Thursday, September 22, 2016

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Julia - Gödel 5


0. Two Given Styles Of Lectures
1. The Ampere/Voltage/Ohm
2. The Gödel Numbers
3. The Turing Machine
4. The Nash Equilibrium
5. More than Analogy
6. The Greek Example

0. Two Given Styles Of Lectures
There are two lectures, which are confidently designed for the listener. One is extremely short and to the point, and actually has some hope of being understood in real time. These are “do” lectures. The other one is extremely long and will have to be absorbed over time, and contains hints of things yet to come. These are “think” lectures; both of these are badly done because training a lecture to do this is not an immediate process.

And who knows, you might actually learn something, even if the lecture is disabled.
Obviously this is the second kind of lecture, and the lecturer does not think that all you who will get it will not get right way. In fact I would be surprised if any of them got it, though one or two of you just might. Given that this is a long lecture, and does not come with an immediacy of understanding, it means that you will take time to really understand. So let us begin, first with the obvious parallel to a battery, then by going through the three talking points, then closing with a distinct problem – and some questions.

As I said, you are not going to get this at once. But that is all right, because now that you know the information: you can digest at your own pace, and not rush to produce it on a test. You are at the point of having to digest at your own pace, and not by the cycles of semester or quarterly information. While not everyone will treat you as grown-up, I will, and it takes you days or weeks or months to get this, that is all right by me. After all it took me a great deal of time to come up with this, so it is going to take you time to understand it.

First of all, though, I would like to thank everyone involved in giving these lectures, because it is tough to get together a lecture that will be understood. And each and every one involved deserves a hand. And I would also like to thank all of you for attending these lectures, because they are not easy to absorb.

1. The AVO

By now we know what AVO is: an Ampere driven by a Volt, against a resistance of one Ohm. And if we do not there are a large number of websites willing to explain this for you. We do not need to know everything about physics, just where to find that stuff that we do not know when to know it. The AVO is the basic unit of electricity, and everything about electricity can be expressed by it, or by numbers which come the same thing, usually with a square somewhere in the calculation. Is so basic and so obvious that it will take four years to just know what you are looking for, and another five or so to actually make a contribution to the field of EE.

What this means, if you think about it, this field is rich in density with possibility, and produces interactions that are complex and extraordinary. You can spend your entire life working with just such equations and workings out of the field. Airplanes, automobiles, trains, and all manner of appliances – from very large to the very small screen out for just a little nudge of EE. This means that a triangle of forces is at work in any complete electrical circuit. Even if Ohms is zero, because after all zero is a number. But it leads to two sorts of superconductivity.

When first you start experimenting with electricity, everything seems novel – and if you will excuse the expression, shocking. That is because electricity goes where it wants to, rather than where you wanted it to go. And that means you have to learn the language of electricity if you want it to go anywhere. But there is a saving grace – and that is, it will ignore, most of the time, detours which do not interest it. Compare this with water, which will squeeze out any little gap and come flushing out of every pore if you give it a chance – and even if you do not think there is anything to squeeze. Water will find a way – whereas electricity will not.

What makes electricity so useful is that it provides a framework for introducing a novel concept: GTN as a unit of measurement. Because if you think about it, it is basically the same concept: you have a way of current running on a system which will work if the current times the system is over the backlog. But what has not been made clear to everyone is what GTN actually works out to being.
So let us take a moment to review the AVO, and then introduce the information equivalent. This way if you get lost in the world of GTN, you can slip back to an old standby and reason by analogy. So what is AVO?

Let us start with amperage, and what it is actually doing. Amperage is the amount of electrical current present at a given point, When it is expressed the current is in Amps, whereas the charge accumulated is measured in coulombs. But that basically means that a charge will not move anywhere unless there is voltage which is expressed as kilogram meters squared over Amperes times seconds cubed. In other words a weight times a distance over seconds cube. This is more easily expressed as Watts over Amperes. Now here is where physicists divide from electronic engineers. Physicist will know that there is some conversion factor which he will remember two digits of, or look up if more precise is needed – where as the electronic engineer will know the precise nine digit, and have them memorized. And if you look at their phone, it will be (xxx) 483-5979. They will even take issue with the water flow analogy, because everyone in the EE space knows that water flow is not the same thing.

Then everything slips in two places, the average does the work, the voltaic is the hurdle to cross, and Ohm is the resistance between two points on a conductor. Thus Voltage, Amper, and Ohmage are nice neat one-for-one equations.

But there is a small catch: it took a little over 100 years to do this. Which seems a bit long for some rather simple equations, not one of them uses more than cubed. Which brings me to what is new here, not defining one cell by a current, but by information.

So for the moment hold on to Ampere, Volt, and Ohm in a triangle which is the position in current space.

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