Edit: switched example to hex
Edit2: actually this is still slightly out of whack, but I don't feel like switching to binary so take it as a loose representation rather than literal
On computers however, we basically always use exact arithmetic and exact, fixed logic where learning the higher order doesn't help (we're not doing approximations and decisions based on incomplete information), in fact for mathematical reasons in the exact cases it's usually better to compute and utilize the lowest bits first (e.g. in the case of sums and multiplication algos I am familiar with). [note1]
Overall I'm slightly surprised some automatic/universal translation methods for the most common languages haven't been made, although I guess there may be some significant difficulties or impossibilities (for example, if you send a bunch of bits/bytes outside, there's no general way to predict the endianess it should be in). I suspect LLMs will make this task much easier (without a more traditional universal translation algorithm).
[note1] Also, the time required to receive all bits from say a 64b number as opposed to the first k bits tends to be a negligible or even 0 difference, in both human terms (receiving data over a network) and machine terms (receiving data over a bus; optimizing an algorithm that uses numbers in complicated ways; etc.), again different from human communication and thought.
And yet in Arabic, the numbers are written in order from the least to the most significant digit, even if they are not really pronounced that way, starting from the numbers in the hundreds and up: "1234" is read as essentially "one thousand two hundred four-and-thirty", the same way the German does it. And yes, the order looks like it's the same as in e.g. English, but Arabic is written right to left. So, no, it's absolutely fine to write numbers in little endian even in the language that pronounces it the big-endian or even the mixed-endian way.
"One Five Five Two Three One" is 6 words, 6 syllables long where as "One Hundred and Thirty Two Thousand" is 6 words, 9 syllables long and conveys less information. Even shortening it to "One Hundred Thirty Two Thousand" is still 5 words, 8 syllables long and conveys less information.
You can also easily convey high order digits first by using a unambiguous "and/add" construction: "Thousand Two Three One Add One Five Five". You have now conveyed the three high order digits in 5 words, 5 syllables. You also convey the full number in 9 words, 9 syllables in contrast to "One Hundred Thirty Two Thousand One Hundred Fifty Five" which is 9 words, 14 syllables.
You could go even further and express things in pseudo-scientific notation which would be even more general and close to as efficient. "Zero E Three (10^3) Two Three One" which is 6 words, 6 syllables, but no longer requires unique separator words like "Thousand", "Million", "Billion", etc. This shows even greater efficiency if you are conveying "One Hundred Thirty Thousand" which would be something more like "Zero E Four (10^4) Three One" since the scientific notation digit position description is highly uniform.
This distinction might seem somewhat arbitrary since this just seems like it is changing the order for the sake of things. However, the advantage of little-endian description is that it is non-contextual. When you say the number "One" it literally always means the one's place "One". If you wish to speak of a different positional "One" you would prefix it with the position e.g. "Zero E Three (10^3) One". In contrast, in the normal way of speaking numbers "One" could mean any positional one. Are you saying "One Hundred", "One Thousand", "One Hundred Million"? You need to wait for subsequent words to know what "One" is being said. Transcription must fundamentally buffer a significant fraction of the word stream to disambiguate.
It also results in the hilariously duplicative "One Hundred Thirty Two Thousand One Hundred Fifty Five" which has positional signifiers for basically every word. "One Hundred Thir-ty Thousand One Hundred Fif-ty Five”. Fully 8 of the 14 syllables are used for positional disambiguation to reduce necessary lookahead. "And/Add" constructions get you that for a fraction of the word and syllable count. They allow arbitrary chunking since you can separate digit streams on any boundary. It also reinforces the fact that numbers are just composites of their components which may help with numeracy.
Little endian is actually just better in every respect, expect for compatibility and familiarity, if we use our modern robust knowledge of arithmetic to formulate the grammar rules.
> this is a weak argument for what computers should do; if LE is more efficient for machines then let them use it
Computers really don't care. Literally. Same number of gates either way. But for everything besides dumping it makes sense that the least significant byte and the least significant bit are numbered starting from zero. It makes intuitive mathematical sense.
Definitely not, which is why many 8-bit CPUs are LE. Carries propagate upwards, and incrementers are cheaper than a length-dependent subtraction.
For the use of a computer, yes, if you are doing multi-word arithmetic, it can matter.
OTOH, to be perfectly fair and balanced, multi-word comparisons work better in big-endian.
Eh. That depends; the computer architectures used to be way weirder than what we have today. IBM 1401 used variable-length BCDs (written in big-endian); its version of BCDIC literally used numbers from 1 to 9 as digits "1" to "9" (number 0 was blank/space, and number 10 would print as "0"). So its ADD etc. instructions took pointers to the last digits of numbers added, and worked backwards; in fact, pretty much all of indexing on that machine moved backwards: MOV also worked from higher addresses down to lower ones, and so on.
> FWIW, this is a weak argument for what computers should do; if LE is more efficient for machines then let them use it
I should have fleshed it out more fully, but basically, it was about how when you design an ALU, it's literally the same number of gates whether you swap the pins when you connect it to the rest of the system or not.
Using the computer is, of course, a different story that depends a lot on design decisions made when implementing it, and depending on your usage, endianness can matter more.
This sounds confused. The "order" of bits is only an artifact of our human notation, not some inherent order. If you look at how an integer is implemented in hardware (say in a register or in combinational logic), you're not going to find the bits being reversed every byte.
You're still confused, unfortunately. (Note: In everything that follows, I'm just pretending "Arabic numerals" came from Arabic. The actual history is more complicated but irrelevant to my point, so let's go with that.)
First, you're confusing intuitive with logical. They are not the same thing. e.g, survivorship bias (look up the whole WWII plane thing) is unintuitive, but extremely logical.
Second, even arguing intuitiveness here doesn't really make sense, because the direction of writing numerals is itself intrinsically arbitrary. If our writing system was such that a million dollars was written as "000,000,1$", suddenly you wouldn't find big-endian any more intuitive.
In fact, if you were an Arabic speaker and your computer was in Arabic (right to left) rather than English (left to right), then your hex editor would display right-to-left on the screen, and you would already find little-endian intuitive!
In other words, the only reason you find this unintuitive is that you speak English, which is (by unfortunate historical luck) written in "big-endian" form! Note that this has nothing to do with being right-to-left but left-to-right, but rather with whether the place values increase or decrease in the same direction as the prose. In Arabic, place values increase in the direction of the prose, which makes little-endian entirely intuitive to an Arabic speaker!
To put it another way, arguing LE is unintuitive is like claiming something being right-handed is somehow more intuitive than left-handed. If that's true, it's because you're used to being right-handed, not because right-handedness itself is somehow genuinely more intuitive. (And neither of these has anything to do with one being more or less logical than the other.)
AFAIK it was only IBM whose CPUs were consistently BE for both bit and byte order (i.e. bit 0 is also the most significant bit.) Every other CPU which is BE for bytes is still LE for bits (bit 0 least significant.)
