51动漫

Feedback is our weekly column of bizarre stories, implausible advertising claims, confusing instructions and more

Plumbing to be proud of

FEEDBACK鈥橲 random-access piling system has thrown up Wayne Plummer鈥檚 intriguing photograph of a sign in a hotel in Saffron Walden, UK. 鈥淭his en-suite bathroom,鈥� it declares, 鈥渋s fitted with a Saniflow toilet which will not allow alien products to pass through its system鈥︹��

Has the European Space Agency been informed of this advanced detector of extraterrestrial matter?

Max Lang was the first reader to forward a photo of a sign in a cycleway reading 鈥淐aution: signage in cycle way鈥�. Yes. Tautologies are true. Why, though?

Papering over differences

RESPONSES to our sceptical inquiry into figures for annual consumption of toilet paper (3 May) continue to fill our virtual mailbag. Ian Buchanan follows up on an observation we quoted that 鈥渢he British Army stocked toilet paper on the assumption that the soldier would use three sheets per day; the American ration was twenty-two and a half sheets鈥� (7 June). He recalls that the British paper was the hard stuff 鈥� 鈥渢hin, smooth, air and water resistant, an excellent medium for letter-writing and also escape maps for downed airmen, I believe鈥�.

Alan Chattaway concurs: 鈥淚t鈥檚 not hard to see how three sheets would do the job of 22.5 sheets of fluff pulp.鈥� Robert Cailliau observes that US paper is still 鈥渢erribly thin鈥�, whereas Swiss paper 鈥渋s thick and soft, and that鈥檚 where we buy ours, though we live in France鈥�. Then Brian Darvell chips in with the observation that in Hong Kong the paper is very absorbent: he has commonly found a roll on restaurant tables for general mopping-up use.

Perplexing pagination

FEEDBACK reader Bob Lang has another papyrological question: why has 51动漫 recently acquired odd single-leaf pages? Further: 鈥淪ince the loose pages all appear on the left-hand side of the staples, I can only assume that this is reflecting some bias on the part of the printers.鈥�

Our production editor explains that we have switched to a press that prints 64 pages 鈥渋n one big hit鈥�. Printing a number not divisible exactly by 64 produces what are called, in the trade, 鈥済uards鈥�.

This gives us a further example of topology affecting publication on paper. We earlier observed the pesky First Directive of publishing: 鈥渢he words must go all the way to the bottom right-hand corner and no further鈥� (11 February 2012). And are we now in some sense a tad closer to Feedback鈥檚 lifelong ambition to edit a paper publication with an odd number of pages?

Paper nomenclature puzzle

MEANWHILE we must face questions about toilet paper nomenclature. Stefan Bojczuk is puzzled by the unit of rate of use in the New York Times we cited: 鈥渞olls per capita per year鈥�(3 May). 鈥淪urely rolls per anus per annum?鈥� he suggests.

Platonists deny patentability

SOMEHOW this discussion drew Feedback back to databases of patents. Specifically, to look up , filed by Roger Penrose on 25 June 1976, covering uses of non-periodical 鈥渢iling鈥� of surfaces.

The patent鈥檚 first unusual feature was that its validity depended on your position on the philosophy of mathematics. A strict Platonist, for example, would be someone who agrees with the Greek philosopher Plato that the pattern, like all other mathematics, already existed in the space of 鈥渋deal forms鈥�. So it would be waiting to be discovered, and therefore not patentable.

The other point of interest is that Penrose is reported to have sued the Kleenex company for using a non-periodic pattern on toilet paper. we have so far found, however, seem to mix up patent and copyright law. The patent has expired.

Property of Her Majesty

THE legality of toilet paper leads us to Noel Cramer鈥檚 鈥渁musement, visiting the Science Museum in London in the early 1960s, to see on each sheet of paper the printed words 鈥楪overnment Property鈥� 鈥�. That led him to 鈥渟teal鈥� part of a roll 鈥� 鈥渨hich has unfortunately gone lost since鈥�. That reminds Feedback of acquiring some of the same stock while making an appearance at the Royal Courts of Justice in the 1970s. There is a statute of limitations, isn鈥檛 there?

Paradoxical numbers鈥� plethora

FINALLY, and returning to matters mathematical, several readers were suitably puzzled by Todd Moody鈥檚 definition of 鈥渋neffable numbers鈥� as 鈥渢he real numbers that cannot be individually named by any finite string of symbols in any language鈥� (14 June). Tony Kline 鈥渟at for far too long contemplating the sentence 鈥榥othing cannot be named in any language鈥� until finally escaping from paradox by summoning the non-existent ghost of Bertrand Russell and quietly strangling it.鈥� Todd refers, of course, to Russell鈥檚 paradox, concerning the barber who shaves all the villagers who do not shave themselves.

Jeremy Colman and Ken Zetie give essentially the same argument for the number of such numbers being zero. As Ken puts it: 鈥淪uppose there are two. Then you could name them 鈥榯he first ineffable number鈥� and 鈥榯he second ineffable number鈥�.鈥�

Feedback thinks this may be an example of 鈥渟econd-order naming鈥� and cheating. But for discussion of this topic takes us no further than the of the late-Roman philosopher and theologian and a headache. Help?