I will be gradually moving this blog over to my new site DrJaeger.com. Thanks to everyone for the great feedback I received over the last years on my theoretical work on Yin and Yang. I will continue to write about these two mighty forces in my new blog, and I hope we will meet there again soon.

Yours truly,

Stefan Jaeger

*The Neurological Principle: a Mathematical Theory of Yin-Yang and Body-Mind Unity Motivated by Neural Signal Transduction*

has been rescheduled to **February 27**. The location and time will be the same, only the room has changed: **Building 50 (first floor), Room 1227 / 1233, 3:30-5:00 pm**. I will be available for discussions before and after the talk.

A Mathematical Theory of Yin-Yang and

Body-Mind Unity Motivated by Neural Signal Transduction

** ****by**

** ****Dr. Stefan Jaeger
**

**Address: 38A / 9N912B
**

**Date: Thursday, ****February 27, 2014****
**

**KEY WORDS****: Yin-Yang, Chinese medicine, neural networks, information theory, theory of relativity, uncertainty principle, anthropic principle, fine-structure constant, golden ratio, acupuncture**

**PRESENTATION DESCRIPTION****: Bridging the gap between western medicine and traditional healing methods has turned out to be a formidable challenge. For example, the abstract philosophical ideas in Chinese medicine are a major obstacle for western researchers trying to find a more concrete explanation of the efficacy of traditional healing methods, such as acupuncture. Among the prominent concepts that have eluded western researchers so far are Yin and Yang, the two opposite forces that pervade the universe and that manifest in every object and process. Starting from the omnipresent black-and-white Yin-Yang symbol, this talk presents a formal mathematical framework for Yin and Yang. In particular, the talk shows how the Yin-Yang symbol can be rendered by following the sun’s shadow throughout the year. Based on this insight, the talk will elaborate the formal Yin-Yang model into an information-theoretical model of synaptic signal transduction. It turns out that several physical phenomena, such as time dilation in Einstein’s theory of relativity or Heisenberg’s uncertainty principle, can be related to this model. The talk will also show how two well-known mathematical constants, namely the golden ratio and the fine-structure constant, can be derived from the proposed model, either directly or as a close approximation. Both constants play meaningful roles in physics, among other areas. These observations suggest that Yin and Yang play an important role in neuroscience as well as physics, combining principles of different worlds in a common framework. The talk therefore proposes the neurological principle as a new principle that subsumes existing principles in a more general idea. The neurological principle considers body and mind as a unity, arguing that the physical universe is as much a result of our brain as our brain is the product of the laws governing our universe. The mathematical foundation of the neurological principle lends itself to analytical studies that are arguably more in accordance with western approaches to medicine and physics. This opens new research alleys and makes body-mind unity accessible to rigorous scientific investigation. A formalization of ancient philosophical concepts and traditional healing methods, as presented in this talk, is essential to reaching acceptance in modern science.**

**SPEAKER****:**** Dr. Stefan Jaeger is a Visiting Scientist at the Lister Hill National Center for Biomedical Communications at the United States National Library of Medicine (NLM), National Institutes of Health (NIH). He received his diploma in computer science from University of Kaiserslautern and his PhD from University of Freiburg, Germany. Dr. Jaeger has an international research background, both in academia and industry. He has held, among others, positions at Chinese Academy of Sciences, University of Maryland, Tokyo University of Agri. & Tech., University of Karlsruhe, and Daimler. Dr. Jaeger was instrumental in developing several state-of-the-art character classifiers for postal automation, document processing, and human-computer interaction, in Latin and Asian scripts. More recently, he has implemented methods for cell classification and tracking. At NIH, he is developing a screening system for detecting tuberculosis and other lung diseases in chest X-rays. His research interests include biomedical imaging, medical informatics, pattern recognition, machine learning, and Chinese medicine. He has about sixty publications in these areas, several of which received best paper awards and nominations, including two patents.**

*** DIRECTIONS TO BUILDING 50 ROOM 1328/1334****: If you enter the NIH at the main gate on Rockville Pike just proceed straight into the NIH campus for one block and cross the street in the direction you are going. Building 50 will be on your left. Enter the lobby, walk straight, pass the elevators on your right, make a right turn and look for the number 1328 or 1334 on a door on your right. If you are driving onto the NIH campus, there is a metered parking lot at the end of Building 50 on the left. (It might be a good idea to bring these directions with you.) **

**PRE-EVENT COFFEE SOCIAL****: There is a terrific coffee shop and lounge area just inside the door to Building 50. From 3:00 to 3:30 p.m., we will meet with Dr. Jaeger for coffee and an informal discussion there. Everyone is welcome to attend.**

**For more information, please contact Jim DeLeo by e-mail at jdeleo@nih.gov or by phone at 301-496-3848.**

**BCIG, an NIH Scientific Interest Group, is a learning organization.
**

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Yin-Yang Symbol by Dr. Stefan Jaeger is licensed under a Creative Commons Attribution 3.0 Unported License.

