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"What Do You Believe Is True Even Though You Cannot Prove It?"

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Alun Anderson

Chris W. Anderson

Philip W. Anderson

Scott Atran

Simon Baron-Cohen

John Barrow

Gregory Benford

Jesse Bering

Susan Blackmore

Ned Block

Paul Bloom

David Buss

William Calvin

Leo Chalupa

Mihaly Csikszentmihalyi

Paul Davies

Richard Dawkins

Stanislas Deheane

Daniel C. Dennett

Keith Devlin

Jared Diamond

Denis Dutton

Esther Dyson

Freeman Dyson

George Dyson

Jeffrey Epstein

Todd Feinberg

Christine Finn

Kenneth Ford

Howard Gardner

David Gelernter

Neil Gershenfeld

Steve Giddings

Daniel Gilbert

Rebecca Goldstein

Daniel Goleman

Brian Goodwin

Alison Gopnik

Jonathan Haidt

Haim Harari

Judith Rich Harris

Sam Harris

Marc D. Hauser

Marti Hearst

W. Daniel Hillis

Donald Hoffman

John Horgan

Verena Huber-Dyson

Nicholas Humphrey

Piet Hut

Stuart Kauffman

Alan Kay

Kevin Kelly

Stephen Kosslyn

Kai Krause

Lawrence Krauss

Ray Kurzweil

Jaron Lanier

Leon Lederman

Janna Levin

Joseph LeDoux

Seth Lloyd

Benoit Mandelbrot

Gary Marcus

Lynn Margulis

John McCarthy

Pamela McCorduck

Ian McEwan

John McWhorter

Thomas Metzinger

Oliver Morton

David Myers

Randolph Nesse

Tor Nørretranders

Martin Nowak

James O'Donnell

Alex Pentland

Irene Pepperberg

Stephen Petranek

Clifford Pickover

Steven Pinker

Jordan Pollack

Carolyn Porco

Robert R. Provine

Martin Rees

Howard Rheingold

Carlo Rovelli

Rudy Rucker

Douglas Rushkoff

Karl Sabbagh

Robert Sapolsky

Roger Schank

Jean Paul Schmetz

Stephen H. Schneider

Gino Segre

Martin E. P. Seligman

Terrence Sejnowski

Rupert Sheldrake

Michael Shermer

Charles Simonyi

John R. Skoyles

Lee Smolin

Elizabeth Spelke

Maria Spiropulu

Tom Standage

Paul Steinhardt

Bruce Sterling

Leonard Susskind

Nassim Taleb

Timothy Taylor

Arnold Trehub

Robert Trivers

J. Craig Venter

Alexander Vilenkin

Margaret Wertheim

Donald I. Williamson

Ian Wilmut

Ellen Winner

Anton Zeilinger


Computer Scientist; Founder, Intentional Software; formerly Chief Architect, Microsoft

I believe that we are writing software the wrong way. There are sound evolutionary reasons for why we are doing what we are doing—that we can call the "programming the problem in a computer language" paradigm, but the incredible success of Moore's law blinded us to being stuck in what is probably an evolutionary backwater.

There are many warning signs. Computers are demonstrably ten thousand times better than not so long ago. Yet we are not seeing their services improving at the same rate (with some exceptions—for example games and internet searches.) On an absolute scale, a business or administration problem that would take maybe one hundred pages to describe precisely, will take millions of dollars to program for a computer and often the program will not work. Recently a smaller airline came to a standstill due to a problem in crew scheduling software—raising the ire of Congress, not to mention their customers.

My laptop could store 200 pages of text (1/2 megabytes) for each and every crew member at this airline just in its fast memory and hundred times more (a veritable encyclopedia of 20,000 pages) for each person on its hard disk. Of course for a schedule we would need maybe one or two—or at most ten pages per person. Even with all the rules—the laws, the union contracts, the local, state, federal taxes, the duty time limitations, the FAA regulations on crew certification; is there anyone who believes that the problem is not simple in terms of computing? We need to store and process at the maximum 10 pages per person where we have capacity for two thousand times more in one cheap laptop! Of course the problem is complex in terms of the problem domain—but not shockingly so. I would estimate that all the rules possibly relevant to aircraft crew scheduling are expressible in less than a thousand pages—or 1/2 of one percent of the fast memory.

