- In the Industrial Revolution, it was a great discovery
that the use of interchangeable parts
was a powerful principle that would allow you
to do mass production, to make things efficiently.
And people worked hard to make precise machinery
so that you could have these reproducible parts.
Nature has been using that principle, however,
for billions of years with great artistry
to create the world around us.
People sometimes ask, "What does it all mean?"
That's a very hard question to address
because it's not clear what an answer would look like.
The question that I found much more fruitful is:
"Does the world embody beautiful ideas?"
"What is the world and what is beauty?"
What is beauty, is something that art and philosophy
and human culture addresses.
What is the world, of course,
is the kind of question that science addresses.
- We've gotten this extraordinary grip
on the fundamental laws.
They're very strange,
but they have a kind of internal logic and beauty.
Some of the things that people at the beginning
of this adventure were hoping for,
and had in their visions, was the idea
that the world embodies harmonies.
They were hoping that our sense of harmony
somehow agreed with what nature likes to use
in her construction of the world-
the idea that symmetry and mathematical perfection
provide the building principles
that the world embodies.
Einstein was a great hero of mine,
and he's played an important role in my life.
He advanced the idea that symmetry
is what's very basic to the operation of fundamental law.
Consider a circle:
A circle is a very symmetric object.
You can rotate it around its center by any angle and,
although every point on the circle may move,
the circle as a whole doesn't change.
And that's what makes it symmetric in the intuitive sense.
You can change it, you can make changes on it,
which might've changed it,
but although they transform each part of it,
don't transform the thing as a whole.
The great advantage of that definition
is that you can apply it in very broad contexts,
not only to describing the symmetry of objects,
but to describing the symmetry of physical laws
or the symmetry of equations.
The idea that the laws of physics don't change
as a function of time is also a symmetry.
Symmetry is a very powerful constraint
on our description of the world
that nature seems to respect in many ways.
The kind of symmetry that leads to quantum chromodynamics
or general relativity or quantum electrodynamics
is mathematically considerably more complex,
but it's the same idea.
There are transformations of the equations
that change the different terms in them.
So they might change an electric field
into a magnetic field or a magnetic field
into a combination of electric and magnetic-
that change the way the equations look,
but don't change their consequences.
That's the kind of equations
that are like the circles among equations;
are ones that have this symmetry property.
What leaps out from profound understanding
of the fundamental laws of nature
that we seem to have achieved,
is that you get much more out than you put in.
So nature manages to use fundamentally simple principles
to power emergent complexity.
It's striking when you look at it
that the equations have this kind of generative power.
That you start with simple building blocks
that have very precisely determined properties,
and like LEGO blocks, you can put them together
to make chemistry and pharmaceuticals
and Large Hadron Colliders;
all these very complex engineering projects.
You can reliably produce,
because you know how the little parts work.
By example, in the 19th century with Maxwell's synthesis
of the laws of electricity and magnetism,
physicists started to realize
that what we perceive as light
is deeply understood as a kind of disturbance
in electric and magnetic fields.
That gave us a new concept of the possibilities
of perception of light.
Visual imagery is very important to our understanding
of the world because humans are intensely visual creatures.
Depending on how you do the accounting,
between 20 and 50% of our brain is devoted
to processing visual information.
We have some very impressive capabilities in that direction.
We face in interpreting the world,
a very challenging problem that we're good at solving;
we're so good at it that we don't consciously realize
how difficult it is.
That's the problem of taking the electromagnetic radiation,
the light, that impinges on our retina,
giving a two-dimensional image that's all scrambled,
and interpreting that as a world
of three-dimensional objects moving around
in three-dimensional space.
That's a very difficult, in fact,
impossible mathematical problem.
But we have many sophisticated tricks and rules of thumb,
plus a systematic, although unconscious, knowledge
of projective geometry so that we can recognize
that the same thing seen from different positions
represents the same object.
When they were made conscious,
as geometric theorems and discoveries,
astonishing achievements, that when Brunelleschi discovered
the science of perspective in 1420,
helped kick off the glorious episode
of the Italian Renaissance,
and has been a foundation of art ever since.
And so, we can look at the record
of what people have found beautiful,
what they were hoping for in their understanding
of the world, with what the remarkable understanding
of the world we've achieved in recent years looks like,
and we can therefore frame a meaningful discussion,
and a meaningful question,
a meaningful meditation on the issue of:
Does the world embody beautiful ideas?