Max Tegmark: “Our Mathematical Universe” | Talks at Google

Max Tegmark: “Our Mathematical Universe” | Talks at Google


MALE SPEAKER: Good afternoon. Welcome to talks at Google
in Cambridge, Massachusetts. Today, it’s my great pleasure
to introduce Max Tegmark. Dr. Tegmark is an
MIT physics professor who loves thinking about
life’s big questions. He is author or co-author of
more than 200 technical papers, and has worked with the
Sloan Digital Sky Survey collaboration on galaxy
clustering, shared the first prize in
“Science” magazine’s “Breakthrough of the Year 2003.” He’s here today to discuss his
book, newly out in paperback, “Our Mathematical Universe–
My Quest for the Ultimate Nature of Reality.” This book is his quest to
explore the ultimate nature of reality, from the microcosm,
to our universe, and beyond. This sounds like a
pretty big undertaking. So we’d better let
him get right to it. Please join me in
welcoming Max Tegmark. [APPLAUSE] MAX TEGMARK: Thank you so much. It’s a great
pleasure to be here. You guys at Google
like to think big. Today, I want to encourage you
to think really big, because we humans are really the
masters of underestimation. We’ve repeatedly underestimated
not only the size of our cosmos again, and again, and again,
realizing that everything we knew existed was just a
small part of a much grander structure– a planet, a solar
system, a galaxy, a universe, and perhaps a hierarchy
of parallel universes. But we’ve also
repeatedly underestimated the power of our human mind
to understand our cosmos. And it’s through
this understanding, of course, that we’ve also
been able to develop so much cool technology like what you
guys are doing here at Google. So let’s start with the first
kind of underestimation, underestimating
the size of things. And let’s just remind ourselves
of what we humans have managed to figure out so far during
the first 13.8 billion years of cosmic history about
our place in space. So let’s start here
in the Himalayas and go for a little ride. As we zoom out,
when Eratosthenes, over 2,000 years ago,
first figured out the size of this great ball,
Earth, that we live on, people were pretty
shocked by how big it was, that it was actually
40,000 kilometers all the way around. But of course, now we think
of this as pretty puny in comparison. What’s cool about both
what Eratosthenes did and what his contemporaries
did when they figured out the distance to the
moon, and the sun, and so on was that they actually did
it without rocket power, without even having telescopes,
just with mental power, letting their minds
fly, and using really clever
observations with angles, and a lot of neat logic. Of course, it was this
kind of cleverness which gave us rocket power,
which in turn gave us these satellites, which you
can see orbiting Earth here. I love this video. This is made by
the American Museum of Natural History in New York. Because everything
is exactly to scale. So, for example,
shortly when the moon comes into view– this is
the moon’s orbit there, seen as the white line–
you won’t actually see the moon, because
it’s to scale. That’s how big the
moon’s orbit is. And then we’re going to see
the sun coming into view, which of course, is so far
away that, as you know, it’s taken eight minutes for
the sunlight to reach us. So we’re seeing the sun
the way it was in the past. If someone looked at
us from the sun now, they would see this talk
not having started yet. Raise your hand if
you know anybody who was born before 1925. Cool. So if we think about these
people, my grandma for example, it’s interesting to reflect
what kind of universe they grew up in. It was a much smaller
one than ours. They knew about
the solar system. Pluto hadn’t been demoted
yet, so they knew, they thought there
were nine planets. They knew there was
this wispy thing in the sky they
called the Milky Way. But they didn’t know that
there were other galaxies yet. Because that only became
settled in 1925 by Edwin Hubble. That’s how recently we
got a vast expansion again on the size of things. It takes hundreds of
years for starlight to reach us from
typical stars you might see in Cambridge
tonight if it’s clear. So someone there
would not see us. They wouldn’t see anything
to do with Google, but they might see the Boston
Tea Party, for instance. This galaxy that
we’re a part of, this incredible pizza
shaped structure with hundreds of
billions of stars, is so vast that it takes
100,000 years for life to traverse it
from side to side. Yet, as we zoom out,
that’s just one galaxy out of enormously large numbers. Because every other dot here
in this data from the Sloan Digital Sky Survey that I’ve
had a lot of fun working on with my colleagues
is another galaxy. Every dot in here has
hundreds of billions of stars of its own. And even these galaxies,
these much bigger structures, are again part of even
larger structures. You can see, they come
here in groups, clusters, super clusters, and
enormous filaments, with the Sloan–
Great Wall, and so on. So again, things we
thought were huge turn out to be part of
something even grander. And even this,
even this massive, three dimensional map of
galaxies, which when we first made it was the largest
3D map of its time, is part of something even
bigger, what we affectionately call our universe, or
our observable universe, this ball here. And if you promise to be kind,
and loving, and gentle to it, you’re welcome to play with it. So so far, everything
was pretty intuitive. The farther away we looked,
the more stuff we saw, more and more galaxies. But what on Earth
is this sphere, this green, yellow, round thing? To understand that, we cannot
just speak of our place in space. We have to understand
also our place in time. Fortunately, we can
learn a great deal about our place in time, simply
by looking out into space. Because as we just
mentioned, we see the past. The sky is like a time machine. We see the sun eight minutes
ago, a lot of stars hundreds or even thousands of years ago. And many of the galaxies here
in the Hubble Ultra-Deep Field, we see them billions
of years ago, even 12 billion
years ago, or more. So by looking at things at
very different distances, we can put together a
very interesting history of our universe. And what have we learned
from these kind of pictures? We’ve learned something
which I find very surprising. And just to make you appreciate
how surprising it is, I want you for a moment to
imagine that each one of you is a galaxy, and I’m looking
at you now with my telescope. And I see something
kind of funny. You guys here in the front row
are all about 100 years old, as far as I can tell. You look healthy, but about 100. And you guys are
90, and then 80. And then I see
farther back, a line of teenagers, a
bunch of toddlers. And on the second
last row, I see only infants who can’t walk yet. And the very last room
here of this lecture hall is empty completely. Why did you guys have this
OCD idea to arrange your, self by age when you came in? And as if that
weren’t weird enough, the whole rear wall of this
room is glowing with microwaves. And even more odd,
you’re all blushing. Why? Was it something I said? You guys look just
a little bit pink. But those in the back are
tomato red in the face. This is exactly
