Xjyuk

When coming across thoughts on linguistics, concerning some words as having common origins in similar context, how is it evidently clear to know what is so?

One example: 'Ich' in German, meaning 'I' , having developed from or beside the Hebrew word 'Ish' , meaning 'man'.

What is the way to prove such theories or test them for the laymen in linguistics?

There are two main ways.

① If there's a good reason to suspect borrowing.

For example, English and Hebrew aren't etymologically related at all, but English chutzpah looks very similar to Hebrew חוצפה (ħuzpa, "audacity"). Could they be connected?

Well, we don't see the word chutzpah in English before the 20th century, it contains a sound that's extremely rare in English (what linguists call [x]), and we don't see cognates in any other Germanic languages. On the other hand, we do see cognates in other Semitic languages, like Aramaic.

This is a convincing argument that chutzpah is a loan into English (in this case, from Hebrew via Yiddish). If it weren't a loan, we'd expect to see a history within English, and cognates in other Germanic languages, but we just don't.

② If there's a consistent, well-attested correspondence.

There's a long-standing principle in linguistic that language change is consistent. That is, if the "P" sound turns into an "F" sound at the start of words, it'll happen to all words starting with "P", not just one or two. This is in fact something that happened in early Germanic, and there are hundreds of words that show the correspondence: compare the English/Latin pairs fish/pisc-, father/patr-, foot/ped-, felt/pell-, fowl/pull-, fee/pec-, fear/per-, and so on.

Now, there can be exceptions for various reasons, but the vast majority of the time, "language change is consistent" holds true. So if you want to show a correspondence between German and Hebrew, you need a consistent rule with plenty of examples.

In this case, neither one holds.

On the surface, your comparison of ich with iš seems solid. The two words have similar meanings, and similar sounds.

But if we look at German ich, we see it has cognates all across the Germanic languages. An older form of English "I" was ic, for example, while Dutch has ik, Old Norse has ek, the extinct and somewhat obscure Gothic language has ik, and so on. We can hypothesize that Germanic originally had a word like *ik meaning "I" which evolved into all these descendants.

This Germanic *ik is supported further when we look at other Indo-European languages: compare Latin ego, along with the rule that Latin g tends to correspond to Germanic k. So there's decent evidence that this word goes back to Proto-Indo-European, which is as far back as we can reconstruct.

Could Hebrew איש have been borrowed from some Indo-European language, then? Probably not: it also has solid cognates in related languages, like Phoenician אש. It seems the two words are thoroughly unrelated.

Coincidences are more likely than you'd think.

It seems crazy that this could just be random chance, doesn't it? After all, the words look remarkably similar.

But the average dictionary for a popular language has somewhere between 100,000 and 1,000,000 words in it. That's a lot of words. And with such an enormous number of words in each language, you'll statistically end up with an enormous number of seemingly-unlikely coincidences.

The sheer number of coincidences between any two languages is why consistent, predictable sound changes are so important in linguistics. If one English word starting with F happened to look like one Latin word starting with P, it would be most likely a random coincidence. Same for ten, or twenty. "Grimm's Law" (the sound change that turned initial P's into F's) only holds up to scrutiny because there are several hundred separate examples of it.

Finding these sound changes, accordingly, is really hard. So the best way to check for a connection is to look in a good etymological dictionary; Wiktionary has been getting better and better for this in recent years. It'll show you what linguists have already discovered over the past few centuries, and give you good points to jump off from.

P.S. The "Grimm" in "Grimm's Law" is indeed the same as in "Grimm's fairy tales": all the different dialects Jakob Grimm documented were what led him to discover Grimm's Law, and that was really the start of modern linguistics. Grimm's Law is traditionally used as the first example of a consistent sound change in intro ling classes, to honor that contribution.