Response by Sam Cox to "Simplicity in Nature" by Wu Chi Kay
Hello:
Wu Chi Kay is very enthusiastic about Physics! In a few pages, he briefly communicates his feelings on a plethora of reality related concepts. My response will show that I share his deep interest in a Grand Unified Theory.
Being human means having a single frame of reference in a vast universe. This fact gives meaning to our lives and makes us what we are. While we can visualize other realities up to a point, we are by our very nature, limited. Our four dimensional reality is literally "on the floor", at the lowest workable level of conscious dimensional complexity in the universe. If we think what we observe is complex- and it is, we should try to visualize the universe as perceived from 50,100 or 1,000 dimensions! Readers have written and told me how stunning the universe becomes when we visualize it via the mathematical formulae of General Relativity in only 7 dimensions!
Our readers may still be unconvinced about the dimensional complexity of the universe, not just 50, 100 or 1,000 dimensions, but some vast, exponential number. How can we visualize a universe with so many, and so many kinds of dimensions?
My wife has taken quite an interest in this General Relativity cosmology description in "Cosmology Review". I didn't know how interested she was until she woke me up one morning with a very profound question: "Sam, when we make decisions in our lives, isn't that dimensional?" I sat straight up in amazement! We speak about "the direction of our lives", and decisions are not only directional and thus essentially geometric, they influence the universe. In the lives of the six billion people on this one planet, how many decisions do you think are being made today?
To be sure, most of our decisions are not seemingly more than of personal consequence: What (if anything) will I eat today? Yet even such small things can, if we are starving, cause profound changes in the direction of our personal and collective history.
As we grow, are trained and educated, our lives take on a certain resolved direction. The inertia of this combined effect of our biological and environmental heritage grows in strength. We become like a large ship. It is not possible, or usually desirable to change direction rapidly, or stop quickly. Our "heading", like that of a ship or airplane, only needs minor adjustments. Nevertheless, sudden stops and great changes are sometimes necessary. Whether we change "heading" by 1 degree, 10 degrees, or 180 degrees is a matter of degree only...these changes are dimensional. From this 1, 10, or 180 degree description we can infer the meaning of "importance", which if I had the space, I could discuss in detail. In fact in English, we use an allusion to a 90 degree dimensional change when we advise: "Be careful turning corners"!
Also in English, we advise: "When life sends lemons, make lemonade". The ability to adapt and surmount tragedies and difficulties is crucial to a good life adjustment....and reflects the role of life in reducing entropy in the Einsteinian Hyperspherical Universe. Implied in the servo role of life in the universe is the reason for the difficulties we individually and corporately must overcome, in order to fulfill our destinies as eternal stones in the cathedral of the sky.
I realize many of the multitudes of dimensions of the universe may seem to be minor, but two points need to be made. First in a GR universe, we find infinity INWARD. The Earth seems a tiny speck of dust in a vast cosmos, but in a General Relativity universe, that speck of dust is where we find "ultimate reality". Second, although we seemingly live in four dimensions, we actually see (better yet, "look at") but cannot conceptualize the meaning and true significance of millions! I have no doubt that there will come a time and place, a frame of reference, from which we will truly understand.
As I ponder the meaning of this complexity, I'm reminded of a verse in the Judeo-Christian Scriptures (Isaiah 64:4) which says: "For since the beginning of the world, men have not heard, nor perceived by the ear, neither hath the eye seen, O God, beside thee, what he hath prepared for him that waiteth for him".
I honestly can tell our readers that at best, as we evaluate "The Einsteinian Hyperspherical Universe", we can see a shadow of "ultimate reality"...enough to awe, inspire and perhaps even scare us a little! Jewish people say that humans cannot look on the Divine face- and live. I strongly agree that if we were meant to understand everything, we wouldn't be human!
Since I have begun working on this "Einsteinian Hyperspherical Universe" project, I have come to understand, more than at any other time in my life, how little I know, and how small I am. I said in my remarks elsewhere on this site that General Relativity opens the door to the infinite a crack...and I MEANT a CRACK...yet the GR vision is truly awesome.
