Sunday, April 20, 2014

A Method for Monitoring Fitness and Avoiding Overtraining Using the Ithlete App

 My Basic Endurance Training Philosophy

It is my belief that the balancing act of approaching optimal fitness can best be accomplished through an improved understanding of the ways in which activity and rest progressively complement each other. Thus in order to experience sustained improvement as an endurance runner it is necessary to master the subtle balance between the act of running, and the process of recovery. Fitness improvements take hold as adaptations take place during recovery from exercise, not during the act of running. The stimulus from active exercise disturbs the bodies homeostasis, and when the exercise is repeated consistently the body then responds in turn with numerous adaptations. As an example two such adaptations in response to consistent running are  mitochondrial bio-genesis ( in both the muscles and the brain), and increased capillarisation, which each help to improve running economy.

This is how researchers Stanley, Peak & Buchheit put it in a recent review 'Cardiac parasympathetic reactivation following exercise: implications for training prescription'  for the journal Sports Medicine:

"The objective of exercise training is to initiate desirable physiological adaptations that ultimately enhance physical work capacity. Optimal training prescription requires an individualized approach, with an appropriate balance of training stimulus and recovery and optimal periodization."
 
 Yet in my opinion most runners place too much emphasis on the act of running ( often trying to keep to a rigid training schedule), and place too little awareness on the body's response to training during recovery.  This can lead to a less than optimal progression of fitness in 1 of 2 ways:

  1. Too much running volume, or too much running intensity, with insufficient recovery. This will likely result in at best less than ideal progress (or worse lead to injury or over-training syndrome).
     
  2. Too little training, and too much downtime. This will result in less than ideal fitness gains. There are days when the body and mind are primed to make ideal use of a strenuous workout. Going too easy or skipping a workout on these may be an opportunity lost.
 On the other hand, if subjective awareness of the body's response to training is combined with reliable objective bio-markers ( such as HRV ), then endurance training may be adjusted to fit the body's readiness on any given day.

Using HRV as a Biomarker to Inform Training

 Now that I have laid out my basic philosophy I would like to delve into some tools I will be using to help guide my objective understanding of how well I am responding to training. I will be using HRV   data obtained from a simple app available for i-phones or tablets (ithlete). So far it has been my experience that the HRV data can ( if used properly ) greatly inform a runners knowledge of the state of their fitness and recovery. Collection of HRV data used to be time consuming and expensive, but now requires only a 10 dollar app and a bluetooth heart monitor (in addition to the smartphone or tablet most of us already own ).  Each Ithlete app  collection session only takes 1 minute, results are instantaneous and are kept in history for reference, and there are some nice automatic graphs produced as I will show below. As a quick disclaimer I do not work for Ithlete or benefit in any way by promoting their product.

Based on my personal  experience and a fairly thorough scouring of the research I believe the most informative use of the HRV data for monitoring endurance training  requires consistent tracking of 3 types of HRV readings. It can also be useful to keep track of your training load ( TL) with miles run or a more complex measure that includes training intensity. This may sound like a lot to do, but remember this only requires less than 5 minutes of total collection time. Below are the types of HRV collection I find most informative collectively. I will follow with a graphic example of the approach using my recent data, and will finish with some of the peer reviewed research that describes why this approach can be so useful.

The three types of HRV information I will collect & present are:

  1. Morning Resting HRV (mrHRV) - A Good measure of overall well-being prior to daily stress accumulation
    .
  2.  Morning Standing HRV (msHRV) - A Good measure of the current state of the bodies resilience to physical stress.
  3. Evening HRV (eHRV) - When the bodies homeostasis has been disturbed from an exercise session it requires more than usual amount of oxygen to support the adaptation process. This is known as excess post exercise oxygen consumption (EPOC). Taken at rest each evening, (eHRV) shows how hard & how quickly the body is working to return to it's morning resting state.
It has been my experience that a larger the gap  between morning standing HRV and morning resting HRV ( in other words mrHRV minus msHRV) indicates better resilience. This formula informs the capability of parasympathetic withdrawal (and sympathetic activation) to a low level of physical stress and is I think the best indicator of exercise readiness.

There are two very informative findings that relate to these HRV measures from the work of Stanley, Peak & Buchheit that I sourced above:
 
  • Complete cardiac parasympathetic reactivation requires up to 24 h after low-intensity aerobic exercise, 24–48 h after threshold-intensity exercise and least 48 h after high-intensity exercise. Individuals with greater fitness are more resilient to training stress and require less time to recover.
  • Metaboreflex stimulation (e.g. muscle and blood acidosis) is likely a key determinant of parasympathetic reactivation in the short term (0–90 min post-exercise), whereas baroreflex stimulation (e.g. exercise-induced changes in plasma volume) probably mediates parasympathetic reactivation in the intermediate term (1–48 h post-exercise).
 The first finding provides a clue for why including a large percentage of low intensity training may be important for sustained fitness improvements allowing sufficient recovery each day while establishing the necessary volume of training. Since threshold and interval training require more recovery time it is not wise to schedule these sessions back to back unless possibly in an overload phase prior to a race taper.

The second finding points to the importance of examining standing HRV in addition to resting HRV. The orthostatic challenge involved in standing makes (mrHRV-msHRV) a better proxy for exercise-induced changes in plasma volume then mrHRV alone.  

I say this in part because an earlier study of Dr Bucheitts 'Exercise-induced plasma volume expansion and post-exercise parasympathetic reactivation' which demonstrated the following phenomenon:
 "significant increase in all vagal-related HRV indices (and a decrease in the sympathetic related index) 2 days following a single bout of supramaximal exercise"
 This result indicates that high intensity exercise can lead to a super-compensation effect whereby resting (not standing) HRV is elevated 2 days after the exercise. A resting HRV that is elevated due to a supercompensation effect however, shoud not necessarily be interpreted as an indicator improved readiness for a difficult workout.


Thus (mrHRV-msHRV) would seem better equipped to identify the lingering effects of threshold and high intensity workouts on current exercise readiness, especially if HRV appears to rise in the initial days after threshold or high intensity exercise. I have seen exactly this pattern occur as I will show below.

Edit -- I have seen some conflicting results in the following week. In some cases high msHRV seems to indicate good fitness readiness. As usual with a closer look things are not so simple as they seemed with limited data. I have a feeling that acute fatigue, & long term fatigue have differing effects that may reverse some training interpretations.

