What does The GenoType Diet, Sudoku, and musical harmonics have in common? They are all based on matrix relationships; tables (really arrays) in which the constituents relate to each other in particular ways.
Many years ago, I took a summer course in computer music composition with Charles Dodge. Dodge, primarily known for a piece he created out of the Earth's magnetic field, was a gifted and supportive teacher, who in no short time clued me into the fact that I was no composer, but rather something that he termed a 'musical systems pre-programmer.' In short, the guy who wrote the programs that composers used to make music.
One of the things he was working on that I found especially fascinating was a concept that he called 'harmonic foldover', the idea that at certain points the sonorities ('resonance') of certain base frequencies could be manipulated to produce new harmonics, which would be created a precise intervals.
One of the most striking things that you hear when people talk about foods and diets, is who often they express their preference in musical terms.
"I try to eat in harmony with my local agriculture."
"I'm really in tune with this diet."
"A high protein diet really resonates with me. I can feel more balanced."
Working on the GTD food choices, I often reminisced about Dodge's theories. Although I've long forgotten his exact modus operandi I suspected that one could do this by using a series of mathematical tools called linear transformations, especially what are called Fourier transformations. Any example of a Fourier transformation would be to split up a radio frequency into its more basic fundamentals. Most of these functions work on matrices, not terribly different than those found in any Sudoku puzzle.
Here is a Latin Square, a matrix where each number occurs exactly once in each row and exactly once in each column.
The early Chinese mathematicians also had something called "Magic Square' which did something similar.
Again, art mimics life.
Fast Fourier transformations of matrix data are useful for many things, from the symmetry analysis of numbers and determining trajectories of comets. Because matrix data falls into the realm of linear algebra, transformations of the data always leave behind parts which have not been changed, the direction of the change, and how much change has occurred. These are called the Eigenvalues and Eigenvectors of the transformation. I love Eigenvalues, because they so easily plug into the multivariate characterizations that comprise the GenoTypes.
Now for the mimic part: 'Matrix' is derived from the Latin word matrices for 'womb'. Embryos are interested in symmetry, since it is an index of stability in their developmental environment and subsequent fitness. And, it would not be unkind to describe your journey through life from birth on as a type of epigenetic trajectory.
'All that openeth the matrix is mine.' --Ex. xxxiv. 19.
With this type of analysis, I can see that the future development of The GenoType Diet system will occur by way of food relationships, not individual foods. Put a live food, a piece of fish and a carbohydrate into that Latin Square and you will see what I mean*.
I described it at a recent working lunch for the NAP folks as 'visiting a deep cavern, having a normal conversation and soon realizing that all the words, their tones and inflections were blending into a constant drone of overtones as echoes and reverberations of each prior word are added to the base sound ---but a drone that is as identifiable as the voices of the people speaking. Now imagine that by being able to hear that sound, you could add more words and noises to make the overtone more pleasing and enjoyable.
That would be Geno Harmony.
* And maybe also see why the GTD products have names like 'Activator' and "Catalyst'.
2. A recent blog entry features this statement:
Frankly, I'm finding that naturopathic education is still leaving a lot to be desired (amazingly, they don't teach nutrigenomics; have one class each in genetics and immunology; and do not learn any statistics or bioinformantics). I know that there are the â€˜nuts and bolts' to teach, such as the anatomy and physiology, but it is surprising just how little space these students have for the real aspects of naturopathic practice, since they are so busy learning and memorizing a lot of things which will allow them to pass a board exam, but could more easily be simply looked up while in practice.
Which caused some upset with one of the clinic interns, who felt that this might give the impression that the education that they are receiving is not up to standard. I know my tone was a bit harsh, and I do apologize for that.
But like Laurie Anderson once said, "It is not the bullet that kills you; it's the hole."
I don't think naturopathic education is sub-standard. Far from it. NDs graduating from CNME approved schools are very highly trained medical professionals. My gripe (and it is only my opinion) is that the education is insufficiently non-standard, and perhaps unnecessarily formalized. But one should not take these things too far. Decrying and dissecting your education is the official national pastime of naturopathic medicine.
The John Bastyr College of Naturopathic Medicine, graduating class of 1982.
I've come back from paradise... or at least Saint Martin.