I believe there is a little bit of the scientist in everyone, because consciously or unconsciously we observe and absorb the reality around us. Yet, as I have just stressed, understanding how little we know is the beginning of wisdom! Scientists search for truth honestly and objectively, knowing from experience that there is a metaphysical quality about the universe which rewards honesty and objectivity.
Still, it is hard to be objective. Accepting the fact that what we have believed since childhood might be wrong for most people, even scientists is impossible. For this reason, it is usually necessary to divorce our philosophical bias from our scientific work. In the course of scientific endeavor, if we see human intuitive insights being verified in a systematic way, as scientists we note that fact, but we continue our use of the scientific method until we have reached the goal of our inquiry.
The other day, worldwide headlines proclaimed: "Space is flat"! Euclidean space prevails! Recent studies of the Cosmic Background Radiation in Antarctica, four times more refined than the COBE satellite have given scientists a much improved set of data, which can be used, among other things, to tell the geometry of space. For readers who have not studied the particulars, the key factor in these investigations is the "Omega". A less than one "Omega" represents a universe with hyperbolic space. An "Omega" of exactly 1.0000 represents a universe with flat or Euclidean space. ANY "Omega" over ONE, even in the tiniest decimal fraction, represents a closed Einsteinian Hyperspherical Universe. Because the EHU might be shaped like the Einsteinian "Hyperspherical" Lady finger Banana, we could get strange "Omegas", but in my opinion, this is unlikely.
Dr. Ned Wright , Vice Chair of the Department of Astronomy at UCLA (http://www.astro.ucla.edu/~wrightb4u-write.html) says the following about an "Omega" of exactly one in his excellent web site tutorial on the shape of space: "Thus Omega = one is an unstable stationary point, and (in fact) it is quite remarkable that "Omega" is anywhere close to one now", unquote. A universe with an "Omega" of one is analogous to a fat man trying to walk the tightrope to eternity with no pole, and without falling off. The fact that the universe is so close to flat confirms what we already know about the cosmological model based on General Relativity. It is absolutely poised, so perfect in its specifications that it betrays design- and its eternal nature.
Any topologist will confirm that it is possible for a hyperbolic universe to be finite...in fact the antiverse may have a poised hyperbolic space configuration. Nevertheless, stability in our modeling requires a marginally closed, universe for our side of the hypersphere. Perfectly flat space conflicts with the circular motion of energy, space and time in General Relativity, is heterodox to the model and brings GR, a well verified concept, into question. It is inconceivable that GR does not apply cosmologically. If it is correct, it applies to the ends of the universe- "Big Bang" to "Microscopic Singularity" within its own dynamic constraints.
I wondered why my Euclidean space friends didn't call me to "crow" a bit- until I saw the experimental data (posted on the Internet) by "Nature" magazine. The data was beautiful, strong, and showed clearly that the "Omega" was greater than one...a General Relativity universe!
I couldn't believe my eyes. I sent an E-mail to a leading expert on CBR research and asked him if I was cross-eyed or something! He returned my E-mail within hours and told me my eyes were not deceiving me, but because the possible statistical error was three times greater on the high side of the data than on the low side of the data, this team had come to the conclusion the universe was FLAT. He wanted to be a good team player, but he clearly implied it was OK to draw my own conclusions! There are thousands of scientists around the world who are drawing THEIR own conclusions too. (see postscript)
I've taught probability, and depending on the engineering of the equipment, can completely agree there is probably a "high side" error in that data. Interpreting the data literally (so far as I can determine at first glance) would give a much TOO closed universe. Yet considering the beauty of the raw data, the verification of Relativity to date, and the very slight decimal fraction over one needed to close the universe, a public assertion of a flat universe could most tactfully be called, "premature".
What causes redshift?...a hot plasma in the intergalactic medium?! Dr. Crawford has to be smiling! A casual reader of this web site can hardly begin to understand the problems and contradictions of existing observations precipitated by a "flat space" universe; I've only scratched the surface. Readers also need to remember that time, space and energy are observed by symmetry to pass in a linear direction in an Einsteinian Hyperspherical Universe. Also, the universe is vast, and thus the decimal fraction of an "Omega" over one must be small.
