WEBVTT 00:00:00.000 --> 00:00:03.240 Imagine, if you will, the ultimate life hack 00:00:03.240 --> 00:00:05.280 for the modern housing market. You know, you 00:00:05.280 --> 00:00:07.879 want more square footage, but physical land is 00:00:07.879 --> 00:00:10.279 at a premium. Right. Especially in a city. Exactly. 00:00:10.400 --> 00:00:13.599 So what if you could just bypass the limitations 00:00:13.599 --> 00:00:15.880 of geography entirely? What if you could save 00:00:15.880 --> 00:00:18.660 an absolute fortune on real estate simply by 00:00:18.660 --> 00:00:20.940 building a house that folds out into the fourth 00:00:20.940 --> 00:00:23.620 dimension? I mean, it sounds like the setup to, 00:00:23.620 --> 00:00:27.039 well, a highly specialized, very nerdy architectural 00:00:27.039 --> 00:00:29.589 joke. It does. It sounds completely absurd, but 00:00:29.589 --> 00:00:31.890 that is exactly the bizarre proposition we are 00:00:31.890 --> 00:00:33.969 exploring today. So welcome to the deep dive. 00:00:34.149 --> 00:00:36.549 We are thrilled to have you with us because today's 00:00:36.549 --> 00:00:39.570 source material is an absolute classic of science 00:00:39.570 --> 00:00:42.549 fiction, and it actually doubles as a master 00:00:42.549 --> 00:00:44.929 class in theoretical mathematics. Yeah, it really 00:00:44.929 --> 00:00:47.250 does. We are looking at a Wikipedia article detailing 00:00:47.250 --> 00:00:49.869 a story by the legendary American writer Robert 00:00:49.869 --> 00:00:52.969 A. Heinlein. The story is called And He Built 00:00:52.969 --> 00:00:55.729 a Crooked House, which, of course, is a play 00:00:55.729 --> 00:00:57.770 on the old nursery rhyme. you know, there was 00:00:57.770 --> 00:00:59.990 a crooked man. Right, and it was published all 00:00:59.990 --> 00:01:04.170 the way back in February of 1941. Wow, 1941. 00:01:04.689 --> 00:01:06.349 Yeah, an astounding science fiction magazine. 00:01:06.890 --> 00:01:10.069 It is this amazing piece of literature that has 00:01:10.069 --> 00:01:13.230 been baffling and educating readers for over 00:01:13.230 --> 00:01:16.280 80 years now. And our mission today is to explore 00:01:16.280 --> 00:01:19.760 how this vintage sci -fi story about a mathematically 00:01:19.760 --> 00:01:23.500 obsessed, highly eccentric architect somehow 00:01:23.500 --> 00:01:26.340 serves as the perfect vehicle for understanding 00:01:26.340 --> 00:01:29.159 four -dimensional geometry. Okay, let's unpack 00:01:29.159 --> 00:01:31.060 this. Well, to understand the genius of this 00:01:31.060 --> 00:01:32.900 story, we really must start with the literal 00:01:32.900 --> 00:01:36.060 foundation. We are introduced to our protagonist, 00:01:36.400 --> 00:01:39.140 Quintus Teal. Right. He is a graduate architect 00:01:39.140 --> 00:01:41.670 operating in the Los Angeles area. And this is 00:01:41.670 --> 00:01:43.629 during a time when the city was experiencing 00:01:43.629 --> 00:01:45.969 a massive boon in experimental architecture. 00:01:46.189 --> 00:01:48.230 Right, a lot of weird houses being built. Exactly. 00:01:48.769 --> 00:01:51.250 But Thiel is not interested in designing, you 00:01:51.250 --> 00:01:53.750 know, standard Spanish colonials or mid -century 00:01:53.750 --> 00:01:57.629 moderns. He is deeply, deeply obsessed with topology 00:01:57.629 --> 00:01:59.890 and something called the Picard Vessio theory. 00:02:00.090 --> 00:02:01.650 Okay, for those of you listening who might not 00:02:01.650 --> 00:02:03.709 have a degree in advanced mathematics, let's 00:02:03.709 --> 00:02:06.489 break that down a bit. Topology is often described 00:02:06.489 --> 00:02:08.909 using a classic analogy. Oh, the coffee mug one. 00:02:09.069 --> 00:02:12.810 Yeah, exactly. So to a topologist, a coffee mug 00:02:12.810 --> 00:02:15.990 and a donut are the exact same shape. Which sounds 00:02:15.990 --> 00:02:19.509 insane to anyone else. Right. But because topology 00:02:19.509 --> 00:02:22.069 studies the properties of a geometric object 00:02:22.069 --> 00:02:24.289 that are preserved under continuous deformations 00:02:24.289 --> 00:02:27.189 like stretching or bending, but