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The Two-Dimensional Arrow of Biological Time

Biological time is best described by a two-dimensional surface that takes the shape of a second order helix, says a new theory.

It’s tempting to think of time as a linear sequence of events best captured by a straight line, the x-axis on a graph for example. But physicists have never felt constrained by such a definition, on the contrary they’ve never hesitated to mould time to their own ends.

In thermodynamics, for example, the arrow of time comes about because of irreversible phenomena such as phase transitions, bifurcations and chaos. In relativity, space and time are as one, and Minkowski, in his famous formulation, used the idea of a ‘causality cone’ to explain the correlation between physical objects.

In quantum mechanics, the notion of time becomes even more strange. Time is sometimes two-dimensional, sometimes reversible to maintain CPT (charge, parity, time) symmetry and at other times discontinuous and fractal-like.

In short, physicists reformulate time in whatever suits them, or at least in whatever way provides the best predictive or explanatory power.

So why shouldn’t biologists try the same trick? Today, they get their chance thanks to some innovative thinking by Giuseppe Longo at the Ecole Normale Superieure in Paris et deux amis.

Longo and co argue that biological entities require a non-linear formulation of time because their existence is characterised by rhythms and cycles rather than linear processes.

So the team has formulated a notion of time which captures the essential rhythms and cycles of biology.

The idea is to take a standard linear representation of time and to represent a rhythm using a second, perpendicular dimension of time. Being cyclical, this dimension takes the form an angle, represented by a short perpendicular rotating line, like the hand of a clock.

Extra rhythms can simply be added to this perpendicular line. So a circadian rhythm might take close to 24 hours to rotate, while on top of this the rhythms of breathing and heartbeats take just seconds.

The result is that a point in this ‘time-space’ moves along the surface of a kind of two-dimensional helicoid (see picture above). Longo and co call this shape a second order helix.

That’s all very well. The question is what explanatory and predictive powers does this representation bring. How useful is it?

Longo and co say first that it provides a visual representation of the scale of life’s rhythms and periodicities which make comparisons between and within species particularly easy.

They plot, for example, the periodicity of heartbeats during sleep and wakefulness saying that the new representation of biological time makes it easy to distinguish important features at a glance.

They also look at the difference between biological aging and physical aging, showing how biological aging can tend to zero in certain circumstances while physical aging continues unabated, such as during hibernation.

They also raise the question of whether biological aging can go into reverse while physical aging continues, a phenomenon that appears to occur in certain types of stem cells.

Finally, they examine that difference in periodicities between the young and old, suggesting (not entirely convincingly) that this may explain the difference in the perception of time between young and old people ie that time passes slowly for the young and quickly for the old.

So there’s certainly some useful explanatory power in this formulation of biological time–it looks a powerful new way to represent biological data.

Whether it has any predictive power is another question entirely and one that Longo and co must surely be puzzling over.

What they need now is to show that this new approach provides genuinely new insights into the problems of biology and aging, something they don’t quite manage that in this paper.

Ref: A 2-dimensional Geometry for Biological Time

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