As I pointed out, only a tiny fraction above an "Omega"of 1 will absolutely close the universe. The raw data (which is of excellent quality) STRONGLY suggests that the Omega IS slightly higher than one.
Remember what I have said about little things making a fundamental difference? Mr. Homann made a good point. 43 SECONDS OF ARC PER CENTURY....(in the precession of the orbit of Mercury) and our whole vision of reality changes. This will hold in the matter of the Omega as well. Only a tiny decimal fraction over one will be another nail in the coffin of Classical dynamics and Euclidean space. One final thing; I was much more concerned by previous observations which indicated an Omega of .6 or .7, a hyperbolic universe. Now that we have the big one point zero, all we have to do is nail down that tiny little fraction....that "43 seconds".
I'm very interested in Unified Field Theory. I do not feel a Theory of Everything (TOE) or Grand Unified Theory (GUT) will answer all our questions, but these things will put us on the right track in our investigations. We will only have a Unified Field Theory, a TOE or a GUT when our CONCEPTUAL understanding of the universe conforms to reality. Wu Chi Kay and I strongly agree on this principle, and in fact, this is the reason these conceptualizations of Special Relativity, General Relativity, and Quantum Mechanics are on this web site!
Special and General Relativity succeeded because Einstein conceptualized them before he did his more formal work. In my opinion, the reason Einstein failed in his search for a Unified Field Theory was his failure to properly conceptualize the proportions and relationships of and between space, time matter and energy in their many forms. He filled blackboards with equations, but as Wu Chi Kay implies, he did not succeed because he failed to correctly conceptualize.
I was reading an article on the Internet in which it was asserted that humans would be unsuccessful in any attempt to conceptualize adequately above seven dimensions. I don't completely agree, although the use of the word "adequately" is appropriate. Increasing dimensions, as I have already discussed, increases degrees of freedom and unleashes vast possibilities. Beyond the "triad" at 11 dimensions, it gets difficult to keep track of, and relate the many things going on at the same time.
Although I must repeat many things, the careful reader of this web site will find something completely new in each response. General Relativity in seven dimensions is like a house with many rooms, closets, and even a cellar. There is plumbing and electrical...even furniture- the metaphysical implications.
The importance of conceptualizing cannot be over stressed. Wu Chi Kay emphasizes and reemphasizes this in his paper. I'm reminded of Einstein, who said: "God does not care about our mathematical difficulties. He integrates empirically". The fact which makes the universe complicated is its almost unlimited frames of reference with respect to Energy, Space and Time.
I agree with Wu Chi Kay that at its heart, the universe is founded on simple principles and relationships. Although mathematics can be misused, I do not belittle it. I believe the principles by which the universe operates can be mathematically described. Even more important, I believe mathematical relationships and principles can be our guide in the search for new worlds we as yet cannot conceptualize- and lead us to a better understanding of our own.
A can of shaving cream is soap and water before and after it is spayed into our hands. Energy Space and Time in different proportions, and viewed in different ways, are still, Energy, Space and Time. Yet the miracle of reality is created by observing the infinite variety of configurations of these things possible according to certain MATHEMATICAL parameters, over eternity.
Folks have told me they read my paper, "The Einsteinian Hyperspherical Universe" several times before the full impact of what I was saying hit them. I think this is more a reflection on my writing ability than it indicates a complex cosmos, for there is a charming simplicity about the EHU which is overpowering. General Relativity in 7-Dimensions and up is absolutely the answer. We see that answer in the math. We see that answer in the observations. We see that answer as we logically follow and describe the EHU concept in words.
My biggest frustration is that we will all be back here 100 billion years from now, thrashing this whole theory out again! Yet what Einstein is (note tense), and what we are doing is a part of a very important process which relates to the continued existence of the universe. An interesting reality is that eternity is an important dimension. I seriously doubt that we are in free fall to nowhere in General Relativity.
