According to the theory of evolution one species does not turn into another species. How one species can evolve into two species without ever crossing a "species border" is apparently more difficult to understand than I thought.

When I first learned about the theory of evolution, understanding how different species evolve was no problem for me. I didn't know it was difficult for others. It is.

If you don't understand evolution (for example, if you believe that evolution is about one species changing into another), perhaps this essay will help you understand evolution in time.

Let's use linguistics instead of biology.

English and German are two distinct languages and are not to a useful degree mutually intelligible. Yet they have both emerged from a common ancestor language (about 1500 to 2000 years ago).

Individual languages are the species in the world of linguistics.

And even though English and German are distinct languages there was no point ever in time where one language became another (each generation of speakers understood the language of the previous generation to be the same as theirs).

And there is no limit to changes within languages that would prevent one language from becoming two over time if the population of speakers becomes two distinct populations without much contact.

It is easy to see now how there is no point in time at which one species becomes another just as there is no point in time at which one language becomes another.

Now, let's look at probabilities.

German and English (the Germanic words in English) follow regular sound changes. (An English /d/ usually corresponds to a German /t/ and so on.) It would be ridiculously improbable that all speakers of some Germanic language would suddenly decide to change all /d/ into /t/ and follow all the other sound changes. But yet it clearly happened.

Angels? Not so fast. What happened was that speakers in one population started pronouncing specific phonemes in specific cases differently (because it appeared easier to them and because other people did it, the change reinforces itself). If this population becomes dominant (perhaps the other tribes died or adapted to the more powerful tribe), the sound change manifests itself and over a few generations, everyone in a given population pronounces the particular consonant differently.

And while the probability of German changing into English is very low indeed, the probability of people changing individual sounds is much higher, and the probability of some consensus being established by people speaking a language which sound changes to keep is also very high. And over time those probabilities add up and beat the odds we came up with in our original faulty (because it didn't take time into account) calculation.

If German did change into English over night, the linguistics theory of common descent from a proto-Germanic language would be proven wrong, because the theory relies on the assumption that that doesn't happen. Similarly Darwin's theory relies on the assumption that one species does not change into another.

Sometimes, people start writing words down. If we find an old inscription, we have a "fossil" of a "missing link". (For example very old English looks very German.) And sometimes we encounter living fossils. If you look at the spelling of "night", you find a "gh" part that stood for an original /x/ sound (like "ch" in "Loch Ness", actually it's not /x/ but a similar sound based on /g/ as in "good"). And in German the corresponding word "Nacht" actually still features an /x/ sound in its pronunciation.

(Incidentally, a lack of inscriptions does not "prove" that the people in question didn't have a language. It just means they didn't write much or that we simply didn't find anything.)