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Maxwell’s Equations

Introduction

On Quora, Mark Eichenlaub writes –

The history of electromagnetism is one of unification. Over and over, different ideas about how things work were subsumed into the same theoretical framework…. Electromagnetism is an example of a field theory, the central object of study in theoretical physics.

A “field” means that at any point in space and time, there’s an electric and magnetic vector there. These fields pervade all of space – they are in the room around you right now, and in outer space, even within you…

We don’t have a mechanical picture of what the field is, or why it is a certain way. It’s not like waves in the water or anything like that. It just exists, but we do have mathematical rules that describe how it works….

Michael Faraday investigated things like the way a wire carrying electric current deflects a compass needle. His crowning achievement was to discover that changing magnetic fields create electric fields, a phenomenon called induction.

James Clerk Maxwell looked at all that, sat down with pen and papers, and mathematically described Faraday’s results in a complicated set of differential equations, importantly including the idea that changing electric fields would create magnetic fields, completing the symmetry between the two.

When Maxwell finished his theory, he discovered that it allowed waves of electromagnetism to fly off at high speed – when he calculated the speed, it turned out to be the speed of light.

Experiments with radio waves soon verified that light was nothing more than a special form of electricity and magnetism.

You can think of it as if we had been studying the way hot air balloons and airplanes and things work, and so were thinking about the dynamics of air. In the process, we develop equations for air, and figure out that sound is just waves moving through the air.

The theory of sound and the theory of airplanes are actually the same theory, even though they don’t seem very similar. That’s roughly what happened for light, except that unlike for sound, no one expected it. (Or at least it wasn’t obvious beforehand.)

Maxwell’s equations describe how electric and magnetic fields work, but those fields need to interact with matter – that happens via electric charge.  Charge is an innate property of matter…

Fields

We keep talking about the electromagnetic field. What exactly is a “field” anyways? See What are fields?

Our articles

Maxwell’s equations (our main article, for now)

Ampère’s circuital law

Backup: Get to know Maxwell’s Equations

External articles

Get to Know Maxwell’s Equations—You’re Using Them Right Now, Wired

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Universal Design for Learning (UDL)

UDL is a design framework for providing increased access and reduced barriers to learning.

UDL encourages us to be intentional in our design without adding excessive demands on faculty. Many of us are already implementing good teaching practices that are the basis of universal design.

UDL can involve high-tech, low-tech and no-tech strategies.

Mind Brain Gears Thinking Cognition

Image by Gerd Altmann, Pixabay, Free for commercial use

Engagement – motivating students

Offer both group and individual work

Engage in-class and online

Allow students to select topics within a given assignment that is based on their interest and relevancy

Presenting information

Offer visual and auditory (text, video, visuals, infographics) works

Provide clear, detailed directions and instructions with rubrics and examples

Record lectures for review after class

Ways to demonstrate learning

Offer flexibility and choice in ways in which students demonstrate learning outcomes (e.g. presentation, essay, show step-by-step problem solving on a whiteboard, etc.)

Provide opportunities for feedback and revision of work

Increase amount of “low stakes” assignments

Mind Thinking Thoughts

How teachers transform these ideas into action

Scaffolding: Making the standard curriculum and assignments more accessible.

* study guides
* tapping into student’s prior knowledge
* many opportunities to ask questions
* frontloading selected vocabulary
* relating ideas with analogies and visualizations
* Clear instructions and expectations.
* Frequent checks for understanding
* Have students use interactive apps
* Guided notes
* Graphic organizers
* Showing students how to color code notes, diagrams, etc.
* Historical, cross-curricular connections
* Recording lectures so students can review it later.

Differentiation: Providing a different level of curriculum and assignments. We adapt the topics covered to suit a student’s processing speed and ability.

* Text-to-speech (computer reads aloud documents to students)
* Speech-to-text (student dictates words and the computer writes them in a document.)
* Material from alternative textbooks. Offer a reduced wordcount and embedded vocabulary support for reluctant or struggling readers.
* Use a teacher-developed website: Utilize step-by-step explanations, color graphics, and interactive apps from a variety of sources.
* Shorter homework assignments.
* extra time for assignments
* Mastery grading
* Offer option for units to be self-paced.
* Replace traditional written lab directions with less text and more step-by-step diagrams/drawings.

Provide multiple ways for a student to show what they have learned

Draw – create a comic strip to show a process.