My HRV Training Graph for 1 Week

 Due to the superior graphic tracking capabilities of the ithlete package I will use it to track my results. Ithlete allows me to simultaneously graph training load against changes in HRV both supine at rest and standing at different time points (within the day, and day to day). This will allow me to clearly display and examine 3 key indicators relevant to training. Here is an example:





Here is how to interpret the graph:


The green dots represent morning resting HRV (mrHRV) - This informs the  health of the parasympathetic nervous system at rest. It is a good measure of overall well-being prior to daily stress accumulation. My scores which tend to range in the 80's are quite high for my age group (probably in the top 1%). It is not uncommon for those doing a lot of running to have a high HRV. The blue line represents a rolling average of the mrHRV score. If the green dot drops one standard deviation below the blue line for 1 day a relatively easy training day is recommended. If the green dot drops below the blue line for 2 consecutive days a day off is suggested.

The height of the vertical white lines on any given day represents morning resting HRV minus morning standing HRV (mrHRV-msHRV). For example, in the graph above on Tuesday my morning resting HRV was 82, and my morning standing HRV was 48 so that (82-48=34).   The length of this line informs the capability of parasympathetic withdrawal (and sympathetic activation) to a lower degree of stress ( in this case the stress of standing, which is referred to in the literature as an orthostatic challenge). The 34 point HRV difference is a large gap indicating that this would be a good day for a challenging workout. As mentioned above it is my view (supported by literature and subjective experience ) that this is the best HRV indicator of exercise readiness. Generally I find the longer this vertical line is, the better I am prepared for a good training session.

The purple bars represent the training load in the form of miles run which I manually entered. It can be useful to compare HRV levels to this measure over from the previous day in order to see how a hard or easy training day effects the trend in resting HRV or the exercise readiness on any given day. Generally this is confirmed as tall purple bars ( high training load ) tend to lead to lower HRV the following day. It is also important however to keep in mind the intensity of the run as well as the research findings I bulleted above indicate that it is high intensity exercise that is likely to have the biggest effect on the vertical white lines (lowering exercise readiness ).

I would stress here that HRV is just one tool. Results need to always be interpreted with care taking into account subjective feelings of fatigue and soreness, sleep patterns, diet, emotional state, and of course the relationship between HRV results and the intended goals of recent training. For example I tend not too place much validity on my Saturday morning results as my dietary patterns on Friday evening are quite different in preparation of a long run on. I also tend to get less and lower quality sleep Friday nights.

Example of Daily HRV Interpretation and Usefulness

 

The first thing to notice regarding the resting HRV is it tends to be lower after long runs. This is expected . So for example on the first Sunday resting HRV with a score of 80 approaches the blue line which is about a standard deviation below it's typical level. This drop was in response to a 20 mile run on the previous Saturday. While the 20 mile run was at a comfortable overall pace this training load  was enough to provide a useful training stimulus without dropping the resting HRV too drastically. The shorter vertical line on Sunday completes this coherent picture and suggesting some limited exercise readiness and thus relatively easy training day.

On Sunday I restricted my running to just 7 miles, although I also taught a tai chi class and did some weight training. Monday was a very easy day with just 5 miles of easy running . Coinciding with the easier training loads are a gradual increase in resting HRV on Monday Tuesday and Wednesday reflected by the rising green dots. While the highest resting HRV score ( 88 ) is seen on Friday, Tuesday reflects the best exercise readiness level as indicated by tall white vertical line.

On Wednesday I completed a moderately taxing 15 miles that included 3 miles at marathon pace effort in the evening. As expected there was a resulting dip in my resting HRV the following morning. On Thursday I only ran 6  miles, but I did run steep long hill in the morning at a fairly high intensity. On Friday morning my resting HRV was quite high (88), leading me to suspect a transeint super-compensation effect of the prior higher intensity work-outs. I became especially wary noticing that the exercise readiness measure (mrHRV-msHRV) was somewhat low (88-67=21). In response I planned for an easy day which turned out to be a very good idea. On my easy 2.5 mile jog into work I began experiencing some reactive hypoglycemia symptoms* which I am prone to. I was able to avoid a full on event, but had I just trained with a hard effort based on the high morning resting HRV score (88) the results would likely not have been pleasant.



I should also mention that you can also see evening HRV (eHRV) in the deflection of the slope of the white line from one day to the next. Evening HRV which is taken at 9pm, had a score of 71 on Monday evening and 76 Tuesday evening. These evHRV scores as expected are lower then the mrHRV scores on the same day which were 80 and 82 respectively. This shows that excess post exercise oxygen consumption was likely occurring in the evening. By the following morning however resting HRV continued to rise showing the importance of a good nights sleep.

* notes this was the 2nd time I experienced reactive hypoglycemic symptoms with a pattern of high resting HRV and a low exercise readiness measure (mrHRV-msHRV).

**I also identified  what appears to be a mild allergic reaction to cashews and peanuts based on their effect on morning resting HRV. Resting HRV was substantially lower on mornings when I had eating substantial amounts of these nuts ( especially the cashews ) on the prior evening.

My mrHRV had dipped a bit Saturday morning. I had taken in extra carbs the evening before and had woken up quite early for this reading so I went ahead with my long run for Saturday. This was an important run for me nearing the peak of my marathon training cycle. I had been running lots of volume but a strained hamstring had prevented any faster running. With the hamstring feeling better I wanted to get a substantial number of miles a my ideal goal marathon pace. This graph includes the Saturday run and Sunday morning HRV results:


On my 18.5 mile Saturday run I included a 2 mile warm-up followed by 10 miles at ideal marathon pace (8 min miles), followed by 4 miles at a comfortables pace, and finally another 2 miles close to marathon pace at the end. After this run I am thinking my current fitness probably supports 8:10 min marathon pace but 8 flat may be stretching it. Sunday morning (April 20th) HRV results show that I am still recovering from that run. My mHRV is a bit low but more importantly the short white vertical line indicates low exercise readiness. This is also in line with my subjective sense, so as a result I will skip my planned morning easy run and check HRV again later in the day to see if an easy evening run makes sense. I am already at about 60 miles for the week so even though I had planned for 67 a day off would not hurt if waranted.

