Sep 302014
 

Measuring distances in astronomy is notoriously difficult.  Indeed, a quick glance at the night’s sky reveals only a two-dimensional image, with no depth information.  Yet, knowledge of precise distances is crucial, since that’s the only way to determine the true, intrinsic luminosity of an object, from the apparent one, measured by our telescopes.  The determination of distances therefore constitutes a major component of almost every astronomical study, whether that involves the evolution of stars or the accelerating expansion of the universe.

The most direct and precise method to measure distances is using trigonometric parallaxes (Figure 1).  This method is based on the fact that as the Earth orbits the Sun, relatively nearby stars appear to move against the more distant stellar background.  By measuring the angle associated with this apparent motion from two positions along the Earth’s orbit (say, in January and in July), and knowing the diameter of the Earth’s orbit, the distance to the star can be calculated using simple trigonometry.  Unfortunately, ground-based telescopes can only perform such distance measurements to stars that are no farther than a few hundred light-years, due to the blurring effects by turbulence in the Earth’s atmosphere.  Astronomers have therefore come up with a variety of other ingenious (if somewhat less precise) methods to determine distances to more distant objects.

Figure 1.  Measuring distances to stars through the method of trigonometric parallax.  (Credit: STScI.)

Figure 1. Measuring distances to stars through the method of trigonometric parallax. (Credit: STScI.)

Figure 2.  An artist’s impression of the Gaia Satellite deploying its sunshield.  (Credit: ESA.)

Figure 2. An artist’s impression of the Gaia Satellite deploying its sunshield. (Credit: ESA.)

On December 19, 2013, however, the European Space Agency launched its Gaia space observatory (Figure 2), which promises to open a new era in precision measurements of distances.  From its orbit at the so-called L2 Lagrangian point (about a million miles from Earth, in the direction opposite to the Sun), Gaia will use its two telescopes and three science instruments to observe each one of its target stars about 70 times during the five-year mission duration.  This will allow Gaia to generate a three-dimensional map of about a billion stars in our Milky Way galaxy.  In addition to extremely precise positions, Gaia will map the stellar motions, and will determine the luminosities, temperatures and compositions of the observed stars.  To appreciate the expected precision, suffice it to note that for stars about 4000 times fainter than those we can see with the naked eye or brighter, Gaia will determine the position to about 24-millionths of an arcsecond (equivalent to the width of a human hair at 600 miles!).

In addition to this extraordinary 3D map of the Galaxy, Gaia is expected to detect thousands of extrasolar planets, about half a million quasars (supermassive black holes that accrete mass at the centers of distant galaxies), and tens of thousands of asteroids and comets within our own solar system.

Shortly after Gaia’s launch, the European Space Agency discovered some ice deposits in the observatory that appear to cause a problem with stray light entering the telescope.  The current assessment is, however, that this will only degrade the science performance for the faintest stars among Gaia’s targets, so that the overall mission goals will not be significantly affected.

Douglas Adams, the author of The Hitchhiker’s Guide to the Galaxy, once wrote:  “There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and  inexplicable.  There is another theory which states that this has already happened.”  Irrespective of whether it has already happened or not, it appears that once all the results from Gaia are in, we will have such a better understanding of our Galaxy and of the Universe that we may find ourselves much closer to the imaginary cosmic scenario envisioned by Adams.

Sep 242014
 
Figure 1. The BICEP2 telescope at the South Pole is in the foreground; in the background is the South Pole Telescope. (Credit:  Steffen Richter/Associated Press.)

Figure 1. The BICEP2 telescope at the South Pole is in the foreground; in the background is the South Pole Telescope. (Credit: Steffen Richter/Associated Press.)

You may remember that about six months ago, scientists got all excited about the potential detection of ripples from the Big Bang—direct evidence (if it were to be confirmed) for the event known as “cosmic inflation” (see e.g., “A Visit from the Big Bang,”).  What happened then was that a team of scientists analyzing data from the BICEP2 telescope at the South Pole (Figure 1) claimed to have detected “B-mode polarization”—an imprint in the cosmic microwave background that could have been created by gravity waves resulting from cosmic inflation.

If that result were to hold, this would have undoubtedly been one of the most dramatic discoveries  in decades.  However, extraordinary claims require extraordinary proof, and a few scientists were quick to point out that dust in our own Milky Way galaxy could, at least in principle, produce a polarization signal similar to the one observed by the BICEP2 team.

Figure 2.  The black curve shows what one would see from gravity waves generated by cosmic inflation, if their strength were as stated in the original paper of the BICEP2 team. The light blue (and pink) areas show what the Planck satellite observes, and attributes to dust. The figure shows that the entire BICEP2 signal could be attributed to Galactic dust. (Credit: The Planck Collaboration, R. Adam et al. 2014.  arXiv:1409.5738.)