what we actually see when we look at these
galaxies with our telescopes. Why? Well, first of all,
it’s easy to see how the business with them
being arranged by age works, because nearby, we
see galaxies the way they actually more or
less are these days, or were pretty recently. Whereas farther away,
we see galaxies the way they were very,
very long ago when our universe are still young. So they haven’t had time
to age and grow up yet. We see smaller galaxies,
little baby galaxies. They’re very young. Still farther away–
and this is what corresponds to the
empty, last row of the room– we see
no galaxies at all. Because we’re looking at things
that happened so long ago that galaxies hadn’t
yet had time to form. All there was back then
was the raw material out of which galaxies
later were formed, mostly hydrogen gas,
which is transparent. So we just don’t see
it in the picture. Now, why is it that
you’re all blushing? Well, you know, if you
walk down to the I-93, at least on a day with less
snow, that the cars will go– [MIMICS SPEEDING CARS] They don’t go– [UPWARD INFLECTING SOUNDS] Because the Doppler
effect says, of course, that the frequency goes
down when something is receding from you,
moving away from you. Ehh. And that works for any
waves, not just sound waves. It works for light, as well. So a galaxy flying
away from you will have its light stretched to
long, lower frequencies, which makes it look redder. We call this redshift
in astronomy. And that’s why you guys all look
like you’re blushing, the fact that you’re all flying
away from me, which is why Edwin Hubble said, hey,
our universe is expanding. And the fact that you guys in
the back are blushing much more means you’re flying away faster. How long ago were
you guys all here? Well, that’s easy. Just look at how far you are
and compare that with the speed. Since it turns out that there’s
an interesting relation, that the galaxies twice
as far typically fly away twice as fast. You get the same
answer, whatever galaxy you look at, pretty much. It was around here– it seems,
if you extrapolate backwards– about 14 billion years ago. If you do it really carefully
and take into account the fact that it accelerated
and decelerated a bit, you get 13.8 billion years
ago, something really weird happened. We still don’t know exactly
what it was that happened. But we have a nice name for it. We call it our Big Bang. But what we know
a great deal about is what happened after that,
during the subsequent 13.8 billion years. Because as I’ve
said, we can actually watch most of that unfold
with our telescopes. And since we see
everything flying apart, that must mean that
this expansion also affected the gas
between the galaxies. If you expand the
gas, it cools off. That’s how air conditioning
works, of course. So my universe got
cooler and cooler. Which means that as we
go backward in time, this gas would be
hotter and hotter. If you take an ice cube
and you heat it up, what does it turn into? Water. A liquid, that’s right. If you heat up a
liquid, it actually turns into a gas– steam,
in the case of liquid water. If you heat up a gas, what
does it turn into eventually? Plasma, that’s right. So what we can predict is
simply from this expansion of our universe, if
we go far enough back, if things were more and
more squished together, eventually all this hydrogen
gas would have been a plasma. So what it would
look like is this. A plasma is opaque. You can’t see through it. So it should look to us as if
beyond on all these galaxies. First, through this empty
region with no galaxies. And then you should
see a plasma screen. But you should see this in
whatever direction you look, of course. Whatever direction you peer, and
you’re looking far enough back in time, there’s
a plasma screen. So it looks to us like we’re
actually surrounded by a plasma ball that we can
photograph from the inside. And when this idea
was first put forth by George Gamow and others
in the ’40s and ’50s, people felt this was totally
nutty, and way too extreme an extrapolation of things we
knew to really take seriously. But then it was found in
1965, and got the Nobel Prize. And now, we’ve taken these
amazing precision pictures of this. This is from the Wilkinson
Microwave Anisotropy Probe. It’s a fantastic NASA satellite
for a cost of $0.40 per American, one of the highest
impact science experiments ever. And the one thing you’ve got
to worry about when you’re taking baby pictures of our
universe from 13.8 billion years ago, when our cosmos
was only 400,000 years old is did they screw up somehow? This is a very hard measurement. In fact, here, you
see these patterns. They had to stretch the color
scale by a factor of 100,000, because the differences
in temperature are only a thousandth of a
percent from place to place. Fortunately, another team–
independent technology, independent people– now have
made it an even better map. So we can compare. This is the Planck
data that was just released last year
in its latest format. And it’s really fun to just sit
and flip these back and forth and see A+ for both experiments. See all of the places where
there’s a big hotspot? It’s still a hotspot, even
when you go from the three megapixels to the 50 megapixels. It’s similar for the cold spots. So looking at this map,
which are basically the cosmic DNA that encode
within them information about what’s going
to happen later, you can see that where there
is more stuff, the clump back then, you can predict that later
on that will form galaxies. And where there
is less stuff, you can predict that’s going
to turn into a giant void. So we’ve learned a
lot about our cosmos, thanks to the technology that’s
given us these better pictures. But it’s important
to be humble and be mindful of how much
we have left to learn. For example, in
this quest– Google likes to map stuff, of course. So you have Google Earth. And now, you also put our
Sloan Digital Sky Survey data into Google Sky. But I would like to have
Google Universe, frankly. Can you guys do that,
where it can just fly to any part of our
observable universe and see what’s going on there? And look how little
we’ve accomplished. All those galaxy maps
we flew around then are just this tiny part near the
center that are well covered. We have some sparse
outliers in here. And then there is this cosmic
microwave background radiation that we just talked
about, which is just a photograph of the
outside surface. I want to map all of it. There’s 100 times
more information or more in there to be had. How can we do that? Can we just take
pictures of galaxies here by building
really big telescopes? No, because there
weren’t any galaxies that long ago that
had formed yet. There’s just the hydrogen gas
out of which they later formed. That’s the bad news. But the good news
is hydrogen gas itself can also be photographed,
because it gives off radio waves. They’re 21 centimeters
long when they’re emitted, and then they reach us,
and they get stretched out. We can pick them up
with radio telescopes. And the wavelength of the
waves when they get here tell us how far
away they came from. So we can build up
three dimensional maps. And we’ve had a lot of fun
at MIT looking at a way to do this much cheaper
