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How Physicists Are Redefining Quantum Phases Beyond Traditional Models · The Quark Side - Quantum Physics Podcast

• 0:01
  Speaker 1: Welcome to the Quarkside Quantum Physics Podcast, an exploration of
• 0:05
  Speaker 1: the fundamental structure of reality, where quantum laws govern matter, energy,
• 0:11
  Speaker 1: and information. Here, uncertainty is a feature, not a flaw,
• 0:16
  Speaker 1: and understanding begins at the smallest scales.
• 0:27
  Speaker 2: I want you to imagine like looking inside the memory
• 0:30
  Speaker 2: of a future quantum computer. But instead of seeing this neat,
• 0:34
  Speaker 2: orderly grid of ones and zeros. Right.
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  Speaker 3: The usual picture we all have.
• 0:38
  Speaker 2: Exactly. Instead of that, you are looking at a chaotic, boiling,
• 0:44
  Speaker 2: just totally unpredictable storm of energy.
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  Speaker 3: Leaking heat everywhere. Yes.
• 0:50
  Speaker 2: It is constantly bleeding heat into the environment. Information is scrambling.
• 0:55
  Speaker 2: And by every classical metric we have, it just looks
• 0:58
  Speaker 2: like complete noise. So how on earth do you even
• 1:01
  Speaker 2: begin to classify what phase of matter that storm is in?
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  Speaker 3: Well, it sounds like a trick question, but it's actually
• 1:08
  Speaker 3: the most pressing roadblock in modern physics right now. Really? Oh, absolutely.
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  Speaker 3: I mean, we are so used to the elementary school
• 1:16
  Speaker 3: version of matter. You know, an ice cube holds its shape.
• 1:19
  Speaker 3: Water splashes, gas expands. You look at the behavior and
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  Speaker 3: you immediately know the bucket it goes into.
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  Speaker 2: Right.
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  Speaker 3: But when you step into the real messy out of
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  Speaker 3: equilibrium quantum world, that neat categorization system just it entirely
• 1:34
  Speaker 3: falls apart.
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  Speaker 2: Which brings us to the core of our conversation today.
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  Speaker 2: We are exploring a completely groundbreaking theoretical framework from physicists
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  Speaker 2: at the University of Illinois.
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  Speaker 3: Yeah, they've done some incredible work.
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  Speaker 2: They really have. They have essentially rewritten the rulebook for
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  Speaker 2: how we classify quantum phases of matter when they are
• 1:51
  Speaker 2: actually interacting with their environment, like when they're imperfect. But okay,
• 1:56
  Speaker 2: let's unpack this. Before we jump into the absolute chaos
• 1:58
  Speaker 2: of the quantum realm, let's set a baseline. How did
• 2:01
  Speaker 2: physicists define a phase of matter before all this quantum
• 2:04
  Speaker 2: weirdness threw a wrench in the gears?
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  Speaker 3: So to understand why the new framework is so revolutionary,
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  Speaker 3: you really have to understand the paradigm it's replacing. If
• 2:13
  Speaker 3: we go back to the 1930s, The physicist Lev Landoff
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  Speaker 3: came up with this brilliantly simple way to classify matter
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  Speaker 3: based entirely on symmetries.
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  Speaker 2: Okay, when you say symmetry, my brain immediately goes to geometry,
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  Speaker 2: like folding a piece of paper in half and seeing
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  Speaker 2: the exact same shape on both sides.
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  Speaker 3: It is a really similar concept, actually, but applied to
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  Speaker 3: the internal structure of a material. I want you to
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  Speaker 3: visualize shrinking down to the sides of a molecule and
• 2:39
  Speaker 3: floating inside a drop of liquid water. What do you see?
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  Speaker 2: Just a lot of water molecules, I guess? Right.
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  Speaker 3: It's a uniform soup. Molecules are tumbling past you randomly
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  Speaker 3: in every single direction. If you turn your head up, down, left, right,
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  Speaker 3: the environment looks roughly identical.
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  Speaker 2: Okay.
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  Speaker 3: That is a very high degree of continuous symmetry.
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  Speaker 2: But if the temperature drops and that water freezes into
• 3:02
  Speaker 2: an ice cube, that environment changes drastically.
