J T R Sharrock has written a puzzle book ( see post # 8) and it includes quite a few problems based on bird surveys........ But I've got a much more baffling one.... and here it comes. Suppose you do a bird survey.... and here's the result... In your first site you found 2 male waxwings out of 8 ... that's 2/8 are males. In your 2nd survey you find 4 males out of 10 birds ... that 4/10 are males. So we combine the results... 2/8 + 4/10 = 6/18 So 6/18 are males. ...that's one-third of them are males. You get that 6/18 by adding the top numbers ... 2 + 4 =6 and then the bottom numbers .... 8 + 10 = 18 And it's true that you have got 6 males out of 18 birds. Here's the same process, with the same results, in a different setting ... You'll all remember tests at school ... often you would have two "papers" and the teacher would write the marks at the top for you. It might look like this .... 2 + 4 8 10 = 6/18 or 1/3 Fair enough. A third. And it's 6/18 because you've added the tops ( 2 + 4) and the bottoms (8+10 =18) And it's true that you got 6 questions right out of 18. Fair enough. BUT BUT BUT BUT BUT BUT ........ when you add fractions in school you don't add the tops and the bottoms. It gives you stupid results. An obvious example is a ½ + ½ ► add tops and bottoms ► 2/4 = ½ !!! Now that is an obviously bonkers result ! So .... we have a paradox here ... when we add fractions in school, we don't add the tops and the bottoms ...we've just seen how it gives you daft results. But ... it gave us "correct" results in our bird survey .. and that test. If you still don't believe it, here's another example to really make it clear that adding the tops and bottoms will give a stupid answer ... ¾ + ¼ add tops and bottoms ► 4/8 = ½ !!!!!! How can that be right ? It can't ... it's bonkers again. Yes, it's a paradox all right In our survey results, adding the tops and bottoms gave us the "right" answer. But when we do it in maths lessons, it doesn't. Cripes !!! There's something funny going on!! Could I possibly have led you all down the garden path ? But if I've misled you, how ? So now, I'll leave you all to go mad trying to work out what's right and what's wrong ! And more importantly, why ! Tell you what ...we'll have a bit of music. Y Cyrff .... " Seibiant" ... Y Cyrff = The bodies ( though you won't find it in a dictionary) Seibiant = leisure, respite. And now, as a "mystery" bonus thing, exactly two years into the future I'm going to ask you lot a question, and here's the answer .....
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AuthorThat's the author up there ... I was young and sprightly then. Archives
October 2022
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