Transcriber: Phuong Quach Reviewer: Maria K.
(Applause)
Hi. Today I would like to talk about dimensions.
What do you see on this picture?
Clearly, that’s a circle.
But that’s a flat, two-dimensional image.
What could that be in a 3D space?
I asked many people, and the most frequent answer was a sphere.
Yes, indeed, that could be a sphere.
But it could also be an egg, or a pyramid, or a cylinder.
Judging from only one two-dimensional image,
you can never tell.
So that was an example of dealing
with a projection of 3D onto 2D in our eyes.
Good for us that we have a pair of them.
And more importantly, we have a brain
that instantly processes all that visual information
and makes important assumptions that let us live and move
in a 3D world around us.
But I thought that our brain itself is also an instrument of perception,
which is limited in its dimensionality.
So it can only treat some projections of the real world.
So what is a dimension in this case?
Let’s look at the simple example.
First of all, we'll introduce one axis,
which will consist of notions bad and good.
Pretty much anything can be projected on this line.
The second thing would be the beauty.
And beauty is absolutely independent of wellness,
so we can add one more axis which will go from ugly to beautiful.
So, now we have two dimensions, and so on and so forth.
You can add many more, but be sure in the real life there are always more.
For me, lateral thinking
is about trying to add more dimensions to the model in your brain
because a more complex model usually gives more accurate estimations,
assuming we do not have the problem of overfitting,
simply because our brain is lazy and tends to simplify things.
How do you add these dimensions?
Well, theoretically, at first,
you have to observe as many projections as possible,
as if your were walking around a 3D object,
trying to memorize everything you see.
And after that, you need to process all those pictures into one model,
so that it all makes sense.
And after repeating several times with different objects,
eventually, a new dimension will be there.
But that’s too theoretical and abstract.
What could you do in the real life?
I can share my experience on that matter.
Since I was in school, I was always more passionate about science
and less about humanities.
So that made me choose a specialized program
where I had more classes of mathematics and physics
and less of literature and history.
By the end of the school,
I was convinced that mathematics dominated the rest of science.
So that made me choose a computer science department
of the Lomonosov Moscow State University.
At that point, I thought I would never have to deal with humanities again.
I was wrong though, because on my second year of studies,
I started learning a second foreign language,
which by pure chance happened to be French.
Two years later, I found out that there existed Moscow French College,
where French professors teach you humanities in French for free.
And I wanted to practice my freshly-acquired skills in French,
so I decided to join.
I started taking classes in literature and sociology.
And I have to admit that these were the most complicated classes in my life.
After four hours of new notions in literature, sociology,
all that in French, my head was literally steaming.
But, at the end of the first year, I got notes
that actually let me pass to the second and the last year of studies.
And I decided to go for it,
although this way, I had to do three big things simultaneously:
preparing a diploma in the university,
preparing a diploma in sociology at college,
and working part-time as software engineer at Yandex in Moscow.
Not to forget that I was also learning to drive
and participating in ballroom dancing competitions in my spare time.
A huge thanks to my family;
without their help and support, that would have been impossible.
So, what did I learn?
What was the outcome of that supplementary humanitarian education?
Apart from learning many new things in literature and sociology,
I've also learned the difference
between the humanitarian and mathematical approaches.
In mathematics, you always have very clear definitions
of entities you are dealing with, so that you can find the exact words
to describe the objects and relationships between them.
In humanities, it doesn’t happen that way.
You cannot give a completely strict definition,
and any generalization that you make would have at least one exception.
And I have to confess, I was pretty skeptical
about such lack of precision before joining the college.
But after two years of studies, I started thinking
that actually the biggest drawback of mathematics is its precision.
It supposes that the world around us is discreet.
But do we have any evidence of that?
No, we don't.
So, humanitarian approach deals more efficiently
with nebulous concepts,
and preserves the natural ambiguity and continuity of the world around us.
But I still love mathematics,
and it is a very powerful instrument of reasoning.
So I had to look for a compromise.
And finally I came to the conclusion
that it is impossible to describe anything precisely
using only one of these scientific methods.
But when you have a couple of them,
you get to see the problem from different points of view,
and that's when a new dimension emerges.
One more important outcome of that last year at college for me
was that I applied and received a scholarship
to go to Ecole Polytechnique in France.
That is actually one more place
where the dimensionality I was talking about plays a big role.
Before joining the college,
I had never thought that it could be possible
to be paid by some other country for your studies.
In Russia, that happens very rarely.
So I never considered that to be an option.
But at college, our professors told us
that there exists problems for people who want to study humanities.
So I started looking for the same thing in mathematics
and finally succeeded.
It made me move to France, which was not easy,
especially at first, but which I never regretted.
If I were to name one thing that changed my life most dramatically,
that would be moving to Paris.
I was alone to arrive to a foreign country with all my life in one suitcase,
Now that sounds all so romantic,
but at that time, it was very heavy and cumbersome,
and my memories of the first day in Paris consists of a cramped airport,
endless staircases, and lots of sweat
because I had to wear some of my winter clothes
not to exceed luggage limits.
But moving to another country and living for a long time there,
made me realize one more thing:
When you live in one place,
your would never get that truly multi-dimensional view of the world.
And this idea has a nice geometric interpretation.
In your home country, you are surrounded by people
who have of course different points of views,
but not different enough, because physically,
you are quite close together.
So when you look at something that is quite distant,
like looking at stars,
you see pretty much the same picture
because you get the same projection of those stars.
Only moving to another country
brings you some really fresh and surprising points of view.
For instance, the educational systems
are quite different in Russia and in France.
In Russian higher education,
most exams are oral, theoretical, and without textbooks.
They make students focus on learning and presenting theory
rather than on applying it.
In France, on the contrary, exams are mostly written,
and they pose some applied problems to solve.
These two approaches make students acquire very different skills.
Before moving to France, I hadn’t thought
that the theoretical part of exams can be completely put aside.
So when you see something you've never questioned before
being done in a different manner, your mind becomes more flexible,
and you start seeing new variants in other situations too.
Apart from moving to another country, changing your activities helps too,
like it happened for me with sociology.
I’ve also tried dancing, teaching, learning new languages,
and many other things,
and each one of them changed my perception of reality in a different manner.
So if there was one thing I could convince you in,
it would be the following:
Even if you’re sure that you are really bad at something,
please try it.
I can't promise that you would get any better at it.
But you will definitely learn something new
that would change your point of view,
and that would even add a new dimension to your picture of the world.
Thank you.
(Applause)