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Thinking Mathematically

September 18, 2011

In this post, I’m hoping to give a little insight into the way a mathematician thinks. This has been inspired by a conversation with the other teachers in my faculty.
(This may well apply to computer programmers too.)


Dishwashers have the potential to annoy us. A lot. More specifically, badly packed ones annoy us. One teacher admitted to completely unloading his wife’s attempt and re-loading it. This all seems to come down to a desire for efficiency and, perhaps surprisingly, this seems to be with a desire for better unloading. Essentially, a well planned load leads to a swift emptying. In the picture, you can see I have all the same types of plates/bowls next to each other so I can pick them up in one go and place them in the cupboard. I didn’t do the cutlery for this load but, generally, I go for all the knives in one compartment, all the forks in another etc. If you’re a mathematician the advantage of not having to sort at the end is obviously huge given that putting them in this way takes virtually no extra time. Controversially, I’m a handles up kind of person. I find that the fork prongs and knife blades get cleaned perfectly well and removing cutlery by the handles is both preferable (more comfortable) and quicker – straight in the drawer with no change of grip needed.


The other thing that I’ve seen people do and just can’t understand is this: they get a mug and teaspoon out, get a tea bag and then put the kettle on. This is madness. It should be glaringly obvious that putting the kettle on first and doing those other things while it is boiling is far more time efficient. In fact, there’s a whole area of maths called discrete or decision maths dedicated to this sort of thing. Decision maths is what gets your Sat Nav to pick the best route. It’s what helps make sure your baggage ends up in the right place (and it’s not the maths fault when it goes wrong). The kettle is a classic example of something called Critical Path Analysis

All these (possibly minor) things come about as a result of planning and thinking ahead. This is why mathematicians are often better at writing questionnaires because we think through what might happen before we’ve even done it. It is this planning ahead that is one of the signature features of mathematical thinking. When there was statistics coursework, there were marks available for planning ahead for potential problems and thinking about what you would do should they arise. 

Some might say that thinking about how best to pack the dishwasher is in itself a waste of time. Well, there are two answers to that:

1) It isn’t. It saves time,

2) I have more time to ‘waste’ thinking about these things because I think about these things.

Finally, I’m aware that this may sound a little like I have OCD. I don’t think I do. It’s just that planning ahead and being logical about certain things has such obvious benefits. To me, and I think mathematicians in general, the ‘putting the kettle on first’ situation is clearly the right answer. The other way is glaringly wrong. Really, really wrong. Essentially, the way I do this is the correct way.

I’m aware that this may well be exactly the way people with OCD reason about their behaviour too.

I hope you enjoyed this little insight into the mind of a mathematician.


From → Uncategorized

  1. Sabine McKenna permalink

    Hi Dave, You’re so right! There is no question that putting the kettle on first is the only way to make a cuppa efficiently. And I too wish the others in my house would load the dishwasher better… I probably would have put the yellow plates next to each other, because I think it’d look better, as well as sorting them by shape, but hey, that’s just me!Love your blog, only came across it tonight through twitter – thanks for being a reflective teacher online, not just for yourself! 🙂

  2. Anonymous permalink

    Hi Sabine, pleased you agree with the kettle.Just for the record – I didn’t say I wished others in my house loaded the dishwasher better!!Interestingly, I’ve thought about the whole same colour plates together thing and decided that organising them by colour really is a waste of time. I accept that it’d look better (probably) but that isn’t important while they’re being washed. Another quality of mathematical thinking is knowing when to draw the line…Pleased you like the blog. Do have a look around and leave some more comments – all appreciated.

  3. chris_harrow permalink

    I’ve tried to explain the logic of efficient loading to my family for years to no avail. Glad to hear I’m not the only one thinking along these lines.While I agree there are considerable time savings when unloading, there is also great satisfaction to my mathematical side at discovering a good packing scheme/algorithm for the machine that maximizes the load (and thereby minimizing the cost of additional loads) without sacrificing the cleaning ability of the dishwasher.Great post & blog. Thanks for sharing.

  4. singinghedgehog permalink

    I have been on dishwasher duty this holiday and have tried handles up. I would agree that it makes loading and unloading much easier. However, spoons in particular are an issue as the bowls tend to fit together; this is especially a problem with serving spoons covered in thick sauces or mashed potato. If they are placed handles down the bowls can splay out beyond the confines of the cutlery container, allowing good cleaning. This week I shall try a compromise with knives and forks down but spoons up. I’ll report back in a week!

  5. Anonymous permalink

    You might enjoy this song about how to load a dishwasher::

  6. I think it makes perfect sense – I have to pack my shopping in an order relative to unpacking at the other end!

    Oh – and the baggage – I know a bloke who works for a company who sorts out the laser equipment to get it all to the right place…technical stuff!

    • Cool. I’ve always been impressed with the automated sorting of things since I saw it on TV with the Amazon processing.
      Thanks for the comment.

  7. Well, he is always at work, so I guess there is a high demand…not just in airports though 🙂

    You’re welcome…I’m new, but followed you a lot on Twitter 🙂

  8. Mathematician walks into the kitchen, sees mugs with teabags in, milk out, kettle just boiled.

    He throws out the teabags, puts the mugs away, empties the kettle and fills it with cold water, then smiles with satisfaction: he’s reduced it to a previously-solved problem.

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