Figure 2. The black curve shows what one would see from gravity waves generated by cosmic inflation, if their strength were as stated in the original paper of the BICEP2 team. The light blue (and pink) areas show what the Planck satellite observes, and attributes to dust. The figure shows that the entire BICEP2 signal could be attributed to Galactic dust. (Credit: The Planck Collaboration, R. Adam et al. 2014;
arXiv:1409.5738.)

Here is where the scientific method kicks in big time.  Scientists knew that maps of the Galactic dust distribution from the Planck satellite, coupled to the determination of the polarization signal from this dust, would shed light on the question of whether what BICEP2 saw could indeed be coming from polarizing dust, rather than from the B-modes produced by inflation.  The Planck team has now published its results, and those are not encouraging for the inflationary interpretation.  At face value, the Planck results suggest that polarization by dust from the Milky Way could explain the signal detected by BICEP2 (Figure 2).

The Plank team is careful to note that their results do not entirely rule out the possibility that BICEP2 did detect something from inflation, and the team’s paper highlights the need to reduce the uncertainties through an ongoing, joint analysis of the data sets from both Planck and BICEP2.  Moreover, new results are expected soon from the Keck Array experiment and those should further clarify the picture.

As disappointing as these new results may sound, they provide for a powerful demonstration of how science truly progresses.  Advances in science are far from being a direct march to the truth.  Rather, they consist of a zigzag path which often results in false starts or blind alleys.  The important point, however, is that through continuous checks, testable predictions, and new observations, science is able to self-correct and find the right way.

Sep 162014
 

There are numerous websites entitled “Top 10 Unsolved Science Mysteries,” or some slight variations on this theme.  However, even a cursory examination of these sites reveals that the choices for the “top 10” are far from being unanimous.  Here I have identified three “mysteries” that appear on many—but definitely not all—lists (in no particular order).

(1)  Are We Alone?

Figure 1. A potential design for the Advanced Technology Large-Aperture Space Telescope (ATLAST) that would be able to detect biosignatures in the atmospheres of extrasolar planets. Credit: Northrop Grumman Aerospace Systems & NASA/STScI.

Figure 1. A potential design for the Advanced Technology Large-Aperture Space Telescope (ATLAST) that would be able to detect biosignatures in the atmospheres of extrasolar planets. Credit: Northrop Grumman Aerospace Systems & NASA/STScI.

With billions of Earth-size planets orbiting their host stars in the “habitable zone” (the region that is neither too hot nor too cold, so that it allows for liquid water to exist on the planet’s surface) is it possible that Earth is the only planet in the Milky Way galaxy hosting life?  Fortunately, we don’t need to speculate.  For the first time in human history, we find ourselves in the position that we may be able to answer this question in the coming two to three decades (Figure 1).  Needless to say that a discovery of extrasolar life will constitute a scientific revolution that will rival the Copernican and the Darwinian revolutions combined.

A related “mystery” that appears on many lists is that of the origin of life.  On that front, researchers predict that we may be able to create life from ordinary chemistry in the laboratory within the next five years!  (See a brief summary at: Creating Life in the Lab.)

(2)  Is the Speed of Light the Ultimate Speed Limit?

Figure 2.  A process that splits photons (particles of radiation) into entangled pairs that have perpendicular polarizations. Credit: J-Wiki at en.wikipedia – Transferred from en.wikipedia (http://en.wikipedia.org/wiki/Quantum_ entanglement#mediaviewer/File:SPDC_figure.png).

Figure 2. A process that splits photons (particles of radiation) into entangled pairs that have perpendicular polarizations. Credit: J-Wiki at en.wikipedia – Transferred from en.wikipedia (http://en.wikipedia.org/wiki/Quantum_ entanglement#mediaviewer/File: SPDC_figure.png).

According to Einstein’s theory of Special Relativity, the speed of light in vacuum (about 186,000 miles per second, or about 300,000 kilometers per second) is the maximum speed at which matter, energy, or information can travel.  If not for this limit, causality would be violated.  In other words, effects would be observed prior to their causes.

This is not to say that nothing can move faster than light.  For example, spacetime itself can stretch faster than the speed of light, and indeed it apparently had done so, during the brief period at the beginning of our universe known as “cosmic inflation” (see for example the discussion at: Eternal Inflation).