It was good to get some time out in the sun and swim in the beautiful blue Caribbean. I also rediscovered the pleasure of reading from books, versus all the reading that I do from computer monitors. With proper lighting it is just so much easier on the eyes. Everyone at the hotel was reading different books... except that they were all written by someone named Gresham.
I've never cultivated much of a taste for fiction, since you have to work so hard at populating a mental space to hold all the necessary components; the setting, theme, characters. I find that many people who do like fiction seem to have a type of RAM memory in a certain part of their brains that they can fill with all the plot details, then erase for use with the next novel. I feel sometimes that if I did too much of that it might push some of the other stuff out, so in the midst of all those murder mysteries, there I was with Paul Kennedy's â€˜Freedom From Fear' (a 900 page thriller on US history during the 1930's depression) and Larry Wall's â€˜Programming Perl' (made especially interesting by the fact that none of us took our computers with us).
I'm in the process of completing the SWAMI GenoType software (which is mostly written in Perl) and in a blitz of activity since my return it is now at the point where we can beta test it in the clinic. Pretty cool, if I do say so myself. It takes between 90 and 230 individual client parameters (blood groups, asymmetries, etc) and analyzes 700 individual foods according to 200 nutrient parameters (antioxidants, propensity to foster microbial overgrowth, acetylcholine content, etc.) For all those 12,600,000 individual calculations, the program is quite fast, though I do admit to a perverse pleasure sitting there for about 30 seconds watching it groan under the strain.
One of the mottos of Perl is that â€˜There is more than one way to do it' (TIMTOWTDI, usually pronounced "Tim Toady"). The more that I think about it, there is a lot of Tim Toady in my nutrition research as well.
Probably because at heart I am fundamentally a post-modernist.
Post modernists believe in AND more than OR, whereas modernists tend to give OR precedence in their lives and thoughts. The folks who get all bent out of shape about â€˜the GTD versus the BTD' are probably modernists and think that there is only one path to the truth. There is certainly one truth (or fact, or whatever) but that is not the same as saying that there is only one way to find it.
We've been rearranging the clinic this past weekend. My office is being converted into a more general-use, conference-type room. While this sounds perhaps like a demotion, it is actually being done at my request. With the addition of Dr. Colicci to the D'Adamo Clinic staff, we are doing more of a team approach to the patients, and this did not work with an office devoted to just one physician.
Probably the best thing we're adding to the room is a 4' by 8' white dry erase board. This will allow us to 'teach' the patient about the particulars of how we plan to structure their approach. I normally do a lot of this, most often drawing on the examination table paper (which many people take home as a souvenir). I love to explain stuff, but I'm a very 'visual' type person (love to draw, etc.) and if truth be told have always been a bit nonplussed by the whole 'performance' component of doctor consultations, i.e me behind the desk, across from the patient.
It is amazing what this small change in visit structure has done to my perspective. Whereas I used to think 'I've got six patients today,' I'm now finding that I'm thinking 'Hey, I've got six classes to teach today.'
This will also be helpful with regard to the practitioner training that we do at the Clinic, since I can't think of the last time I've seen a patient when there was not an extern or preceptor in as well. Frankly, I'm finding that naturopathic education is still leaving a lot to be desired (amazingly, they don't teach nutrigenomics; have one class each in genetics and immunology; and do not learn any statistics or bioinformantics). I know that there are the 'nuts and bolts' to teach, such as the anatomy and physiology, but it is surprising just how little space these students have for the real aspects of naturopathic practice, since they are so busy learning and memorizing a lot of things which will allow them to pass a board exam, but could more easily be simply looked up while in practice.
SWAMI is coming along nicely. I've written another 1,000 lines of code; mostly the 'calculation' subroutines. A bit more of that and I'll more onto the 'search and sort' and 'report' modules. I'm thinking of licensing a consumer version (SWAMI-lite) of the program that will allow anyone for a small fee to input their own data and run a single version of the SWAMI program. I'll just have to see how practical it is.
Final plug for the lecture that I will be giving at the New York Open Center, February 15th at 7:30 PM. It is only $30, and they give you a free hardcover copy of The GenoType Diet which I would be most happy to personally inscribe for you. Click here for more info.
