Is it possible to do the impossible? - page 5
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For example, a computer cannot know in advance whether a problem handed to it has a solution or not. By the way, elementary everlasting loops are still not recognizable by the compiler, so the program with such a loop enters a deadlock.
and a person can understand it beforehand? Perpetual loops are a common behavior of many programs. A dead hang is the consequence of a programmer error.
And I find it mauvais ton to describe a program's behavior with the words "computer can't".
Here is another quote on this subject - http://elementy.ru/trefil/21142
"The English mathematician and physicist Roger Penrose (b. 1931) has shown that Gödel's theorems can be used to prove that there are fundamental differences between the human brain and the computer. The point of his reasoning is simple. A computer works strictly logically and cannot determine if statement A is true or false if it falls outside axiomatic limits, and such statements, according to Gödel's theorem, inevitably exist. When faced with such a logically unprovable and irrefutable assertion A, a person is always able to determine its truth or falsity - based on everyday experience. At least in this, the human brain is superior to the computer, which is constrained by pure logical schemes. The human brain is capable of understanding the depth of truth contained in Gödel's theorems, but the computer brain never does."
Such statements from 80 years ago are outdated.
Just like a human, an expert system type program can only make decisions based on its "experience". And humans have limitations in understanding the truth or falsity within the "current axiomatics".
I believe it is a human peculiarity to go beyond one's experience and make non-standard decisions. Although this too can be reduced to random wandering and going from version to version building and trying new models.
ha ha ha
Francis of Assisi
When I started thinking about: "How to make the impossible possible" :) I concluded: Anything that does not contradict mathematical logic can be done. From this I conclude: Until it is proven that the market is unpredictable it is predictable, regardless of whether we can or can't do it.
You're an economist, you were once touted as the smartest of the alternative American economists. Can you at least explain why there is no sensible textbook on market economics, but all of this is bullshit? Or maybe there is?
Andrey
About ten years ago I decided to write a good market economy textbook. I wondered why no one has written one yet. I decided to strictly follow the maths maths model, not draw crosses like all textbook authors. I honestly built a model of Bem-Bawerk's bargaining, a model of market price formation in general. I started to prove the convergence of processes, ergodicity...
And then I discovered that the processes of such a class are in the general case irreducible. That is, in the general case the market price simply does not exist. It follows that market regulation is only possible in a very limited class of sectors. In the rest, it inevitably entails imbalances and therefore must be subject to external, violent adjustment.
Then I also discovered the impossibility of forming a universal equivalent in a natural way. The price matrix was in general asymmetric. Consequently all the theories of the natural origin of money are groundless.
It is the same with the case law market models. As soon as I began to solve them analytically instead of drawing crosses, it was revealed that there is no equilibrium in the markets, a generally divergent process, like Friedman's universe: without a cosmological term, there is no equilibrium to be fitted. So the whole Keynesian theory generally speaking turned out to be a bluff.
And a lot of anecdotes like that came out. After which I gave up the idea of writing a textbook on market economics. For the lack of a realistic description of the subject.
Modern market attitudes are best described in Gregory Mankew's textbook "Macroeconomics". It is clear that it is intended to educate clerks, and has nothing to do with real business.
Here is another interestingGödel's Theorem on the incompleteness of axiomatics in popular parlance
"In the popular sense this means that any scientific theory without exception has to rely on a belief in the truth of certain axioms which cannot be proven."
"So science has never strayed that far from blind faith. The only question is what everyone chooses to believe and how much of it corresponds to the reality they observe."
And then I discovered that processes of this class are, in the general case, irreducible. That is, in the general case a market price simply does not exist. It follows that market regulation is only possible in a very limited class of sectors. In the rest it inevitably entails imbalances and therefore must be subject to external forced adjustment.
So a market economy, as such, has not existed anywhere else for a long time. Well, probably except for the Russian Federation, where it continues to be stubbornly built. And perhaps in Yasin's head.
Everything is highly regulated everywhere. Well, and no one is going to count iPhones, of course. :) Apple will figure it out.
Causes, causes, effects... We all try to find the causes of a phenomenon without realising that there may be no causes at all.
Bertrand Russell, a mathematician and philosopher who won the Nobel Prize for Literature in 1950, wrote in "On the concept of cause":
"All philosophers, whatever school they belong to, imagine that causality is one of the fundamental axioms of science, but, strangely enough, in a science as advanced as gravitational astronomy, the word 'cause' never occurs... The principle of causality seems to me a relic of the last century, surviving, like a monarchy, only because it has been wrongly considered harmless." (M.Klein Mathematics. Search for truth. M.1988)
Reasons may be mutually exclusive. Hence paradoxes. When the cause of the phenomenon cannot be found, "Determinism" comes to the rescue. Determinism is replaced by statistical laws. Without statistics and the methods of probability theory, it is unthinkable, say, a large insurance business, which is closer to the subject of economics.
The statistical approach and probability theory, I believe, are the most fruitful, in terms of making "the impossible possible".
I find the statistical approach and probability theory to be most fruitful, in terms of making the "impossible possible".