Quantum entanglement presents a phenomenon in which information at least appears to be transmitted faster than light.  The idea is that when a property of one member of a pair of “entangled” particles (e.g., photons that have been prepared in a particular combination of their polarizations; Figure 2) is measured, the value of that property for the other member of the pair can be determined instantaneously.  A simple classical analogue of this situation would be if someone puts each shoe of a pair into a separate box without telling you which shoe is in which box.  Then she sends one box to London and leaves one with you.  Clearly, as soon as you open your box and see that it contains the left shoe, you instantaneously know that the box in London contains the right shoe.  The precise implications of this so-called “spooky action at a distance” are still an active research area.

(3)  Can Humans Become Immortal?

Figure 3. Human chromosomes (in gray). The telomeres are the white caps. Image is in the Public Domain (https://en.wikipedia.org/wiki/Immortality#mediaviewer/File:Telomere_caps.gif).

Figure 3. Human chromosomes (in gray). The telomeres are the white caps. Image is in the Public Domain (https://en.wikipedia.org/wiki/Immortality#mediaviewer/File:Telomere_caps.gif).

The fact that everybody dies at the end has so far been an undeniable fact of life.  But is that truly inevitable?  Research into the possibility of prolonging life is proceeding in several directions.  One such effort concentrates on an enzyme called telomerase, which was shown to slow down the death of cells, by arresting the age-induced shortening of the protective tips at the ends of chromosomes (known as telomeres; Figure 3).  Experiments done with mice in recent years did demonstrate a reversal in the aging process through telomerase reactivation.  Whether or not similar effects can be obtained in humans is still an open question.

Another direction of research, taken, for instance, by the New England Centenarian Study, is to examine in detail the genes of a couple thousand people who have reached the age of 100 for clues as to their unusual longevity.

Finally, some scientists, such as computer scientist and futurist Ray Kurzweil, argue that nanotechnology could produce tiny “maintenance” robots that would circulate through the human body and repair age-related damages.

The lesson from all of these “mysteries” is clear.  There is no shortage of fascinating open questions in science, and I feel confident in predicting that even if the particular mysteries that I have listed here are solved, new, exciting ones will emerge.

 

Aug 192014
 

Humans have always been fascinated with the heavens.  Our distant ancestors understood that Mother Earth was receiving its daylight warmth from the majestic Sun, and its pale, nocturnal light from the Moon.  In addition, there were those twinkling point sources of light that the ancients connected by imaginary lines to form mythical constellations.  A few “stars” were observed to wander across the sky and they were dubbed “planets” (meaning “wandering stars”) by the ancient Greeks.

Not surprisingly, the stars have been the subject of many poems.  Perhaps none is more romantic than John Keats’s “Bright Star.”  This may have been Keats’s last poem before his untimely death in 1821, at age twenty-five.  In that poem, which Keats transcribed into a volume of The Poetical Works of William Shakespeare (Figure 1), Keats wished to be as constant as a star:

Bright star, would I were steadfast as thou art—
Not in lone splendor hung aloft the night…”

Figure 1.  The poem “Bright Star” by John Keats was transcribed into a volume of The Poetical Works of William Shakespeare.  Image in the Public Domain. (https://en.wikipedia.org/wiki/Bright_star,_would_I_were_steadfast_as_thou_art#mediaviewer/File:Brightstar.jpg)

Figure 1. The poem “Bright Star” by John Keats was transcribed into a volume of The Poetical Works of William Shakespeare. Image in the Public Domain. (http://en.wikipedia.org/wiki /Bright_star,_would_I_were_steadfast_as_thou_art #mediaviewer/File:Brightstar.jpg)

The most familiar poem about the stars is probably “The Star” by English poet Jane Taylor (1783–1824). The poem is better known through the sung version of its first line, “Twinkle, twinkle, little star.”  The music that accompanies the first stanza was taken from an eighteenth century French melody.

Another beautifully romantic poem, “Ah, Moon—and Star!” by Emily Dickinson, laments the fact that even though the Moon and the star are very far, the poet’s beloved is even less reachable.  The last, desperate-sounding stanza, reads:

But, Moon, and Star,
Though you’re very far—
There is one—further than you—
He—is more than a firmament—from me—
So I can never go!”

Poems about the stars, and their perceived perfection, are not only common in the western tradition.  The great Indian author and poet Rabindranath Tagore (Figure 2 shows him with Albert Einstein), wrote a poem entitled “Lost Star,” in which he described how one star—“the glory of all heavens,” was thought to have been lost at the time of creation.  In the poem, this perception triggered a ceaseless quest to find the “lost” star.  The poem concludes, however, by saying that this search is futile, since all the stars (and thereby perfection) are in fact there.

