Supplemental Lecture (97/03/31 update) by Stephen T. Abedon (email@example.com)
Illustration, universal expansion
- Chapter title: Origin of the Universe
- A list of vocabulary words is found toward the end of this document
- Organisms are chemical/physical entities that store, propagate, and process information. To understand life is to understand the chemistry of life. But chemistry itself has a history. The atoms that make up the molecules that make up you did not exist in the beginning. Instead, they were created over time as our universe evolved. In fact, in the beginning nothing existed that you would recognize as being of our universe. First, however, a little philosophy:
- "Our universe may be viewed in many lights--by mystics, theologians, philosophers or scientists. In science we adopt the plodding route: we accept only what is tested by experimentation or observation." (Peebles et al., 1994)
- Then a taste of the physics of big bang cosmology:
- "Many people believe that everything in nature has to have a causal explanation. Although this may be true at the macroscopic level, it is not necessarily the case at the microscopic level, as quantum physics has demonstrated. Transitions, decays, and nuclear reactions do sometimes occur spontaneously without apparent cause. Similarly, the universe itself does not require a cause" (Crowe, 1995)
- In this lecture we will walk through the big bang cosmology of an inflationary universe, completing our tour just prior to the formation of planet Earth.
- Overview (of the origin of the universe)
- Our universe consists of all known mass, energy, space, and time. Evidence suggests that our universe began as an incredibly hot and dense region referred to as a singularity. The science called cosmology studies and hypothesizes on how the universe has evolved from singularity to its present as well as possible future states. The dominant theory of universal evolution goes by the familiar name of big bang (or big bang cosmology). At its simplest the big bang refers to a explosive expansion of the entire universe, starting from singularity and continuing to today. Thus, the big bang encompasses all of the events in our universe that have occurred subsequent to singularity. Particularly, all of the energy and mass in our universe was formed within and subsequent to singularity. Every atom that ever was and every atom that ever will be (such as those in our bodies) was created in the course of the big bang.
- It is thought that the very early rate of expansion of the universe was much faster than it could have been had gravity then existed. This period of rapid expansion is referred to as inflation. It is thought that inflation occurred particularly because the physical force of gravity, as we know it, did not yet exist (temperatures were too high, distances too short). That momentum and subsequent separation of matter into a huge, expanding cloud, is taken to be the fundamental origin of all energy subsequently generated by gravitational collapse, e.g., that harnessed during the formation of stars. Following this brief period of inflation, the initial, extremely hot universe began cooling right away (expanding gasses cool). An important consequence of cooling of the universe is that subatomic particles were able to condense into the matter that we recognize in today's universe. These include such things as electrons, neutrons, and protons. Later, with additional cooling (about 1 million years), there was a condensation of subatomic particles into hydrogen atoms. In addition to the creation of these condensed forms of matter, as temperatures declined there was a similar formation of the physical forces recognized as operating in the universe today.
- The univeral expanding cloud was initially completely homogeneous. In the absence of inhomogeneities (a.k.a., clumps or clumping), the expanding universal cloud probably would have remained an expanding homogeneous cloud, and thus one ultimately lacking in galaxies, stars, star light, solar systems, and planets. Therefore, it is thought that inhomogeneities in this universal cloud must have existed early on. Indeed, evidence for such inhomogeneities exists. Once clumps were formed, their associated gravitational force tended to lead to further clumping. This clumping lead directly to star, formation.
- The difference between a hydrogen cloud that collapses to become a star and one which collapses but does not become a star is whether sufficient pressure, density, and heat is obtained to initiate the fusion of hydrogen nuclei to form helium nuclei. Thus, the energy formed in the process of fusion is essentially a consequence of gravitational collapse. Gravitational collapse is, in turn, a reversion from the high energy potential resulting from the big bang to a lower energy potential as matter attempts to return, locally, to singularity. In a sufficiently large star further fusion can then begin leading to the creation of atoms with higher atomic weights. However, it takes the explosion of a star (a supernova) to supply the energy necessary to lead to the creation of elements with atomic numbers higher than that of iron. These supernova also are the means by which the elements created within these stars find their way out of stars. Supernovae thus lead to the formation of star systems that consist of elements in addition to the hydrogen, helium, and lithium (which were all, instead, created during the condensation of matter in the cooling universe). In addition to those elements formed during supernova, further elements form, as fission products of radioactive elements produced by supernova.