crucially not 00:02:27.189 --> 00:02:30.229 tearing. So since both a donut and a coffee mug 00:02:30.229 --> 00:02:32.830 have exactly one hole, they are topologically 00:02:32.830 --> 00:02:35.009 identical. It's the perfect way to visualize 00:02:35.009 --> 00:02:38.129 it. I mean, a topologist doesn't care about rigid 00:02:38.129 --> 00:02:40.719 distance. or angles, you know, they care about 00:02:40.719 --> 00:02:43.379 connectivity. And then you add in his obsession 00:02:43.379 --> 00:02:46.719 with the Picard -Vizio theory, which is, well 00:02:46.719 --> 00:02:49.319 essentially it's the Galois theory of differential 00:02:49.319 --> 00:02:51.020 equations. Okay, now you're losing me again. 00:02:52.060 --> 00:02:54.840 Basically it deals with finding the hidden symmetries 00:02:54.840 --> 00:02:57.740 for complex mathematical systems. So Thiel wants 00:02:57.740 --> 00:03:00.020 to take these highly abstract concepts, symmetries 00:03:00.020 --> 00:03:02.180 of equations and the fluid connectivity of shapes, 00:03:02.759 --> 00:03:04.659 and actually apply them to physical lumber and 00:03:04.659 --> 00:03:07.060 plaster. Which creates a beautiful, yet kind 00:03:07.060 --> 00:03:10.360 of terrifying friction. Because, I mean, in architecture, 00:03:10.680 --> 00:03:12.500 rigid distances and angles are literally the 00:03:12.500 --> 00:03:14.879 only things keeping a roof over your head. But 00:03:14.879 --> 00:03:17.479 Thiel takes this obsession to his friend Homer 00:03:17.479 --> 00:03:20.280 Bailey, and he pitches a house design that is 00:03:20.280 --> 00:03:22.919 just mind -boggling. He wants to build a house 00:03:22.919 --> 00:03:25.819 shaped like the unfolded net of a tesseract. 00:03:26.039 --> 00:03:27.930 Right. A tesseract being the four -dimensional 00:03:27.930 --> 00:03:31.830 equivalent of a cube. Just as a flat two -dimensional 00:03:31.830 --> 00:03:34.490 square can be extruded into a three -dimensional 00:03:34.490 --> 00:03:37.870 cube, a cube can be mathematically extended into 00:03:37.870 --> 00:03:40.949 a four -dimensional tesseract. Let me try to 00:03:40.949 --> 00:03:43.349 visualize this with an analogy for you. Imagine 00:03:43.349 --> 00:03:46.830 you take a regular, everyday cardboard box. If 00:03:46.830 --> 00:03:49.289 you take a box cutter and you slice along the 00:03:49.289 --> 00:03:52.129 vertical edges and lay it completely flat on 00:03:52.129 --> 00:03:55.569 the ground, it forms the shape of a cross. You 00:03:55.569 --> 00:03:58.310 have just taken a 3D object and unfolded it into 00:03:58.310 --> 00:04:02.030 a 2D plane. Teal is essentially doing that exact 00:04:02.030 --> 00:04:04.629 same process, but taking it one dimensional level 00:04:04.629 --> 00:04:07.509 higher. He wants to unfold a 4D object into our 00:04:07.509 --> 00:04:10.389 3D world. He even uses toothpicks and clay to 00:04:10.389 --> 00:04:12.849 map out the projections for his friend just to 00:04:12.849 --> 00:04:14.830 prove it can actually be done. And the structure 00:04:14.830 --> 00:04:17.290 they ultimately design and build is described 00:04:17.290 --> 00:04:20.949 as an inverted double cross. It consists of eight 00:04:20.949 --> 00:04:23.779 cubical rooms in total. So there is a central 00:04:23.779 --> 00:04:27.279 vertical stack of four cubes. Then surrounding 00:04:27.279 --> 00:04:29.540 the second cube from the bottom, there are four 00:04:29.540 --> 00:04:31.660 additional cubes jutting out in each cardinal 00:04:31.660 --> 00:04:34.500 direction. Like a cross. Yeah, this is the classic 00:04:34.500 --> 00:04:37.779 mathematically accurate 3D footprint of a 4D 00:04:37.779 --> 00:04:39.639 shape. But wait, I have to push back on this 00:04:39.639 --> 00:04:42.259 from a pure engineering standpoint. You have 00:04:42.259 --> 00:04:45.360 a central tower of four rooms and then four separate 00:04:45.360 --> 00:04:47.500 rooms just hanging off the sides of the second 00:04:47.500 --> 00:04:49.839 floor. Suspended in midair, basically. Yeah. 00:04:50.009 --> 00:04:52.910 Practically speaking, how does an inverted double 00:04:52.910 --> 00:04:55.569 cross of cubical rooms not just immediately tip 00:04:55.569 --> 00:04:58.050 over under its own weight like it sounds structurally 00:04:58.050 --> 00:05:00.930 impossible? What's fascinating here is that Heinlein 00:05:00.930 --> 00:05:03.430 entirely bypasses the deep engineering logistics 00:05:03.430 --> 00:05:08.410 by leaning into Thiel's eccentricities and his 00:05:08.410 --> 00:05:11.149 surprisingly grounded motivation. Wait, grounded? 