> The Rule : Every Structure requires a foundation.
>
> The Equations.
>
> Introduction
>
> Let us assume then that we have limited our recording capaity using
> quantum computers and three new units have come into being. These
> units are almost already into being and at current our technology
> supports down to approx 3 Atoms per bit, or .333 bits per atom.
>
> These units are - Bits/Atom Digit/Atom and Symbol/Atom
>
> This means Bits per Atom, Digits per Atom and Symbol Per Atom. You
> see, just like our MP3 files which record music at 197Kilobits per
> Second, we must not forget that the MP3 file also has a mass.
> According to my Hard drive on a clunkier technology which weighs .6kg
> ang contains 2781197205504 bits a bit has a mass of 2.15 X
> 10^(-13)kgs.
>
> As an architect, I am accustomed to the fact that my ruler, i.e. the
> thing I am measuring with has a mass. If we were to count seconds with
> a machine, we would also require a certain mass in order to keep
> count, just like our ancient abacus beads.
>
> The Equation.
>
> Eternity = Mass(universe) / Mass (Unit of record or the SI unit)
>
> If quantum computers manages to utilise the atom, as a unitary
> recording device, where 1 bit, digit or symbol can be stored using a
> single atom. The total number of bits that can be used for any number.
> Which also means the total number of seconds countable
>
> Eternity = Mass(universe) / Mass(Unit of record or the SI unit)
>
> Eternity = 1.59486 × 10^(55) kg / 1.660538782(83)×10(-27)kg
>
> Even if in the most effient of number representation such as. . .
>
> 9^9^9^9^9^9^9^9^9^9^9^9^9^9 etc etc. . .
>
> And after that, we could resort to other symbols which gave meaning to
> numbers for example Where k=1000
>
> K^K^K^K^K^K^K^K^K^K^K^K^K^K etc etc. . .
>
> However there is a problem with this which I will provide in a
> following Example. You see, once you run out of numbers, you run out
> of numbers of
> symbols. Beyond this, whatever it was that was recording will have
> lost mathematical meaning. You will find examples of this after the
> following questions.
>
> First then I will ask some very easy High School difficulty questions,
> and then I will provide examples. I have complied some short
> Questions, which are not too difficult to answer. The questions regard
> the concept of Eternity, where Eternity is not the stuff of the bible,
> but rather the stuff defined as a limit of count. (it is important to
> understand this definition before making any sense of the above.)
>
> Question 1A. Difficulty Level (low)
>
> What is the maximum recordable ammount of seconds in a 12 Atom
> universe, where
>
> Eternity = mass(universe) / mass(unit of record)
>
> Mass of Atom = 1.6 x 10^(-27)kg
>
> Recording unit = 1 digit / atom
>
> Question 1B.
> How many times more than the mass of the 12 Atom universe was your
> answer to the last question, if one of your digits was measured to be
> 2.15 X 10^(-13)kg ?
>
> (2.15 X 10^(-13)kg is the approx average mass of a digit on my
> computer's hard disk where I aquired this mass by
>
> 1. Measuring the weight of my hard drive
> 2. Dividing this mass by number of available bits on the Hard drive.
> 3. Multiplying by number bits required of the digits.
>
> ---------
>
> Question 2. Difficulty Level (low)
>
> What is the maximum recordable ammount of seconds in a 12 atom
> universe, where
>
> Eternity = mass(universe) / mass(unit of record)
>
> Mass of Atom = 1.6 x 10^(-27)kg
>
> Recording unit = 1 bit / atom.
>
> (just to clarify: a bit is considered as either 1 or 0. There will be
> a maximum number of bits for example on your PC's hard disk.) In this
> case, we would have already figured out that the mass of 1bit of
> information = the mass of the atom.
>
> Question 2B.
> How many times quicker or slower did the 12 Atom universe run out of
> time, if your answer took 35.5 years to complete. ?
>
> ---------
>
> Question 3. Difficulty Level (medium)
>
> What is the maximum recordable ammount of seconds in a 12 Atom
> universe, where
>
> Eternity = mass(universe) / mass(unit of record)
>
> Mass of Atom = 1.6 x 10^(-27)
>
> Recording unit = 1 symbol/atom.
>
> Question 3B.
>
> Providing they began at the same moment, How many seconds will have
> been recorded in our our own universe, at the same moment that the
> last integer was erased from the memory of the 12 atom universe ?
>
> (this is a trick question, the answer will be the same as 3.)
>
> EXAMPLES.
>
> Now here is an example of a 10 atom universe.
>
> Because this little universe is trying to survive counting seconds on
> its parts, its life in seconds is as follows.
>
> BINARY
>
> Lets say this were binary bits per atom (bit/atom). . .i.e each second
> needed to be 1 or 0
>
> 1,1,1,1,1,1,1,1,1,1 - it would now have run out of space to record
> seconds. 10 seconds.
>
> or
>
> DIGIT
>
> Lets say this were a Digit per atom universe. . .i.e each second
> needed to be integer's 1 to 9
>
> from begining
>
> 0000000001
> to
> 9999999999 = maximum seconds
>
> SYMBOL
>
> Lets say this were Symbol per atom universe, (similar to our own) and
> when it got to 10 seconds it was unable to place a two digit integer
> on the storage medium. Therefore it had to invent a new symbol.
>
> 1 2 3 4 5 6 7 8 9 R (where to us R = 10)
>
> R 1 2 3 4 5 6 7 8 G (where to us G = 19)
>
> R G 1 2 3 4 5 6 7 Y (where to us Y = 27)
>
> R G Y 1 2 3 4 5 6 B (where to us B = 34)
>
> R G Y B 1 2 3 4 5 P (where to us P = 40)
>
> R G Y B P 1 2 3 4 O (where to us O = 45)
>
> R G Y B P O 1 2 3 C (where to us C = 49)
>
> R G Y B P O C 1 2 M (where to us M = 52)
>
> R G Y B P O C M 1 W (where to us W = 54)
>
> R G Y B P O C M W N (where to us N = 55)
>
> To us, we could continue counting at 56 seconds from here. We also
> wouldn't
> need numbers because we have the space to write things like
>
> Example of a rule.
> (where to us R = 10)(where to us G = 19)(where to us Y = 27)(where to
> us B = 34)(where to us P = 40)(where to us O = 45)(where to us C = 49)
> (where to us M = 52)(where to us W = 54)(where to us N = 55)
>
> But as you can see, by the end of this graph the 10 atom universe @ 1
> Symbol/atom has gradually erased the digits to keep up with the count.
> Also, it did not maintain a correct record of its rules regarding the
> quantity of 10 seconds when it got to G. When it got to G, there only
> remained 8 digits to express the rule of R which required 9 other
> digits as well as itself. The theory of inevitable lack of resource
> for numbers would eventually be the same for a 10^80atoms universe
> (such as our own).
>
> There are ways that this 10 atom (10symbol) universe could become more
> efficient. But only again by a finite amount before the rules fill up
> the space and begin to write over eachother and numbers will begin to
> lose meaning thereafter until altogether.