Math Is Fun Forum

2370) Murray Gell-Mann

Gist:

Work

During the 1950s and 1960s, new accelerators and apparatuses helped identify many new elementary particles. In theoretical works from the same period, Murray Gell-Mann classified particles and their interactions. He proposed that observed particles are in fact composite, that is, comprised of smaller building blocks called quarks. According to this theory, as-yet-undiscovered particles should exist. When these were later found in experiments, the theory was accepted.

Summary

Murray Gell-Mann (born September 15, 1929, New York, New York, U.S.—died May 24, 2019, Santa Fe, New Mexico) was an American physicist, winner of the Nobel Prize for Physics in 1969 for his work pertaining to the classification of subatomic particles and their interactions.

At age 15 Gell-Mann entered Yale University, and, after graduating from Yale with a B.S. in physics in 1948, he earned a Ph.D. (1951) at the Massachusetts Institute of Technology. His doctoral research on subatomic particles was influential in the later work of the Nobel laureate (1963) Eugene P. Wigner. In 1952 Gell-Mann joined the Institute for Nuclear Studies at the University of Chicago. The following year he introduced the concept of “strangeness,” a quantum property that accounted for previously puzzling decay patterns of certain mesons. As defined by Gell-Mann, strangeness is conserved when any subatomic particle interacts via the strong force—i.e., the force that binds the components of the atomic nucleus. Gell-Mann joined the faculty of the California Institute of Technology in Pasadena in 1955 and was appointed the Robert Andrews Millikan Professor of Theoretical Physics in 1967 (emeritus, 1993).

In 1961 Gell-Mann and Yuval Ne’eman, an Israeli theoretical physicist, independently proposed a scheme for classifying previously discovered strongly interacting particles into a simple orderly arrangement of families. Called the Eightfold Way (after Buddha’s Eightfold Path to Enlightenment and bliss), the scheme grouped mesons and baryons (e.g., protons and neutrons) into multiplets of 1, 8, 10, or 27 members on the basis of various properties. All particles in the same multiplet are to be thought of as variant states of the same basic particle. Gell-Mann speculated that it should be possible to explain certain properties of known particles in terms of even more fundamental particles, or building blocks. He later called these basic bits of matter “quarks,” adopting the fanciful term from James Joyce’s novel Finnegans Wake. One of the early successes of Gell-Mann’s quark hypothesis was the prediction and subsequent discovery of the omega-minus particle (1964). Over the years, research has yielded other findings that have led to the wide acceptance and elaboration of the quark concept.

Gell-Mann published a number of works on this phase of his career, notable among which were The Eightfold Way (1964), written in collaboration with Ne’eman, and Broken Scale Variance and the Light Cone (1971), coauthored with K. Wilson.

In 1984 Gell-Mann cofounded the Santa Fe Institute, a nonprofit centre located in Santa Fe, New Mexico, that supports research concerning complex adaptive systems and emergent phenomena associated with complexity. In “Let’s Call It Plectics,” a 1995 article in the institute’s journal, Complexity, he coined the word plectics to describe the type of research supported by the institute. In The Quark and the Jaguar (1994), Gell-Mann gave a fuller description of the ideas concerning the relationship between the basic laws of physics (the quark) and the emergent phenomena of life (the jaguar).

Gell-Mann was a director of the MacArthur Foundation (1979–2002) and served on the President’s Committee of Advisors on Science and Technology (1994–2001). He also was a member of the board of directors of Encyclopædia Britannica, Inc.

Details

Murray Gell-Mann (September 15, 1929 – May 24, 2019) was an American theoretical physicist who played a preeminent role in the development of the theory of elementary particles. Gell-Mann introduced the concept of quarks as the fundamental building blocks of the strongly interacting particles, and the renormalization group as a foundational element of quantum field theory and statistical mechanics. Murray Gell-Mann received the 1969 Nobel Prize in Physics for his contributions and discoveries concerning the classification of elementary particles and their interactions.

