Tag Archives: neat science

Embryogenesis Explained Feedback 1


We sent out a message to everyone of of the 1900+ scientists we referenced in our book. Some of the answers we have gotten back have been fun to read.

Dear Richard,

I can’t imagine why you might have cited my work in ecology in Embryogenesis Explained.  You’ve certainly piqued my curiosity, though. Can you give me a hint?  :o)
Congratulations on your achievement.  I look forward to hearing back from you.
All the best,

Dear Peter,

Well, I’ve lived in Canada long enough to know how to build a quinzhee. Here’s the paragraph in Chapter 12 ending with a reference to:

Marchand, P.J. (2014). Life in the Cold: An Introduction to Winter Ecology. Hanover,  University Press of New England, 4th.

In biology, the atom is generally the level at which we start our studies.

The energies involved in splitting atoms or fusing atomic nuclei releases

ionizing radiation which damages living organisms. So we think of

organisms as made up of stable atoms, and usually do not have to trouble

our thoughts with what is going on at lower, subatomic levels. Exceptions

are when we have to think about the key role of natural background

radiation in generating mutations, and thus in evolution23. This energy

also keeps the ground warm in winter (ref 24), permitting life to go on under

the snow (ref 25).

This is part of the background setting up reductionism vs holism in solving embryogenesis. The rub is that quantum mechanics is holistic, as I show. Had this checked by a friend who writes books on quantum mechanics.

While it’s not my forte, I have taught Pollution Biology, and learned some ecology in the process. There seems to be a nice overlapping field of ecoembryology waiting to be developed. I coined the word while writing a grant application:

Rudloe, J., N.K. Björklund-Gordon, R. Gordon, A. Hodges, M. Hodges, K. Lu, E.W. Cake & C. Rudloe (2013). A Vision for Sustainable Farming of Oysters Along Florida’s Forgotten Coast: A Restore Act Proposal. Panacea, Florida,  Gulf Specimen Marine Laboratory.

which didn’t get funded. I suspect that oyster embryos differ in salinity tolerance depending on the salinity in which their mothers existed, and that seeding with spat would be more successful if this were understood.
So that’s the tale, and you might enjoy our book. Thanks.
Yours, -Dick Gordon

Embryogenesis Explained is printed!

We got an email message today from someone who had preordered their copy of our book Embryogenesis Explained. His copy has arrived and he was reading it and enjoying it! How exciting is that? Our own personal copies are somewhere in transit. Hopefully they will arrive in Alonsa shortly.

We are also sending out a personal email to every single one of the over 1900 scientists whose work is cited in the book. This assumes that they are still with us, as some have gone on to that great laboratory in the sky. And it also assumes that we can find a correct email. Some of these scientists are retired and some have vanished from academia, or are students who have graduated and gone on to other careers.

We are also sending out emails inviting book reviewers. If you are a scientist or someone interested in science written at a popular level and would like do a review for publication, we can arrange for you to have a free copy for review purposes. Just contact us and we can start the ball rolling.

If you use the code WSGSML20 you will get a 20% discount. The code is good until December 31.


Biocommunication Sign-Mediated Interactions between Cells and Organisms

Gordon&Seckbach2016 Biocommunication Table of Contents

Dick’s latest book published by World Scientific as coeditor with Joseph Seckbach is now off to the printers. It includes a chapter on the Cybernetic Embryo which is an expansion of the idea in the final chapter of our book Embryogenesis Explained. The book will be out about December 2016.

Table of Contents:

Part I Theoretical Approaches

1. Molecular Biocommunication by Alexei A. Sharov

2. Key Levels of Biocommunication by Guenther Witzany

3. Zoosemiotics, Typologies of Signs and Continuity Between Humans and Other Animals by Dario Martinelli

4. Communication as an Artificial Process by Massimo Negrotti


5. Cybernetic Embryo by Richard Gordon and Robert Stone

6. Superfast Evolution via Trans and Interspecies Biocommunication by Ille C. Gebeshuber and Mark O. Macqueen

7. Channel Capacity and Rate Distortion in Amino Acid Networks by Boaz Tamir and Avner Priel

8. Communication Languages and Agents in Biological Systems by Subhash Kak

Part II Experimental Approaches


9. Chemical Communication by Ally R. Harari and R. Sharon

10. Paenibacillus vortex — A Bacterial Guide to the Wisdom of the Crowd by Alin Finkelshtein, Alexandra Sirota-Madi, Dalit Roth, Colin J. Ingham, and Eshel Ben Jacob