00:05:11.449 --> 00:05:13.689 Yeah, I mean, Thiel isn't just some mad scientist 00:05:13.689 --> 00:05:15.649 trying to break physics for the fun of it. His 00:05:15.649 --> 00:05:17.589 motivation is highly humorous and practical. 00:05:18.379 --> 00:05:20.720 It's California real estate costs. Oh, of course. 00:05:20.980 --> 00:05:23.740 Right. By building this structure in this specific 00:05:23.740 --> 00:05:26.560 footprint, Teal is getting an eight -room house 00:05:26.560 --> 00:05:30.439 while only taking up the ground space and, crucially, 00:05:31.259 --> 00:05:33.180 paying for the land of a single cubicle room. 00:05:33.449 --> 00:05:36.589 That is, I mean, it's the ultimate density workaround. 00:05:36.850 --> 00:05:40.029 He is gaming the Los Angeles zoning laws using 00:05:40.029 --> 00:05:43.170 theoretical topology. Exactly. So they actually 00:05:43.170 --> 00:05:46.410 build this magnificent, impossible -looking 3D 00:05:46.410 --> 00:05:48.930 structure. The foundation is laid, the precarious 00:05:48.930 --> 00:05:51.360 rooms are stacked, but... You know, building 00:05:51.360 --> 00:05:53.839 a structurally dubious house in Southern California 00:05:53.839 --> 00:05:56.800 comes with a very specific geographic ticking 00:05:56.800 --> 00:05:59.500 clock. The fault lines. The San Andreas fault, 00:05:59.560 --> 00:06:01.160 to be exact. Right. So the night before Teal 00:06:01.160 --> 00:06:03.139 is scheduled to give his friend Homer and Homer's 00:06:03.139 --> 00:06:05.439 wife Matilda a grand tour of the finished house, 00:06:05.959 --> 00:06:08.180 a classic California earthquake strikes the region. 00:06:08.279 --> 00:06:10.439 A big one. And the next morning, when Teal, Homer 00:06:10.439 --> 00:06:12.800 and Matilda arrive at the property, the grand 00:06:12.800 --> 00:06:15.660 eight room inverted double cross is gone. Just 00:06:15.660 --> 00:06:18.370 vanished. Or at least it appears to be. From 00:06:18.370 --> 00:06:20.949 the outside, the house just looks like a single 00:06:20.949 --> 00:06:24.389 cubicle room sitting on the lot. The entire upper 00:06:24.389 --> 00:06:26.990 structure and those four cubes hanging off the 00:06:26.990 --> 00:06:29.730 sides have seemingly vanished into thin air. 00:06:29.810 --> 00:06:32.350 Right. So naturally, they go inside to see what 00:06:32.350 --> 00:06:35.149 happened, and inside the house, the laws of physics 00:06:35.149 --> 00:06:38.170 are entirely broken. Yeah, the spatial relationships 00:06:38.170 --> 00:06:41.009 between the rooms have gone completely mad. They 00:06:41.009 --> 00:06:43.050 find that all the upper floors are completely 00:06:43.050 --> 00:06:45.350 intact. Which is what? The eight rooms are still 00:06:45.350 --> 00:06:50.230 there? but the stairs now form a dizzying closed 00:06:50.230 --> 00:06:52.269 loop. Okay, I want you to picture this in your 00:06:52.269 --> 00:06:54.709 own home. Imagine walking up the stairs from 00:06:54.709 --> 00:06:56.730 your ground floor, reaching the second floor 00:06:56.730 --> 00:06:59.050 landing, deciding to take another flight up to 00:06:59.050 --> 00:07:01.230 the attic, and as you reach the top of those 00:07:01.230 --> 00:07:03.449 stairs, you step right back into your ground 00:07:03.449 --> 00:07:05.509 floor living room. It's totally paradoxical. 00:07:05.750 --> 00:07:08.149 You walk up and somehow you end up exactly below 00:07:08.149 --> 00:07:10.420 where you started. And it isn't just the stairs. 