Software is surely the bottleneck on the high-tech horn of plenty. The scheduling program for the airline takes many thousand times more memory than what I believe it should be. Hence the software represents complexity that is many thousand times greater than what I believe the problem is—no wonder that some planes are assigned three pilots by the software while the others can't fly because the copilot is not scheduled. Note that the cost of the memory is not the issue—we could afford that waste. But the use of so much memory for software is an indication of some complexity inflation that occurs during programming that is the real bottleneck.

What is going on? I like to use cryptography as the metaphor. As we know, in cryptography we take a message and we combine it with a key using a difficult-to-invert function to get the code. Programmers using today's paradigm start from a problem statement, for example that a Boeing 767 requires a pilot, a copilot, and seven cabin crew with various certification requirements for each—and combine this with their knowledge of computer science and software engineering—that is how this rule can be encoded in computer language and turned into an algorithm. This act of combining is the programming process, the result of which is called the source code. Now, programming is well known to be a difficult-to-invert function, perhaps not to cryptography's standards, but one can joke about the possibility of the airline being able to keep their proprietary scheduling rules secret by publishing the source code for the implementation since no one could figure out what the rules were—or really whether the code had to do with scheduling or spare parts inventory—by studying the source code, it can be that obscure.

The amazing thing is that today it is the source code—that is the encrypted problem—which is the artifact all of software engineering is focusing on. To add insult to the injury, the "encryption", that is programming, is done manually which means high costs, low throughput and high error rates. In contrast with software maintenance, when the General realizes that he is about to send a wrong encrypted message, no one would think of editing the code after the encryption or "fixing the code"; instead the clear text would be first edited and then this improved message would be re-encrypted at computer speeds and computer accuracy. In other words the message may be wrong, but it won't be wrong because of the encryption and it is easily fixed.

We see that the complexity inflation comes from encoding. The problem statement above is obviously oversimplified, but remember that we used just two lines from our realistic budget of a thousand pages and we haven't even used the aviation jargon which can make these statements even more compact and more precise. But once these statements are viewed through the funhouse mirror of software coding, it becomes all but unrecognizable: thousand times fatter, disjointed, foreign. And as any manual product, it will have many flaws—beyond the errors in the rules themselves.

What can be done? Follow the metaphor. First, refocus on recording the problem statement—the "cleartext" in our metaphor. This is not a program in any sense of the word—it is just a straightforward recording of the subject matter experts' contributions using their own terms-of-art, their jargon, their own notations. Next, empower the programmers to program not the problem itself, but to express their software engineering expertise and decisions as a computer code for the encoder that takes the recorded problem statement and generates the code from it. This is called generative programming and I believe it is the future of software.

Editor-In-Chief, Wired

The Intelligent Design movement has opened my eyes. I realize that although I believe that evolution explains why the living world is the way it is, I can't actually prove it. At least not to the satisfaction of the ID folk, who seem to require that every example of extraordinary complexity and clever plumbing in nature be fully traced back (not just traceable back) along an evolutionary tree to prove that it wasn't directed by an invisible hand. If the scientific community won't do that, then the arguments goes that they must accept a large red "theory" stamp placed on the evolution textbooks and that alternative theories, such as "guided" evolution and creationism, be taught alongside.

So, by this standard, virtually everything I believe in must now fall under the shadow of unproveability. Most importantly, this includes the belief that democracy, capitalism and other market-driven systems (including evolution!) are better than their alternatives. Indeed, I suppose I should now refer to them as the "theory of democracy" and the "theory of capitalism", to join the theory of evolution, and accept the teaching of living Marxism and fascism as alternatives in high schools.

