Saturday, 14 November 2015

Big Numbers

What do we know about very large numbers? Even the dullard knows that numbers continue forever..... Think of a very large number and add 1; repeat as necessary. But what about very large, useful numbers. How big can it get? Well, the googol is very large and is represented as 1, followed by a 100 zeros. This is more than enough to deal with all the particles in the known universe, which comes in at an understated 1 with 80 zeros. There is also the googolplex or 1 followed by a googol of zeros. Tis enough to goggle ya mind, eh? This number is so large that if you converted the universe into paper it would not be enough to write all the zeros on. But sadly we inhabit the real world and are forced to contemplate numbers which have meaning.

I'm bothered by very large numbers. To be honest, I'm bothered and perplexed by many things but numbers have a special place in my botherment and plexibility (yes, I know I've just made these words up. But one day they will appear in a lexicon, near you- mark my words). When I close my eyes, all I see is a sea of numbers cascading over themselves in vivid colours.

Graham's number
Ronald Graham is an American mathematician. He was working on a particularly obtuse mathematical problem which required the application of very big numbers. The problem is illustrated below:   
Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured complete sub-graph on four coplanar vertices?

Bloody mathematicians are just weird. Graham came up with a solution back in 1977. Weirdly this number has entered the Guinness Book of Records as the largest number used in a serious mathematical proof. Unlike the very large numbers most of us can come up with, given a boring wet Sunday afternoon, Graham's number is not arbitrary and has a use in the wonderful world of mathematics. This number is so mind-bogglingly large that conventional mathematical notation won't do. A special notation is required. A notation by the name of: 'The hyperoperation sequence'. I'm not going to delve into the concept too deeply as it will become tedious to readers not schooled in number theory. For our purpose, it is necessary to note that it involves the application of iteration: where each operation in the sequence is an iteration up from the previous operation. It is enough to say that the notation enables the manipulation of extreme numbers without the need for an infinite number of pencils or writing pads. This notation enables serious mathematicians to go into a frenzy of number operations and keeps them from the dining table and stops them interacting with normal human beings. This has got to be a good thing, because as I mentioned earlier, professional mathematicians, unlike myself (just a none weird amateur), are exceedingly strange folk and should not be approached unless you are armed with a particularly difficult mathematical proof which you can lay at their feet as tribute. Then you are free to rifle their home at will and violate their women folk unrestrained. Oh, I forgot to mention a very salient fact, you will find no women folk in a mathematician's abode- unless its their mother; I'll stop there.     

By the way, Graham's number is so fucking huge, that in comparison I can contemplate death with veritable aplomb. 

 I've just thought of another number larger than Graham's number, tis Graham's number to the power of Graham's number. Beat that!


  1. Well Flax, I hate to prove you wrong, but I once knew a mathematician who had a wife. To be accurate, he lived next door but didn't come out much. But I'm sure I saw him once.

    His wife though was very popular (in many ways - to many people - of both sexes).

    They're divorced now.

    1. Hello Billy, still pondering whether to put up a piece about NZs wind farms.........

  2. This comment is not only applicable for this post, but also for the preceding one - which I missed because I was out copulating with the canine of late.

    Just imagine what the author could have done with that piece had he had the knowledge of Large Number Mathematics? The mind boggles it does.

    And by 'fucking the dog' I mean I have been labouring to translate this for The Tutor. I don't read or speak a word of German. Googelplex Translate helps.

    Otherwise this post is:

    Yawny Yawny Cunt and a Graham's Number worth of 'Cunts".

    1. Eternity - as Flax will confirm - is akin to an autumnal* weekend in Tipton...

      *Autumn - the proper name for what you colonials refer to as "Fall".

    2. Dearest Ted Treen the patronizing cunt! I am not a North American colonial - from either the revolted or non-revolted colonies. I know what Autumn and Autumnal are and mean

      Season of mists and mellow fruitfulness
      Close bosom-friend of the maturing sun
      Conspiring with him how to load and bless
      With fruit the vines that round the thatch-eves run;

    3. Autumn, bring me leaves of golden hue,
      And lay the land in pastel shade.
      Come hither with closing days,
      And bequeath the silent summer with thy bitter sweet, embrace.

      Excerpt from 'Autumn' by James Joyce (the cunt)

    4. Wot no comment about my excerpt from James Joyce's 'Autumn'. Tis sublime, it it not?

    5. Ted, tis my mission in life to bring a bit of Tipton into everyones lives.

  3. I like the fact that one infinity can be 'bigger' than another.
    All odd numbers can be continued to infinity as can all the evens. Now add them together... :-)

    1. Infinity is a strange concept and wonderfully complex and frustrating.

  4. 2 comments:
    Flaxen Saxon said...
    I heard a similar analogy about a fly landing on an earth sized steel ball every 1,000,000 years. Infinity/eternity would be the time required to wear away the ball. Actually it would be longer as undoubtedly the fly would deposit a tiny piece of detritus, every couple of million years or so.

    Apart from the obvious profundity, this post is yawny, yawny, cunty etc.
    3:57 p.m.

    Sterculian Rhetoric said...
    You moron!
    This 'post' as you call it is a verbatim copy-pasta from A Portrait of the Artist as a Young Man the first novel of Irish writer James Joyce.
    6:41 p.m.

    1. Why do you reply to my comment, at 'your place', here? I'm a frequent visiter and would have read it within the hour. Also you need to sort out that double comment milarkey. I have a tenuous grasp on reality as it is. Tis likely to push me over the edge into the abyss of inanity.

    2. Why not here? It irks you. That's my vocation. And neither The Tutor nor I can figure out why our Handy Comments Facility is duplicating comments. But since it irks you, I am by default, all for it.

  5. Thanks for the education Dr M. I can't know everything, but with you as my constant spur and sage mentor, I have a feeling I'm going to get close. James Joyce, was a cunt by the way.

    1. Agreed.
      His hero Dedalus was a real piece of work. And the 'stream of consciousness' technique really got on my teats!

    2. I consider myself fairly well-read and do not judge any work until I have read it, but in my younger years, I found A Portrait of the Artist as a Young Man utterly unreadable. Over a period of two or three years, I tried repeatedly to 'get into' this novel but never once got past page 50. Even when I got that far, I felt I had not read anything cohesive with a progressing heart. I accept that it might have been just me...