- Thus, gravitational collapse has led to all features of the universe, large scale (up to but not including the universe itself) and small scale (down to but not including hydrogen and other small atoms created immediately subsequent to inflation). Ultimately, four fundamental features describing the early universe (singularity, inflation, cooling, inhomogeneities) lead, through the action of gravity, to the five fundamental requirements for the existence of life: mass, energy, space, time, atoms, and complexity (the latter being the ultimate consequence of universal inhomogeneities).
- All known mass, energy, space, and time.
- There could be universes in addition to ours. By definition, however, we cannot be aware of them.
- Universal expansion
- Our universe is expanding.
- The majority of the objects in the universe are moving away from the Earth.
- Moving away faster the farther from earth:
- The farther an object is from the Earth, the faster it is moving away from the Earth.
- Think of the universe as spherical, like a ball or a balloon.
- (Even better, consider the universe to be rising raisin bread where we are a raisin. Peebles et al., 1994)
- Backwards extrapolation yields singularity:
- If we blow up a spherical balloon, the balloon becomes larger. Indeed, it expands.
- If we trace the rate of expansion and extrapolate back in time, we predict that the universe in the past was smaller than the universe of today (which, again, is smaller than the universe of tomorrow).
- If we keep extrapolating back in time, thus further collapsing the universe as we picture it in our minds, we eventually reach a time in which the universe has been so thoroughly collapsed that it no longer exists.
- This point in time and space is known as singularity.
Early universe [the beginning]
- The early universe, according to an inflationary big band hypothesis, can be traced through four steps key to the subsequent evolution of life:
- existence of inhomogeneities
- This sequence represents the genesis and evolution of a universe that owes its existence (as we know it) to an inflationary big bang.
Big bang [big bang cosmology]
- In the beginning there was singularity:
- In the beginning (about 8 to 15 billion years ago) the universe in which we inhabit did not exist. In its place there was an incredibly hot and dense region referred to as a singularity.
- we are not sure where singularity came from
- we are not sure of its properties
- we are not sure how old it was
- we are not even sure if time (i.e., causation) had meaning in the beginning
- All we really know for sure are those events that followed singularity. That is, observations made billions of years later (i.e., recently) are consistent with some concept of singularity: an extremely hot and dense universal beginning.
- Cosmology jargon:
- As a cosmologist might put it:
- "In this scenario, once our universe grows beyond about 10-33 centimeters in size (the Planck scale), 10-43 seconds after quantum genesis, it evolves classically and can be completely described by general relativity. Prior to that moment, it cannot be described by general relativity, which tells us that within the Planck scale, space becomes 'infinitely small' and energy density becomes 'infinitely large.' To describe the precise physical conditions (e.g., temperature, density, volume) requires a quantum theory of gravity that is still forthcoming." (Crowe, 1995)
All of the energy and mass in our universe was formed within and subsequent to expansion from singularity. Every atom in our bodies and every atom that ever was and every atom that will be in our bodies were created in the course of the big bang.
- Literally an explosive expansion of the entire universe (the term big bang dates from an effort by a cosmologist named Fred Hoyle to discredit the theory by associating it with a ridiculous but otherwise catchy moniker).
- Continuing to today:
- The big bang encompasses all of the events in our universe subsequent to singularity.There was singularity. Then there was the big bang.
- Except for details, that sequence describes our entire universe including as it exists today. We literally live within a universal expansion that began 8 to 15 billion years ago.
There exists no evidence indicating that we do not live in an expanding universe.
"At present, there are no fundamental challenges to the big bang theory, although there are certainly unresolved issues within the theory itself" (Peebles et al., 1994).
There also exists in every direction in space a strong electromagnetic signature of an immense explosion that began cooling 10-15 billion years ago (thermal cosmic background radiation); exactly what one would expect (and exactly what was predicted prior to its discovery) of the after glow of big bang-like expansion from a super hot singularity or product of inflation.
Big bang cosmology is the study of the origin and evolution of the universe that posits a universal expansion (big bang). In other words, a branch of science that considers and reconciles known observations of the universe with the theory of a big bang origin.
- Universal energy input:
- One detail concerning the course of a big bang expansion (not necessarily true but consistent with some though not necessarily all observations of today's universe) is the concept of inflation.
