And a new place to look for them?

George Dyson is the author of Turing’s Cathedral. This book was newly released when we saw copies at Princeton’s celebration of the Alan Turing Centennial last May. It covers John von Neumann and his wife Klára von Neumann even more than Alan Turing in a multifaceted canvas of the emerging digital age. He also wrote Darwin Among the Machines: The Evolution of Global Intelligence. His works show both the lyricism and the futurism of his renowned physicist father, Freeman Dyson.

Today we discuss evolution and technology as we close the Turing centennial year, and consider how Nature provides scientific gifts.

We are thinking of gifts in the Christmas season, of course. Often you receive a gift you wished for, maybe even after circulating the idea to loved ones or putting it on a public wish list. There are gifts of things you need that aren’t exciting. Some gifts alas you’d like to return. But then there are gifts that are unexpected and yet deeply appropriate, which bring the “aha” of discovery and are relished most afterward. We like to think of gifts from science as being this kind.

Dyson’s two books make a complicated argument and prediction about communications technology and the near future of humanity, not all of which we follow. It accords with Ray Kurzweil’s famous assertions that a “Technological Singularity” is at hand, but argues that humanity will not be able to control natural processes of evolution and selection at work in it. We have a few simpler points to offer.

## Darwin Drawn Inward

Here is a representative quotation from “Darwin Among the Machines,” to ponder amid possibilities such as Internet search engines already “re-wiring” our brains:

“…[I]t appears to us that we are ourselves creating our own successors … we are daily giving them greater power and supplying by all sorts of ingenious contrivances that self-regulating, self-acting power which will be to them what intellect has been to the human race. In the course of ages we shall find ourselves the inferior race…

Day by day, however, the machines are gaining ground upon us; day by day we are becoming more subservient to them; more [people] devoting the energies of their whole lives to the development of mechanical life. The upshot is simply a question of time, but that the time will come when the machines will hold the real supremacy over the world and its inhabitants is what no person of a truly philosophic mind can for a moment question.”

Did we fool you, or did you notice our use of quotes—which are not the style for book titles? These words were penned not recently but almost 150 years ago, in an anonymous letter published under that title in 1863, and later acknowledged as his by the essayist and polymath Samuel Butler. Dyson named his book after that letter.

Butler was already extending the argument of Charles Darwin’s Origin of Species, which was published in 1859 just four years before, to intimate aspects of human societal development. Dyson brings this up to date. Well, even in 2013 we think people “of philosophic mind” can question the supremacy of computers as an inevitable evolutionary outcome.

What we observe is simply that much of today’s technology comes from scientific facts that seem to be separate from both the long-term process of evolution by natural selection, and the civilizing process of the last 10,000 or so years. Hence we think of them as “gifts.” This already has consequences.

## What Makes a Scientific Gift?

Here are some things we don’t mean: That carbon is wonderful for biology, and that we breathe oxygen and expel carbon dioxide, while flora largely does the opposite, are vital facts—but life as we know it is already predicated on them. We are enjoying a humanly long interval of temperate climate over most of the Earth’s surface after a series of ice ages, but civilization needed this to flourish. To have complex materials at all may require supernovas, and to have matter at all may require physical constants to be just-so, but precisely because of their necessity for life we exclude all such anthropic coincidences from our notion of “gift.”

Muons provide a boundary case. In response to the discovery of the muon particle, when it seemed to have no larger purpose in physical theory, Isidor Rabi famously exclaimed, “Who ordered that?” Now we know that muons—aided by a relativistic phenomenon that we explain as lengthening their lifetimes so they can reach the Earth’s surface from cosmic-ray bursts high in the atmosphere—are a significant source of mutations. [Update: see note.] Hence we could class them as necessity not gift. On the other hand, evolution was already well established without a preconceived need for the muons’ agency, so they were a freely-made discovery.