than by building this ginormous, big dish that
points in various directions. So let me show you
in just two minutes how you can make your
own radio telescope, at least if you move fast. That was [INAUDIBLE],
right down the road. So we’ve had a lot
of fun with this. And the technologies we
built this to test out, I’m happy to report,
have worked so well that we’re now teaming up with
a bunch of other universities across the US to build a
dramatically larger one, starting to build
in South Africa. We want to cover many
football fields worth of land. And what you can see
here is that this looks really different
from a normal telescope. That’s why it’s so cheap. Just get a bunch of mass
produced little things, hook them together, and
let the computer figure out what the sky looks
like, just from the volts that you measure, and
all these antennas. I think about this as the same
philosophy as Google Earth. Instead of first
figuring out, I want to know what’s going
on there, actually going there and looking, you
just image the whole thing. And then you can
figure out later what part you’re
most interested in. This radio telescope, since
the computer is figuring out what part of the sky you’re
interested in right now by combining volts
in different ways, it just measures
everything, all the volts, which means you’re gathering
information from the entire sky all the time. It’s omnidirectional. That’s why we call
it the omniscope. And this is the
future, in my opinion, of this quest to
make the biggest map ever of our universe in 3D. And we need this kind
of additional data, because we have a
lot of questions left we haven’t answered, even
though we’ve come a long way. For example, we have no clue
what 95% of our universe is made out of. And we would like to know better
what happened before this epoch with a plasma screen and the
cosmic microwave background. So let me take a
little bit of time to update you on
that, because there was a sensational announcement
last Friday, which was in “The New
York Times” and all over the world about inflation. And this is something I’ve
had a lot of fun working on, and I want to share with you. So last March, there was a big
splash all around the world. There was a press conference
I was at at Harvard where a team announced, we
have found the first evidence of something super exciting
supporting this idea that our whole
universe underwent this process called inflation. Pretty quickly,
a bunch of people started pouring cold water
on this and saying maybe the data wasn’t as
compelling as they said. What’s going on? What is inflation, first of all? Well, inflation is the
most popular theory we have for what
happened earlier on, what created all this hot,
expanding plasma. And the basic idea
of inflation– this is how I think about it. It’s that our universe
began just like you guys. You were originally 1 cell,
then 2, 4, 8, 16, 32 cells. You just kept doubling. Fortunately, you
didn’t keep doubling for nine months,
which would have been very painful for your mom. Because after nine months of
doubling about once per day, you would have had a mass
greater than the whole universe that we’re in. What happened instead
was once you reached the size of about
5 centimeters, you stopped this exponential
doubling, this crazy doubling, and started growing in
a more leisurely rate. And this is exactly
what inflation says our universe did. It started– tiny
subatomic speck of stuff, doubled, doubled, doubled. And when it was
about 5 centimeters, the doubling stopped. And it started
growing more slowly. Inertia kept it flying apart. And these two curves
look very similar. I promise you, I
didn’t fudge it. When I made this for the book,
I actually spent more time than I care to admit
looking up data from prenatal observations of
baby growth and plotted here. That’s why it’s a
little bit wiggly. I have no idea why we have this
funny 5 centimeter coincidence, why they have the
same vertical axis. I can’t even think of an
anthropic explanation for it. But the x-axes are
kind of different. You doubled about once per day. Our universe doubled
once every maybe 10 to the minus 36
seconds or thereabouts. If you double something
frequently, of course, you’ll soon get a
huge amount of stuff. And moreover, the stuff will
be moving apart very fast, because expansion
speeds also doubled. So inflation is an idea which
actually causes the Big Bang. You take something which
is not big and not banging, you’re not moving very much. You make something
huge expand very fast. And I want to first
emphasize that there’s a lot of misconceptions
about this. Even in “The New York
Times” article here that my friend, Alan
Guth, wrote for MIT, they say in the instance
after the Big Bang inflation happened– no. That’s not at all
what inflation said. Inflation rather
creates the Big Bang. It’s the mechanism
that takes something which is neither big
nor bang-ey– it’s more like a cold little
swoosh– and creates a big bang. It sounds like black magic,
the way I described it. If we had another
half hour, I could tell you the whole
mechanics of this and how this is actually
not something you have to put in by hand. It’s actually something
that comes out of Einstein’s equations
of general relativity if you put in only one little
assumption that you have a certain kind of substance,
which is really hard to dilute. You can ask me
about it afterwards. But for now, if you just
take the predictions of this, you can ask, how
can you test them? It predicts a
whole lot of stuff. It predicts that
there was a Big Bang, that things are expanding. And it predicts a
whole bunch of numbers that I and many of
my colleagues have had a lot of fun measuring. For example, how that space
should be really, really flat. Well, we’ve measured
that now and tested it to better than 1% accuracy. And that’s why Alan Guth
looks so happy here, maybe, because it works. It predicts a bunch
of other stuff, and it predicts all
these funny patterns you saw in the microwave
background, the properties, really nicely. But there was one
more prediction that it never actually
tested, which was often considered the holy
grail of inflation. If we saw this, this should send
Alan Guth, and Andrei Linde, and perhaps some other
pioneers of inflation to Stockholm to collect
the Nobel Prize. Because there was no
other reasonable thing that could have
produced that signal. What is that signal? Well, we call it B-modes. It’s a very geeky name. And the way I think about it
is if you take an image– Alan Guth and Andrei Linde here were
blissfully unaware that I took this photo at a
party in Sweden– if you make gravitational
waves, distortions and the very fabric
of space time itself, and you send them between you
and this background image, it’ll look distorted. Because of course, when
space is distorted, then the light waves get bent. If there’s a gravitational wave
now going between me and you– (MUMBLING) I will get
distorted this way. We can test exactly
this by looking at these pictures, the pictures
of the cosmic micro background, the baby photos of
our universe and see, do they look distorted by some
kind of gravitational wave? Because the idea is when
you work through the math, you’d that inflation, this crazy
doubling of space early on, was so violent. They had so much violence