Edit -- I have seen some conflicting results in the following week. In some cases high msHRV seems to indicate good fitness readiness. I have read multiple recent studies making the case for using weekly HRV averages rather than daily values. The daily values are more contain more noise ( more variable ) which clouds interpretation. In my soon to come update I will include weekly averages as well as a weekly fitness test indicator.

Some links to peer reviewed research for those interested:

 

On the use of HRV in monitoring fitness training

see Simon Wegerifs excellent summary  of Dr. Martin Buchheits research here  

A few of the interesting findings

  • Participants with the highest starting HRV were the fastest runners, but those with lowest starting HRV showed the most improvement.
  • All 11 responders showed increases in their morning HRV, and the ones with the largest gains in performance showed the biggest increases in HRV.
  • An improvement of 10% in 10k run time required an average of 15% improvement in morning HRV, though two participants who achieved improvements of 15% in HRV achieved a more modest 3-4% improvement in 10k time.
Buchheit MChivot AParouty JMercier DAl Haddad HLaursen PBAhmaidi S.
Eur J Appl Physiol. 2010 Apr;108(6):1153-67. doi: 10.1007/s00421-009-1317-x. Epub 2009 Dec 22.
http://www.ncbi.nlm.nih.gov/pubmed/20033207


also

"In conclusion, when controlled for changes in body mass
 M. Buchheit,  M. B. Simpson, H. Al Haddad,  P. C. Bourdon,  A. Mendez-Villanuev
* note that Ln rMSSD is the HRV measure Ithlete uses

And

 Antti M. Kiviniemi ·Arto J. Hautala ·Hannu Kinnunen · Mikko P. Tulppo 2007

Hautala AJ1, Kiviniemi AM, Tulppo MP. 2009

 

 

More on the importance of testing HRV standing as well as supine

"Exercise-induced changes in sympathetic and parasympathetic ANS control differ, depending on posture and period of measurement. Exercise induced changes in parasympathetic and sympathetic outflow, respectively, can be extracted from measurements from supine, through the orthostatic response, to standing, thereby detecting changes in ANS that are otherwise obscured.
"However, this study also clearly demonstrates the novel relationship between HRV indicators and indicators of physical fitness during an orthostatic stressor. Participants with greater physical fitness showed increased responsiveness (indicated by increased sympathetic activity and vagal withdrawal) to the orthostatic challenge." 
 
Grant CC1, Viljoen M, Janse van Rensburg DC, Wood PS. 2012

Relationship between exercise capacity and heart rate variability: Supine and in response to an orthostatic stressor 

"However, this study also clearly demonstrates the novel relationship between HRV indicators and indicators of physical fitness during an orthostatic stressor. Participants with greater physical fitness showed increased responsiveness (indicated by increased sympathetic activity and vagal withdrawal) to the orthostatic challenge. "

Catharina C. GrantaJimmy R. Clarkb, Dina C. Janse van Rensburga, Margaretha Viljoenc
2009


also see Andrew Flatts Ithlete blog


Monday, January 13, 2014

Documenting My Marathon Training With Heart Rate Variability

Back in May 2013 I finally found a solution to a series of nagging knee injuries that had plagued me for 2 1/2 years restricting the volume of running I could manage to about 20 miles a week. Since that time I have gradually been able to increase that volume up to the 60 miles a week I am currently running (yippee  ).

I run primarily for the joy it brings me which is closely linked to the health benefits running provides, but I am now also looking forward to the challenge of attempting to qualify for the Boston marathon. I signed up for a May marathon thinking that the qualifying time for my age group was 3 hrs 35 minutes. Last week however, I discovered that I actually would need to run the marathon in less than 3 hrs and 30 minutes to potentially qualify. It will be a difficult challenge to reach the necessary fitness level in the time before the marathon while also losing about 10 pounds.

In order to attempt this challenge in a healthy way I will be monitoring my heart rate variability (HRV). HRV is a catch all term for a number of measures that capture the hearts subtle response patterns at rest (see this link for more description). A high HRV score is generally associated with good health and well-being. The primary measure of HRV recommended for use in studies of endurance is the root mean square of successive differences in heartbeats (RMSSD). I am also including  two other measures HRV which have shown to correlate with cognitive stress (Shannon Entropy  and Correlation Dimension (D2)) mostly for my own interest to see how they vary with training.

There are two primary uses of HRV data in endurance training.
  1.  Day to day variations in HRV data in response to training are very useful to recognize when rest or an easy workout are a good idea to avoid over-training.
  2. Weekly averages can be compared to identify gradual improvement in fitness over time.

It is my view that while an objective measure such as HRV can be an extremely useful tool we should also keep in mind it's limitations. If the subtle beating pattern of a heart at rest projects the state of harmony between the body, mind, and environment, we must remember that HRV data is still a partial map of the territory, an abstraction from the reality of the continuous ongoing relationships. Our subjective perceptions of our internal state of wellness are also limited and prone to any number of biases. Therefore the objective HRV data is most useful as a complement to our own internal perceptions, not as a replacement of those perceptions. Without further ado lets get to the results.

Week beginning Jan 6

I began collecting data on Thursday January9. To set the stage I had run 61 and 63 miles in the two previous weeks respectively. I count my weeks starting on Monday as my marathon will take place on a Sunday. I ran 3 miles on Monday, 12 on Tuesday, and 12 on Wednesday leading to the beginning of HRV data collection Thursday morning.



Thursday Jan 9

After waking 7:02 AM
Beats Per Minute = 47.9
RMSSD=61.2, Shannon Entropy =2.82, Correlation Dimension (D2)=3.57

The results indicate that I was responding well to the previous running this week as morning HRV indicators suggest full recovery from prior workouts. An RMSSD of 61.2 is a high HRV score and is consistent  with my typical score when I am well rested and feeling good.

I taught a 2 hr Tai Chi class in the AM, then ran an easy 9 miles on Thursday (4.5 to work, 4.5 back) carrying my backpack and clothes for the day. I felt especially good on the return run given the miles I had run on Tuesday and Wednesday.

Friday  Jan10

After waking 6:12 AM:
Beats Per Minute = 46.5
RMSSD=54.5, Shannon Entropy =2.94, Correlation Dimension (D2)=3.48

Again the HRV data suggest good recovery from the prior workout. My legs however felt a bit stale/tired during the easy 7 miles I ran to and from work on Friday.


