digital rising

[AntonioLao]

Is God or the Designer of the cosmos a natural mathematician? A direct answer to this question is not possible. However, observing the workings of the visible universe, one can indirectly come to a conclusion that the constructive mechanism of the cosmos indeed is describable by the laws of mathematics. These laws do not have to obey the decimal system of numbers. But they certainly always obey the system of binary numbers. All is well and good since the decimal base 10 system of numbers can be transformed into the binary system of numbers, vice versa, although it is still easier to count using the 10 fingers of one’s two hands. However, the advantage disappears if reality contains more than 10 objects since in the widely use Hindu Arabic symbols of numbers there are only 9 symbols: 1, 2, 3, 4, 5, 6, 7, 8, 9. Uniqueness of the symbol zero (0) as a place value becomes true advantage of the decimal system. For the decimal number 1000 there are 3 place values of zero and each can take on any value from 1 to 9 making a total of one thousand distinct number symbols from 1000, 1001, 1002, …,1999. If 1 is added to 1999 then the next higher number symbol is 2000 so on and so forth.

Although the number zero is useful as a place value in decimal system it is useless for the binary system. However, zero becomes useful in the binary system as a multiplicative factor. This idea becomes clear since binary system uses exponential counting for the base number 2 such that 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256, 2⁹=512, 2¹⁰=1024, so on and so forth. Therefore, any real whole number from 1 to infinity can be symbolized using a multiplicative factor ��ₑ where the subscript �� denotes the exponent of 2 and ��ₑ only take on two values 1 and 0 such that any number, say between 1 and 16, can be represented by ��₄��₃��₂��₁��₀. 1=00001, 2=00010, 3=00011, 4=00100, 5=00101, 6=00110, 7=00111, 8=01000, 9=01001, 10=01010, 11=01011, 12=01100, 13=01101, 14=01110, 15=01111, and 16=10000. The increasing value of the exponent of 2 becomes the universal digital rising as foreseen by the great Designer of the cosmos and infinity is represented by endless sequence of 11111111111111111111111111111111111...

[SteveA]

Notice that we'd either need nested infinite structures for approximation, or different versions of time if we were to perform something similar to a perfect base conversion.

For example, 1/3 really can't be represented in binary. There isn't a n/2^m that equals 1/3, though we could construct two binary values that existed with a 1:3 ratio, but in that case the representation is in a different form and would require something similar to an orthogonal number line, either than or have something dynamically rescale space on different infinite orders to construct all these on a single number (with the potential for various quantum units of imprecision).

In that event, the "quanta" used for something like 1/3rd would themselves end up being potentially infinite quantities.

[SteveA]

endless sequence of 11111111111111111111111111111111111...

We can simplify that and describe the quantity of 1s , but I get what you're saying. It's just infinite "space", energy, time or love etc. Whatever someone wants to call it.

[SteveA]

Actually we can use a lower form of representation - Unary numbers http://en.wikipedia.org/wiki/Unary_numeral_system

Now you can just say 000000000....

Though if you want a specific termination point at which something happens, then you'd need to place some alternate symbol in this sequence. For example, to describe a set of numbers as counting, 0,1,2,3,... we could have a space in which the distance between 1s determined the quantity represented by that 1:

11010010001000010...

That's a more realistic interpretation of what a truely binary representation might appear as, because we need spaces to isolate binary symbols into specific quantities and this means we need at least 3 symbols to represent arbitrary binary numbers. So a binary representation, on an absolute scale would give us unary represented quantities. (If we had a "random" distribution of binary symbols, then these unary values would have an exponentially decaying probability of occuring and 0 would occur ~1/2 the time, 1 would occur ~1/4th the time etc.).

Here's a famous expression: 1000000001000000100000001000001000110000000001

(Oh no, I'm telling jokes in binary now!!! That's geek status for certain )

Seriously though, I don't think it's the size that matters ... it's what you do with it.

[austintorn@aol.com]

Antonio, Bell, Aspect, Zellinger, and Austin

Indeed, God plays the numbers’ game,
And, in deed, God is a gambling dame,
(He’s a woman, you know)
Playing dice with the universe
Ever since its storied birth.

As a first (and lovely) cause,
She must ever be randomly lawed,
For there would be nothing prior
To determine the outcomes higher.

[AntonioLao]

For a binary computer with a 16 bits register its overflow is represented by 11111. However in hexadecimal it is represented by an F. 32 bits 111111 in hex FF.64 bits 1111111 or in hex FFF. infinite size register can be overflowed by ...1111111 and ...FFFFF. Infinity minus 1 is represented by ....111111111111111111111111110.

[SteveA]

For a binary computer with a 16 bits register its overflow is represented by 11111. However in hexadecimal it is represented by an F. 32 bits 111111 in hex FF.64 bits 1111111 or in hex FFF. infinite size register can be overflowed by ...1111111 and ...FFFFF. Infinity minus 1 is represented by ....111111111111111111111111110.

Did you mean that for a 16 bit number in binary, the overflow/maximum count is 1111111111111111 and for 32 it's 11111111111111111111111111111111 etc.?

In hexadecimal these are (16 bits) FFFF, (32 bits) FFFFFFFF and (64 bits) FFFFFFFFFFFFFFFF. Each hexadecimal digit is represented by 4 bits (a group of 4 bits is often called a 'nibble' and would be half a byte).

For anyone interested, counting in hexadecimal proceeds as:

0
1
2
...
9
A
B
...
F (=15)
10 (=16)
11
12
...
19
1A
..
1F (=31 decimal or 11111 in binary)
20 (=32 decimal or 100000 in binary)
21
22
....
9F
A0
A1
...
FF (255 decimal or (2^8)-1)
100 (256 decimal or 2^8)
101
..
etc.

[AntonioLao]

Thanks for the recap. It has been a long time since I work with HEX I got confused with bits and bytes but hopefully you get the picture. My contention is that the overflow of an infinite size register can both be represented by binary 11111111111... infinite sequence of 1's or FFFFFFFFFFFF....infinite sequence of F's.

[AntonioLao]

Indeed, God plays the numbers’ game,

My question would be whether He loses, wins, or breakevens all the time, most of the time, some of the time, or never.