The mathematician pondered the situation and proposed a possible explanation, “I think your arrival is linked to the visit from those time travellers. I have not mentioned it before but I can see in your face a close resemblance to that of young Alice who has gone exploring. Are you related?” Rosalie nodded and replied, “Alice is my great-great-grandmother and I was walking in these meadows almost a hundred and fifty years from now when I sank though the ground and landed here.” The scholar nodded and chortled, “Calooh callay! A most excellent conundrum. I suspect that you were pulled here by the wake of that time travelling contraption that carried my other visitors here. Let me think about this.”
He tented his fingers and closed his eyes, almost if as at prayer, but his facial expression was that of intense thought rather than any religious feeling. The pair sat in almost complete silence, apart from the occasional sob and sniffle from Rosalie, for a good ten minutes. With a sudden movement the mathematician opened his eyes and rummaged round in his pockets, pulling out a notebook and a pencil and started scribbling furiously. Paused for another few moments, scribbled again,, scratched out some lines, added more and finally sat back and smiled. Rosalie asked, “Sir, may I enquire as to what has pleased you after such intense work?”.
The lecturer replied, “My dear young lady, I think I may have solved your problem, and if I say so myself, in a way that is both elegant and logical.”, he paused, “I am not sure if your estimable Ladies College will have introduced you to the principles of mathematical logic? No! Ah then let me try and explain. While I was conversing with the lady you refer to as Deety, though in fact Doctor D T Burroughs, we engaged in a game of sorites. You are familiar with the term, from the Greek you know, for a heap? No! Tsk-tsk what is modern education coming to. Consider the following.
Premise 1: 1,000,000 grains of sand is a heap of sand
Premise 2: A heap of sand minus one grain is still a heap
If you repeat premise 2 sufficient times you are forced to accept that one grain of sand is still a heap of sand. Repeat it once more and no grain of sand is still a heap, and again and a negative number of grains is a heap. This is a sorites paradox. It is possible however to create a stack or heap of premises about facts that do not result in a paradox and from which a logical and possibly unexpected solution can be derived. Those are known as sorites polysyllogisms. Those can form a game of sorites, which is what I was playing with Doctor, erm, Deety. She in fact told me that she had learned much about sorites in a book I have not yet written to be called Symbolic Logic, which I will publish five years before the end of the reign of our dear Queen Victoria. I have just written a rather clever set of premises that I will, some day, include in that book and which Deety will or alternatively will have read and at some time realise that to solve the problem she needs to return here one hour after she departed for the first time. That gives us time to light the spirit lamp and make a fresh pot of tea for their arrival with their time machine.”
Rosalie stared open mouthed at the eminent mathematician. Her brain churning and spinning as she tried to resolve the possible temporal paradoxes that might just have been set in train. She sputtered, “But Sir, if you did include/will include, the puzzle in the book and Deety has already/will sometime read it then why did she not just stay and wait?” The logician smiled and replied, “Because to prevent a paradox as soon you depart with them back to your own time I will tear up the note I have made and the puzzle will never have been there. Is that not a neat solution?”.
(With thanks to the works 'Number of the Beast' by R A Heinlein and 'Alice's Adventures in Wonderland' by Lewis Carroll [Dr Charles Lutwidge Dodgson] for the loan of some words, characters and plot lines in the spirit of the Universe of fiction as fact.)
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