(urth) Wolfe's Puzzles

[Gerry Quinn]

From: "Jeff Wilson" <jwilson at io.com
> On 7/10/2010 3:24 AM, Gerry Quinn wrote:

>>> 5553 8783 4223 9700 34
>>>
>>> 2221 0401 1101 7276 56
>>>
>>> SEALED FOR THE MONARCH
>>>
>> I take the view that it is essentially random. It is a fundamental point
>> of algorithmic information theory that almost all numbers are. Why
>> should this number, essentially a barcode for one not especially
>> important storeroom, be special?
>>
>> I don't see it as a 'trick' to make them random, because logically they
>> should be random. Of course I cannot tell whether they are in fact
>> random. [There is also an important theorem that strings - or numbers -
>> above a certain length cannot be *proven* to be random!]
>
> Oh, no, there are huge amounts of correspondence here - you see how often 
> the same digit appears in series, or in the same group? There are many 
> parallels between the upper and lower lines, considerable amounts of 
> consecutive digits and those separated by a single digit.
>
> Overall, English has an entropy of just a little more than one bit per 
> character; totally random digits have ln10/ln2 or about 3.2 bits per of 
> entropy per character. This number stream (based on the difference between 
> consecutive digits) has about 2 - almost certainly some kind of selection 
> going on here.

You can't say "almost certainly" for such a short string without applying 
some kind of statistical test.

That aside, there is the strong likelihood that even if the digits were not 
selected randomly, they do not mean anything in particular.  Perhaps Wolfe 
felt that it would add verisimiltude to have a low entropy string, certain 
components of which would have from a restricted set indicating type or 
origin of items stored.  That doesn't mean he has thought about what exactly 
they represent in a given instance.

- Gerry Quinn