# Main Page

### From Biomatics.org

Welcome to *openfree* Biomatics home

The seamless development of mathematics and computation from a few clearly stated axioms and rules of inference in pure logic as embodied in an atomic/molecular medium. A gateway into the era of the molecule.

Biomatics is a discipline that networks biology, philosophy, mathematics, informatics, and mechanics to describe all biological information structures in holistic ways. It is also a short name of Systems Bioengineering. Unlike bioinformatics which is the science of information retrieval from textual data, biomatics involves engineering, cellular and molecular biology, and hardware. design and construction of biological objects and machineries under mathematical principles. |

The future of Biomatics and Biology

Biology and mathematics are perhaps the closest disciplines in science | Biomatics versus Omics

## Contents |

## Biomatics lab

Philosophical, mechanical, mathematical and informational understanding of Biome. A place to theorize,propose and work on projects in a collaborative environment.

## Applications

- Smart molecules
- Molecular Mechanics
- Development of artificial organs and appendages
- Development of human machine interfaces
- BioMaterials

- Molecular Mechanics
- Medical Biomatics
- BioMedical Imaging
- Protein Folding
- Molecular Codes
- Computational Oncology
- Computational Psychology and Psychiatry
- Biomatic Therapies
- Pharmacogenomics (Pharmacoepigenomics)
- Pharmacobiomatics
- DNA Microarray Analysis and Gene Expression Profiling
- Intervention of Aging

- BioMedical Imaging
- Molecular Electronics
- Forensic Biomatics
- Sports Biomatics
- Biomatic Political Systems
- Discovery of Mathematical Techniques and Theory

## Biological Mathematics or Principia BioMathematica

It is evident that some form of computation takes place in biological systems and indeed within single molecules. It thus follows that some form of mathematics occurs in these computations. Whether it be basic set theoretical concepts such as subsets, intersection, and union or more complex manipulations such as Fourier transforms of visual data.

The term “Biomatics” consists of a cross contraction of Biological Mathematics. The concept that is meant to be defined is the study of mathematics as it occurs in biological systems. This is in contrast to the concept of mathematical biology, which is the use of mathematics to describe or model biological systems.

A tentative definition might be: The seamless development of mathematics and computation from a few clearly stated axioms and rules of inference in pure logic as embodied in an atomic/molecular medium. Or, the study of "smart molecules".

### Background

Gottfried Leibniz considered the following thesis in the late 17th century: (Some or all of) mathematics can be reduced to formal logic.

It is often described as a two-part thesis.

1. All mathematical truths can be translated into logical truths.

2. All mathematical proofs can be recast as logical proofs.

In other words, that all mathematical truths and proofs can be restated in the vocabulary of logic.

By the late 1800s Karl Weierstrass, Richard Dedekind and Georg Cantor had all developed methods for defining the irrationals in terms of the rationals. Giuseppe Peano had also gone on to develop a theory of the rationals based on his now famous axioms for the natural numbers. Thus, by Gottlob Frege's (predicate calculus) day (1848-1925) it was generally recognized that a large portion of mathematics could be derived from a relatively small set of primitive notions

In 1910, Bertrand Russell and Alfred North Whitehead collaborated on Principia Mathematica, an attempt at a detailed deduction of mathematics from logic, which proved to be greatly influential yet controversial.

In Bertrand Russell's words, it is the logicist's goal "to show that all pure mathematics follows from purely logical premises and uses only concepts definable in logical terms".

As a result, the question of whether mathematics can be reduced to logic, or whether it can be reduced only to set theory, remains open. However, in light of modern theories of evolution, fractal geometry, physics, chemistry and computer science, some concepts are now self-evident. Given that biological systems perform some sort of mathematics, and acceptance of evolution, it follows that these mathematical systems have evolved and therefore must have started from some initial state. Biomatics further raises at least the possibility that all of mathematics may be based on elemental algebraic structures as embodied in such molecules as the amino acids.

### Intramolecular Computation

Consider an algebraic system embodied in a molecule consisting of N atoms. In the case where N = 3 we find the cube group (in terms of abstract algebra). (Note that N = 1 and N = 2 can represent groups as well).

Group theory (abstract algebra) is a well-developed branch of mathematics that provides many theorems and definitions. The key concept is that it describes, formally, a small (fundamental?) mathematical system consisting of a set and an operation on the members of that set. Could this then be nature’s way of evolving a system of mathematics and computation from a set of primitive notions? It seems it must inevitably be so, for ultimately what separates the different species, from viruses to man, is the complexity of the molecules that carry the blueprint for the ontogeny of the species.

As computer scientists, we seek and think in terms of information storage and processing. We seek to compare and contrast biological manifestations of computer science paradigms including:

Algorithms

Data structures

Theorems

Computer Architecture

Switching elements (gates)

Circuitry

Finite State Machines

Mathematics

Cubology

Hexagonology

We apply our knowledge and linguistics to analyzing, describing, and comparing natural phenomena to artificial processing. For example, image processing, graphics, Artificial Intelligence, are well-developed bodies of scientific endeavors, with many potential candidate concepts.

**See Also**

**External Links**

BioMathematics.org

Biomatics Inc. Japan: Bioinformatics company in Japan. It is nothing much to do with Biomatics.org

SystemsBiology Institute

Biomatics Inc.: Digital Imaging analysis company.

Biomatics Germany: Web development for life science.

Self organization FAQ

Creation of artificial life forms

Wim Hordijk's home page

CALResCo, home of this FAQ

Links to SOS online papers/sites

Complex Systems virtual library

Complex Adaptive Systems

VCU complexity research group

Artificial Life links

Complex Systems & Chaos Theory

SOS bib

Measures of Complexity

Self-org measures

SOS on the Web

What is complexity ?

The Avida Group

Santa Fe Institute

Biology's Gift to a Complex World (The Scientist, 9/2008)

Machine Nature (New Scientist, 28/9/2002)

Computer Design Meets Darwin (Science, 26/9/1997)

Bioism.org | Funktopia | Biolicense | Bioreligion.org | Omics.org | Matics.org | Biocompany.net