Bremmerman Limit - Uncomputable Tasks

Jokes jokes, but what if you think about the volume of such a "hard" disk?
In 1964, Hans Bremmerman published an article “Optimization through evolution and recombination,” the main conclusion of which is:

There is no data processing system, artificial or natural, that can process more than 2 × 10 ^ 47 bits per second per gram of its mass.
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The mass of the Earth is estimated at about 6 × 10 ^ 27 g, and the age of 10 ^ 10 years, the year consists of approximately 3.14 × 10 ^ 7 seconds. Our imaginary computer system could handle 2.56 × 10 ^ 93 bits, rounding up to about 10 ^ 93 bits.

Tasks that require processing more than 10 ^ 93 bits of information are called transcomputational tasks. Unfortunately, combinatorics tells us that such a limit can be reached for problems of even relatively small size. For example, in pattern recognition: let there be an array q * q, each element of which can be colored with one of k colors, then the whole coloring options can be k ^ (q * q). If the array is 18 × 18, then the task is transversal with two colors; for a 10 × 10 array it becomes transversal with 9 colors. It is clear that it is impossible to consider all variants of retinal images, having about a million photosensitive cones. Another example of such a task is testing the microchip, which has 308 inputs and only 1 output.

The most natural way to solve transversal problems is the reformulation, weakening of conditions, the probabilistic nature of the solution. I want to believe that all the same algorithms of artificial intelligence will appear, in particular, for solving the problem of pattern recognition, which can allow to automatically solve transversal tasks, similar to how a human brain can do it.

Bremmerman limit proof:

For processing information must be encoded. Suppose that it is encoded as energy levels in the interval [0, E]. Let the energy levels be measured with an accuracy of dE. Thus, on the entire interval there will be N = E / dE subintervals, each of which can be occupied or not (1 or 0).
The maximum number of bits will be log2 (N + 1)

In order to provide more information, it is necessary to reduce dE. According to the Heisenberg uncertainty principle, energy can be measured with an accuracy of dE if dE * dt> = h, where dt is the duration of the measurement time, h = 6.625 × 10 ^ -27 erg / s (Planck constant)

We get, N <= Edt / h
If we present the available energy E with an appropriate amount of mass according to Einstein's formula E = mc ^ 2
N = mc ^ 2 * dt / h

Substituting c and h, we have N = 1.35 × 10 ^ 47 * m * dt

For a mass of 1 g (m = 1) and a time of 1 s (dt = 1), we obtain the indicated value
N = 2 × 10 ^ 47 bits

PS According to the book by J. Clear “Systemology. Automation of solving system problems”

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