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  Speaker 3: Drastically. Those tumbling molecules suddenly lock into a rigid crystalline grid.
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  Speaker 2: Now.
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  Speaker 3: If you are floating inside that ice cube, you can't
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  Speaker 3: just look anywhere and see the same thing.
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  Speaker 2: Oh, because they're locked in place.
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  Speaker 3: Exactly. You only see repeating patterns if you look along
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  Speaker 3: very specific, well-defined axes of the crystal. The continuous symmetry
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  Speaker 3: is broken. And Landau mathematically defined a phase transition as
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  Speaker 3: that exact moment when the fundamental symmetry of a system changes.
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  Speaker 2: That seems like an incredibly elegant way to handle it.
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  Speaker 2: You can clearly distinguish a solid from a liquid without
• 3:40
  Speaker 2: needing to know, like, every single detail about the atoms themselves.
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  Speaker 3: Yeah, it was the gold standard for decades. But by
• 3:46
  Speaker 3: the 1980s, physicists started discovering these bizarre new materials in
• 3:50
  Speaker 3: the laboratory. They would observe a material clearly transitioning from
• 3:54
  Speaker 3: one state of matter to an entirely different one, exhibiting
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  Speaker 3: wildly different physical properties.
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  Speaker 2: But let me guess, the symmetry didn't change.
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  Speaker 3: Nothing changed. The internal grid was completely identical. Landau's paradigm changed.
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  Speaker 3: Just couldn't explain it.
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  Speaker 2: I'm assuming this is where things get really mathematical. If
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  Speaker 2: symmetry fails, what is the metric?
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  Speaker 3: Topology.
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  Speaker 2: Topology?
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  Speaker 3: Yeah. Topology is a branch of mathematics that cares about
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  Speaker 3: the fundamental global properties of a shape while completely ignoring
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  Speaker 3: the local small-scale details.
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  Speaker 2: Give me a visual here. How does a topologist look
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  Speaker 2: at a shape differently than, say, a geometrician?
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  Speaker 3: Well, a topologist would tell you that a coffee cup
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  Speaker 3: and a donut are the exact same shape.
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  Speaker 2: Okay, wait. I am going to need you to walk
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  Speaker 2: me through that one because a coffee cup holds my
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  Speaker 2: morning roast and a donut definitely does not.
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  Speaker 3: Fair enough. Think about it like this. Imagine you are
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  Speaker 3: holding a coffee cup made out of really soft, pliable clay.
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  Speaker 3: In topology, you are allowed to stretch, squish, you know,
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  Speaker 3: massage that clay as much as you want.
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  Speaker 2: So I can completely deform it.
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  Speaker 3: Yes, but the only rule is The absolute banned operation
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  Speaker 3: is that you cannot tear the clay and you cannot
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  Speaker 3: fuse two separate pieces together.
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  Speaker 2: Okay, so if I take that clay cup, I can
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  Speaker 2: push down the bowl part where the coffee goes, just
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  Speaker 2: sort of flattening it out into a thick disk.
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  Speaker 3: Right, and what are you left with? You have a
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  Speaker 3: flattened piece of clay attached to a handle. And the
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  Speaker 3: handle is really just a ring of clay with a
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  Speaker 3: hole in the middle.
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  Speaker 2: Oh, wow.
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  Speaker 3: So you can smooth that all out into a perfect donut.
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  Speaker 3: Because you deformed one into the other smoothly, without tearing anything,
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  Speaker 3: they are considered globally identical. They belong to the same
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  Speaker 3: topological class.
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  Speaker 2: So to jump to a different class, I would have
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  Speaker 2: to violently break the rules. Like I would have to
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  Speaker 2: take a pencil and stab a second hole through the clay,
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  Speaker 2: turning it into a figure-eight pretzel.
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  Speaker 3: Exactly. That brings us to what mathematicians call topological invariance.
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  Speaker 3: These are core properties, like the number of holes in
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  Speaker 3: a shape, that survive any amount of continuous deformation.
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  Speaker 2: Okay, but how does this apply to quantum physics?
