Lest you all think this is some sort of minor matter, see this official early ARPANet Document (also published in the IEEE Computer Society "Computer" magazine.)
Thank you westfw, great text.
I'm old enough in the unix world to remember I had to do a "dd if=aaa.tar of=bbb.tar conv=swab" to a tar archive copied from a Unisys 5000 (Motorola 68000) to a ESIX/386 (Intel) using QIC150 tapes. This of course was before networking was available.
But so far I always thought that the weight of the bits inside a byte was really a standard, never stopped to think that it is not very logical to have
BYTE0 - BYTE1 - BYTE2 ... BYTEN
Grows from left to right, naturally, like any Cartesian referential.
But inside each byte we have
BIT7 - BIT6 - BIT5 - BIT4 - BIT3 - BIT2 - BIT1 - BIT0
I guess it is just luck that we did not end with serial protocols with arbitrary bit order.