# A 2-dimensional geometry for biological time.

@article{Bailly2011A2G, title={A 2-dimensional geometry for biological time.}, author={F. Bailly and G. Longo and Ma{\"e}l Mont{\'e}vil}, journal={Progress in biophysics and molecular biology}, year={2011}, volume={106 3}, pages={ 474-84 } }

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal...) and properly biological (heart beating, respiration, metabolic...). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocksβ¦Β Expand

#### 34 Citations

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#### References

SHOWING 1-10 OF 53 REFERENCES

BIOLOGICAL ORGANIZATION AND ANTI-ENTROPY

- Computer Science
- 2009

This paper proposes a systemic perspective for some aspects of both phylogenesis and ontogenesis by expressing biological organization in terms of "anti-entropy", a notion to be defined below andβ¦ Expand

The neurogeometry of pinwheels as a sub-Riemannian contact structure

- Mathematics, Medicine
- Journal of Physiology-Paris
- 2003

The core of the paper consists first in showing that the horizontal cortico-cortical connections of V1 implement what the geometers call the contact structure of the fibration pi, and secondly in introducing an integrability condition and the integral curves associated with it. Expand

Orgons andbiolons in theoretical biology: Phenomenological analysis and quantum analogies

- Physics, Medicine
- Acta biotheoretica
- 1993

This paper defines two types of formal biological entities corresponding to biological levels of organization, thebiolons and theorgons, and examines then, in a rather speculative manner, how some characteristics of these entities may suggest analogies between properties of biological systems and some special features of quantum systems. Expand

The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization

- Biology, Medicine
- Journal of Experimental Biology
- 2005

A set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which are assumed to have invariant terminal units, are space-filling and are optimised by the process of natural selection are proposed. Expand

Body Size, Physiological Time, and Longevity of Homeothermic Animals

- Biology
- The Quarterly Review of Biology
- 1981

Life span, like the other scales of physiological time, may be regarded, not as a direct product of natural selection, but rather as an allometric consequence of other characteristics subjected to natural selection. Expand

The geometry of biological time

- Biology, Physics
- 1980

The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways is presented. Expand

The predominance of quarter-power scaling in biology

- Biology
- 2004

It is shown that interspecific variation in BMR, as well as field metabolic rates of mammals, and basal or standard metabolic rates for many other organisms, including vertebrates, invertebrates, protists and plants, all scale with exponents whose confidence intervals include 3 / 4 and exclude 2 / 3. Expand

A General Model for the Origin of Allometric Scaling Laws in Biology

- Medicine
- Science
- 1997

The model provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with data and predicts structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks. Expand

Scaling the amplitudes of the circadian pattern of resting oxygen consumption, body temperature and heart rate in mammals.

- Biology, Medicine
- Comparative biochemistry and physiology. Part A, Molecular & integrative physiology
- 2004

In mammals, despite the huge differences in physical characteristics, the amplitude of the circadian pattern is a fixed ( for V (O(2)) and HR), or almost fixed (for T(b), fraction of the 24-h mean value. Expand

Disentangling the dynamic core: a research program for a neurodynamics at the large-scale.

- Medicine
- Biological research
- 2003

A rough cartography of a comprehensive approach that offers a conceptual and mathematical framework to analyze spatio-temporal large-scale brain phenomena and emphasizes how these nonlinear methods can be applied, what property might be inferred from neuronal signals, and where one might productively proceed for the future. Expand