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: “The information herein may not be stored in any information retrieval system whatsoever.”
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, “No electronic devices are permitted in the theatre.” Unwilling to extract his cardiac pacemaker, he “went home, bored and discouraged, to pass the time instead with my favourite magazine”.
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Giuseppe Sollazzo wonders how soon aspiring Britons can expect to hear from the Nationality Checking Service of London’s Haringey council: it warns that “processing can take up to 6 months or more”
Silence and gold
SOMEHOW the above paranoiac expressions of corporate copyright remind us of David Sharman’s 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 – which pays a mere $0.007 for each track users stream.
Are these a violation of the rights composer John Cage holds for 4′ 33″ – four-and-a-bit minutes of silence, in which we are invited to appreciate ambient sound? In 2002 Mike Batt, a musician, “a six-figure sum” 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 “great scam”.
Not worth stealing
SO-CALLED “piracy” 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. “If a system hasn’t yet been hacked, it proves only one thing: the content isn’t yet worth stealing.”
Infinitely many ineffables
AT LAST plucking up courage to read our emails on “ineffable numbers”, we find readers coming to conclusions very different to those we last reported. One Todd Moody had defined them as “the real numbers that cannot be individually named by any finite string of symbols in any language” (14 June). Readers argued that the number of such numbers is zero since, if there were two, you could name them “the first ineffable number” 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 “natural” (whole) numbers. But the number of “real” numbers – including fractions – is a larger, uncountable infinity. So there must be numbers without names. Ruth Le Sueur points out that this means ineffable numbers “make up the vast majority of real numbers”.
We do not regret anything
DO WE regret raising this question of the number of “ineffable numbers”? Jacob Zelten predicts that “if you don’t now, you soon will”, before briefly and clearly putting an argument equivalent to the above. Thanks. Ian Baudains “really wishes I hadn’t read that article at bedtime: it’s been bugging me ever since, so I’m hoping that if I set this down and send it I can finally get some sleep”. Sweet dreams. Or at least countable ones.
Naming numbers by making
WE SHOULD have predicted Rachel Lunnon’s observation that “we need to define what we mean by ‘naming a number'”. 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 – the algorithm – you use to compute a number may serve as its name.
There is a countably infinite number of algorithms. So we’re taken back to the foundations of computing emerging as a by-product of Alan Turing’s consideration of this concept of computability (now, astonishingly, about to be released as – 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 “ineffably infinite” 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 – apart from on the logic of “dialethic paraconsistency”, in which “some but not all contradictions are true”. 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: “The value must be a number less than infinity,” it insisted. He regrets that “it doesn’t tell me which infinity the value must be less than”.