Sat Jan 11

After waking 5:48 AM:
Beats Per Minute = 48.9
RMSSD=42.0, Shannon Entropy =2.70, Correlation Dimension (D2)=3.62

The RMMSSD result suggests that the accumulation may have resulted in less then full recovery this morning.

Nevertheless I had an excellent (if difficult) workout  with my running group the LA Leggers. We ran 11 miles. I ran the first 4.6 miles at an 8:20 pace uphill (over 400 foot gain), the next 1 1/2 miles at 7:40 pace, and the last 5 miles at 8 minute per mile pace. I would not have been able to maintain those paces on the same course a month ago.

To demonstrate the effect that a hard workout can have resting HRV data I collected my heart rate data twice more on Saturday (4 and 8 hrs after the run)

After Hard Run 12:36 PM:
Beats Per Minute = 59.7
RMSSD=24.4, Shannon Entropy =3.18, Correlation Dimension (D2)=0.85

Later 4:34 PM:
Beats Per Minute = 56.6
RMSSD=28.1, Shannon Entropy =2.83, Correlation Dimension (D2)=3.43

It is clear that HRV measures drop sharply after a hard workout and recovery takes time. This is the time when beneficial fitness adaptations are taking place.

Sunday Jan 12 (Happy Birthday #51 to me )

I also collected my heart rate data twice more on Sunday to further document the recovery/adaptation process. In the am I still had not fully recovered. This shows why it is generally not a great idea to string hard workout efforts on consecutive days if you are running on most days.

By 4 pm however my HRV data was at it's high point for the week.

After waking 7:13 AM:
Beats Per Minute = 42.0
RMSSD=45.5, Shannon Entropy =2.77, Correlation Dimension (D2)=3.95

Later after teaching Tai Chi 4PM:

Beats Per Minute = 49.0
RMSSD=61.7, Shannon Entropy =2.56, Correlation Dimension (D2)=3.35

 I then ran an easy 6 mile run in the evening.

Friday, October 25, 2013

The Logic of the Four Possibilities

"In scrubbing and cleansing your profound mirror Are you able to rid it of all imperfections? In loving the common people and breathing life into the state, Are you able to do it without recourse to wisdom? With nature’s gates swinging open and closed Are you able to remain the female? With your insight penetrating the four quarters Are you able to do it without recourse to wisdom?"

Ames, Roger; Hall, David (2010-05-12). Dao De Jing- Chapter 10: A Philosophical Translation (Kindle Locations 844-846) Chapter 10. Random House Publishing Group. Kindle Edition.  

"The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function."

F. Scott Fitzgerald


Ever since the time of Aristotle, logic (and most philosophy) in the western world has been constrained to obey the principle of non-contradiction. This simply means that what is true, and what is false do not overlap. If something is said to be true it cannot also be false, and if something is said to be false it cannot also be true. Intuitively this seems to be a reasonable logical axiom. It is so reasonable on it's face that it has rarely been questioned. How could we after all, make any sense of our language if truth and falsity overlapped in logical space?

As it turns out the principle of non-contradiction may not be so logically necessary as it seems. Graham Priest is a mathematician/logician /philosopher who has been making arguments for a para-consistent logic that allows for the possibility of true contradictions for 25 years. This type of logic goes back more than 2,500 years to the original Buddha in what is known as the Catuskoti. The Catuskoti (sometimes termed as the tetralemma) is translated to mean the four corners (or the four possibilities). Much argument in Buddhist philosophy takes this form with Nagarjuna (known as the 2nd Buddha) the most well known practitioner. The four possibilities include not only standard conceptions of truth or falsehood, but also seemingly contradictory possibilities such as both (true and false) or neither (true or false).

Why Turn to a Para-Consistent Logic?

Is there a good reason however, to allow for the ambiguity and lack of consistency that arguments from the four possibilities entail when the classical logic of mutually exclusive truth and falsehood seems so intuitive? Graham Priest points to how unavoidable contradictions seem to be persistent in language, mathematics, and the physical world. Here is an example from language known as the liars paradox.

This sentence is false.

Due to it's self-reference one cannot determine the sentence to be purely true or false with out contradicting it's own contents.

Another example comes from the world of numbers. It is true that the sets of (a) natural numbers, (b) even natural numbers, (c) odd natural numbers, and (d) prime numbers are all infinite sets. It is then a contradiction that b,c, & d are all also subsets of a. How could there be an infinite number of odd numbers if the number 2 is not an odd number? This is a true contradiction.

There is also the great mathematician Kurt Godel who showed that any logical system:
  • could not be both consistent and complete; and also
  • could not prove itself consistent without also proving itself inconsistent. 
Godel's proof is beyond my expertise and beyond what could be presented here, but I think it is fair to say that he was a pretty brilliant dude.

Another example comes from the mathematics behind the phase changes of a fluid. The emergence of new properties due to phase change is often accompanied by mathematical singularities (infinities). The concept of emergence calls into question a reductionist approach to science. For example,  even if fundamental physics were to find an ultimate 'Theory of Everything' that links the very small (quantum mechanics) to the very large ( theory of relativity) that 'Theory of Everything' would be of little use in describing the new properties that come into play as we move from physics to chemistry, biology and the problems facing modern social beings.

Finally of course there is the inconsistent logic in play in interpreting the results of the double slit experiments from quantum mechanics itself. See this article for a brilliant description of how the logic of the four possibilities might best model those results.

Given these examples, it seems that a logic which allows for more than just the standard two possibilities of truth and falsehood might better model the inevitable unknowns and inconsistencies we are presented with as we attempt to navigate and make sense of the world.


How About the Drawbacks to a Para-Consistent Logic? 

The main argument against para-consistent logic ( including dialetheism which is the type of para-consistent logic that Graham Priest argues for ) is called the 'Argument from Explosion'. This is something like a 'slippery-slope' argument. Basically if something can be said to be both true and false then anything can be argued and argument itself loses all meaning. But Priest makes clear that only some, (not all) contradictions are true. Thus dialethism is not vulnerable to the 'Argument from Explosion'.

Another argument is the 'Argument from Exclusion '. This argument claims that a sentence is only meaningful if it rules something out. Again Priest argues that dialtheism ( & also the logic of the Catuskoti ) is also protected against this argument for similar reasons as to the 'Argument from Explosion'. This dialetheism link also describes how this form of para-consistent logic is also protected from another argument known as the 'Argument from Negation'.

So How Does All This Relate to the Catuskoti (the Four Possibilities)?