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  Speaker 3: When you cool certain materials down to near absolute zero,
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  Speaker 3: the random thermal jostling of the atoms completely stops. In
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  Speaker 3: that deafening silence, quantum fluctuations take over, and the entire
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  Speaker 3: system falls into a state of system-wide quantum entanglement.
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  Speaker 2: Wait, let me make sure I'm conceptualizing this correctly. If
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  Speaker 2: the electrons are entangled across the entire material, then the
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  Speaker 2: phase of matter isn't determined by what one individual atom
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  Speaker 2: is doing. Right. The information that defines the phase is
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  Speaker 2: smeared out across millions of atoms simultaneously. It sounds almost
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  Speaker 2: like a holographic image. Like, if you take a physical
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  Speaker 2: hologram and cut it in half, you don't get the
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  Speaker 2: top half of the image and the bottom half. The
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  Speaker 2: entire picture is stored everywhere.
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  Speaker 3: That is a fantastic analogy. The topological information is stored non-locally.
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  Speaker 3: And because the shape of the entanglement is global, it
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  Speaker 3: gives rise to bizarre phenomena like quasiparticles called anions.
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  Speaker 2: I've heard of bosons and fermions, you know, the building
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  Speaker 2: blocks of everything around us. What makes an enneon different?
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  Speaker 3: Bosons and fermions follow very strict rules about how they
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  Speaker 3: can swap places and share space. Enneons, which only exist
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  Speaker 3: in these two-dimensional topological systems, essentially ignore those rules. They
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  Speaker 3: remember their past trajectories. If two enneons orbit around each other,
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  Speaker 3: the global entanglement of the entire system fundamentally changes.
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  Speaker 2: So they're physically altering the global structure.
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  Speaker 3: Yeah, they are like knots being tied in the underlying
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  Speaker 3: fabric of the quantum state.
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  Speaker 2: If the information is locked into these global topological knots
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  Speaker 2: and not tied to any single fragile atom, it seems
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  Speaker 2: like that would be the ultimate way to store data.
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  Speaker 2: Is that why tech companies are so obsessed with building
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  Speaker 2: topological quantum computers?
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  Speaker 3: You've hit the nail on the head. A standard quantum
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  Speaker 3: computer uses individual quantum bits or qubits, which are incredibly fragile.
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  Speaker 3: If a straight cosmic ray hits a single qubit, or
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  Speaker 3: the temperature fluctuates by a fraction of a degree, the
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  Speaker 3: information is completely destroyed.
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  Speaker 2: It just vanishes.
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  Speaker 3: Proof. Gone. But if you encode your data in the
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  Speaker 3: global topology, in the number of holes in the donut,
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  Speaker 3: a local disturbance won't ruin the calculation. You can scratch
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  Speaker 3: the icing all you want, but the hole in the
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  Speaker 3: donut is still there.
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  Speaker 2: It sounds perfect. So what is the problem? Why haven't
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  Speaker 2: we built these indestructible quantum computers yet?
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  Speaker 3: Because the math we use to define these topological phases
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  Speaker 3: relies on a total fiction. Historically, physicists have only studied
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  Speaker 3: these phases as pure states.
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  Speaker 2: Pure states?
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  Speaker 3: Yeah, perfectly isolated systems, completely cut off from the rest
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  Speaker 3: of the universe. And classifying them relies on a mathematical
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  Speaker 3: object called a gapped Hamiltonian.
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  Speaker 2: Okay, break down gapped Hamiltonian for me. What is it
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  Speaker 2: actually doing in the math?
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  Speaker 3: Think of it as the ultimate set of instructions for
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  Speaker 3: the quantum system. It dictates the energy levels of every
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  Speaker 3: possible state. The gap is an energy buffer zone. Imagine
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  Speaker 3: a ball resting at the bottom of a really deep valley.
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  Speaker 2: Okay, I'm picturing it.
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  Speaker 3: If a small perturbation comes along, like a little gust
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  Speaker 3: of wind, it might push the ball slightly up the hill,
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  Speaker 3: but gravity pulls it right back down to the stable bottom.
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  Speaker 3: It takes a massive, specific spike in energy to kick
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  Speaker 3: that ball completely out of the valley and over the
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  Speaker 3: mountain into a new phase.