in the very fabric of space that it actually would cause
these gravitational waves. It would cause these
ripples, these distortions, in the very fabric
of space itself. And so you can look for them. It turns out that
the best way to see the distortions is to look
through this polarized light. Because then you get rid
of a lot of other effects, and there’s a certain
kind of signal. For the geekiest part of
the audience, what you do is you take the polarization. And just like you could take
vectors and decompose them in a part with no curl,
and no divergence, and the part that
has no divergence, we call the magnetic
fields, or B in physics, you can do the analogous
thing for these vectors, these polarization things,
and two dimensions, and a curved sky,
and blah, blah. Don’t worry about
the details at all. Inflation predicts that if
you do this geeky process, you can make a picture like this
where there should be signal, for which we have no
other explanation. There’s no other
known physics that would produce
anything like this. And last March, 10
months ago, right here in Cambridge, Massachusetts,
it was announced, boom– it’s been found by
the BICEP2 team. And when they measured
the detailed properties of this– plot whose units
and axes really don’t matter, except for the fact
that this red curve here is a prediction from inflation
and the black things are measurements– people
got very excited. But then people
started wondering, is it really true
that what they’ve seen comes from our baby universe? Or could there be
some other source of microwaves that got
added to that along the way? And suspicion started to fall
on dust from our own galaxy. Last fall, in Europe, this
Planck satellite dimension that had the 50 megapixel
picture of the baby universe released some data saying, yeah. It might be that
everything they saw was dust, or maybe half of it. We don’t know yet. Just this Monday, three days
ago, this paper came out, February 2 here, where
what you see on the x-axis is the amplitude of
these gravitational waves from inflation. Which Alan Guth will be
very happy if it’s not 0, because that means
inflation happened. On the vertical axis,
you see the amplitude of signal caused by
dust in our galaxy. And what you see here is
what the data prefers. Look, for example, at the
data they take most seriously here is shown by heavy lines. This is a 68% chance that
the truth is in there, 95% chance that it’s
in there somewhere. And you see, there’s a slight
preference for inflation to have happened, for this
number to not be zero. And if this is the
truth, for example, that will actually
be a very nice fit for a lot of simple
inflation models. But you can absolutely
not look at this and say, we have proof of
inflation from this. Because there’s more than a 5%
chance that the truth is zero and there was just a bit of
a statistical fluke here. So what have we learned so far? Well, this has been a real
roller coaster ride, of course. This is not at all
what the team hoped when they made the
announcement last spring. They had underestimated
how much dust there was, or overestimated their
confidence in their models. Right now, all we can say is
we don’t have the smoking gun evidence at all that
inflation happened. On the other hand,
inflation used to be the most popular
theory for inflation before this even took place. And there’s absolutely nothing
here arguing against inflation. If anything, there’s
a little hint there, if you squint a little
bit, and have a beer, and then squint some more,
that it might already have started to see the
signal of inflation. We’ll see. The good news is that
both this team measuring from the south pole and
a number of other groups is a super competitive field,
are making awesome experiments. And we should know a lot more
about this in the one or two years to come here. So this is one of the hottest
frontiers in all of science. And it’s very
audacious, frankly, to think that we little humans
can sit here with our equations and extrapolate them all
the way back not just to 400,000 years
after our Big Bang, but back to 10 to the minus
20, minus 36 seconds, when everything out there
was squished together, less than the size of a proton,
and make predictions, and then even be able to test them. It’s quite shocking. But that’s exactly what
we’re talking about here. So think big. Now, let’s come back
to where we started. I said that we’ve underestimated
greatly the size of our cosmos. But I also said that we’ve
underestimated greatly the capability of our human
minds to figure stuff out. Why is that that we’ve been
able to do so much more than we thought? Leonardo da Vinci would
have been so blown away if he had known what you
guys at Google can do today. Where does this power come from? Yeah, the human mind is awesome. This is certainly part of it. We didn’t evolve to do
integrals or even send emails. But somehow, our mind is
so flexible that it can. But I don’t think
that’s the whole story. I think if you look back
at the roots of our success in science, there
are two really, really powerful ideas to
have helped us enormously. One is do experiments. In other words, measure a
bunch of numbers from nature. And the second is
less talked about. When you have a
bunch of numbers, try to make mathematical
models of them. In other words, look for
mathematical patterns in there. Look for mathematical hints. Because nature has,
again and again, dished out these kind
of hints in the form. That’s the equations that I
teach down the road at MIT. And that’s what
really has enabled us to build this technology,
that we see these patterns and can exploit them. This is an old insight. Pythagoras already said
over 2,000 years ago that numbers rule our universe. And then Galileo 400
years ago famously said that our universe is
like a grand book written in the language of mathematics. But what does he mean by this? You look around, where is all
this math he’s talking about? I don’t see any big
numbers written in the sky. But if you look more
closely at what he says, he talks about how
this book is written in the language of
mathematics, and its characters are triangles, circles, and
other geometric figures, et cetera. So geometric shapes,
geometry is also math. He’s taking a
broader view of math. He’s not talking about
math as just a bag of tricks for multiplying
numbers together or a sadistic form of
torture that schoolteachers invented to make us feel bad. This is my mommy’s view of math. He’s looking at it
in a more broad way. And if you look for
patterns, then it’s pretty obvious that yes,
nature’s full of them. Whatever you throw
up in the air, it’s going to move
in this shape, which we call a parabola. And it’ll be this very
simple quadratic equation, y equals x squared. And if you look in space, again,
everything orbiting anything under gravity goes in this
shape, which is called an– AUDIENCE: Ellipse. MAX TEGMARK: –ellipse. And if you look
more closely, you can see that what we
learned in high school was the parabola isn’t
actually a parabola. It’s just a small piece
of an ellipse, which is very well approximated
by a parabola. So it’s all ellipses. Why? And let me ask you a
little pop quiz here. What tool was it that triggered
