Abstract Zero vs Ontological Zero (∅ vs 0)
Abstract Zero vs Ontological Zero (∅ vs 0)
by Thomas Foster – hyperian
Division by Zero
(N<x> indicates N subscript x)
Empiricist scientists and abstract mathematicians deny that division by zero is possible, but that is a faith-based position and contrary to reason. Division by zero is in fact ontologically valid, and represents the interface between matter and mind.
What is zero divided by zero? Undefinable? Indeterminate? Surely we can do better than that!
Two conflicting arguments are typically advanced for 0 / 0:
[Case 1] 0 / X = 0, therefore when X = 0, 0 / 0 = 0
[Case 2] N / N = 1, therefore when N = 0, 0 / 0 = 1
This kind of arguing comes from failing to understand what zero actually is. There is in fact no discrepancy:
Case (1) is correct for abstract zero: ∅ / X does indeed give ∅ / ∅ = ∅ if X = ∅.
Case (2) is correct for ontological zero: 0<1> / N is a mathematical impossibility due to monads’ indivisibility – if N is finite but NOT if N is monadic (dimensionless).
i.e. N = 0 = 0<1>
When x = 0 is substituted into x(∞<α>) = x/0 [equation E from my previous post “Counting Infinities”] we obtain:
x(∞<α>) = x/0
0(∞<α>) = 0/0
Since 0(∞<α>) = 1,
1 = 0/0
Therefore 0 / 0 = 1.
Ontologically, this makes perfect sense:
0 / 0 = 0<1> / 0<1>
i.e. 1 monad divided by 1 monad equals 1, just as 1 / 1 = 1.
One monad ‘goes into’ one monad exactly one time.
Now, there is a caveat here – we are assuming 0 / 0 means ” 0<1> / 0<1> “.
In certain cases, in calculus for example, 0 / 0 actually represents an unknown number of monads divided by another unknown number of monads. Therefore 0 / 0 would be the equivalent of saying x / y = z; or 0<x> / 0<y> = z (x divided by y could equal anything since we don’t know what the numbers are, and therefore the result could be any number).
Otherwise, when the number of monads is known, division involving quantities of zeroes acts exactly the same as finite division (involving different quantities/multiples of 1).
Example: 0<10> / 0<5> = 2. In this case 0 (the base unit of mind) acts just the same as operations involving 1 (the base unit of matter).
What happens if you split 10 monads into 2 groups i.e. 0<10> / 2 = ?
You get 5 monads. 0<10> / 2 = 0<5>.
OBJECTIONS TO DIVISION BY ZERO:
From Wikipedia:
“With the following assumptions:”
0 * 1 = 0
0 * 2 = 0
“The following must be true:”
0 * 1 = 0 * 2 therefore 0/0 * 1 = 0/0 * 2
“Simplified, this yields:”
1 = 2
Needless to say, the initial assumptions are incorrect:
0 * 1 = 0<1> (one monad)
0 * 2 = 0<2> (two monads)
Therefore 0<1> ≠ 0<2> (One monad does not equal two monads, just as 1 does not equal 2!)
From mathforum.org:
“Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related.”
12/6 = 2 because 6*2 = 12
12 / 0 = X would mean that 0 * X = 12
“But no value would work for X because 0 * X = 0. So X / 0 doesn’t work.”
Wrong!
For abstract zero, it is true that ∅ * X = ∅. (“Non-existence” is not affected by multiplication).
However 0 * X ≠ 0 (ontological zero can be multiplied, monads are COUNTABLE).
Therefore:
12 / 0 = 12(∞<α>) i.e. finite matter to dimensionless mind.
0 * 12(∞<α>) = 12 i.e. infinite monads ‘making up’ matter.