To use a four dimensional projection, all free fall in our universe ends somewhere, at some time. Orbits decay, stars die and singularity occurs. Black holes consume matter, merge with other such objects and eventually bring an entire hemisphere of the universe to singularity and renewal in a "Big Bang".
In human reproduction, we produce our own kind in a Biological cycle; human, human children, human grandchildren, human, human, human for seemingly endless generations. Yet gradually, over hundreds of thousands of generations, a transformation occurs in our species, in response to the changing stimuli of the environment. We become something else.
Individually, although I am an eternal stone in the cathedral of the sky, I believe I can safely infer that the next time around will be almost...but not quite the same experience. Taking chips out of the stones of a cathedral will not affect the stability of the edifice...not immediately, anyway! This idea is NOT conjecture- it is based on the not quite infinite, and therefore "poised" nature of a GR reality.
Life is the edge. In fact, life is more than the edge. It can and does, (for safeties sake) push the universe toward increasing order. In card-playing parlance, life is the ace of trump. Gradually, over the dimension we call eternity, it further organizes the universe in such a way as to decrease entropy and bring about a new vision of reality. As trillions upon trillions of years pass, a miracle happens...all things become new. We are somehow part of what the universe is to be.
Gee Whiz! Is this Physics or metaphysics? Let me share a profound truth with our readers. If Physics and Mathematics cannot explain the metaphysical, our Physics and Mathematics are wrong. The link between human intuition and observation is Biologically part and parcel of the same thing. The two are, in fact, so closely related science cannot correctly escape religion, and religion can never correctly escape science. Einstein understood this well, but his fear of both science and religion willfully running on their own can be seen in the following quote: "Science without religion is lame; religion without science is blind".
"A new theory must contain the old theory as a classical limit"....sometimes yes and sometimes no. General Relativity was constructed by adding terms to Newtonian formulae, and yet many times we have to throw away the old and replace it with the new. Ptolemys' vision of an observer centered universe has been partly redeemed by Einstein, but so far as I know, scientists are not reconsidering epicycles. In theory, concept and reality, the totals of complex physical and biological systems are not equal to, but greater than the sum of their parts. Each system plays many distinct roles, and has a multiplicity of functions. The perceptive reader will see a life prompted, entropy decreasing effect in the previous two sentences. Reality is usually completely redefined in a new concept.
"Mysteries indicate the necessity of mainstream knowledge being enriched by a new and wider theory". Let me revise that a bit! Unexplained and unexplainable observations indicate the necessity ...etc. Semantics is important. Definitions are important. In his attempt to "Demystify" the cosmos, Wu Chi Kay, fails to note that we as humans are what we are by definition. Assuming that on this side of the Hypersphere at least, order does not proceed from disorder, we by definition can assume correctly that we have come from higher, not lower order. To refuse to call this higher order "God" and assign consciousness to it, when we are conscious ourselves at a lower level of order, is a serious matter.
This denial of the existence of any higher consciousness than our own is a problem which has historically plagued science, but NOT without reason! All scientists remember how Galileo -and other scientists- have been treated by religious zealots! Partly because of the abuses of organized religion, some scientists have "thrown the baby out with the bath water" and abandoned any willingness to consider the presence of the Divine. Relativity and Quantum Mechanics have revived this issue.
I believe that consciousness of various kinds is the result of certain complex dynamic conditions in a material universe defined by the relative proportions and relations of space, time, matter and energy. Eternal life, if it exists, and I believe it does, will be experienced in a REAL body, where the complex dynamic conditions necessary for life exist. The fact that "biological creation" SEEMS to result from energy input, chance and random events, natural selection and the self-organizing tendencies of matter, in no way permits me to assert that the source of my life is any less conscious than my own.
"Nature doesn't know about equations". In the light of what I just said, I wouldn't be too quick to make that assertion. When my students begin to discover order in Binomial Expansion their reaction is fun to watch. In one experiment, we bounce coins off the wall, build a model up to (a+b) to the fifth or sixth power and evaluate the results. While no individual event can be predicted, the overall behavior of our coins can be predicted with emerging certainty. We relate this to a universe with 10200 frames of reference and BEGIN to understand from where reality comes. Do we understand the predictive power of General Relativity? Do we know what 43 seconds of arc per CENTURY means in an orbit of 360 degrees repeated hundreds of times?
