Engineering a Trainset of Inter-Communicating Functions for Astronomical Numbers

Of course, it is not enough to have a train-shaped function, it should be modified.

A solution is engineered for modulating values at intervals representing the order of magnitude to be modulated.

Segment one allows the removal of the specific digit in a series (n, m), Seg two the input of a new value (n2, m2).

With the conductor seeing to the destination, the train ahead can now be engineered to lay down a series of values along the railway, in any order.

A replace function, two dimensional addressing (x, y or n, m) of a digit (n ) at a series of magnitudes (m ).

F(x) = i - [(n * 10^(m - 1)] - [(n2 * 10^(m2 - 1)]

Let's try it...

Replacing the middle digit, a nine at the nineth order with a value of one.

= 12345678987654321 - [(9 * 10^(9 - 1)] - [(1 * 10^(9 - 1)]

..calculator err ..or ..it is not complicated math, I can change one digit at a time using my mind. Calculators have registers that are too short to contain operations requiring base two values comprised of too many binary bits. Too long, fifteen orders of magnitude should not break every calculator.

By way of an accommodating function and ideal scenario, changing the value in only one order of magnitude, no matter how many are declared in coordinates of (m), is a matter for mental calculation.

I know that only the nineth digit changed, all else about the astronomical number remains.

With 270 zeros (orders of magnitude) we know that changing/replacing only the two-hundred and sixty-eighth digit, is a simple operation for even the mind's-eye.

Our minds can show that taking away (9 - 1) from the nineth order of magnitude, resulted in the correct change of value .. without a calculator imposing the limits of calculations.

Tired of those error-prone calculators that fail after one too many orders of magnitude.

I see diagonally moving bands of digits allowing multiplication and divisions, modules that can be used for astronomical calculations. Within ASICs first designed as stand-alone units. Later available as a datapath, co-processing for the motherboards of future CPUs.

Filesystems of today, allow for numbers that contain billions of digits and more, to be calculated using an experimental number of open iterations (testing the limits of n^P).

I think the best way to attempt this, continuance of engineering concise and useful additions to the trainset of communicating functions.

The limit for opened instances of encapsulated calculation, depends on the number of said "bands of digits" which can be supported by a hardware configuration and open files.