So does the mass-energy conversion represented by Albert Einstein’s ${E = mc^2}$. That we get so much ${E}$ from so little ${m}$ was unexpected, and has been a driver of technology for good and ill. But this is fundamental to how the world works to begin with. Other facts of quantum mechanics are transparently basic to life processes. Also at issue is how far beauty in mathematics is concomitant with these facts, and how far beauty in Nature is at the behest of natural selection.

A gift is a fact where we could still expect the world as we know it if it were false, but can hope for a better life tomorrow because it is true. Many facts underlying technology covered in Dyson’s book strike us here.

For example, it is remarkable that radio waves broadcast from New York City and Chicago can both reach my basic car radio driving on the NY Thruway upstate, going through my body without damage. We did not evolve with radio receivers, and although one can note living beings’ imperviousness to ambient waves, this doesn’t automatically give carte blanche to powerful human-pumped radiation. A still-controversial related matter is radiation exposure from cellphones. As described by Dana Mackenzie in his book The Universe in Zero Words, this theoretically avoids being a cancer risk owing to a fundamental equation governing rates of absorption after emission.

There are also technological bummers: desirable applications that might need a slight rewrite of natural laws. Hot fusion—not to mention cold fusion—may prove no better as an energy source than lumps of coal in our stockings. Just talking on cellphones makes us wish light could be a little faster. Whether quantum computers will scale or fail has been our running subject this year.

This draws into computational complexity as a bearer and arbiter of gifts. One of the central questions of our times, broadly stated, concerns the computational complexity of natural processes needed to build complex structures. We don’t expect a simple answer, but need ask only whether we can put a simple upper bound on it. Perhaps ${\mathsf{P}}$, or going higher to ${\mathsf{BQP}}$ or lower to ${\mathsf{NC}}$?

Whatever the particular level C bounding the great mass of life-building processes, functions f above C meet our main stated qualification for being gifts. Of course f must still be realizable in Nature, but need artifice to harness.

A new development we caught at the end of the last post illustrates our intent. Scott Aaronson and his student Alexander Arkhipov showed how to rig n-many interacting bosons to reflect properties of the permanent function that may not be feasibly simulable by non-quantum means. Scott announced a week ago that several teams of researchers have built and verified his mechanism for n = 3.

The previously-known facts this rests on are simple. Bosons are characterized by having integer spins, so that interchanging two of them cycles components of the overall quantum state a whole number of times around the unit circle, and so leaves them unchanged. Fermions have half-integer spins, which causes a sign flip from rotating 180 degrees upon interchange. For n-by-n matrices whose rows correspond to the n particles, the property of flipping sign upon interchanging two rows or columns characterizes the determinant function, which is in ${\mathsf{P}}$. Whereas, complete invariance under interchange is characteristic of the permanent function, which is ${\mathsf{NP}}$-hard.

The facts themselves give rise to the Pauli exclusion principle and the periodic table, and hence are basic to life. The involvement of the permanent, allowing computations that are otherwise hard, is the gift. As Scott commented in further detail here, there are still obstacles to scaling up the mechanism, and it is doubtful to help with ${\mathsf{NP}}$-hard problems themselves, but it can aspire no less than full universal quantum computers to provide real benefits beyond what is classically feasible.

What other gifts may come in complexity wrapping paper? Maybe our points are innocuous, but at least they differ from philosophical presentations we have seen: Many features of the natural world that support life are philosophically contingent, but we are passing them over as conditional necessities of life. While truths of mathematics are classed as necessary and a-priori, we are thinking as if they are contingent. At least this reflects discovery the way we as mathematical theorists experience it.

## Open Problems

Do you find our notion of “scientific gift” worthwhile? Can you add examples for discussion, also of possible “bummers”?

December 29, 2012 8:21 pm

“Now we know that muons—aided by a relativistic phenomenon that we explain as lengthening their lifetimes so they can reach the Earth’s surface from cosmic-ray bursts high in the atmosphere—are the main engine of mutations.”

http://xkcd.com/285/

• December 30, 2012 3:06 pm

OK, I’m thinking along lines of this: “At the earth’s surface the cosmic radiation is > 99% muons (ignoring neutrinos), and they are an important source of the random mutations in the genome that provide ‘raw material’ for survival of the fittest to work upon to generate the evolution of new species.” Well, “xkcd” may do a followup strip on people who just take the top hit for a search like Google muons mutations and copy some random comment in a forum.

