**A fundamental measure of brain activity is the coherence of EEG signals. EEG is the acronym for electroencephalography which measures the electrical activity of the brain at different locations on the scalp. The resulting brain wave recordings are called electroencephalogram also abbreviated as EEG. In electroencephalography coherence is a mathematically defined quantity which measures the degree of synchronization or correlation between two EEG-measurements, the elements of the EEG data set.**
**The mathematical definition of EEG coherence is discussed here because of its fundamental significance and widespread use in brain research.**

The mathematical formula of coherence is also called "coherence function" or "magnitude-squared coherence". The elements of the data set to which the measure is applied are referred to as brain wave recordings or EEG signals or continuous time series of brain activity.

All phenomena observed in nature as sounds, the motion of objects or optical phenomena, are open to the same analysis when converted to an electrical signal via technical devices called sensors (e.g. microphone, radar, charge-coupled device).

Neurons (nerve cells) are such devices. They utilize changes in their electrical potential to process information which is the main function of nervous system and brain.

The electroencephalographic study of brain activity

*"is valuable but gross, it is roughly comparable to measuring the activity in Chicago by placing a dozen microphones around the city.*" (R. Walsh)

Despite all the advances in quantitative EEG analysis (Q-EEG) there is not yet a satisfactory understanding how EEG coherence is related to the collective behavior of neurons (neural synchrony).

2013 , in a critical review of the present status of EEG theory Gerald Ulrich recognizes *" a lack of coherent theory to describe the EEG"*:* "Instead, EEG is dominated by data-driven Q-EEG where one looks at mathematical correlations without a coherent theory to guide interpretation."*

The key to establish a satisfactory theory of brain waves is finding the EEG correlates of self-referral consciousness. Research in Transcendental Meditation plays a leading role in this endeavor, because it is a scientific method giving the experience of Transcendental Consciousness.

Topics of discussion:

1. Measures utilized in EEG Research,

2. Mathematical formula of EEG coherence,

3. Assumptions underlying EEG coherence,

4. Methods of computing EEG coherence,

5. Typical applications of EEG coherence,

6. Unsolved questions related to EEG coherence
**Introduction to the Discussion**
**its cause, strategy and aim:**

Original-Nachricht

Betreff: EEG coherence theory

Datum: Fri, 13 Feb 2015

Von: "Dr.Zeiger"

An: "Dr. Heinz A. Krug", "Klaus Weber"

Dear Heinz,

**inspired by the discussion on EEG coherence you kicked off recently I started to look into the problem you expressed "with a cosmic smile" under the subject heading "EEG coherence measure should be abolished or replaced".**

It turned out that the topic of coherence is still a frontier of EEG research, but the difficulty is not the definition of coherence and are not the empirical findings which appear to be contradictory. The real challenge is, that there does not yet exists a consistent theory of the EEG which can resolve the problem you pointed out.

In Chapter 17 of the "Textbook of Transpersonal Psychiatry and Psychology" entitled "Meditation Research: The State of the Art" Roger Walsh expressed in 1996 the same situation in more cautious words:

"Some TM researchers suggest that this (coherence )effect provides a basis for enhanced creativity and psychological growth. However it is always difficult in EEG research to extrapolate from brain waves to specific states of the mind. It is humbling to realize that greater coherence can also occur in epilepsy and schizophrenia."

Now 20 years later it is high time to resolve this question.

To contribute towards the development of a satisfactory theory of EEG a discussion on the mathematical measure of coherence has been started at the Darmstadt Science Forum

In the course of time the available contributions towards a theory of EEG coherence will be posted and discussed in non-technical, simple words to stimulate further development.

I hope you and others interested in this field will participate to make the discussion lively and fruitful.
Hoping to hear from you

with best wishes

Bernd

Original-Nachricht

Betreff: AW: EEG coherence measure

Datum: Sat, 31 Jan 2015

Von: "Dr.Zeiger"

An: "Dr. Heinz A. Krug"

Dear Heinz,

Yesterday I received from Klaus Weber several strings of Emails with responses to your challenge to amend or replace the EEG coherence measure used in research on Transcendental Meditation since the mid 1970s.

In which way does this measure differ from the coherence measure used in the papers you cite in your table?

With great interest I am reading all the mails.

Soon some more thoughts from the perspective of a "retired" theoretical chemist.

Best wishes

Bernd

Original-Nachricht

Betreff: EEG Coherence

Datum: Thu, 29 Jan 2015

Von: "Dr.Zeiger"

An: "Dr. Heinz A. Krug"

Dear Friends,

please excuse me if the following point has already been made in the discussion so far.

It is certainly valuable to study other measures of brain orderliness than those used up till now in EEG research on Transcendental Meditation.

But ideally all such investigations should clearly state right from the beginning the theory and assumptions on which the measure is based. In other words: the measures used for brain research should relate directly to the basic principles of nature as discovered by studying different phenomena of coherence found in nature and life .

Brain coherence should be seen as related to coherence in nature and life in general.

As an example I attach a theoretical investigation which I undertook together with M. Bujatti in the early 1990th. This study uses a brain model based on the transition dynamics as described in chemistry and which may be related experimentally to the experience of Transcendental Consciousness.

In addition in the late 1990s I had the opportunity to develop and publish a two-fluid model of collective coherence in the context of biophoton research. The resulting Quantum-Electro-Dynamical measure of coherence matches with the experience of Cosmic Consciousness.

So it seems to me that the type of coherence which we describe, depends on the theoretical model we adopt, which in turn is based on the state of consciousness we use as reference.

The view point of the observer should never left out of consideration.

There exist not only one but many measures or levels of coherence.

Physics today describes at least three distinct types of coherence:

(1) quantum coherence (infinite correlation),

(2) optical coherence (LASER) and

(3) collective coherence (e.g. superfluidity, superconductivity).

The search for an appropriate measure of brain orderliness has to be undertaken in a way which clearly identifies the theoretical assumptions on which this measure is based.

Hopefully these ideas will contribute to the current discussion.
With best wishes

Bernd Zeiger

Original-Nachricht

Bereft: AW: EEG coherence measure

Datum: Sun, 01 Feb 2015

Von: "Dr. Zeiger"

An: "Dr. Heinz A. Rug", "Klaus Weber"

Dear Heinz,

Indeed you are right saying that a solely classical thermodynamic model of the brain (as Chr. Tourenne proposed in the early 1980s) is not satisfactory. But if the Third Law of Thermodynamics is included, which has its roots in Quantum Mechanics, naturally principles and measures of coherence emerge, as Bujatti and I have shown in our analysis of Tourenne`s EEG data.

Again you are very right in saying that a quantum based model would be more valuable. In the late 1990s I had the rare opportunity to develop and publish a Quantumelectrodynamic Two-Fluid Model of collective coherence in the context of biophoton research at the International Institute of Biophysics (Prof. F.-A. Popp) in Kaiserslautern. At that time there did not yet exist experimental studies of photon emission of TM practitoneers, so only predictions where possible. But when many years later such studies appeared they fully confirmed the validity of the Quantum-Electro-Dynamical Theory of coherence which I developed between 1994 and 2000.

I have learnd to be very patient and modest concerning the receptivity to theories. To cognize a theory and then formulate it in a mathematically rigorous manner, is a very serious endeavour.
With best wishes

Bernd