11. The Crosstalk Between Plants and Their Arbuscular Mycorrhizal Symbionts: A Mycocentric View by Cristiana Sbrana, Alessandra Turrini, and Manuela Giovannetti

12. Attraction of Preferred Prey by Carnivorous Plants by Douglas W. Darnowski

13. Animal Communication: Competition for Acoustic Space in Birds and Fish by Hans Slabbekoorn

14. The Contribution of Biocommunication (BICO) to Biomedical and Tissue Engineering: A Tech Mining Study by Angela Machado Rocha, Fernando Palop, Maria Clara Melro, and Marcelo Santana Silva

15. Communication Languages and Agents in Biological Systems by Noga Gershoni-Emek, Eitan Erez Zahavi, Shani Gluska, Yulia Slobodskoy, and Eran Perlson

16. Ethical Methods of Investigation with Pan/Homo Bonobos and Chimpanzees by E. Sue Rumbaugh, Itai Roffman, Elizabeth Pugh, and Duane M. Rumbaugh

17. Conversing with Dolphins: The Holy Grail of Interspecies Communication? by Toni Frohoff and Elizabeth Oriel

On a Mathematical Limitation to Lawn Mowing

Natalie and I avoid shoveling snow by heading to the Deep South each winter. But now that we’ve acquired a wheelless house in Manitoba (to distinguish it from our wheel house, our trailer, as named by grandson Nick), we are subject to the opposite season’s green scourge, luxuriant growth of grass over the brief summer that, due to long days here up North, is faster by far than my beard growth, which I also prefer to neglect. Now this is great for our tall grass prairie quarter section, with stalks that reach over my head, but in nearby small town Alonsa the one sin no one dare yield to is not mowing one’s lawn.

The first year of sessile life we hired a fellow with his ride-on to mow our lawn. He was delayed, and the grass, not understanding the situation (despite its undoubtedly self-centered intelligence: Mancuso & Viola 2015) grew beyond its legal height. I was summoned and reported for my imminent handcuffing and arrest. I was told sternly that if I don’t cut my lawn in a timely fashion, the local government would do it and charge me $16/hour. I said “Great”, as I was already paying $20/hour, and they immediately backed off. So much for Justice. Nevertheless, in the name of civil peace, realizing that our community relations should not be left to a busy intermediary, we bought our own lawn mower.

Now despite my lifelong interest in local/global interactions (Gordon, 1966; Portegys et al., 2016), the way I mow grass is strictly local. I mow a line, and then I follow that line, then go back following that line, etc. I don’t look where I’m going. Of course, with laser guided tractors which can hoe a straight line to an accuracy of 0.6 centimeter over a track length of 220 meters (van Zuydam, Sonneveld & Naber, 1995), my approach is antiquated. But I do it deliberately, to amuse myself with a mathematical puzzle, which today I realized I can try to formulate precisely and share with you. What else is there to think about while chopping off the heads of dandelions and developing green toes, if not a green thumb (due to mowing with open toed slippers, not recommended)?


Given a semi-infinite plane (which we can approximate by a strip infinite in one dimension, with periodic boundary conditions in the other direction), we start aligned with its straight edge at, say, x=0 and mow a strip of unit width. Then we do it again. If perfection attained, sequential curves could be designated by y(i,x) = i, i.e., we would have no excuse to stop mowing until the job is done. The excuse lies in our own imperfection.

SAM_7653So we need a function to represent my inability to walk a straight line. Now, blindfolded we walk in circles as small as 20 meters in diameter (Souman et al., 2009), which would be great for limiting the duration of mowing, though I would then chop through the electric cord tethering our mower. While this fundamental result, attributed to “accumulating noise in the sensorimotor system”, has been cited 53 times already, we must look elsewhere for a function to represent noise in the mowing trajectory. For this I turn to boids.