the discovery of these three things– the planet Neptune,
the radio wave, and the Higgs boson? What tool was it that
triggered their discovery? AUDIENCE: Least squares
error approximation. MAX TEGMARK: Least squares
error approximation. Doesn’t anyone want to try a
one word answer in that spirit? Statistics. Or just more generally,
you could say math. Or if you want to be
really, really nitpicky, you could say the pencil. Because they were all
predicted through mathematics. You know the stories. In 1846, the French
astronomer, Urbain Le Verrier, was using Newton’s
equations to figure out how the recently-discovered
planet Uranus was supposed to move, and why
it wasn’t moving the way it was supposed to. And he wrote this letter to
this astronomer, Galle in Berlin and said, hey,
point your telescope to such and such a
place, and I predict that you will there
see a new planet. The guy did– boom,
there was Neptune, predicted with mathematics. Just a few decades later,
James Clerk Maxwell was sitting around
with equations that I was teaching over at MIT
this morning to 90 freshman– the Maxwell equations,
we of course call them now in his honor–
and realized when he solved them with his pencil that if you
build a certain kind of device that had never
hitherto been built, you could use it
to send information at the speed of light
through empty space. Now, raise your hand
if you have a cell phone in your pocket–
predicted through mathematics. And most recently,
Peter Higgs sat down with the most advanced
mathematical description of the time in namely,
the standard model of particle physics,
and figured out that if you built the
most complicated machines humans have ever
built in Geneva, and you use it to smash
particles together near the speed of
light in a certain way, you would there make this new
particle, the Higgs boson. You know how that went. He built the machine, and he
got a free trip to Stockholm to pick up his Nobel Prize. So why is it that math
is so powerful like this? And it’s not just
these predictions. But we’ve been able to
summarize so much about nature with these very,
very simple equations that capture these
patterns, these hints that nature has given us. Some people, they like
their equations so much they even put them
on their tombstone. I took this one when
I visited Alpbach in Austria, Schrodinger’s grave. And it’s not just
equations and shapes. It’s also numbers. You’ll find this list in
chapter 11 on my book. These 32 numbers, pure
numbers with no units. From these 32 numbers,
we can, in principle, calculate every pure
number ever measured in the history of science. So why is it that nature
is so mathematical? By the 1960s, Eugene
Wigner wrote a famous essay where he argued that this
enormous usefulness of math in the natural science
is really something bordering on the mysterious. And there’s no rational
explanation for it. I agree with Wigner that
it’s really mysterious. But I think there actually
is an explanation. I explore the whole range
of possibilities in the book from people who think
that math is just something we humans have
made up– it’s just a tool, and it means nothing special–
to the opposite extreme, which is where I personally would bet
my money on– namely that there is an explanation, that our
universe is very profoundly mathematical. Specifically, my guess is
that our universe isn’t just described by math, but
that it is math in the sense that it’s actually a
mathematical structure. Let’s unpack a bit
what I mean by that. I mean in plain English that
our universe doesn’t just have some mathematical
properties, but that it fundamentally has
only mathematical properties. Now, that sounds really
nutty when you first hear it. So let me introduce you to our
neighbor here, Mr. Hoggles. He lives in our
backyard, except I think he thinks that we
live in his backyard. Well, look at him. I said the universe has only
mathematical properties. Well, what properties
does he have? Maybe a cuteness, a
fluffiness, herbivorousness, a passion for digging
holes in our backyard. Those don’t sound like
mathematical properties at all. But if I look at
him as a physicist, I see a blob of quarks
and electrons arranged in a certain
interesting pattern. What properties does
an electron have? It has the property minus
1, 1/2, 1, and so on. And we physicists have
made up nerdy names for these properties. You can see them in the table
here– like electric charge, and spin, and lepton number. The electron doesn’t care
what we call these properties. They’re just
mathematical properties. They’re just numbers. And as far we can tell,
none of the other particles that make up stuff in this
room have any properties either other than numbers. It’s just that they
have different numbers than the electron does. In fact, as far
as we understand, the only difference
between an electron, and a proton, and
a photon is which numbers it has as
its properties. Now, that’s the stuff in
space made of particles. What about space itself? What properties does space have? Well, it has the property 3. That’s the largest
number fingers that I can hold
perpendicularly to one another. Again, we have a geeky
name for this, of course. We call it the
dimensionality of space. But again, space doesn’t
care what we call it. The property is 3. It’s a number. And we now have
discovered that space also has two more properties, the
curvature and the topology, which are equally mathematical. So if you take
seriously the idea that both the space
and space itself has only mathematical
properties, it starts to sound
a little bit less nutty, the idea that
maybe everything is just mathematical. So we’ve talked about how we
humans keep underestimating both the size of our world
and the power of our minds to understand it. So let’s look
forward, see what we can do with this
if we think big. First of all, this
guess that it’s all mathematical is either
right or it’s wrong. If it’s wrong, that means that
physics is ultimately doomed, because we’ve kept
making progress by finding these
mathematical clues. And if we run out of them
without understanding things, then we won’t get
any more clues, and we’re always forever
going to be stuck. Whereas if this guess is correct
and it’s all mathematical, that means there are more
clues we haven’t yet found. We can keep searching for them. And in principle,
there is no road block. There’s nothing that we can’t,
in principle, understand. And our ability to
actually figure stuff out is only going to be limited
by our own imagination. I think that’s the
optimistic view. And I think since
we don’t know which it is, I think it’s a good
working hypothesis that it’s true. Because then, we’re
going to try harder. There’s no better way to
set up to guarantee failure than to tell yourself that
what you’re trying to do is impossible, and therefore,
eh, I’m not even going to try. Now, what about the future–
not of physics, but of humanity? If we look at the
path ahead here, what lies around the corner? This universe has been here
for 13.8 billion years. We humans, newcomers
on the scene, been in our present form,
ballpark of 100,000 years. We’ve only had the internet
since I was since a high school student. And what lies around the corner? A lot of people have