- All of the potential energy in the universe was imparted during inflation.
- Explosive expansion:
- Inflation is a hypothesis concerning the rate of increase of the size of the universe very soon after the transition from singularity to the big bang (approximately 10-12 seconds post-singularity).
- According to one account, "The inflationary model . . . proposes that the universe ballooned by a factor of 1050 to about the size of a grapefruit in 10-32 seconds." (Crowe, 1995)
It is thought that the very early rate of expansion of the universe was much faster than it could have been had gravity existed.
In particular, it is thought that the very early universe was so hot and dense that gravity did not exist during this period of inflation.
Thus other forces, or even what was to be gravity, were free to drive a rapid, early expansion of the universe.
As a cosmologist might put it:
In a sense, then, very early in the universe momentum was applied to the outwardly expanding universal stuff that could not have been applied had the universe been operating under the physical laws (constraints) that the subsequent (cooler and/or larger) universe now operates under.
When energy grew on trees:
- "The universe at this early stage can be described as a superposition of waves because it has energy density. In other words, 'nothing' in the case of the universe means that it could start out as a vacuum of negative pressure (negative spacetime curvature) having the lowest possible energy state (ground state) consistent with the Uncertainty Principle. A negative pressure would allow it to expand in volume and increase its internal energy by doing work on itself, thus satisfying total energy conservation at each moment in time. There is no violation of the first law of thermodynamics. As the expansion continues through the Planck time (10-43 seconds after genesis) and then the inflationary era (which begins 10-35 seconds after genesis), a phase transition occurs at some critical temperature (about 1027 K). At this point, rapid inflation would give way to more leisurely positive-pressure expansion, and the internal energy of the universe would stop increasing and then decline (Crowe, 1995)."
That momentum and subsequent separation of matter into a huge, expanding cloud, is the fundamental origin of all energy subsequently generated by gravitational collapse, e.g., that harnessed during the formation of stars.
The energy imparted during inflation represents essentially all the energy known in the entire universe including the energy found in our sun, that warming our planet, and that captured by bacteria and plants in photosynthesis. In a very real sense, the energy you derive from your lunch was literally created during the extremely brief inflation stage of the big bang, approximately 8 to 15 billion years ago.
Cooling [condensation of matter]
condensation of atoms:
- Expanding gasses cool:
- The initial extremely hot universe began cooling right from the start as the transition was made from inflation to mere coasting (expanding gasses cool).
- The universal expansion did not generate heat post-inflation. Thus, subsequent to inflation the universe was free to cool and, indeed, apparently did.
- In fact, expanded gasses typically cool (i.e., when there is no input of energy into the system) as heat is converted into volume.
- You can test this yourself by letting the air out of a bicycle tire and informally monitoring the temperature of the value (don't try this unless you have means of reinflating your tube). Conversely, conpressed gasses, all else held constant, heat up.
- Condensation of subatomic particles:
- An important consequence of cooling of the universe is that subatomic particles were able to condense into the matter that we recognize in the universe today. These are such things as electrons, neutrons, and protons.
- This condensation occurred approximately 1015 degree Kelvin (about 100 million times the temperature of the Sun's core; about 1 minute post-singularity).
Later and cooler (about 1 million years), there was a condensation of subatomic particles into hydrogen atoms (and much fewer helium atoms and even fewer lithium atoms).
These hydrogen atoms did and continue to make up today a large fraction of the matter in the universe.
In addition to the creation of these condensed forms of matter, there was a similar formation of the physical forces recognized as operating in the universe today.
The end of the beginning
- A not quite perfectly smooth universe:
- Without singularity, big bang, inflation (not definitely), and subsequent cooling, life in this universe (as we know it) would not and, indeed, could not exist. This is because these four events created the energy- and matter-rich expanding universe in which we exist.
- These four events (i.e., the formation of mass, energy, and universal expansion otherwise know as space and time) alone are not sufficient to create a universe in which life can evolve, however
- A fifth fundamental criteria is (was) the existence of inhomogeneities in the expanding universal cloud.
- Without inhomogeneities, the expanding universal cloud would have remained just that, a (homogeneous) cloud, one lacking in galaxies, stars, star light, solar systems, and planets. A slight clumpiness early in the universe is thought to have resulted in regions of higher density (mass/volume) that serve(d) as gravity wells for the formation of galaxies, etc.