Gell-Mann played key roles in developing the concept of chirality in the theory of the weak interactions and spontaneous chiral symmetry breaking in the strong interactions, which controls the physics of the light mesons. In the 1970s he was a co-inventor of quantum chromodynamics (QCD) which explains the confinement of quarks in mesons and baryons and forms a large part of the Standard Model of elementary particles and forces.

Life and education

Gell-Mann was born in Lower Manhattan to a family of Jewish immigrants from the Austro-Hungarian Empire, specifically from Czernowitz in present-day Ukraine. His parents were Pauline (née Reichstein) and Arthur Isidore Gelman, who taught English as a second language. Gell-Mann married J. Margaret Dow in 1955; they had a daughter and a son. Margaret died in 1981, and in 1992 he married Marcia Southwick, whose son became his stepson.

Propelled by an intense boyhood curiosity and love for nature and mathematics, he graduated valedictorian from the Columbia Grammar & Preparatory School aged 14 and subsequently entered Yale College as a member of Jonathan Edwards College. At Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University (along with Murray Gerstenhaber and Henry O. Pollak) that won the second prize in 1947.

Gell-Mann graduated from Yale with a bachelor's degree in physics in 1948 and intended to pursue graduate studies in physics. He sought to remain in the Ivy League for his graduate education and applied to Princeton University as well as Harvard University. He was rejected by Princeton and accepted by Harvard, but the latter institution was unable to offer him needed financial assistance. He was then accepted by the Massachusetts Institute of Technology (MIT) and received a letter from Victor Weisskopf urging him to attend MIT and become Weisskopf's research assistant. This would provide Gell-Mann with the financial assistance he required. Unaware of MIT's eminent status in physics research, Gell-Mann was "miserable" and in characteristic dark irony, said he first considered suicide.

Gell-Mann received his Ph.D. in physics from MIT in 1951 after completing a doctoral dissertation, titled "Coupling strength and nuclear reactions", under the supervision of Weisskopf.
Subsequently, Gell-Mann was a postdoctoral fellow at the Institute for Advanced Study at Princeton in 1951, and a visiting research professor at the University of Illinois at Urbana–Champaign from 1952 to 1953. He was a visiting associate professor at Columbia University and an associate professor at the University of Chicago in 1954–1955, before moving to the California Institute of Technology, where he taught from 1955 until he retired in 1993.

Gell-Mann died on May 24, 2019, at his home in Santa Fe, New Mexico.

2422) Nebula

Gist

A nebula is a giant cloud of dust and gas in space, which can be a birthplace for new stars or the remnants of a dying star. The term is Latin for "mist" or "cloud" and was once used for any diffuse-looking object, but today specifically refers to these interstellar clouds. Nebulae are often regions of star formation, where gas and dust clump together to form new stars and planetary systems. 

A nebula is a giant cloud of dust and gas in space, located between stars. These clouds can be the birthplace of new stars, earning them the nickname "star nurseries," or they can be the remnants of dying stars, such as from a supernova explosion. Gravity causes the material within a nebula to clump together, eventually leading to the formation of stars and planets. 

Summary

A nebula (Latin for 'cloud, fog'; pl. nebulae or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral, or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regions, such as the Pillars of Creation in the Eagle Nebula. In these regions, the formations of gas, dust, and other materials "clump" together to form denser regions, which attract further matter and eventually become dense enough to form stars. The remaining material is then thought to form planets and other planetary system objects.

Most nebulae are of vast size; some are hundreds of light-years in diameter. A nebula that is visible to the human eye from Earth would appear larger, but no brighter, from close by. The Orion Nebula, the brightest nebula in the sky and occupying an area twice the angular diameter of the full Moon, can be viewed with the naked eye but was missed by early astronomers. Although denser than the space surrounding them, most nebulae are far less dense than any vacuum created on Earth ({10}^{5} to {10}^{7} molecules per cubic centimeter) – a nebular cloud the size of the Earth would have a total mass of only a few kilograms. Earth's air has a density of approximately {10}^{19} molecules per cubic centimeter; by contrast, the densest nebulae can have densities of {10}^{4} molecules per cubic centimeter. Many nebulae are visible due to fluorescence caused by embedded hot stars, while others are so diffused that they can be detected only with long exposures and special filters. Some nebulae are variably illuminated by T Tauri variable stars.

