Here is a conundrum for you: sources of Three. We learn extremely early that the exterior environment has 'properties' built into it, which we discover, including, for example, the property of oneness and threeness and so on.
It is only a short leap from here into contemplating number theory, playing with qualities such as prime numbers (a property inherent in the creation of numberness), why certain assumptions string out certain strings of numbers such as Fibonacci's or Lucas'; and again why, when you turn back to the space and construct of the material world and measure things you discover -- que milagro! -- these numbers describe the patterns of order, and sometimes even the patterns of chaos!
Then you can discuss how to prove, using numbers, what numbers will have in them and what they will not and where primes are and so on and on until your very brain goes numb, and number still.
So examining these things, a new question can well be taken up in order to ease these endless mechanical rattles and trappings and self-eating universes of postulated apparition called number theory.
Consider, for the joy of it, that when you look at a space and within it agree to see three objects; let us say three perfectly circular polished brass napkin-rings. This is a good example because in the endless flux of perception the forms described by these napkin rings are similar enough for us to easily convince ourselves that each is identical to the next. This of course is idiocy. But we can convince ourselves of it. It's not unusual, especially in mathematical work, and it isn't difficult.
The truth is that these three napkin rings are in different spaces with different histories and their brasses are derived from different deposits of copper, and different people have used them and abused them differently; and they have been used at different meals; and they are under different degrees of bombardment as we look at them because one, say, is in the shade and another half in the bright sunlight. But forget all that. They are each scratched up entirely differently, but never mind. Each of them, if you could read electron locations and patterns clearly, would be telling an entirely different set of patterns, within limits. But let us ignore that. We are determined, these three napkin rings are identical.
WELL! in that case we can say there are three of them, can't we; we have hammered that out nicely. Putting all that difference rubbish aside where it belongs, we can say, yes we have three identical objects -- or close enough for imprecise work. We can therefore count them with the same list of numbers.
So we set about doing this -- we take a bead on the table-top or whatever space these napkin-rings are in and we let fire: 'One!! Two! Three!', and there we have it. there are three, count them three, rings.
What a fine ability! We could carry it over to all kinds of things: tires (four), children (2.3), dollars on hand (342.74) and the number of miles light goes across space in one second (186,000). Why, this is fine!
Those miles, for example, if you had had to walk them, would have taken forever; and each one would have been a little different -- a number of them would have been in mountains, or skimming along the edge of an asteroid belt, or crossing a Texas desert, or perhaps carving a path through some strange wall of cosmic moon-stuff dancing in the middle of the ether -- there is no telling. But with this system of counting we can claim ALL those miles are the same and tuck up 186,000 of them in a single second. Never mind differences. It's the sameness that counts, right? So all 186,000 can be strapped up and stowed down inside the hatch of that one number, and we can be proud of our strength in doing this. In fact, this power of ours is intoxicating! We could steam-roll the entire universe with these numbers! Count up everything we chose to identify -- ALL flowers (never mind which are which); ALL states of the Union; we can get really randy with this powerful killing-stick and add up the number of souls on Earth! There now! That solves a great deal; if we can put that bitchy Mrs. Kingle down the way into one of our numbers -- or better still, put her into a bunch of them -- we NEVER have to find out if there is anything she might want to say from her own point of view. No matter what, it will be a cross section from the numbered bunches we have placed her in so firmly with our new power. We can just face her off completely with our new number power. And sigh with relief, at that.
She is speaking 11.5 per cent on the basis of being one millionth of the Protestants in California; 22 per cent of her feelings derive from the fact that she is one of 720 under-paid white female administrative personnel in our town; another nine per cent of her emotion stems from the obvious and irrefutable fact that she is speaking as part of the 11,234,976 left-handed people on planet Earth; and the rest is due to her batting average in the Girl Guides' Little League, in that one-of-many Summers of 1952.
Well, if numbers are good for anything, that may be it - we can finally cross section Mrs. Kingle so we do not have to know anythig about her. Now there's value for you.