3.4

 ---- Closures

Parallelisms : Accounting - Classical mechanics- Quantum mechanics - Business management - Marketing - Economy - Intelligence

Accounting

- "Closures" - The next table shows all the cases that will need to be completed by the "camera":

Accounting

The text and the figure of the upper frame of this page have been restrained at the most simple instance for the sake of introducing the concept of closures.

Nothing is wrong with it but the adjacent figure highlights that when we adopt the conventions which are introduced at the next page, we may find more comfortable to introduce two [u] and two [v] accounts in another fashion - i.e. like displayed in the adjacent figure.

This will make such that the accounts are all available when eventually required.

Accounting - Quantum mechanics

- "Uncertainty principle" - We do not know - at least at this stage - what those two closing accounts mean so that they account per se for an uncertainty on the system when we like to keep its description within a complete view.

Noticeable is the fact that we obtain here a non resolvable uncertainty as a consequence of our decision to constantly maintain the system description complete and not from a principle necessary to accept - i.e. as introduced by Heisenberg in physics.

Classical mechanics- Quantum mechanics - Business

- "Commutability - Non Commutability" - Classical mechanics correspond to observation that are unique - say that the actors-objects or bodies are individualized. In consequence, they are separable and observing them in any sequence leads to the same results - classical mechanics own the property of commutability.

At the reverse, quantum mechanics applies in general for cases that are not commutative.

In the exceptional case where quantum mechanics exhibit commutability, multiple records appear at the same time showing a multiple nature - in this case one say that the records are compatible.

To illustrate those aspects, let's imagine that we collect observations by two different sequences of measurements: in the first one, we will first make an observation with our left eye, next with the right one and retain the last observation; for the second sequence we will opt for the inverse suite of observations and still retain the last one.

When we obtain the same results for the two sequences, the system is commutative and when the results are not the same for the two sequences, the system is not commutative.

The next table summarize those cases: out of the first line which a trivial case where nothing is observe, only the cases 8 and 9 are commutative and unique - say correspond to classical mechanics.

All the other cases correspond to quantum mechanics: 2 to 7 and 10 to 15 are non commutative while 16 is commutative but exhibits a compatible multiplicity of nature - i.e. like a chair can be a chair and a non chair at the same time when seen via a configuration of our "camera".

[Note: on the lines 7 and 10, the results of the observation sequences are between brackets ( ) as they do not represent the same objects - as it can be seen from the 4 first column. So the results do not commute].

An example for the line 16 can be constructed from an holotomy configured for "Is this a chair?" and an holotomy configure for "Is this a furniture?". When only the holotomy "Is this a chair ?" is configured by the camera, the case will be "classic" as in the line 8 and 9. When both holotomies are combined only in the first holotomy, both observations will always show up at the same time as compatible and like in the line 16 of the table.

One can also have the case 16 initiated by a statistical observation: say that we configure an holotomy for "Is this a chair?" and "Is this a table?". When we combine the two and we give our eyes the focus only on one object, the result will end up being only a chair or a table - say like the classical cases in like 8 or 9.

If we give our holotomies the focus on several sets containing chairs and tables i.e. being in a collections of kitchens, both chairs and tables will be observed and the averages of their occurrences will be observations that are compatible like in the line 16.

The line 16 may also reflect the famous case of "entanglement" like illustrated by the following example: let's observe two different item-clusters representing two companies that are different but that have the same business owner.

By using an holotomy configured on this two companies, the business owner can be seen as two particles - one being in the first company and the other being in the other company - or as one particles seen in two different places at the same time.

Obviously, at a question given to the first particle, one may not know the answer in advance while at a related question given next to the second particle, we may receive an answer having a correlation with the answer of the first particles.

Holotomies made on day life or business space may frequently exhibit such entanglements.

I.e. we are currently at several places in day life - like in our family, at work, with friends groups, in associations; in business, its is a frequent case that business owners own several businesses and belong to commerce associations and a diversity of lobbies so that behaviors in one place of the holotomy may correlate with reified situations in other places. 

- "Bell theorem" - We shortly summarize the Bell theorem by saying that - for a given sequences of experiments - the number of observations has an upper bond for both the classic and the quantum case and that the quantum case upper bond is higher than the upper bond for the classic case.

In our case, from the above table we see the classical case is at the most equal to 2 while the quantum can go to up to 4.

We will show at the end of the next section that in our case, the classical case is only 2 and the quantum case is only 4 and that not other value than 2 or 4 can be achieved.

Business management - Marketing - Economy - Intelligence

The [u] and [v] closures - as introduced here above - are of particular interest for the accounting of information chains which are incomplete, interrupted or embedding intangible variable or distributed sets of causes-effects interconnections.

To mentally illustrate this aspect, imagine that you are the boss of a business and that you ask your accountant to provide quarterly a balance sheet that embeds your balance but also the balances of your complete surrounding environment - say including clients, competitors and suppliers.

Obviously, your company may not own a complete information set about the whole environment - i.e. you may know the sales of competitors but not all their clients or you may know clients that buy from manufacturers but not via which distributors.

For all those informations for which you only own one entry, the [u] and [v] accounts will enable your accountant to make the balance - say the second writing.

This provides you with the principles to create a coherent "intelligence data service" and eventually with the capability to locate where you own uncertainties to possibly act upon the critical ones.

Noticeable is the fact that not only risks can be evaluated so but also possibly opportunities in the sense that innovation may raise out of spots of uncertainty.