Fourth Dimensional Math?

hehehe...this is a serious question, isn't it?

of course there is math for higher dimensions. you can deal with as many dimensions as you want with math. 1,2,3,4,1 million....

in many cases we might think about high dimensional spaces but they don't necessarily have to correspond to spatial dimensions. for instance, we might consider objects that have a position (x,y,z) a time (t) a weight (w) and a length (l)...we could consider each property as another dimension and project it into a 6 dimensional space if we wanted to.

visualizing higher dimensions is, not surprisingly, problematic. but time, which is often considered the 4th dimension, makes visualizing things in 4D relatively simply, via an animation.

does the real world have 4 dimensions? yes of course there are the three spatial coordinates and time so that's at least 4. due to some complications in understanding and predicting Einstein's theory of general relativity, in an attempt to find a unified theory of the forces of the universe, there are some string theories that propose that the universe has as many as 11 (possibly more) dimensions...not my cup of tea though.

how many dimensions are there REALLY? hells if i know.

Your desire to confuse math and science with religion makes me uncomfortable, but I will answer you question.

In math you can have any number of dimensions (depending on the problem you are trying to solve). A 'Dimension' is part of a mathematical idea called a vector. A vector is just a set of numbers. You can think of the number of dimensions in a problem as the number of independent variables (variables that are not the result of calculations using other variables) .

Let's say you want to do calculations on the number of members on A2K at any given time. Any problem based on this would have two dimensions.

Now your question deals with a special set of dimensions we call "spatial" dimensions (because they deal with a position in space). In any problem dealing with our common experience there are three spacial dimensions (although what these dimensions are sometimes changes).

You can add any non-spatial dimension (i.e. indendent variable) as a fourth dimension. The dimension you may add depends on the problem you are trying to solve. Time is very often used. I have also used temperature and pressure as fourth dimensions (my specialty is Physics).

In some branches of Physics we posit additional spatial dimensions. Any fourth spatial dimension is certainly out of our common experience, but there is no mathematical reason that there couldn't be a spatial dimension.

Mathematicians have named the mathematical shape that is the four dimensional equivalent of a cube; the "tesseract".

But many problems use non-spatial dimensions, and any independent variable will do. I recently worked on a natural language analysis problem. This involves using statistics to try to get meaning from written text. In this problem there are big vectors which have one dimension for each word in the dictionary. I was doing a problem with around 60,000 dimensions (and we really use the term dimensions to describe this problem).

So to answer the question, the holy scripture could be extended to any number of dimensions. To make sense the additional dimensions would have to be non-spatial (to deal with the indenpendece reqirement) and probabaly have to be properties that could be assigned to a point in space;

How high and wide and deep and hot and bright and water-logged is the love of Christ would be a fine 6 dimensional formulation.

Re: Fourth Dimensional Math?

Only because that's often how many dimensions you need for modelling real-world problems. But math itself places no limits on the number of dimensions you can use. And linear algebra, the sub-discipline of math that deals with dimensions, has problems in any number of dimensions between one and infinity.

(Or in other words, what eBrown said. I should have read his reply before I answered.)