Midpoint Motivation And The Science Of Timing

By Barry Rycraft

I’ve been working on my timing for most of my live as musician, but more in a physical way than a strategic way. Hours practicing with a metronome or performing with drummers can certainly make you think about time in a deeper way than someone who simply uses time to mark the passing of their day. There is also the ability to make the most of your time, which is a popular subject among entrepreneurs who tend to work long hours and strive for a work/life balance. However, being productive is very different from knowing when is the best time to do something.

“Time is an illusion, timing is an art” – Stefan Edmunds

Recently I’ve been reading a great book called ‘When’ (The scientific secrets of perfect timing) by Daniel H Pink. A few key insights jumped out to me. Firstly, there is a natural slump in the middle of any activity. This is true for a thirty minute lesson or over a ten week course. Our work and focus naturally wanes as we become comfortable and lose track of our objectives. We become bogged down or distracted. According to the book, the surprising antidote to this is highlighting the midpoint. Scientists did a number of tests and found that when we are told or realise we have reached the halfway point of an activity, we begin to reorganise our approach and take action in order to succeed. Interestingly, this plateau of progress followed by disruption is mirrored throughout the natural world, even in the process of evolution. However, If we set the alarm bells to go off at the midpoint it kick starts the active stage in any process and gives us the best chance of avoiding our middle slump.

Let’s use Rockjam as an example: Our ten week term will start with the activity of choosing songs and writing. During the middle section of the term there will be a natural slow down followed by a frantic last two weeks when we realise we have a performance. A practical way to mitigate for the slump is to mark the midpoint of the term (week 5). We can give it a name and celebrate it. Let’s call it Hump Week. Hump week can be marked in many ways, but something as simple as mentioning it to the class should have the necessary effect. A solution for short lessons might be to stack the more cognitively demanding work for the start and end of a lesson when the students attention is more focused.

The book also contains many great insights into the best time for focus depending on age. The obvious one is that teenagers focus better after 11am, but I also learned that the midpoint of our day holds a natural slump of energy. The author sites examples of Judges deliberations which are more severe after lunch. If you are in the position to do so, it would be wise to organise your day around your own natural rhythms and sleep cycle. If like most, you are at the mercy of someone else’s timetable you can mitigate by adding naps, walks and strategic caffeine breaks to your day.

For anyone interested in how to decide the best time to start any activity I recommend Daniel H Pinks book ‘When’. Personally I intend taking a hard look at the ‘when’ of all my activities.

Review on Godël, Escher, Bach—an Eternal Golden Braid

(A book review & a mimic of the dialogues in the book, borrowing Mr T. and Mr.A.)

Disclaimer: this only shows my partial opinion of an amazing book which has a lot of ideas interwoven within them. There is so much to this book, and to the Godel’s theorem, that it is not quite realistic to capture them all accurately in one article. I just hope to recommend this book and to provide an relaxing and fun read.

Achilles and Tortoise are visiting the Escher Museum in The Hague

Achilles: Why, will you look at these wonderful paintings! They combine different perspectives in one frame and create a paradoxical world. Tangled hierarchy and strange loops are everywhere.

Tortoise: Yes, I can see why Escher is your favourite painter.

Achilles: Speaking of Escher, were you not reading a book a few months back about Escher? You were fascinated by the book and promised to tell me about it.

Tortoise: Why yes. The book is called Godël, Escher, Bach—an Eternal Golden Braid, written by Douglas R. Hofstadter.

Achilles: My my, what a long title! And what a long name the author has!

Tortoise: The book itself is long as well. It is seven hundred pages long. You can see why it took me so long to read.

Achilles: Seven hundred? That definitely won’t make a relaxing read. But as long as it is interesting, I guess it is worth the time.

Tortoise: I assure you it is deeply intriguing. I have never read any book like this.

Achilles: What kind of book is it?

Tortoise: It is a marvellous book.

Achilles: …Mr Tortoise, you are known for your wise remarks and clarity of mind. I beseech you to offer me a more explicit explanation.

Tortoise: I would be willing to do that, but it would take quite a while to explain. Say, why don’t we sit down at the nice little cafe and have a chat?

Achilles: Yes of course! (sitting down in one of the bean bags offered by the cafe) Wow, comfy! And the cafe is playing music by your favorite Baroque composer, J.S.Bach! What a wonderful coincidence.

Tortoise: (straining his ears to listen) Yes… It is the cello suite No 2 in D minor, I always find it particularly calming.

Achilles: Yes, it does have a pleasing air. Waiter! (motioning to a waiter in a smart white shirt) A cup of cappuccino, please. And for you, Mr Tortoise?

Tortoise: Tea, please. No sugar.

Achilles: Now, you were telling me about this book…what IS it really about?

Tortoise: Dear Achilles, you do pose for me a hard question to answer. Even the venerable author himself admits in the preface that, quote, “This question hounded me”. It is a book that explores different layers of interpretations that arise in life and all fields across maths (hence Godël), art (Escher) and music (Bach). It is also about strange loops and paradoxes that we encounter, and how, when used correctly, things that arise from these things will seem…well, how do I put this…seem to have a life of their own. It is as if we are creating animate things from the inanimate.