But from the same forum: “…evolution runs on genetic variation. only a very small amount of that is due to radiation, and only a small part of THAT is cosmic radiation[—]sexual reassortment and chromosomal transpositions are more important. and there is chemically-induced mutation too. radiation isn’t really any kind of evolutionary driver. Oh well, that contradicts something else I read that was in print…

Third comment update: This Physics StackExchange item has various views, including “This is a ridiculous idea, and it is basically unsupported, and I am certain that it is completely wrong (although among biologists, I might be in the minority).” I’ll backtrack to saying it is “significant” and put a note down here.

December 29, 2012 11:12 pm

It is interesting the way the word “bummer” has entered common English usage. The term “bummer” was synonymous with and derived from the phrase “bum trip” referring to an unpleasant experience taking LSD (and by extension any other hallucinogenic drug). The features of the world that support life may be contingent but they are contingent upon the truths of mathematics and the laws of physics being what they are. In the anthropic sense, they are true because were they not, we would not be here to consider these issues. Perhaps they are contingent.

• December 30, 2012 3:32 pm

They are contingent unless one subscribes to the unrestricted multiverse hypothesis: that every consistent finite material structure and sequence has physical existence somewhere, and that the world cannot be any other way. My point, however, is that from the view of conditional probability—conditioned on broad features of the life we see—they are necessary.

December 30, 2012 5:07 pm

Physician Paul Brand’s celebrated (among physicians) book The Gift of Pain begins with a quotation from Shakespeare’s Romeo and Juliet

“He jests at scars who never felt a wound”

And yet paradoxically, Dr. Brand’s books is an extended meditation upon the horrifying medical and spiritual sequelae of inability to feel pain.

Nerves are of course the body’s physical means of conveying and transforming information, and (for me anyway) it is congenial to regard physicians, mathematicians, scientists, and engineers as naturally united in a broadly-conceived quest for order that is natural and human.

In this regard, here is a birth-ordered list of surnames of celebrated order-seekers:

☐  Osler
☐  Hilbert
☐  Nernst
☐  Codman
☐  Carrel
☐  Kilvington
☐  Noether
☐  Bunnell
☐  Colonna
☐  Wiener
☐  Black
☐  Pauling
☐  Dirac
☐  Kolmogorov
☐  Onsager
☐  von Neumann
☐  Bloch
☐  Mac Lane
☐  Charnley
☐  Turing
☐  Hamming
☐  Shannon
☐  Feynman

And here is a GLL Christmas quiz:

• What are their first names?

• What seminal scientific gifts did they give us (that

• On what single Christmas day were they *all* alive
(and so comprise a single generation)?

• What entropy-reducing gifts will the generation alive
today convey to the 21st century?

• Who is the sole woman on the list, and how
many women will appear on the 21st century list?

Happy New Year to all Gödel’s Lost Letter readers!

December 30, 2012 5:09 pm

(sigh) here’s a (hopefully) corrected post
——————–
Physician Paul Brand’s celebrated (among physicians) book The Gift of Pain begins with a quotation from Shakespeare’s Romeo and Juliet

“He jests at scars who never felt a wound”

And yet paradoxically, Dr. Brand’s books is an extended meditation upon the horrifying medical and spiritual sequelae of inability to feel pain.

Nerves are of course the body’s physical means of conveying and transforming information, and (for me anyway) it is congenial to regard physicians, mathematicians, scientists, and engineers as naturally united in a broadly-conceived quest for order.

