Algorithm Optimisation Championship. - page 23
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
There are rules, goals are set in the first posts of the branch. And the fact that here are further discussions - well, you would like to be only one my post in this thread and silence? .... It's not that hard to arrange, ask the moderators to clean up a branch and that's it... And then deal with the optimization yourself, without explanations or comments.
Here... I've compiled a few of your posts... There are mistakes in all of them. That's OK, we'll fix it now.
There are notions of Function - some dependence on parameters, you even have parameters mixed up with coefficients in some places. And there are Equations - all parameters are reduced to a general dependence.
So, let's start with a simple one. Equation:
2*x+3=0, is an equation of the form a*X+c = 0. Now let's represent this equation as a function : x=-c/a=-3/2=-1.5. It is a one dimensional object in one dimensional space because there is only one dimension, length. In our example, the object has a length of -1.5, that is, a segment deferred to the left of point 0.
Now, tell me, is everything clear here? If it's not clear, we can't move on.
ZS. Find your own free time, though, and read old Penrose's book. At least a very entertaining read.
Please forgive my mathematical errors. They may be... But the essence of my question lies beyond mathematics.
Technically, you're right. You can create additional axes of coordinates. In the equation. I have no doubt about that. Just write in the equation of the analytic function. But then what? Why would we do that? We're not going to build a curved line through the new dimensions we've created, we're not going to build a surface... We'll still have the same three-dimensional picture. We can't physically take it beyond the boundaries of three-dimensional space. Only mathematically.
Why?
Because search optimization has to have a practical application, in our four-dimensional world. Otherwise, why do it at all?
I'm sure that's the only mistake. If we imagine optimization of search for vertices (peaks) in three-dimensional space, the task becomes very clear for everyone. Otherwise, people will constantly "lose their orientation in space". ))
I will definitely read Penrose now)).
Please forgive my mathematical errors. They may be... But the crux of my question lies beyond mathematics.
Technically, you're right. You could create additional coordinate axes. In the equation. I don't doubt it. Just write in the equation of the analytic function. But then what? Why do we need to do that? We're not going to build a curved line through the new dimensions we've created, we're not going to build a surface... We'll still have the same three-dimensional picture. We can't physically take it beyond the boundaries of three-dimensional space. Only mathematically.
Why?
Because search optimization has to have a practical application, in our four-dimensional world. Otherwise, why bother doing it at all?
I'm sure that's the only mistake. If we imagine optimization of finding vertices (peaks) in three-dimensional space, the problem becomes clear to everyone. Otherwise, people will constantly "lose their orientation in space". ))
Very well. I can skip the examples with two-dimensional objects. Let's go straight to 3-dimensional ones.
An equation of the form a*x+b*y+c*z+d=0 This is the equation of a 3-dimensional object. Where x, y, z are dimensions, or coordinate axes, length, height, depth. For a 3 dimensional object to exist, you need a space with a minimum of 3 dimensions. The function for z will look like this z=(-a*x-b*y)/c. The functions for x and for y will be represented in the same way.
Now let's see if a 1-dimensional object can be located in 3-dimensional space? - It can. And can a 2-dimensional one in 3-dimensional space? - It can. But the opposite is not the case! That is, any object, can only exist in space with a number of dimensions where as many or more than the object itself.
But 3-dimensional objects can be in 4-dimensional space, and higher. Someone said that in 4-dimensional space, the 4th dimension is time. This is done to understand the physical meaning of time. but not to describe space.
We cannot imagine spaces having dimensions greater than 3, because we are part of a 3-dimensional world (it is not the fault of meta-quotes that we cannot imagine graphs with greater dimensions than 3-dimensional).
A 4-dimensional object, by the way, is called a tesseract and a 5-dimensional penteract.
Why do we need measurements in our reasoning in quantities greater than 3? To understand that the function f(x1,x2,x3.....x500) cannot be graphically defined in three-dimensional space. It is in multidimensional space. So to say that it is some flat surface from our 3-dimensional world is not true. We cannot even imagine where the top and bottom are in 500-dimensional space. We can only talk about the maximum values of a function that represents a 500 dimensional object.
Dmitry has told you correctly. Try to optimise a function with 1 variable (2 dimensional object), then with 2 variables (3 dimensional object). The work of the optimizer can be checked visually in these cases. But as soon as you go to functions with 3 variables, i.e. with 4-dimensional objects, you realize that you cannot check the algorithm's work visually, and it can be felt even at the level of feelings that you pass to a certain level which is not accessible for physical perception.
But how should we be? How do we visually check and track the algorithm? Look at what I suggested earlier, there is a small trick - a multidimensional object is represented as a sum of 3-dimensional objects (the same way we do when we represent 4-dimensional or more objects in pictures). Then why did we talk about spaces with more than 3 dimensions at all? So that you can imagine that searching is much more difficult than simply probing the surface with a walking stick.
Please forgive my mathematical errors. They may be... But the crux of my question lies beyond mathematics.
Technically, you're right. You could create additional coordinate axes. In an equation. I don't doubt that. Just write in the equation of the analytic function. But then what? Why do we need to do that? We're not going to build a curved line through the new dimensions we've created, we're not going to build a surface... We'll still have the same three-dimensional picture. We can't physically take it beyond the boundaries of three-dimensional space. Only mathematically.
Why?
Because search optimization has to have a practical application, in our four-dimensional world. Otherwise, why do it at all?
I'm sure that's the only mistake. If we imagine optimization of search for vertices (peaks) in three-dimensional space, the task becomes very clear to everyone. Otherwise, people will constantly "lose their orientation in space". ))
I'll definitely read Penrose now)).
There is a practical optimization task: we need to fit into an interior a parallelepiped with different sizes of sides (the sizes are optimized), and choose the strength and colour. Robustness and colour are also optimizable parameters, which have their own scales (in this case, the colour can be divided into three RGB components, so only one colour has three scales). For example a big red looks bad, but a small red looks just as good as a big blue.
Durability is also optimized by material, you can make a paper of wood metal plastic or their composition (well take the 3 basic materials and weighed in the product of each percentage, how much should be optimized).
In total we have 3 scales of optimization of materials.
Three scales of optimization by colour
3 scales of optimization by size.
3+3+3=9
9 dimensions of optimization.
Lift your head and you will see a lot of optimization problems in multidimensional spaces.
HZZY We live in a closed infinite plane 40 000 km long, in a narrow strip of 8 km, and you want to say that our world is three dimensional? Three dimensions are only an illusion of perception, it may as well be 4-dimensional, 5-dimensional and 11-dimensional, just our perception organs are configured only three, because we have two eyes, one-eyed man has a flat world.
A dog, on the other hand, can smell a man from a week ago, a man from a week ago is still in the present and not, as with us, in the past. Are you saying that dogs have a three-dimensional world?
Your talk has brought to mind...
Your talk brought back memories...
Good cartoon, illustrative. They say it's better to see it once... :)
And this cartoon goes even further. Don't watch for the faint-hearted and epileptic!