Video summary
The discussion begins with an examination of Isaac Newton's classical mechanics and his specific concerns regarding gravity, particularly the concept of action at a distance. While Newton could accurately predict planetary trajectories using his laws, he found it philosophically troubling that the Earth should exert or feel gravitational force from the Sun across 93 million miles without any visible medium connecting them. This intuition led him to suggest in *Principia Mathematica* that such an explanation was left for future generations because he could not conceive of a mechanism for this interaction. However, it is noted that Newton also anticipated issues with stability; even though he lacked the mathematical tools at the time, he recognized that including perturbations from other planets like Jupiter and Saturn would destabilize orbits unless some divine intervention occurred periodically to reset them. The evolution of gravitational theory addressed these conceptual hurdles by shifting from a force-based model to field theories. In the early 19th century, Pierre-Simon Laplace demonstrated that Newtonian gravity could be reformulated as a field theory involving the gravitational potential or field governed by Laplace's equation. This mathematical reframing eliminated "action at a distance" within the classical framework because changes in the Sun's position would propagate through this intervening field rather than acting instantaneously across space. Later, Albert Einstein resolved these issues further with General Relativity, which introduced the speed of light as a fundamental limit for information transfer. In this modern view, gravitational disturbances radiate outward at finite speeds as gravitational waves, meaning that if one were to shake an object here on Earth, its effect would not be felt instantly across the universe but only after the signal had time to travel. A significant portion of the conversation addresses whether humans can truly "understand" scientific concepts that defy common intuition or rely heavily on abstract mathematics rather than visualization. The dialogue uses Andrew Wiles' proof of Fermat's Last Theorem as an example where one might state understanding a theorem without fully grasping its implications for incredibly large numbers, suggesting that intuitive comprehension has limits in such cases. Similarly, while physicists may have strong intuitions about fields pervading space-time—such as the gravitational or electromagnetic fields—the complexity increases drastically with quantum field theory and new phenomena like the Higgs field. Sean Carroll argues that human intuition is not fixed but can be trained; much like cognitive muscles developed through exercise, our ability to grasp abstract concepts improves over time even if we are biologically constrained in how we visualize things. The transcript explores whether there are hard-coded biological limits to human understanding or if the only constraints are computational and calculational abilities. It is argued that while humans cannot easily perform complex calculations like taking cube roots of million-digit numbers mentally, this lack of calculation speed does not equate to a failure of conceptual understanding. The ability to manipulate logical formal structures symbolically allows humans to comprehend highly abstract mathematical spaces with hundreds of dimensions, even if they cannot visualize them directly. This capacity for symbolic manipulation represents a leap beyond the cognitive abilities of animals like dogs and cats, suggesting that once this threshold is crossed, there may not be inherent limits to what we can understand about the scientific world, provided our tools and methods continue to advance. Ultimately, the speakers conclude that humanity has likely not reached any fundamental limit in its ability to comprehend the natural world. Historical perspective supports this view; thinkers from five hundred years ago were nowhere near understanding classical mechanics or quantum mechanics yet still believed they had grasped their respective worlds of inquiry. Since we know more now than those predecessors and face new puzzles rather than solved ones, there is no reason to assume current limitations are nearing a ceiling. Consequently, the inability of the human mind to rationally comprehend every aspect of reality ranks low among Sean Carroll's worries at night, as he remains optimistic that our combination of cognitive training, mathematical prowess, and experimental technology will continue to expand our understanding indefinitely.
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Isaac Newton developed what we now call
classical mechanics that you describe
very nice in your new book because you
do with a lot of basic concepts and
physics so was classical mechanics I can
throw a rock and can predict the
trajectory of that rocks flight but if
we could put ourselves back into
Newton's time his theories work to
predict things but as I understand he
himself thought that they were their
interpretations of those predictions
were absurd perhaps he just said it for
religious reasons and so on but in
particular sort of a world of
interaction without contact so action at
a distance it didn't make sense to them
in a sort of a human interpretation
level does it make sense to you that
things can affect other things at a
distance it does but you know that so
that was one of Newton's worries you're
actually right in a slightly different
way about the religious worries he he
was smart enough this is off the topic
but still fascinating Newton almost
invented chaos theory as soon as he
invented classical mechanics he realized
that in the solar system so he was able
to explain how planets move around the
Sun but typically you would describe the
orbit of the earth ignoring effects of
Jupiter and Saturn and so forth just
doing the earth and the Sun he he kind
of knew even though he couldn't do the
math that if you included the effects of
Jupiter and Saturn the other planets the
solar system would be unstable like the
orbits of the planets would get out of
whack so he thought that God would
intervene occasionally to sort of move
the planets back into orbit which is how
you could only way you could explain how
they were there presumably forever but
the worry about classical mechanics were
a little bit different to worry about
gravity in particular it wasn't a worry
about classical mechanics worry about
gravity how in the world does the earth
know that there's something called the
Sun 93 million miles away
that is exerting gravitational force on
it and he said he literally said you
know I leave that for future generations
to think about because I don't know what
the answer is and in fact the people
under emphasize this but future
generations figured it out Pierre Simone
Laplace in circa 1800 showed that you
could rewrite
and gravity as a field theory so instead