Figure 2.  Rabindranath Tagore with Albert Einstein. Photo in the Public Domain.  (https://en.wikipedia.org/wiki/Rabindranath_Tagore#mediaviewer/File:Rabindranath_with_Einstein.jpg)

Figure 2. Rabindranath Tagore with Albert Einstein. Photo in the Public Domain.
 (http://en.wikipedia.org/wiki /Rabindranath_Tagore#mediaviewer/File:Rabindranath_with_Einstein.jpg)

Even though we know much more about the stars now—about how they are born, live and die—our physical existence is so tethered to them, that I am convinced that the stars will continue to inspire magnificent poetry.  Astronomy continues to fascinate, and it serves as one of the most powerful magnets, attracting young minds into the sciences. We are star dust after all.

Aug 052014
 
Figure 2.  The elliptical galaxy NGC 4150.  (http://hubblesite.org/newscenter/archive/releases/2010/38/image/a/format/ web_print)

Figure 2. The elliptical galaxy NGC 4150. (http://hubblesite.org/newscenter/archive/ releases/2010/38/image/a/format/
web_print)

Figure 1. The spiral galaxy M74.   (http://hubblesite.org/newscenter/archive/releases/ 2007/41/image/a/format/web_print)

Figure 1. The spiral galaxy M74. (http://hubblesite.org/newscenter/archive/ releases/ 2007/41/image/a/format/ web_print)

 

 

 

 

 

 

 

 

There is a common phrase “no two snowflakes are alike.”  Astronomers in the early part of the twentieth century felt the same about galaxies (or “nebulae,” as they were called then).  Indeed, at the very detailed level, each galaxy is different.  Nevertheless, in 1926, Edwin Hubble (after whom the Hubble Space Telescope is named) published a seminal paper in which he identified a few broad classes of galaxies, based upon their shapes.  At the crudest level, he divided galaxies into “Spirals” (S; e.g., Figure 1), “Ellipticals” (E; e.g., Figure 2) and those that did not fit into these two categories, which he called “Irregulars” (Irr; Figure 3).  At the next level, he further subdivided the spirals into two subgroups.  First, there were those in which the spiral arms appeared to emanate directly from the very core at the center of the galaxy, which he dubbed “normal” spirals (and they were denoted by “S”; e.g., Figure 4).  Second, there were the “barred” spirals (denoted by “SB”; Figure 5), in which the arms appeared to be connected to a straight “bar” crossing the galactic center.  Within each of the subdivisions E, S, and SB, Hubble introduced a certain progression of shapes.  For instance, the ellipticals ranged from E0, denoting a perfectly circular profile, to extremely eccentric (elongated) ellipses, denoted by E7.  For the normal and barred spirals, the sequence started with very tightly wound spiral arms (denoted by Sa or SBa) and ended with rather loosely wound or barely discernable arms (Sc or SBc).

fig3

Figure 3. The irregular dwarf galaxy NGC 4449. (http://hubblesite.org/gallery/ album/galaxy/irregular/pr2007026a/web_print)

Figure 4.  The normal spiral galaxy M101.  (http://hubblesite.org/gallery/album/galaxy/pr2006010a/web_print)

Figure 4. The normal spiral galaxy M101. (http://hubblesite.org/gallery/album/galaxy/ pr2006010a/web_print)

 

 

 

 

 

 

 

 

About a decade later, Hubble added yet another class of “lenticular” galaxies that he regarded as transitional objects between the spirals and the ellipticals, and these were denoted by S0.  While Hubble’s classification in itself has been extremely influential, it has gained additional power and appeal from a suggestive diagram that Hubble published in his 1936 book The Realm of the Nebulae.  The diagram (Figure 6) resembles a musical tuning fork and (perhaps somewhat unfortunately) it guides the eye, and indeed the mind, toward a perceived evolutionary scheme.  To Hubble himself and to quite a few of the astronomers that followed him, this elegant representation indicated a simple picture in which the galaxy shapes marked an evolutionary sequence.  Galaxies were assumed to continuously evolve from ellipticals to spirals along the fork.  This expectation turned out not to be true at all.  Galaxies form and evolve through a series of complex processes that involve (among others) the formation of dark matter halos, the accretion of gas via cold flows and hierarchical mergers in which smaller building blocks coalesce to form larger objects, the birth of stars in bursts, and the growth of massive central black holes.  Our understanding of the sequence of these events and their precise effects is still evolving.  In fact, one of the main goals of the upcoming James Webb Space Telescope (to be launched in 2018) is precisely to detect the very first galaxies that formed in our universe and to follow their evolution.

Figure 5.  The barred spiral galaxy NGC 1300.  (http://hubblesite.org/newscenter/archive/releases/2005/01/image/a/format/ web_print)

Figure 5. The barred spiral galaxy NGC 1300. (http://hubblesite.org/newscenter/ archive/releases/2005/01/image/a/format/ web_print)

Figure 6.  Hubble's tuning fork diagram for the classification of galaxies.  Credit: Sloan Digital Sky Survey/ SkyServer.

