I know how lead and lead are pronounced, but what is lead? I've never heard of that word.
IPA /lɛd/, /liːd/, /lid/. It turns out one of those is American pronunciation, the other two English. Dunno about aussies, though; there could be more (/lɛ:d/?)
I don't know what LEAD /lid/ is. The pronunciation of this is like the word "lid". I can't find any reference that indicates this is a pronunciation of LEAD.
Here, with
audio.
I think the priority is established, the question is, why are the two multiply operators handled differently?
For the same reason a pint is approximately 568 ml, or approximately 551 ml, or approximately 473 ml, depending on who you ask and in which context: because humans.
That is not a reason. This is math, with rules and structures. Without that, math literally doesn't exist.
It is, because we have two layers of definitions here.
The surface layer is the words, acronyms, symbols, and glyphs we use. These mutate, change, and evolve constantly. These are the ones you are fully allowed to play with; the only requirement in science and math is that you define them. In math, this is
notation. There are many valid notations, and if you do complex work, you often end up inventing your own if a suitable one does not yet exist.
The deep layer is the things and rules being described. These are not to be messed with willy-nilly, because we've discovered them only through hard work and critical peer review.
Math is the deep layer. What we are talking about is the notation, the surface layer, that is completely up to humans to define.
It is no different than defining "elektroni" = "electron" and "sähkälehitu" = "electron" (which does imply "elektroni" = "sähkälehitu").
Or what base (radix) we use when writing numbers.
The answer to the question
"Why would implicit multiplication have a different priority than explicit multiplication?" is that the human surface layer, the notation layer, is always in flux, and not something you can blindly rely on. (Well, currently, we can somewhat rely on the priorities of explicit operators, and use parentheses to ensure a specific order, as many have pointed out earlier in this thread.)
Personally, I only use implicit multiplication between numeric constants and variables. This is because I find \$2 \pi x\$ easier to read than \$2 \times \pi \times x\$. I do believe that human perception detail is at the core of why two different notations for multiplication exist. I also believe that it is most likely human shortsightedness –– specifically, "out of sight, out of mind" –– that has caused implicit multiplication being omitted when humans have agreed upon the priorities of operators. The priorities of the operators being just another notational detail: the math itself does not change, even if the notation does.
Having two operators with the same functionality is silly and pointless. There must be a usage that makes a higher priority for the implied multiplication significant, even if it's only convenience. But there has to be a use case where it makes a difference.
That assumes humans are rational beings. Evidence suggests otherwise.