Originally, the term "nebula" was used to describe any diffused astronomical object, including galaxies beyond the Milky Way. The Andromeda Galaxy, for instance, was once referred to as the Andromeda Nebula (and spiral galaxies in general as "spiral nebulae") before the true nature of galaxies was confirmed in the early 20th century by Vesto Slipher, Edwin Hubble, and others. Edwin Hubble discovered that most nebulae are associated with stars and illuminated by starlight. He also helped categorize nebulae based on the type of light spectra they produced.

Details

A nebula is any of the various tenuous clouds of gas and dust that occur in interstellar space. The term was formerly applied to any object outside the solar system that had a diffuse appearance rather than a pointlike image, as in the case of a star. This definition, adopted at a time when very distant objects could not be resolved into great detail, unfortunately includes two unrelated classes of objects: the extragalactic nebulae, now called galaxies, which are enormous collections of stars and gas, and the galactic nebulae, which are composed of the interstellar medium (the gas between the stars, with its accompanying small solid particles) within a single galaxy. Today the term nebula generally refers exclusively to the interstellar medium.

In a spiral galaxy the interstellar medium makes up 3 to 5 percent of the galaxy’s mass, but within a spiral arm its mass fraction increases to about 20 percent. About 1 percent of the mass of the interstellar medium is in the form of “dust”—small solid particles that are efficient in absorbing and scattering radiation. Much of the rest of the mass within a galaxy is concentrated in visible stars, but there is also some form of dark matter that accounts for a substantial fraction of the mass in the outer regions.

The most conspicuous property of interstellar gas is its clumpy distribution on all size scales observed, from the size of the entire Milky Way Galaxy (about {10}^{20} metres, or hundreds of thousands of light-years) down to the distance from Earth to the Sun (about {10}^{11} metres, or a few light-minutes). The large-scale variations are seen by direct observation, and the small-scale variations are observed by fluctuations in the intensity of radio waves, similar to the “twinkling” of starlight caused by unsteadiness in Earth’s atmosphere. Various regions exhibit an enormous range of densities and temperatures. Within the Galaxy’s spiral arms about half the mass of the interstellar medium is concentrated in molecular clouds, in which hydrogen occurs in molecular form (H2) and temperatures are as low as 10 kelvins (K). These clouds are inconspicuous optically and are detected principally by their carbon monoxide (CO) emissions in the millimetre wavelength range. Their densities in the regions studied by CO emissions are typically 1,000 H2 molecules per cubic cm. At the other extreme is the gas between the clouds, with a temperature of 10 million K and a density of only 0.001 H+ ion per cubic cm. Such gas is produced by supernovae, the violent explosions of unstable stars.

Classes of nebulae

All nebulae observed in the Milky Way Galaxy are forms of interstellar matter—namely, the gas between the stars that is almost always accompanied by solid grains of cosmic dust. Their appearance differs widely, depending not only on the temperature and density of the material observed but also on how the material is spatially situated with respect to the observer. Their chemical composition, however, is fairly uniform; it corresponds to the composition of the universe in general in that approximately 90 percent of the constituent atoms are hydrogen and nearly all the rest are helium, with oxygen, carbon, neon, nitrogen, and the other elements together making up about two atoms per thousand. On the basis of appearance, nebulae can be divided into two broad classes: dark nebulae and bright nebulae. Dark nebulae appear as irregularly shaped black patches in the sky and blot out the light of the stars that lie beyond them. Bright nebulae appear as faintly luminous glowing surfaces; they either emit their own light or reflect the light of nearby stars.