In this regard, here is a birth-ordered list of surnames of celebrated order-seekers:

☐  Osler
☐  Hilbert
☐  Nernst
☐  Codman
☐  Carrel
☐  Kilvington
☐  Noether
☐  Bunnell
☐  Colonna
☐  Wiener
☐  Black
☐  Pauling
☐  Dirac
☐  Kolmogorov
☐  Onsager
☐  von Neumann
☐  Bloch
☐  Mac Lane
☐  Charnley
☐  Turing
☐  Hamming
☐  Shannon
☐  Feynman

And here is a GLL Christmas quiz:

• What are their first names?

• What are their seminal accomplishments
(that relate to entropy-reducing order)?

• On what single Christmas day were they *all* alive
(and so comprise a single generation)?

• What entropy-reducing gifts will the generation alive
today convey to the 21st century?

• Who is the sole woman on the list, and how
many women will appear on the 21st century list?

Happy New Year to all Gödel’s Lost Letter readers!

• December 30, 2012 6:52 pm

Thanks! I can add that the one woman on John’s list was still referenced with the German masculine article “der”…

December 31, 2012 6:07 pm

Between Bloch and Mac Lane I have added Levi-Montalcini

“At [age] 100, I have a mind that is superior — thanks to experience — than when I was 20,”

De. Levi-Montalcini is my new role model!

• December 30, 2012 6:54 pm

It is interesting/sad that order seeking “stopped” in forth quarter of XX century. Or may be I’m reading your list wrong😦

December 30, 2012 7:08 pm

The list was inspired when I noticed that Osler (arguably medicine’s greatest teacher?) and Feynman (arguably science’s greatest teacher?) were alive in the same year … it was natural to fill-in a list of order-seeking physicians, mathematicians, scientists, and engineers who also were alive in that year.

During the 19th and 20th centuries, their individual ordering quests were regarded as separate enterprises … now in the 21st century we are beginning to perceive the natural unity of their efforts. Very slowly (too slowly) I am completing a summary of the Kalai/Harrow debate that views quantum information theory as one more aspect — a key aspect — of this multi-generation entropy-reducing order-increasing quest.

• December 30, 2012 7:17 pm

John, may we are seeking order (or may be linear order) too much. If one accepts that every piece of art (visual,auditory,scripted) is a perceptual experiment, than one would see that this direction departed from “order” around the beginning of your list.

December 30, 2012 9:00 pm

mkatkov, please allow me to commend to you (and all students) this passage:

Awakenings

We students, interns, and residents in the early 1940s had the vague sense of living in a breakthrough era in the history of medicine. Sometimes older professors would say wistfully, “Oh, to be starting out now.” It soon became apparent that I had happended to enter medical school at the very threshold of a revolution.

— from The Gift of Pain, by Paul Brand MD

Like young Paul Brand, students toda are living in a breakthrough era in the history of medicine. And these medical breathroughs surely wil depend upon, and surely will reciprocally inspire, a broad span of dovetailed breakthroughs in every branch of mathematics, science, and engineers.

It was Paul Dirac who said “A Golden Era is an era in which ordinary people can make extraordinary contributions.” We are all of us entering a 21st century Golden Era (as it seems to me anyway), and that is why (like Paul Brand’s teachers) older researchers nowadays (like me anyway) sometimes reflect wistfully “Oh, to be starting out now.”

• December 31, 2012 12:22 am

may be the revolution is passing me by, or may be i used to think about russian/french revolutions as a definition of speed, and of cause i have no citations.

December 31, 2012 4:00 am

mkatkov posts  “Maybe the revolution is passing me by … I used to think about russian/french revolutions as a definition of speed.”

Mkatkov, the foundations of the Russian, French, and American revolutions were laid slowly, over decades and centuries, and many mathematicians and scientists participated in laying those foundations, and played leading roles too in the (messy, hard-fought, yet wonderful) revolutions that ensued. This enduring “scientific gift” (in the GLL phrase) to humanitythat is well-described by the historian Jonathan Israel in his A Revolution of the Mind: Radical Enlightenment and the Intellectual Origins of Modern Democracy

The last three decades of the eighteenth century were an age of much turmoil, instability, and revolutionary violence. But they were also an age of promise. The emancipation of man via forms of government promoting the “general good” and life in a free society that accords protection to all on an equal basis, argued d’Holbach in 1770, is not an impossible dream:
“if error and ignorance have forged the chains which bind peoples in oppression, if it is prejudice which perpetuates those chains, science, reason and truth will one day be able to break them” (si l’erreur et l’ignorance ont forge les chaines des peuples, si le prejuge les perpetue, la science, la raison, la verite pourront un jour les briser).