Figure 6. Hubble’s tuning fork diagram for the classification of galaxies. Credit: Sloan Digital Sky Survey/ SkyServer.

 

 

 

 

 

 

 

 

In spite of its limited scientific value as an illustration of galaxy evolution, Hubble’s musical tuning fork continues to provide an almost poetic depiction of the beautifully rich cosmic treasure of galaxies. In this sense, it is the modern equivalent of the “music of the spheres” of antiquity.

Jul 222014
 
Figure 1.  Jupiter's satellite Europa. Image in the public domain.  (http://en.wikipedia.org/wiki/Europa_(moon) #mediaviewer/File: Europa-moon.jpg)

Figure 1. Jupiter’s satellite Europa. Image in the public domain. (http://en.wikipedia.org/wiki/Europa_(moon) #mediaviewer/File: Europa-moon.jpg)

Recently, the search for extraterrestrial life has started to gain significant momentum. NASA has just announced, for instance, that it is setting aside $25 million to develop the scientific instruments needed for a mission to Europa (Figure 1).  This is the ice-covered moon of Jupiter that could harbor life in the ocean underneath its icy exterior.  Finding any form of life on a solar system body other than Earth—be it Mars, or one of the satellites Europa, Enceladus, or Titan—would indeed be very exciting.  The true revolution, however, will ensue once we find extrasolar life—life on a planet orbiting another star.  The main reason that makes extrasolar life the much bigger prize is very simple.  If extraterrestrial life is found within the solar system, unless it is absolutely clear that it has arisen independent of our lineage, there will always be the possibility that life on Earth and this newly found life had the same origin.  The discovery of life in a planetary system around another star, on the other hand, will immediately imply that life is not exceedingly rare, with all the extraordinary biological and cultural implications.

Figure 2.  The Transiting Exoplanet Survey Satellite (TESS). Credit: TESS team.

Figure 2. The Transiting Exoplanet Survey Satellite (TESS). Credit: TESS team.

Several factors have combined to advance the search for life to the level of a high-priority quest.  First, the statistics of the discoveries by the Kepler space observatory have made it clear that there are billions of planets in our Galaxy that orbit their host stars in the so-called “habitable zone.”  This is the range of distance that is neither too hot nor too cold, which allows for liquid water (thought to be a necessary ingredient for life) to exist on the planet’s surface.  Second, the Hubble and Spitzer space telescopes have already demonstrated that they can (at least partially) determine the composition of the atmospheres of extrasolar planets (only gas giants so far).  Third, and most important, the upcoming Transiting Exoplanet Survey Satellite (TESS; Figure 2), to be launched in 2017, and the James Webb Space Telescope (JWST; Figure 3), to be launched in 2018, could (at least in principle) discover biosignatures in the atmospheres of Earth-size planets orbiting small (M-dwarf) stars.  To constitute an unambiguous detection of life would probably require a combination of potential biosignatures, such as: inferred liquid water, oxygen and ozone, and an atmosphere that exhibits an extreme thermodynamic disequilibrium.  To be sure, the chances that TESS and JWST will actually find life are small, but definitely not zero.

Figure 3.   The James Webb Space Telescope (JWST). Image in the public domain.  (https://en.wikipedia.org/wiki/James_Webb_Space_Telescope#mediaviewer/File:James_Webb_Telescope_Design.jpg)

Figure 3. The James Webb Space Telescope (JWST). Image in the public domain. (https://en.wikipedia.org/wiki/James_Webb_Space_Telescope#mediaviewer/File:James_Webb_Telescope_Design.jpg)

The key point is that with the currently upcoming and the proposed telescopes (such as a 16-meter optical-ultraviolet space telescope with the acronym ATLAST), it appears that finding extrasolar life is, for the first time in human history, within reach.  A similar optimism seems to be associated with the search for extraterrestrial intelligent life (SETI).

In fact, I would venture to state that if extrasolar life is not found within the next thirty years, I would be amazed.  Ultimately, what makes the search for extrasolar life one of the most (if not the most) fascinating scientific endeavors, is the fact that you don’t have to be a scientist to realize that its discovery would dwarf by comparison even the Copernican and Darwinian revolutions combined!

