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Name: davida
Status: N/a
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
In the response to the original article, Sam Bowen stated that it is not difficult to imagine 4-dimensional objects but it is difficult to think about what they look like. My question is what is the difference between imagining them and thinking about what they look like? Sure its easy to write equations for 4- dimensional objects that are representable by functions but take for example a hyper-cube. How would one go about finding what the projections of this would be onto a 2-dimensional surface? I have seen the projection of a hyper-cube onto 2-dimensions but cant imagine what the actual hyper-cube would 'look like.' On the note of 4 dimensional space-time, I do realize that we live in a 4 dimensional universe, but I am talking about objects that are in 'mathematical' four space. It seems that since we experience time instantaneously and that it seems to be uni-directional that it is different from the other 3 dimensions. I still think that it is impossible to 'see' anything that exists in four 'physical' dimensions since we exist in only 3 'physical' dimensions, the temporal dimension would not seem to help in realizing what these four dimensional objects really are.


Replies:
I guess we have a semantic problem. I was considering problems in spaces larger than 3 where the dimensions might be different products or activities and we might be trying to minimize or maximize some function over these spaces. Developing some imagination about what the volume in that space can aid in the seeking of a solution. If you are insisting on four physical dimensions I would have to agree with your original statement that these cannot be seen. In relativity there are often needs to calculate integrals over time and space and that leads to four dimensional integrals and their evaluation. While this is only mathematics it is very "real".

Sam Bowen


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