00:07:10.839 --> 00:07:12.899 All the doors and windows inside the house lead 00:07:12.899 --> 00:07:15.899 directly into other interior spaces. There is 00:07:15.899 --> 00:07:19.120 no exterior anymore. You open a front door expecting 00:07:19.120 --> 00:07:21.259 to look outside at the street and you are just 00:07:21.259 --> 00:07:23.639 looking into another hallway. They are entirely 00:07:23.639 --> 00:07:25.680 sealed off from the outside world. Here's where 00:07:25.680 --> 00:07:28.579 it gets really interesting. At one point, the 00:07:28.579 --> 00:07:31.319 trio looks down a long hallway and they are shocked 00:07:31.319 --> 00:07:34.759 to see their own backs. Yes. I cannot stop thinking 00:07:34.759 --> 00:07:37.560 about the sheer visual horror of that moment. 00:07:38.109 --> 00:07:40.389 Imagine standing in a hallway looking forward 00:07:40.389 --> 00:07:42.430 and seeing the back of your own head staring 00:07:42.430 --> 00:07:45.769 down the same hallway. But from a physics perspective, 00:07:45.889 --> 00:07:48.910 how does that work? Light travels in straight 00:07:48.910 --> 00:07:52.569 lines. How is a reader, or anyone for that matter, 00:07:53.009 --> 00:07:55.350 supposed to mentally map a space where a straight 00:07:55.350 --> 00:07:57.829 line of sight circles back on itself? Well, to 00:07:57.829 --> 00:07:59.550 understand that, we have to look at what the 00:07:59.550 --> 00:08:02.129 earthquake actually did. Okay. The earthquake 00:08:02.129 --> 00:08:04.720 provided this necessary cosmic jolt. It wasn't 00:08:04.720 --> 00:08:06.819 just shaking the ground. It essentially acted 00:08:06.819 --> 00:08:09.560 as the box cutter folding the cardboard box back 00:08:09.560 --> 00:08:12.220 together. Oh, wow. Yeah. It folded the 3D net 00:08:12.220 --> 00:08:15.300 of the house into an actual fully functional 00:08:15.300 --> 00:08:18.160 4D tesseract. So the rooms haven't moved in a 00:08:18.160 --> 00:08:20.939 way we can physically perceive, but their boundaries 00:08:20.939 --> 00:08:23.920 now intersect through the fourth dimension. Exactly 00:08:23.920 --> 00:08:27.910 that. Just as folding a 2D cardboard cross creates 00:08:27.910 --> 00:08:30.550 a 3D box where the flat edges suddenly touch 00:08:30.550 --> 00:08:33.529 in new ways, the earthquake folded their 3D rooms 00:08:33.529 --> 00:08:35.909 into a higher dimension. And the light bending. 00:08:36.250 --> 00:08:38.669 Right. Regarding the light. Light does travel 00:08:38.669 --> 00:08:41.610 in a straight line through space. But if space 00:08:41.610 --> 00:08:43.649 itself is curved and folded through a fourth 00:08:43.649 --> 00:08:46.590 dimension, that straight line wraps around. So 00:08:46.590 --> 00:08:49.629 like walking on a globe. Exactly. Much like how 00:08:49.629 --> 00:08:51.450 an airplane flying in a quote unquote straight 00:08:51.450 --> 00:08:53.909 line over the Earth's surface eventually circles 00:08:53.909 --> 00:08:56.299 the globe. When they look down the hallway and 00:08:56.299 --> 00:08:58.980 see their own backs, their line of sight is traveling 00:08:58.980 --> 00:09:01.419 through the curved space of a tesseract and wrapping 00:09:01.419 --> 00:09:04.019 right back to their own retinas. That is just 00:09:04.019 --> 00:09:06.539 wow. So they are entirely enclosed in a shape 00:09:06.539 --> 00:09:08.799 that has no outside, at least from their three 00:09:08.799 --> 00:09:11.059 -dimensional perspective. They are trapped in 00:09:11.059 --> 00:09:13.799 a loop where every single door leads to another 00:09:13.799 --> 00:09:16.620 hallway. By nightmare. Realizing they are essentially 00:09:16.620 --> 00:09:19.659 rats in a geometric maze, they decide they only 00:09:19.659 --> 00:09:22.179 have one option left to try and interact with 00:09:22.179 --> 00:09:24.440 the physical world, and that's the windows. And 00:09:24.440 --> 00:09:26.740 this is where the house shifts from being a mere 00:09:26.740 --> 00:09:30.960 architectural puzzle to quite literally a window 00:09:30.960 --> 00:09:34.500 into the multiverse. Teal tries the first seemingly 00:09:34.500 --> 00:09:37.440 logical exit. He opens a French window on the 00:09:37.440 --> 00:09:39.559 ground floor, fully expecting to step into the 00:09:39.559 --> 00:09:42.299 dining room, but instead... He falls awkwardly 00:09:42.299 --> 00:09:44.759 outside and lands face first in some shrubbery. 