Jul 082014
 
Figure 1.  A photograph entitled “Hypatia,” by the nineteenth century pioneering photographer Julia Margaret Cameron.   The model is Marie Spartali. (Image in the Public Domain at http://en.wikipedia.org/ wiki/Hypatia#mediaviewer/File: Hypatia,_by_Julia_Margaret_Cameron.jpg)

Figure 1. A photograph entitled “Hypatia,” by the nineteenth century pioneering photographer Julia Margaret Cameron. The model is Marie Spartali. (Image in the Public Domain at http://en.wikipedia.org/ wiki/Hypatia#mediaviewer/File: Hypatia,_by_Julia_Margaret_Cameron.jpg)

In 2009, the International Astronomical Union (IAU) held its General Assembly in Rio de Janeiro.  Of the 2109 participants, 667 (or 31.6%) were women.  Indeed, in recent years, the fraction of women among astronomers is continuously growing.  Who, however, is considered to have been the first female astronomer?  Most would agree that this title belongs to Hypatia of Alexandria (c. 350–415 CE; Figure 1), a remarkable philosopher, mathematician, and astronomer.

Unfortunately, apart from a few, very brief references in other works, there are only four primary sources on the life and work of Hypatia, and even those give somewhat conflicting accounts.  While very little, if any, of Hypatia’s own work has survived, one of her admiring pupils, Synesius of Cyrene, left a considerable body of letters addressed to her.  These are overflowing with admiration and reverence to Hypatia’s knowledge and scientific achievements.  In some, he asks for her advice on the design of scientific instruments, such as a hydroscope (used to determine density of fluids) and an astrolabe (used to predict positions of planets).

Figure 2.  A drawing showing a scene from the stage play “Hypatia,” written by G. Stuart Ogilvie. The play opened at the Haymarket Theatre in London on January 2nd, 1893. (Image in the Public Domain at http://en.wikipedia.org/wiki/ Hypatia#mediaviewer/File:Hypatia_at_the_Haymarket_theatre_-_The_Graphic_-_21_January_1893.jpg.)

Figure 2. A drawing showing a scene from the stage play “Hypatia,” written by G. Stuart Ogilvie. The play opened at the Haymarket Theatre in London on January 2nd, 1893. (Image in the Public Domain at http://en.wikipedia.org/wiki/ Hypatia#mediaviewer/File:Hypatia_ at_the_Haymarket_theatre_-_The_Graphic_-_21_January_1893.jpg.)

 

Hypatia was the daughter of the philosopher and mathematician Theon of Alexandria.  Around 400 CE she became the head of the Platonic school in Alexandria—an achievement that in itself is nothing short of astonishing.  Hypatia and her father wrote an eleven-part commentary to the Almagest—the celebrated astronomy book by Ptolemy, the most influential Greek astronomer of his time.  She also wrote explanatory notes to several books in mathematics, most notably on Apollonius’s Conics and on Diophantus’s multi-volume Arithmetica.

Hypatia was brutally murdered in 415 CE, either by a fanatical sect of monks or by an Alexandrian mob.  While the precise details of the murder remain unknown, there is little doubt that people who felt threatened by the level of knowledge and encouragement for learning that Hypatia had inspired, committed the murder.

Over the years, Hypatia’s name has become synonymous with learning and her life story was used as the subject of many books, plays (e.g., Figure 2), and works of art (Figure 1).  In astronomy, a main belt asteroid discovered in 1884 was named after her, as well as a crater on the Moon.  In 2013, geologists discovered evidence showing that a fiery comet struck the Sahara desert some 28 million years ago.  The comet was named Hypatia, to celebrate two “firsts.”  She was the first female astronomer, and the findings in the Sahara represented the first direct evidence for a comet hitting the Earth.

 

Jun 242014
 
Figure 1. A portrait of Archimedes painted in 1620 by Domenico Fetti. At Alte Meister in Dresden. Image is in the public domain (http://en.wikipedia.org/wiki/ Archimedes#mediaviewer/File:Domenico-Fetti_Archimedes_1620.jpg).

Figure 1. A portrait of Archimedes painted in 1620 by Domenico Fetti. At Alte Meister in Dresden. Image is in the public domain (http://en.wikipedia.org/wiki/ Archimedes#mediaviewer/File:Domenico-Fetti_Archimedes_1620.jpg).

The historian of mathematics E. T. Bell once wrote: “Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit.”  Indeed, each one of these three luminaries inspired awe in both their contemporaries and in the mathematicians that followed them.  When judged against the background of their times (third century BCE for Archimedes, seventeenth century for Newton, eighteenth century of Gauss), some put Archimedes at the very top of the list of math’s “greatest.”

Somewhat amusingly, Archimedes (Figure 1), is best remembered today for two striking exclamations, rather than by his outstanding mathematics.  The one, “Eureka, eureka” (“I have found it, I have found it”), he shouted, according to legend, while running naked in the streets of Syracuse, then a Greek settlement in Sicily.  The other, “Give me a place to stand and I will move the Earth,” has since been cited by such prominent leaders as Thomas Jefferson (in a letter written 1814) and John F. Kennedy (in a campaign speech in 1960).