written a lot of things about this, mostly speculation. Some are very
optimistic and have a vision of how life
will spread from Earth and eventually flourish
throughout the cosmos. Others have more dystopic
visions of various ways in which we can
destroy ourselves, maybe creating an
accidental nuclear war, maybe building machines that are
smarter than us, where things somehow go wrong, maybe
messing up our climate, or some combination
of the above. There are many dystopic ideas. Which one is it going to be? In the last chapter of the
book, I take all of the things that people like to worry about. And I sort them by urgency. So how far into the
future they will be most likely to wipe us out. And what’s interesting about
this is you see that all the things which are most urgent
that could happen the soonest are things we cannot
blame our universe for. We can only blame ourselves. They’re the self-inflicted ones. But if you flip this around,
that’s also good news. It means if we can get
our act together and not annihilate ourselves,
we have much more time to confront all
these other things. And if you ask me afterwards,
I can tell you actually pretty straightforward
technical fixes for how to avoid
death by asteroid, how to avoid death by sun. If we don’t do anything,
the sun, for example, will evaporate the Atlantic
Ocean in about a billion years as it gets hotter. But there’s a clever technique
involving asteroid deflection, which can move us out to
a more comfortable orbit, give us billions of
years more, as long as we start this project about
1/2 a billion years from now. So you can ask me
about this later. But I think, obviously,
the game plan should be let’s first
get our act together, and then we have a lot of
time to sort out the rest. So being a professor,
I have this bad habit. I just love giving out
grades, even unsolicited. So I decided to give humanity a
grade for risk management 101. So I asked around a little bit
what people thought was fair. And some people said,
maybe a B minus. We’ve done some stupid
stuff like cutting it a bit close a few times, like
the Cuban Missile Crisis. But we’re still here. So maybe a B minus, a
decent passing grade. I decided to give a D minus,
even though actually, that’s not a legal grade at MIT. Because I really think
from a cosmic perspective, it’s pathetic. There’s a huge uncertainty
in what the probability is that we annihilate
ourselves in any given decade. Some people think it’s
very unlikely, maybe only one chance in 10,000. Some people think
it’s pretty likely, like 10% chance per decade. Doesn’t really matter. None of those extremes
is a good recipe for lasting for
millions of years. It’s like if you play Russian
roulette often enough– not the smartest strategy. Moreover, from the
standard perspective, we kept obsessing about the
next election cycle and life here on Earth. We have so much more
potential for life. We have 10 to the 57
times more volume, for crying out loud, out
there– billions of years. Let’s take advantage
of this and not keep playing
Russian roulette now and risk just
jeopardizing it all. And why is this that
we’re so shortsighted, taking these unnecessary risks? Well, the most common answer I
get when I ask people is money. We just can’t afford it. Yeah, it would be nice
to safeguard humanity. But the economy’s
tough, budget cuts. But I like numbers. So I decided let’s drill a
little bit deeper and see if that argument actually works. Some small nonprofit
organizations actually spend some money that they
raise philanthropically to try to reduce risks. Like down the road
here in Cambridge, we have the Union of
Concerned Scientists. They spend about
$20 million a year, for example, on trying
to reduce the risk of accidental nuclear war. Let’s let $20 million
correspond to that box and shrink it down
to a few pixels. That’s $20 million. And let’s see what other things
we spent money on last year so that we couldn’t
afford spending more on reducing nuc risk. $10 billion last year on
cosmetic surgery in the US alone. $20 billion on air conditioning. Not for you, just for US troops. $100 billion on smoking. And the biggest item didn’t
even fit on my screen. I have to shrink it by
another factor of 10, to make room for it,
the military budget. So if someone says, the reason
we can’t spend twice as much on that is because we just
really don’t have the money, we can’t cut that much out
from anything else, that’s obviously not the real answer. So what is the real answer then? Well, another answer
I often get, actually, is that it would be
irresponsible to spend money on mitigating a risk
that hasn’t been proven. Think about that a little bit. You hear it a lot on
certain news channels, that it would be
irresponsible to spend money to mitigate climate
change risk that hasn’t been proven, for example. But let’s think about
that a bit more. You can easily see
the logical flaw in it if you make the same argument,
apply it to this situation. You can go out to the
store to buy a stroller for the baby of a
good friend of yours. And the salesman
comes up and says, hey, I have this really
nice model on the left here, very robust stroller, $49.95. We sold it for over
a decade, never had any safety complaints. Solid buy. But I also have this
other model on the right. I know there have been some
press reports of it sometimes collapsing and crushing
the baby and all. But there’s never been
any proof, especially in a courtroom, that any of
these deaths of these babies were actually caused by any
design flaw on the stroller. So wouldn’t it be
irresponsible to spend 20% more money on reducing a risk
that hasn’t been proven? Which stroller are
you going to buy? So if you’re willing to
spend 20% more reducing your risk for one child,
I think you would happily do the same when you’re
talking about all children, not just alive today, but for all
future generations that we might have. And in summary, I think
it’s very important when we talk about science
not just use it to figure out how to build cool new gizmos,
but also take a step back and ask, what does
this mean for us? What we really learn
from studying cosmology is that life has so much more
potential in the future than we thought, and that it’s extremely
important that we don’t blow it, that we actually make
the most of this potential, rather than act very
recklessly and screw things up. And for this reason,
I’ve actually had a lot of fun during
the past year spending some time starting up
an organization called the Future of Life Institute,
that’s here in Cambridge, if you want to
join a bunch of us scientists and others thinking
about concrete things we can do to reduce some
of these risks. Shoot me an email and come
to one of our get togethers. We just organized a
conference, for example, on artificial intelligence in
Puerto Rico earlier this month where we had many of
the top AI builders in the world coming together
with no journalists– so we didn’t have to deal with
stupid articles with a picture of the Terminator
afterwards– and talked about what can we actually do? What research can
we do now to make sure we get the benefits
of AI while avoiding risks? And then Elon Musk was there. And it was really
fun working with him. And he said, yeah. I hear you guys. You have a lot of concrete
