Algorithm Optimisation Championship. - page 24
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I hope I am not offending anyone by trying to break down the theory of multiple dimensions in a spatial sense. Whether I will succeed or not, judge for yourself.
And so - let's untangle an obvious confusion between concepts:
Every object summarises many properties of its own. The more complex an object, the more properties it possesses.The properties of an object can be physical and non-physical.
All physical properties of objects have their own scale of measurement.
Space is the sum of the three properties of a physical object: Length, Height, Width.
Colour of an object is the sum of the three components of electromagnetic radiation of the optical range.
Density of the body of an object is a physical characteristic.
Time - a scale for measuring processes.
And so on...
We understand that these are simply properties of a single object in front of us.
We should not confuse measurements of space (the sum of the three properties), with measurements of other properties of objects, many of which are in the zone of subjective perception.
By the way, to 'see' an object in the fourth dimension, all you need is memory. Scroll through the last minutes of rotation of a three-dimensional object.
To "see" an object in the fifth dimension, you need eyes capable of distinguishing colours.
To "see" an object in the sixth dimension, you need fingertips able to feel the softness of the surface.
To "see" an object in the seventh dimension, you need a sensitive nose capable of detecting a mixture of chemicals emitted into the air by the object.
To "see" an object in the eighth dimension one must be able to feel heat.
And the last dimension, the most fantastic: To "see" feelings of object one should have brain.
Of course, all these abilities are far beyond the capabilities of an ordinary person, and to expand one's perception of reality one needs a lot of training.))
I hope I am not offending anyone by trying to break down the theory of multiple dimensions in a spatial sense. Whether I will succeed or not, judge for yourself.
And so - let's untangle an obvious confusion between concepts:
Every object summarises many properties of its own. The more complex an object, the more properties it has.The properties of an object can be physical and non-physical.
All physical properties of objects have their own scale of measurement.
Space is the sum of the three properties of a physical object: Length, Height, Width.
Colour of an object is the sum of the three components of electromagnetic radiation of the optical range.
Density of the body of an object is a physical characteristic.
Time - a scale for measuring processes.
And so on...
We understand that these are simply properties of a single object in front of us.
We should not confuse the measurements of space (the sum of the three properties), with the measurements of other properties of objects, many of which are in the zone of subjective perception.
I view the dimensions of search space precisely as spatial. Some see the dimensions of search space as properties of objects. In both cases it is only an abstraction which helps to understand and represent properties of an optimized function.
And how does your reasoning help you? On the one hand you reject the idea of representation of properties of objects as spatial dimensions of search space, and on the other hand you deny a possibility of existence of spatial dimensions in quantities greater than 3.
One thing that might help is to understand that "search space" is literally the domain of values that a FF can take on. It does not matter how a researcher imagines this "space", the important thing is not to limit oneself to conventional scientific norms, otherwise one will very likely never find what he/she is looking for.
I see the dimensions of search space precisely as spatial. Some see the dimensions of the search space as properties of objects. In both cases, this is just an abstraction that helps in understanding and representing the properties of the function being optimized.
And how does your reasoning help you? On the one hand you reject the idea of representation of properties as spatial dimensions of search space, and on the other hand you deny possibility of existence of spatial dimensions in quantities greater than 3.
One thing that might help is to understand that "search space" is literally the domain of values that a FF can take on. It does not matter how a researcher imagines this 'space', what is important is not to limit oneself to conventional scientific norms, otherwise one will very likely never find what one is looking for.
As I see it, space is the sum of the three properties of the object. No more than that. Space-time is the sum of four properties. You can try combining space with smell or space with colour, but I don't think anyone will understand what we're talking about...
The search space you're talking about is one thing. A search space can contain all kinds of dimensions. You can search for a moment in time in the past, you can search for the perfect colour combination in a painting, you can search for the scent of your girlfriend's perfume, or the temperature for a bath...
Another thing is searching in space, which I talked about earlier and which I wanted to optimize. If someone were to tell you: Find a sphere that has a diameter of 15 cm and a face height of 25 cm in another dimension, where it is a cube. What would you say? You will say that you cannot find such a sphere, and you will be told that you have to use your imagination.
