I have a recurring need to understand numbers at a deeper level. The current blog is in addition to the one I have written about numbers before with which I have not been entirely satisfied

So, again, what is a number? I want to approach this question from the following hypothetical scenario. Let us say there is a world inhabited by only two intelligent human beings and call them and . Let us also assume and have, until now, developed their language but this language is devoid of any couting terminology.

Now, assume that there is *one* apple in their world. As and are intelligent beings they come up with a symbol (say) to denote the *one* apple. Whenever they want to talk about the apple they would write the symbol and immediatley the image of an apple flashes in their brain.

Now, say there are many types of fruits in their world and also that each of these fruits is only *one* in number. As these beings are intelligent, they come up with a simple method for denoting these :

- orange
- pumpkin etc.

So, every time writes , remembers the image of *one* orange, etc. Similarly, for *two* apples, *two* oranges, *two* pumpkins, let us say they come with symbols, respectively.

Until now, the inhabitants have been perfectly logical about the understanding of their world. Whatever these beings could do can be replicated by any automatic machine (a computer) as these beings are only following an algorithm to represent any new object with symbols already in their language, .

A significant leap of thinking / imagination is required on the part of and to start denoting *one* apple, *one* orange, *one* pumpkin as , , and *two* apples, *two* oranges, *two* pumpkins as , , , etc. The advantage of this representation is that the total number of symbols used has decreased from (q,r,s,t,u,v) to (1,2,a,o,p). The advantage is more evident when one considers *three*, *four* or more of those fruits.

How can and come up with this new representation? The main requirement is that both and have to be capable of **abstract** thinking. That is, being able to think of “a detached fruit” as representing the number *one* whatever the fruit is. It is extremely important to note here that the number *one* is an abstract idea which cannot be expressed without the help of the language, .

Therefore, I think that numbers came into existence only because of the Human being’s ability to think abstractly. A question that pops up now is : Can an automatic machine discover the concept of a number OR is a computer capable of abstract thought?