Friday, February 25, 2011

Uh-Oh

"Three minutes and fifty seconds into the final ascent of Discovery, several large and many small pieces of debris - apparently External Tank insulation foam – careen between tank and Orbiter."



Discovery's Final Launch, viewed from an airplane, courtesy of Cosmic Log, here

Theaetetus and his Beautiful Proof

There can be only five regular polyhedra. Somebody had to prove that once, and the proof is beautiful. 

The man who proved it was the little known (except to mathematicians) Theaetetus, instructor/professor at Plato's Academy. Along with Plato, Aristotle and Euclid, he stands out as the greatest of the great from that important time and place.


To read more about him (I'll close with his Wikipedia entry) I strongly recommend reading Chapter 4 of this book:
 Euler's Gem by Dave Richeson


In fact, buy the book and read all the chapters. The proof below comes from Chapter 5 soon thereafter.


The Proof:


Consider a regular polyhedron. Each face is a regular polygon having n sides, and m edges of the polyhedron meet at each vertex (corner).


Because every face must have at least three sides, n is greater than or equal to 3, and because at least three edges meet at each vertex, m is greater than or equal to 3.


Every angle of every face has the same measure, call this angle: theta. 

At each vertex there are m faces, each contributing a plane angle with measure theta.


From Euclid's theorem, it follows that m times theta must be  less than 360 degrees.


For which m and which n is this possible?


When n = 3, the faces are equilateral triangles, so theta = 60 degrees. (The measure of an interior angle of a regular n-sided polygon is 180 degrees times (n-2)/n.)


Insisting that m times theta is less than 360 degrees, we have m times 60 degrees is less than 360 degrees, or m is less than 6. 


So m = 3, 4 or 5 are the only possibilities.


These values of m yield the tetrahedron, the octahedron, and the icosahedron, respectively.


When n = 4, the faces are square, so theta = 90 degrees.


This implies that m times 90 degrees is less than 360 degrees, or m is less than 4. 


So we can only have m=3, and we obtain the cube.


When n = 5, the faces are regular pentagons and theta = 108 degrees. Thus m times 108 degrees is less than 360 degrees, or m is less than 10/3.


So we can have only m = 3, and we obtain the dodecahedron.


When n = 6, the faces are regular hexagons and theta = 120 degrees. But m times 120 degrees being less than 360 degrees implies than m is less than 3, which is impossible.


So there is no regular polygon with hexagonal faces.


We encounter the same problem when n is greater than 6. 


Thus there are no other Platonic solids.


Finis.


So-o beautiful.


This is from Book XIII of Euclid's Elements, the final book, which it is believed Euclid wrote directly from Theaetetus' notes. The most important part of Book XIII is considered to be the proof that there are 5 and only 5 regular (Platonic) solids. 


"Many historians contend that all of the mathematics in Book X and XIII of the Elements is due to Theaetetus." ... Dave Richeson




Theaetetus, Theaitētos, (ca. 417 BC – 369 BC) of Athens, possibly son of Euphronius, of the Athenian deme Sunium, was a classical Greek mathematician. His principal contributions were on irrational lengths, which was included in Book X of Euclid's Elements, and proving that there are precisely five regular convex polyhedra.

Theaetetus, like Plato, was a student of the Greek mathematician Theodorus of Cyrene. Cyrene was a prosperous Greek colony on the coast of North Africa, in what is now Libya, on the eastern end of the gulf of Sidra. Theodorus had explored the theory of incommensurable quantities, and Theaetetus continued those studies with great enthusiasm; specifically, he classified various forms of irrational numbers according to the way they are expressed as square roots. This theory is presented in great detail in Book X of Euclid's Elements.

Theaetetus was one of the few Greek mathematicians who were actually natives of Athens. Most Greek mathematicians of antiquity came from the numerous Greek cities scattered around the Ionian coast, the Black Sea and the whole Mediterranean basin. Likewise, most Greek scientists came from the scattered Greek cities and not from Athens. Athens, and later Alexandria were centers of attraction because of the philosophical schools of Plato (the Academy) and Aristotle (the Lyceum), and the renowned Museum and Great Library. The Academy of Plato operated in Athens for almost 600 years, and served as educational center even for some of the early fathers of the Christian church.