There is no point in even attempting to describe all of Archimedes’s achievements in mathematics, physics, astronomy, and engineering in a short blog piece.  Rather, I want to concentrate here on one of his original treatises, entitled The Sand Reckoner.  In this document, addressed to Gelon, the son of King Hieron II of Syracuse, Archimedes wanted to demonstrate that the number of grains of sand in the universe is not infinite.  Even the preliminary paragraphs of this treatise are remarkable:

“Now you are aware that ‘universe’ as the name given by most astronomers to the sphere whose center is the center of the Earth and whose radius is equal to the straight line between the center of the Sun and the center of the Earth.  This is the common account, as you have heard from astronomers.  But Aristarchus of Samos brought out a book consisting of some hypotheses, in which the premises lead to the result that the universe is many times greater than that now so called.  His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in the circumference of a circle, the Sun lying in the middle of the orbit.”

In other words, not only did Archimedes seriously consider Aristarchus’s heliocentric model (1,800 years before Copernicus!), but in a later treatise he even corrected one of the assumptions made by Aristarchus.

Figure 2.  A reproduction of a mosaic found in Herculaneum, illustrating the death of Archimedes.  Credit: Reproduced with permission from the Biblioteca Speciale di Matematica “Giuseppe Peano,” University of Torino, through the assistance of Laura Garbolino.

Figure 2. A reproduction of a mosaic found in Herculaneum, illustrating the death of Archimedes. Credit: Reproduced with permission from the Biblioteca Speciale di Matematica “Giuseppe Peano,” University of Torino, through the assistance of Laura Garbolino.

In the main body of The Sand Reckoner, Archimedes progressed with astonishingly insightful steps, to estimate the number of grains of sand.  First, he evaluated how many grains, placed side by side, it would take to cover the diameter of a poppy seed.  Then, how many poppy seeds would fit in the width of a finger; how many fingers in a stadium (a length of about 600 feet), and up to ten billion stadia.  Along the way, Archimedes invented a new system of notations for large numbers.  Finally, assuming that the sphere of the fixed stars has a radius that is about ten million times larger than the Earth–Sun distance, he estimated that the number of grains in a sand-filled universe would be less than 1063 (one followed by sixty-three zeroes).

Archimedes’s greatness is revealed here by his ability to connect the smallest scales to the largest, and through the way in which his imagination allows him to use properties of the universe to advance mathematical notation.

Unfortunately, this singular genius was killed by an angry soldier when Syracuse fell to the Romans.  According to some historical accounts, when the soldier ordered Archimedes to follow him to the Roman general Marcellus, the geometer (who was busy drawing geometrical diagrams on a dust-filled tray) infuriated his captor by saying:  “Fellow, stand away from my diagram.”  Figure 2 is an eighteenth-century reproduction of a mosaic depicting the final moments in the life of the man who may have been the greatest mathematician. His death symbolized a transformation from the more visionary attitude of the Greek world to the more practical Roman world.  In the words of philosopher Alfred North Whitehead: “No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram.”

Jun 102014
 
Figure 1.  Portrait of Sir Isaac Newton by Sir Godfrey Kneller.  (Image in the public domain at: http://en.wikipedia.org/wiki/File:GodfreyKneller-IsaacNewton-1689.jpg.)

Figure 1. Portrait of Sir Isaac Newton by Sir Godfrey Kneller. (Image in the public domain at: http://en.wikipedia.org/wiki/File:GodfreyKneller-IsaacNewton-1689.jpg.)

In his memoirs of Sir Isaac Newton’s (Figure 1) life, William Stukely, a physician who was Newton’s personal friend, tells the story that has become legendary in the history of science:

On 15 April 1726 I paid a visit to Sir Isaac… dined with him and spent the whole day with him… After dinner, the weather being warm, we went into the garden and drank thea, under the shade of some apple trees…  Amidst other discourse, he told me he was just in the same situation, as when formerly [in 1666, when Newton returned home from Cambridge because of the plague], the notion of gravitation came to his mind.  It was occasion’d by the fall of an apple, as he sat in contemplative mood.  Why should that apple always descend perpendicularly to the ground, thought he to himself.  Why should it not go sideways or upwards, but constantly to the earth’s center?”

Thus apparently started Newton’s quest for something unprecedented in science—to formulate a universal unification of forces.  Newton eventually managed to demonstrate that the force that held the Moon in its orbit around the Earth and the planets in their motions around the Sun, was one and the same as the force that caused apples to fall.  In a memorandum written around 1714, Newton described that happy moment when he “compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, and found them answer pretty nearly.”

