FiNiTE iNFiNiTiES

How can an Infinity be Finite? 

How can something 

that appears to travel forever 

be contained or tamed 

or boxed or handled?

This is what appears to happen to the Entity named “The Squared Root of 2” which is the diagonal of the Unit Square (1x1 Square) and its diagonal, being 1.41421356… has its decimals traveling forever without any discernible repetition or pattern, an infinity of decimals, yet we know we can measure this entity from one corner of the square to the other opposing corner of the same square so somehow this infinity of decimals is contained, is finite, is apparently measurable, but we just can't put our finger on it.

We try to define it, so all we can do is make a close approximation, so really Root 2 is not a Number, not a whole number that we understand, but some other Phantom. So mathematicians don’t know what to do with these root harmonics, like Root 2, Root 3, and Root 5 (you can google these graphics) etc that are indeed infinities but infinities that are contained in finite geometrical boundaries…

Though these invisibilities are made visible to the maths world via the gem known as Pythagoras’ Theorem: 32 + 42 = 52 a true gift from the gods.
The 3 most primal or primitive or important Root Harmonics are those of 3, 4 and 5:
Root 2 is the Diagonal of the Unit Square 1x1,
Root 5 is the Diagonal of the Double Unit Square 1x2, and
Root 3 is the Space Diagonal of the Unit Cube 1x1x1.
They are all touchable, definable yet untouchable!

There exist other Infinities, that are not contained by boundaries, they are genuine Infinities that have no apparent boundaries, they really go on and on and on forever into some distant land. One such sequence is the Doubling Sequence:
1 – 2 – 4 – 8 – 16 – 32 – 64 – 128 etc…

The good news is that the tool known as “Digital Compression”, which is really “Continued Subtraction From 9” gives us a handle, something to grab, of these infinities. Thus when mathematicians digitally compress say the Fibonacci Sequence or the Doubling Sequence, by adding the individual digits and reducing the big numbers down to smaller single digits, patterns appear. This Doubling Sequence has a Periodicity of 6 meaning that this sequence reduces down to 6 single digits that infinite repeat, like a necklace of pearls and now becomes known as The Binary Code:
1 – 2 – 4 – 8 – 7 – 5.
This gives us a sense of control regarding where this infinity is going, albeit circular, its like mounting a wild horse with a saddle and riding its infinite-ness.


Jain Mathemagics