Interpretation of the Catuskoti is notoriously difficult, especially for those steeped in western cultural logic. In this paper (warning : requires some familiarity with logic to digest), Priest outlines his interpretation of Nagarjuna's writings on the Catuskoti. An important concept that Priest relies upon when understanding contradiction from Nagrarjuna's perspective is a Buddhist principle that distinguishes two types of reality, conventional reality and ultimate reality. Priest uses these two types of realities ( or truths ) along with the four possibilities to  connect his interpretation to a many valued logic of relational semantics. In this logic 'conventional truths' are knowable but 'ultimate truths' are not. This relates to the Buddhist concepts of non-separability & emptiness whereby any thing or concept only exists in relation to some other thing or concept. Thus every thing or concept is empty of it's own pure essence and therefore must be known in context or relation to other things..

This also reminds me of the physicist Neils Bohr's conceptions of truth and contradiction as Bohr famously said:

"There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."
 I find this way of thinking about truth, contradiction and the limits of knowledge both very reasonable and of great practical importance. I believe it is easy to confuse our models or maps of the the world for the ontology of what ultimately exists. Instead of seeing these models  as useful descriptions we often take them as ultimate truth. Our models can be based on subjective perceptions and beliefs or on objective science yet each of these methods tends to avoid contradiction rather then embrace it's inevitability.

On the other hand  I think it is also dangerous to fall into the trap of using the inevitability of ultimate uncertainty and contradiction as a crutch to avoid the hard work of subjectively and objectively discovering that which we can. Whether from the viewpoint of an individual or a society, much of what currently is uncertain, and much of what is currently unknown is waiting to be discovered. Not all contradictions are 'true' contradictions, but it is our current uncertainties that can serve as the springboard to fill in some of those gaps.


Monday, July 1, 2013

Attention as the source of Consciousness (By way of Neural Synchrony)

“The real voyage of discovery consists not in seeking new landscapes, but in having new eyes.”
Marcel Proust

One of the great mysteries in the field of conscious studies relates to our ability to experience the world as a coherent whole. Many details are known for example, about how the brain processes visual information in the form of relflected light photons eventually creating our visual experience. But this process includes many seemingly independent modules with specific functions operating in different spatial locations. For example, when we look at an object (lets say a red chair) we process the color of the object separately from it's shape, separately from depth, separately from  it's texture. And if an object is moving we process that movement in yet another distinct process.

Our visual experience however is unified. We do not see color separately from form, or depth, or texture. We do not consciously combine these features to experience a red chair, instead we receive our perceptions as ready-made wholes. In studies of consciousness the problem of how this constructed experience can take place in real-time is known as the binding problem. Our visual experience is not alone in  this regard. When we communicate through speech we do not contemplate each word. Instead we have some general meaning in our consciousness we wish to express and the words seem to flow from some unknown source in an attempt to capture that meaning. Similarly, when we process the symbols of a written language the individual words take a backseat to the flow the contextual meaning and the individual letters hardly enter our conscious process at all.

Jesse Prinz a neuro-philosopher, and Jonjoe McFadden, a molecular biologist each have been making strong arguments that to increase our understanding of consciousness instead of focusing on the firing individual neurons we need to consider the phenomenon of neural synchrony. Neural synchrony is the phenomena where the firing rate of neurons in distinct regions of the brain seem to harmonize within a similar frequency. There is an ever continually expanding amount  scientific evidence that correlates this neural synchrony in the brains electromagnetic field with the manner in which we orient our attention .

Prinz has been instrumental in synthesizing this evidence into a leading theory of conscious. I am currently reading his densely informative book 'The Conscious Brain: How Attention Engenders Experience '. If interested one can also check out this shorter paper When is Perception Conscious? In a nutshell Prinz presents evidence that attention is the key to consciousness. in his own words:
"Perceptual states become conscious when and only when the perceiver is attending."
 When we attend, either narrowly to a selected feature of our environment, or more diffusely to a larger view the neurons in the regions of the brain correlated with that functional attention fire together in synchrony. Prinz argues that this attentional process makes information available to our working memory, and this availability to working memory corresponds with consciousness. Interestingly in those regions not directly associated with our functional attention the neuronal firing is chaotic. Prinz believes our phenomenal experience is unified and orderly because the spotlight of our attention is the locus of this order which emerges from chaos. We cannot access the unconscious chaos because the act of attending is an intrinsically unifying process.
Prinz focuses much of his theory on the relationships between perception, attention, neural synchrony and consciousness. McFadden in contrast places more emphasis on the brains electromagnetic field as a source for the unity of our conscious experience. Whereas both Prinz and McFadden each lean heavily for empirical support from neuroscience imaging studies, behavioral psychology experiments, and brain disease findings, McFadden's theory on the unity of consciousness also leans on holistic connections from gestalt. quantum mechanics, and information theory. Like Prinz, McFadden's theory and it's justifications are complex and cannot be giving proper due in a short blog post from a non-expert and limited writer like myself. Two good recent papers from McFadden can be found here & here. Nevertheless I will attempt a very brief summary.

In the first paper McFadden lays out a good deal of evidence similar to Prinz detailing the phenomenon of neuronal synchronicity. He links this phenomenon to the brains electromagnetic field ( which he sees as the 'seat of consciousness') which like all fields represents a unity of formless information. Like Prinz, McFadden sees our awareness as the breeze that swings the gate between unconscious mechanistic fragmentation and conscious unity.
"The key mechanistic difference between unconscious and conscious information in the brain is not the presence or absence of firing in any particular neuron or region of the brain but a particular level of synchrony of firing between distantly separated neurons . Information that you are not aware of is encoded in asynchronously firing neurons but when you become aware of that information those same neurons fire in synchrony."
McFadden goes beyond simply describing the brains EM field as an effect of neuronal activity. Instead he uses recent evidence that points the EM field as also having a causal functional role that influences neuronal activity. This is not a one-way relationship, but an interdependent feed-back loop. This is an important argument given that a number prominent current philosophers such as David Chalmers argue that consciousness is epiphenomenal (not having a causal influence on the physical world).

In the second linked paper, McFadden describes the properties he sees necessary to accommodate both the binding problem of visual perception, and the problem of deriving meaning from information. He points out that this is not just a matter of complexity. We have many powerful information processing computers, yet these digital computers  have made little progress in performing many 'common sense' tasks. The features (or properties ) that McFadden describes, feel as though if they were communicated by a different author they could poetically be describing the principles of some eastern philosophies.