Dark nebulae are very dense and cold molecular clouds; they contain about half of all interstellar material. Typical densities range from hundreds to millions (or more) of hydrogen molecules per cubic centimetre. These clouds are the sites where new stars are formed through the gravitational collapse of some of their parts. Most of the remaining gas is in the diffuse interstellar medium, relatively inconspicuous because of its very low density (about 0.1 hydrogen atom per cubic cm) but detectable by its radio emission of the 21-cm line of neutral hydrogen.

Bright nebulae are comparatively dense clouds of gas within the diffuse interstellar medium. They have several subclasses: (1) reflection nebulae, (2) H II regions, (3) diffuse ionized gas, (4) planetary nebulae, and (5) supernova remnants.

Reflection nebulae reflect the light of a nearby star from their constituent dust grains. The gas of reflection nebulae is cold, and such objects would be seen as dark nebulae if it were not for the nearby light source.

H II regions are clouds of hydrogen ionized (separated into positive H+ ions and free electrons) by a neighbouring hot star. The star must be of stellar type O or B, the most massive and hottest of normal stars in the Galaxy, in order to produce enough of the radiation required to ionize the hydrogen.

Diffuse ionized gas, so pervasive among the nebular clouds, is a major component of the Galaxy. It is observed by faint emissions of positive hydrogen, nitrogen, and sulfur ions (H+, N+, and S+) detectable in all directions. These emissions collectively require far more power than the much more spectacular H II regions, planetary nebulae, or supernova remnants that occupy a tiny fraction of the volume.

Planetary nebulae are ejected from stars that are dying but are not massive enough to become supernovae—namely, red giant stars. That is to say, a red giant has shed its outer envelope in a less-violent event than a supernova explosion and has become an intensely hot star surrounded by a shell of material that is expanding at a speed of tens of kilometres per second. Planetary nebulae typically appear as rather round objects of relatively high surface brightness. Their name is derived from their superficial resemblance to planets—i.e., their regular appearance when viewed telescopically as compared with the chaotic forms of other types of nebula.

Supernova remnants are the clouds of gas expanding at speeds of hundreds or even thousands of kilometres per second from comparatively recent explosions of massive stars. If a supernova remnant is younger than a few thousand years, it may be assumed that the gas in the nebula was mostly ejected by the exploded star. Otherwise, the nebula would consist chiefly of interstellar gas that has been swept up by the expanding remnant of older objects.

Additional Information

A nebula is a giant cloud of dust and gas in space. Some nebulae (more than one nebula) come from the gas and dust thrown out by the explosion of a dying star, such as a supernova. Other nebulae are regions where new stars are beginning to form.

A nebula is a giant cloud of dust and gas in space. Some nebulae (more than one nebula) come from the gas and dust thrown out by the explosion of a dying star, such as a supernova. Other nebulae are regions where new stars are beginning to form. For this reason, some nebulae are called "star nurseries."

How do stars form in a nebula?

Nebulae are made of dust and gases—mostly hydrogen and helium. The dust and gases in a nebula are very spread out, but gravity can slowly begin to pull together clumps of dust and gas. As these clumps get bigger and bigger, their gravity gets stronger and stronger.

Eventually, the clump of dust and gas gets so big that it collapses from its own gravity. The collapse causes the material at the center of the cloud to heat up-and this hot core is the beginning of a star.

Where are nebulae?

Nebulae exist in the space between the stars—also known as interstellar space. The closest known nebula to Earth is called the Helix Nebula. It is the remnant of a dying star—possibly one like the Sun. It is approximately 700 light-years away from Earth. That means even if you could travel at the speed of light, it would still take you 700 years to get there!

How do we know what nebulae look like?

Astronomers use very powerful telescopes to take pictures of faraway nebulae. Space telescopes such as NASA's Spitzer Space Telescope and Hubble Space Telescope have captured many images of faraway nebulae.

Hi,

#5817. What does the verb (used without object) deign mean?

#5818. What does the noun deism mean?

Hi,

#9771.

Hi,

2622.

Hi,

#5815. What does the adverb de jure mean?

#5816. What does the noun deliberation mean?

Hi,

#6276.

