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This week's poser: shadows of the 4th dimension

Another vexed question only you can answer...

It started off as a pub conversation. One of those rare, rambling pub conversations where every topic you touch on seems to be full of wonder or mystery... A friend of mine was telling me about a documentary he’d seen that was all about the 4th dimension. Everything he told me about it was fascinating, but the bit that rally stood out was the idea that the shadow of an object is always one dimension less than the object casting the shadow. Thus if you shine a light on a 3-D object like a cube you get a two-dimensional shadow something like this:

It follows therefore, that you should be able to construct the shadow cast by a four-dimensional object in three dimensions. This concept is well known in physics and such a shadow is called a tesseract:

I think the idea is that if you could make all the lines in the tesseract run at right angles to each other, you’d have a four-dimensional object, just as if all the lines in the two-dimensional shadow were at right angles you’d have a 3-D cube.


Now all that’s well and good. It’s just that I’ve still got few outstanding questions: If a four-dimensional object were to appear in our midst, would we even be able to see it? Or would we be able to see only part of it? What would it look like? Is it possible to conceive what it would be like to exist in a two-dimensional world? Has anyone got a picture of an actual 3-D tesseract, rather than a two-dimensional image like the one above?


These are questions only you can answer. And after your less than impressive showing with the Magic Rectangle (see Issue One), I’m afraid you’ve got a lot to prove. So- off you pop. And don’t come back till you’ve got results. Otherwise I’m afraid it’s going to be an extended spell on the three-dimensional Naughty Step for you...

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