Figure 2.  The frontispiece of the second edition of the Principia (which appeared in 1713).  Credit: Reproduced with permission from the Special Collections at the Milton S. Eisenhower Library, at the Johns Hopkins University.

Figure 2. The frontispiece of the second edition of the Principia (which appeared in 1713). Credit: Reproduced with permission from the Special Collections at the Milton S. Eisenhower Library, at the Johns Hopkins University.

In the remarkable penultimate paragraph of his celebrated Principia (Figure 2), the book in which he introduced his law of universal gravitation, Newton clearly described what he was unable to achieve:

Hitherto we explained the phenomena of the heavens and of our sea [referring to tides] by the power of gravity, but have not yet assigned the cause of this power…  I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”

In his book Opticks (which he wrote in 1675 but only published in 1704), Newton even anticipated the existence of short-range nuclear forces: “I had rather infer from their cohesion [of atoms], that their Particles attract one another by some Force; which in immediate Contact is exceedingly strong.”  He thereby speculated on the existence of a force that dominates over gravity, electricity, and magnetism in the shortest distances.

Still, in his manuscript “Principles of Philosophy,” Newton wrote: “To explain all nature is too difficult a task for any one man or even for any one age.  Tis much better to do a little with certainty and leave the rest for others that come after you.”

The Principia was published in July of 1687.  Newton did not know the value of the gravitational constant G that appears in his law of universal gravitation (basically representing the strength of gravity). That constant was measured for the first time seventy-one years after Newton’s death, by Henry Cavendish. Today, three hundred and twenty-seven years after the publication of the Principia, we still have not found a theory that would unify gravity with all the other forces of nature.  The arduous quest that Newton initiated continues!

 

 

May 132014
 

Take a look at the five Hubble images of planetary nebulae in Figures 1–5.  Even though all of them represent late stages in the lives of Sun-like stars, like snowflakes, each one is different.  I think you’ll agree that they are all also breathtakingly beautiful.  What are these spectacular astronomical objects we call planetary nebulae?

The name itself is actually the result of a blunder.  When astronomer William Herschel observed these objects through his telescope in the late eighteenth century, he mistakenly interpreted them as planetary systems in formation.  While we know today that planetary nebulae have nothing to do with newly formed planets, the name stuck.

Rather than birth, planetary nebulae signify the death throes of stars in the range of 1–8 solar masses.  As these stars exhaust the nuclear fuel in their cores, the cores start contracting under gravity’s ever-present pull.  Energy is deposited into the stellar envelope, causing it to expand to giant dimensions, hundreds of times larger than the original stellar radius.  Eventually, through a combination of stellar pulsations and the pressure exerted by intense radiation, the envelope is ejected.  Our own Sun will go through this process in about five billion years (hence, no need to panic yet).  The ejection of the outer layers exposes the hot stellar core, and ultraviolet radiation from the scorching central object ionizes the nebulous gas causing it to shine.

Figure 1. The planetary nebula NGC 6302.   Credit: NASA, ESA, and the Hubble SM4 ERO Team.

Figure 1. The planetary nebula NGC 6302. Credit: NASA, ESA, and the Hubble SM4 ERO Team.

Figure 2.  The Helix nebula, NGC 7293.

Figure 2. The Helix nebula, NGC 7293.

 

 

 

 

 

 

 

 

 

 

Many planetary nebulae have largely opaque dusty areas.  The infrared vision of the upcoming James Webb Space Telescope will be able to penetrate through that dust and reveal to us never-before-seen structures.

Figure 3.   Cat’s Eye nebula, NGC 6543.

Figure 3. Cat’s Eye nebula, NGC 6543.

Figure 4.  The planetary nebula M2-9.

Figure 4. The planetary nebula M2-9.

Figure 5.  Planetary nebula MyCn18. Credits: Raghvendra Sahai and John Trauger (JPL), the WFPC2 science team and NASA.

Figure 5. Planetary nebula MyCn18. Credits: Raghvendra Sahai and John Trauger (JPL), the WFPC2 science team and NASA.

 

 

 

 

 

 

 

 

 

Planetary nebulae are relatively short-lived (compared to stellar lifetimes), remaining visible only for about ten thousand years.  They have been essential, however, for the emergence of life in the universe.  Most of the cosmic carbon—the element that all known forms of life depend upon—was formed in intermediate-mass stars.  This carbon then enriched the interstellar medium through the ejection process of planetary nebulae, providing the raw materials for the formation of new stars, planets, and life.  These dazzling stellar deaths are therefore much more than “eye candy”; they have been crucial for our existence.  We literally are “star dust.”