- Clumping and further clumping:
- That is, once clumps (actually, regions of higher density within the expanding hydrogen cloud) were formed, their associated gravitational force tended to lead to further clumping.
- Ultimately this led to all large scale (up to but not including the universe itself) and small scale (down to but not including hydrogen and other atoms created immediately subsequent to the singularity-big bang transition) features of the universe.
- In terms of big bang cosmology, four fundamental features describe the early universe:
- These four features lead directly through existing physical forces (though not correspondingly) to six fundamental requirements for the existence of life.
- The logic:
- Mass, energy, space, and time are all consequences of inflation from singularity.
- Matter as we know it came about upon cooling.
- The inhomogeneities present in the early universe are at the root of the complexity necessary for the existence of life. Particularly, the gravitational collapse of clouds of matter around inhomogeneities led to the formation of galaxies, stars, solar systems, and planets. Solar systems and planets allowed the formation and aggregation of complex carbon based molecules and other materials that form the basis for life.
- Clouds of hydrogen:
- Inhomogeneities led to the formation of vast, dense clouds whose visible mass consists mostly of hydrogen.
- Further gravitational collapse of these clouds resulted in the formation of especially dense regions within which star formation could occur (approximately 1 billion years post-singularity).
- Localized gravitational collapse of clouds of hydrogen can lead to localized regions of high pressure, density, and heat. Given sufficient pressure, density, and heat (the occurrence of which is a function of the amount of mass in the original collapsing cloud), these localized gravitational collapses become stars.
Supernovae [stellar evolution]
- Function of mass:
- The difference between a cloud that collapses to become a star and one which does not become a star is whether sufficient pressure, density, and heat is obtained to initiate the fusion of hydrogen nuclei to form helium nuclei. This, in turn, is a direct correlate of the mass of the cloud collapsing. "Ignition" requires greater mass.
- Fusion gives off a tremendous amount of heat (witness the heat given off by hydrogen bombs). This heat, contained by the high pressures maintained by the high density and mass of the interior of stars, contributes to the fusion of further hydrogen nuclei.
- Thus, a fusion chain reaction occurs which continues until essentially all hydrogen nuclei found within the star are converted to helium nuclei.
- Energy from local reversion to singularity:
- All of the energy formed in the process of fusion is essentially a consequence of gravitational collapse.
- Gravitational collapse is, in turn, a reversion from the high energy potential resulting from the big bang to a lower energy potential as matter attempts to return locally to singularity.
- "A gravitational repayment on the huge gravitational investment in outward momentum at the big bang." (von Hippel, 1994)
- Ignition of helium:
- Once a star's hydrogen stores have been exhausted, the star stops converting matter to energy (no more fusion).
- Without fusion, additional gravitational collapse occurs.
- In a sufficiently large star this further collapse leads to pressures, densities, and temperatures great enough to cause the fusion of helium nuclei.
- Further collapse:
- Once helium stores are exhausted, further gravitational collapse occurs.
- Again, in a sufficiently large star further fusion can then begin leading to the creation of atoms with higher atomic weights.
Things continue like this until fusion produces 56Fe (iron).
Iron is produced in only comparatively huge stars (minimally 20 times the size of our sun).
The iron atomic nuclei displays the highest density of all elements. Thus, once iron is formed, though additional collapse may occur, this additional collapse does not lead, in itself, to further fusion to nuclei of higher atomic weights than iron.
Additional gravitational collapse, however, can be of sufficient force that the newly formed iron atoms can be crushed into neutrons (electron + proton = neutron).
Thus created is essentially an extremely large (10 to 20 kilometers in diameter) atomic nuclei also known as a neutron star.
Fortunately for the existence of you (and me), this is not necessarily an end point of stellar evolution. Instead, the momentum of gravitational collapse can lead to an attempt at further collapse of this already maximally collapsed ball of neutrons.
Since further collapse at this point is energetically unfavorable, the winding down of the momentum of collapse is rapidly reversed and the resulting shock wave leads to a magnificent explosion known as a supernova (actually, a type II supernova).
This explosion leads to two things.
Local galactic enrichment:
- First, it supplies the energy necessary to lead to the creation of elements with higher atomic numbers than iron.
