Magic Number

Photograph:- As mentioned in passing in the tribute to Davenport, the Cyclists Memorial Opening Ceremony.

Dear Blog,

                 Some long time ago if you check your mail, I pose a little puzzle for you and then in my next missive I explained how important it was and called the new number, 2321, Kirkham’s Constant or some such.

To remind you I asked what the next line in the sequence was

Viz:-

1

11

21

1112

And I explained that the rest of this wonderful set of numbers was

3112

211213

312213

212223

And I explained the pattern was produced by stating the amount of numbers which appeared in the preceding line (the line above)

114213

31121314

31122314*

31222314

21322314

And then a wonderful thing happens

Viz:- the next line is then

21322314

And the next and the next and the next ..... ->∞

If the numbers you are listing are then stripped out, you are left with 2321.

And with certain provisos which I detailed in my last letter to you, no matter what you start with, you always end with 2321!!!!!!!!!!!!! (Read my previous letter to you for all the procedures with more complex repeats.

Now a couple of years may have elapse since my original message to you, during which time I have consulted a couple of eminent mathematics and a philosopher because .....

Go to line eleven, say [which you chose does not matter] and instead of  31122314 you make a mistake and write 31322314 say [the mistake does not matter] but then carry on

Viz:-

31322314

21223314

21322314

21322314

    .................strip out the numbers you are listing as before and => 2321 arrives!!!!

Now, the problem arises ...If you make a mistake but end up at the same place anyhow, how do you know that you have ever made a mistake? And if you write a programme to check or do a manual check, you have to pose the question of yourself, ‘Why bother’ because you get the same answer whether you are accurate or not!! Just think how useful the procedure would be for genetic engineers and social control. We would not know about any mistake, would they?

... and I have had no satisfactory answer as to why 2321 and more importantly, why, it is ‘self correcting’ [an inaccurate use of a bad term really] i.e. if you make an error you always end up with the same answer (which logically you must do if every starting pattern ends up with 2321, the error made is just a pseudo starting place!)

                                                                Colin