How to pronounce “invariant” in English

And they're different, so our knots are different.That's what an invariant is.And when people want to study sliceness, they still use invariance, but they come up with some invariant.

Now in order to make this work, we're going to have to preserve an invariant.And the invariant is that all committed and all stuck ballots are going to have to have the same value x.So how are we going to preserve this invariant?

It might look something a little bit more like jazz as an analogy.So there's something invariant about that geometry, of those spatial, temporal relationships.

It might look something a little bit more like jazz as an analogy.There's something invariant there, which is the speed of light, which basically retains the length of the four-dimensional geometry.

So there's a power operator-- which you see is a very similar symbol to the mathematical exponentiation, it just has a dieresis above it--It's rank invariant code.

But if you run the test of walking around it in a circle, you will eventually see it disappear.Because it's not invariant.It's not ultimately real.

So in a Newtonian universe the speed of light is instantaneous, which means everyone sees the same thing.So everything's invariant. And in Einstein's universe this is no longer true.So Einstein realized that in order for every observer to see the same laws of physics, every observer

It was a rigorous physics question.What is invariant? And so we were out to breakfast at a pancake house, and we wrote a list of possible ingredients of ultimate realityon a napkin. So things like spacetime, dimensionality, particles, strings, et cetera.

So you see what's happening here.The particles are not invariant.And that's what Hawking discovered that's so important.

That's the idea of a horizon.is by definition invariant in every possible reference frame.

That's the idea of a horizon.Why are strings not invariant?

That's the idea of a horizon.But membranes are not invariant in that theory.

considered to be eye pleasing.And these properties involve invariants to similarity transformations and roundness and smoothnessand symmetry and a couple more.

makes sense. it's been 50 years.They probably have already tried every invariant they could find.That's right. So what I study is four-dimensional spaces.

So this is where I come in, actually, in our team in India, where we do it.So we have found this invariant of space and time.

Almost everything that can be measured looks like this.So heart rate times lifespan is an invariant.

It might look something a little bit more like jazz as an analogy.So the thing that's actually invariant is a four-dimensional lengths measured in the four-dimensional length.

It might look something a little bit more like jazz as an analogy.But the thing that's invariant is the 60-fold cycle.

And so I think if you want to know one thing about fundamental physics, this is the one thing to know.Something is only real if it's invariant.And I'll explain what that means.

And Einstein figured out the solution.Something is real if it's invariant in every reference frame.So it was this way of thinking that led Einstein to his famous discovery.

Right. So that's what people usually do.And there's lots and lots of invariants.And they're very powerful, and interesting, and hard.

And the point here is that by encoding time in these trajectories, in the dynamics of these neural networks, it naturally solvesthe problem of what we call temporal invariants, the issue of how you can recognize a song or speech, whether it's spoken very quickly or very slowly.So overall, as far as we know, one of the major computational strategies the brain has to process time varying information, which

It's like what nature did is just discover these neural processes that allow us to build models of the world and then just repackage themReference frames essentially allow us to create a single invariant structure, or a stable structure, that completely describes an object or a concept in a manner

And the invariant is that all committed and all stuck ballots are going to have to have the same value x.So how are we going to preserve this invariant?Well, the way we preserve this invariant, this thing, you can't just vote to commit a ballot arbitrarily.

So there's a power operator-- which you see is a very similar symbol to the mathematical exponentiation, it just has a dieresis above it--I have a function which is also rank invariant, because it's just parsing those arrays to primitive functions.

And why do you know that?Because you know that something is only real if it remains invariant in every reference frame.OK. So just because something's not ultimately real it doesn't mean it has to be a hallucination, right?

That's what relativity is.But he found that there is something that remains invariant.And that is this combination of space and time.

That's the idea of a horizon.You said there is a trajectory and what is invariant's become smaller and smaller, and it may be nothing.

That's the idea of a horizon.So we continued our search for these ever-elusive invariants, these fundamental ingredients of ultimate reality.

It's like what nature did is just discover these neural processes that allow us to build models of the world and then just repackage themAnd by incorporating reference frames and these properties into machine learning and creating these invariant structures, we think we'll be able to dramatically increase the generalization

So how are we going to preserve this invariant?Well, the way we preserve this invariant, this thing, you can't just vote to commit a ballot arbitrarily.Before you vote to commit a ballot, you have to prepare that ballot.

It might look something a little bit more like jazz as an analogy.In this case, the speed of light remains invariant.

But Einstein actually cared more about the second part.Because he knew that the key to finding ultimate reality is to find the invariant.And actually later in life he said that he regretted calling it the theory of relativity and wished that instead he had called

That's the idea of a horizon.So Susskind realized that the location of the elephant in spacetime is not invariant.

That's the idea of a horizon.Does it end with one fundamental ingredient, one invariant, one thing that everything else is made of?

That's the idea of a horizon.And so now M-theory basically undermined the idea that you can have an invariant fundamental ingredient.

And if you actually have a quorum that votes to commit n, x, then we'll say that it's safe to output the value x.Now in order to make this work, we're going to have to preserve an invariant.And the invariant is that all committed and all stuck ballots are going to have to have the same value x.

It might look something a little bit more like jazz as an analogy.If I perform discrete transformations on the edges of this pentagram, it remains invariant in a five-fold manner.

So what I see as space, you might experience as time.And vice versa. And so space and time are not invariant.They are relative to your reference frame.

That's the idea of a horizon.So spacetime-- this unified, four-dimensional spacetime that was left invariant by Einstein's theory of invariance-- turns out not to be invariant after all.

That's the idea of a horizon.Because once you know this one thing about physics, that what's real is what's invariant, the entire trajectory of physics snaps into focus.

It just has one variable and one parameter.But the shocking truth of that is that-- well, on the one hand, we have an exact analytical solution for what we call the invariant measure or the probability distributionfor how that system develops over time.

That's what an invariant is.And when people want to study sliceness, they still use invariance, but they come up with some invariant.Maybe it's still integer valued, but it has this property that when you compute this integer for a slice knot, you're supposed to get zero.

It might look something a little bit more like jazz as an analogy.And he got Einstein's idea of invariance, the idea of using symmetry to understand what remains invariant if I change perspective.

It might look something a little bit more like jazz as an analogy.That's pretty cool. But if I start coloring this diagram with notes of the pentatonic scale, it's no longer invariant.

It might look something a little bit more like jazz as an analogy.All right. So the puzzle is, how do I make it invariant?

It's not a fundamental ingredient of ultimate reality.And so if you want to find the fundamental ingredients of ultimate reality, the something that arose from nothing, you have to find what's invariant.So if there's one thing that you remember about physics, let it be that.

That's the idea of a horizon.The whole history of physics, from Einstein to exactly what's going on right now, has been a steady and relentless progression of invariant

That's the idea of a horizon.But the most exciting and interesting and challenging thing that's happened in string theory in recent years is that it's turned out that strings are not invariant.