Create a PowerPoint (or Google Slide presentation)

Record a podcast or video (easy with iPads or Chrome extensions like Screencastify)

Create a commercial or skit

Create a concept map

For mathematics and physics problem-solving, it is essential for students to understand and use mathematical equations, and to use and create carefully labelled diagrams. Traditionally students use a pencil, paper, and calculator to do such work, fully writing out solutions on a sheet of paper. This process can be adapted for special education. I will write up a section on how this can be done in a physics class.

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Fun books to inspire science teachers as well as students

Fun books to inspire science teachers as well as students

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Gonzo Gizmos: Projects and Devices to Channel Your Inner Geek, by Simon Quellen Field

Gonzo Gizmos book

Step-by-step instructions to building more than 30 fascinating devices …e.g. how to construct a simple radio with a soldering iron, a few basic circuits, and three shiny pennies. Instructions are included for a rotary steam engine that requires a candle, a soda can, a length of copper tubing, and just 15 minutes. To use optics to roast a hot dog, no electricity or stove is required, just a flexible plastic mirror, a wooden box, a little algebra, and a sunny day. Also included are experiments most science teachers probably never demonstrated, such as magnets that levitate in midair, metals that melt in hot water, a Van de Graaff generator made from a pair of empty soda cans, and lasers that transmit radio signals.

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Physics, Fun, and Beyond: Electrifying Projects and Inventions from Recycled and Low-Cost Materials, by Eduardo de Campos Valadares

Physics Fun and Beyond Book

Build more than 110 projects that uncover the physics beneath everyday life! Most o are amazingly easy to build: all you’ll need are your everyday household tools and cheap (sometimes free) materials.

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Why Toast Lands Jelly-Side Down: Zen and the Art of Physics Demonstrations, by Robert Ehrlich

Toast Lands Jelly Book

A collection of physics demonstrations that prove that physics can, in fact, be “made simple.” Intentionally using low tech and inexpensive materials from everyday life, Why Toast Lands Jelly-Side Down makes key principles of physics surprisingly easy to understand. After laying out the basic principles of what constitutes a successful demonstration, Ehrlich provides more than 100 examples.

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The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science, by Robert Crease

Prism and the Pendulum Book

We see the first measurement of the earth’s circumference, accomplished in the third century B.C. by Eratosthenes using sticks, shadows, and simple geometry. We visit Foucault’s mesmerizing pendulum, a cannonball suspended from the dome of the Panthéon in Paris that allows us to see the rotation of the earth on its axis. We meet Galileo – the only scientist with two experiments in the top ten – brilliantly drawing on his musical training to measure the speed of falling bodies. And we travel to the quantum world, in the most beautiful experiment of all.

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How Things Work: The Physics of Everyday Life, by Louis A. Bloomfield

Uses familiar objects to introduce basic physics concepts with real-life examples. For example, discussions of skating, falling balls, and bumper cars are included to explain the laws of motion. Air conditioners and automobiles are used to explore thermodynamics.

 

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The Way Things Work Now, by David Macaulay

Explainer-in-Chief David Macaulay updates the worldwide bestseller The New Way Things Work to capture the latest developments in the technology that most impacts our lives. Famously packed with information on the inner workings of everything from windmills to Wi-Fi, this extraordinary and humorous book both guides readers through the fundamental principles of machines, and shows how the developments of the past are building the world of tomorrow.

This sweepingly revised edition embraces all of the latest developments, from touchscreens to 3D printer…. What possible link could there be between zippers and plows, dentist drills and windmills? Parking meters and meat grinders, jumbo jets and jackhammers, remote control and rockets, electric guitars and egg beaters? Macaulay explains them all.

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Building Big, by David Macaulay

Why this shape and not that? Why steel instead of concrete or stone? Why put it here and not over there? These are the kinds of questions that David Macaulay asks himself when he observes an architectural wonder. These questions take him back to the basic process of design from which all structures begin, from the realization of a need for the structure to the struggles of the engineers and designers to map out and create the final construction. Macaulay engages readers’ imaginations and gets them thinking about structures they see and use every day — bridges, tunnels, skyscrapers, domes, and dams.

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Insultingly Stupid Movie Physics: Hollywood’s Best Mistakes, Goofs and Flat-Out Destructions of the Basic Laws of the Universe, b y Tom Rogers

Would the bus in Speed really have made that jump? -Could a Star Wars ship actually explode in space? -What really would have happened if you said “Honey, I shrunk the kids”? The companion book to the hit website (www.intui tor.c om/moviephy sics), which boasts more than 1 million visitors per year, Insultingly Stupid Movie Physics is a hilarious guide to the biggest mistakes, most outrageous assumptions, and the outright lunacy at work in Hollywood films that play with the rules of science.