- Second, it leads to the spreading of all of these newly created elements all around the galactic neighborhood local to the supernova. Thus, this "star stuff" (as the late Carl Sagan was fond of calling these newly minted elements) mixes with hydrogen clouds that are themselves induced to collapsed by the explosion.
Supernovae lead to the formation of star systems that consist of elements in addition to the hydrogen, helium, and lithium (which were instead created during the condensation of matter in the cooling universe).
In addition, some large stars are capable of spewing out fusion products without actually exploding. (Zinner, 1996)
Fission [radioactive decay]
- In addition to those elements formed during supernova, further elements form as fission (splitting of atomic nuclei) products of radioactive elements produced by supernova.
- The concept that for certain pairs of events, a and b, event a must occur for event b to occur. That is, there is complete statistical correlation (100% to a zillion zeroes) between a and b and it is a direct correlation going from a to b. Note that while causality may seem obvious, the reason that time marches forward (and not backward or not at all) is not understood. Nevertheless, given the existence of forward time, how might we define it? From Webster's: "1 a : the measured or measurable period during which an action, process, or condition exists or continues . . . b : a continuum which lacks spatial dimensions and in which events succeed one another from past through present to future." Thus, an event b that is not dependent on the occurrence of any previous event may be said to occur without cause. radioactive decay is one example of such a truly spontaneous event, one that occurs without cause.
- The capacity for doing work. That is, energy either has the potential for doing work or is having that potential realized. It is important to recall that mass may be converted to vast amounts of energy (energy = mass * constant, where the constant is the speed of light multiplied by itself). Energy is often used synonymously with ATP in biological systems.
- No entry.
- No entry.
Planck scale [length]
- From Webster's: "1 : the property of a body that is a measure of its inertia (tendency of a body to remain at rest or to continue, once started, to move in a straight line), that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field, and that along with length and time constitutes one of the fundamental quantities on which all physical measurements are based." Just why particles possess the masses that they possess is not understood and actually appears to be somewhat arbitrary. It was hoped that through the use of the now defunct Superconducting Super Collider a fundamental understanding of mass would be achieved. Why bodies should have inertia is an additional, to a large extent separate question, and one for which a widely accepted explanation is still lacking. Basically, the question comes down to, why should a body traveling in a straight line through a vacuum under no influence of gravity (an ideal situation) resist changing direction?
- The shortest possible physical distance between two points. In other words, the limit to which the universe may be resolved.
- No entry.
- Accepting the universe as an entity displaying (existing in) four dimensions, the term space describes three dimensions and time the fourth. Remember that space is not immutable but actually bent by gravity.
How old is the universe
- No entry.
- The oldest stars in the observable universe are thought to be approximately 12 billion years old. This, for obvious reasons, makes an estimate of the universe's of less than 12 billion years problematic. However, many argue that the universe is indeed as young as 8 billion years old; while the bulk of the rest argue that the universe is 15 billion years old. Why the controversy? We know the the universe is expanding given the red-shifting of star light (which implies that the sourse of the light is moving away from the Earth). Velocity is proportional to red-shifting (indeed, red-shifting is a measure of velocity). If we throw a ball and we know both its position (including distance from us) and velocity, we can extrapolate back (within the bounds of precision dictated by Heisenberg's uncertainty principle) to determine how long it has been since the ball was thrown. To determine the age of the universe, all one thus needs to know is how far away any given red-shifted star is from Earth. Unfortunately, determining distance unambiguously has been one big controversy for the past 50 years and the reason why their is so much uncertainty associated with the consensus estimate for the age of the universe. The current state of art involves estimating the absolute brightness of what are known as type 1a supernova. It is thought that the brightness of these explosions is fairly constant. Hence, their associated brightness as viewed from Earth should be proportional to their distance from Earth. Thus we have a distance measurement which gives an estimate for the age of the universe in excess of the age of the oldest observable stars, approximately 12 billion years. (Finkbeiner, 1995) (Though very recently--late 1996--some have suggested that the manner in which the age of the oldest stars is estimated may be flawed in a way which makes those estimates greater than they should be.)
