The key to the information revolution
Many years ago, while still a student, I thought about why we solve equations, and not look for their particular solutions in some big table? Probably took the old joke as a call to action.
Then the understanding came that such a table should be infinitely large and at the same time constantly expand just like our universe. But in life it is often necessary to use both tables and functions that can generate tabular data. In other words, instead of a single data array, it is possible to use an equation that, under certain conditions, can repeat all the values ​​of the array.
The only question is what is preferable for us - storing the finished array or solving the equation that generates it?
Storage implies allocated space on the carrier, and computation implies the computational capabilities of the processor.
Thus, the natural scales of the scales are determined: in the first, the speed of access to the elements of a ready-made, written somewhere array that does not require large computational abilities to read values; in the other, there is practically no space occupied by the equation and the required large computational capacity for generating information.
But in the array, or matrix, you can write any values, incl. and multimedia content data, such as songs, photos or videos (binary file with zeros and ones).
Thus, for analysis, we have a binary sequence of a certain size, consisting of zeros and ones.
This means that if we find a function (formula, equation) that generates this sequence of zeros and ones in the right order, then instead of a music file that takes a certain place, we can solve its equation with certain initial conditions, which takes a couple of bytes and get the same composition, video sequence or document is simply “loading” the processor.
This seems like a crazy idea, because finding an equation that can produce several billionaires of zeros and ones in the same sequence as in the original mentally leads us to the equation of unimaginable sizes, or even their system. Perhaps, using, for example, the polynomial regression analysis of the Nth degree will be so, but what if the answer lies in a simple equation with several variables?
For example, a sine wave can be described by a regressive polynomial of a certain order, or you can simply write sin (x). That is, we have 2 approaches that lead to an identical result. Only one requires significant computational abilities, and the second only a few crystal cycles (to calculate a single value).
As you know, in the binary form the information file (with the semantic loading) for the outside observer is noise. Well, or if in a scientific way - a noise signal. And if it is completely scientific, with a pseudo-noise signal or a sequence if we consider a digital file (due to the limited capacity of the machine). And only having the necessary decoding algorithm can be read information from this file.
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Wouldn't it be a revolution in the world of digital information, finding the functions generating it? Imagine that cloud storage no longer needs thousands of physical storage drives in racks. To watch a movie you no longer need to download the file, but only information about it. How much then will the communication lines be unloaded? The "race" bandwidth will stop for a long time. And the new stage of the race of computing abilities will begin, from which the society will only benefit. This is a progressive way of developing IT technologies.
My name is Siegurd, and I will prove to you that this is possible!
Attention, anecdote!
Physics, mathematics and engineer were given the task to find the volume of a red ball.
The physicist plunged the ball into a glass of water and measured the volume of the displaced fluid.
The mathematician measured the diameter of the ball and calculated the triple integral.
The engineer took out his “Table of volumes of red rubber balls” from the table and found the desired value.
The physicist plunged the ball into a glass of water and measured the volume of the displaced fluid.
The mathematician measured the diameter of the ball and calculated the triple integral.
The engineer took out his “Table of volumes of red rubber balls” from the table and found the desired value.
Then the understanding came that such a table should be infinitely large and at the same time constantly expand just like our universe. But in life it is often necessary to use both tables and functions that can generate tabular data. In other words, instead of a single data array, it is possible to use an equation that, under certain conditions, can repeat all the values ​​of the array.
The only question is what is preferable for us - storing the finished array or solving the equation that generates it?
Storage implies allocated space on the carrier, and computation implies the computational capabilities of the processor.
Thus, the natural scales of the scales are determined: in the first, the speed of access to the elements of a ready-made, written somewhere array that does not require large computational abilities to read values; in the other, there is practically no space occupied by the equation and the required large computational capacity for generating information.
But in the array, or matrix, you can write any values, incl. and multimedia content data, such as songs, photos or videos (binary file with zeros and ones).
Thus, for analysis, we have a binary sequence of a certain size, consisting of zeros and ones.
This means that if we find a function (formula, equation) that generates this sequence of zeros and ones in the right order, then instead of a music file that takes a certain place, we can solve its equation with certain initial conditions, which takes a couple of bytes and get the same composition, video sequence or document is simply “loading” the processor.
This seems like a crazy idea, because finding an equation that can produce several billionaires of zeros and ones in the same sequence as in the original mentally leads us to the equation of unimaginable sizes, or even their system. Perhaps, using, for example, the polynomial regression analysis of the Nth degree will be so, but what if the answer lies in a simple equation with several variables?
For example, a sine wave can be described by a regressive polynomial of a certain order, or you can simply write sin (x). That is, we have 2 approaches that lead to an identical result. Only one requires significant computational abilities, and the second only a few crystal cycles (to calculate a single value).
As you know, in the binary form the information file (with the semantic loading) for the outside observer is noise. Well, or if in a scientific way - a noise signal. And if it is completely scientific, with a pseudo-noise signal or a sequence if we consider a digital file (due to the limited capacity of the machine). And only having the necessary decoding algorithm can be read information from this file.
')
Wouldn't it be a revolution in the world of digital information, finding the functions generating it? Imagine that cloud storage no longer needs thousands of physical storage drives in racks. To watch a movie you no longer need to download the file, but only information about it. How much then will the communication lines be unloaded? The "race" bandwidth will stop for a long time. And the new stage of the race of computing abilities will begin, from which the society will only benefit. This is a progressive way of developing IT technologies.
My name is Siegurd, and I will prove to you that this is possible!
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I know that it sounds pathetic =), just because I see a solution to the problem, like every scientist is breathtaking. Ahead - the night of research. Periodically I will post the results here with examples, unless of course you are interested. Besides, I argued with my colleagues for a beer that I could turn a video file into a small equation. Now, as you understand, I have no choice =)
See you soon!
See you soon!
Source: https://habr.com/ru/post/303014/
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