Mathematician, Emeritus Professor, Dept of Philosophy, University of Calgary; Author, Gödel's Theorems

Most of what I believe I cannot prove, simply for lack of time and energy; truths that I'd claim to know because they have been proved by others. That is how inextricably our beliefs are tied up with labors accomplished by fellow beings. And then there are mathematical truths that we now know are not provable. These phenomena have become favorites with the media but can only be made sense of by a serious scrutiny of the idea of mathematical truth and a specific articulation of a proof-concept,

But running across Esther's contribution I came up with a catchy response:

I believe in the creative power of boredom.

Or, to put it into the form suggested by the Edge question:

I believe that, no matter how relentlessly we overfeed our young with prepackaged interactive entertainments, before long they will break out and invent their own amusements. I know from experience; boredom drove me into mathematics during my preteens. But I cannot prove it, till it actually happens. Probably in less than a generation kids will be amusing themselves and each other in ways that we never dreamt of.

Such is my belief in human nature, in the resilience of its good sense.

Here is an observation from mathematical practice. By now the concept of an algorithm, well- defined, is widely hailed as the way to solve problems, more precisely sequences of problems labeled by a numerical parameter. The implementation of a specific algorithm may be boring, a task best left to a machine, while the construction of the algorithm together with a rigorous proof that it works is a creative and often laborious enterprise.

For illustration consider group theory. A group is defined as a structure consisting of a non-empty set and a binary operation obeying certain laws. The theory of groups consists of all sentences true of all groups; its restriction to the formal "first order" language L determined by the group structure is called the elementary theory TG of groups. Here we have a formal proof procedure, proven complete by Gödel in his PHD thesis the year before his incompleteness proof was published. The elementary theory of groups is axiomatizable: it consists of exactly those sentences that are derivable from the axioms by means of the rules of first order logic. Thus TG is an effectively (recursively) enumerable subset of L; a machine, unlimited in power and time, could eventually come up with a proof of every elementary theorem of group theory. However, a human group theorist would still be needed to select the interesting theorems out of the bulk of the merely true. The development of TG is no mean task, although its language is severely restricted.

The axiomatizability of a theory always raises the question how to recognize the non-theorems. The set FF of those L-sentences that fail in some finite group is recursively enumerable by an enumeration of all finite groups, a simple matter, in principle. But, as all the excitement over the construction of finite simple monsters has amply demonstrated, that again is in reality no simple task.

Neither the theory of finite groups nor the theory of all groups is decidable. The most satisfying proof of this fact shows how to construct to every pair (A, B) of disjoint recursively enumerable sets of L-sentences, where A contains all of TG and B contains FF, a sentence S that belongs neither to A nor to B. This is the deep and sophisticated theorem of effective non-separability proved in the early sixties independently by Mal'cev in the SSSR and Tarski's pupil Cobham.

It follows that constructing infinite counter-examples in group theory is a truly creative enterprise, while the theory of finite groups is not axiomatizable and so, to recognize a truth about finite groups requires deep insight and a creative jump. The concept of finiteness in group theory is not elementary and yet we have a clear idea of what is meant by talking about all finite groups, a marvelously intriguing situation.

To wind up with a specific answer to the 2005 Question:

I do believe that every sentence expressible in the formal language of elementary group theory is either true of all finite groups or else fails for at least one of them.

This statement may at first sight look like a logical triviality. But when you try to prove it honestly you find that you would need a decision procedure, which would, given any sentence of L, yield either a proof that S holds in all finite groups or else a finite group in which S fails. By the inseparability theorem mentioned above, there is no such procedure.

If asked whether I hold the equivalent belief for the theory of all groups I would hesitate because the concept of an infinite counterexample is not as concrete to my mind as that of the totality of all finite groups. These are the areas where personal intuition starts to come into play.