- Age of universe
- Big bang
- Big bang cosomology
- Early universe
- Existence of life
- general relativity
- Planck length
- Planck scale
- Potential energy
- Radioactive decay
- Stellar evolution
- Universal expansion
- Universal expansion, illustration
Practice question answers
- All of the usable energy in today's universe is generated in the course of gravitational collapse (e.g., fusion ignited during star formation occurs as a result of gravitational collapse). During the occurrence of what feature in the evolution of the universe did pre-gravitational collapse potential energy come into being? (circle best answer) [PEEK]
- all of the above
- none of the above
- What are the five fundamental requirements for the existence of life? (limit list to five answers) [PEEK]
- The existence of which in the universe today is a consequence of its clumpiness? (circle best answer) [PEEK]
- visible light
- all of the above
- none of the above
- True or False, three elements that make up a substantial portion of our bodies, carbon, nitrogen, and oxygen, but not hydrogen, were created in massive stars that ultimately became supernova (circle best answer). [PEEK]
- Stars form when (circle best answer) [PEEK]
- fusion to form iron occurs
- subatomic particles condense to mostly hydrogen
- gravity does not exist as we know it
- clouds of hydrogen gravitationally collapse
- all of the above
- none of the above
- In addition to the fact that most of the energy utilized by life can be traced back to fusion occurring in our sun, of what consequence is fusion to life. [PEEK]
- All of the potential energy in the universe was/is ultimately created __________. (circle best answer) [PEEK]
- in stars.
- during the inflationary period (assuming, of course, that we do actually live in an inflationary universe).
- from fossil fuels, atomic energy, and various fringe sources.
- through plants via photosynthesis.
- all of the above.
- none of the above.
- The early universe is thought to have been far too hot for the existence of atoms, much less life. Subsequently, however, there has been a universal cooling. How did this cooling come about? (circle best answer) [PEEK]
- expanding gasses tend to cool (i.e., heat energy is converted to volume; e.g., some time try releasing through the valve the compressed gas in a bicycle tire).
- things tend to cool.
- stars start with a finite amount of fuel so eventually reach a point where they can no longer generate heat.
- through the same forces which generate ice ages on earth.
- all of the above.
- none of the above.
- True or false, the universe began with all of the atomic elements of life already formed (circle one correct answer). [PEEK]
- What does (i) singularity, (ii) inflation, (iii) cooling, and (iv) the existence of inhomogeneities describe? [PEEK]
- ii, inflation. In other words, gravity pulls things together. Since everything in the universe is not yet pulled togeher, gravity associated potential energy exists. During what phase of the evolution of the universe was this potential energy put into the system? During the brief inflationary period during which gravity as a force which pulls things together did not yet exist.
- mass, energy, space, time, and complexity
- iv, visible light. Protons and atoms exist as a consequence of the cooling of the universe following inflation. space is a product of inflation. Visible light is formed in stars and other products of graviational collapse, thus things whose existence required that the universe be clumpy in addition to having expanded then cooled.
- True, hydrogen of course was formed long before stars existed.
- iv, clouds of hydrogen gravitationally collapse
- It is through fusion that most the elements that make up biological systems were created.
- ii, during inflation.
- i, expanding gasses tend to cool.
- False, the universe began with no atomic elements at all, and even upon the condensation of subatomic particles to atoms, the universe still contained basically only three elements: hydrogen, helium, and lithium (the three lightest atoms).
- The early universe, the beginning of the universe, a big bang inflationary universe, an inflationary universe, the big bang, four steps key to the evolution of life, etc.
- Crowe, R. A. (1995). Is quantum cosmology science? Skeptical Inquirer 19:53-54.
- Finkbeiner, A. (1995). Closing in on cosmic expansion? Science 270:1295-1296.
- Kirshner, R. P. (1994). The Earth's elements. Scientific American October:58-65.
- Linde, A. (1994). The self-reproducing inflationary universe. Scientific American November:47-55.Peebles, J.E., Schramm, D.N., Turner, E.L., Kron, R.G. (1994). The evolution of the universe. Scientific American October:52-57.
- Starrfield, S. and Shore, S.N. (1994). The birth and death of nova v1974 cygni. Scientific American January:75-81.
- von Hippel, Arndt (1994). Human Evolutionary Biology. Stone Age Press, Anchorage, AK. pp. 1-23 (chapter 1).
- Wienberg, S. (1994). Life in the universe. Scientific American October:43-49.
- Zinner, E. (1996). Stardust in the laboratory. Science 271:41-42.