I think this is not cared for programming, but do we know it?

There is no "left" or "right" when we speak about bits.
There are (D0..D7 for byte) D0..D31 for DWORD pins on CPU

7...0 for intel

Please correct me if I am wrong.

But I thought that there were not any differences between OS's in the order of a single byte.

So that 10 decimal is always stored as 0000 01010

But multiple bytes the order would be different.

So 65280 could be stored as 11111111 00000000 or 00000000 11111111.

It is simply human way of thinking that most significant digits (in every radix) are most "left" and less significant are most "right". (Hm, interesting how the people from arabian countries think? ) As a result we have mnemonics for shift operation: shl,rol - from less to most significant bits, shr,ror - from most to less significant bits.
Though these directions have phisical meaning only on the sceen and on piece of paper.

Regards.

Yes, x86 (Intel and AMD) are Little Endian CPUs, they place first the least significant byte in memory: 00h,FFh
Other CPUs (like Motorola 68XX0) are Big Endian, so they use another order: FFh,00h

Also there are CPUs which can use both modes,
but they are not so cool, because of incompatibility with FASM

Just the same as we do, because numerical system we use was developed by them.

They write right to left but they do arithmetic in the same way we do (only the characters are different)

And that's why we write numbers from right to left...

Very interesting thoughts I admit, on the writing side, shouldt my age be written 9 and 1, so the least significant numbers go first. Hmm, 0000001 one million:D
It seems confusing, but got used to *-hand traffic and reading/writing L2R or R2L so why wouldn't we start getting used to left 2 right writing of numbers

Intel microps do not handle numbers directly in bigendian, but you have these instructions:

xchg ah,al ; invert 16bit number
bswap eax ; invert 32bit number

which can be very useful.

liu: i think you really could use my tutorial
http://board.flatassembler.net/topic.php?t=1178
this is one of things answered there