The Parable of Next Thursday

Dafydd Gibbon

12 November 1995

Jill jacked and Jack jilted

Say Jack meets Jill at a fashion show on Tuesday, and asks `How about next Thursday?' She acquiesces and turns up at the usual time, the usual place, on the next day but one. No sign of Jack, and, boiling inside, Jill phones to see if Joe is still interested. He is. A week later, Jack turns up in good time, only to see Joe and Jill turn up together a few minutes later. `Bitch,' growls Jack, controlling an urge to do something violent.

What went wrong? A similar misunderstanding could have taken place in a report of the same event in the past, perhaps with less drastic consequences. `Saw you last Tuesday with Mamie Woo', said Sunny Wong on Thursday. `Couldn't have done. I was with Fanny Cheng. She'll vouch for it.' Sunny got very excited about this apparent lie. Was Sunny talking about an event two, or nine days before this encounter? And, overheard on Sunday, `When's Marj's birthday?' - 'This Saturday. You've blown it'. So, is her birthday the day before, or the following weekend?

Wishful thinking

Jill thought of herself, implausibly, as an uncomplicated person. In the complicated matrix of space and time within which all Jill's communication tended to take place, she and Jack and Joe each have a special place as a deictic centre, each with a special perspective on the surrounding world. The space around Jill is `here' to her and `there' to Joe, and she is `I' to herself and `you' to Joe (and `she', perhaps, to Jack). Jill's perspective on space time coordinates may differ from Jack's and Joe's in more subtle ways. They may vary from occasion to occasion, or as her (or more likely, their) attention wanders, or perhaps as her Macchiavellian streak makes itself apparent. Or maybe as the outcome of wishful thinking.

The rays of time which reach from Jill into her past and her future, and along which she relates to events she remembers or hopes for, divide into chunks which are not fixed in length by natural laws, though she originally thought they are, misled by the discrete chopping of time into days, weeks, and more. Jill's Law of Proximate Thursdays may well differ from Jack's, and neither of them may ever know it. As she discovered, almost too late.

In Jill's understanding of the meaning of deictic expressions, she later found out, her complicated space time coordinate system is inhabited by a speaker and at least one hearer, and brightly marked for times (and places) of speaking. And Jill must always entertain the possibility that two people will not only have different positions in this coordinate system, indicated by the role-switching of `I', `you' and `he' or `she', but will very likely have somewhat differently structured models of it. Jill may take a myopic view of relating best to events which are relatively close, and then perhaps regretting it. Jack may need a bit of time to work things out carefully before the big day. Joe may just take things as they come without worrying too much.

But the trio `last', `this' and `next' have a special place in Jill's complicated system of space time coordinates. They are subtle sources of systematic ambiguity, which Jill was not conciously aware of, and thus potential wreckers of Jill's happy relationships. But back to the chain of events.

A communicative model

Jill, being a sensitive girl, felt Jack's inner turmoil radiating across her complicated space time coordinates and sent Joe on a pretext to buy a copy of the Herald Tribune. `Hi, Jack,' she cooed. `Busy last week? Thought that since you didn't show ...' At this decision point, things could have got even worse. Seeing Jack's patent incredulity, Jill's mind ticked a bit faster, and by the time Joe returned with a set of Web addresses, but no copy of the Herald Tribune, she had things figured out, and had already wrapped Jack just very slightly round one of her two little fingers again. Joe, for whom the other was still reserved, was greeted with mildly radiant smile, `Joe, meet Jack. We've just thought of a new quiz game, let's go for a coffee and work it all out together', Jill enthused.

Puzzled, but a real gentleman at heart despite appearances, Joe agreed. Jack's hopes were already rising again. Jill had decided that boring them out of their minds was the only way out of this one. `The rules are very strange,' Jill explained, with unnoticed mockery. `This is how they go. Just remember a time called ST, let's say it was last Tuesday. Or maybe even today. Let's call it Speaking Time, or perhaps Sunday Time, and let's affectionately christen it ST. And,' she prayed, `let it really mean Stop Thinking.' Then, a little too loud, she said, `The game is called ``This year, next year, sometime, never'', okay?' Last week all this needn't have been necessary, she thought wryly. And anyway, this Sunday's less compromising than last Thursday.

Scoring

`Scoring's the most important thing. Let's get into that first. The last shall be next and the first shall be thirteenth,' Jill's logic was well-known, though not yet to Joe or Jack. `Right? One scoring rule each, then ...

Scoring `last' (Joe's rule)
Scoring `this' (Jill's favourite rule, because it even flips between past and future, depending on how she sees it)
Scoring `next' (Hopefully, Jack's rule)

Joe's attention began to wander, and when Miss Woo sauntered by, he waited a minute, then said, clapping his palm to his forehead, `Just realised where I can get the Herald Tribune. May take time.' Jill pouted, so Joe thought, and frowned, concentrating on not unwinding the wrong little finger. `Okay, then. May be gone in a little while too.' Jack could hardly believe his ears. So far so good, thought Jill. But what kind of a nerd is this? `Now Jack,' she said earnestly. `Listen. Here we go.'

The rules

`The days of the week form a cycle, from Saturday to Sunday to Saturday. and so on. The length of one cycle defines a fundamental deictic interval of relevance, IRa, for a in {`last', `this', `next'}.

The length of IRa, |IRa|, is quite similar for a = `last' and a = `next'. And, Jill pointed out, the structure of IRlast is a a mirror-image of the structure of IRnext.

Now, for each a in {`last', `this', `next'}, |IRa| < 2 weeks.

So, `two weeks ago today' (or `two weeks from today') is the absolute cutoff point for `last' (or `next'), and and `one week ago' or `in one week's time' is the absolute cutoff for `this'.

There is thus a total interval IT < 4 weeks which covers all three cases.

If the days in IT are numbered i-13, ... i, ... i+13, where i denotes ST, then

The value of k signifies proximity to ST. But k is fuzzy, and varies with focus of attention, from person so person, from you to Joe and me to you and him.

The use of `<<' and `<' is a bit strange, but it is supposed to mean `higher number preferred'. For `last', `next', preferences tend to be for setting k further from ST, while for `this', on the other hand, preferences tend to be for setting k nearer to ST. And I like preferences to get really low as they approach 13. Otherwise it's unlucky.' Jill crossed most of her fingers.

Conclusion

`Now I realise this is a side of me you may not have thought existed', Jill continued. `But I know you always said you valued my mind, on principle.' Or, she pondered, did he say `in principle'? By this time, Jack was sound asleep, with his head on the table, dreaming perhaps of fuzzy proximities, deictic centres, and relevant intervals. Joe the gentleman had apparently found his Herald Tribune and would no doubt be examining it closely.

Jill was overjoyed that she had found an adequate solution and tiptoed away soundlessly, unwinding the other little finger, knowing that Jack would willingly pay for three coffees. This will be the last time, she hummed. Until next Thursday.