#Tesseract 4d shapes how to#

The inverse square law which governs gravitational attraction between 2 objects would be violated on the microscopic level if there were extra dimensions – as the gravitational force would “leak out” into these other dimensions. The current theory expects that the extra dimensions are themselves incredibly small – and as such we would only notice their effects on an incredibly small scale. Michio Kaku has a short video (with transcript) here and Brian Greene also has a number of good videos on the subject.Īll of which brings us onto empirical testing – if a mathematical theory can not be empirically tested then does it differ from a belief? Well, interestingly this theory can be tested – by looking for potential violations to the gravitational inverse square law. It might also be worth touching on why mathematicians believe there might be 11 dimensions.

#Tesseract 4d shapes how to#

It’s also possible to create a 3 dimensional representation of a Tesseract using cocktail sticks – you simply need to make 2 cubes, and then connect one vertex in each cube to the other as in the diagram below:įor a more involved discussion (it gets quite involved!) on imagining extra dimensions, this 10 minute cartoon takes us through how to imagine 10 dimensions. The page allows you to model 1, then 2, then 3 dimensional traces – each time representing a higher dimensional cube. We can see an Autograph demonstration of what the fourth dimensional cube looks like here. Next we can move onto the Hypercube (or Tesseract). In both cases have students predict what they think will happen. Next start again with a new strip, but this time start cutting from nearer the edge (around 1/3 in). Next, cut along the middle of the strip and see the resulting shape. There are some nice activities to do with Mobius strips – first take a pen and demonstrate that you can cover all of the strip without lifting the pen. Mobius strips are a good gateway into the weird world of topology – as they are 2D shapes with only 1 side. This imagines reality as experienced by two dimensional beings. Mathematical models have consistently been shown to be accurate in describing reality, but when they predict a reality that is outside our realm of experience then what should we believe? Our senses? Our intuition? Or the mathematical models?Ĭarl Sagan produced a great introduction to the idea of extra dimensions based on the Flatland novel.

Neat, huh? See also: Flatland: A Romance of Many Dimensions, a sci-fi story from 1884.ĭid you know that Carl Sagan came up with ideas for a Contact video game? Or that he didn't like the Space Shuttle program? Head here to find out more facts about Carl Sagan.Imagining extra dimensions is a fantastic ToK topic – it is something which seems counter-intuitively false, something which we have no empirical evidence to support, and yet it is something which seems to fit the latest mathematical models on string theory (which requires 11 dimensions). The video is only seven minutes long - have a look: He explains dimensionality as a notion, expanding from a two-dimensional 'flatland' to our three-dimensional world, and onward to the fourth dimension. I stumbled across a wonderful video of Carl Sagan explaining the fourth dimension in a way that anyone can understand. Anyway, let's not get carried away with tesseracts just yet. You may have heard of the fourth dimension via Madeleine L'Engle's A Wrinkle in Time, which mentioned the tesseract, a four-dimensional 'hypercube.' In L'Engle's work, the tesseract had properties that could bend space-time, though a real tesseract would simply be an object in four-dimensional space. But scientists and mathematicians have long gone three dimensions using thought experiments, conceptualizing a fourth dimension - and of course, to many more dimensions beyond. We're all pretty familiar with the first three dimensions - after all, we experience those dimensions daily as we move about our world.