This late breaking bit of news: I've just received an email that the supplement facts boxes are now online for all The GenoType Diet products. Hopefully this will provide folks with the information that they need to decide whether they want to include these products in their supplement plans. A big thanks to my friends Jon Humberstone and Keith McBride for working over the weekend to make this happen.
Video of the Month:
Michael Moore is a guy it is not hard to have an opinion on, and I actually have a few. However his film 'Sicko' does cast aside the curtain on the con-job that Americans are fed about just how 'great' our health care system is. In the meantime in this video clip he also shows just how flaccid and conformist the US major media is:
A possible reason why the long headed GT5 Warriors are often taller than GT3 Teachers and GT4 Explorers:
In the article the development of skull measurements and head measurements (length and breadth) and of the cephalic index, calculated from these measurements, since the Neolithic period are presented. The results obtained from the historical material are compared with those of living persons. The measurements as well of the skull as of the head show secular changes. The following general trend was found: an increase of body height is connected with a debrachycephalisation* and a decrease of body height is connected with a brachycephalisation. It can be emphasized that brachycephalisation/debrachycephalisation are part of the secular trend. Therefore environmental factors are responsible for the described changes of measurements of the skull and the head in a broadest sense.
* Debrachycephalisation: the tendency for head shapes to become less 'square-like' and more elongated over succeeding generations. Brachycephalisation is the opposite.
Is head size modified by environmental factors? Z Morphol Anthropol. 1998;82(1):59-66.
A hypothesis is framed about which any influences of the nutrition may cause variations of the cranium, but concerning physiological data, kinds of nutrition and special victuals' ingredients cannot still be mentioned. If such connexions are proved, at last the well known brachycephalization among European populations since the Middle Ages and the beginning debrachycephalization in the present time could partially be interpreted.
The brachycephalisation problem, a nutrition constitutional problem? Gegenbaurs Morphol Jahrb. 1989;135(5):689-96.
Probably why GT4 Explorers usually are thicker boned than GT1 Hunters:
A growing body of archeological evidence suggests that the dramatic climatic events of the Last Glacial Maximum in Europe triggered important changes in foraging behavior, involving a significant decrease in mobility. In general, changes in mobility alter patterns of bending of the midshaft femur and tibia, resulting in changes in diaphyseal robusticity and shape. This relationship between levels of mobility and lower limb diaphyseal structure was used to test the hypothesized decrease in mobility. Cross-sectional geometric data were obtained for 81 Upper Paleolithic and Mesolithic European femora and tibiae. The sample was divided into three time periods: Early Upper Paleolithic (EUP), Late Upper Paleolithic (LUP), and Mesolithic (Meso). In addition, because decreased mobility often results in changes in sex roles, males and females were analyzed separately. All indicators of bending strength decrease steadily through time, although few of the changes reach statistical significance. There is, however, a highly significant change in midshaft femur shape, with LUP and Meso groups more circular in cross-section than the EUP sample, supporting archeologically based predictions of decreased mobility. Sexual dimorphism levels in diaphyseal strength remain low throughout the three time periods, suggesting a departure in Upper Paleolithic and Mesolithic foragers away from the pattern of division of labor by sex observed in modern hunter-gatherers. Results confirm that the onset of the Last Glacial Maximum represents a crucial stage in Late Pleistocene human evolution, and signals the appearance of some of the behavioral adaptations that are usually associated with the Neolithic, such as sedentism.
Mobility in Upper Paleolithic and Mesolithic Europe: evidence from the lower limb. Am J Phys Anthropol. 2003 Nov;122(3):200-15.