He evidently resembled Socrates in the snubness of his nose and bulging of his eyes. This and most of what we know of him comes from Plato, who named a dialogue after him, the Theaetetus. He apparently died from wounds and dysentery on his way home after fighting in an Athenian battle at Corinth, now widely presumed to have occurred in 369 BC.

The crater Theaetetus on the Moon is named after him.

External links

Thursday, February 24, 2011

Scott Carpenter, the First Scientist-Astronaut


Scott Carpenter, father of 7,  is one of the last two surviving Mercury astronauts along with John Glenn, and the Second American to orbit the Earth, in the next mission after Glenn's.

He was also the first person to "experiment" in space, and thus the first true Scientist-Astronaut. Problem is, that didn't sit well with NASA, because his experiments were of his own design and definitely not in NASA's gameplan for the flight. He never flew again, based on the principle I reckon that generally speaking, it's not all that helpful to one's career to piss off the boss.

But he's a hero of mine regardless. God speed, Scott Carpenter. For a man of your years, you're looking pretty awesome, cool, and VERY American. With a Rebel yell, etc.

From Wiki:

Malcolm Scott Carpenter (born May 1, 1925, in Boulder, Colorado) is an American engineer, former test pilot, astronaut, and aquanaut. He is best known as one of the original seven astronauts selected for NASA's Project Mercury in April 1959.

Scott Carpenter was the second American to orbit the Earth and the fourth American in space, following Alan Shepard, Gus Grissom, and John Glenn. Carpenter and Glenn are the last living members of the Mercury Seven.

Contents

Early life

Born in Boulder, Carpenter moved to New York City with his parents (Marion Scott Carpenter and Florence [née Noxon] Carpenter) for the first two years of his life. (His father had been awarded a postdoctoral research post at Columbia University.) In the summer of 1927, young Carpenter returned to Boulder with his mother, then ill with tuberculosis. He was raised by his maternal grandparents in the family home at the corner of Aurora Avenue and Seventh Street, until his graduation from Boulder High School in 1943.[2]

Naval aviator

Upon graduation, he was accepted into the V-12 Navy College Training Program as an aviation cadet (V-12a), where he trained until the end of World War II. The war ended before he was able to finish training and receive an overseas assignment, so the Navy released him from active duty. He returned to Boulder in November 1945 to study aeronautical engineering at the University of Colorado at Boulder. At the end of his senior year, he missed the final examination in heat transfer, leaving him one requirement short of a degree. After his Mercury flight, the university granted him the degree on grounds that, "His subsequent training as an Astronaut has more than made up for the deficiency in the subject of heat transfer."[2][3]

On the eve of the Korean War, Carpenter was recruited by the USN's Direct Procurement Program (DPP), and reported to NAS Pensacola in the fall of 1949 for pre-flight and primary flight training. He earned his wings on April 19, 1951, in Corpus Christi, Texas. During his first tour of duty, on his first deployment, Carpenter flew Lockheed P2V Neptunes for Patrol Squadron SIX (VP-6) on reconnaissance and ASW (anti-submarine warfare) missions during the Korean War. Forward-based in Adak, Carpenter then flew surveillance missions along the Soviet and Chinese coasts during his second deployment; designated as PPC (patrol plane commander) for his third deployment, LTJG Carpenter was based with his squadron in Guam.[2]

Carpenter was then appointed to the United States Naval Test Pilot School, class 13, at NAS Patuxent River in 1954. He continued at Patuxent until 1957, working as a test pilot in the Electronics Test Division; his next tour of duty was spent in Monterey, California, at the Navy Line School. In 1958, Carpenter was named Air Intelligence Officer for the USS Hornet.[2]

