En el foro de malabaristas, a alguien se le ocurrió preguntar si sería posible malabarear una infinidad de objetos. Entre decenas de respuestas muy originales e interesantes, surgieron algunas discusiones matemáticas. Les pongo la parte final de una de ellas (los últimos párrafos son míos)
Ender756@hotmail.com.nospam (Ender) wrote in message
> No. Here's why:
> It is theoretically (and in practice) impossible to manipulate an infinite
> set of tangible objects simultaneously. To juggle an infinite amount of
> balls, it would be necessary to launch an infinite amount before any were
> caught. This would require that the juggling take place over an infinite
> period of time, each ball thrown to an infinite height. With appropriate
> alterations of the siteswap system, and bad interpretations of the ladder
> of alephs, it might be possible to create a system which could accommodate
> this mind-twisting concept. Even then, however, problems would occur
> depending on the respective orders of the infinities in question (quantity
> of balls, height of throw, time). Then again, if you assume that it could
> be possible to collect and manipulate an infinite set of objects, the
> logic is already so twisted and bent out of proportion that you could
> prove anything you wanted to.
> Ender>
Ender, actually, it is matematically posible, and you don´t need to modify the siteswap system .The problem you have is you are using the ladder of alephs, that meansthat you are using cardinal numbers, but you should use ordinals. Infact, if you want to juggle as many objects as there are naturalnumbers, you could get a cascade pattern with the siteswap [omega]that is: [omega][omega][omega]... where [omega] is a number greaterthan any natural number.
This is hoy it works:
At time 1 you throw ball 1, with a height of [omega], at time 2, makean [omega] throw and repeat this. After you have thrown all the balls,that is, at time [omega], you will be catching ball 1. Then, you canthrow this ball at time [omega] + 1, ball 2 at time [omega] +2, etc.By time 3*[omega] you would have qualified an infinity number ofballs, but of course, if your arms aren´t still tired enough, you cancontinue with the same cascade pattern.