This is a crazy question but I would like to receive any ideas from native English speakers.

I sing a song.

I sing songs.

You sing a song.

You sing songs.

They sing a song.

They sing songs.

He sings a song.

He sings songs.

It (a bird) sings a song.

It sings songs.

Is there anything in common between the 's' for verbal inflection and the plural 's' as a suffix to a noun?

I studied over this 's' very hard and reached an idea that the 's' may have something to do with a linguistic process in which the speaker's cognition of the word changes from superficial definition out of dictionary into real 'things' materialized in the world.

When you say 'I', it's me in the real world. When you say 'you', you are in the real world because 'you' is now in front of me. When you say 'they', they also are in the real world because 'they' is a plural pronoun (the definition of 'plural' is based on a 'thing' in the real world)

However, when you say 'he', 'she', or 'it', it seems they only exist in your mind not yet materialized into an entity in the real world. That's why you need 's' to the verb in order to make the sentence to be real.

Any ideas, please.

The third-person present tense -s ending is (almost) the last surviving remnant of a more complicated system of verb inflection in Old English and its predecessors. I learned that it was altered from -eth (which is still encountered in archaic Biblical language), but it seems that this is not universally agreed upon. I doubt your explanation has anything to do with reality. You might find this article interesting.
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Many thanks for your comment and the article!

So when you are using a singular noun,eg:mary,kwame,will u add' s'to the verb.