Black Hole Fenhan just asked him to pass on a few supercomputing models and papers related to the Turing-Church thesis. Why did he make Fu Difenhan lose his temper so much that his thighs were swollen?
Let’s first talk about what a supercomputing model is.
The basis of computer theory is computability theory, and the cornerstone of computability theory is "Turing machine" and "Church-Turing thesis".
The latter is named after the mathematicians Alonzo Church and Alan Turing. Just like the second law of thermodynamics, it has many different forms of expression.
For example: all calculations or algorithms can be performed by a Turing machine.
Or: a computer program written in any conventional programming language can be translated into a Turing machine, and conversely any Turing machine can be translated into programs in most programming languages.
Or: Efficient or mechanical methods in logic and mathematics can be represented by Turing machines.
Everyone is in a fog, and you don’t know what’s going on, right?
In fact, the main reason is that I am not familiar with the concept.
Like the mass-energy equation, all matter has hidden energy with mass multiplied by the square of the speed of light. Everyone can understand it immediately because they are familiar with the concepts of matter, mass, light speed, and energy.
The concepts involved in the Church-Turing thesis are generally not familiar to everyone, so they all know the words, and the connection is inexplicable.
In fact, how to define effective methods, execution algorithms, and limited steps are also the focus of this topic.
For example, the Caiting constant that appeared in Chapter 1 is called an uncomputable number.
This is because if we take numbers as a collection of objects, computable numbers refer to the numbers that can be obtained by Turing machines through limited universal algorithms, which are basically all real numbers. Rational numbers rely on addition, subtraction, multiplication and division, irrational numbers rely on exponentiation, and transcendental numbers can be used
series……
If you want to know what the 100 millionth digit of √2 or π is, just write a program and run it.
But although the uncomputable number is a constant in theory, it has been proven theoretically that it can never be calculated.
Because the process of finding it will affect the result.
It's like the butterfly effect. If you don't want the current ending, you go back to the past and try to change it, but you don't know what the ending will be like before you return and iterate.
Even after this, there are even weirder numbers that cannot be defined in language, called undefinable numbers. Although no mathematician has yet successfully constructed one...
In short, in a 1936 paper, Alan Turing introduced the Turing machine to prove that the "decision problem" is unsolvable;
Alonzo Church made a similar thesis using recursive functions and lambda definable functions to describe effective computability;
Still in 1936, based on Church's work, Turing further proved that the Turing machine actually describes functions of the same set;
Later, more mechanisms for describing efficient computation were proposed, such as register machines, Post systems, combinatorial definability, Markov algorithms, etc.
These are all proven to have the same computational capabilities as Turing machines and can simulate each other with universal Turing machines, which is called Turing complete.
"Minecraft" has been proven to be Turing-complete, Lego is said to be too, and Magic: The Gathering...
Going too far, what's the point of all this?
The meaning is that mathematicians and computational scientists have gradually figured out that although the forms, languages, and systems are different, modern computers are essentially equivalent to Turing machines - tasks that modern computers can complete, Turing machines can also complete.
;What the Turing machine cannot do, computers cannot do now.
This is called computability.
But this is all research from the last century.
Beginning in 1936, in the following years, the theoretical foundation of modern computers was laid. From then on, there were industrialization, miniaturization, large-scale integration, Moore's Law... There were only engineering breakthroughs, and no theoretical innovations.
But, is that really the case?
Scientists have finally opened up a field, but will they be satisfied with their achievements and hesitate to move forward?
nonexistent!
In fact, it didn't take long for scientists to be dissatisfied with the computability described by Turing. They began to think about whether there was a new model that was stronger than the Turing machine and could solve difficult problems that the Turing machine could not compute.
That is, the supercomputing model!
Quantum computers are one of them.
However, its computing power is essentially equivalent to that of a Turing machine, but its computational complexity is much better. It can reduce exponential problems to polynomial time.
Is this the end?
of course not!
In addition to quantum computers, there is also a metaphorical machine proposed by Alan Turing himself to solve "decision problems" by metaphorically "black box".
Most subsequent supercomputing models are also based on the concept of metaphorical machines - by introducing other characteristics into Turing machines, they are not limited by previous computing capabilities.
Therefore, Alan Turing is great and is known as the "Father of Computer Science" and "The Father of Artificial Intelligence". The equally famous Von Neumann is just the "Father of Modern Computers".
In fact, the relationship between the two is like Einstein, who proposed the mass-energy equation, and Oppenheimer, who organized the construction of the atomic bomb.
I’m going too far again. There are similar supercomputing models——
C Maes; Hypertask model; Tachyon model; Probabilistic Turing machine; Infinite state Turing machine, etc...
One category particularly attracted the attention of two Fenhans!
That's called: a closed time-like curve computer.