00:09:44.919 --> 00:09:48.120 Not very dignified. No, it is a very ungraceful 00:09:48.120 --> 00:09:50.980 exit for an architect of his stature. But it 00:09:50.980 --> 00:09:53.100 proves the house still has some tenuous connection 00:09:53.100 --> 00:09:56.139 to the real world. However, the real chaos happens 00:09:56.139 --> 00:09:58.679 when they explore the original top room of the 00:09:58.679 --> 00:10:01.059 house. Right, because the windows in this room 00:10:01.059 --> 00:10:03.980 no longer connect to mathematically logical spaces. 00:10:04.120 --> 00:10:06.720 They act like portals. Let me walk you through 00:10:06.720 --> 00:10:08.460 what they see out of these four windows, because 00:10:08.460 --> 00:10:11.210 the imagery is just wild. It really is. Window 00:10:11.210 --> 00:10:14.330 number one gives them a dizzying, vertigo -inducing 00:10:14.330 --> 00:10:16.750 view from high above the Empire State Building 00:10:16.750 --> 00:10:19.090 in New York. Across the entire country. Right. 00:10:19.470 --> 00:10:22.090 Then window number two reveals an upside -down 00:10:22.090 --> 00:10:25.289 view of a seascape, like the ocean is literally 00:10:25.289 --> 00:10:27.809 hanging above them. And then window number three 00:10:27.809 --> 00:10:30.730 is the most unsettling. It looks out into a place 00:10:30.730 --> 00:10:34.190 of absolute no space. The story describes it 00:10:34.190 --> 00:10:37.659 as having no color at all, not even black. just 00:10:37.659 --> 00:10:40.919 complete, incomprehensible nothingness. Yeah, 00:10:41.080 --> 00:10:42.860 that one gives me the chills. And finally, window 00:10:42.860 --> 00:10:46.500 number four looks out onto an unearthly, bizarre 00:10:46.500 --> 00:10:49.379 desert scene. This raises an important question 00:10:49.379 --> 00:10:53.279 about how we perceive our reality and how Heinlein 00:10:53.279 --> 00:10:55.960 uses these completely disconnected windows to 00:10:55.960 --> 00:10:58.899 illustrate a profound mathematical point. A higher 00:10:58.899 --> 00:11:02.600 dimension completely mocks our standard 3D understanding 00:11:02.600 --> 00:11:05.460 of geography. Because in 4D space, two points 00:11:05.460 --> 00:11:07.960 that are thousands of miles apart in 3D space 00:11:07.960 --> 00:11:10.620 might actually be adjacent. Think about a piece 00:11:10.620 --> 00:11:13.179 of paper. If you draw two dots on opposite ends 00:11:13.179 --> 00:11:15.159 of a long sheet of paper, they are far apart 00:11:15.159 --> 00:11:17.139 in two dimensions. Sure. But if you take that 00:11:17.139 --> 00:11:18.700 paper and fold it through the third dimension 00:11:18.700 --> 00:11:21.399 so the two dots touch, the distance between them 00:11:21.399 --> 00:11:24.299 becomes zero. Oh, I see. The house, now existing 00:11:24.299 --> 00:11:26.500 in four dimensions, is doing exactly that to 00:11:26.500 --> 00:11:29.179 our universe. It is intersecting different points 00:11:29.179 --> 00:11:32.360 of our 3D world simultaneously. So the Empire 00:11:32.360 --> 00:11:34.980 State Building, an upside -down ocean, and an 00:11:34.980 --> 00:11:38.100 unknown desert are all just next door from the 00:11:38.100 --> 00:11:40.059 perspective of a tesseract's adjacent faces. 00:11:40.639 --> 00:11:42.720 That perfectly explains the geographic jumps. 00:11:43.299 --> 00:11:46.259 But what about that third window, the no space? 00:11:46.679 --> 00:11:48.620 You know, it isn't described as black, but as 00:11:48.620 --> 00:11:50.889 an absence of everything. Well, that is Heinlein 00:11:50.889 --> 00:11:52.870 attempting to describe the sensory deprivation 00:11:52.870 --> 00:11:54.850 of looking outside the bounds of our universe 00:11:54.850 --> 00:11:57.889 entirely. Outside the universe. Yeah. If the 00:11:57.889 --> 00:12:00.970 house is a 4D object intersecting our 3D plane, 00:12:01.409 --> 00:12:03.309 some of its faces might not intersect with our 00:12:03.309 --> 00:12:06.470 universe at all. So looking out that window is 00:12:06.470 --> 00:12:08.929 looking into the void between dimensions. There 00:12:08.929 --> 00:12:11.730 is no light to be black. It is the visual equivalent 00:12:11.730 --> 00:12:14.629 of a blind spot. That is so conceptually heavy. 