The POWER of mathematical equations is staggering. To understand what E=mc2 means, we would have had to stand on a dark New Mexico desert and watch that flash of light for ourselves!. Robert Oppenheimer was a calm, reflective man, but he reacted to the sight of that explosion by saying: "I am become death, the destroyer of worlds". In my considered opinion, to assume that these formulae which perfectly reflect conditions in the cosmos are not intelligently conceived requires a leap of faith beyond that of a religious fanatic. Can the reader imagine how PAM Dirac felt when, on the basis of the positive and negative values of General Relativity, he predicted antimatter- and then saw his predictions verified? I wish Paul could be alive today to read the following item from the April issue of a major scientific publication, which reported that recent studies of the "Dark Matter" show it is likely invisible Neutrons (and presumably Protons) and concluding that, if true. this is a breakthrough of major proportions...and that there may be another world silently "interleaved" with our own.
Honestly, I'm quite sure "nature" knows about equations! Our readers may remember my referring to "forms", and a "pouring of the concrete" analogy in my description of the early birth of a "hemisphere" of the Einsteinian Hyperspherical Universe. How good was that analogy?
When the infant "hemisphere" emerges from singularity in a "Big Bang", the "forms" are the equations! The established proportions of time, space and energy; probabilities for each frame of reference; all these are predetermined and imposed when the universe comes into being, as preserved in the space/time energy lattice of the symmetrical hemisphere. The presence of these "forms" is determined by the mass of the universe, the speed of light, the absolute size of the universe, and most important, their preexistence in the other "hemisphere", but their intelligent creation is strongly inferred by the fact that life appears, and is involved in the "feedback" system which causes the universe both to exist, and continue.
Concrete forms must be made according to an intelligent plan or they are useless...everything comes to naught. The forms (equations) of the universe are analogous. I'm strongly inclined to believe the regular patterns of microscopic singularity in space, determined by ironclad quantum probabilities based on vast sample sizes, act as forms, to which free energy and particles are attracted in the creation of Hydrogen and Helium.
I think, at this point in time, most scientists are very open to the idea of a geometrical basis in the solution of their problems describing physical reality. Not all scientists specialize in Geometry, to be sure, but the lessons of Relativity are clear. I strongly agree with Wu Chi Kay that the solution to the Unified Field puzzle will be geometric.
"Nature has a zero IQ". Needless to say, I'm not inclined to agree. It takes genius, not a zero IQ to make things, in principle elegantly simple, and then create the almost infinitely complex. The greatest challenge of engineering is something foolproof, yet simple....and brother does that challenge require intelligence! Yet the challenge not only requires intelligence, but in the Einsteinian Hyperspherical Universe, it required an eternity of experience, great patience, grace and forgiveness...or am I beginning to speak like a theologian? Yet these verities have a physical basis in science and engineering as well as a theological application.
Ocams razor states: "On the average, given a wide variety of possible solutions, the simplest answer is most likely to be correct"....a perfect reason to believe in, and trust God.
String theory is fascinating, and I believe it is one of our greatest hopes for a better understanding of the sub-microscopic. I feel great strides are being taken in this field, and I'm watching developments with interest.
"Get rid of the paradox of material creation". Here Mr. Kay and I again strongly agree. Mr. Kay, Dr. Crawford and Sam Cox all like to stand back and view the universe in its static, eternal and complex beauty. Of course, the universe, so far as we can tell anyway, was made to be lived in, so having had a good look, we have to return to our dynamic universe and pay the bills, drive to work and take care of the kids.
For reasons I've discussed, I'm not too definite about the exact dimensional configuration of the universe. General Relativity requires a minimum of four dimensions as I implied. Dr. Nanduri spoke of seven and Mr. Kay speaks of 10. I have described the cosmology of the Einsteinian Hyperspherical Universe in seven dimensions, but because of the need for stability and almost unlimited possibilities in an eternal universe, I'm inclined to feel the possible number of dimensions is exponentially vast.