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  Speaker 2: So two materials are in the same phase if their
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  Speaker 2: Hamiltonians can smoothly connect without eliminating that protective energy valley.
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  Speaker 2: It ensures stability.
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  Speaker 3: Exactly. But here's the problem. Pure states do not exist
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  Speaker 3: in the real world. A real quantum computer has wiring.
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  Speaker 3: It has a cooling system. It sits in a room
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  Speaker 3: with electromagnetic fields. The quantum state inevitably interacts with its environment.
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  Speaker 3: It leaks energy and information.
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  Speaker 2: Decoherence.
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  Speaker 3: Decoherence. The system degrades into a messy, out-of-equilibrium statistical soup
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  Speaker 3: known as a mixed state. And when it becomes a
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  Speaker 3: mixed state, that deep valley, the Hamiltonian, literally ceases to
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  Speaker 3: exist mathematically. The map is just gone.
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  Speaker 2: So what does this all mean? If pure states are
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  Speaker 2: like a perfectly sealed terrarium, but mixed states are like
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  Speaker 2: opening the window to a hurricane, and we've just lost
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  Speaker 2: our mathematical map because the Hamiltonians are gone... How do
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  Speaker 2: scientists even begin to categorize this mess? You're basically blindfolded.
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  Speaker 3: That is the exact wall the field has been slamming into.
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  Speaker 3: How do you classify a phase when the fundamental anchor
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  Speaker 3: is missing? And that is what Zhang Yanli, Bowen Shi,
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  Speaker 3: and Taishuang Yang figured out at the University of Illinois.
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  Speaker 3: They developed a new classification scheme called entanglement bootstrapping.
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  Speaker 2: Bootstrapping usually implies pulling yourself up by your own resources
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  Speaker 2: when you have nothing else. How do you apply that
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  Speaker 2: to a quantum system without a Hamiltonian?
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  Speaker 3: By working backward, directly from the entanglement itself. If you
• 10:57
  Speaker 3: can't rely on the energy rules, you have to look
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  Speaker 3: for fixed points in the chaos. A fixed point is
• 11:03
  Speaker 3: a property that remains identical no matter what length scale
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  Speaker 3: you observe it from.
• 11:08
  Speaker 2: Wait, how do you change the length scale of a
• 11:10
  Speaker 2: quantum system?
• 11:12
  Speaker 3: Through a process called coarse graining. It's essentially zooming out.
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  Speaker 2: Oh, kind of like a pointillist painting?
• 11:19
  Speaker 3: Yes. Perfect analogy.
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  Speaker 2: Like if you stand one inch away from a massive
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  Speaker 2: pointillist painting, all you see is a chaotic, meaningless array
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  Speaker 2: of colored dots. But as you step back, as you
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  Speaker 2: zoom out, the microscopic details blur away and a broader,
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  Speaker 2: stable pattern emerges, a landscape or a face.
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  Speaker 3: Exactly. Entanglement bootstrapping zooms out to see the overarching patterns
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  Speaker 3: of quantum correlations.
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  Speaker 2: But a messy mixed state is full of random errors.
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  Speaker 2: How do they separate the real topological patterns from just
• 11:50
  Speaker 2: environmental noise?
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  Speaker 3: By instituting three rigorous stability criteria. If a state can
• 11:56
  Speaker 3: satisfy these three rules as you zoom out, it is
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  Speaker 3: stable enough to be classified.
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  Speaker 2: Let's hear the rules.
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  Speaker 3: The first condition is called M0. It demands that two
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  Speaker 3: physically separated regions of the material, let's say a cluster
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  Speaker 3: of atoms on the far left and a cluster on
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  Speaker 3: the far right, do not influence each other strongly.
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  Speaker 2: Wait, I thought the whole point of a topological phase
• 12:16
  Speaker 2: was that everything was entangled globally. Why wouldn't you want
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  Speaker 2: the left side talking to the right side?
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  Speaker 3: Because in a mixed state, unregulated long-range influence is dangerous.