Project Mercury


Carpenter inspects the honeycomb protective material on the main pressure bulkhead of his Aurora 7 spacecraft
After being chosen for Project Mercury in 1959, Carpenter served as backup pilot for John Glenn, who flew the first U.S. orbital mission aboard Friendship 7 in February 1962. When Deke Slayton was withdrawn on medical grounds from Project Mercury's second manned orbital flight (to be titled Delta 7), Carpenter was assigned to replace him. He flew into space on May 24, 1962, atop the Mercury-Atlas 7 rocket for a three-orbit science mission that lasted nearly five hours. His Aurora 7 spacecraft attained a maximum altitude of 164 miles (264 km) and an orbital velocity of 17,532 miles per hour (28,215 km/h).[2]

Carpenter in a water egress training exercise before his Mercury Atlas 7 mission.
Working through five onboard experiments dictated by the flight plan, Carpenter helped among other things to identify the mysterious 'fireflies' (which he renamed 'frostflies,' as they were in reality particles of frozen liquid around the craft), first observed by John Glenn during MA-6. Carpenter was the first American astronaut to eat solid food in space.[2]

Chris Kraft, directing the flight from Florida considered Carpenter's "mission the most successful to date; everything had gone perfectly except for some overexpenditure of fuel" [4]

Unnoticed by ground control or pilot, however, this "over-expenditure of fuel" was caused by an intermittently malfunctioning pitch horizon scanner that would later malfunction at reentry. Still, NASA later reported that Carpenter had:
"exercised his manual controls with ease in a number of [required] spacecraft maneuvers and had made numerous and valuable observations in the interest of space science. . . . By the time he drifted near Hawaii on the third pass, Carpenter had successfully maintained more than 40 percent of his fuel in both the automatic and the manual tanks. According to mission rules, this ought to be quite enough hydrogen peroxide, reckoned Kraft, to thrust the capsule into the retrofire attitude, hold it, and then to reenter the atmosphere using either the automatic or the manual control system."[5]
At the retrofire event, however, the pitch horizon scanner malfunctioned once more, forcing Carpenter to manually control his reentry ("The malfunction of the pitch horizon scanner circuit [a component of the automatic control system] dictated that the pilot manually control the spacecraft attitudes during this event."[6] The PHS malfunction jerked the spacecraft off in yaw by 25 degrees to the right, accounting for 170 miles (270 km) of the overshoot; the delay caused by the automatic sequencer required Carpenter to fire the retrorockets manually. This effort took two pushes of the override button and accounted for another 15 to 20 miles (32 km) of the overshoot. The loss of thrust in the ripple pattern of the retros added another 60 miles (97 km), producing a 250-mile (400 km) overshoot.[2]

Forty minutes after splashdown, Carpenter was located in his life raft, safe and in good health by Major Fred Brown under the command of the Puerto Rico Air National Guard,[7] and recovered three hours later by the USS Intrepid.[2]

Postflight analysis described the PHS malfunction as "mission critical" but noted that the pilot "adequately compensated" for "this anomaly . . . in subsequent inflight procedures.",[8] confirming that backup systems—human pilots—could succeed when automatic systems fail.[1]

Some memoirs[9][10] have revived the simmering controversy over who or what, exactly, was to blame for the overshoot, suggesting, for example, that Carpenter was distracted by the science and engineering experiments dictated by the flight plan and by the well-reported fireflies phenomenon. Yet fuel consumption and other aspects of the vehicle operation were, during Project Mercury, as much, if not more, the responsibility of the ground controllers. Moreover, hardware malfunctions went unidentified, while organizational tensions between the astronaut office and the flight controller office — tensions that NASA did not resolve until the later Gemini and Apollo programs — may account for much of the latter-day criticism of Carpenter's performance during his flight.[2]

Carpenter never flew another mission in space. After taking a leave of absence from the astronaut corps in the fall of 1963 to train for and participate in the Navy's Sealab program, Carpenter sustained a medically grounding injury to his left arm in a motorbike accident. After failing to regain mobility in his arm after two surgical interventions (in 1964 and 1967), Carpenter was ruled ineligible for spaceflight. He resigned from NASA in August 1967.[2]

