“Excuse me, but what’s the time?” I’m guessing that you, like
me, are guilty of having asked this question, as if it were obvious that there
is such a thing as the time. Yet you’ve probably never approached a stranger
and asked “Excuse me, but what’s the place?”. If you were hopelessly lost,
you’d probably instead have said something like “Excuse me, but where am I?
thereby acknowledging that you’re not asking about a property of space, but
rather about a property of yourself. Similarly, when you ask for the time,
you’re not really asking about a property of time, but rather about your
location in time.

But that is not how we usually think about it. Our language
reveals how differently we think of space and time: The first as a static
stage, and the second as something flowing. Despite our intuition, however, the
flow of time is an illusion. Einstein taught us that there are two equivalent
ways of thinking about our physical reality: Either as a three-dimensional
place called space, where things change over time, or as a four-dimensional
place called spacetime that simply exists, unchanging, never created, and never

I think of the two viewpoints as the different perspectives
on reality that a frog and a bird might take. The bird surveys the landscape of
reality from high “above,” akin to a physicist studying the mathematical
structure of spacetime as described by the equations of physics. The frog, on
the other hand, lives inside the landscape surveyed by the bird. Looking up at
the moon over time, the frog sees something like the right panel in the figure,
“The Moon’s Orbit”: Five snapshots of space with the Moon in different
positions each time. But the bird sees an unchanging spiral shape in spacetime,
as shown in the left panel.

The Moon’s Orbit: We can equivalently think of the moon as a position in space that changes over time (right), or as an unchanging spiral shape in spacetime (left), corresponding to a mathematical structure. The snapshots of space (right) are simply horizontal slices of spacetime (left). To keep things legible, I’ve drawn the orbit much smaller than to scale and made several simplifications. To get snapshots of space (right) from spacetime (left), you simply make horizontal slices through spacetime at the times you’re interested in.Max Tegmark

For the bird—and the physicist—there is no objective
definition of past or future. As Einstein put it, “The distinction between
past, present, and future is only a stubbornly persistent illusion.” When we
think about the present, we mean the time slice through spacetime corresponding
to the time when we’re having that thought. We refer to the future and past as
the parts of spacetime above and below this slice.

This is analogous to your use of the terms here, in front of
, and behind me to refer to different parts of spacetime relative to your
present position. The part that’s in front of you is clearly no less real than
the part behind you—indeed, if you’re walking forward, some of what’s presently
in front of you will be behind you in the future, and is presently behind
various other people. Analogously, in spacetime, the future is just as real as
the past—parts of spacetime that are presently in your future will, in your
future, be in your past. Since spacetime is static and unchanging, no parts of
it can change their reality status, and all parts must be equally real.

The idea of spacetime does more than teach us to rethink the
meaning of past and future. It also introduces us to the idea of a mathematical
. Spacetime is a purely mathematical structure in the sense that it has
no properties at all except mathematical properties, for example the number
four, its number of dimensions. In my book Our Mathematical Universe, I argue
that not only spacetime, but indeed our entire external physical reality, is a mathematical structure,
which is by definition an abstract, immutable entity existing outside of space
and time.

The most interesting property of your spacetime tube isn’t its bulk shape, but its internal structure, which is remarkably complex.

What does this actually mean? It means, for one thing, a
universe that can be beautifully described by mathematics. That this is true
for our universe has become increasingly clear over the centuries, with
evidence piling up ever more rapidly. The latest triumph in this area is the
discovery of the Higgs boson, which, just like the planet Neptune and the radio
wave, was first predicted with a pencil, using mathematical equations.

That our universe is approximately described by mathematics
means that some but not all of its properties are mathematical. That it is
mathematical means that all of its properties are mathematical; that it has no
properties at all except mathematical ones. If I’m right and this is true, then
it’s good news for physics, because all properties of our universe can in
principle be understood if we are intelligent and creative enough. It also
implies that our reality is vastly larger than we thought, containing a diverse
collection of universes obeying all mathematically possible laws of physics.

This novel way of viewing both spacetime and the stuff in it
implies a novel way of viewing ourselves. Our thoughts, our emotions, our
self-awareness, and that deep existential feeling “I am”—none of this feels the
least bit mathematical to me. Yet we too are made of the same kinds of
elementary particles that make up everything else in our physical world, which
I’ve argued is purely mathematical. How can we reconcile these two

Chad Hagen

The first step is to consider how we look as a spacetime
structure. The cosmology pioneer George Gamow entitled his autobiography My
World Line
, a phrase also used by Einstein to refer to paths through spacetime.
However, your own world line strictly speaking isn’t a line: It has a non-zero
thickness and it’s not straight. The roughly 1029 elementary particles (quarks
and electrons) that your body is made of form a tube-like shape through
spacetime, analogous to the spiral shape of the Moon’s orbit (“The Moon’s
Orbit”) but more complicated. If you’re swimming laps in a pool, that part of
your spacetime tube has a zig-zag shape, and if you’re using a playground
swing, that part of your spacetime tube has a serpentine shape.

