KYLE. D EVANS - POEMS AND PARADOXES

POEMS AND

PARADOXES

KYLE. D EVANS

ILLUSTRATED BY HANA AYOOB

For Edwin & Juno x

To my mother Mina, who was my first maths and art teacher. Thank you for encouraging my passion for drawing and numbers ever since.

Thank you to Andrew at Tarquin for helping to make this project happen. Thanks to Hana for putting up with my ridiculous illustration requests ("can you draw a two that looks jealous?") Thanks to the families Inskip, Jeffs and Smith for giving me feedback throughout. Most of all, thank you to my family for their love and support.

Heres a riddle a friend of mine found in their Christmas cracker:

What do you think? Is no the answer to the question? Feel free to put the book down and have a little think about it.

Lets try out the two possibilities:

Is no the answer to this question? Yes!

There is a contradiction here: if we answer with a yes, were saying that we think no is the answer to the question: but we just answered yes.

Is no the answer to this question? No!

Unfortunately here we are answering the question with a no, by which were saying that no is not the answer to the question. But we answered the question with a no!

However you try to answer this question, you will be wrong. Its all very confusing, and its meant to be: this is an example of what is known as a paradox . A paradox is a logically selfcontradictory statement or set of statements. Heres another fun paradoxical question my son recently came up with: whats smaller than nothing?

A more famous example: imagine a village, and in that village imagine there is a barber shop. A rule of this strange village is that the barber shaves only those villagers who do not shave themselves . The question is, who shaves the barber ? Again, you may wish to put the book down and have a think about it first.

Let us once again try out the two possibilities:

The barber shaves himself. After all, he should be pretty good at shaving people! But if the barber shaves himself, then the barber is shaving someone who shaves himself, which breaks our earlier rule.

Again, this is meant to be frustrating and confusing. Heres a poem to maybe help you feel better about it all.

The barbers the friendliest man in the town

From the pauper in rags to the prince in his crown

And the shop-keeper hustling to earn every buck

To the lowly street-sweeper whos down on his luck

From the haughtiest priest to the clock makers son

The barber takes time out to shave every one

Regardless of family, stature or wealth

He shaves every man who does not shave himself

Theres only one question I harbour

Tell me please:

Who shaves the barber?

The barber cares not for the size of your wage

Your caste or your creed or your background or age

From the college athletics team running their laps

To the pensioners fresh from their afternoon naps

And the inpatients dressed in their hospital gowns

He shaves every man in each part of the town

Regardless of attitude, wisdom or health

He shaves every man who does not shave himself

Theres only one question I harbour

Tell me please:

Who shaves the barber?

Heres a neat trick you can try next time you encounter a well or any source of water that is directly below you and want to know how far below you the surface of the water is:

Drop a stone, penny or other small object, and time how long (in seconds) after you release it you hear a splash.

Take that time and multiply it by itself: this is called squaring .

Now take the new number you have and multiply it by five.

The number you now have is the distance between you and the water (in metres.)

For example, if you counted 3 seconds, the water is roughly 3 3 5 = 45 metres below you. But why?

The key fact to know here is that any object dropped in any place on earth will accelerate towards the ground at increases by ten metres-per-second every second, starting from a speed of zero when the stone is held in your hand. So a graph of velocity against time for the example above would look like this:

The area of the triangle under the graph represents displacement: the distance the stone has travelled since it was dropped. The area of a triangle is base height, so in this case 3 30 = 45 metres. Heres a little rhyme to help you remember this rule

I dropped a penny in a well

And listened as the penny fell

And only when I heard a plop

Did I let my stopwatch stop

The time it took to make its dive

I timesd that by itself, then five

And now I hate to make you jealis -

I know just how deep the well is!

How much would you be willing to pay for a one pound coin? Just a normal, regular one pound coin, not a special commemorative coin to celebrate Southampton winning the Premier League in 2022. You wouldnt be tempted to spend more than a pound, right? Not unless there were some special conditions, perhaps

If youve ever been to an auction, witnessed one on TV or even bid for something on eBay, youll know how an auction works. But just in case, heres an example:

Lets say you want to win an auction for a signed Ed Sheeran record, so they raise their hand and bid 15. The auctioneer asks if anyone is happy to bid 20 and you raise your hand and become the lead bidder again. But the auctioneer then asks if anyone is willing to pay 25 and your rival swoops in with such a bid. You are tempted to go on and bid 30 for the record, but you decide to step back at this point and concede defeat. Your adversary now owes the auction house 25 for the record, and you walk away empty handed, but still with the 20 you came with.

Now, back to our special 1 auction, in which all the rules are the same except for one: when you make a bid you are resigned to losing that money, even if you dont end up winning . So if you bid 50p for the 1 coin, but someone else outbids you, you still lose your 50p.