The relationships of energy, space and time in General Relativity are defined mathematically. Time can be defined in terms of energy and space. Space can be defined in terms of energy and time. Its a "what came first, the chicken or the egg" kind of thing. Scientists find that mathematically, energy and time can be defined by space- and feel they have made a major discovery. I'm not so sure, and it is important that we always remember: NONE of the three are passive. They are all active, and none can exist without the other.
I haven't seen Mr. Kays other work, but I'm not inclined toward "potential space", "Pseudo-space" or presumably "void space", for reasons rooted in General Relativity.
I have never seen so many ideas presented in such a short paper. I'm sure I was not able to completely and correctly interpret every idea, for details in the paper are necessarily sparse. Still I found the paper very interesting and stimulating, and I hope there will be something in my response which will be of use to Wu Chi Kay ...and the readers of "Cosmology Review".
Sincerely,
Samuel A. (Sam) Cox College of Micronesia: May 9, 2000
POSTSCRIPT:
One day after I wrote my comments on the recent Cosmic Background Study in Antarctica, I noticed the following posting: (Postscript; Even with additional data from the Maxima project...the implications of this work seem to point in the direction of marginally closed space and a parallel universe of the kind described on this site. See the second posting, below "Boomerang returns unexpectedly"
Boomerang returns unexpectedly
Authors: Martin White, Douglas Scott, Elena Pierpaol
Comments: 11 pages, 3 figures, submitted to ApJL
- Experimental study of the anisotropy in the cosmic microwave background (CMB) is gathering momentum. The eagerly awaited Boomerang results have lived up to expectations. They provide convincing evidence in favor of the standard paradigm: the Universe is close to flat and with primordial fluctuations which are redolent of inflation. Further scrutiny reveals something even more exciting however -- two hints that there may be some unforeseen physical effects. Firstly the primary acoustic peak appears at slightly larger scales than expected. Although this may be explicable through a combination of mundane effects, we suggest it is also prudent to consider the possibility that the Universe might be marginally closed. The other hint is provided by a second peak which appears less prominent than expected. This may indicate one of a number of possibilities, including increased damping length or tilted initial conditions, but also breaking of coherence or features in the initial power spectrum. Further data should test whether the current concordance model needs only to be tweaked, or to be enhanced in some fundamental way.
Paper: Source (50kb), PostScript, or Other formats
<(N.B.: delivery types and potential problems)
WITH THANKS TO THE SCIENTIFIC AMERICAN; JULY 2000;
| ........... | COSMOLOGY_BACKGROUND RADIATION Boomerang Effect Balloon data confirm the big bang--and challenge it, too Usually cosmology goes like this: new observations come in, scientists are baffled, models are upended. After the dust settles, however, patches are affixed and the prevailing theory emerges largely intact. But when the measurements by the Boomerang and Maxima telescopes came in, the sequence was reversed. Scientists were elated. "The Boomerang results fit the new cosmology like a glove," Michael S. Turner of the University of Chicago told a press conference in April. And then the dust settled, revealing that two pillars of big bang theory were squarely in conflict--a turn of events that could be nearly as monumental as the discovery of cosmic acceleration just over two years ago. Both telescopes observed the cosmic microwave background radiation, the remnant glow of the big bang. Boomerang, lofted by balloon in December 1998 for 10 days over Antarctica, had the greater coverage--3 percent of the sky. Maxima, which flew above Texas for a night in August 1998, scrutinized a tenth the area but with higher resolution. The two instruments made the most precise maps yet of the glow on scales finer than about one degree, which corresponds to the size of the observable universe at the time the radiation is thought to have been released (about 300,000 years after the bang). On this scale and smaller, gravity and other forces would have had enough time to sculpt matter. For those first 300,000 years, the photons of the background radiation were bound up in a broiling plasma. Because of random fluctuations generated by cosmic inflation in the first split second, some regions happened to be denser. Their gravity sucked in material, whereupon the pressure imparted by the photons pushed that material apart again. The ensuing battle between pressure and inertia caused the plasma to oscillate between compression and rarefaction--vibrations characteristic of sound waves. As the universe aged, coherent oscillations developed on ever larger scales, filling