Gaining "deep knowledge" by taking charge of your own educational journey

I am currently trying to understand how the concept of quantum tunneling can help explain the way in which  enzymes can accelerate reactions to such an extent, that they make life possible. This is where my research is taking me: out of my comfort zone and into areas of Science that I haven't had to get to grips with for a long time. It really doesn't matter what aspect of knowledge I am struggling with, I need to be able to fall back on fundamental principles of language, maths and maybe some chemistry and physics. A few years ago I was grappling with an the logic behind algorithms that help us compare genes from Badgers and the rest of the animal kingdom, and how to interpret a set of completely unexpected results caused by addition of a short piece of DNA to a strain of bacteria. In fact, in most areas of professional life, employees (teachers, accountants, journalists, doctors, nurses etc.) are expected to embrace new ways of working, new technologies, changes in policies, or most commonly, must find ways of delivering a higher quality product or service for less money. And in half of the time! 

In order to rise to such challenges and remain fulfilled, a strong educational platform is vital. It is only with such strong foundations, first at school and then in the work-place, in further or higher education, or both, that it is possible to realise your ambitions and fulfil your potential. Of course there are many other factors that are also important, but let's look at school, where we will all typically spend around 20 000 hours of our early lives! [I'll return to the much simpler phenomenon of quantum mechanics at the end, if you're still reading!]

My title includes "deep knowledge". What do I mean by that? It's simple, I mean a level of understanding that relies on "first principles" rather than memory. If an Egyptian builder wanted to lay out the plans for a new pyramid, s/he would need to be able to make sure all the corners were at right angles to each other, or "square". The same would be true today if you were painting the lines for a new football pitch. From experience, or with help from senior colleagues, the Egyptian builder would get three pieces of rope: one measuring 3 cubits, another 4 and the third one 5 cubits (it doesn't matter what a cubit is, it is just a unit of length like feet, metres or miles). What is important, is that a triangle (above) with sides of these proportions will always contain a right angle! If you don't believe me, get three drinking straws and try it. The builder has to remember the 3-4-5 rule. But s/he doesn't understand why it works.

In fact it wasn't until around 2000 years later, that a well known mathematician, Pythagoras, worked out a simple mathematical formula, that would allow builders to work out how to make sure the perimeter wall of any building was going to be perfectly square. This was the early days of a field of mathematics, that we call geometry. Pythagoras's theorum, states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Personally, I think the language used here is a barrier to understanding the concept, shown more clearly by the diagram, in which three squares are made from the sides of the 3-4-5 triangle. In another way, this can be expressed using algebra, where letters are used to represent numbers. In algebraic terms, Pythagoras's theorum becomes:
                                              
in which the letter c represents the length of the hypotenuse (or diagonal). Try it: 3x3=9, 4x4=16 which means that the length of the hypotenuse multiplied by itself, is 25. And we know that 5 x 5 is 25, so it follows the diagonal is 5. But how did I know that 5x5 is 25? Well, when I was at school we were made to memorise our "Times Tables", so I instantly know that 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36 and so on. If calculators had been invented when I was at school, I might even have a button that allows me to obtain the square root of 25. [The square root is the term used to define a number (5 in this example) that when multiplied by itself gives the number, in this case, 25]. However, no need to memorise "Times Tables" now that we have calculators! Well, maybe this is OK for some, but maybe not for all. One of the things I have come to realise is that there are some things that it helps to memorise, because it provides a short cut to understanding more difficult things. Importantly, I am memorising the product of 5x5, but I understand the principles. [So do you! You know that 5 lots of 5 apples or playing cards, amounts to 25].

Pythagoras's theorum enables anyone to design a building, lay out a square (or rectangular) pitch, make sure a new car is assembled properly or make sure your mobile phone is symmetrical.... or not, if you buy a Japanese You-Phone! I said above that the language used to express Pythagoras's theorum is a little odd. That's simply because language changes with time, and in fact Pythagorus would have written his theorum as follows: το τετράγωνο της υποτείνουσας ισούται με το τετράγωνο για τις άλλες δύο πλευρές. In fact, he never wrote anything down! This translation almost certainly came from a later scholar of Greek mathematics. And this brings me to my second part, which relates to language.

Without language, we can only pass on experiences by word of mouth. My dad's family were blacksmiths in Garston during the 19th century, and I am pretty sure than many of the Hornby family of that period could not read or write. I am also pretty certain that none of them spoke or read Greek; although one or two church-goers might have known a small amount of Latin. I was talking with one of my PhD students last week, commenting on his excellent written English (he had grown up speaking Arabic in Libya). How did he get to write so well? "A few old Charles Dickens novels, an English-Arabic dictionary, long hot summer holidays and a desire to live a different life". His secret to learning English (which wasn't taught in his school) was simply to put in the effort: his motivation being the dream of a better life than that of his father and grandfather. Thanks to the teachers at the NLA , I now have a copy of some English examination papers and I am going to test myself and see what they think of my understanding of English. Whatever mark I get, good or bad, I will want to do better next time. I will want to know what I did wrong and I will want advice on how to improve. I will then make the time to do it. 

Deep knowledge of Biochemistry is my goal in my work. In particular I want to understand how enzymes, the engines of life can convert the food we eat into the energy we need to grow and move around. Chemistry has ground to a bit of a halt in understanding how enzymes achieve this and I believe the answer may lie in the field of Physics that we call Quantum Mechanics. It is a little daunting for me to dust off my old maths and physics books, which left me on the brink of understanding some very simple aspects of quantum theory in 1978. No-one is making me do it. My motivation is a result of my enjoyment of Science and my own curiosity, sparked by a fantastic primary school teacher. I firmly believe that by taking charge of your own educational journey, you will have a much greater chance of a better life. For those of you who aren't doing this already; why not give it a try? 

In my next post I am going to look at how our understanding of the brain developed, without which we wouldn't be able to understand anything!