how is ontology of natural numbers naturally natural?

What are researches done in this line of inquiry??????

Nature dont bother whatever conventions human prepare for humans own social needs. Sanjoy Nath 's materialistic arithmetic systems try to understand so inquires

1 how much naturally natural are human's conventions?

2 how much nature friendly are humans convention with which humans calculate the values of humans natural numbers?

3 if nature had to design a number system for humans then would that number system ever looked like decimal systems? How much quantum like structure is present inside encryption encoding process (convention as rule of game to evaluate valuation of a decimal systems string) as humans follow everyday??????

One analogy here is 

States are like balls and nature tries to arrange these balls are stored in certain sieve (special kind of bag which has several bins of different capacities and the most compact form to arrange capacities of these bins (discrete ball holding capacity of each bins are crucial for different purpose such that humans can easily remember the preset universal conventtions and whole society of mankind learns this convention of bin addressing system which address of bins also carry the bins ball holding capacity. The valuation process is dependent on convention to address these bins and this convention is just human's mnemonic tool and nature has not generated this convention. This convention fulfilling three purpose at a time. First it is easy for humans to remember process of evaluation,second it is easy to calculate which (r th bin from left side)bin has ball holding capacity (10/10)*(10^(n - r+1-1 )) and this rule is fixed,thirdly the evaluation means total number of balls present in whole bag and size of the bag is of least possible string length n. Now we can think each such bins as orbitals and each such balls as states. All such states are equally likely. These states are arranged in bins just to fulfill above convenience for human cognitive load reductions and these compacification scheme has nothing to do with natures law .These compacification and arrangements of total number of balls (evaluation means total number of balls in the bag whatever compacification conventions we choose the total numbers of balls don't change. We need to change evaluation algorithm if we change convention for compacification encoding systems. This means our evaluation process is not naturally natural. These evaluation process need to change if we change our compacification schemes. 

Strict note that whatever scheme we take whatever standards of encoding decoding systems we adopt the fundamental evaluation need to remain same after encoding and decoding of compactified representation and evaluation means counting of all balls (that is total available contained positive states) are there in whole codified such bag.

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Sanjoy Nath dont consider natural numbers as numbers.Instead Sanjoy Nath has deep philosophy to consider 0 1 2 3 4 5 7 6 8 9 are just names of 10 states which occupy r th positions on a n position string (state container string) each of such r th positions in n long state string which are having orbital like fixed storage capacities each. This means all different r th position is r th orbital and we calculate state storing capacity of r th orbital from left side of  n position long string is (10^(n - r+1-1 )) and actual states stored in that orbital is states orbital is (d/10)*(10^(n - r+1-1 ))

The rule for calculating total state storing capacity in r th state storing orbital is fixed in 10 state dependent system

But actually stored states in each of such orbital are less than or equal to 9 means how many named states are valued as ordinal characteristics and rule is fixed as

0<1<2<3<4<5<6<7<8<9

If we change this order then our whole system changes and all behaviors of prime states also changes and all characteristics of the usage rules drastically change.

The total amount of states actually stored in any r th orbital in n orbital long orbital string governs as a fraction f_r which is always between 0 to 1

0<= f_r<=1

The value of f_r creates pressure on neighbourhoods of such state filled strings. These state filled strings have every r th orbital having fixed upper limit to store such states. . In n orbital long string r th orbital has (n -r) numbers of right side orbitals. All of such of all These right side orbitals total state holding capacity is always less than state holding capacity in r th orbital (r and n are measured from left side of the n orbital string.

All other dependent rules of games like 

+ as a interaction game,

- as a interaction game,

× as a interaction game,

÷ as a interaction game,

= as a interaction game,

√ as a interaction game,

^ as a interaction game,

Log as a interaction game,

Note that all there rules of games are entirely dependent upon our conventions of compaction of states in our mnemonic dependent convention of encoding and mnemonic dependent storage arrangement of orbitals addressing schemes. All rule of game are changeable if we change our orbital wise capacity calculation mnemonic standard or/and if we change orbital addressing schemes.

Strict note that whatever scheme we take whatever standards of encoding decoding systems we adopt the fundamental evaluation need to remain same after encoding and decoding of compactified representation and evaluation means counting of all balls (that is total available contained positive states) are there in whole codified such bag.All above rules of game are representation dependent (evaluation convention dependent)

All the above rules of game are revised accordingly when encoding decoding convention are changed but every such rules of games are verified with evaluation (value of total count of states/balls) 

Strict note that whatever scheme we take whatever standards of encoding decoding systems we adopt the fundamental evaluation need to remain same after encoding and decoding of compactified representation and evaluation means counting of all balls (that is total available contained positive states) are there in whole codified such bag.