00:12:14.710 --> 00:12:17.230 And while they're trying to process this impossible 00:12:17.230 --> 00:12:19.370 panorama and the sheer existential dread, of 00:12:19.370 --> 00:12:22.909 the no space, a second earthquake hits. The house 00:12:22.909 --> 00:12:25.690 starts shaking violently in an absolute panic, 00:12:25.750 --> 00:12:28.710 realizing the geometry might shift into an even 00:12:28.710 --> 00:12:31.629 worse configuration or trap them in that void 00:12:31.629 --> 00:12:34.389 forever. They all dive head first through the 00:12:34.389 --> 00:12:37.210 desert window. It is a total leap of faith. And 00:12:37.210 --> 00:12:42.110 they land amid twisted, bizarre, tree -like vegetation. 00:12:42.269 --> 00:12:44.970 And the window they just jump through completely 00:12:44.970 --> 00:12:47.610 vanishes behind them. Right. So at first, looking 00:12:47.610 --> 00:12:49.470 at these weird trees, they are terrified that 00:12:49.470 --> 00:12:51.389 they have been transported to an alien planet. 00:12:52.029 --> 00:12:54.929 But then comes the twist. A passing truck driver 00:12:54.929 --> 00:12:57.570 spots them and casually informs them that they 00:12:57.570 --> 00:13:00.570 are simply in Joshua Tree National Park. I love 00:13:00.570 --> 00:13:03.129 that. Or, as the driver refers to it, Joshua 00:13:03.129 --> 00:13:05.149 Tree National Forest, which is just a couple 00:13:05.149 --> 00:13:08.250 of hours east of Los Angeles. So the desert window 00:13:08.250 --> 00:13:10.570 wasn't an alien world at all. It was just a fold 00:13:10.570 --> 00:13:12.779 in the map of Southern California. I have to 00:13:12.779 --> 00:13:15.019 point out the sheer absurdity of their reactions 00:13:15.019 --> 00:13:17.860 here though, especially Thiel's. I mean, he built 00:13:17.860 --> 00:13:20.259 a house that shatters the laws of reality, traps 00:13:20.259 --> 00:13:22.559 him in an infinite loop, shows him the absolute 00:13:22.559 --> 00:13:25.139 void of no space, and his response throughout 00:13:25.139 --> 00:13:27.480 the ordeal is to just excitedly go exploring. 00:13:27.559 --> 00:13:30.559 Like, is the man entirely sane? Well, Thiel's 00:13:30.559 --> 00:13:33.139 sanity isn't the issue. He's just adapting to 00:13:33.139 --> 00:13:36.019 the math way faster than his friends are. His 00:13:36.019 --> 00:13:38.220 obsession with the Picard -Vessio theory means 00:13:38.220 --> 00:13:40.080 he already accepts that the universe operates 00:13:40.080 --> 00:13:43.779 on unseen symmetries. To him, the house is just 00:13:43.779 --> 00:13:45.899 confirming his life's work. I guess that makes 00:13:45.899 --> 00:13:48.600 an eerie kind of sense. So our characters are 00:13:48.600 --> 00:13:51.200 safe among the Joshua trees, but what happens 00:13:51.200 --> 00:13:54.139 to the house itself? After finding their way 00:13:54.139 --> 00:13:56.480 back from the desert, they return to the original 00:13:56.480 --> 00:13:59.279 Hollywood construction site, but the house has 00:13:59.279 --> 00:14:01.679 completely vanished. There's not a single toothpick 00:14:01.679 --> 00:14:05.509 or brick left. Teal, ever the unfazed architect, 00:14:05.789 --> 00:14:08.190 nonchalantly deduces that during the second earthquake, 00:14:08.730 --> 00:14:10.690 the house must have fell through into another 00:14:10.690 --> 00:14:12.850 section of space. And falling through space is 00:14:12.850 --> 00:14:15.889 actually a brilliant way to describe a 4D movement. 