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**Attempt to unify all science information into mathematical objects**

Hi Kea:

and CarlB:

and all others:

I admire your knowledge of bio-mathematics.

I search for the unification with other types of mathematics.

I suspect this will result in a mathematical game of energy exchanges through attractors and dissipators of various gauges.

I prefer your tree branch analogy [of this thread] to your pair of pants analogy [of the Application of topology in nature - auditory energy mapping thread].

https://www.physicsforums.com/showthread.php?t=134962

Such an analogy, may allow physicists [particle, astro, geo, bio, et al], mathematicians, biologists, physicians and engineers of all types, to make translations among disciplines easier, if all science information is translated into mathematical objects.

I am greatly influenced by Nobel Laureate Christian De Duve, most recently.

‘Singularities: Landmarks on the Pathways of Life’ [Cambridge University Press]:

p161 - “ ... be they microbes, plants, fungi, or animals, including humans. It is clear that such similarities can be explained only ...”

p171 - “... Eukaryotes, which may be unicellular (protists) or multicellular (plants, fungi, and animals) ...”

p186 - “,,, eventually, with all plants, fungi and animals; without it we wouldn’t be around ...”

p214 - “... all fungi, and all animals are derived each from a single common ancestor ...”

I only have read the abstract of

“From sphere to torus: A topological view of the metazoan body plan”

Harald Jockusch (Corresponding author)

Email: h.jockusch@uni-bielefeld.de

Pages 57-65

Saturday, June 17, 2006

Journal Bulletin of Mathematical Biology

Publisher Springer New York

ISSN 0092-8240 (Print) 1522-9602 (Online)

Subject Mathematics and Statistics

Issue Volume 65, Number 1 / January, 2003

DOI 10.1006/bulm.2002.0319

Abstract From the viewpoint of mathematical topology, membrane systems in intact living cells can be described as closed and orientable surfaces, i.e., as surfaces with two sides and no boundary lines so that an ‘inside’ and an ‘outside’ can be distinguished. Usually, biomembranes represent topological spheres, often one embedded in another one. Toroidal membranes are occasionally observed, e.g., in specialized structures of plant cells like the prolamellar body. Here, we propose that rules analogous to those that govern the topology of biomembranes hold for the epithelial cell sheets that cover anatomically external as well as internal surfaces of multicellular animals. We suggest to study the emergence of morphological complexity during metazoan development using concepts from mathematical topology, and propose experimental analyses of those topological transitions that appear to be relevant in development and evolution.

Based on a lecture held by H J at the Max Planck-Institute for Physics of Complex Systems, Dresden, 26 April 2001.

http://www.springerlink.com/content/47q7pvkr03882252/

I tend to probably oversimplify [and perhaps confuse] the possible relationships in this effort to demonstrate that evolutionary biology has apparently used experimental mathematics [likely related to the GUT / TOE quest of QM and GR] that we as humans now attempt to understand.

These manifolds from different disciplines probably differ primarily in gauge with similar but not necessarily identical structure and function.

I find that my math ability is like using a foreign language - some understanding with visual aids and a dictionary or reference text - but clearly unable to express thoughts attempting to relate one discipline to another in the language of mathematics [I am trying to improve.

Analogies?:

A tree trunk from the upper most root to the lower most limb can have its tree rings almost perfectly represented by cylindrical coordinate tensor calculus.

Reference diagram - JD Fehribach, Vector & Tensor Calculus, Worcester Polytechnic Institute

http://www.math.wpi.edu/Course_Materials/MA2251C99/images/cylndrcl.gif

The only thing that appears to prevent perfect symmetry is a lack of background independence. Tree ring growth is influenced by magneto, gas, liquid and solid influences - sources of actual perturbations.

Consider the whole tree: roots, cylindrical trunk [with pores?], branches and leaves.

Reference diagram - from VA TECH

http://fwie.fw.vt.edu/rhgiles/trevey/img/TreeBasic2.gif [Broken]

Omitting the leaves for a moment, we appear to have a smooth manifold, bounded but infinite [from the fractal perspective] in surface area with a finite volume.

Add leaves, the surface area may almost be doubled [more than one infinity as per George Cantor] and the volume possibly also doubled but still finite.

For simplicity, again omit the leaves.

Technically this tree manifold may be transformed into a fungus manifold.

Fungi appear to be intermediate to flora and fauna.

Reference diagram - from Sydney [text with links to some pictures]

http://bugs.bio.usyd.edu.au/Mycology/StructureFunction/hyphalStructure.shtml [Broken]

The fungus can be transformed into porifera manifold.

The roots become a holdfast.

The branches [become reduced but tend to reappear in Cnidaria] with inflow / outflow pores as ostia and osculum [or branched oscula].

Cnidaria life cycle more tree-like

Reference diagram - Western Kentucky U

Porifera with Cnidaria life cycle - holdfast demonstrated but not named

http://asm.wku.edu/faculty/Lienesch/225/225lab2.html

Reference diagram - U Miami

Porifera [magnified illustrations] holdfast not demonstrated

http://www.bio.miami.edu/dana/pix/spongeanatomy.jpg

Other body plans omitted for some brevity.

Eventually transformation to sequentially segmented genus-1 toroid manifolds of vertebrate, chordates with respect to the gastrointestinal tract.

Holdfast becomes sphincter.

Genus-3 torus of nares and mouth with lungs more like porifera; oral cavity shared with GI torus.

Reference diagram - Central Middlesex Hospital, London, England

http://www.ibs-research-update.org.uk/ibs/digestion1ie4.html

Nerves and blood vessel are branch-like in providing nutrients and information to various organs and single cells. This symmetry is relatively reversed from flora.

Reference diagram - Netterimages.com

http://www.netterimages.com/images/vpv/000/000/004/4621-0550x0350.jpg [Broken]

These life manifolds can interact with earth [magneto, gas, liquid and solid] manifolds and star [sun] manifolds.

The finest roots and branches [capillaries] appear to serve as gauge interfaces - allowing trans-membrane flow; while coarser branches allow for a generally one way cis-membrane flow [regurgitation may occur, usually in illness].

Most of life might be considered as attractors [contained energy] with a predator v prey [dissipator or uncontained energy] relationship.

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