From Trees To Networks


When I was very itty-bitty and went to synagogue, there were certain moments when I felt the presence of the Deity so clearly and strong that my eyes and ears would be fixed on the events on the pulpit and I would tremble. This happened at the point in the liturgy when the Cantor held the Torah over his head. The Torah is the set of scrolls that contain the first five books of the Old Testament, hand copied onto the parchment in Hebrew. This alone was a marvelous achievement for this man with a deformed hip who did not exactly look as if he pumped iron.  He sang majestically, and the whole congregation knew this tune cold. Everyone also knew the words.

The words were those of Proverbs 3:18. “It is a tree of life to those who hold it fast….” As a child I regularly visited the cemetery with my family.  My Father-Of-Blessed-Memory would speak the prayers for the dead for the whole family, as my mother did not know how and my brother was too young and I probably believed I was, too — except really I was too female, but not yet in any way ready to deal with that fact. Many graves had the shape of — or at least a drawing of — a tree of which the trunk or a major branch had been cut.  For a child in a sunshine-filled cemetery, the idea of death being like a pruned version of the tree of life was accessible and acceptable in the context of nature.

I am grateful to Project Gutenberg for making Darwin’s “On the Origin of Species” 1st edition available to all. Conspicuously missing from this edition is the only illustration for this text.  A diagram to show how species evolve.

It is a diagram of a tree. Metaphor is powerful, maybe more powerful than we believe.

I had always thought of metaphor as magnifying, maybe even liberating. By using metaphor, we can set up an analogy that is as rich as it is economical. The tree metaphor has been used for more things than I can tell. My old family album had a diagram of a “family tree,” where my Mother-Of-Blessed-Memory dutifully filled in dates of birth and death. Also, one grade school textbook on civics pictured government as some kind of tree.

The pictures helped me understand where my DNA came from and how my nation worked. But there is something wrong with the tree metaphor when dealing with today’s world. We have lots of things that are so complex we cannot imagine them in the analogy to a tree. The branches of a tree, once separated, do not get back together. Yet often we are surrounded by things that get together in myriad ways. When Freud tried to describe the brain, he compared it to a steam engine, the highest level of technology during his time. A brain seems to me to be more complex than a computer.  It is a pretty sure bet that both are more complicated than a tree. This is not blasphemy. Whatever Creator you (and I) believe in, there is no force that reveals incomprehensible truths.  Genetic recombination exists and is as real as any one of us.  It was not revealed with — for example — the Ten Commandments, because a bunch of ancient nomadic folks could not have understood.

But it is still part of an unquestionable truth, and no less beautiful, no less a reality capable of generating wonder. So when we get to something as wonderful as computer networks, and brain networks, we want desperately to understand them. We are driven to understand ourselves. We have progressed beyond the ancient abstract query as to whether the brain can understand itself.  We must believe that it can, and plow fearlessly forward. Me, I think it might be necessary to visualize before imagining. I drove with my husband through a landscape that looked barren.  The only thing I could think was that if I had been born here, and spent my early childhood here, the only thought I could have was that I would live to be able to move out. One of many things that my parents of blessed memory did for me was expose me to the cultural wonders of Boston, Massachusetts. I loved music but figured pretty early I was unlikely to create something as beautiful as what I could hear.  Although music is eternal, it is also ephemeral, vanishing in the air, fortuitously sometimes captured with recording. Tastes and smells are fragile, and disappearance is part of their nature, as well as their delight. By the time I stepped forth from my first flight to Paris, the city of the impressionist painters was more a friend to me than any human.  I had the layout of the city from maps in books. Likewise, my brain had the whole of the human body from cherished anatomical atlases I had visited in my prep school library. As I look back on the process, I spent a lifetime seeing things.  I went on to visualize them, and from there — only from there — to make them my own. So powerful were my visualizations that when I had to remember tremendous amounts of verbal information, sometimes I would simply close my eyes and see the information on the page where I had first seen it.  On some of my medical school examinations, I would simply close my eyes, and sometimes smile, and give professors their own words back (which was what they actually wanted, I think). I am not sure I can deeply learn — “own” — a concept, unless I have visualized it first. So how can anybody, including me, “own” something like a neural network map of a computer network?

As far as I can figure, the first person to attack this concept, the need to visualize complex systems, was Edward Tufte. This Yale professor, whose background was in political science and statistics, ended up teaching a course at Yale in statistics for journalists who wanted to learn economics. Rendering those statistics understandable in a visual way was the idea that gave birth to this field.

He wrote a book called “The Visual Display of Quantitative Information.”  He took a mortgage on his house to publish it himself, and it was a wild success, and he became an information scientist. The idea here is to help people really understand numbers and what they mean and visualizing them seems to be the way to do it. Curiously enough, this man now works for the feds.  His job is allegedly rendering “transparent” to the public the American Recovery and Reinvestment Act of 2009. I am not ready to condemn this man even though I certainly don’t understand the American Recovery and Reinvestment Act of 2009. I am a little jealous of him because of the way he gets to work, processing ideas from disparate sources and pulling them together and  — oh my word! I think that is exactly what I am doing. Somehow the arts have a role in this kind of expression.

Tufte has originated ways of showing data such as “sparklines,” which are the now-familiar squigglies used to depict the action on the stock exchanges on the evening news.

He has criticized ways of presenting data that don’t deliver the goods accurately. Notably, he has been wildly critical of PowerPoint. He doesn’t like that it “elevates form over content” and “turns everything into a sales pitch.” His criticism is not without some merit, but I do wish he would come up with something that does the job better. The idea of moving on to something else is wildly uncomfortable for me.  I have, more than once, given PowerPoint talks and turned back to see the slides projected to remember what I wanted to say next, as I generally don’t use notes.

I don’t know how to show the complex relationship of ideas.  Tufte has used Feynman diagrams, and maybe some of his sculptures tell things I still cannot understand about how neurons — and computer elements — interrelate.  If a tree diagram is no longer enough, what am I to do?

Manuel Lima is one person who has been cited as Tufte’s heir apparent.  He has done a book about trees, and designed for high tech companies, and talked for TED and RSA. (See below for an explanation)

I am glad he has done a historical work on the image of the tree, but disappointed his website has no given me real ways to visualize the complexity of neural networks.  I mean, I reviewed the page on Lima’s “Visual Complexity” website devoted to biological systems in some detail. There are artistic things of great beauty here, but I am looking for more. Maybe I am looking for an aid, a crutch, to bring me forward to a higher understanding.

I have told many people who want to understand me that I am a “knowledge junkie,” taking joy, real joy, when I have a concept not only assimilated, in both knowledge and feeling, but also reproducible by my brain and mouth — something I can cite to, for example, a patient who asks me something I can only answer by telling them how the brain inside their head is working. I will surely continue trying to absorb TED talks and RSA talks and try, and never give up trying, to learn better ways to understand my universe.

(Note: TED talks are free to view streaming or to download and offer transcriptions in many languages that also may be downloaded.  RSA has similar free downloads with lively animation to accompany the speech instead of showing the speaker onstage. Both are highly recommended and are entertaining and thought-provoking ways to learn new things or explore new topics).


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