However marauding GT1 Hunters are on average, taller than glacial refugee GT4 Explorers:
Long bone lengths of all available European Upper Paleolithic (41 males, 25 females) and Mesolithic (171 males, 118 females) remains have been transformed into stature estimates by means of new regression equations derived from Early Holocene skeletal samples using "Fully's anatomical stature" and the major axis regression technique (Formicola & Franceschi, 1996). Statistical analysis of the data, with reference both to time and space parameters, indicates that: (1) Early Upper Paleolithic samples (pre-Glacial Maximum) are very tall; (2) Late Upper Paleolithic groups (post-Glacial Maximum) from Western Europe, compared to their ancestors, show a marked decrease in height; (3) a further, although not significant, reduction of stature affects Western Mesolithics. Evaluation of possible causes for the great stature of the Early Upper Paleolithic samples points to high nutritional standards as the most important factor. Results obtained on later groups clearly indicate that the Last Glacial Maximum, rather than the Mesolithic transition, is the critical phase in the negative trend affecting Western European populations. While changes in the quality of the diet, and in particular decreased protein intake, provide a likely explanation for that trend, variations in levels of gene flow probably also played a role. Reasons for the West-East Mesolithic dichotomy remain unclear and lack of information for the Late Upper Paleolithic of Eastern Europe prevents insight into the remote origins of this phenomenon. Analysis of regional differentiation of stature, particularly well supported by data from Mesolithic sites, points to the absence of today's latitudinal gradients and suggests a relative homogeneity in dietary, cultural and biodemographic patterns for the last hunter-gatherer populations of Western Europe.
Evolutionary trends of stature in upper Paleolithic and Mesolithic Europe. J Hum Evol. 1999 Mar;36(3):319-33.
Not because of shorter upper legs, but rather shorter lower ones..
Among recent humans brachial and crural indices* are positively correlated with mean annual temperature, such that high indices are found in tropical groups. However, despite inhabiting glacial Europe, the Upper Paleolithic Europeans possessed high indices, prompting Trinkaus (1981) to argue for gene flow from warmer regions associated with modern human emergence in Europe. In contrast, Frayer et al. (1993) point out that Late Upper Paleolithic and Mesolithic Europeans should not exhibit tropically-adapted limb proportions, since, even assuming replacement, their ancestors had experienced cold stress in glacial Europe for at least 12 millennia. This study investigates three questions tied to the brachial and crural indices among Late Pleistocene and recent humans. First, which limb segments (either proximal or distal) are primarily responsible for variation in brachial and crural indices? Second, are these indices reflective of overall limb elongation? And finally, do the Late Upper Paleolithic and Mesolithic Europeans retain relatively and/or absolutely long limbs? Results indicate that in the lower limb, the distal limb segment contributes most of the variability to intralimb proportions, while in the upper limb the proximal and distal limb segments appear to be equally variable. Additionally, brachial and crural indices do not appear to be a good measure of overall limb length, and thus, while the Late Upper Paleolithic and Mesolithic humans have significantly higher (i.e., tropically-adapted) brachial and crural indices than do recent Europeans, they also have shorter (i.e., cold-adapted) limbs. The somewhat paradoxical retention of "tropical" indices in the context of more "cold-adapted" limb length is best explained as evidence for Replacement in the European Late Pleistocene, followed by gradual cold adaptation in glacial Europe.
* Crural index is the result of multiplying the length of the lower leg (tibia) by 100 and dividing it by the length of the upper leg (femur).
Brachial and crural indices of European late Upper Paleolithic and Mesolithic humans. J Hum Evol. 1999 May;36(5):549-66.
Here are a few more scientific studies which could pass for the more outlandish claims of The GenoType Diet. Finger digit ratios (the comparison of the lengths of the ring and index fingers) correlate with other facial structures used in The GenoType Diet, such as jaw angle and other asymmetries. Put it all together and you get (drum roll, please):
The second-to-fourth-digit ratio (2D:4D) may be related to prenatal testosterone and estrogen levels and pubertal face growth. Several studies have recently provided evidence that 2D:4D is associated with other-rated facial masculinity and dominance, but not with facialmetric measures of masculinity. We found that localized face shape differences, shown here to be sexually dimorphic* and related to ratings of dominance, were associated with direct and indirect measurements of 2D:4D. In this study we examined various localized features of the face, showing nose width, jaw angle, and lip height to be sexually dimorphic. We then had faces rated for dominance and saw that the most dimorphic characteristics were those most associated with rated dominance, with typically masculine characteristics tending to be associated with high ratings of dominance. Finally, 2D:4D measurements were made using three different techniques. High (feminine) values of 2D:4D were associated with feminine facial characteristics in women, but not in men. It was concluded that certain aspects of facial development are governed by factors that are established prenatally. These aspects may be associated with perceptions of the self by others that are important in the social environment, particularly in terms of intra-sexual competition and mate acquisition.
* Dimorphism is the systematic difference in form between individuals of different sex in the same species.
