The AppleWorld beyond infinity
LIKE most 5-year-olds, Matt Tapsellâs son Ethan has an inquisitive and questioning mind. Recently he has wanted to know what the biggest number in the world is.
Matt explained that there is no such thing: numbers can continue to get bigger and bigger, never reaching what is called âinfinityâ. Unsurprisingly to anyone who has ever discussed things with a young child, this does not satisfy Ethan. He insists that there is a largest number and has given it a name: âAppleWorldâ. It is a one surrounded by zeros, he declares, and it takes the shape of an apple â of course.
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One bedtime, Ethan and Matt were discussing number sequences. Matt gave Ethan a series of numbers, leaving Ethan to fill in the next one in the sequence. They did this counting in twos, fives, tens and so forth, until a cunning Ethan said, âLetâs do AppleWorld.â Matt was just about to say, âOne AppleWorld, two AppleWorldsâŠâ when Ethan stopped him by reminding him that there is no such sequence: itâs just AppleWorld.
Matt says: âThose who mock this idea by saying âsimply add 1 to AppleWorldâ havenât quite grasped Ethanâs concept, since that new number is also AppleWorld; and to those who say, âisnât that infinity?â, the answer is that itâs not, because infinity is by definition never-ending and AppleWorld is a definite number.â
Matt muses: âPerhaps the universe is limited rather than never-ending, so why canât there be an ultimate limit on numbers?
âIf nothing else, this shows that the exploration of theoretical mathematics is not the preserve of university professors, but sits quite comfortably in a 5-year-oldâs break between the latest Doctor Who episode and stints on the games console.â
Or perhaps, since the AppleWorld idea was raised just before bedtime, it was simply a plot by Ethan to infinitely postpone sleep.
âCAUTION: Avoid contact with any plastics.â This was the instruction on the plastic bottle of Dentyl Active Plaque Fighter mouthwash that Nick Rutter bought
FEEDBACKâs mathematics consultant couldnât resist commenting on the above. âI suspect that Ethan has rediscovered the surreal numbers,â he observes. âYes, really. Just as there are infinitely many real numbers between each pair of whole numbers, there are infinitely many surreal numbers between each pair of real numbers.
âThis was discussed by Robert Matthews in his 51¶ŻÂț feature âThe man who played God with infinityâ (2 September 1995, p 36). And there is a logical machine, devised in 1969 by John Horton Conway while exploring his and the game of Go, for enumerating the surreals â and it also generates definite infinite numbers.â
So now you know. Ethan really was on to something.
ON A different topic, reader Elizabeth Romanaux draws our attention to what she aptly calls an âenigmatic productâ. Itâs a fluorite crystal that has been âactivatedâ by a company called Celestial Lights of Colorado, for $49.95 a throw.
The website explains, in the lurid colours we have come to expect from such adverts, that: âOur crystals are unique because we activate or âchargeâ them energetically in our Pranava Energy Activator.â What might that be? It says Prana is Sanskrit for âthe Breathe of the Creatorâ, and that the Activator âbasically charges each crystal with a special Lifetronic Light Frequency or Prana. The crystal is now charged and activated permanently to attract and transmit charged Lifetrons or Prana healing energy.â
Thereâs more. Before we hurt our brain by trying to read on, can anyone tell us what âLifetronsâ are? âI wonder,â Elizabeth says, âif they are like positrons?â
The good news about climate change
AN ARTICLE by Don Aitkin, former chairman of the Australian Research Council, was published in The Australian newspaper on 19 January. Headlined , it attacks the Australian Broadcasting Corporation, the countryâs public broadcaster, for its negative reporting of the effects of climate change.
One sentence stood out for Feedback reader Luke Wilson. Aitkin wrote: âMy memory may be faulty, but I cannot recall the ABC telling any good news stories about rising sea levels.â
Lukeâs comment on this has, we think, a distinctively Australian flavour: âWhat, pray, would constitute such a story? That the beach will soon be closer?â
FINALLY, Guy Cox tells us about an email he received from an Indian scientist who contributes to the journal he edits. It said: âMy Gmail account was hacked. Please do not act on any mail sent from my Gmail account. I am taking necessary steps. Thanks.â
Guyâs problem is that this message was sent from the scientistâs Gmail account.
âI suppose I therefore should not act on it. But then if I get another message that must mean I should act on itâŠ
