The AppleWorld beyond infinity
LIKE most 5-year-olds, Matt Tapsell鈥檚 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 鈥渋nfinity鈥�. 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: 鈥淎ppleWorld鈥�. It is a one surrounded by zeros, he declares, and it takes the shape of an apple 鈥� 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, 鈥淟et鈥檚 do AppleWorld.鈥� Matt was just about to say, 鈥淥ne AppleWorld, two AppleWorlds鈥︹�� when Ethan stopped him by reminding him that there is no such sequence: it鈥檚 just AppleWorld.
Matt says: 鈥淭hose who mock this idea by saying 鈥榮imply add 1 to AppleWorld鈥� haven鈥檛 quite grasped Ethan鈥檚 concept, since that new number is also AppleWorld; and to those who say, 鈥榠sn鈥檛 that infinity?鈥�, the answer is that it鈥檚 not, because infinity is by definition never-ending and AppleWorld is a definite number.鈥�
Matt muses: 鈥淧erhaps the universe is limited rather than never-ending, so why can鈥檛 there be an ultimate limit on numbers?
鈥淚f 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-old鈥檚 break between the latest Doctor Who episode and stints on the games console.鈥�
Or perhaps, since the AppleWorld idea was raised just before bedtime, it was simply a plot by Ethan to infinitely postpone sleep.
鈥淐AUTION: Avoid contact with any plastics.鈥� This was the instruction on the plastic bottle of Dentyl Active Plaque Fighter mouthwash that Nick Rutter bought
FEEDBACK鈥檚 mathematics consultant couldn鈥檛 resist commenting on the above. 鈥淚 suspect that Ethan has rediscovered the surreal numbers,鈥� he observes. 鈥淵es, 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.
鈥淭his was discussed by Robert Matthews in his New 杏吧原创 feature 鈥楾he man who played God with infinity鈥� (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 鈥� and it also generates definite infinite numbers.鈥�
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 鈥渆nigmatic product鈥�. It鈥檚 a fluorite crystal that has been 鈥渁ctivated鈥� 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: 鈥淥ur crystals are unique because we activate or 鈥榗harge鈥� them energetically in our Pranava Energy Activator.鈥� What might that be? It says Prana is Sanskrit for 鈥渢he Breathe of the Creator鈥�, and that the Activator 鈥渂asically 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.鈥�
There鈥檚 more. Before we hurt our brain by trying to read on, can anyone tell us what 鈥淟ifetrons鈥� are? 鈥淚 wonder,鈥� Elizabeth says, 鈥渋f they are like positrons?鈥�
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 country鈥檚 public broadcaster, for its negative reporting of the effects of climate change.
One sentence stood out for Feedback reader Luke Wilson. Aitkin wrote: 鈥淢y memory may be faulty, but I cannot recall the ABC telling any good news stories about rising sea levels.鈥�
Luke鈥檚 comment on this has, we think, a distinctively Australian flavour: 鈥淲hat, pray, would constitute such a story? That the beach will soon be closer?鈥�
FINALLY, Guy Cox tells us about an email he received from an Indian scientist who contributes to the journal he edits. It said: 鈥淢y Gmail account was hacked. Please do not act on any mail sent from my Gmail account. I am taking necessary steps. Thanks.鈥�
Guy鈥檚 problem is that this message was sent from the scientist鈥檚 Gmail account.
鈥淚 suppose I therefore should not act on it. But then if I get another message that must mean I should act on it鈥