The features include context-dependence, inter-dependence, emergence, unity and compression. Ok, compression is not a common term associated with eastern philosophy, but McFadden is using the term to describe how many separate fragments can be experienced at once 'in a flash'. It is interesting to me how this sense of 'compression' seems to be the complementary opposite to the common term in modern science 'reductionism'.

Here is McFadden's concluding sentence:


"The information underpinning meaning, understanding and commonsense knowledge is holistic and gestalt in character. This gestalt information can only be encoded in a physical field: the CEMI field. "
CEMI stands for conscious electromagnetic field information. The paper describes how the CEMI field has the potential to satisfy all the necessary features to serve as the 'seat of consciousness'. Fields are by definition, waves of possibility, holistic and unifying, and uncertain in their nature. As McFadden describes:
"Each point in the space of the field is thereby potentially receptive to the information encoded by the entire field."
"In a very real sense, the field unifies the distributed information at the point of absorption such that a change in the firing state of any neuron in the network will be communicated to all neurons that are influenced by the brain’s EM field. The field integrates and unifies the information encoded in the firing rates of all neurons to which it is causally connected."

What most interests me in the theories of Prinz and McFadden is the enormity their potential implications. Implications that point to the potential importance of mindfulness practices in developing our capacity to attend both selectively to the particular, and diffusely to context. That we may only see and be conscious of that which we attend to helps explain introspective shortcommings such as confirmation bias. This also points to the importance of humility, and the acceptance of uncertainty giving how easy it can be to confuse  a narrow internal coherence with a wider 'truth'.

Perhaps like the theorized CEMI field itself, I see these implications suggesting the promise of unification. If the theories are correct the scope of that unification will only be limited by the receptivity of our attention/awareness to the potential implications.

Monday, May 27, 2013

Introspection, Mindfulness and the 'Blind Spot' Bias

Image credit: retrieved from http://izquotes.com/.

There is an recent interesting post  at the Scientific American blog that delves deep into the underlying nature of human biases. There is a vast and robust literature of scientific social research findings detailing the many ways our introspective intuitions can lead us astray. A long time leading resercher in the field of human bias has been nobel prize winner Daniel Kahnemen. Kahneman summarizes much of his work over many years in his recent book 'Thinking Fast and Slow' which cover a multitude of these biases such as the confirmation bias, over-confidence bias, halo effects framing effects etc....... A good summary of the book can be found here.

The blog a Scientific American 'The Blindspot Bias' by Samuel McNerney can be found (here). McNerney points out an interesting phenomon that tends to occur when the research behind theses biases is presented to individuals.

"Here’s my worry. The same thing occurs when lay audiences read books about thinking errors. They understand the errors, but don’t notice the trick – that simply learning about them is not enough. Too often, readers finish popular books on decision making with the false conviction that they will decide better."
"The overlooked reason is that there are two components to each bias. The first is the phenomenon itself. Confirmation bias, for example, is your tendency to seek out confirmation information while ignoring everything else. The second is the belief that everyone else is susceptible to thinking errors, but not you. This itself is a bias – bias blind spot – a “meta bias” inherent in all biases that blinds you from your errors."
Ok, then what is this 'blind spot bias and how can we avoid falling prey to  it? According to McNerney:
"The problem is rooted in introspection. Biases are largely unconscious, so when we reflect on thinking we inevitably miss the processes that give rise to our errors. Worse, because we’re self-affirming spin-doctors, when we introspect, we only identify reasons for our infallibility. In this light, we see why mere exposure to biases compounds the problem: they actually make us more confident about how we decide."
This presents a delemma for those who would like to apply a rational approach to objectively seeing the world more closely for how it is rather than for how it suits our current motivations. If the thoughts that unconsciously feed our introspection are themselves fraught with bias how does one avoid a cycle of rationalization? I think McNerney points us in the right direction by making a distinction between introspection and mindfulness.
"Mindfulness, in contrast, involves observing without questioning. If the takeaway from research on cognitive biases is not simply that thinking errors exist but the belief that we are immune from them, then the virtue of mindfulness is pausing to observe this convoluted process in a non-evaluative way. We spend a lot of energy protecting our egos instead of considering our faults. Mindfulness may help reverse this."
One way to think about mindfulness is the training of our awareness to bring some objectivity into our normally subjectively dominated experience. Like any useful acquired skill mindfulness training requires consistent practice. We have a natural default mechanism which we are otherwise blind to.

 The leading researcher behind the blind spot bias is Emily Pronin of Stanford University. Pronin has identified that this bias is rooted in a fundamental asymmetry in the way we value our own introspections and behavoirs in comparison to the credence we apply to the behaviors and introspections of others. This is not just some researchers pet theory, these are robust findings validated across multiple studies.

We tend to define ourselves (usually in a favorable light) based on our own best intentions ( which are available on introspection) rather than on our own actual behaviors. When it comes to others, however, we have more access to their behaviors than we do regarding their intentions. This is why when others behave in ways that are hurtful to us we tend to believe they acted with intention to be hurtful, while when we ourselves act in hurtful ways we are more likely to credit some external factor. We might say 'That wasn't me, I don't do that kind of thing, it was because........', and then try to compose a coherent reason that casts us in a better light.

This asymmetry can go beyond our person to person interactions and can lead to very damaging effects on larger levels. For example we sometimes apply the same logical asymmetries to groups we see ourselves a part of, as compared to those groups we feel a separation from. This is a primary source of discrimination and helps explain the inability to understand and tendency to demonize other cultures.

Update: Some Wittgenstein qoutes from "On Certainty" that are relevant to the 'blind spot bias:

94. But I did not get my picture of the world by satisfying myself of its correctness; nor did I have it because I am satisfied of its correctness. No: it is the inherited background against which I distinguish between true and false.
97. The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I distinguish between the movement of the waters on the river-bed and the shift of the bed itself; though there is not a sharp division of the one from the other.
253. At the core of all well-founded belief, lies belief that is unfounded.


For Wittgenstein we will always have some blindness regarding the origins of our beliefs. The stream of consciousness we experience is constrained by the river-bed of our unconsciously formed world views. Through a receptive nonjudgmental and mindful practice perhaps we can connect the narrow steams into a wider riverbed.