Ocean research

In July 1964 in Bermuda, Carpenter sustained a grounding injury from a motorbike accident while on leave from NASA to train for the Navy's SEALAB project.[2] In 1965, for Sealab II, he spent 28 days living on the ocean floor off the coast of California. He returned to work at NASA as Executive Assistant to the Director of the Manned Spaceflight Center, then returned to the Navy's Deep Submergence Systems Project in 1967, based in Bethesda, Maryland, as a Director of Aquanaut Operations for Sealab III.[11][12] Carpenter retired from the Navy in 1969, after which he founded Sea Sciences, Inc., a corporation for developing programs for utilizing ocean resources and improving environmental health.[2]

Honors and awards

In 1962, Boulder community leaders dedicated Scott Carpenter Park and Pool in honor of native son turned Mercury astronaut. The Aurora 7 Elementary School, also in Boulder (at 3995 Aurora Ave.), was named for Carpenter's spacecraft.[2][13]

Scott Carpenter Middle School in Westminster, Colorado was named in his honor,[14] as was M. Scott Carpenter Elementary School in Old Bridge, New Jersey.[2][15]

The Scott Carpenter Space Analog Station was placed on the ocean floor in 1997 & 1998. It was named in honor of his SEALAB work in the 1960s.[16]

Personal life

Carpenter has been married and divorced three times. He married Rene Louise Price in 1948. In 1972, he married Maria Roach, daughter of film producer Hal Roach. He married Barbara Curtin in 1988. He has four children from his first marriage: Marc Scott, Kristen Elaine, Candace Noxon, and Robyn Jay. He also has two children from his second marriage: Matthew Scott and filmmaker Nicholas Andre, and one child from his third marriage, Zachary Scott.[17][18]

In popular culture

Speaking from the blockhouse at the launch of Friendship 7 (MA-6), Scott Carpenter, Glenn's backup pilot, said "Godspeed, John Glenn," as then Lieutenant Colonel John H. Glenn, Jr., USMC rose off the launch pad to begin his historic orbital mission on February 20, 1962.[2]

This quote was included in the voiceovers of the teaser trailer for the 2009 Star Trek film."[19] The audio phrase is used in Kenny G "Auld Lang Syne" (The Millennium Mix).[20] It is also used as a part of an audio introduction for the Ian Brown song 'My Star.'[21]

In the 1983 film, The Right Stuff, Carpenter was played by Charles Frank. Although his appearance was relatively minor, the film played up Carpenter's friendship with John Glenn, as played by Ed Harris. This film is based on the book of the same name by Tom Wolfe.[22]

The character of Scott Tracy in the Thunderbirds was named after him.[23]

His recovery is referred to in the Peanuts comic strip of June 28, 1962 after Linus' security blanket is rescued under similar circumstances.[24]

Books

  • For Spacious Skies: The Uncommon Journey of a Mercury Astronaut, ISBN 0-15-100467-6 or the revised paperback edition ISBN 0-451-21105-7, Carpenter's biography, co-written with his daughter Kris Stoever; describes his childhood, his experiences as a naval aviator, a Mercury astronaut, including an account of what went wrong, and right, on the flight of Aurora 7.

External links

We all had our salad days

    Superfluid Core of Neutron Star Formed 100 Years "Ago"




    Make that 100 apparent  years ago, as Cas A the new neutron star is 11,000 light years away. Amazing isn't it what Astronomers can figure out from photographs alone?

    Superfluidity, Superconductivity, Lasers and quantum Hall effect are the 4 ways we can see the quantum world here in the size range of the Macroscopic. Together they represent the largest field of Nobel Prizes in Physics.

    Here's the amazing thing, from photography alone Astronomers have deduced the CORE of this recently created Neutron Star is in Superfluid form. You can read the details here at Space.com and here at Universe Today.