Media Analyst; Documentary Writer; Author, Media Virus

I can't prove it more than anecdotally, but I believe evolution has purpose and direction. It appears obvious, yet absolutely unconfirmable, that matter is groping towards complexity. While the laws of nature—and time itself—require objects and life forms attain durability and sustainability for survival, it seems to me more a means to an end than an end in itself.

Theology goes a long way towards imbuing substance and processes with meaning—describing life as "matter reaching towards divinity," or as the process through which divinity calls matter back up into itself—but theologians repeatedly make the mistake of ascribing this sense of purpose to history rather than the future. This is only natural, since the narrative structures we use to understand our world tend to have beginnings, middles, and ends. In order to experience the pay-off at the end of the story, we need to see it as somehow built-in to the original intention of events.

It's also hard for people to contend with the great probability that we are simply over-advanced fungi and bacteria, hurling through a galaxy in cold and meaningless space. Our existence may be unintentional, meaningless and purposeless; but that doesn't preclude meaning or purpose from emerging as a result of our interaction and collaboration. Meaning may not be a precondition for humanity, but rather a byproduct of it.

That's why it's so important to recognize that evolution, at its best, is a team sport. As Darwin's later, lesser-known, but more important works contended, survival of the fittest is not a law applied to individuals, but to groups. Just as it is now postulated that mosquitoes cause their victims to itch and sweat nervously so that other mosquitoes can more easily find the target, most great leaps forward in human evolution—from the formation of clans to the building of cities—are feats of collaborative effort. Better rates of survival are as much a happy side effect of good collaboration as their purpose.

If we could stop relating to meaning and purpose as artifacts of some divine creative act, and see them instead as the yield of our own creative future, they become goals, intentions, and processes very much in reach—rather than the shadows of childlike, superstitious mythology

The proof is impossible, since it is an unfolding one. Like reaching a horizon, arrival merely necessitates more travel.

Mathematician, Computer Scientist; CyberPunk Pioneer; Novelist; Author, Infinity and the Mind

Reality Is A Novel.

I'd like to propose a modified Many Universes theory. Rather than saying every possible universe exists, I'd say, rather, that there is a sequence of possible universes, akin to the drafts of a novel.

We're living in a draft version of the universe—and there is no final version. The revisions never stop.

From time to time it's possible to be aware of this. In particular, when you relax and stop naming things and forming opinions, your consciousness spreads out across several drafts of the universe. Things don't need to be particularly one way or the other until you pin them down.

Each draft, each spacetime, each sheet of reality is itself rigorously deterministic; there really is no underlying randomness in the world. Instead we have a great web of synchronistic entanglements, with causes and effects flowing forward and backwards through time. The start of a novel matches its ending; the past matches the future. Changing one thing changes everything. If we fully know everything about the Now moment, we know the entire past and future.

With this in mind, explaining an given draft of the universe becomes a matter of explaining the contents of a single Now moment of that draft. This in turn means that we can view the evolution of the successive drafts as an evolution of different versions of a particular Now moment. As Scarlett's climactic scene with Rhett is repeatedly rewritten, all the rest of Gone With The Wind changes to match.

And this evolution, too, can be deterministic. We can figure we think of there as being two distinct deterministic rules, a Physics Rule and a Metaphysics Rule. The Physics Rule consists of time-reversible laws that grow the Now moment upwards and downwards to fill out the entire past and future of spacetime. And we invoke the Metaphysics Rule to account for the contents of the Now moment. The Metaphysics Rule is deterministic but not reversible; it grows sideways across a dimension that we might call paratime, turning some simple seed into the space-filling pattern found in the Now.

The Metaphysics rule is...what? One possibility is that it's something quite simple, perhaps as simple as an eight-bit cellular automaton rule generating complex-looking patterns out of pure computation. Or perhaps the Metaphysics rule is like the mind of an author creating a novel, searching out the best word to write next, somehow peering into alternate realities. Or, yet again, the big Metaphysics rule in the sky could be the One cosmic mind, the Big Aha, the eternal secret, living in the spaces between your thoughts.