See also: This link for perspectives from Dewey and Zhaungzi




Suppose we were able to share meanings freely without a compulsive urge to impose our view or conform to those of others and without distortion and self-deception. Would this not constitute a real revolution in culture.  - David Bohm

Saturday, May 4, 2013

Heart Rate Variability

“Small is the number of them that see with their own eyes and feel with their own hearts.”
Albert Einstein



In my previous post I discussed a paradox regarding the evolution of complex living organisms and entropy. Entropy in its classical definition is always directed from away from order and towards disorder. Living systems are able for a time to resist this entropic force maintaining internal integrity by flexibly adapting to an outside environment.

This interplay between internal stability and external adaptability is made possible through the  communication of many nested interacting physiological systems. It is known that autonomic nervous system modulation plays an integral role in many aspects of this complementary interplay by maintaining stability through homeostasis, and by changing in response to the environment through allostasis. The autonomic nervous system has a prominent role in this process and has two complementary sub-components corresponding to the sympathetic and parasympathetic branches. The sympathetic nervous system is predominate during stress while the parasympathetic nervous system is predominate when relaxed.

So What is Heart Rate Variability

Recently there has been a great deal of research related to heart rate variability (HRV) as a non-invasive bio marker of stress. Heart rate variability is related to the regulation of the sinoatrial node, the natural pacemaker of the heart.
The rhythm of the heart is primarily under the control of the vagus nerve, which inhibits heart rate and the force of contraction. When you inhale, you take your foot off the parasympathetic brake and your heart rate accelerates. When you exhale, you press down on the parasympathetic brake and your heart rate slows. This change in your heart rate from beat to beat is called heart rate variability (HRV), and HRV is a widely used method for studying cardiac autonomic modulation.
HRV can also be considered a measure of vagal tone, and is elevated in those with active lifestyles and low in those who are sedentary. Paradoxically HRV is higher when relaxed and lower under stress. A high resting HRV indicates that the heart is manifesting complex patterns subtly responding to its environment in an adaptive manner. This is a good sign and tends to correspond with a sense of well-being.
Low HRV is thought to reflect excessive sympathetic and/or inadequate parasympathetic activity and is a strong predictor of mortality in patients with Congestive heart disease. Reduced HRV is a powerful and independent predictor of an adverse prognosis in patients with cardiac disease. It has a potential to become a non-invasive diagnostic and prognostic index in clinical practice. HRV is also lowered in psychological disease states, such as anxiety, depression, and PTSD.
Julian Thayer has been one of the leading researchers relating neuroimaging studies and HRV indices to stress. Here is a review of much of his work. Thayer and his colleagues propose a model they refer to the "Neural Visceral Integration Model"
"We further propose that the default response to uncertainty is the threat response and may be related to the well known negativity bias. Heart rate variability may provide an index of how strongly ‘top–down’ appraisals, mediated by cortical-subcortical pathways, shape brainstem activity and autonomic responses in the body. If the default response to uncertainty is the threat response, as we propose here, contextual information represented in ‘appraisal’ systems may be necessary to overcome this bias during daily life. Thus, HRV may serve as a proxy for ‘vertical integration’ of the brain mechanisms that guide flexible control over behavior with peripheral physiology, and as such provides an important window into understanding stress and health."

This model specifies a central autonomic network (CAN) brain network including prefrontal and sub cortical regions that function to support adaptability and health. The primary output of the CAN are sympathetic and parasympathetic neurons that innervate the heart. Top (prefrontal) down (subcortical) inhibition is associated with increased vagal input (^ HRV). 

A Neurovisceral Integration model (NIM)
A neurovisceral integration model (NIM) proposes that the autonomic nervous system is a final common pathway that links psychological and physiological states and that HRV can be a useful index of NIM and organism self-regulation. This can be thought of as a western model that describes the heart-mind concept that is familiar to eastern philosophy, traditional Chinese medicine and tai chi practice. Or more simply as Nelson Mandela said:
"A good head and a good heart are always a formidable combination."
Heart rate variability is also gaining a great of interest in the field of endurance exercise.  Endurance training is one of my interests and I own a watch and heart rate monitor that allow me to capture HRV data.  Oscar Wilde was onto something when he said  “Hearts Live By Being Wounded”,  yet there is a fine line between the stress that causes a healthy progressive adaptation, and the stress that can lead to imbalance and disharmony. Attention to HRV levels over time may help those undergoing strenuous training  attempting to attain peak condition while avoiding over training.

There are many measures used to quantify heart-rate variability some of which come from complexity, chaos and information theory. Included among these HRV measures are measures of entropy. In future posts if time avails I plan to keep something of a diary capturing my HRV in various activities, rest, biking, running, cognitive stress states of composing a blog or writing up statistical results at work. This should allow me to see how sensitive and reliable these indices are to various activities over time. Here are some examples:

First this is my HRV data yesterday at rest before heading out on my bike to work:

Beats Per Minute = 50.36
Shannon Entropy =2.84
Correlation Dimension (D2)=3.44

Beats per minute is simply a measure heart rate. Low beats per minute in a resting heart rate is associated with high HRV, thus 50 beats per minute resting HR suggests a likely high HRV. For the measure labled Shannon Entropy, a low score indicates more complexity and high HRV. Compared to this study of engineering students at rest in which their average Shannon Entropy was 3.17 my score of 2.84 is good sign. HRV reduces with age (I am 50 yrs old), but perhaps my endurance training is paying off (or maybe engineering students have trouble resting ) . Correlation Dimension (D2) is another measure of complexity. In this case a high score means high HRV. Again my results here look good as the average for the engineering students was 2.83.

Now here is my HRV data on the 1st 30 minutes of my bike to work (the software only allows a 30 minute max period).

Beats Per Minute = 124.8
Shannon Entropy =5.32
Correlation Dimension (D2)=0.547

This all makes sense. My HR speeds up due to the stress of the physical activity. Both the entropy and D2 measures indicate less complexity (thus lower variability) in my heart rate.

Now here is my HRV data on a mildly stressful writing task sitting at work:

Beats Per Minute = 60.67
Shannon Entropy =3.39
Correlation Dimension (D2)=3.24

Again this all makes sense. My HR is 10 beats higher than at rest in the morning. The entropy and D2 measures both indicate less complexity in the HRV thus somewhat more stress. Interestingly the paper I linked above with the engineering students was a study of HRV and stress on exams. According to table 5 in the paper I wouldn't have qualified as being under stress with the entropy or D2 measure (although D2 was very close). The data does suggest more stress than my earlier resting test. These measures seem to be doing a good job so far of quantifying stress loads.