• 12:27
  Speaker 3: If a stray photon hits the left side of the
• 12:29
  Speaker 3: material and there is a direct, rigid correlation to the
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  Speaker 3: right side, that local error could instantly ripple across the
• 12:35
  Speaker 3: entire system and destroy the phase.
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  Speaker 2: Oh, this is like a highway car crash. Right. If
• 12:40
  Speaker 2: cars are jammed too closely together on the freeway, one
• 12:43
  Speaker 2: crash causes a massive pileup that propagates down the road.
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  Speaker 2: M0 basically ensures the regions are spaced out enough that
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  Speaker 2: a local perturbation doesn't destabilize the whole system.
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  Speaker 3: That is exactly how it functions. It quarantines local perturbations.
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  Speaker 2: Okay, what's the next rule?
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  Speaker 3: The second condition is P0. This rule leverages that non-local
• 13:04
  Speaker 3: holographic storage you mentioned earlier. It dictates that if the
• 13:07
  Speaker 3: information in one small local region is totally corrupted by
• 13:11
  Speaker 3: the environment, the immediate surrounding neighborhood must be able to
• 13:15
  Speaker 3: completely recover the lost data.
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  Speaker 2: Because the information isn't just sitting in that one corrupted spot.
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  Speaker 2: It's a distributed backup. If one server goes down, the
• 13:24
  Speaker 2: network just rebuilds the file using fragments stored on the
• 13:27
  Speaker 2: neighboring servers. Yes.
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  Speaker 3: So between quarantining the damage with M0 and repairing the
• 13:33
  Speaker 3: damage with P0, The state exhibits profound resilience. But there
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  Speaker 3: is a third condition, M1, and it is arguably the
• 13:41
  Speaker 3: most mathematically crucial.
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  Speaker 2: Let's not shy away from the math. What does M1
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  Speaker 2: actually enforce?
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  Speaker 3: M1 ensures algebraic consistency. Remember those anions we talked about?
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  Speaker 3: The weird particles that act like knots in the entanglement?
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  Speaker 2: Yeah.
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  Speaker 3: If two anions collide and fuse together, they must produce
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  Speaker 3: a predictable result. M1 is the underlying grammar of the
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  Speaker 3: quantum system. It ensures that the entangled correlations aren't just
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  Speaker 3: random unstructured noise, but rather they obey a strict set
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  Speaker 3: of logical rules. Without M1, you just have chaos. With M1,
• 14:17
  Speaker 3: you have a tractable topological phase.
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  Speaker 2: So any quantum state that survives these three conditions simultaneously
• 14:24
  Speaker 2: at all zoomed out length scales is a stable fixed point.
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  Speaker 2: You have your anchor back. Yes.
• 14:30
  Speaker 3: But the true genius is how they define the phase itself.
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  Speaker 3: They realize that in the laboratory, a state is never
• 14:36
  Speaker 3: going to perfectly align with a fixed point. It will
• 14:39
  Speaker 3: always be slightly messy. So they define a phase by
• 14:42
  Speaker 3: looking at how the deviations behave as you coarse-grain the system.
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  Speaker 2: As you zoom out. Right.
• 14:48
  Speaker 3: If you take two messy mixed states and you start
• 14:51
  Speaker 3: zooming out and the mathematical differences between them drop off
• 14:55
  Speaker 3: exponentially fast, the further back you step, they belong to
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  Speaker 3: the same phase.
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  Speaker 2: That makes perfect sense. If the differences vanish into microscopic
• 15:03
  Speaker 2: rounding errors, as you look at the big picture, they
• 15:06
  Speaker 2: are practically identical. And this gives them a way to
• 15:10
  Speaker 2: extract those topological invariants, the number of holes in the donut,
• 15:14
  Speaker 2: directly from the messy data.
• 15:15
  Speaker 3: Exactly. You don't have to rebuild the entire Hamiltonian from scratch.
• 15:19
  Speaker 3: You can just measure the topological data. And crucially, if
• 15:23
  Speaker 3: you apply this new bootstrapping method to perfectly clean pure states,
• 15:27
  Speaker 3: it gives you the exact same answers as the old methods.
• 15:29
  Speaker 3: It works universally.