things you want to do now. Research is going to help. And you’re complaining
it’s not funded. Well, let me give
you some money. So he gave us $10 million,
and there’s a research program that we’re running now
through our organization. You can go apply. Deadline is March 1 if you have
concrete ideas for research, again, in AI that could
help get the benefits, while reducing risks. But we’re interested
in not just AI. We’re interested in
anything that humans can do to become better at
thinking more long term. So let’s make a difference. Thank you. [APPLAUSE] Questions? AUDIENCE: So how much of a risk
is collision with the– I mean, we are going to collide
with the Andromeda galaxy. But I thought we were just
going to pass through. Is it actually dangerous? And what can we do to stop it? MAX TEGMARK: The collision
with the Andromeda galaxy is tough to stop. But the good news
is you don’t really need to worry so much about it. When two galaxies collide, it
sounds worse than it really is, because most of the stars
don’t actually hit each other. The stars are very far between. So what happens is more
like a corporate merger where, actually,
the galaxies are going to kind of fly
through each other once and get kind of messed
up, and then they come back– that’s 3.5 billion
years from now. 5 billion years from
now, they collide again. And this time, they just
merge into a single galaxy. I don’t know what
our descendants are going to call it, maybe the
Milkomeda, or maybe something else in Andromodese. But most of the
stars will be fine. So I think that’s pretty far
down on the list of things I worry about. But the cool thing is, even
with the limited understanding we have today, we can actually
forecast a lot of these things and in cases where
it makes sense, actually start taking
some precautions. It’s pretty likely that when
that happens, for example, that our solar system would be
put in a less favorable orbit. Maybe we’ll have a close
encounter with another star. Maybe we’ll get
detached from the sun. So it might be
smart to be energy self-sufficient at that point,
so we don’t need the sun. But we have a few billion
years to figure that out. More questions? AUDIENCE: Hi. This is about the unreasonable
effectiveness of mathematics. It seems to me
that a lot of math was especially designed to
understand the physical world. So there’s a little
bit of drawing a target around the arrow going on here. MAX TEGMARK: Yes. AUDIENCE: And perhaps it’s a
more limited puzzle of yeah, math was 60% designed to
understand the world and 20% to do financial calculations. And then you have
the puzzle well, why does the same math sometimes
work at both physics grads and to get good
jobs on Wall Street? MAX TEGMARK: That’s
an excellent question. So there’s obviously
an element here of us figuring out a
mathematical language to do the tasks that we
are interested in doing, guided by the physical world. It’s very important
though to distinguish between the language of
mathematics, which we invent, like the notation for how
we write the number 5, and the structures
of mathematics, which are the things
that I’m claiming exist independently of people. So to clarify this a little bit,
think of Plato, for example. He was really interested
in this simple question of how many regular
three dimensional shapes there were that you can make
just out of identical polygons. And he figured out that
there are five of them, which we call Platonic solids. Now, he was free to invent the
language for describing them, to call them the tetrahedron,
the cube, the octahedron, the dodecahedron,
and the icosahedron. He could have called the last
one shmicosehedron or something else, right? But he was not free
to invent a sixth one. That’s the aspect that
just exists mathematically, that we are not free to invent
the structures themselves, that there is such a thing as
a dodecahedron that has exactly four cousins–
not five, not two. That’s the thing
which is out there. So the way I envision
this is we have all these mathematical
structures, the Platonic solids, the
integers, Hilbert space, the 3 plus 1 dimensional,
pseudo-Riemannian manifolds– put in your favorite. There’s an infinite set of
these mathematical structures out there. Some of them we find
useful to study, because they help with
finance, or building bridges, or whatever. And we give them names,
and we teach them to our children at school. Others, we haven’t even
discovered them yet, because they weren’t
relevant before us. But the set of them
that’s out there has nothing to do with us. It’s not because of
our doing that there are five platonic solids. So I think of it as
much like if someone comes to Boston
for the first time, they’ve never been here, which
exact streets they choose to explore will depend a
lot on their preferences, like where they work, what
food they like to eat. But then if no one tells them
what these things are called, they might even invent
their own language for it. We’re exploring this
mathematical space, to first explore the things
that are useful for us. If you have an alien
civilization which start to study math,
they would probably start exploring a lot
of other structures that we haven’t bothered
with, and maybe vice versa. But I also suspect that
there are some things which are so central in math that
pretty much any aliens that want to do any kind
of serious technology would find it useful to,
again, discover the integers, for example, and doing Boolean
logic with zero and ones, and maybe they
would make computers that had logic much
like ours, and so on. Because it’s just
like anyone who spends enough time
in Boston is at least going to discover Boston
Common and downtown. Question? AUDIENCE: Yes. So intuitively, I
agree with and I believe what you claim about
that it is just math all the way down, that it’s
not just the description of some underlying
reality and these numbers, these relationships
just emerge from those. But at the same time,
it seems like if there is an underlying material
reality, and these numbers and equations, part
of the clue I think is we talk not about expressions
so much, but about equations. Because it’s about the
relationships of things. MAX TEGMARK: That’s right. AUDIENCE: Math is
fundamentally about that. It’s uninteresting or not
being applied if you’re just talking about expressions not
in the context of an equality, or an equation, or a
comparison to something else. So it’s all about relations. MAX TEGMARK: That’s right. It is all about relations. I agree. AUDIENCE: And the
fact that we know there’s not some underlying
reality that we can never directly perceive,
because we can only see the indirect relationships
and the transitive relationships that we can
measure these numbers about. MAX TEGMARK: Yeah. You’re making a very
good set of points there. Let me just add a little bit
how I think to them, as well. First of all, in
mathematics, the way a mathematical
structure is defined is simply as an abstract set
of elements and relations between them. You can give names to
these abstract elements and call them the edges of
your dodecahedron, or whatever. But that’s not necessary. The elements of a
set in mathematics don’t have any
properties at all. And when physics began, when