Boids are idealizations of flocking birds and schooling fish. I actually did the first computer simulation of such “swarms”, back in the mid-1960s, while I was a graduate student corresponding with and then visiting the master of schooling fish, Charles Breder (Breder, 1929, 1951, 1954, 1965, 1967) at the Mote Marine Lab in Florida where he retired. This was 2 decades before the first boids simulation in 1986 (Reynolds, 2001). Unfortunately I didn’t think much of the result, because I placed the “fish” into a circular mill, which slowed down as they swam. Breder thought this was realistic, from his personal observations of milling fish. However, I simulated only 300 fish in a plane, on a mainframe computer so slow in those days that the “fish” didn’t get far during the computer time I could command, but a fraction of a turn. I couldn’t tell if the mill was stable, even though we knew that ants would follow each other in a mill unto their death (Schneirla, 1944).  (That’s what local rules will get you! So much for emergence.) So we didn’t publish it. Nowadays whole murmurations of hundreds of thousands of boids in full 3D can be simulated with ease (Ikegami, 2015), and milling is old hat mathematically (Lukeman et al., 2009; Calovi et al., 2014).

The relation between boids and lawn mowing is that a boid aligns with the average direction of its near neighbors, while I align with my former self, at least insofar as my nearby previous track across the grass is what I use to estimate my next direction, moment by moment. So-called “error” of alignment for boids has been discussed (Watson, John & Crowther, 2003) but not its physical and/or mental source. But we may not have to have our heads examined (except as to why we mow grass in the first place). A simple trigonometric error analysis shows that if boids make small errors in the vectorial direction of their motion, their net random motion perpendicular to the mean direction of motion is much larger than that along the direction of motion (Toner & Tu, 1998). Thus the wavy curvature of my lawn mowing will amplify, until my mowing path closes upon and crosses itself and my need to mow ceases (invoking my local-only rule and my goal of death to lawnmowing). This is what mathematics is for: justifying as little mowing as I can get away with. The only thing left to do is calculate how much alcohol I would have to consume so that my error and thus the curvature reaches this closing point before my (finite) lawn is completely mowed. For math aficionados, note that local lawnmowing is an example of a stochastic wave in an active medium, but a peculiar one, as propagation is in finite steps, opening up great new insights into discrete aspects of the continuum. I rest my case and my lawn mower, and leave it for the ambitious computer programmer and/or mathematician to work out the details, while I lounge on my lawn chair. RAASAM_7651

Breder, C.M. (1929). Certain effects in the habits of schooling fishes, as based on the observation of Jenkinsia. Amer Mus Novitates 382, 1-5.

Breder, C.M. (1951). Studies on the structure of the fish school. Bulletin of the American Museum of Natural History 98(1), 1-28.

Breder, C.M. (1954). Equations descriptive of fish schools and other animal aggregations. Ecology 35(3), 361-370.

Breder, C.M. (1965). Vortices and fish schools. Zoologica New York 50(2), 97-114.

Breder, C.M. (1967). On survival value of fish schools. Zoologica-New York 52(2), 25.

Calovi, D.S., U. Lopez, S. Ngo, C. Sire, H. Chaté & G. Theraulaz (2014). Swarming, schooling, milling: phase diagram of a data-driven fish school model. New J. Phys. 16, #015026.

Gordon, R. (1966). On stochastic growth and form. Proceedings of the National Academy of Sciences USA 56(5), 1497-1504.

Ikegami, T. (2015). A dynamics of large scale swarms. https://carnegiescience.edu/events/lectures/re-conceptualizing-origin-life

Lukeman, R., Y.X. Li & L. Edelstein-Keshet (2009). A conceptual model for milling formations in biological aggregates. Bulletin of Mathematical Biology 71(2), 352-382.

Mancuso, S. & A. Viola (2015). Brilliant Green: The Surprising History and Science of Plant Intelligence, Island Press.

Portegys, T., G. Pascualy, R. Gordon, S. McGrew & B. Alicea (2016). Morphozoic, cellular automata with nested neighborhoods as a metamorphic representation of morphogenesis [invited]. In: Multi-Agent Based Simulations Applied to Biological and Environmental Systems. Ed.: D.F. Adamatti, IGI Global: Submitted.

