unreasonable numbers and intimations of infinity

A couple of weeks ago we went to the local vide grenier, which is a communal yard sale where people reserve a spot in the square and bring their stuff to sell. That's where we found these two trottinettes for a grand total of 13 euros...it was perhaps the best purcahse we've made all year to date. They love em. The fact that each scooter is distinctly different from the other has prompted the kids to trade back and forth continually. The irresistable novelty of whatever someone else has in their hands remains a constant in their lives.
Of course we don't always get things in pairs, just as often things belong to the house or the family.
Hence the need to share things, the importance of possession vs the legitimacy of ownership ...these are the issues that animate and agitate our kids on a daily basis. Often they are able to sort out their claims without our help, sometimes they are so free and generous that we burst with pride. But just as often, they snarl at one another, and/or they come crying and complaining about how they've been wronged by the other.
We've pretty well established the "don't grab things, use your words" protocol, but that doesn't preclude either one from responding to a very nicely worded question like, "Can I play with the red car, please?' with a curt, "When I'm finished." Each of them has come to understand how to wield this answer and neither one of them has yet learned how to accept such an answer in good faith... (perhaps because they sense that it is seldom given in good faith?)
In order to help them not be overwhelmed by the utter vastness of open ended responses like, "When I'm finished," Beth has introduced the use of a timer. It works pretty well actually. If a dispute arises, the plaintive has the right to ask for the kitchen timer to be set. When it goes off, the possession arrow changes. Initially, Beth would set the timer...usually for five or ten minutes.
It was inevitable that the kids would become interested in the mechanism of the timer and that they would want to set the timer themselves. This of course led to further explorations into the correspondance between numbers and the experience of time passing. Being further advanced in numerology Tess was the first to get the concept of big numbers and doing serious time, while Colm remained primarily intrigued by the technology and the act of turning the dial and watching the lighted display change numbers. The end result of course is that Tess is better at gaming the system than her brother, but since he is not yet aware of that fact, no big deal.
But numbers are beginning to take hold of their imaginations. Just this morning Tess asked for the biggest number. Googleplex, said Beth. They loved that name and repeated it over and over. I threw out the word infinity and Tess gave it a moment's consideration but clearly she preferred googleplex.
Later, we overheard Colm ask Tess if he could play with something.
"When I'm done." A pause, then she added. "After googleplex."
Instantly Colm sent up a hue and cry. Clearly he understood his sister's intentions.
Beth suggested the timer. Colm agreed and went to the kitchen. On his way we heard him say, "Set the timer for zero."
I thought to myself...is anyone up there keeping score?
K