2D:4D and sexually dimorphic facial characteristics. Arch Sex Behav. 2007 Jun;36(3):377-84.
The average human male face differs from the average female face in size and shape of the jaws, cheek-bones, lips, eyes and nose. It is possible that this dimorphism is determined by sex steroids such as testosterone (T) and oestrogen (E), and several studies on the perception of such characteristics have been based on this assumption, but those studies focussed mainly on the relationship of male faces with circulating hormone levels; the corresponding biology of the female face remains mainly speculative. This paper is concerned with the relative importance of prenatal T and E levels (assessed via the 2D : 4D finger length ratio, a proxy for the ratio of T/E) and sex in the determination of facial form as characterized by 64 landmark points on facial photographs of 106 Austrians of college age. We found that (i) prenatal sex steroid ratios (in terms of 2D : 4D) and actual chromosomal sex dimorphism operate differently on faces, (ii) 2D : 4D affects male and female face shape by similar patterns, but (iii) is three times more intense in men than in women. There was no evidence that these effects were confounded by allometry or facial asymmetry. Our results suggest that studies on the perception of facial characteristics need to consider differential effects of prenatal hormone exposure and actual chromosomal gender in order to understand how characteristics have come to be rated 'masculine' or 'feminine' and the consequences of these perceptions in terms of mate preferences.
Second to fourth digit ratio and face shape. Proc Biol Sci. 2005 Oct 7;272(1576):1995-2001.
Sex steroids are supposed to moderate the differences between male and female facial characteristics. Studies on women's preferences for male faces reported increased preferences for facial architecture developed under the influence of testosterone as this may indicate masculinity, dominance and social status. Recent research demonstrates that facial sexual dimorphism does not only develop at puberty but may be organized much earlier in ontogeny. However, the actual cause and timing of variation in facial shape due to sex-steroids remains speculative. This study uses data from Neave and colleagues who measured digit ratio (2D:4D) as a proxy to prenatal testosterone and also salivary testosterone samples in order to study differential effects of androgens on perceived male facial shape. Male facial shape was regressed upon 2D:4D ratio and circulating levels of testosterone by means of geometric morphometric methods. We found some evidence for opposite effects of early androgen action (via 2D:4D ratio) on the upper and the lower face respectively (i.e. low 2D:4D ratio results in a relatively robust and prominent lower face), whereas circulating testosterone seems to cause a rather uniform elongation of the face. Local deformations primarily show pronounced and medially tailed eyebrows for the shapes associated with increasing salivary testosterone. These preliminary results suggest that prenatal and pubertal testosterone have differential effects on male facial shape that should be considered in future studies on women's preferences towards male facial appearance.
Visualizing facial shape regression upon 2nd to 4th digit ratio and testosterone. Coll Antropol. 2005 Dec;29(2):415-9.
Deviations of physical characteristics from bilateral symmetry, in otherwise symmetric individuals, are supposed to result from environmental perturbations during development. One cause of such perturbations may be sex steroids such as testosterone and estrogen. AIM: The study examined the relationship between second to fourth digit ratio (2D:4D), a putative negative correlate with prenatal testosterone and a positive correlate with prenatal estrogen, and asymmetry. METHODS: Eleven traits (including the second and fourth finger lengths) were measured in a sample of 680 English children aged 2-18 years, and second to fifth finger lengths in samples of 120 Austrian and English undergraduate students aged from 17 to 30 years and 213 Polish adults aged from 26 to 90 years. RESULTS: Significant U-shaped curvilinear associations between 2D:4D and all 11 traits were found in English children with the strongest associations between 2D:4D and composite asymmetry of second plus fourth digit, and second to fifth digits. Further investigation of the relation between 2D:4D and digit asymmetries in the sample of Austrian and English undergraduates and the Polish adults confirmed significant U-shaped relationships between 2D:4D and finger asymmetries. CONCLUSION: Our data show that both low 2D:4D (a marker of high prenatal testosterone) and high 2D:4D (a marker of high prenatal estrogen) are associated with elevated levels of asymmetry and this relationship applies particularly to finger asymmetry.
The second to fourth digit ratio and asymmetry. Ann Hum Biol. 2006 Jul-Aug;33(4):480-92.