Biologist, London; Author of The Presence of the Past

I believe, but cannot prove, that memory is inherent in nature. Most of the so-called laws of nature are more like habits.

There is no need to suppose that all the laws of nature sprang into being fully formed at the moment of the Big Bang, like a kind of cosmic Napoleonic code, or that they exist in a metaphysical realm beyond time and space.

Before the general acceptance of the Big Bang theory in the 1960s, eternal laws seemed to make sense. The universe itself was thought to be eternal and evolution was confined to the biological realm. But we now live in a radically evolutionary universe.

If we want to stick to the idea of natural laws, we could say that as nature itself evolves, the laws of nature also evolve, just as human laws evolve over time. But then how would natural laws be remembered or enforced? The law metaphor is embarrassingly anthropomorphic. Habits are less human-centred. Many kinds of organisms have habits, but only humans have laws.

Habits are subject to natural selection; and the more often they are repeated, the more probable they become, other things being equal. Animals inherit the successful habits of their species as instincts. We inherit bodily, emotional, mental and cultural habits, including the habits of our languages.

The habits of nature depend on non-local similarity reinforcement. Through a kind of resonance, the patterns of activity in self-organizing systems are influenced by similar patterns in the past, giving each species and each kind of self-organizing system a collective memory.

Is this just a vague philosophical idea? I believe it can be formulated as a testable scientific hypothesis.

My interest in evolutionary habits arose when I was engaged in research in developmental biology, and was reinforced by reading Charles Darwin, for whom the habits of organisms were of central importance. As Francis Huxley has pointed out, Darwin's most famous book could more appropriately have been entitled The Origin of Habits.

Over the course of fifteen years of research on plant development, I came to the conclusion that for understanding the development of plants, their morphogenesis, genes and gene products are not enough. Morphogenesis also depends on organizing fields. The same arguments apply to the development of animals. Since the 1920s many developmental biologists have proposed that biological organization depends on fields, variously called biological fields, or developmental fields, or positional fields, or morphogenetic fields.

All cells come from other cells, and all cells inherit fields of organization. Genes are part of this organization. They play an essential role. But they do not explain the organization itself. Why not?

Thanks to molecular biology, we know what genes do. They enable organisms to make particular proteins. Other genes are involved in the control of protein synthesis. Identifiable genes are switched on and particular proteins made at the beginning of new developmental processes. Some of these developmental switch genes, like the Hox genes in fruit flies, worms, fish and mammals, are very similar. In evolutionary terms, they are highly conserved. But switching on genes such as these cannot in itself determine form, otherwise fruit flies would not look different from us.

Many organisms live as free cells, including many yeasts, bacteria and amoebas. Some form complex mineral skeletons, as in diatoms and radiolarians, spectacularly pictured in the nineteenth century by Ernst Haeckel. Just making the right proteins at the right times cannot explain such structures without many other forces coming into play, including the organizing activity of cell membranes and microtubules.

Most developmental biologists accept the need for a holistic or integrative conception of living organization. Otherwise biology will go on floundering, even drowning, in oceans of data, as yet more genomes are sequenced, genes are cloned and proteins are characterized.

I suspect that morphogenetic fields work by imposing patterns on the otherwise random or indeterminate patterns of activity. For example they cause microtubules to crystallize in one part of the cell rather than another, even though the subunits from which they are made are present throughout the cell.

Morphogenetic fields are not fixed forever, but evolve. The fields of Afghan hounds and poodles have become different from those of their common ancestors, wolves. How are these fields inherited? I believe, but cannot prove, that they are transmitted by a kind of non-local resonance, and I have suggested the term morphic resonance for this process.

The fields organizing the activity of the nervous system are likewise inherited through morphic resonance, conveying a collective, instinctive memory. The resonance of a brain with its own past states also helps to explain the memories of individual animals and humans.

