Arithmetic is at the core of mathematics. Together with mathematics, arithmetic is metaphorically referred to as a "language of nature," even if arithmetic, and in particular its decimal syntax, were conceived by, and always reside, in our mind. Only written versions of the arithmetic become apparent externally as static symbols of manuscripts or as dynamic symbols of abaci and computers. In this chapter we apply the known arithmetical syntax to the genetic code just as Champollion juxtaposed the ancient Greek to the Egyptian alphabet. We do not go beyond the limits of elementary arithmetic that everyone studied at primary school. Calculations done are simple; they can be carried out even manually. We only refer to a few well-known abstract entities of arithmetic listed in Fig. 1.

Arithmetic begins with zero and natural numbers. The zero is the supreme abstraction of arithmetic. Its use by any alphabet, including the genetic code, can be an indicator of artificiality. But how can one identify the abstract entity of nothing in practice? Well, there is a simple and elegant method to detect the zero. It is of common knowledge that the natural numbers are aligned into a natural series 1, 2, 3, ... and so on endlessly. The zero occupies its own abstract position on the only flank of the natural series 0, 1, 2, 3, ... One can look for zero in that position inside the newly systematized genetic code in Sections 11 and 13.

Fig. 1 The inanimate outer world and living mind. The outer world is governed rigidly by immutable laws of nature. On the contrary, the human mind voluntarily makes its own conventional codes including the decimal syntax of arithmetic for the sake of information exchange and scientific activity. A vertical line demarcates lifeless substance from basic abstractions of arithmetic that are residents of mind. Computerized robots working in the outer world are equipped with instructions that use these abstractions in the form of written symbols.

The early Greek philosopher and mathematician Pythagoras looked for a numerical harmony in the Cosmos. His image here symbolizes abstract entities of mind and new arithmetical features of the genetic code. Pythagoras had proved a theorem that the sum of the squares of each of the two sides of any right triangle is equal to the square of the hypotenuse. The genetic code has within itself a numerical symbol of the "Egyptian triangle" that is by far the best-known example of a right triangle

Fig. 1 The inanimate outer world and living mind. The outer world is governed rigidly by immutable laws of nature. On the contrary, the human mind voluntarily makes its own conventional codes including the decimal syntax of arithmetic for the sake of information exchange and scientific activity. A vertical line demarcates lifeless substance from basic abstractions of arithmetic that are residents of mind. Computerized robots working in the outer world are equipped with instructions that use these abstractions in the form of written symbols.

The early Greek philosopher and mathematician Pythagoras looked for a numerical harmony in the Cosmos. His image here symbolizes abstract entities of mind and new arithmetical features of the genetic code. Pythagoras had proved a theorem that the sum of the squares of each of the two sides of any right triangle is equal to the square of the hypotenuse. The genetic code has within itself a numerical symbol of the "Egyptian triangle" that is by far the best-known example of a right triangle

The Hindus had devised a zero during the time when the text on the Rosetta Stone was written, i.e. almost 2000 years ago. They applied zero in the place-value number system and perfected it once and for all. The decimal system is a syntactic rule for symbolic writing of words whose meaning is the quantity of anything. These words are referred to as numbers. It is commonly accepted that people chose the radix or base ten for their number language voluntarily, being guided only by an anatomic feature - ten fingers. But this choice becomes more intriguing in the light of the decimal syntax discovered inside the code. Could it be that the decimal system through arranged decimally genetic code and through translated by such code genes predetermine the system's own choice recognized by people as a voluntary one?

It belongs to the world of culture, whereas any physical quantity described as a number is separated from this description. The counter assumption is that some "elements of numbers" are inherent to all things. This fancy is very ancient and belongs to the so-called Pythagorean doctrine. Modern science, however, shares Plato's views that numbers exist as abstract ideas apart from physical bodies. Such understanding establishes the distinction between mathematics and physics. Our subject matter skips knotty philosophical problems focusing instead on the syntax of the numerical language of arithmetic. Its symbolical notations done by the rule of some positional number system could only arise from information experimentations of the mind. Therefore, we can consider the positional system as indicator of artificiality. The fact that the zero is a component part of this system becomes an even clearer indicator.

Let us consider how indicators work. For instance, everyone uses digital signs and syntactic rules of arithmetic to do number notations and to perform certain procedures, say, summing up. Such calculations looking for quantitative properties of some physical object are routine acts. If some additions were originally performed in the decimal system, it would be an absurd idea to repeat the same calculations, say, in the binary system because important data would be lost. Indeed, physics and chemistry are indifferent to the internal syntax of arithmetical language. All they require from arithmetic is quantitative data. The absence of a privileged numerical system is therefore usually indicative of natural objects.

Computers are quite different in this matter. They are internally based on one privileged numerical system - binary - but communicate externally and can handle data in other systems. So, this time it is not an absurd idea at all to care about potential loss of data at investigation of a computer design when using systems other than the binary one. The presence of a privileged numerical system(s) in computers is unambiguously indicative of an information artifact. In a hypothetical case, if an issue of the origin of the robot-geologist in Fig. 1 was raised at the Meridiani Planum area on Mars, the zero-one system of the robot's microprocessors would instantly bring the issue to resolution. In a similar manner, the numerals written in the Egyptian scale of notation, say, in the phrase "10 gold crowns of the Pharaoh" would additionally confirm artificiality of the Rosetta Stone, if there were doubts to its origin. Of course, any given artificial object does not necessarily have inside itself a privileged numerical system. However, if this is the case, such a system indicates an indisputable artifact.

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