00:14:16.309 --> 00:14:18.909 How so? Imagine a two -dimensional world, like 00:14:18.909 --> 00:14:21.809 a flat piece of paper. If a 3D sphere passes 00:14:21.809 --> 00:14:24.029 through that paper, the 2D inhabitants would 00:14:24.029 --> 00:14:26.850 just see a circle appear, grow larger, shrink, 00:14:26.970 --> 00:14:28.929 and then completely vanish. Oh, because they 00:14:28.929 --> 00:14:31.049 only see the slice of the sphere intersecting 00:14:31.049 --> 00:14:33.840 their plane. Exactly. The sphere didn't cease 00:14:33.840 --> 00:14:36.759 to exist. It just moved along a spatial axis 00:14:36.759 --> 00:14:39.659 the 2D world cannot perceive. The house did the 00:14:39.659 --> 00:14:42.159 exact same thing. It shifted slightly along the 00:14:42.159 --> 00:14:44.580 fourth -dimensional axis, effectively vanishing 00:14:44.580 --> 00:14:46.879 from our 3D coordinate system. And Teal's only 00:14:46.879 --> 00:14:49.139 regret. He casually notes that he really should 00:14:49.139 --> 00:14:51.700 have anchored it at the foundations, as if a 00:14:51.700 --> 00:14:53.659 few more steel bolts would have stopped a four 00:14:53.659 --> 00:14:56.279 -dimensional spatial fold. Right. The story ends 00:14:56.279 --> 00:14:59.080 wonderfully. Teal is already excitedly talking 00:14:59.080 --> 00:15:02.500 about a great new revolutionary idea for a house. 00:15:03.080 --> 00:15:05.100 Homer Bailey, who has been put through absolute 00:15:05.100 --> 00:15:07.980 dimensional hell, finally snaps and tries to 00:15:07.980 --> 00:15:10.960 punch Teal right in the face. But Teal effortlessly 00:15:10.960 --> 00:15:13.299 dodges the punch because, as the story notes, 00:15:13.320 --> 00:15:16.279 he was always a man of action. It is a comedic, 00:15:16.419 --> 00:15:19.419 perfectly paced ending to a genuinely mind bending 00:15:19.419 --> 00:15:22.019 premise. And there are a few incredible real 00:15:22.019 --> 00:15:24.460 world details attached to this story that really 00:15:24.460 --> 00:15:27.700 anchor it to history. The actual given for Quintus 00:15:27.700 --> 00:15:30.720 Teal's architectural nightmare is 8775 Lookout 00:15:30.720 --> 00:15:32.980 Mountain Avenue in Hollywood. Wait, really? Yeah. 00:15:33.820 --> 00:15:36.559 And that location is described in the story as 00:15:36.559 --> 00:15:39.200 being across the street from the hermit, the 00:15:39.200 --> 00:15:42.059 original hermit of Hollywood. What is amazing 00:15:42.059 --> 00:15:45.480 is that 8775 Lookout Mountain Avenue was actually 00:15:45.480 --> 00:15:47.659 across the street from Robert A. Heinlein's real 00:15:47.659 --> 00:15:50.100 -life home at the time he wrote the story. That's 00:15:50.100 --> 00:15:53.269 hilarious. He essentially placed this... reality 00:15:53.269 --> 00:15:56.610 breaking, world folding house right in his own 00:15:56.610 --> 00:15:59.210 front yard. It's a great Easter egg and beyond 00:15:59.210 --> 00:16:02.340 the fun trivia. This story had a massive cultural 00:16:02.340 --> 00:16:05.740 and scientific impact. In a 1978 article for 00:16:05.740 --> 00:16:07.980 the New York Times, the legendary astronomer 00:16:07.980 --> 00:16:11.220 Carl Sagan explicitly praised, and he built a 00:16:11.220 --> 00:16:14.000 crooked house. Wow, Carl Sagan. Yeah. Sagan stated 00:16:14.000 --> 00:16:16.860 that for many readers, this story was the first 00:16:16.860 --> 00:16:19.000 introduction to four -dimensional geometry that 00:16:19.000 --> 00:16:21.379 held any promise of comprehensibility. That quote 00:16:21.379 --> 00:16:23.419 from Sagan is so telling. It really highlights 00:16:23.419 --> 00:16:26.460 how fiction acts as a Trojan horse for hard science. 00:16:26.669 --> 00:16:29.210 If you hand the average person a dense textbook 00:16:29.210 --> 00:16:31.850 on geometric topology, they will likely close 00:16:31.850 --> 00:16:34.750 it in five minutes. The abstract math is simply 00:16:34.750 --> 00:16:38.149 too disconnected from human experience. But if 00:16:38.149 --> 00:16:40.850 you hide that exact same math inside a witty 00:16:40.850 --> 00:16:43.210 survival story about a greedy architect trapping 00:16:43.210 --> 00:16:45.710 his friends in a haunted geometry house, they 00:16:45.710 --> 00:16:47.929 are suddenly learning complex physics without 00:16:47.929 --> 00:16:50.669 even realizing it. If we connect this to the 00:16:50.669 --> 00:16:53.590 bigger picture, Sagan is hitting on a fundamental 00:16:53.590 --> 00:16:57.250 truth about human cognition. We are biologically 00:16:57.250 --> 00:17:00.250 wired for narrative. Yeah, we remember stories. 00:17:00.590 --> 00:17:03.250 Exactly. We remember cause and effect, struggle 00:17:03.250 --> 00:17:05.809 and resolution far better than we remember raw 00:17:05.809 --> 00:17:09.029 data. Heinlein took an abstract spatial concept 00:17:09.029 --> 00:17:11.410 and turned it into a sensory experience. You 00:17:11.410 --> 00:17:13.230 feel the vertigo of the Empire State window, 00:17:13.369 --> 00:17:15.650 you feel the claustrophobia of the looping stairs, 00:17:15.829 --> 00:17:17.869 and we see the ripple effects of this narrative 00:17:17.869 --> 00:17:20.690 approach in so many other works. Right, the Wikipedia 00:17:20.690 --> 00:17:23.309 article actually notes several spiritual successors 00:17:23.309 --> 00:17:26.390 and thematic cousins to Heinlein's story. Flatland, 00:17:26.450 --> 00:17:29.490 for example, the classic Victorian satire, uses 00:17:29.490 --> 00:17:31.349 the perspective of a two -dimensional square 00:17:31.349 --> 00:17:33.690 to force readers to comprehend the limitations 00:17:33.690 --> 00:17:36.089 of their own dimensions. And then you have popular 00:17:36.089 --> 00:17:39.609 television, Star Trek. Voyager features an episode 00:17:39.609 --> 00:17:41.650 called Twisted, where the ship encounters an 00:17:41.650 --> 00:17:44.630 anomaly that subjects the interior to mysterious, 00:17:44.750 --> 00:17:47.829 seemingly impossible physical reconfigurations. 00:17:48.009 --> 00:17:50.490 Like the Cricket House. Exactly. The corridor 00:17:50.490 --> 00:17:52.670 stopped making sense, and the crew cannot reach 00:17:52.670 --> 00:17:55.619 the bridge, the classic tesseract problem. There 00:17:55.619 --> 00:17:58.559 is also a 1950 short story mentioned called A 00:17:58.559 --> 00:18:01.720 Subway Named Mobius, where the Boston subway 00:18:01.720 --> 00:18:03.920 system accidentally acquires an extra -dimensional 00:18:03.920 --> 00:18:06.839 topology, causing a train to vanish into a mathematical 00:18:06.839 --> 00:18:09.539 fold. All of these stories take incredibly complex 00:18:09.539 --> 00:18:12.859 geometry and turn it into a comprehensible, gripping 00:18:12.859 --> 00:18:15.500 human problem. If you have ever sat in a classroom 00:18:15.500 --> 00:18:18.920 or been in a meeting feeling entirely overwhelmed 00:18:18.920 --> 00:18:20.960 while trying to learn a highly abstract concept, 00:18:21.319 --> 00:18:24.500 this is exactly why narrative matters. It isn't 00:18:24.500 --> 00:18:26.619 just entertainment. It is the ultimate tool for 00:18:26.619 --> 00:18:28.960 turning the inaccessible into the unforgettable. 00:18:29.279 --> 00:18:31.859 Beautifully said. When you attach a dry fact 00:18:31.859 --> 00:18:34.420 to a human struggle, even a funny one like an 00:18:34.420 --> 00:18:36.599 architect dodging a punch from his frustrated 00:18:36.599 --> 00:18:39.859 friend, it sticks in your brain forever. So what 00:18:39.859 --> 00:18:41.839 does this all mean? It means the next time you 00:18:41.839 --> 00:18:43.619 are trying to understand something difficult, 00:18:43.920 --> 00:18:46.619 try to find the story in it. Look for the quintis 00:18:46.619 --> 00:18:49.720 teal in the math. And if you find yourself house 00:18:49.720 --> 00:18:51.740 hunting in Los Angeles, maybe have a topologist 00:18:51.740 --> 00:18:53.519 look over the blueprints before you sign anything. 00:18:53.630 --> 00:18:55.789 Excellent advice. I want to leave you with one 00:18:55.789 --> 00:18:58.089 final thought today. Next time you are sitting 00:18:58.089 --> 00:19:00.990 in a perfectly square, normal room, well, take 00:19:00.990 --> 00:19:03.289 a moment to really look at the walls, the ceiling, 00:19:03.349 --> 00:19:06.450 and the floor around you. We assume these rigid 00:19:06.450 --> 00:19:09.349 right angles are the absolute truth of our universe. 00:19:09.710 --> 00:19:12.089 But what if our entire three -dimensional reality, 00:19:12.329 --> 00:19:15.130 everything we know and can touch, is just an 00:19:15.130 --> 00:19:18.190 unfolded blueprint of a much larger, unseen structure? 00:19:18.630 --> 00:19:20.289 And what if it's just waiting for the right kind 00:19:20.289 --> 00:19:22.269 of earthquake to finally snap it into its true 00:19:22.269 --> 00:19:24.609 shape? Until next time, keep diving deep.