Archimedes, and Galileo, and others were doing
their stuff, at that point, the relations they
discovered with equations could only capture
a very small subset of all the properties of
nature, mostly motion of things. So Galileo was very good at
figuring how this would move. But he had no idea where
the atoms came from or why this was black
and why this was hard, even though his skin
was soft, and so on. So it seemed like you had
these mathematical relations between things which were
very non-mathematical in their properties. Gradually, that changed. Then we got the
Maxwell equations which explains, actually,
what colors are. And then we got the Schrodinger
equation of quantum mechanics, which actually lets me
calculate why this is black, and why my shirt looks
blue, and why this is soft, and why this is hard, and all
the other properties of matter. And now, we instead
have realized that we can understand all
this with quantum mechanics, and looking at these
smaller building blocks, quarks and electrons. And as I said earlier, a quark
isn’t actually soft, or hard, or yellow, or blue. It doesn’t have any
of those properties. In fact, we’ve
looked really hard and haven’t discovered
any property yet that a quark or an electron has
other than just some numbers. So that’s why our
world is feeling more like a mathematical structure. The relations are
there, and we found more and more relationships. We know more relationships
now than ever before. But the things that the
relationships or relationships between have lost
much of their magic. And as far as we can
tell, actually, they don’t have any properties
at all except numbers. But this ain’t over yet. There are still
things in the world that we have epically failed
to describe with math, so we should be humble
and acknowledge that. For example, our consciousness. Some people think we’ll
never be able to understand our consciousness with
mathematics and equations. Other people think we do. For example, Giulio
Tononi and Christof Koch, two famous neuroscientists,
have this theory where they argue that
conscious is actually certain mathematical pattern to
do with information processing. And we don’t know yet
what’s right or wrong. And I think one of
the coolest things to watch to see which
way this is going to break is to see
whether ultimately even that aspect of nature is
something we can understand better with science,
or whether we’re going to hit the
road block there. Do we have time for
one more question? MALE SPEAKER: Yeah. MAX TEGMARK: OK. AUDIENCE: So this a little
bit of a loopy question about deep time and long
term– very, very long term prospects for humanity. So one of the
things you run into is the notion that as
everything, the universe, is expanding, the things, the
edges of what we can detect are now receding at
the speed of light. And if this process goes on
for a while, at some point, you couldn’t even see that there
had ever been other galaxies, because all the other
galaxies are moving faster than the speed of
light away from you. So there’s no way to get
any information about them. And at an irrational level, this
seems really offensive to me. Is there a scientific
way out of this trap? MAX TEGMARK: Can someone
throw me our universe? Little bit short, but
the pass is complete. So just to make sure I answer
your question properly, is the part you find
offensive that things seem to go faster than light? Or is it that there are
things that we have no access to experimentally? The latter? AUDIENCE: Well,
they basically leave the universe, because
there’s no exit. MAX TEGMARK: OK, good. So first of all– AUDIENCE: So the
universe shrinks? MAX TEGMARK: We have
to be careful with how we use our words here. Some people choose to
use the word universe to refer to everything
that exists. And then by
definition, of course, nothing can leave our universe. Our universe would
just be everything. I’m using the word
universe instead to refer to simply everything
which we can possibly observe with even the best
telescopes, namely this sphere from which light has had time
to reach us during the 13.8 billion years
since our Big Bang. If you want to be
more precise, you’d call this our
observable universe. If you want to have a
word for everything you get to if you travel
forever in all directions, I would use a different
word for that. Mainly, just space. So space is bigger
than our universe. We don’t know for
sure yet whether space is infinite or not. It might curve back on
itself or something. But right now, we
have no evidence whatsoever that space ends here. In fact, if we wait
one hour, we can see light reach us
from farther away and falsify that hypothesis. And moreover, inflation,
this most popular theory we have for what
created our Big Bang, typically predict
that space actually is much bigger than this,
perhaps even infinite. So we’re in this situation
where most likely, we can only observe a part
of everything that exists. And some people don’t
like that, and they feel it’s disappointing
and humbling. They think it’s bad for
our egos or whatever. But frankly, I think a little
bit of humility is good for us humans. And second, if we think about
it the other way around, to me, it feels pretty
arrogant if we were to assume that there’s
some law of nature that says that we have to be able to
observe everything that exists. It’s like an ostrich with
its head in the sand, saying, oh, if I can’t see
you, then you don’t exist. That feels way too
arrogant for me. We humans have had this
tendency in history, again, and again, and again,
to assume that everything we knew of was
everything that existed. That’s why we got so freaked
out by the whole Galileo spat, and then with the
realities that we live in a galaxy, the
universe, and so on. I think it’s
overwhelmingly likely that there are parts of
space that we can’t see now. Many of these
galaxies out here, we can see if we wait
the billion years. Eat your vitamins. But there might be other regions
of space which you will never be able to see, because the dark
energy will keep pushing them away from us farther. Let me also just
comment on the thing you said about speed of light. So we all learned
in kindergarten that nothing can go faster
than the speed of light. But it turns out
actually that that’s only what special relativity said. And then Einstein came along
with general relativity that overruled this. And general relativity
is a bit more liberal about the speed limit. In general relativity, you
can’t go faster than light through space itself,
but space can stretch out as fast as it wants. General relativity says
that space is better thought of not as a static
boring stage where stuff happens, but
as a rubber sheet. It can vibrate. That’s what those
gravitational waves are. It can curve, even making
things like black holes. And it can stretch. That’s what the
expanding universe is. So if you keep
stretching it uniformly, there will be some parts of
space which right now actually are going away from us faster
than the speed of light. And that’s OK. If you try to look at them,
you simply can’t see them. Light hasn’t made it over here. So on that note, I
think time is up. So let me thank you
all so much for coming. It was a pleasure. [APPLAUSE]