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Another free hour in 1st BSc Mathematics – junior to the bunch I introduced in How to Blabber Mathematics, my last article posted here.
If math is such an important subject (and it is) why teach it in a way that is dependent on a child’s weakest mental ability: memory, rather than her strongest mental ability: imagination?”— Geoff White
The world turned upside down! How will it look like?
Will the fishes fly? Will the birds be swimming?
Will we be walking with our hands on the ground?
Or will we be falling off the ground into the sky?
The possibilities are endless, and to imagine it all, it takes only a fraction of a second with your mind running faster than any computer in this world!
Imagination. That’s the word I am heading to.
Remember how I told you, we mathematicians are superheroes? Superheroes must have super imagination!
Now, close your eyes!
(First year, the second month in college – almost all of them did, except for a few unbelievers.) I will show you a magic. I will disappear before you open your eyes!
(Giggles here and there – majority got the joke) Nah, I’m just joking! Now, close your eyes for real! Imagine your classroom – with your eyes closed, look around, see your classmates sitting around? All of a sudden, your turn to the door and see your best friend walking into the class – don’t miss any details – how they stopped at the door, waved at me, and walked into the front and stood next to me!
(Snapping my fingers) Wake up! Open your eyes!
(Many of them were already happy – such vivid mind they have – I’m sure they will turn into vivid mathematicians!)
How was the journey?
That’s what all those poets and writers do as well – imagine – without boundaries – a lion with body of a zebra – a man with horse legs – the list goes on!
And we are not too far away from them!
When I say 3, what comes to your mind? (Some of them draw 3 in the air)
But if I say “3” (drawing in the air) is nothing but a symbol to represent the idea, do you disagree? Let me illustrate it to you – what’s 10 plus 3?
(Almost everyone immediately responded saying it’s 13)
Did you imagine (Drawing in the air) 10 and 3 and put a plus in between before calculating that it’s 13? (‘No’s floating all around) Then how did you do it?
In our little imaginary world, the idea of 10, and the idea of 3 was put into a machine called “+” and lo! We have 13 – and not the symbols “1” or “0” or “3”! It may be like how Calvin’s (Calvin and Hobbes) Spaceman Spiff does math!
We need those symbols sometimes to express our ideas – that’s why we stick to them while writing down our thoughts. But in our imaginary world – it’s not limited by these symbols or writing – we are free to fly anywhere, anytime!
Let me give you another example – suppose I say matrix 2 3, 4 6? What is it’s determinant? (They were quick to say zero) But what if it’s extended to a bigger matrix, a 3 x 3 matrix? Will we be able to do it this quickly? May not be! That’s why we must develop our imagination, especially to imagine mathematics!
Remember I told you about Euler? He went for a walk in the city – imagined few dots and lines on the map of the city (Graph Theory) and how, 300 years later, it helps us understand computers, social networks and many things related to technology way better?
Well, we all know how a circle looks (draws it in the air, looking at staff and students passing by our class in corridor staring at us) – definitely people passing by are going to think that we are crazy – but look at all the fun we are having – writing on our imaginary board all the way! Coming back – we all know how a circle looks – like a bangle! Now, spin that bangle, and we get a sphere!
In our language, we are talking about a circle in 2D space or a plane as we call it, and a sphere in 3D space.
Well, all those are muggle business! Let’s do cooler math business – how would a circle look in a 4D space? Spooky enough? What about 5D? This is the point where most of the normal humans faint – but not us Superhumans!
In a few semesters, you will see yourselves playing around 4D and 5D like it’s an everyday business – you will, in fact, be talking about n-dimensional objects, talking about how things look there – isn’t it cool?
We can’t see it, but we imagine how it will be – we can’t touch it, but we know how things will be like there – we definitely can’t keep talking like this forever, because we are just a minute away from finishing this hour!
So, imagine. Better you are at it, better mathematician you are.
Imagine. Without boundaries.
(This lecture was given when I was formulating my view on Mathematics as a language we use to describe things we observe in nature – on how to nurture reading, thinking and listening skills in mathematics to gain knowledge and writing and speaking skills to share your knowledge. My perspective has evolved a lot ever since, and I am still pondering about the same – for example, use of the word “imagination” here is a little inept, but couldn’t find a better word to substitute it. Well, if you find this line of thought interesting, do drop a word, I’d love to discuss!)