Language is something we breathe in and out every moment of our lives. It is everywhere, everyone is exceptionally good at it. Yet, no one knows how it got into our heads. The number of sentences you can form with any given language is virtually infinite. It makes zero sense to say that we learn language by memorizing individual sentences. But, what if we wanted to memorize every sentence in a given language? How long would that take?
Go to a library and pick up a sentence at random from any book and chances are you will fail to find an exact repetition no matter how long you keep looking in any other book inside any other library. So, the sheer vastness of language is unparalleled. The number of sentences that a normal person can produce throughout their lifetime is breathtaking, and every day every person produces sentences that have never been said in the history of the universe and never will be ever again.
Let’s use some basic mathematics to give you a sense of how long it would take for a person to memorize all the sentences in a given language. Suppose a speaker is interrupted at a random point in a sentence. To continue the sentence in a grammatical and meaningful way, a person has an average of ten different words that could be inserted to carry on with his/her sentence. At some points in a sentence, only one word can be inserted, and other points, there is a choice among thousands; ten is the average.
Now let’s assume that a person is capable of producing sentences up to twenty words long. In fact, twenty words is a very severe limitation since sentences can be much longer than that. But let’s just keep the limit at twenty words for the sake of exposition. Therefore, in principle, the number of sentences that a person can deal with is 10²⁰. This number will not seem like much until you start writing it down; it’s one with twenty zeros after it:
100.000.000.000.000.000.000
That’s a hundred million trillion sentences that a person can deal with in principle. Now let’s see how much time it would take to memorize all of these sentences. At a rate of five seconds a sentence, a person would need about a hundred trillion years, with no time for eating or sleeping, to memorize them all.
Each one of us learned Language, with all its ins and outs, by age four. You can use a finite set of rules and words to produce an infinite number of sentences. So you can imagine how powerful is the human brain. There is nothing that comes close to the processing power of our brains.
In principle, the number is infinite, as you can always add something like “, which is XXX” etc. So, one sentence can be extended infinitely. That however counts for every sentence you can build, which is always a variation/combination of known words. This is infinite, because the lenght of the sentence may vary. So, there is an infinite number of sentences which you can use as base to build an infinite number of sentences. Based on that, I would assume … that the answer is … (gosh, how do you call that in english? *überabzähbar unendlich*) that sort of infinity you cannot even Count in principle, because every element you have creates an nfinite number of possibilities itself. So it is a “not countable” number of infinite sentences, which can themselves be used as “baseline” for building a “not countable” number of infinite sentences.