Achilles: This reminds me of the endeavour of creating Artificial Intelligence.

Tortoise: AI is indeed mentioned with great zeal in the book, as it uses self-reference to improve itself. See, the way AI learn is from the past experiences and the information that it had already processed. It has the ability to self-repair. We haven’t achieved it yet, clearly, but the magic of self-reference is in use in that branch of study. The book also touches on topics like neuroscience, genetics, physics and linguistics. They all involve strange loops and paradoxes. It would seem that we could never do without self-reference. The author used art, music, and more importantly, maths to demonstrate this point. It actually ties in with a new and exciting branch of maths called “Metamathematics”.

Achilles: Very deep and philosophical. I hope this is not one of you maths books. You know how bored I get, reading those books. No offence, Mr T., but the book you gave me the other day on Statistics nearly killed me. (yawn)

Tortoise: (The waiter came on with the cup of coffee) Here, some caffeine will wake you up. No, I assure you, the book is extraordinarily well written, with amazing illustrations and playful dialogues inserted between each chapter. To make things easier for the reader to understand, the writer borrowed two characters from Lewis Carroll, Mr Tortoise and Mr Achilles, to explain the concepts.

Achilles: Who, you?

Tortoise: Why, you!

Achilles: Coincidence upon coincidences! The two characters share our name!

Tortoise: Yes, I wonder why I have never noticed it before. Anyways, the two characters debate in miniature dramas to explain things to the reader. The drama are sometimes a mimic of a piece of music, very likely a Bach piece, a piece of Escher artwork or a maths story.

Achilles: Much like the conversation we are having now?

Tortoise: Yes, just like what we are doing right now. The dialogues are one of the parts I enjoy the most in the entire book. They are ingenious and awe-inspiring… No really, the book is completely readable, the author took his time in explaining the maths, and invented a new system to explain in detail Godël’s theorem. It is not at all hard. Afterall, this is not a book on maths.

Achilles: Still, I fear that the book might be too long and boring for me. I am not the best reader of maths books.

Tortoise: No matter, I personally took delight in the parts that are not about maths as well. You can always skip around the chapters, and that would be totally enlightening too.

Achilles: You mentioned a Doodle theorem, what is that?

Tortoise: You mean Godël theorem. It is a theorem put forward by the logician, mathematician and philosopher Kurt Godël. It is quite intricate and complicated, but in its core, it states that not all theorem can be proven.

Achilles: Not all theorem can be proven? Is that you being pessimistic and cynical again, Mr T.?

Tortoise: Unfortunately, no. this fact has been proven already, fair and square.

Achilles: You mean… there are conjectures that cannot ever be proven no matter how hard and how long we try?

Tortoise: Precisely.

Achilles: (trembling, takes a sip from his cup) This is too frightful! I feel like I am approaching the end of the world at the speed of light. Would you like to give an outline of how he proved it?

Tortoise: Very gladly, but I’m afraid it would take far longer than necessary, and besides, you can find out about it as you go through the book. At the moment I’ll give the basic idea. The proof involves creating a strange loop in any formal system using self reference. An example of this is the sentence “This sentence is false”.

Achilles: Ha! I know this trick. Don’t try to trick me with this. This is the classic paradox, if you say that this is correct, then that means that this is wrong. If it is wrong, then it is correct. Such a decease of a sentence is obviously not relevant and completely trivial.

Tortoise: Maybe, but trivial or not, it is a valid statement. And if it is a valid statement in a formal system, we must be able to decide if it is true. And we would have to prove it, true or false. However, as this sentence is paradoxical, it is undecidable. What Godël did was to create a self-referent sentence like that inside a mathematical system and concluded that this is a theorem that is undecidable—therefore the system is incomplete.

Achilles: Hmm…you do sound convincing. But I still am skeptical. To me, this sentence is not true–nor false– it is pointless. Self reference does not lead to anything and it is better just to not ask this question!

Tortoise: You don’t realise, but you just touched on another part of the book! It is another interpretation and approach to these kind of problems. It is the Zen Buddhism approach to the problem, by “unasking” the question.

Achilles: Unasking? How can you unask a question once it is spoken?

Tortoise: That’s the one of the core ideas of Zen. In order to understand and able to interpret the hole in the mathematical system that creates that paradox, we must ascend to a more powerful level, a “metalevel”, if you will. But then again this level face the same problem as the ordinary level, so it also need a “meta-metalevel” to mend its hole, and so on and so forth. You will need an infinite amount of “meta”s to be able to describe the final level that gives us a complete system without defect. This is impossible to contain in our finite world, so the Zen approach to transcend infinity is to “unask” the problem instead.

Achilles: (trembling, takes a big gulf from his cup) Pft! It is cold. We have talked for so long. I fear my head might burst.