2421) Elevator phobia

Gist

Elevator phobia, or elevatophobia, is an intense, irrational fear of elevators that can stem from claustrophobia (fear of enclosed spaces), acrophobia (fear of heights), or fear of malfunctions. Symptoms include intense anxiety and panic attacks, and it can lead to avoiding elevators by taking the stairs, even in high-rise buildings. Overcoming it often involves techniques like cognitive behavioral therapy (CBT) or exposure therapy, along with relaxation methods and breathing exercises. 

Summary:

Where Elevator Phobias Might Originate

It’s different for each person, but there are some common elevator phobia origins. They include the following.

Agoraphobia – This is when someone fears being stuck somewhere that is nearly impossible to escape from. Individuals with agoraphobia could fear the elevator because it closes them in and they begin to panic that they won’t be able to get out again.
Claustrophobia – This is when someone fears being in enclosed spaces. Elevators are typically small in size, making people feel tightly enclosed when they are in them.
Previous Experiences – Whether someone had a previous experience with an actual elevator, or the enclosed space of the elevator makes him or her relive a past trauma, previous experiences could cause fear in someone when riding an elevator.
Hollywood – Even though everyone understands a movie is just a movie, those that include frightening elevator scenes can tell the subconscious that elevators are scary, leading someone to avoid riding in them.

How to Overcome an Elevator Phobia

One of the best ways to overcome many phobias is to understand the thing or situation one is afraid of. Someone might speak with an elevator maintenance worker to learn how the elevator works, then observe it for a time or two before trying to take a ride. If you have tenants who have anxiety surrounding elevators, it may be helpful to call in your elevator maintenance company.

If the phobia is quite extreme, a psychologist may be able to provide more insight on getting over a fear of elevators. If someone lives or works somewhere that an elevator is necessary on a regular basis, this might be a great option.

Details

If you get anxious or panicky while on an elevator, or you go out of your way to avoid taking elevators altogether, you are not alone! Many people have a fear of elevators. If this is you, read on to learn more about this problem and how you can overcome it.

Different Phobias Related to Elevators

A fear of elevators can stem from what’s known technically as a “specific phobia.” About 12.5% of adults in the United States will have a specific phobia in their lifetime. There are different types of specific phobias that can be associated with elevators, as you’ll see described below.

If you have a specific phobia, you’ll experience anxiety symptoms when in the presence of the feared object or situation. These include increased heart rate, shortness of breath, sweating, and nausea.

The phobias related to elevators are:

Claustrophobia

Claustrophobia is the fear of small, confined spaces. It can be triggered by many different places ranging from trains to tunnels to elevators. For many people, being in a small elevator, particularly if it is crowded, might trigger feelings of panic related to claustrophobia.

Cleithrophobia

Cleithrophobia is the fear of being trapped. It is a fear of a situation, rather than a specific place. This phobia is not specific to elevators but is commonly triggered by them. In an elevator, you might feel trapped if you think you might not be able to open the doors or get out. The lack of control over escaping is the defining feature of this phobia.

Acrophobia

Acrophobia is the fear of heights. This might be activated by elevators in tall buildings or skyscrapers. People with acrophobia might have trouble working or living in tall buildings with elevators because of the fear of being high off the ground. If you have acrophobia and live in an area like New York City, where you frequently encounter tall buildings with elevators, you might find it difficult to navigate your daily life.

Basophobia

Basophobia is the fear of falling. While an aversion to falling is a natural human instinct, people with basophobia have an intense fear of falling that is out of proportion to the situation. You might have trouble riding in elevators if you are afraid of the elevator suddenly falling, despite the safety features built into elevators.

Agoraphobia

Agoraphobia is a fear of being in places or situations that might cause feelings of helplessness, anxiety, or panic. You might have trouble leaving your home or other places that feel safe if you have agoraphobia. Going into public or riding an elevator might trigger feelings of panic for someone with this phobia.

