The problem and paradox in locating one of Quantum Accounting’s two key values in the qubit
In Part 1 of our series on the two key values in quantum account, we understood that every transaction in the spherical qubit divides into equal halves debit and credit. The sum of debit and credit is zero, because the fact that they are opposites and one equals the other means there is no difference in their combination.
The location of zero difference in the quantum account is critical. Zero is the point of “balance” that is necessary to achieve in the record of any transaction, since it is at the point of zero difference that the account is complete.
The theory of quantum accounting highlights that “account” is both “a record of information about its particular subject, in logical order from beginning to end” and the action of making such a record. An individual record that forms part of a sequence in quantum accounting begins and ends at an input that is paired to an output with zero difference in their connection. The numbers of pairings in any combination of sequences can differ without limit, but all pairings inevitably combine to a single account that must achieve a balance of 0. The zero balance indicates that there are no remaining differences between sequences, and the sum of all inputs equals the sum of all outputs in entire account.
When the quantum account achieves zero difference, it signifies a complete record of all information in the account in which all inputs are in complete agreement with all outputs. Where there is no difference, nothing remains to be accounted for.
But where do we find zero, which is the point of no difference?
The unlimited potential of any account in the middle
When the entire account consists of many differences, logically zero has to find its place in the middle of all differences. In that position, it would ensure equality of each half of the account to its opposite, and thereby ensure the sum of debits equals the sum of credits with zero difference. Difference can exist only where inequality creates variability, and the account’s inputs and outputs achieve the equality of zero in its middle. The account does not vary in its middle, which we can think of as the account’s logical core.
From the logical core of the quantum account, information is divided in two equal parts. Half of the information of any transaction is recorded as a “credit” (belief received) and the other half is recorded as a “debit” (belief owed). These two halves are of equal quantity, but opposite in their effect. Accountants represent debits as positive and credits as negative, and since they are each part of the same total the sum of positive and negative equals zero.
The transaction in the quantum computer’s spherical qubit will contain both credit and credit and maintain zero difference – the one point to which both debit and credit both agree – in its middle. Since debit and credit are opposite measures of belief, the middle of the qubit sphere represents the complete account of belief itself, always as its own beginning and end with the capacity to divide into equal halves received and owed. Every exchange that transmits in the qubit retains its potential to exist in both states positive (debit) and negative (credit) simultaneously, which is called “superposition”, in the middle of the qubit sphere.
Let’s consider, then, that in the quantum account the word “zero” means no difference and therefore no further account. At the point of no difference in the middle of the qubit there is therefore only the potential of any account, either as a thing or as an action, in a paradoxical superposition of both.
The quantum account is spherical
In the architecture of the sphere, zero’s location at the middle gives it the capacity to extend as the radius to any of the points on the circumference of the sphere. This is a powerful capacity for zero, since once it reaches the surface of the sphere it will encounter no limit in the ratio of the circumference to diameter.
While zero retains the ability to achieve all circular extremities of the quantum account, the debit and credit are constrained to two extremes of the diameter. The diameter is the longest straight line that divides both the two-dimensional circle and its three-dimensional analogue the sphere into two equal parts.
When we divide the diameter of a sphere in two, we call each half the “radius” and both halves combined the “radii”. Two radii make one diameter, and on one radius we can find the debit while its opposite radius will contain the credit. Each of debit and credit are half of a combination of belief in its entire measure. The radii extends the belief’s equals and opposites from the middle of the sphere to the circumference, where belief’s potential is unlimited in its ratio to the diameter.
“Round is surely that whose extremities are equidistant in every direction from the middle … straight is that whose middle stands in the way of the two extremities.” – Plato, Parmenides 137(e)
The sphere is a geometric object, and therefore the quantum account is necessarily geometric. The geometer Plato observed the powerful difference that can exist between an account’s diameter – which has only two limits – and its circumference that has an undefined number of limits. Plato used the word “extreme” to denote “limit”.
The problem of Pi
With respect to the sphere, part 1 of this series raised the question, “how do we find the middle when the ratio of circumference to diameter (in other words, π) never ends?
Pi, represented by its Greek symbol π, is the ratio of a circle’s circumference to its diameter, which is the longest straight line that can be drawn between two points on the circumference. If we draw a line from the circumference to the middle of the diameter we divide the diameter into two parts – or maybe we don’t?
The ratio π is both irrational and transcendental. Irrationality, or as the ancients called it “incommensurability”, means that π can never be represented as a fraction or ratio of one number divided by another number. Since we can’t define π as a specific fraction with a limit, it forms what is called a “continued fraction” which is a fraction that never ends. There are many continued fractions for π, the generalized ones being the most interesting. A transcendental value, like π, is one that is not “algebraic” and therefore cannot be a solution of an equation involving only addition, multiplication, powers, and integers. (Division by 2, which we need to do to situate each of debit and credit, is the same as multiplication by one-half).
The problem with pi is that its fractions (represented in the decimals of 3.14159…) never end. Therefore, locating the middle of the circle and its diameter, to divide the radius into equal parts debit and credit for the quantum account, is both a mathematical and geometric challenge. The sphere is composed of an unlimited number of circles all of which share the same midpoint but their radii are angled in differing directions. Finding the middle of the circle in two dimensions, and then the sphere in three dimensions, is difficult because the middle of anything is, by definition, the fraction of precisely one-half. That fraction, unlike pi, is rational. How do we connect rational and irrational?
The paradox of the “middle”
When the middle of the qubit is composed of zero, and zero is defined as “no difference”, the point that we call the “middle” is no different from any other point. But by its own definition, however, the “middle” is different from that which is “not middle”.
In a circle – which by definition has no point on its circumference that we can call either “beginning” or “end” – the radius from any point on the circumference to the “middle” is the same as the radius from any other point, with no difference. Since π is irrational, existing in an unending series of continued fractions, there is no limit to the number of points on the circumference of a circle when all radii extend to the “middle”.
How do we locate the rational fraction one-half in the middle of the diameter – the point that splits the diameter into two equal radii of debit and credit – when the diameter extends to two points on the circumference whose ratio to the diameter is irrational?
A paradox exists in this difference. We imagine a middle that should rationally exist as the fraction of one-half of the diameter of the circle, but the circumference gives us no rational measure to define the fraction of one-half at any point on the diameter. The irrational fraction of circumference to diameter gives us only continued fractions, to infinity.
Can the “middle” of a circle actually exist as a point of no difference, or is this even mathematically, geometrically, and philosophically knowable? The question is central to quantum accounting and our ability to maintain the balance of debit and credit in equal and opposite measure.
To define the middle, which is the position of 0 in the quantum account, we will need to define – simultaneously – the extent of one-half that forms the radius of the qubit sphere.
“Defining” the middle will be the subject of next instalment of this series, and in the spherical qubit the task will require geometry. The task will not be algebraic, because π is transcendental and therefore defies equations involving addition, multiplication, powers, and integers. Locating 0 and one-half – which are the two key values in quantum accounting – at the same time with no difference in the qubit will be the subject of the next part of our “Two Key Values” series.