• 15:31
  Speaker 2: Okay, here's where it gets really interesting, though, because before
• 15:33
  Speaker 2: this framework dropped, the field wasn't just sitting still. There
• 15:36
  Speaker 2: was an older method people were using to try and
• 15:38
  Speaker 2: classify these mixed states, right? Something called FDLC?
• 15:42
  Speaker 3: Ah, yes. The Finite Depth Local Channel. You can think
• 15:46
  Speaker 3: of an FDLC as a mathematical communication link. The working
• 15:50
  Speaker 3: theory was simple. If you have state A, and you
• 15:52
  Speaker 3: can map it onto state B using this channel, and
• 15:55
  Speaker 3: then map it back again smoothly, they must be in
• 15:58
  Speaker 3: the same phase.
• 15:59
  Speaker 2: That sounds reasonable on the surface. Why did it fail?
• 16:02
  Speaker 3: Well, what's fascinating here is how the Illinois team proved
• 16:05
  Speaker 3: it failed. They set up a theoretical showdown between two
• 16:08
  Speaker 3: very specific states of matter, a generic product state and
• 16:12
  Speaker 3: a maximally dephased Toric code.
• 16:15
  Speaker 2: Okay, break those two down for me visually. What is
• 16:18
  Speaker 2: a generic product state?
• 16:20
  Speaker 3: A generic product state is incredibly boring. Imagine a grid
• 16:23
  Speaker 3: of a million coins sitting on a table. Some are heads,
• 16:27
  Speaker 3: some are tails, but none of them are entangled. They
• 16:30
  Speaker 3: act completely independently.
• 16:32
  Speaker 2: So no loops, no topology, no deep connections, just isolated bits. Right.
• 16:37
  Speaker 3: Now imagine the Torque code. It is also a grid
• 16:40
  Speaker 3: of quantum spins, but they are secretly entangled in complex
• 16:44
  Speaker 3: global loops like the hole in the donut. However, it
• 16:48
  Speaker 3: is maximally dephased.
• 16:50
  Speaker 2: Which means?
• 16:51
  Speaker 3: The environment has come in and aggressively scrambled all the
• 16:55
  Speaker 3: local information. So if you just look at a small
• 16:57
  Speaker 3: handful of spins... They look completely random and unentangled, exactly
• 17:02
  Speaker 3: like the generic product state.
• 17:03
  Speaker 2: But the global loops are still invisibly woven through the
• 17:06
  Speaker 2: whole system. So physically, they are completely different phases of matter. Yes.
• 17:12
  Speaker 3: But when physicists used the old FDLC method to compare them,
• 17:15
  Speaker 3: the math told them they were in the exact same phase.
• 17:18
  Speaker 2: Wait, how could a method be so fundamentally blind? It
• 17:21
  Speaker 2: is like looking at a pile of loose thread and
• 17:23
  Speaker 2: a fully knit sweater and saying they are the same thing,
• 17:25
  Speaker 2: just because they are both made of wool. How did
• 17:28
  Speaker 2: researchers forget this subtlety with FDLC? Is it just human
• 17:31
  Speaker 2: nature to try and force a tool to work on
• 17:33
  Speaker 2: a problem it wasn't designed for?
• 17:35
  Speaker 3: That is a very apt way to describe it, actually.
• 17:38
  Speaker 3: They were relying on a flawed preparation protocol rather than
• 17:41
  Speaker 3: looking at the intrinsic nature of the state itself. It
• 17:44
  Speaker 3: failed because of the mapping process itself. To map state
• 17:47
  Speaker 3: A to state B using FDLC, you have to aggressively
• 17:51
  Speaker 3: shuffle the quantum information around locally.
• 17:54
  Speaker 2: Oh, I see.
• 17:55
  Speaker 3: The researchers discovered that while the FDLC was shuffling the
• 17:58
  Speaker 3: local data, it was accidentally creating or destroying those invisible
• 18:02
  Speaker 3: global loops. It was changing the underlying topology of the
• 18:05
  Speaker 3: system during the test.
• 18:07
  Speaker 2: It is the observer effect on steroids. The test itself
• 18:10
  Speaker 2: alters the material.