The principle is to use the special space-time with a closed time curve in the general theory of relativity to assist computer operations, just like equipping the computer with a time machine.
Then solving the problem is like having the same source code, leaving behind the battlefield, and if you can't pass the level once, then you have to pick up the files and try again. The memory keeps accumulating, wrong options are constantly eliminated, and time is stuck in a loop and will not move forward...
Until the moment when the question is asked, that is the next moment when the question is asked!
In this way, can the seemingly uncalculable Caiting constant be calculated cleverly?
Doesn’t it sound like science fiction?
But this is indeed a model carefully calculated by scientists and has its own scientific reason.
It is even possible to universally execute recursive functions in a time loop, exhausting all possibilities within a limited time, theoretically solving the problem of the grandfather paradox.
Normally, most supercomputing models are unachievable.
For example, some models require that time be discrete; some models require that the universe supports infinite divisibility of space and time, or that the intrinsic time of the world line is infinite; some must not be restricted by thermodynamics...
Another example is that the relativistic time effect computer requires accelerating the computer to close to the speed of light, preferably super-light speed, and using the time effect to compress the computer's solution time to improve efficiency. But the energy required is simply wishful thinking with today's technological means!
Closed timelike curves require a special type of general relativistic spacetime, and again...
etc!
If I remember correctly, the black hole is in a severely distorted general relativistic space-time, right?
So Black Hole Fenhan lists the reference books, and Budi Fenhan will know what he means!
This Fenhan suddenly planned to bend and fold the unpredictable and out-of-control black hole of the fallen world into a Lorenz manifold that can produce a closed time-like curve. This would give him the opportunity to transform the star disk of the super quantum computer into a closed time-like curve.
Time curve calculator!
Or to put it more simply, create a time gem!
It's just a more intelligent time gem that can be programmed and controlled. It can even be said to be a time recursive server.
The idea is really bold! It’s novel! It makes people want to go crazy!
But it is not so easy to achieve.
The Lorenz manifold corresponding to the closed time-like curve is essentially a pseudo-Riemannian manifold with metric symbol (p,1).
Many basic theorems of Riemannian geometry are established for pseudo-Riemannian manifolds, which allows us to use the Lévi-Civita connection and related curvature tensors on pseudo-Riemannian manifolds.
But there are still many theorems that are not true. For example, not every smooth manifold can have a pseudo-Riemannian metric with a given sign, and there are some special topological obstacles.
The mainstream mathematics community has not yet fully understood this.
To comprehensively and thoroughly solve these problems, Black Hole Ye Han needs more references and follows up on more cutting-edge papers.
There are indeed more papers.
This area belongs to the field of geometric analysis and is dedicated to using nonlinear differential equations to solve difficult problems in geometry and topology. In turn, it also uses geometric intuition and ideas to understand the structure of partial differential equations.
Since Hodge's theory, Kunihiko Odaira's embedding theorem laid the foundation, and Calabi-Yau theory emerged, it has become one of the most popular fields in mathematics today.
The two papers I posted before actually count.
If you want to equip a computer with a time machine, you must understand the theory of constructing a time machine.
Ye Han in the blessed land became as busy as a little bee, frantically searching for relevant cutting-edge papers here, and launching nuclear bomb printers and bombing them indiscriminately.
For a moment, the sky and the earth changed color, wind and thunder gathered, and light flowed, creating a magnificent sight!
Alas! My reputation has been completely wiped out!
Fireworks were bright on the screen. In front of the screen, Su Xing looked at the figures of Chen Lu, Liu Jinyan and Zhuang Wei rushing away from the door, feeling as if her heart was filled with despair.
"Ahhhhh!" She rubbed Ye Han's hair, which had just been pushed out, a little fresh and a little tingly, as if she was rubbing her two huskies!
"Don't make trouble, don't make trouble!" Ye Han instinctively stopped Su Xingmou from messing around and delaying him from checking the paper.
But how could the empress's furious struggle be easily suppressed?
Unable to break free after several attempts, Ye Han simply turned around and pulled Su Xing's eyes, and held him captive...
In this way, no matter how hard Su Xingmou tried, it would only be on his back, without delaying reading the paper.
Not good!
The empress, who was rolled into this position, instantly had a premonition.
Before she could figure out where the bad intuition came from, the large screen on the side suddenly switched, showing Qin Fang and a group of village cadres, Lin Hua and a group of ten people, Hu Stan and a group of researchers, and almost all the prominent figures in Blessed Land.
His big face was exposed, and he looked at the two of them through the surveillance camera.
Although not everyone can enter the room to prevent Ye Han who is in seclusion from being harassed, the monitoring... can.
Su Xingmou:(*????)
"We have something urgent! Really, it's very urgent!" Seeing that Su Xingmou was so angry that he was about to get angry, Lin Hua, the leader, quickly explained!