Friday, May 3, 2013

Entropy and Natures Nested Relationships


Yield, and maintain integrity.
To bend is to be upright;
to be empty is to be full.

Those who have little have much to gain,
but those who have much
may be confused by possessions.
Excerpted from Tao Te Ching Chapter 22. Stan Rosenthal Translation

Entropy ( like information as discussed in my last post here ) has many meanings and definitions which can lead to confusion. Increasing entropy has been described as; increasing disorder, a dispersal of energy, an increase in information, an increase in uncertainty, a decrease in information, moving closer to equilibrium, and increase in freedom or possibility, and even as the flow of time itself.

Much of the confusion with the term in my view is related to its great potential for wide applicability across domains. The term entropy originated in physics from the laws of thermodynamics. These original thermodynamic laws however refer to closed systems like a gas within a container. Systems in nature however are never completely closed.

The domains in which entropy has been applied range across a wide spectrum from it's origin in the the purely physical theory of thermodynamics to it's more abstract uses in information theory. In between, entropy has also often been used to describe living systems. Here the great physicist Erwin Schrödinger ( of the quantum mechanical 'Schrödinger equation') providing an example from his wonderful book 'What is life':


"Every process, event, happening—call it what you will; in a word, everything that is going on in Nature means an increase of the entropy of the part of the world where it is going on. Thus a living organism continually increases its entropy—or, as you may say, produces positive entropy—and thus tends to approach the dangerous state of maximum entropy, which is death. It can only keep aloof from it, i.e., alive, by continually drawing from its environment negative entropy—which is something very positive as we shall immediately see. What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive."

As the quote above suggests, the nested quality of natures systems also adds to the potential for confusion. Our interpretation of entropy is relative to our frame of reference. The physicist JB Brissaud authored an interesting article in the journal 'Entropy' in 2005 with title 'The meanings of entropy'. Brissaud speaks to how the nested nature can impact the interpretation:
"Thermodynamics is the physical science which links the microscopic and macroscopic worlds and the meaning of entropy shows a curious mirror effect according to the adopted point of view; what is information for one is lack of information for the other."


Brissaud makes a crucial insight into the paradoxical nature of entropy. For an observer looking from the outside trying to understand a complex system, a low degree of entropy is associated with many interconnected subsystems that constrain each other allowing the system to resist the entropic pull towards dissipation and equilibrium. Yet if we consider the system itself as an observer, then the reverse is true. From the perspective of the system, entropy is associated with possibility, or freedom of choice. In other words from the point of view of an agent/organism, intelligent systems maximize their capacity to extract useful information or energy from their environments. 

Complex living systems are said to have low entropy because they have many inter-related sub-systems which constrain each other in a complex and constant flux of communication. Low entropy systems then are complex due to a large number of internal constraints which provide many pathways to enable the system to flexibly interact with the outside world under conditions of uncertainty. Very simple systems then are less adaptable and more vulnerable to environmental change. 

This resolves a paradox. Low entropy complex systems have an intrinsic intelligence that affords them the opportunity to learn from novel environmental conditions through a receptivity to uncertainty. Highly self-organized systems can be said to have the 'intelligence' to respond to a variety of possibilities. These systems can efficiently exploit resources ( stored energy ) from the environment and dissipate that energy back. Thus from an objective (outside) point of view complex living systems are maximum entropy producers, while from the organisms point of view existence is maintained by keeping internal entropy low.

A fascinating new computer simulation study (bbc news reports on it here) adds support to this conception of entropy by connecting maximum entropy production to the emergence and evolution of intelligence. The simulations are based on a 'causal entropic force' , which is guided by the goal of keeping as many options open as possible. From the BBC report:

"The simplistic model considers a number of examples, such as a pendulum hanging from a moving cart. Simulations of the causal entropy idea show that the pendulum ends up pointing upward - an unstable situation, but one from which the pendulum can explore a wider variety of positions. The researchers liken this to the development of upright walking. Further simulations showed how the same idea could drive the development of tool use, social network formation and cooperation, and even the maximisation of profit in a simple financial market."
"While there were hints from a variety of other fields such as cosmology, it was so enormously surprising to see that one could take these principles, apply them to simple systems, and effectively for free have such behaviours pop out," Dr Wissner-Gross said.
This reminds me very much of the intention one attempts to achieve in tai chi practice. One of the important principles in tai chi is to maintain the ability to respond to an opponent or the environment by moving in any potential direction. The idea is to never over-commit or predetermine ones physical or cognitive awareness or orientation in any given direction. Initially when learning the postures one learns how to place themselves in, and move between specific positions. With practice the awareness becomes more holistic (not on the specific postures), but instead on subtle feedback mechanisms that allow for continuous flowing movement within the context of some core guiding principles.  This is basically a practice in developing an internal body intelligence which once developed frees the awareness so that it may be receptive to the potential surprise that unfolds in an uncertain future.

This is similar to the way human physiology maintains it's vital  systems within a narrow range ( homeostasis ) with the support of other systems that respond more dynamically to unpredictable changes in the surrounding environment ( Allostasis ). Freedom and constraint while seeming to conflict and oppose each other can within the framework of negative feedback systems interact to support an equilibrium where complex self-organizing systems maintain integrity within (core constancy) while flexibly responding to change. The ability to adapt to the unknown represents maximum entropy from the perspective of the self-organizing system. To an outsider observer the same systems ability to maintain it's integrity against the force of entropy represents a far from equilibrium low entropy dynamic.

There is no promise extended however from the nature of entropic forces  that complex systems will maintain a persistent integrity. If the ability to exploit and dissipate the environments stored energy reserves outstrips our capacity to adapt to the entailing environmental changes then the system will no longer be sustainable. Consider our current rate of exploitation with regard to our natural resources (something will have to give).
"Yield, and maintain integrity;
be whole, and all things come to you".
Excerpted from Tao Te Ching Chapter 22. Stan Rosenthal Translation


Update: I had to link this wonderfully produced video of a David Foster Wallace commencement speech which I think beautifully expresses the concept of intelligence, wisdom and meaning being hinged to maximum entropy principles.