Causes of a Fear of Elevators

Previous negative experiences:

You might have a fear of elevators because of a previous scary experience riding in one. For example, you might have been stuck in an elevator for a prolonged period of time. Or maybe you were in an elevator that stalled between floors or felt like it suddenly dropped. Any of these types of experiences could potentially trigger a fear of elevators.

Misconceptions about elevator safety:

Many myths or misunderstandings about elevators and their safety can worsen a fear of elevators. Here are some common misconceptions about elevators:

Running out of air:

A common myth is that elevators only hold a certain amount of air. You might therefore fear that if you get stuck you will have trouble breathing. However, elevators are not air-tight and do not have a limited supply of oxygen! Feelings of breathlessness on elevators are more likely related to panic attack symptoms rather than actually running out of air.

Elevator cable safety:

Some people believe that elevators are suspended by a single rope. This is false. Elevators are constructed with multiple steel cables that allow for safe movement up and down. Learn more about elevator cables here.

Elevators can free-fall:

Many people with a fear of elevators might believe that elevators can free-fall if something goes wrong. This is not the case. Elevators have safety features, both electronic and mechanical, that prevent this type of occurrence.

Safety Tips for Riding in Elevators

When riding in an elevator, it is important to take general safety precautions to ensure a smooth ride. Here are some tips to follow:

* Never hold a door open with your hand or an object. If you need to keep a door open, press and hold the “Door Open” button.
* If you are trying to catch the elevator and the door is closing, don’t stop it. Keeping the doors from closing could result in you getting injured.
* Don’t step onto an elevator if it seems overcrowded. Wait for the next one!
* If the door doesn’t open when the elevator stops at your floor, press the “Door Open” button. If the door doesn’t open after a few seconds, press the “Help” or “Emergency” button and wait for assistance.
* If a problem arises, try not to panic! Take a few deep breaths and press the “Emergency” button.

Additional Information

As a more modern invention, it has no official Greek "phobia" name; however, the fear of elevators is relatively common. According to the National Elevator Industry, Inc., elevators provide 18 billion passenger trips in the U.S. each year with millions of passengers repeatedly arriving safely at their destination. Yet, many people feel at least a slight nervousness when contemplating an elevator ride.

In some people, the fear of elevators is triggered by an existing phobia, but the fear often appears alone. Like any phobia, the fear of elevators ranges from mild to severe.

Fear of Elevators: Are Elevators Safe?

For those of us who work in the elevator industry, it’s hard to imagine anyone having a fear of elevators. Seeing these machines at work and knowing the evolution of elevators, we wouldn’t think twice when stepping into the cab. Yet, we know that elevator phobias are very real, and media is partially to blame for that. Films will often portray elevators in a way that is not accurate in the slightest. Thankfully, we are here to assure you that none of the extreme scenarios you see on the big screen are possible.

In movies, hoistway doors will open when they shouldn’t, characters will get stuck in elevators for days and a superhero will need to save the cab from free falling down the shaft. It may seem like a harmless way to move the plot along, but myths like these contribute to the fear of elevators that a number of commuters suffer from. Elevators are a part of daily life, so being afraid of them can inhibit many from experiencing the ease that they bring to tenants.

So how do you overcome your fear? Perhaps learning more about the many safety features that elevators have is a good place to start.

Are Elevators Safe?

Over the course of one day, elevators will globally carry 325 million people to their destinations. The worldwide popularity of the passenger elevator can be traced directly to its roots in safety. Before the 1800s, elevators were seen as a convenient way to move heavy items or as an attraction.

This all changed at the World’s Fair in 1853 when an inventor showcased his newest idea in front of a crowd. He stood in an elevator and had his assistant cut the cable that was holding him up. To their amazement, he only dropped a couple of feet — his new safety device caught the cab. This revolutionary invention is what we now call a “safety” activated by a governor. It is a component in every elevator you’ve ever ridden in.

Since the debut of the mechanical safety and overspeed governor, elevators have constantly evolved to become the safest form of vertical transportation — even better than stairs. Next time you are debating whether or not to take the stairs, take these safety features into account!