Social groups are likewise organized by fields, as in schools of fish and flocks of birds. Human societies have memories that are transmitted through the culture of the group, and are most explicitly communicated through the ritual re-enactment of a founding story or myth, as in the Jewish Passover celebration, the Christian Holy Communion and the American thanksgiving dinner, through which the past become present through a kind of resonance with those who have performed the same rituals before.

Others may prefer to dispense with the idea of fields and explain the evolution of organization in some other way, perhaps using more general terms like "emergent systems properties". But whatever the details of the models, I believe that the natural selection of habits will play an essential part in any integrated theory of evolution, including not just biological evolution, but also physical, chemical, cosmic, social, mental and cultural evolution.

Archaeologist; Journalist; Writer-in-Residence, University of Bradford; Author, Past Poetic

I have a belief that modern humans are greatly underutilizing their cognitive capabilities. Finding proof of this, however, would lie in embracing those very same sentient possibilities—visceral hunches—which were possibly part of the world of archaic humans. This enlarged realm of the senses acknowledges reason, but also heeds the grip of the gut, the body poetic.

Philosopher and Psychologist, New York University

I believe that the "Hard Problem of Consciousness" will be solved by conceptual advances made in connection with cognitive neuroscience. Let me explain. No one has a clue (at the moment) how to answer the question of why the neural basis of the phenomenal feel of my experience of red is the neural basis of that phenomenal feel rather than a different one or none at all. There is an "explanatory gap" here which no one has a clue how to close.

This problem is conceptually and explanatorily prior to the issue of what the nature of the self is, as can be seen in part by noting that the problem would persist even for experiences that are not organized into selves. No doubt closing the explanatory gap will require ideas that we cannot now anticipate. The mind-body problem is so singular that no appeal to the closing of past explanatory gaps really justifies optimism, but I am optimistic nonetheless.

Philosopher and Novelist, Trinity College; Author, Incompleteness

I believe that scientific theories are a means of going—somewhat mysteriously—beyond what we are able to observe of the physical world, penetrating into the structure of nature. The "theoretical" parts of scientific theories—the parts that speak in seemingly non-observational terms—aren't, I believe, ultimately translatable into observations or aren't just algorithmic black boxes into which we feed our observations and churn out our predictions. I believe the theoretical parts have descriptive content and are true (or false) in the same prosaic way that the observational parts of theories are true (or false). They're true if and only if they correspond to reality.

I also believe that my belief about scientific theories isn't itself scientific. Science itself doesn't decide how it is to be interpreted, whether realistically or not.

That the penetration into unobservable nature is accomplished by way of abstract mathematics is a large part of what makes it mystifying—mystifying enough to be coherently if unpersuasively (at least to me) denied by scientific anti-realists. It's difficult to explain exactly how science manages to do what it is that I believe it does—notoriously difficult when trying to explain how quantum mechanics, in particular, describes unobserved reality. The unobservable aspects of nature that yield themselves to our knowledge must be both mathematically expressible and connected to our observations in requisite ways. The seventeenth-century titans, men like Galileo and Newton, figured out how to do this, how to wed mathematics to empiricism. It wasn't a priori obvious that it was going to work. It wasn't a priori obvious that it was going to get us so much farther into nature's secrets than the Aristotelian teleological methodology it was supplanting. A lot of assumptions about the mathematical nature of the world and its fundamental correspondence to our cognitive modes (a correspondence they saw as reflective of God's friendly intentions toward us) were made by them in order to justify their methodology.

I also believe that since not all of the properties of nature are mathematically expressible—why should they be? it takes a very special sort of property to be so expressible—that there are aspects of nature that we will never get to by way of our science. I believe that our scientific theories—just like our formalized mathematical systems (as proved by Gödel)—must be forever incomplete. The very fact of consciousness itself (an aspect of the material world we happen to know about, but not because it was revealed to us by way of science) demonstrates, I believe, the necessary incompleteness of scientific theories.

