumes the data is smooth, then a non-smooth function will
be poorly extrapolated.
Even for proper assumptions about the function, the extrapolation can
diverge exponentially from the function. The classic example is
truncated power series representations of sin(x) and related
trigonometric functions. For instance, taking only data from near the x
= 0, we may estimate that the function behaves as sin(x) ~ x. In the
neighborhood of x = 0, this is an excellent estimate. Away from x = 0
however, the extrapolation moves arbitrarily away from the x-axis while
sin(x) remains in the interval [−1,1]. I.e., the error increases
without bound.
Taking more terms in the power series of sin(x) around x = 0 will
produce better agreement over a larger interval near x = 0, but will
still produce extrapolations that diverge away from the x-axis.
This divergence is a specific property of extrapolation methods and is
only circumvented when the functional forms assumed by the
extrapolation method (inadvertently or intentionally due to additional
information) accurately represent the nature of the function being
extrapolated. For particular problems, this additional information may
be available, but in the general case, it is impossible to satisfy all
possible function behaviors with a workably small set of potential
behaviors.
The extent to which an extrapolation is accurate is known as the
"prediction confidence interval," and is usually expressed as an upper
and lower boundary within which the prediction is expected to be
accurate 19 times out of 20 (a 95% confidence interval).
[edit] Examples of extrapolation error
An extrapolation's reliability is indicated by its prediction
confidence interval, which often diverges to impossible values.
Extrapolating beyond that range can lead to misleading results.
For example, the death rate from a new disease may increase
dramatically early on. If the graph of the death rate is then
extrapolated linearly, it might appear that the entire human population
will be dead from the disease in a short number of years. In reality,
the death rate from a newly discovered disease may fall as the
susceptible die off and the remainder alter their behavior to avoid
contracting the disease. Those who remain may also have a natural
immunity to the disease or an acquired immunity due to exposure.
Medical treatments affecting the spread and death rate of the disease
may be developed, as well. A simple linear extrapolation assumes that
there is an infinite population, and if the trend is growing faster
than the population it will predict that more will have died than have
ever been alive.
Similarly, if the amount of water in a lake is decreasing over time, a
linear extrapolation will predict that there will be a negative amount
of water shortly after the water is gone. This is an absurd result
which indicates that the extrapolation is being performed in the wrong
domain.
Selection of an improper domain, such as an infinite domain when all
possible values are finite, or a negative domain for nonnegative
values, is the second most common extrapolation error after failure to
include a prediction confidence interval. See also: logistic curve.
[edit] Extrapolation in the complex plane
In complex analysis, a problem of extrapolation may be converted into
an interpolation problem by the change of variable z ’ 1/z. This
transform exchanges the part of the complex plane inside the unit
circle with the part of the complex plane outside of the unit circle.
In particular, the compactification point at infinity is mapped to the
origin and vice versa. Care must be taken with this transform however,
since the original function may have had "features", for example poles
and other singularities, at infinity that were not evident from the
sampled data.
Another problem of extrapolation is loosely related to the problem of
analytic continuation, where (typically) a power series representation
of a function is expanded at one of its points of convergence to
produce a power series with a larger radius of convergence. In effect,
a set of data from a small region is used to extrapolate a function
onto a larger region.
Again, analytic continuation can be thwarted by function features that
were not evident from the initial data.
Also, one may use sequence transformations like Padé approximants and
Levin-type sequence transformations as extrapolation methods that lead
to a summation of power series that are divergent outside the original
radius of convergence. In this case, one often obtains rational
approximants.
Nyx
CoreyWhite wrote:
> The numbers on lost are 4 8 15 16 23 42 .. but what do they mean? If
> we do a little numerology and add them all together we get 108. And
> that is the time it takes on the show for the countdown to D-Day, on
> the island. If they don't punch the numbers into the computer by then,
> there is no hope. But we know the numbers must have a deeper mystry,
> and I have found a pattern in them, by extrapolating a polynomial
> function out of the numbers.
It's an ad, dork.
The UPC code 4815162342 had been assigned to the 8 oz. can of New Coke,
introduced on 4/23/1985 and discontinued on 8/16/1992.
Nyx
Bob
"Nyx" <wayn...@gmail.com> wrote in message
news:1166750404....@n67g2000cwd.googlegroups.com...
That's interesting since UPC codes are 12 digits ... the dork line is
gettin' longer and longer ...
Nyx
Actually the first or last ones are often zeroes and can be left out
when you use them.
