### A little brain work

I'm just about to catch a train to sunny Southend for a couple of days of talks, but before I go, I'll leave you with a little brain stretching challenge.

I have two bottles, one containing water and the other containing wine. I pour one measure of wine into the water bottle. I then pour an equal measure from the water bottle back into the wine bottle. At the end, there is just as much water in the wine as there is wine in the water. Which of the following have to be true to make this possible (you can choose more than one):

• The bottles are the same size
• The water and wine are thoroughly mixed after the measure is poured into the water bottle.
• The wine and water have to be thoroughly mixed after the measure is poured back into the wine bottle
• The wine has the same density as the water
• The water and wine are miscible

… or is it impossible to be certain that there is just as much water in the wine as there is wine in the water?

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Don't go any further until you've attempted some sort of answer.

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In fact, none of the conditions have to hold true - there will always be just as much wine in the water as water in the wine. Think of it like this: at the end of the process, the wine bottle holds exactly the same amount as it did initially, so it must have had exactly the same amount of water added to it as wine was removed.

Notice how the way that the question was phrased can distract you from the true facts. Even if you got the right answer, the chances are that the phrasing proved a distraction. You probably worried about partial mixing of water and wine, for example. Sometimes re-phrasing the question is an essential for knowledge gathering and creativity.

### Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

### Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

### Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope