By A. O. Wallat
Bath Time Thoughts #2 – Visualising 4-Dimensional Objects. Original Audioplay first appeared on http://www.holtandwallt.com
[Wallt] Good evening. Turn on the taps, light some candles, test the temperature with your elbows and dip your toes in the bath as you let your mind dip out, just for a moment, for another episode of bath time thoughts.
This time you won’t be alone in the bath with me. We are joined by..uh…
[Hector] ‘ector.
[Wallt] Yes, quite right. As the heat slowly cooks your brain, Hector and I will guide you through the obscure task of visualising four dimensional objects.
[Hector] So please consider the following: a rambling analogy to help us look at experiences of time.
[Wallt] ‘ector, why don’t you ‘op in?
[Hector] ‘hop, what is ‘op? Oh, is there space?
[Wallt] Why yes of course, let me just…
[Hector] Ah, merci. Let me start again. Putin Right, Merde. Supposed we live in a place with 4 dimensions. How do you perceive a 4 dimensional object? Right now we are in the bath, we are 3D people sitting in a 3D shape but there is time too, the fourth dimension. As time passes, the candles melt, change shape and we change positions. 4 Dimensions, do you agree?
[Wallt] Yes.
[Hector] Well, what does this look like to someone who say, lives only in 3 dimensions?
[Wallt] This? What me and you in a 3D bath, with time passing?
[Hector] Yes with time passing, this is important. You me, drinking a little champagne, moving left and right, not staying the same at all. How does it look to a person who is frozen in time, who cannot perceive time…at all, someone who exists in 3 dimensions only.
[Wallt] I don’t know where to start.
[Hector] Right, exactly. Well let us pretend our person is this cube of soap. Our little person does not know when or where to start.
[Wallt] OK, so the closest analogy I can come up with is to consider this little person is playing the same game. He says he lives in 3 dimensions, and he tries to consider what life is like for a 2 dimensional person who is trying to think of 3D life.
[Hector] Bien, very good. Muah (kisses). So this little person, our 3D soap person, we will say is an ‘appy cube?
[Wallt] Happy.
[Hector] Yes, ‘appy. And from the candle, light shines a light on him – don’t forget he is a cube. What does he see?
[Wallt] Well, he sees a shadow…and the shadow is an object the 2D person can comprehend. Let’s call them paper.
[Hector] Non, non, I mean, yes, there is a shadow, but let’s call the 2D person wafer. Paper and bath is not good. And wafer is wafer thin… eh?
[Wallt] OK, so wafer understands a shadow but doesn’t know the true form behind the shadow.
[Hector] Very good, uh, you had some practice eh? Now. Tell me, what shape is the shadow of the cube?
[Wallt] Square?
[Hector] Yes, but what if the angle of light, is changed – maybe the candle melts a little?
[Wallt] Rectangle, rhombus, parallelogram, are there others? I honestly don’t know, could you even form a triangle from a particular angle. I guess it depends on the position of light.
[Hector] So what does this mean?
[Hector] Well, I tell you, some oddities are notable.
First: That any 3D object we perceive is the shadow of its 4D self. Just like our little sentient 2D wafer sees the 2D shadow of the 3D cube. We see 3D shapes but they are the shadows of 4D objects.
Second point: One seemingly 3D object can appear totally different in the 2D world depending on the angle of light. Maybe the shadow is square, maybe parallelogram.
[Wallt] Then, this suggests that the 4D versions of ourselves are constant, but… the 3D self changes depending on the viewing angle or the position of light?
Hector] And, in our case, it is not light that changes the viewing angle but time.
[Hector] I am pleased, you are a good bath time thinker, my friend. So then, let’s take a wristwatch as an example. In our world, before dawn, the watch is not even a thing. It is little pieces of plastic and metal in a primordial soup called the earth. As light breaks, the watch is assembled. At midday, where the light is highest, it is turned on, a fully functional wristwatch. Then as the sun sets, the strap breaks, at night it is a dead battery and thrown into recycling and incinerated. Heated particles dashed to the atmosphere.
But in the 4D world, it is constant. Yes it was on for a while, when it had a little electricity flowing, then off. Yes it was nothing but separated particles, then whole, then separated particles.
[Wallt] But, in the 4D world, you are saying, does that make any difference – that change in time is a moving shadow?
[Wallt] Does this account for ageing? Or are you saying that people, or in fact all living things are fundamentally the same unchanging objects and though the light moves at the same time for all, depending on their experience of the position and angle of light, they each appear different and then that causes a different shape to be seen?
[Hector] Oui, oui oui. This is what I like to think about.
[Wallt] But what if you have two sources of light and 1 cube?
[Hector] Then there are 2 shadows.
[Wallt] Well, in the analogy, what does that mean?
[Hector] Je ne sais pas. I don’t know.
[Wallt] Well what if you have a shadow that exists across different dimensions, in other words the shadow lands on a corner where the wall and floor meet – a shadow both horizontal and vertical at the same time.
[Hector] What the hell does that mean?
[Wallt] I don’t know…Also, what if you have 2 cubes of different sizes (one large, one small) on the same axle and a shadow rests on the face of the axel bound cubes. If the axles spin at the same rate, but much more of the smaller cube is covered by the shadow than the large cube, do the shadows on both cubes move at different rates? Do the shadows change shape at different rates?
[Hector] What does it mean if there are thousands of cubes on the same axle causing shadows on their neighbours?
[Hector] I guess you can see that the analogy seems to explode into a disorienting array of possibilities and unfathomable… how you say… nonsense.
[Wallt] Is any of this useful to anyone?
[Hector] I mean it is fun, no? But I don’t know if the people in the physics world know how many dimensions there truly are in “reality”.
[Wallt] Yes, do they know or is it predicted that there are 11 or 12 dimensions beyond a shadow of a doubt or is it debatable?
[Hector] Are analogies worth anything?
[Wallt] I mean, what if there are infinite points of light shining from every conceivable direction?
[Hector] Well, uhh in this case does the object even have a shadow?
[Wallt]What if you have a pane of glass between the cube and the floor so that the shadow appears twice? Does that mean anything?
[Hector] I think, all this casts, is severe doubt, on the efficacies of analogies.
[Wallt] Mmm…
[Hector] That analogies are highly deceptive–
[Wallt] Or that we are highly suggestible depending on how the story is formulated.
[Wallt]
[Hector]
Please, could anyone shed some light on this?
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