• 18:12
  Speaker 3: Exactly. Bootstrapping solves this because it doesn't try to force
• 18:15
  Speaker 3: a mapping. It acts as an intrinsic diagnostic, just passively
• 18:19
  Speaker 3: reading the entanglement structure that is already there.
• 18:22
  Speaker 2: Okay, so we have this incredible theoretical triumph. But for
• 18:25
  Speaker 2: everyone listening who isn't, you know, writing a dissertation on
• 18:28
  Speaker 2: topological invariance, why does being able to tell a generic
• 18:32
  Speaker 2: product state from a Toric code actually matter? What changes tomorrow?
• 18:37
  Speaker 3: It is literally the master blueprint for the future of computing.
• 18:40
  Speaker 3: Up until now, attempting to build a topological quantum computer
• 18:44
  Speaker 3: has been like trying to build an airplane without understanding aerodynamics.
• 18:48
  Speaker 3: You know you want to fly, but the wind keeps
• 18:49
  Speaker 3: knocking you out of the sky. By identifying fixed points directly,
• 18:54
  Speaker 3: from how quantum information is organized, researchers can finally incorporate
• 18:58
  Speaker 3: mixed-state topological order into actual devices. We have a mathematical
• 19:02
  Speaker 3: framework that defines exactly how topological information survives inside noisy environments.
• 19:08
  Speaker 3: Engineers can actually start designing physical devices that exploit those rules.
• 19:12
  Speaker 2: We can finally build hardware that is natively resilient to
• 19:16
  Speaker 2: temperature fluctuations and environmental noise because we know the exact
• 19:20
  Speaker 2: mathematical boundaries of that resilience. Yes.
• 19:23
  Speaker 3: And the team at Illinois is already pushing the boundaries further.
• 19:27
  Speaker 3: They are hunting for new topological data to flesh out
• 19:29
  Speaker 3: the framework. They're investigating critical points, the chaotic, highly correlated
• 19:33
  Speaker 3: moments right on the absolute edge of a phase transition.
• 19:37
  Speaker 2: And I imagine they will eventually have to tackle things
• 19:40
  Speaker 2: like fracton phases.
• 19:42
  Speaker 3: Oh, fracton phases are fascinating. They're these bizarre states of
• 19:45
  Speaker 3: matter where particles are fundamentally stuck. Imagine a quantum trafficking
• 19:50
  Speaker 3: where a particle can only move if it moves in
• 19:52
  Speaker 3: perfect coordination with three other particles simultaneously.
• 19:55
  Speaker 2: Wow.
• 19:57
  Speaker 3: The current bootstrapping framework cannot capture fractons yet, but in
• 20:00
  Speaker 3: theoretical physics, a limitation is just a signpost. It tells
• 20:04
  Speaker 3: them exactly what new mathematical rules they need to invent next.
• 20:08
  Speaker 2: It really is a total paradigm shift. I mean, we
• 20:11
  Speaker 2: started this conversation looking at the simple symmetry of an
• 20:15
  Speaker 2: ice cube, and now we are talking about coarse-graining the
• 20:18
  Speaker 2: holographic entanglement of a boiling quantum storm.
• 20:20
  Speaker 3: It's a huge leap. And I think there is a
• 20:23
  Speaker 3: really profound philosophical takeaway here for you to ponder. If
• 20:27
  Speaker 3: this new physics shows us that the chaotic, noisy interactions
• 20:31
  Speaker 3: of the real world, these messy mixed states, can still
• 20:34
  Speaker 3: hold profound, stable topological order when we simply zoom out
• 20:39
  Speaker 3: and look at the big picture. It really makes you wonder.
• 20:42
  Speaker 2: Wonder about the macroscopic world.
• 20:44
  Speaker 3: Exactly. Are the seemingly chaotic, unpredictable systems in our everyday
• 20:49
  Speaker 3: macroscopic lives, weather patterns, biological ecosystems, maybe even human economics,
• 20:56
  Speaker 3: actually hiding fundamental mathematically perfect structures?
• 20:59
  Speaker 2: Are we just standing too close to the pointless painting?
• 21:02
  Speaker 2: Have We just not figured out how to coarse-grain reality yet.
• 21:07
  Speaker 2: That is an incredible thought to end on.