{Reason in Science]}[13th September 1989]

[Redbook6:248-254][19890913:0927]{Reason in Science]}[13th September 1989]

19890913.0927

‘THERE’S an answer to every problem.

‘Young Cyrogenes, who is completely deaf, is assisting Professor Didipotamous on an aviation project.

‘The Professor asks him to provide a time and motion study of the local airport adjoining their research establishment … aeroplanes taking off, landing etc. However, Cyrogenes finds he can only manage to do this now and again., as his laboratory tasks keep him pretty busy. But when he sees an aeroplane, he makes a note of it, and returns to his duties.

‘Didipotamous is not pleased. “This is worse than useless,” he says to his colleague Dr, Catsnup. “We already know that every single hour, day and night, exactly one plane lands, refuels and leaves in perfectly regular fashion. And yet this report states that he finds 11 times as many planes landing as taking off. This tells us nothing useful.

‘“Ah, but it does,” says Catsup.

Q. WHAT INFORMATION DO THESE FACTS CONTRIBUTE TO THEIR TIME AND MOTION PROJECT?

Puzzle devised by Maslanka’*

I suppose it’s a bit cheeky of me, after the sort of speculation and fuzzy-logic of the previous pages, to criticise scientists for poor reasoning; but at least I recognise and acknowledge what I’m doing. As I looked at this problem I felt, not just that I was missing something, but that there was something missing: and that it probably related to the information as to what happens every hour. And it does. Working back from the answer, what must I think be intended in the second sentence of the third paragraph is that each plane takes exactly one hour to go through its landing, refuelling and take off cycle. Therefore, if Cyrogenes is 11 times more likely to see a plane landing as taking off (or, one must assume from the answer, refuelling, although the question does not state it), it follows that 11/12ths of each hourly cycle is spent landing, and => 1/12th ** taking off, ie 5 minutes.

‘You’ll find that a problem shared with I[mperial] C[hemical] I[ndustries] is a problem solved.

‘ICI

‘SOLUTIONS

A. We can calculate that each plane takes 5 minutes to refuel and take off again.

Reader Reply No. 7’*

*N[ew] S[cientist] 1681[,] 890909[,] p54-55 [photocopied into the ms]

**[refuelling &]

***The puzzle also brings out the great strength and weakness of reasoning as a method of problem-solving: that it is parameter-dependent, and therefore is unaffected by ‘common-sense’ knowledge (eg of airports) & is utterly dependent upon its prior assumptions (even# in maths).

****(I appreciate that ‘Maslanka’ is possibly an advertising agent, but ICI and its Scientists must stand or fall by their published writings.) The point is that as a matter of English ‘exactly’#* is sufficient to state that a whole plane, no more and no less, lands, refuels and takes off each hour; but insufficient to state that each plane takes the whole of#** one hour to do so. This is, I think, because a plane is discrete, not continuous.

#[especially?]

#*[as placed]

#**[ie exactly!]

[continues]

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