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Showing posts with label model. Show all posts
Showing posts with label model. Show all posts

Tuesday, 15 November 2022

Generating prime numbers

 Generating prime numbers

 
It is known that over the centuries, some people have been involved in discovering algorithms for generating prime numbers. One would not say that it is a difficult thing, as long as you evaluate such an algorithm mainly in terms of its usefulness.
 
An algorithm must be evaluated in terms of its application goals and also over time in terms of the applications for which it has proven itself suitable. Thus, the complexity of an algorithm cannot be a criterion for its evaluation.
 
For example, with regard to the generation of prime numbers, one could, first and foremost and rightly, refer to the Sieve of Eratosthenes or the model: y = 6 * x ± 1 where x = 1, 2, 3, 4, 5, 6, 7, ... and possibly some other algorithms.
 
But let's look at a new proposal of mine for a prime number generation algorithm, which is obviously easy to program, but also seems to have potential in practical applications of quantum mechanics and quantum computing, where, as we know, what we actually perceive (via classical physics) that is, with bits being counted as "0" or "1," and only one of the four possible states can exist at any time in space, in a quantum superposition state, all four of the possible states can co-exist in time and space simultaneously.
 
So, there is an algorithm that can generate prime numbers, essentially as the integer part of decimals resulting from an iterative inversion process, starting with the irrational decimal 0.43233208718590286890... and then all the products of this inversion process. See in the picture what I mean...



Wednesday, 19 February 2020

The "prisoner's dilemma": A proposal to amend the model to be implemented on international relations strategy


The "prisoner's dilemma": A proposal to amend the model to be implemented on international relations strategy





On the occasion of a video – among other similar ones – circulated on the internet regarding the problem of game theory, known as "the prisoner’s dilemma", an attempt to explain the problem is summarised below, but, moreover, a proposal to extend it, is also attempted towards the implementation of its forecasts, on international relations strategies.

The dilemma (= option of a dual trait), described in the video, is in fact a paradox of analytical calculus, in terms of the conducive part of the analysis, i.e. the decision-making. So, what have we got here? Two individuals, each with personal interests, ultimately (as we usually say at the end of the day) do not achieve the best for them. So they do not succeed it, as they choose, each for themselves, their own salvation and the burden of the other. The result is that they are both in a worse situation than they would have found if they cooperated in the decision-making process! That is to say, the game theory (i.e., optimal decision of independent players participating in a backdrop with various strategic options) of an amended version.

Well, the theoretical approach is good, an approach of numerical analysis – in a broad sense – as we put it above, but it might be appropriate to be more practical.

In this light, on the most practical view, we could extend the (numerical) analysis of an amended model of the problem in question, i.e. the 'prisoner dilemma' and start discussing a realistic approach to a similar problem, of another level: the 'problem of international cooperation'.
States are by definition the players of the international political scene. Consequently, each state, in a role of that kind, aims to profit over the others regardless of its willingness/preference to cooperate (or not). In the conventional "prisoner's dilemma" the analysis does not go into the players' expected gains according to their preferences or the potential/capacity of the players in impeding (vetoing) international cooperation. This is precisely where the conventional problem of the "prisoner’s dilemma" needs the above mentioned amendment, so that its analysis also provides for the preferences of the players-states gains and the profits that correspond to them regarding the management of impeding (or not) the so-called international cooperation.

A typical example of the implementation of this latest case of play (i.e. the management of international cooperation) is, nowadays, the movements of some leaders such as the President of the US,  D. Trump (see refusal to participate in international cooperation on various issues, such as climate change, international trade and business deals, etc.), French President E. Macron (see moves in the opposite of the "player" Trump’s moves, which contribute to international cooperation on the aforementioned issues or even more, discovering, highlighting and throwing at the table of the international game new issues of international cooperation, etc.). Other international leaders, representing players-states of a smaller scope, are working on some similar moves, such as our well-known and non-exceptional Turkish R T Erdogan, who in the early period of his career "played" by promoting international cooperation while later on and still at the current juncture "playing" on the contrary, i.e. with the so-called "adverse" options, blocking international cooperation even within some by definition international cooperative organisations (see NATO, OSCE, etc.).




On the basis of the above analysis of both the conventional standard of the "prisoner’s dilemma" and its proposed amendment/expansion into international relations between states-players, it is obvious that, the application – at least if not the theoretical numerical analysis of the model too – of the amendment/extension of the model into international relations, which we here proudly and urgently attempt to explain, has long been discovered/analysed by the advisors and/or some strategic analysis think tanks, which support the aforementioned leaders and not only those. And, of course, the leaders have not taken away the opportunity to move forward with the implementation!