    In the photograph of Cas A above, "a composite of X-rays from Chandra (red, green, and blue) and optical  data from Hubble (gold) of Cassiopeia A, the remains of a massive star  that exploded in a supernova. Inset: A cutout of the interior of the  neutron star, where densities increase from the crust (orange) to the  core (red) and finally to the region where the "superfluid" exists  (inner red ball)."
                                  CREDIT: X-ray: NASA/CXC/xx; Optical: NASA/STScI; Illustration: NASA/CXC/M.Weiss                                            

    Wednesday, February 23, 2011

    Mechatronics - The Future is Now



    Mechatronics is the combination of Mechanical engineering, Electronic engineering, Computer engineering, Control engineering, and Systems Design engineering in order to design, and manufacture useful products. Mechatronics is a multidisciplinary engineering system design, that is to say it rejects splitting engineering into separate disciplines.

    French standard NF E 01-010 gives the following definition: “approach aiming at the synergistic integration of mechanics, electronics, control theory, and computer science within product design and manufacturing, in order to improve and/or optimize its functionality".

    A mechatronics engineer unites the principles of mechanics, electronics, and computing to generate a simpler, more economical and reliable system. Mechatronics is centered on mechanics, electronics, computing, control engineering, molecular engineering (from nanochemistry and biology), and optical engineering, which, combined, make possible the generation of simpler, more economical, reliable and versatile systems. The portmanteau "mechatronics" was coined by Tetsuro Mori, the senior engineer of the Japanese company Yaskawa in 1969. An industrial robot is a prime example of a mechatronics system; it includes aspects of electronics, mechanics, and computing to do its day-to-day jobs.

    Engineering cybernetics deals with the question of control engineering of mechatronic systems. It is used to control or regulate such a system (see control theory). Through collaboration, the mechatronic modules perform the production goals and inherit flexible and agile manufacturing properties in the production scheme. Modern production equipment consists of mechatronic modules that are integrated according to a control architecture. The most known architectures involve hierarchy, polyarchy, heterarchy, and hybrid. The methods for achieving a technical effect are described by control algorithms, which might or might not utilize formal methods in their design. Hybrid systems important to mechatronics include production systems, synergy drives, planetary exploration rovers, automotive subsystems such as anti-lock braking systems and spin-assist, and every-day equipment such as autofocus cameras, video, hard disks, and CD players.

    Mechatronics has been commonly used in science fiction such as the popular Terminator movies.

    Mechatronic students take courses from across the various fields listed below:
    • Mechanical engineering and materials science subjects
    • Electronic engineering subjects
    • Computer engineering subjects
    • Computer science subjects
    • Systems and control engineering subjects
    • Optomechanics (optical engineering) subjects
    • Robotics subjects

    Application

    Physical implementations

    For most mechatronic systems, the main issue is no more how to implement a control system, but how to implement actuators and what is the energy source. Within the mechatronic field, mainly two technologies are used to produce the movement: the piezo-electric actuators and motors, or the electromagnetic actuators and motors. Maybe the most famous mechatronics systems are the well known camera autofocus system or camera anti-shake systems.

    Concerning the energy sources, most of the applications use batteries. But a new trend is arriving and is the energy harvesting, allowing transforming into electricity mechanical energy from shock, vibration, or thermal energy from thermal variation, and so on.

    Variant of the field

    An emerging variant of this field is biomechatronics, whose purpose is to integrate mechanical parts with a human being, usually in the form of removable gadgets such as an exoskeleton. Such an entity is often identified in science fiction as a cyborg. This is the "real-life" version of cyberware.

    Another emerging variant is Electronical or electronics design centric ECAD/MCAD co-design. Electronical is where the integration and co-design between the design team and design tools of an electronics centric system and the design team and design tools of that systems physical/mechanical enclosure takes place.

    Education

    Countries offering education in mechatronics are México[1][2][3][4],Chile[5], Japan, Malaysia[6], France[7], Germany[8], United States, UK[9], Sweden[10], Canada[11], Australia[12], Ireland[13] Singapore, and Hungary [14] among others.

    See also

    From Wikipedia