Feedback is our weekly column of bizarre stories, implausible advertising claims, confusing instructions and more
Read, watch and forget
ENTERTAINMENT is becoming difficult, reports Geoffrey Milos. Browsing a library recently, each of the newish books he opened included a similar stern warning: 鈥淭he information herein may not be stored in any information retrieval system whatsoever.鈥�
This left him uncertain whether he was permitted to remember anything he might read. So he went to the cinema. There he was admonished that, 鈥淣o electronic devices are permitted in the theatre.鈥� Unwilling to extract his cardiac pacemaker, he 鈥渨ent home, bored and discouraged, to pass the time instead with my favourite magazine鈥�.
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Giuseppe Sollazzo wonders how soon aspiring Britons can expect to hear from the Nationality Checking Service of London鈥檚 Haringey council: it warns that 鈥減rocessing can take up to 6 months or more鈥�
Silence and gold
SOMEHOW the above paranoiac expressions of corporate copyright remind us of David Sharman鈥檚 of the ANZAC Appeal offering a pre-recorded minute of silence for $2.26 to support servicemen and women. More self-interestedly, US band Vulfpeck raised $20,000 to tour by offering 10 half-minute tracks of recorded silence on the Spotify service 鈥� which pays a mere $0.007 for each track users stream.
Are these a violation of the rights composer John Cage holds for 4鈥� 33鈥� 鈥� four-and-a-bit minutes of silence, in which we are invited to appreciate ambient sound? In 2002 Mike Batt, a musician, 鈥渁 six-figure sum鈥� to the John Cage Trust after placing a silent track on an album, for which he credited Cage as co-composer. He later as a 鈥済reat scam鈥�.
Not worth stealing
SO-CALLED 鈥減iracy鈥� has inspired the movie industry to ever-greater efforts in encryption and copy protection. We liked the honest private opinion of one Hollywood studio engineer insider. 鈥淚f a system hasn鈥檛 yet been hacked, it proves only one thing: the content isn鈥檛 yet worth stealing.鈥�
Infinitely many ineffables
AT LAST plucking up courage to read our emails on 鈥渋neffable numbers鈥�, we find readers coming to conclusions very different to those we last reported. One Todd Moody had defined them as 鈥渢he real numbers that cannot be individually named by any finite string of symbols in any language鈥� (14 June). Readers argued that the number of such numbers is zero since, if there were two, you could name them 鈥渢he first ineffable number鈥� and so on (9 August).
John Harris responds that the number of names for numbers is countably infinite, since each name is composed of discrete symbols. It is the same as the number of 鈥渘atural鈥� (whole) numbers. But the number of 鈥渞eal鈥� numbers 鈥� including fractions 鈥� is a larger, uncountable infinity. So there must be numbers without names. Ruth Le Sueur points out that this means ineffable numbers 鈥渕ake up the vast majority of real numbers鈥�.
We do not regret anything
DO WE regret raising this question of the number of 鈥渋neffable numbers鈥�? Jacob Zelten predicts that 鈥渋f you don鈥檛 now, you soon will鈥�, before briefly and clearly putting an argument equivalent to the above. Thanks. Ian Baudains 鈥渞eally wishes I hadn鈥檛 read that article at bedtime: it鈥檚 been bugging me ever since, so I鈥檓 hoping that if I set this down and send it I can finally get some sleep鈥�. Sweet dreams. Or at least countable ones.
Naming numbers by making
WE SHOULD have predicted Rachel Lunnon鈥檚 observation that 鈥渨e need to define what we mean by 鈥榥aming a number'鈥�. If you cannot compute a number, she points out, you cannot tell whether it is equal to another number, and therefore you cannot identify it. The procedure 鈥� the algorithm 鈥� you use to compute a number may serve as its name.
There is a countably infinite number of algorithms. So we鈥檙e taken back to the foundations of computing emerging as a by-product of Alan Turing鈥檚 consideration of this concept of computability (now, astonishingly, about to be released as 鈥� The Imitation Game).
What is ineffably infinite?
WHEN a student in the 1960s, Martin Huxley was introduced to a subtly different concept: a number is 鈥渋neffably infinite鈥� if it cannot be described in terms of smaller numbers. Since this was before the dawn of internet time, we are not surprised that all we find online on this topic is theological 鈥� apart from on the logic of 鈥渄ialethic paraconsistency鈥�, in which 鈥渟ome but not all contradictions are true鈥�. So it is with heart in mouth that we wonder: are there any ineffably infinite numbers?
Numbers are interesting. True
MEANWHILE, if you had any doubt that the above is interesting, be reassured (or reminded) that it is provably so. As Douglas Woodall puts it: suppose that not all numbers are interesting. Then there is a smallest uninteresting number. But being the smallest uninteresting number is enough to make it interesting. Thus we have a proof by contradiction.
Infinitely wrong error message
FINALLY, Nik Whitehead reports trying to convert a number from one format to another in a computer package called Visual Studio 2010: 鈥淭he value must be a number less than infinity,鈥� it insisted. He regrets that 鈥渋t doesn鈥檛 tell me which infinity the value must be less than鈥�.