You consider the dimensions of search space as spatial, but you said that you cannot imagine multidimensional space. How is that possible?
...
Are there engineering majors?
A simple and straightforward example from life. Automotive engineering. A car needs to be built to have the following properties:
1. 1. Its dimensions in a given dimensional "box" of 4500x1800x1500.
2. Fuel consumption should not exceed 5 l/100.
3. Acceleration to 100 km/h in 12 seconds or less.
4. Must be aesthetically pleasing.
5. Comfortable interior.
6. The retail price must not exceed 500000 rubles.
So, what do we see in such a ToR? Totally unrelated, at first glance, object properties, where there are such purely physical space and speed, as well as purely subjective, such as convenience and appearance. But it is precisely the task of optimization, and car makers solve this optimization problem and the commercial success of the car will depend on how they will be able to connect all these contradictory "soft" and "white" properties together.
This example also has its own "search space". And such spaces are being explored by thousands of car companies.
You see the dimensions of search space precisely as spatial, but you yourself said that you cannot imagine multidimensional space. How is that so?
It means that I cannot see multidimensional spaces being 3 dimensional. I am forced to display the results of my search in a way that is accessible to my eyes. I told you already, I even showed you how.
Have you seen cartoons on the previous page? In order for the "Flat Eight Ball" to see the bearded man, he must be projected into his (the ball) flat 2-dimensional world. It is the same here. In order to see the multidimensional search space you need to project it into our 3-dimensional space. Projection, you see?
Are there engineering professions?
A simple and straightforward example from life. Automotive engineering. A car needs to be built to have the following properties:
1. 1. Its dimensions in a given dimensional "box" of 4500x1800x1500.
2. Fuel consumption should not exceed 5 l/100.
3. Acceleration to 100 km/h in 12 seconds or less.
4. Must be aesthetically pleasing.
5. Comfortable interior.
6. The retail price must not exceed 500000 rubles.
So, what do we see in such a ToR? Totally unrelated, at first glance, object properties, where there are such purely physical space and speed, as well as purely subjective, such as convenience and appearance. But it is precisely the task of optimization, and car makers solve this optimization problem and the commercial success of the car will depend on how they will be able to connect all these contradictory "soft" and "white" properties together.
This example also has its own "search space". And such spaces are explored by thousands of automotive companies.
In this example you are talking about The search space for solutions the tasks assigned to the engineer.
Before, you were talking about search in a multidimensional space, which supposedly has dimensions not only of a car's dimensions, but also its colour, softness of seats, comfort of interior and price.
Obviously, these dimensions have nothing to do with physical space, but with the search space, which is a pure abstraction.
In this example you are talking about The solution space the tasks assigned to the engineer.
Previously you talked about search in a multidimensional space which supposedly has dimensions not only of the dimensions of the car, but also of its colour, the softness of the seats, the comfort of the cabin and the price.
Obviously these dimensions have nothing to do with physical space, but have to do with the search space, which is a pure abstraction.
This means that I cannot see multidimensional spaces being 3-dimensional. I am forced to display the search results in a way that is accessible to my eyes. Told you already, and even showed you how.
Have you seen cartoons on the previous page? In order for the "Flat Eight Ball" to see the bearded man, he must be projected into his (the ball) flat 2-dimensional world. It is the same here. In order to see the multidimensional search space you need to project it into our 3-dimensional space. Projection, you see?
The cartoons have been watched.
There is an obvious logical error in the first cartoon:
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 claim that colour, sound, time, are also spatial dimensions, then that creature occupied significantly more dimensions than 2.
As for the second cartoon, I have not been able to trace the logic of the reasoning. Rotating forms were declared to occupy other dimensions, although I see such forms all the time in our world.
The scientific names of wicker baskets and soap bubbles gave them a fantastic image that stirred the imagination, but the rational part of the mind demanded an answer to the question, how many dimensions then do the birds' nests, which are woven by birds in spring, exist in?
How do you know that? You are three dimensional.