A noble and beautiful thought, no doubt, but was he [d’Holbach] right? That perhaps, is the question of our [21st century] time.

Here is a meditation broadly upon d’Holbach’s assertion, and narrowly upon Spielberg’s recent film Lincoln, that was rejected by (what Jonathan Israel calls) a “moderately Enlightened” STEM weblog, that perhaps may find a home here on (what Jonathan Israel calls) the “radically Enlightened” weblog that is Gödel’s Lost Letter:

Does complexity theory have a Lincoln? Chapters 29—34 of Neil Sheehan’s A Fiery Peace in a Cold War: Bernard Schriever and the Ultimate Weapon (2009) can be read as an extended meditation upon that topic, with John von Neumann in the role of Abraham Lincoln.

Like Abraham Lincoln, John von Neumann died young (Lincoln at 54, von Neumann at 53). Neither lived to witness, and comment upon, the bitter-sweet fruits of the great enterprises that they initiated, and so we are sadly deprived of their wisdom regarding those fruits. Von Neumann’s brother Michael once assured me that von Neumann cultivated a public persona as a student of Roman history, in part because of a genuine interest in history, but also in partly to mask internal moral convictions that were more nuanced, and perhaps less publicly acceptable. Were von Neumann’s deeply-considered and passionately-held motivations any less subtle than Lincoln’s?

We will never know. In regard to our bittersweet and tragicomic ignorance, two particularly excellent meditations (in my opinion) are John Ashbery’s bittersweet and tragicomic poem Memories of Imperialism and Borges’ bittersweet and tragicomic story Averroes’s Search (note: Google’s Search finds a lovely audio recording of the former, and the full text of the latter)

“In Alexandria there is a saying that only the man who has already committed a crime and repented of it is incapable of that crime; to be free of an erroneous impression, I myself might add, one must at some time have professed it.”
— from Averroes’s Search

Are our choices in the 21st century any less consequential than Lincoln’s in the 19th century, or von Neumann’s in the 20th? Can our appreciation of these choices be any deeper than Borges’ or Ashbery’s?

As for the pace of the 21st century’s radical Enlightenment, (it seems to me that) we need not fear that that pace will be too slow … quite the contrary! And therefore, in the radical spirit of d’Holbach, Lincoln, and von Neumann, my very best wishes for a radically happy and enlightened New Year’s day, and a radically happy and enlightened 2013, and a radically happy and enlightened 21st century, are extended to all Gödel’s Lost Letter readers!

6. December 31, 2012 6:30 am

hi, typo in the original post: Charles Darwin’s *Orgins* of Species…

• December 31, 2012 12:11 pm

Thanks—what I thought was there was Origin of Species, without the initial “On the”.

7. December 31, 2012 12:12 pm
8. December 31, 2012 4:34 pm

any thoughts on this?
http://www.cs.tau.ac.il/~nachumd/papers/ECTT.pdf

9. January 2, 2013 12:42 am

Re: “While truths of mathematics are classed as necessary and a-priori, we are thinking as if they are contingent. At least this reflects discovery the way we as mathematical theorists experience it.”

The contingencies of temporal creatures discovering eternal truths led Kant to the notion of synthetic à priori judgments. Though this category was rejected by later “analytic” philosophers, I think the basic insight is sound, and similar ideas were given a thorough development in the work of C.S. Peirce.

10. February 8, 2013 7:00 pm

speaking of kurzweil & the singularity, theres a new documentary out on the subj called “transcendent man” …. maybe worthy of a review in the blog? am planning on watching it, lets compare notes :p