of just talking about the force due to
gravity you can talk about the
gravitational field or the gravitational
potential field and then there's no
action at a distance it's exactly the
same theory empirically it makes exactly
the same predictions but what's
happening is instead of the Sun just
reaching out across the void there is a
gravitational field in between the Sun
and the earth that obeys an equation
Laplace's equation cleverly enough and
that tells us exactly what the field
does so even in Newtonian gravity you
don't need action at a distance now what
many people say is that Einstein solved
this problem because he invented general
relativity and general relativity
there's certainly a field in between the
Earth and the Sun but also there's the
speed of light as a limit in Laplace's
theory which was exactly Newton's theory
just in a different mathematical
language there could still be
instantaneous action across the universe
whereas in general relativity if you
shake something here as gravitational
impulse radiates out at the speed of
light we call that a gravitational wave
and we could detect those so but I I
really it rubs me the wrong way to think
that we should presume the answer should
look one way or the other like if it
turned out that there was action at a
distance in physics and that was the
best way to describe things that I would
do it that way it's actually a very deep
question because when we don't know what
the right laws of physics are when we're
guessing at them when we're
hypothesizing at what they might be
we are often guided by our intuitions
about what they should be I mean
Einstein famously was very guided by his
intuitions and he did not like the idea
of action at a distance we don't know
whether he was right or not it depends
on your interpretation of quantum
mechanics and it depends on even how you
talk about quantum mechanics within any
one interpretation if you see every
forces of field or any other
interpretation of action at a distance
he's just stepping back to sort of
caveman thinking like do you really can
you really sort of understand what it
means for a force to be a feel that's
everywhere so if you look at gravity
like what do you think about I think so
this is something that you've been can
addition by society to think that the to
map the fact that science is extremely
well predictive of something to
believing that you actually understand
it like you can intuitively under the
how as the degree that human beings can
understand anything that you actually
understand it are you just trusting the
beauty and the power of the predictive
power of science
that depends on what you mean by this
idea of truly understandings right right
you know I mean I really understand for
mots Last Theorem you know it's easy to
state it but do I really appreciate what
it means for incredibly large numbers
right yeah I think yes I think I do
understand it but like if you want to
just push people on well but your
intuition doesn't go to the places where
Andrew Wiles needed to go to prove
Fermat's Last Theorem and I can say fine
by something I understand the theorem
and I likewise I think that I do have a
pretty good intuitive understanding of
fields pervading space-time whether it's
the gravitational field or the
electromagnetic field or whatever the
Higgs field of course one's intuition
gets worse and worse as you get trickier
in the quantum field theory and all
sorts of new phenomena that come up in
quantum field theory so our intuitions
aren't perfect but I think it's also
okay to say that our intuitions get
trained right like you know I have
different intuitions now that I had when
I was a baby that's okay that's not an
intuition is not necessarily intrinsic
to who we are we can we can train it a
little bit so that's where I'm gonna
bring in Noam Chomsky for a second who
thinks that our cognitive abilities are
sort of evolved through time and so
they're they're biologically constrained
and so there's a clear limit as he puts
it to our cognitive abilities and it's a
very harsh limit but you actually kind
of said something interesting and nature
versus nurture thing here is we can
train our intuitions to sort of build up
the cognitive muscles to be able to
understand some of these tricky concept
so do you think there's limits to our
understanding that's deeply rooted
hard-coded into our biology that we
can't overcome
there could be limits to things like our
ability to visualize okay but when
someone like ed Witten proves a theorem
about you know hundred dimensional
mathematical spaces he's not visualizing
it he's doing the math that doesn't stop
him from understanding the result I
think and I would love to understand
this better but my rough feeling which
is not very educated is that you know
there's some threshold that one crosses
in abstraction when one becomes kind of
like a Turing machine right one has the
ability to contain in one's brain
logical formal symbolic structures and
manipulate them and that's a leap that
we can make as human beings that that
dogs and cats haven't made and once you
get there I'm not sure there are any
limits to our ability to understand the
scientific world at all maybe there are
there's certainly ability limits on our
ability to calculate things right you
know people are not very good at taking
cube roots of million digit numbers in
their head but that's not an element of
understanding it's certainly not a
little bit in principle so of course
there's a human you would say that
doesn't feel to be limits to our
understanding but sort of hey have you
thought that the universe is actually a
lot simpler than it appears to us and we
just will never be able to like it's
outside of our okay so us our cognitive
abilities combined with our mathematical
prowess and whatever kind of
experimental simulation devices we can
put together is there limits to that is
it is it possible there's limits to that
well of course it's possible there is or
is there any good reason to think that
we're anywhere close to the limits is a
harder question look imagine asking this
question five hundred years ago to the
world's greatest thinkers right like are
we approaching the limits of our ability
to understand the natural world and by
definition there are questions about the
natural world that are most interesting
to us that are the ones we
but yet understanding right so there's
always we're always faced with these
puzzles we don't yet know and I don't
know what they would have said five
hundred years ago but they didn't even
know about classical mechanics much less
quantum mechanics so we know that they
were nowhere close to how well they
could do right they could do normally
better than they were doing at the time
I see no reason why the same thing isn't
true for us today so of all the worries
that keep me awake at night the human
minds inability to rationally comprehend
the world is low on the list well put
you