However, the
most interesting property of your spacetime tube isn’t its bulk shape, but its
internal structure, which is remarkably complex. Whereas the particles
that constitute the Moon are stuck together in a rather static arrangement,
many of your particles are in constant motion relative to one another.
Consider, for example, the particles that make up your red blood cells. As your
blood circulates through your body to deliver the oxygen you need, each red
blood cell traces out its own unique tube shape through spacetime,
corresponding to a complex itinerary though your arteries, capillaries, and
veins with regular returns to your heart and lungs. These spacetime tubes of
different red blood cells are intertwined to form a braid pattern as seen in
the figure “Complexity and Life” which is more elaborate than anything you’ll
ever see in a hair salon: Whereas a classic braid consists of three strands
with perhaps thirty thousand hairs each, intertwined in a simple repeating
pattern, this spacetime braid consists of trillions of strands (one for each
red blood cell), each composed of trillions of hair-like elementary-particle
trajectories, intertwined in a complex pattern that never repeats. In other
words, if you imagine spending a year giving a friend a truly crazy hairdo,
braiding the hair by separately intertwining all their individual hairs, the
pattern you’d get would still be very simple in comparison.

Complexity and Life: The motion of an object corresponds to a pattern in spacetime. An inanimate clump of 10 accelerating particles constitutes a simple pattern (left), while the particles that make up a living organism constitute a complex pattern (middle), corresponding to the complex motions that accomplish information processing and other vital processes. When a living organism dies, it eventually disintegrates and its particles separate from each other (right). These crude illustrations show merely 10 particles; your own spacetime pattern involves about 1029 particles and is mind-blowingly complex.Max Tegmark

Yet the complexity of all this pales in comparison to the
patterns of information processing in your brain. Your roughly 100 billion
neurons are constantly generating electrical signals (“firing”), which involves
shuffling around billions of trillions of atoms, notably sodium, potassium, and
calcium ions. The trajectories of these atoms form an extremely elaborate braid
through spacetime, whose complex intertwining corresponds to storing and
processing information in a way that somehow gives rise to our familiar
sensation of self-awareness. There’s broad consensus in the scientific
community that we still don’t understand how this works, so it’s fair to say
that we humans don’t yet fully understand what we are. However, in broad brush,
we might say this: You’re a pattern in spacetime. A mathematical pattern.
Specifically, you’re a braid in spacetime—indeed, one of the most elaborate
braids known.

Some people find it emotionally displeasing to think of
themselves as a collection of particles. I got a good laugh back in my 20s when
my friend Emil addressed my friend Mats as an “atomhög,” Swedish for “atom heap,”
in an attempt to insult him. However, if someone says “I can’t believe I’m just
a heap of atoms!’
’ I object to the use of the word “just”: the elaborate
spacetime braid that corresponds to their mind is hands down the most beautifully
complex type of pattern we’ve ever encountered in our universe. The world’s
fastest computer, the Grand Canyon or even the Sun—their spacetime patterns are
all simple in comparison.

At both ends of your spacetime braid, corresponding to your
birth and death, all the threads gradually separate, corresponding to all your
particles joining, interacting and finally going their own separate ways (As
seen in the right panel of “Complexity and Life”). This makes the spacetime structure of your
entire life resemble a tree: At the bottom, corresponding to early
times, is an elaborate system of roots corresponding to the spacetime
trajectories of many particles, which gradually merge into thicker strands and
culminate in a single tube-like trunk corresponding to your current body (with
a remarkable braid-like pattern inside as we described above). At the top,
corresponding to late times, the trunk splits into ever finer branches,
corresponding to your particles going their own separate ways once your life is
over. In other words, the pattern of life has only a finite extent along the
time dimension, with the braid coming apart into frizz at both ends.1

view of ourselves as mathematical braid patterns in spacetime challenges the
assumption that we can never understand consciousness. It optimistically
suggests that consciousness can one day be understood as a form of matter, a
derivative of the most beautifully complex spacetime structure in our universe.
Such understanding would enlighten our approaches to animals, unresponsive
patients, and future ultra-intelligent machines, with wide-ranging ethical,
legal, and technological implications.

This is how I see it. However, although this idea of an
unchanging reality is venerable and dates back to Einstein, it remains
controversial and subject to vibrant scientific debate, with scientists I
greatly respect expressing a spectrum of views. For example, in his book The Hidden
, Brian Greene expresses unease toward letting go of the notions change
and creation as fundamental, writing “I’m partial to there being a process,
however tentative […] that we can imagine generating the multiverse.” Lee
Smolin goes further in his book Time Reborn, arguing that not only is change
real, but that time may be the only thing that’s real. At the other end of the
spectrum, Julian Barbour argues in his book The End of Time not only that
change is illusory, but that one can even describe physical reality without
introducing the concept of time at all.

If we discover the ultimate nature of time, this will answer
many of the most exciting open questions facing physics today. Did time have
some sort of beginning before our Big Bang? Will it ultimately end? Did it
emerge out of some sort of timeless quantum fuzz into which it will eventually
dissolve? We physicists haven’t found the mathematical theory of quantum
gravity required to convincingly answer these questions, but whatever this
“theory of everything” turns out to be, time will be the key to unlocking its

Max Tegmark is an MIT physics professor who has authored
more than 200 technical papers. Known as “Mad Max” for his unorthodox ideas and
passion for adventure, his scientific interests range from precision cosmology
to the ultimate nature of reality, all explored in his new popular science book
Our Mathematical Universe.