I always think about values in big endian, largest digit first. Scientific notation, for example, since often we only care about the first few digits.

I sometimes think about arithmetic in little endian, since addition always starts with the least significant digit, due to the right-to-left dependency of carrying.

Except lately I’ve been doing large additions big-endian style left-to-right, allowing intermediate “digits” with a value greater than 9, and doing the carry pass separately after the digit addition pass. It feels easier to me to think about addition this way, even though it’s a less efficient notation.

Long division and modulus are also big-endian operations. My favorite CS trick was learning how you can compute any arbitrarily sized number mod 7 in your head as fast as people are reading the digits of the number, from left to right. If you did it little-endian you’d have to remember the entire number, but in big endian you can forget each digit as soon as you use it.

I don't know, when we write in general, we tend to write the most significant stuff first so you lose less information if you stop early. Even numbers we truncate twelve millions instead of something like twelve millions, zero thousand zero hundreds and 0.

Next you are going to want little endian polynomials, and that is just too far. Also, the advantage of big endian is it naturally extends to decimals/negative exponents where the later on things are less important. X squared plus x plus three minus one over x plus one over x squared etc.

Loss of big endian chips saddens me like the loss of underscores in var names in Go Lang. The homogeneity is worth something, thanks intel and camelCase, but the old order that passes away and is no more had the beauty of a new world.