Psychologist, University of Virginia

I believe, but cannot prove, that religious experience and practice is generated and structured largely by a few emotions that evolved for other reasons, particularly awe, moral elevation, disgust, and attachment-related emotions. That's not a prediction likely to raise any eyebrows in this forum.

But I further believe (and cannot prove) that hostility toward religion is an obstacle to progress in psychology. Most human beings live in a world full of magic, miracles, saints, and constant commerce with divinity. Psychology at present has little to say about these parts of life; we focus instead on a small set of topics that are fashionable, or that are particularly tractable with our favorite methods. If psychologists took religious experience seriously and tried to understand it from the inside, as anthropologists do with other cultures, I believe it would enrich our science. I have found religious texts and testimonials about purity and pollution essential for understanding the emotion of disgust.

Biologist, University of Liverpool; Author, The Origins of Larvae

I believe I can explain the Cambrian explosion.

The Cambrian explosion refers to the first appearance in a relatively short space of geological time of a very wide assortment of animals more than 500 million years ago. I believe it came about through hybridization.

Many well preserved Cambrian fossils occur in the Burgess shale, in the Canadian Rockies. These fossils include small and soft-bodied animals, several of which were planktonic but none were larvae. Compared with modern animals, some of them seem to have the front end of one animal and rear end of another. Modern larvae present a comparable set-up: larvae seem to be derived from animals in different groups from their corresponding adults. I have amassed a bookful of evidence that the basic forms of larvae did indeed originate as animals in other groups and that such forms were transferred by hybridization. Animals with larvae are "sequential chimeras", in which one body-form—the larva—is followed by another, distantly related form—the adult. I believe there were no Cambrian larvae, and Cambrian hybridizations produced "concurrent chimeras", in which two distantly related body-forms appeared together.

About 600 million years ago, shortly before the Cambrian, animals with tissues (metazoans) made their first appearance. I agree with Darwin that there were several different forms (Darwin suggested four or five), and I believe they resulted from hybridizations between different colonial protists. Protists are mostly single-celled, but colonial forms consist of many similar cells. All Cambrian animals were marine, and, like most modern marine animals, they shed their eggs and sperm into the water, where fertilization took place. Eggs of one species frequently encountered sperm of another, and there were only poorly developed mechanisms to prevent hybridization. Early animals had small genomes, leaving plenty of spare gene capacity. These factors led to many fruitful hybridizations, which resulted in concurrent chimeras. Not only did the original metazoans hybridize but the new animals resulting from these hybidizations also hybridized, and this produced the explosion in animal form.

The acquisition of larvae by hybridization came much later, when there was little spare genome capacity in recipes for single animals, and it is still going on. In the echinoderms (the group that includes sea-urchins and starfish) there is evidence that there were no larvae in either the Cambrian or the Ordovician (the following period), and this might well apply to other major groups. Acquiring parts, rather than larvae, by hybridization continued, I believe, throughout the Cambrian and Ordovician and probably later, but, as genomes became larger and filled most of the available space, later hybridizations led to smaller changes in adult form or to acquisitions of larvae. The gradual evolution of better mechanisms to prevent eggs being fertilized by foreign sperm resulted in fewer fruitful hybridizations, but occasional hybridizations still take place.

Hybridogenesis, the generation of new organisms by hybridization, and symbiogenesis, the generation of new organisms by symbiosis, both involve fusion of lineages, whereas Darwinian "descent with modification" is entirely within separate lineages. These forms of evolution function in parallel, and "natural selection" works on the results.

I cannot prove that Cambrian animals had poorly developed specificity and spare gene capacity, but it makes sense.

Quantum Mechanical Engineer, Massachusetts Institute of Technology

I believe in science. Unlike mathematical theorems, scientific results can't be proved.They can only be tested again and again, until only a fool would not believe them.

I cannot prove that electrons exist, but I believe fervently in their existence. And if you don't believe in them, I have a high voltage cattle prod I'm willing to apply as an argument on their behalf. Electrons speak for themselves.

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