When referring to this Yin-Yang video, please cite this paper, which contains more information about the mathematical daylight model used for creating the different Yin-Yang symbols:

Stefan Jaeger (2011). A Geomedical Approach to Chinese Medicine: The Origin of the Yin-Yang Symbol, Recent Advances in Theories and Practice of Chinese Medicine, Prof. Kuang Haixue, Heilongjiang University of Chinese Medicine, China (Ed.), ISBN: 978-953-307-903-5, InTech, Available from: http://www.intechopen.com/articles/show/title/a-geomedical-approach-to-chinese-medicine-the-origin-of-the-yin-yang-symbol

]]>Stefan Jaeger (2011). A Geomedical Approach to Chinese Medicine: The Origin of the Yin-Yang Symbol, Recent Advances in Theories and Practice of Chinese Medicine, Prof. Kuang Haixue, Heilongjiang University of Chinese Medicine, China (Ed.), ISBN: 978-953-307-903-5, InTech, Available from: http://www.intechopen.com/articles/show/title/a-geomedical-approach-to-chinese-medicine-the-origin-of-the-yin-yang-symbol

More information, including nice illustrations, is available on Allen Tsai’s webpage.

]]>for their support over the last year. Each and every

discussion we had was a delight and has encouraged

me in my endeavor.

**Merry Christmas and a Happy New Year!**

When we look at the root of mathematics, where it all begins, we find sets and numbers. The entire mathematical edifice, no matter how complex it gets, builds upon these elementary concepts. For instance, natural numbers allow us to do basic things like counting and arithmetic. They also play an important part in theoretical computer science, where they can represent computer programs or theorems. Mathematicians spent a great deal of time investigating natural numbers, and yet, I think natural numbers are still not fully understood.

The Peano axioms, named after the Italian mathematician Giuseppe Peano (1858-1932), are a typical axiomatization of natural numbers. They allow us to construct the natural numbers and derive theorems. Here are a few examples of these axioms:

- There exists a natural number 0 (The first Peano axiom).
- Every natural number n has a successor S(n) that is a natural number.
- The natural number 0 is not the successor of any natural number.
- Distinct natural numbers have distinct successors.
- …

The first Peano axiom is special in the sense that it guarantees the existence of at least one natural number. This number serves as the root number from which all other numbers can be derived via a successor function. It is exactly here, where we encounter intrinsic uncertainty. With no way of knowing whether the root number really exists, the assertion made by the first Peano axiom is intrinsically uncertain. In fact, the first Peano axiom subsumes the uncertainty about existence and non-existence into one single axiom. Unfortunately, we cannot get rid of this uncertainty. Removing the first Peano axiom from the definition of natural numbers merely shifts the uncertainty from the root number to other numbers.

I suspect that Peano and his colleagues had hoped to get rid of intrinsic uncertainty once and for all when they introduced the first Peano axiom. What they overlooked is that the first Peano axiom only subsumes the uncertainty; it does not help us avoid uncertainty. In my recent paper “Computational Complexity on Signed Numbers,”, I exploit this subtlety to tackle the P/NP problem. If any of the readers knows about papers dealing with that intrinsic uncertainty aspect of natural numbers, I would appreciate hearing from you.

]]>While these considerations are valid from a philosophical point of view, they raise several questions:

- Where is the best place to introduce intrinsic uncertainty into mathematics?
- How can we incorporate intrinsic uncertainty into mathematics?
- What are the implications for the current state-of-the-art?

I addressed these questions in a recent article entitled “Computational Complexity on Signed Numbers,” which I presented in an earlier post on the P/NP problem. Let me elaborate more on these questions here and in the following posts.

As for the first question, all places where mathematics explicitly postulates the existence of “something” are good places to introduce intrinsic uncertainty. When mathematics resorts to postulating the existence of things, it usually means that there is no way to prove their existence with the axioms of mathematics alone. Introducing axioms that postulate existence is therefore an act of desperation more than anything else. Unfortunately, mathematicians have been too careless with axioms postulating existence. I think that intrinsic uncertainty is a fundamental principle. It should play a dominant role and form the basis of mathematics.

As for the second question, there are two ways to introduce intrinsic uncertainty into mathematics. One way is to introduce uncertainty explicitly. However, adding explicit uncertainty requires statistical models that are in themselves not uncertain. In fact, statistical models, such as the normal distribution, are well-defined and so is their behavior for large numbers. The other way to introduce uncertainty is to make uncertainty an intrinsic part of mathematics. For instance, removing an axiom that postulates the existence of an entity, a set for example, is a simple way to introduce intrinsic uncertainty into mathematics.

In my following posts, I will discuss this in more detail. I will show exactly where I think is the most appropriate place to introduce intrinsic uncertainty into today’s mathematical edifice.

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