Memory Warning

[RhoSigma]

I have 32 gb and do not recall ever getting an out of memory error. 

Honestly its more what I'm doing to the speed of the processing of an array. If you Dim an array (0 to 1000) is it bigger (in terms of memory set aside) than an array (250,250,500). Is there a correlation between the speed of processing an array and the amount of memory set aside for it?

The correlation is rather on the number of dimensions than on memory usage.
In normal usage each and every access to any array element runs through a function called array_check() for every dimension to verify the given index numbers are in the valid range as dimensioned.
Hence a(x,y,z) = 42 will call that function 3 times while a(x) = 42 will call it only once.

However, once your program runs error free, you may use $CHECKING:OFF to suppress these checks, but hell will open beneth your feet, if you try to access non-existing array elements then.