Negative dimentions?

Looking in Scientific American magazine, they announced the possibility of negative energy(ie antigravity) and thus
exotic matter (with anti-mass…NOT antimatter).
This got me thinking…If there is negative energy and negative matter…why not negative dimensions?

if gravity=lengthwidthdepthtime,
antigravity= -length

Negative matter isn’t too hard to visualize. Take a mirror image of matter (reverse its spin, give it energy that behaves in a opposite fashion from ‘normal’ matter and so on) and you should have it. Whether such a thing is physically possible is another thing entirely.

However, I have a hard time visualizing negative dimensions at all. I mean, how can you have length in a negative fashion? A line may have a length ever decreasing towards zero length but once there how would it have less than zero length?

About the only thing I can conceptualize as a negative dimension is one in which the arrow of time is reversed so fire unburns things, glasses unbreak and so on (this assumes time is the fourth dimension).