Consider this question – who is the smartest man in the world?
Now whenever we say any word, it means that it doesn’t have the meaning of some word which is different from it (unless of course synonym(s)). So the moment one says smartest, he means not tallest. The moment one says man, he throws out animals (4 legged animals), and the moment one says world, it means earth and throws out other planets. All this rests on the simple logical principle that A => not (diff from A). Nothing is the same as something different from it, mostly.
Now, take these non-equivalent alternatives to smartest, man and world – as say, tallest, elephant and Mars respectively. Now convert the question to including these analogous terms – it becomes : Who is the tallest elephant on Mars? Now, these non-equivalents taken the way they are, the new question will never bear the same answer as the original one. No Linguistic “function” applied on the triplet (smartest, man & world) will lead to a question whose answer is the same as that of the question formed by applying the same function on the triplet (tallest, elephant & Mars). It is practically impossible for the mind to conjure up something like that.
Now, Mathematically, suppose you have numbers a1, a2, a3, b1, b2, b3 such that
a1 != b1, a2 != b2 and a3 != b3. Still a function might exist easily (in fact, infinitely many such functions, that too easily) making f(a1, a2, a3) = f(b1, b2, b3).
Hence, semantic meaning is dangerous to be equated with numerical value. Hence, word2vec seems to be a…….