Mathematician suggests extra dimensions are time-like

The analytical structure underlying the spinorial theory can be represented visually. The structure is a Xi-transform, which moves between the three spaces in the directions given by the bendings of the upper case Greek letter Xi. The distorted squares represent the wave operator. The product of a wave operator and a Xi transform, taken in any order, is zero. Image credit: Erin Sparling.
In a recent study, mathematician George Sparling of the University of Pittsburgh examines a fundamental question pondered since the time of Pythagoras, and still vexing scientists today: what is the nature of space and time? After analyzing different perspectives, Sparling offers an alternative idea: space-time may have six dimensions, with the extra two being time-like.

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Sparling’s paper, which was published in the Proceedings of the Royal Society A, lays the groundwork for his theory. He explains how spatial dimensions contain positive signs (e.g., Pythagoras’ 3D space is expressed as the sum of the squares of the intervals in three directions, x, y, and z). Minkowski’s time-like dimension, on the other hand, combines these three dimensions with the square of time displacement, which contains an overall negative sign.
“In three dimensions, the formula reads s2 = x2 + y2 + z2,” Sparling explained to PhysOrg.com. “Our standard spacetime has four dimensions, but the formula has a critical minus sign: s2 = x2 + y2 + z2 - t2. The Lithuanian Hermann Minkowski invented this idea, which was published just six weeks before he died. Indeed, [Sir Roger] Penrose, for one, says that special relativity was not a finished theory until Minkowski's famous Raum und Zeit [‘Space and Time’] paper.”
Up until now, Sparling explains, most theories concerning extra dimensions have dealt with space-like rather than time-like dimensions, which results in a “hyperbolic” rather than an “ultra-hyperbolic” geometry. However, Sparling notes that there are no a priori arguments for a hyperbolic geometry, and he looks into the possibility of a “spinorial” theory of physics, where six dimensions of space-time arise naturally.
“In general dimensions, we say that the space-time is hyperbolic if there is only one minus sign in the formula for s2,” he said. “So, for example, in the ten dimensions of superstring theory, there are nine spatial dimensions with plus signs and one minus sign. Only in that situation is there a clear-cut distinction between the future and the past.”