Tortoise: Do relax a little, Achilles, and listen to the cello sonata, it will clear your head immediately.(calmly sips his tea)

IMO Diary Part 3: Post Contest Adventures

10th of July-11th of July

We had two days of excursions
As such are the traditions
So that the teachers could correct our papers
With no distractions


After two days of examinations
We set the alarm with precision
To catch the bus that will take us far away
2 hours to our destinations

Long bus rides were such an exertion
And the mountain roads were no relaxation
The boredom was the worst part because
There ‘ain't any activity of gratification

Normally at times with no occupation
We memorise a math olympiad question
And reason and calculate in our heads
Or lay down a few equations

But now everybody was in a state of exhaustion,
Our brains too ill to function
Anna sitting on the left side was just too car sick
To start a conversation

Why didn’t we play games for recreation?
But it’s so hard to reach a decision
When you’re in a hot, stuffed car
near the state of suffocation

Poker had been a temptation
But we do not wish the affliction
Of crawling around in a moving car looking
for a card scattered in an acceleration

At last we were here, to our alleviation
And where, exactly, were the tourist attractions?
This time Salt Mine Turda and Alba Iulia
Places of fascination

Only, only we were part of the exhibition
As people took photos and documentations
Of a group of weird people in similar attire
Walking around with no sense of direction

All the fame and reputation
Have no reason for glorification
For they still forbid us to get on the ferris wheel
Due to the age restrictions

Despite the various limitations
We still found delectation
In new bonds formed, new friendships made,  
During the socialisations

And ice creams made perfection
I’ve had several, despite parents’ prohibition:
“At most 3 per 2 weeks!” But who cares?
When I’m out of their domination




Ah, I’m being a bit unfair there, the excursions were very enjoyable, if I say these two days were a little low point of the entire trip it was because the rest of the days were just too marvellous. The bus rides were indeed a bit tedious, but we did work around it in some ways. We also made loads of new friends, and that’s the best part!

12th of July

Today was the closing ceremony and farewell party. So I should probably mention the results now.

We got our results after the trip to the salt mine. When I got off the bus, I saw our deputy leader at the front door. I could feel my heart skip a beat, and I pasted a smile on my face and went over slowly. I knew that I did not do well in the exam, and I had an expectation of a really really low score in my head. So all of us walked up to her…

And she went: “Ok now you got 5, you got 5… we tried very hard to get you more marks but we couldn’t get it higher than that, we think your answer is definitely worth more, though.. You got 16, well done!! I think you have a good chance of getting a medal…” And now she turned to me: ”You got 3…”

Now what happened was I BEAMED!! I was so happy I was actually jumping up and down. Our leader was very kind and caring, she obviously thought I would be disappointed or sad so she was very gentle and tried to sooth me and comfort me, but after a few seconds I think everybody realised that my lunatic behavior was actually from the heart, not trying to appear strong or something.

Lucas patted me: ”There, there.”

Not realising this as a joke, I said: ”No, I am GENUINELY happy that I didn’t get zero!!”

So that’s that. No more anxieties and worries now that the dust has settled, the only thing left was to enjoy the every last minute of the remaining journey.

This morning, we walked around the city under the sunny sky, fed the pigeons, ate traditional Romanian food, went into bookstores after bookstores…it was bliss. I could not have had a better morning than this.

We had to go back for lunch and the closing ceremony in the afternoon. We all knew what the closing ceremony would be like, so we just sat back and secretly read books.

Afterwards, it was the event we’ve all been waiting for: the farewell banquet! We had some prior knowledge about what will happen— in short, a disco.

We had a beautiful dinner together, sitting together with the TTO team. The main dishes there were a little bit weird to my Asian taste, but the desert was superb…I had two creme buleés.

Meanwhile, a band was busy setting up on a stage and soon there was music. People started gathering at the foot of the stage and moving with the music. I was awkward at first, but soon I got comfortable as more people joined in. We were gathering together and lining up and forming circles all the time— I was constantly pulling people into the dancing, and I tried with every effort to pull the Chinese team in. The teachers were very supportive and loved to take part, and followed me into the crowd, but the teammates were less active and only one of them tried it briefly. The teachers confessed to me later that they were mindblown to see this kind of festivity.

I should give a clarification here: My “dance” basically consisted of jumping up and down as long as I could, and lots of other people on the crowd couldn’t dance either. We were just moving together because of the immense force of energy that was flowing around us.

At one point, I had just come down to have a rest when this guy, with his T-shirt soaked in sweat, came up to me and said: ”I don’t understand, why are you not dancing??? I don’t understand why ARE you not DANCING???” I protested ”But I just came down and I was dancing for the last 3 hours…” But he won’t listen, so he pulled me into the crowd and I pulled Anna into the crowd and Anna pulled the TTO team into the crowd and so we started again.

It was one of the best dancing experience I’ve ever had, dancing came so naturally, and moving was like an instinct. There is something about the math olympiad discos.