I am reading the paper on the classical (1985) Church-Touring machine (a tape type one!) published in the web of Quantum Computing department of the Cambridge University, for which you have a link in my previous post, and I have found some quantum computers principles I would like you all to notice, because although magnetic, electric, and electronic media have developed to microSD storage systems, the calculations and physical means are following formal mathematical expressions which are not sometimes completely understood, or I’d better say their implications. So here you are my Hullabaloo to English translation.
About sets, elements and definite operations inside outside and between them.
Mathematics has been widely developed relaying on sets theories and logical assumptions and axioms. I am not to expose an explanation on this large field of reasoning, because it would not clarify anything new, and if you are interested in those basis there are many texts to which you can turn to in order to learn the conventions, notation, principles and all that deals with Mathematical language.
Instead, I will tell you what we all study, but somehow end up forgetting about.
1. A function has to be defined in such a way that you can reverse its output back into the input. If it is not so, it is not a function, it is only a correspondence, and being so, there is not only one value, neither at the input, nor at the output.
Equations in the paper numbered, 2.1, 2.2, 2.3, 2.4, 2.5.
This, in Physical terms, means there are loads of natural processes which are not being properly monitored or used, because there is no way to establish an accurate function in order to describe and reproduce them in a really natural condition.
2. Irrational numbers implicitly by definition do not give an exact inverse value because of their ‘nature’, thus we scientists leave them indicated in equations, and computers compute them if properly implemented, but in any case their inverse values do not give exactly the element from which the function went in one direction of the process being turned into an algorithm.
3. These two important mathematical principia are considered, but what ‘we’ do is define intervals or subsets of the particular field we are studying, and by doing this, what we obtain is a mathematical way of expressing certain processes in order to make them usable for technology, industry, society or economy.
Equations 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12.
4. The more complicated equations, algorithms and constants taking part in calculations the more inaccurate the models will be.
These four mathematical truths I am highlighting have an empirical measurable consequence (;).
In the equation [2.6] of the paper, what is being expressed is that when we have a value of Zero, that I will call in order to clarify concept, OFF, circuitry, oops! sorry, I mean nanotechnology will change that OFF into a One, that I will call an ON value. This was made during the fifties and sixties by simple light lamp switches which turned on and off light-bulbs. There is a logical door to do this; the NOT door. This sort of electronic device is represented as a triangle with a little circle in its pointing arrow, being the meaning in a logical chart the following:
INPUT (ALGORITHM) OUTPUT
Element a value
So I think the electrical equivalent would be a commuter.
It is developed this way as an agreement due to sinusoidal transformations on waveforms, so this way, when the force vector ñ in equations has a parallel or perpendicular value this logical door inverts current and voltage. That is why people who studied say fifty or thirty years ago, get lost in calculations (this paper had not been published then and I studied computer science four years ago), they have inverted polarities, so the apparent circuitry and calculations involved seem much more complicated than they really are.
But that is not all, in addition to this non-non-sense convention, they added another condition for development of related techs; whenever the value is not ZERO circuitry turns the ‘logical’ state to ONE.
This is what I call electrical efficiency!
I will go on reading, while revising, this paper and I will post my ‘logical errors’ about it.