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What do all those asterisk and numbers mean? I feel like I'm missing a key to decode that.
Edit: Damn, that little post lead to an actual TIL moment. I'm actually going to copy all your answers for future reference, since I enjoy etymology and get into contact with these symbols a lot. Thanks, everyone!
Asterisk means that the word has been reverse engineered without any direct evidence backing it up. All proto languages will have asterisks in front of all their words because proto languages are, by definition, languages that were used before anything was written down.
The reverse engineered word is likely to be correct (or at least, as correct as we can be), but in the absence of direct evidence, it's still just guesswork
The numbers you're talking about are because we know that there are different consonants used, but we don't entirely know what sounds those consonants are. So we just write all of the consonants that likely sounded somewhat like the letter h as h1, h2, h3, etc., and repeat for the other uncertain consonants.
So basically h1 definitely sounds different than h2, but as for exactly what they sound like, all we know is that both of them are kinda like h
This is mostly correct so I'll focus on small specific details, OK?
Asterisk means not directly attested. In reconstructions it goes as you say, but you'll also see them before things that you don't expect speakers to use, in synchronic linguistics; for example *me apple eat gets an asterisk because your typical English speaker wouldn't use it.
It is kind of "guesswork" but it follows a very specific procedure, called the comparative method. As in, it is not an "anything goes".
The sounds represented as *h₁, *h₂, *h₃, *h₄ and *H do not necessarily sound like [h]. At this point they're simply part of the notation. For example, a common hypothesis is that *h₁ was [ʔ], it's more like the sound in "oh-oh" than like [h]. And some argue that they aren't even the sounds themselves, but rather the effect of the sounds on descendant words (the difference is important because, if two sounds had the same effect, they ended with the same symbol).
Thanks for the details! I forgot some of the details since I last took a course in linguistics like almost 10 years ago
Since Contramuffin answered most of it, I'll focus on the diacritics.
The acute in *ḱ *ǵ *ǵʰ shows that they aren't the same as *k *g *gʰ. Odds are that the ones with an acute were pronounced with the tongue a bit fronted (palatalised).
The acute over other consonants, plus in *é *ó, is something else entirely. It's the accent - you're supposed to pronounce those consonants with a higher pitch. "Yay, consistency" /s
The macron over *ē *ō is to show that the vowel is loooong.
Those floating ⟨ʰ⟩ refer to aspiration. Aspiration is that "puff" of air that you release when you say ⟨pill, till, kill⟩ but not when you say ⟨spill, still, skill⟩. In English this is not distinctive, but in a lot of other Indo-European languages it is, and the mainstream hypothesis is that it was distinctive in PIE itself.
In the meantime, a floating ⟨ʷ⟩ means that the consonant is pronounced with rounded lips. The difference between something like *kʷ and *kw is mostly that the first one behaves like a single consonant, the other as two.
That ring under some consonants is to highlight that they're syllabic, as if they were LARPing as vowels. It's a lot like writing "button" as "buttn̥".
If you ever see *ə₁ *ə₂ *ə₃ etc., pretend that that "ə" is "h₁". It's simply different ways to annotate the same stuff.
*H means "this is *h₁ or *h₂ or *h₃, but we have no clue on which".
The asterisks mean that it's a reconstructed word, not an actually attested word. No PIE writing exists, so all these words are deduced from the descendant words across the vast IE family, not recorded as definitely existing.
The numbers are h1, h2 and h3. We know that PIE had three different h-like sounds (pharyngeals). But, funny thing, every single daughter language lost them, so it's hard to tell exactly what each one sounded like. If you see overlapping ripples in a pond, you can work out roughly where and how many things dropped, but you can't guess the exact weight or size.