Algorithm Optimisation Championship. - page 25
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I watched the cartoons.
In the first cartoon there is an obvious mistake:
The number of dimensions of multidimensional space, within which the unfortunate creature supposedly occupied only two dimensions, was in fact much wider. That creature had time, colour, sound, even emotions.
If you follow your theory of multidimensional space and argue that colour, sound, time, are also spatial dimensions, then that creature occupied significantly more dimensions than 2.
OK. Then let's go from the other side. I'll give it one last try.
Take a good look. There is a certain object. It has several properties, such as size, colour, smell, and aesthetic appearance. In order to change the properties to get what we need in an optimal form, we need to bring these properties to the same scale, say, from -10.0 to 10.0. Thus, an object with properties of the same range will be presented to computer with properties presented in one scale. Therefore, the object will be presented to the computer as homogeneous, with the same type of properties with the same type of measurements. And since the properties are of the same type, we can say that it is a spatial object with dimensions equal to the spatial dimensions of this object...! Then, to see with human eyes, we project this multidimensional object into our 3-dimensional space, and voila! - we'll see it!...
You see? We can see space, but we can't see anything else, that's why we bring all the properties of the object to a spatial form.
And how do you know otherwise, aren't you also three-dimensional? ))
OK. Then we'll come at it from the other side. Taking one last shot.
Take a good look. There is an object. It has several properties, such as size, colour, smell, and aesthetic appearance. In order to change the properties to get what we need in an optimal form, we need to bring these properties to the same scale, say, from -10.0 to 10.0. Thus, an object with properties of the same range will be presented to computer with properties presented in one scale. Therefore, the object will be presented to the computer as homogeneous, with the same type of properties with the same type of measurements. And since the properties are of the same type, we can say that it is a spatial object with dimensions equal to the spatial dimensions of this object...! Then, to see with human eyes, we project this multidimensional object into our 3-dimensional space, and voila! - we see it!...
Understand?
It all makes sense to me. There is an object. It has several properties. Such as size, colour, smell, aesthetic appearance.
Mathematically, we reduce all these properties to a single scale and examine the optimal values of these properties.
For a computer, these are meaningless numbers and the object is homogeneous to it.
For a mathematical function, it's just a set of parameters.
For us, it's a multidimensional space for us to find the formof object phenomenon we want.
We select suitable characteristics to the object using mathematics, computer and programming as tools.
But then, suddenly... God, we have a multidimensional space! Let's explore it! To hell with the object! We have a new world in front of us!!!
Then I come in and I say, "What are you guys looking for?"
They answer me - "We're optimising the search in multidimensional space. We were looking for optimal values for the object's properties and found a new world beyond our perception. We are having trouble imagining it, but we are trying very hard...".
I ask - "Do you guys want to become the multidimensional beings from the movie Interstellar?" .
How do you guys not lose the ability to communicate with each other like they did...
It all makes sense to me. There is an object. It has several properties. Such as size, colour, smell, aesthetic appearance.
Mathematically, we reduce all these properties to a single scale and examine the optimal values of these properties.
For a computer, these are meaningless numbers and the object is homogeneous to it.
For a mathematical function, it's just a set of parameters.
For us, it is the multidimensional space of our search for the desired formof the object phenomenon.
We select suitable characteristics to the object using mathematics, computer and programming as tools.
But then, suddenly... God, we have a multidimensional space! Let's explore it! To hell with the object! We have a new world in front of us!!!
Then I come in and I say, "What are you guys looking for?"
They answer me - "We're optimising the search in multidimensional space. We were looking for optimal values for the object's properties and found a new world beyond our perception. We are having trouble imagining it, but we are trying very hard...".
I ask - "Do you guys want to become the multidimensional beings from the movie Interstellar?" .
How do you guys not lose the ability to communicate with each other like they did...
They were in really different spaces and for obvious reasons communication was difficult, to put it mildly.
But we are in the same space, so what prevents us from speaking the same language? - It is not clear.
No matter how we talk, but the machine will calculate, and we need to present the task to the machine in a way it can understand it, and present the results of calculations so that we can see and understand them ourselves, and at the same time so that we can control the machine.
Multidimensional representation of a task allows solving optimization problems, but if you do not go further than 3 dimensions, you will not optimize much. Unfortunately, or maybe fortunately....
Algorithms are logic, analysis. 2+2=4. All analogies from the physical world will not be fully adequate.
If we use analogies, we can show for example that 2+2=2.
When programming we must think with the left side of the brain.
I don't know it. I can only describe it, so I can investigate it. And you are not even trying to describe it.))
Andrew, pay attention to your logical fallacies: "I don't know it. I can only describe it and therefore investigate it.
If you do not know something, you can describe it only after you investigate, not before.
First investigate multidimensional space (where there are more than three spatial dimensions), prove that it exists and then describe it.
The guys there were in really different spaces and for obvious reasons communication was difficult, to put it mildly.
But we are in the same space, so what prevents us from speaking the same language? - It is not clear.
No matter how we talk, but the machine will calculate, and we need to present the task to the machine in a way it can understand it, and present the results of calculations so that we can see and understand them ourselves, and at the same time so that we can control the machine.
Multidimensional representation of the task allows solving optimization problems, but if you do not go further than 3 dimensions, you will not optimize much. Unfortunately, or maybe fortunately....
Physical space and search space are different things.
That's the essence of the confusion.
Physical space is three dimensions: height, width, length.
Search space is an abstraction and can have infinitely many dimensions because it is a subjective concept.
Algorithms are logic, analysis. 2+2=4. All analogies from the physical world will not be fully adequate.
If we use analogies, we can show for example that 2+2=2.
Programming must think with the left side of the brain.
Andrew, pay attention to your logical fallacies: "I don't know it. I can only describe it and therefore investigate it.
If you do not know something, you can describe it only after you investigate, not before.
First investigate multidimensional space (where there are more than three spatial dimensions), prove that it exists and then describe it.
Are you aware that we are on planet Earth, a spherical shaped planet that revolves around the Sun, a star in the Milky Way galaxy, which is located in a cluster of gal...
I think you are aware of that. However, you have not been to all these places and have not seen them with your eyes. A man doesn't have to stick his fingers in a socket to be sure it's dangerous, you know what I mean?
Most discoveries were made first "in the head" and only later confirmed by experiments. Not to mention what a person can never achieve with his personal presence, but that does not stop a person from comprehending the world.
ZS. Penrose has never been read as I see it. Too bad....
It is obvious that mathematics does not always relate to reality, which creates a host of pseudoscientific theories.
Such as the one about multiple spatial dimensions.
Where does that come from? Well, for example, from the fact that you can add extra coordinate axes to a quadratic function drawing a parabola, and infinitely many of them...
And if you draw a dog with 10 legs, can you assume that it exists, but nobody has seen it yet?
It is possible to devote years to the study of alien life forms which no one has ever seen, simply by relying on the calculations of a computer program which will itself calculate what forms of life may exist on the planets of the galaxy after entering the scientific data on these planets.
What is the value of such a study?
I want to remind you that concepts of the Earth and stars, laws of heavenly mechanics have been formed for centuries on the basis of empirical method of research (supervision and measurement).
At the same time, there has always been a mess of pseudoscientific theories in the heads of people who do not follow the scientific way of thinking, which are based on subjective sensations and imaginary outbursts beyond the boundaries of reality.
Penrose is a must-read. I promise.