Besides, you people are looking for secret polynomials in a number from
a bad tv show. It's probably the writers ex wife's phone number. It's
got enough numbers for that. Have you tried calling it?
Nyx
Troia
http://www.gullible.info/archive.php
-- Troia
Nyx
Troia wrote:
> >
> > That's interesting since UPC codes are 12 digits ... the dork line is
> > gettin' longer and longer ...
> >
> >
> Well, you know, the URL which the information came from might be a clue:
> http://www.gullible.info/archive.php
>
> -- Troia
Actually, the stuff on Gullible is true. That's just the domain name.
Also, gullible isn't a real word. It comes from a snake oil salesman
from the 19th century named Samuel L Gullible. It's still a registered
trademark and owned by his estate. That's why it's not in the
dictionary.
Nyx
CoreyWhite
I have unraveled the mistry of the numbers finally. Now with the new
component of 42, the numbers 4815162342 are making since. Because you
see 46 is the human component, as we all have 46 chromosones in our
DNA. The formula runs fine until we reach that critical stage in the
development of the universe. After that the function shows us that we
are sure to destroy ourselves. But you can only really understand this
by studying the unit circle in mathematics.
If you multiply 4815162342 by 100, then it fits perfectly on the unit
circle. In fact it is 1337545095 revolutions around the circle. So
when you sin that number, and then arcsin it, you always get exactly 0
degrees. And when you sin the new number is discovered, 4815162342-46,
it automatically takes you back to 46 degrees, regardless of if you
sin, cos, or tan the number, and then do the functions inverse.
This leads me to believe that we can be sure there is one more number
in the Lost TV show to be found, and it is likely 46. Because the
universe is fine in the natural state of existing as a perfect circle,
but when you brake away from the circle, in any direction, there can be
only disaster it would seem. That's what I am pondering now.
But it is a good magic trick. You can tell anyone to just write a
number they are thinking of after the numbers from lost. And if the
sin it and then sin-1 it, it takes them right back to their number.
(At least as long as it is a 2 digit number). Anything greater than
that brakes my calculator.
Troia
> Troia wrote:
>
>>> That's interesting since UPC codes are 12 digits ... the dork line is
>>> gettin' longer and longer ...
>>>
>>>
>> Well, you know, the URL which the information came from might be a clue:
>> http://www.gullible.info/archive.php
> Actually, the stuff on Gullible is true. That's just the domain name.
>
> Also, gullible isn't a real word. It comes from a snake oil salesman
> from the 19th century named Samuel L Gullible. It's still a registered
> trademark and owned by his estate. That's why it's not in the
> dictionary.
>
> Nyx
>
Heh.
I read it on the internet, though, so surely it must be so!
-- Troia
mcv
>
> Here is the master equation
>
> y = -0.225x^5 + 4.25*x^4 -29.375*x^3 + 91.75*x^2 -122.4*x + 60
>
> Just plug in x, and it looks like this
>
> x=1, y=4
> x=2, y=8
> x=3, y=15
> x=4, y=16
> x=5, y=23
> x=6, y=42
>
> next in the series
>
> x=7 y=46
>
> .. But after that part of the series, everything just starts going
> negative! So it looks like whatever formula is creating this formula
> isn't sustainable and will eventually self distruct after exactly 7
> steps.
You can always make a more complex polynomial that fits the numbers
but stays positive for a longer time.
Any function can be simulated by a suitablly complex polynomial. It's
just that they get really big and complex really fast.
mcv.
--
Science is not the be-all and end-all of human existence. It's a tool.
A very powerful tool, but not the only tool. And if only that which
could be verified scientifically was considered real, then nearly all
of human experience would be not-real. -- Zachriel
boson boss
Do you think that 1 to 1 is the reason why mind acts as a background
screen or coordinate system? Is it the most basic form or coordinate
mind? It doesn't have to be 1 to 1. Consider that the next in line
could depend from the previous ones. Sometimes just pressing equal has
no final ending. Can a one dimensional array encode something more than
1 to 1?
> message, but you could still read it as the bible. This seems nearly
> impossible, unless you have a computer figure it out in this way. But
> it worked because there was a direct sequence to the leet speak
> characters, and there is also a direct sequence to the english
I think that leet isn't that strict to copy characters as much as to
portray them like ascii art which can go into pattern recognition
issue.
> alphabet. Extrapolating polynomials, automaticlly determined what
> function would map both of those sequences, to both the bible and to my
> hidden message.
>
> Interesting yes?
Yup.