Reynolds, C. (2001). Boids: Background and Update. http://www.red3d.com/cwr/boids/

Schneirla, T.C. (1944). A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation. Amer Mus Novitates(1253), 1-26.

Souman, J.L., I. Frissen, M.N. Sreenivasa & M.O. Ernst (2009). Walking straight into circles. Current Biology 19(18), 1538-1542.

Toner, J. & Y.H. Tu (1998). Flocks, herds, and schools: A quantitative theory of flocking. Physical Review E 58(4), 4828-4858.

van Zuydam, R.P., C. Sonneveld & H. Naber (1995). Weed control in sugar beet by precision guided implements. Crop Prot. 14(4), 335-340.

Watson, N.R., N.W. John & W.J. Crowther (2003). Simulation of unmanned air vehicle flocking. In:  Theory and Practice of Computer Graphics, Proceedings. Ed.: M.W. Jones: 130-137.




Near Misses: Paths not Crossed with Richard Bellman

World Scientific Publishing recently had a sale of electronic books, in which I came across and downloaded:

Bellman, Richard (1984). Eye of the Hurricane: An Autobiography,  World Scientific. Web:  https://books.google.com/books?id=6rN7QgAACAAJ; http://www.worldscientific.com/worldscibooks/10.1142/0076

for US$9.90. I had heard that Bellman had a reputation of meeting someone, having a chat, and sending them a manuscript to co-author the next day. In this way he was the applied math complement to Paul Erdös, about whom I wrote:

Gordon, R. (2011). Cosmic Embryo #1: My Erdös Number Is 2i.  http://www.science20.com/cosmic_embryo/cosmic_embryo_1_my_erd%C3%B6s_number_2i

While Bellman doesn’t discuss this story, he did love to travel, and much of the book is about the places he has been, even including in some cases the addresses of hotels he liked. He was indeed prolific: “Over the course of his career he published 619 papers and 39 books. During the last 11 years of his life [1920-1984] he published over 100 papers despite suffering from crippling complications of brain surgery” (https://en.wikipedia.org/wiki/Richard_E._Bellman). Whoever added his CV to the end of the autobiography upped it to 620 papers and 40 books. While it was written in 1978, his autobiography seems to have been published after his death in 1984. He doesn’t even mention his medical condition in the book.

What what I found uncanny about his autobiography is how many people he names who I also knew, and one he didn’t name, but undoubtedly knew: my own father, Jack Gordon. I deduce this because both played handball at Brighton Beach near the boardwalk to Coney Island, New York, on one-wall courts. Bellman, born in 1920, was 7 months older than my father, who I recall was winning at handball at age 13, on those courts. Maybe he trounced Bellman. While my father focussed on handball all his life and became a USA national champion (Singer, Stuffy (1994). Gordon honored with Kendler Award. Handball 44(1), 18.), Bellman was an all-round jock, claiming to excel at other sports: tennis, table tennis, track, football, basketball, baseball, swimming. He even did some ballet. I can recall those courts, the boardwalk, the hot summer beach on which one could hard boil an egg, building sand castles, the lines of rocks with oysters perpendicular to the beach, out into the water, and Nathan’s hotdog stand. It was there my mother, then Diana Lazaroff, met my father. This book rang of childhood nostalgia for me. I was raised nearby until age 5, when my parents moved to Chicago about 1948.

But our lives were further intertwined. I postdoced with Stanislaw Ulam; he reviewed Ulam’s “A Collection of Mathematical Problems”, and knew him well. Three more misses: “Nixon announced that two billion dollars would be available for cancer research. The experts in the field were to gather in Warrentown, Virginia, a suburb of Washington, to divide up the pie. I was chairman of a committee on the use of mathematical methods. The other members of the committee were, John Jacques, Fred Grodins, Bob Rosen, Monas Berman, and John Hearon…. At Warrentown, we had a good time deciding how we would spend the money. Alas, it was a typical Nixon trick. He posed for TV cameras and gave away pens, but not a penny ever appeared.” I had postdoced with Bob Rosen at the Center for Theoretical Biology at SUNY/Buffalo, worked under John Hearon at the Mathematical Research Branch at NIH, and knew Monas Berman while there. Natalie and I had a strange encounter with Bellman’s former student John Casti at the Third International Workshop, Open Problems of Computational Molecular Biology, Telluride, Colorado, July 11-25, 1993, albeit after Bellman’s death. Casti, guest of honor, left the conference the first evening, when (not knowing who he was) I said to him “we can explain that” in reference to a remark about embryology by the host. Beyond that, the book is full of names of mathematicians and scientists whose work I knew, a slice in time through that culture, written by someone one generation ahead of me, but overlapping. It was quite a journey, watching Bellman’s parallel life.