the heavens with a deepening roar. But when the plasma cooled and condensed into hydrogen gas, the photons went their separate ways, and the universe abruptly went silent. The fine detail in the background radiation is a snapshot of the sound waves at this instant. Areas of compression were slightly hotter, hence brighter; areas of rarefaction, cooler and darker. From the Boomerang and Maxima data, cosmologists expected a profusion of large spots (oscillations that had most recently begun), spots half that size (oscillations that had gone on for longer), spots a third the size (longer still), and so on. On either a Fourier analysis or a histogram of spot sizes, this distribution would show up as a series of peaks, each of which corresponds to the spots of a given size [see illustration on opposite page]. The height of the peaks represents the maximum amount of compression (odd-numbered peaks) or of rarefaction (even-numbered peaks) in initially dense regions. Lo and behold, both telescopes saw the first peak--which not only confirms that sounds reverberated through the early universe, as the big bang theory predicts, but also shows that the sounds were generated from preexisting fluctuations, as only inflation can produce. The next implication is for the geometry of the universe. If the rules of Euclidean trigonometry apply (as they do on a flat sheet of paper), the dominant spots should subtend 0.8 degree after accounting for cosmic expansion. If space is instead curved like a sphere, the spots will look larger; if it is curved like a saddle, they will look smaller. Boomerang measured an angle of 0.9 degree--close enough for the team, led by Paolo de Bernardis of the University of Rome and Andrew E. Lange of the California Institute of Technology, to declare in Nature that space is Euclidean. The Maxima team, in papers by Amadeo Balbi of Rome and Shaul Hanany of the University of Minnesota, reached the same conclusion, as did results from earlier telescopes, albeit with less precision. Yet follow-up studies soon showed that the lingering discrepancy, taken at face value, indicates that the universe is in fact spherical, with a density 10 percent greater than that required to make it flat. Such a gentle curvature seems awkward. Gravity quickly amplifies any deviations from exact flatness, so a slight sphericity today could only have arisen if the early universe was infinitesimally close to flat. Modified versions of inflation might explain this fine-tuning, but most cosmologists regard them as last resorts. A more palatable alternative is that the trigonometric calculation somehow did not properly account for cosmic expansion. This would happen if the radiation did not travel as far as assumed--that is, if it was released later in cosmic history, if the famous Hubble constant were larger (making the universe younger), if the universe contained more matter (holding back the expansion) or if the cosmological constant were smaller (taming cosmic acceleration). All these possibilities, however, seem to contradict other observations. A way to keep the peace is if the cosmological constant has not, in fact, been constant. Its inconstant cousin, known as quintessence, would impart a milder acceleration. As Paul J. Steinhardt of Princeton University has argued, quintessence would also explain why the first peak is lower than it should be. Something seems to have monkeyed with the radiation since its release, and quintessence would indirectly do exactly that. The second big mystery in the data is even more dire: there is only the merest hint of a bulge where the second peak should be. That suggests that the primordial plasma contained surprisingly many subatomic particles, which would weigh down the rarefaction of the sound waves and suppress the even-numbered peaks. But accounting for those extra particles is no easy matter. According to Max Tegmark of the University of Pennsylvania and Matias Zaldarriaga of the Institute for Advanced Study in Princeton, N.J., the Boomerang results imply that subatomic particles account for 50 percent more mass than standard big bang theory predicts--a difference 23 times larger than the error bars of the theory. "There are no known ways to reconcile these measurements and predictions," says nucleosynthesis expert David R. Tytler of the University of California at San Diego. One mooted solution, a steeply "tilted" version of inflation that did not create fluctuations uniformly on all scales, also contradicts the data. New information due out soon could resolve some of the problems: only part of the Boomerang and Maxima data has been analyzed, and both balloons will fly again this year in search of the decisive third peak, an inkling of which appeared in the Maxima observations. Several other experiments are planned, and the long-awaited Microwave Anisotropy Probe is now scheduled to launch next spring. That roar in the heavens may have been laughter at our cosmic confusion.
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