It was from a couple of Bellman’s math books that I learned about concepts such as differential-delay equations and invariant embedding. The former helped me understand the 30 year cycle in academic hiring, reported going back to the 1800’s in:

Nyhart, L.K. (1995). Biology Takes Form: Animal Morphology and the German Universities, 1800-1900. Chicago,  University of Chicago Press.

Let’s say jobs are available for would-be professors. Lots of students decide to go into the open disciplines. By the time they are trained (the delay), the jobs are being snarfed up. So the next generation of students seek other disciplines. And so it goes, with no one doing long-range, 30 or more year planning, to equalize supply and demand. I suppose we could call the oscillating academic job market an emergent phenomenon! I actually hit one of those peaks, at age 33 in 1977, when I applied for 100 jobs, got a couple of interviews, and no offers. Out of luck, with 300 to 500 younger applicants per job opening at that time, I answered a phone call from Winnipeg asking me to recommend someone for a job there with “How about me?”. And so I ended up at the University of Manitoba.

Like Ulam (who is discussed in my blog on Erdös), Bellman was a mathematician first. For instance, he had a moral compunction to work on the H-bomb, but when his math didn’t prove useful to the project, he dropped out, rather than solve the problem with whatever it took. As with Ulam, we would not have seen eye to eye: “There is a subtle difference between mathematical biologists and theoretical biologists. Mathematical biologists tend to be employed in mathematical departments and to be a bit more interested in math inspired by biology than in the biological problems themselves, and vice versa” (Gordon, R. (1993). Careers in theoretical biology. Carolina Tips 56(3), 9-11, http://life.biology.mcmaster.ca/~brian/biomath/careers.theo.biol.html).

I was about to wind up this blog by adding a photo of Bellman, but came across something even better, a movie by his grandson:

Bellman, G.L. (2011). The Bellman Equation [movie].  http://www.bellmanequation.com; http://www.amazon.com/Equation-Goldstein-Betty-Jo-Dreyfuss-Landauer/dp/B00C6WHRM4

So rather than color my blog by the movie, I’ll post this first, and enjoy the movie tonight with Natalie.

20% off our book thanks to GSML

Thank you Gulf Specimen Marine Lab!

Big news at Gulf Specimen     
“Embryogenesis Explained”
Now available for pre-order!!
Announcing the newest book by co-authors Dick and Natalie Gordon, about embryology; that Gulf Specimen fully recommends to anyone interested in conception of life and the development of cells.
Here’s a video directly from the author herself, explaining the purpose behind their book, “Embryogenesis Explained”

For years, these Canadian scientists have been involved as volunteers and advisors on a wide variety of technical subjects.  Such as digitizing all of Jack & Anne Rudloe’s book to be available on Kindle, applying for government grants to improve the facility, helping  with the success of our online fundraising campaigns and studying the behavior of octopuses and their human interactions.

They also have decades of experience of raising aquatic life in captivity, including disease control and nutrition. Over the past few months, Dick and Natalie have spent their evenings finalizing their book, ” Embryogenesis Explained” right here in Panacea, FL.

Now is your chance to get in on the ground floor of this unique and easy to understand book.  Pre-order your copy today and use the code “WSGSML20” and receive an extra 20% off.
Click the link below to find out more:


Our latest publication!

Gordon, N.K. & R. Gordon (2016). The organelle of differentiation in embryos: the cell state splitter [invited review]. Theoretical Biology and Medical Modelling 13(Special issue: Biophysical Models of Cell Behavior, Guest Editor: Jack A. Tuszynski), #11. (The publication is open source, no fee to read.)


The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on “Embryogenesis Explained” (World Scientific Publishing, Singapore, 2016).