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Don’t Try This At Home!: The Physics of Hollywood Movies, by Adam Weiner

A fresh look at the basics of physics through the filmmaker’s lens. It will deconstruct, demystify, and debunk popular Hollywood films through the scientific explanations of the action genre’s most dynamic and unforgettable scenes.

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The Cosmic Code: Quantum Physics as the Language of Nature, Heinz R. Pagels

One of the best books on quantum mechanics for general readers. Heinz Pagels, an eminent physicist and science writer, discusses the core concepts without resorting to complicated mathematics. He covers the development of quantum physics. And although this is an intellectually challenging topics, he is one of the few popular physics writers to discuss the development and meaning of Bell’s theorem. Anecdotes from the personal documents of Einstein, Oppenheimer, Bohr, and Planck offer intimate glimpses of the scientists whose work forever changed the world.

A reviewer on Goodreads notes – “Pagels assumes a lay audience, but one prepared, after single paragraphs of description, to thereafter carry the technical terms across the finish line. Unlike other popsci, he also favors technical description–albeit written in smooth, clear prose over metaphor… The commitment to not talking down to his audience is rather commendable…

[His] intellectual project [is] reconciling the impossibility of visualizing quantum processes with a remit to communicate the science to non-scientists who, lacking the requisite mathematical literacy, necessarily require metaphor, universal human logics, and everyday comparisons to grasp most science in the first place.”

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Quantum Reality: Beyond the New Physics, Nick Herbert

Herbert brings us from the “we’ve almost solved all of physics!” era of the early 1900s through the unexpected experiments which forced us to develop a new and bizarre model of the universe, quantum mechanics. He starts with unexpected results, such as the “ultraviolet catastrophe,” and then brings us on a tour of the various ways that modern physicists developed quantum mechanics.

And note that there isn’t just one QM theory – there are several! Werner Heisenberg initially developed QM using a type of math called matrix mechanics, while Erwin Schrödinger created an entirely different way of explaining things using wave mechanics. Yet despite their totally different math languages – we soon discovered that both ways of looking at the world were logically equivalent, and made the same predictions. Herbert discussed the ways that Paul Dirac and Richard Feynman saw QM, and he describes eight very different interpretations of quantum mechanics, all of which nonetheless are consistent with observation…

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In Search of Schrödinger’s Cat: Quantum Physics and Reality, John Gribbon

“John Gribbin takes us step by step into an ever more bizarre and fascinating place, requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrodinger’s Cat – a search for quantum reality – as he brings every reader to a clear understanding of the most important area of scientific study today – quantum physics.”

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The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Brian Greene

“Brian Greene, one of the world’s leading string theorists, peels away the layers of mystery surrounding string theory to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy….

Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years.

Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom.”

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How can we see photos taken in UV, Infrared or Radio?

How is it possible that we can see photos taken in UV, Infrared or Radio?

Gamma rays Spectrum Properties NASA

Humans can only see visible wavelengths of light. Visible light has 𝜆 (wavelengths) of about 380 to 700 nm (nanometers.)

Yet in science class we often see infrared photos, like this!

 

Or we see photos taken in ultraviolet light. Bees see UV light, and so see flowers differently than we do. On the left is a primrose in visible light, but on the right we see it in UV light.

Bjorn Roslett Primrose in visible and UV

We see radar images of the Earth from an orbiting satellite, or radio telescope images of the galaxy. And those wavelengths of light just aren’t visible to humans.

Multiwavelength whirlpool galaxy astronomy

UV light 𝜆 = 100 to 400 nm.

Infrared light 𝜆 = 700 nm to 1 mm

Radio waves 𝜆 = 1 millimeter to 100 kilometers.

Okay, the easy part is the technology: we can build equipment that detect such wavelengths. But what is the resulting image that we are looking at? Something visible to the human eye – which is in the visible spectrum.

So what does it even mean to translate something invisible to something visible?

Think about transposing music on a piano. We can play a melody in the middle of a piano keyboard. Then we can play the exact same melody one octave higher just by moving our hands to the right. We can do this again, and again. Each time the same melody is preserved, just an octave higher.

Octaves on piano keyboard

We can keep doing this until the notes are so high pitched that human ears can’t detect them (although maybe dogs and bats could hear this.) The resulting melody would be the same as the original melody, yet undetectable to us.

We can compare this to “seeing” higher frequencies of light – they get higher and higher until they become ultraviolet or X-rays.

Now, we can do the same thing again, but in reverse. Play a melody in the middle of a piano keyboard. Then we can play the exact same melody one octave lower just by moving our hands to the left. We can do this again, and again. Each time the same melody is preserved, just an octave lower.

Musical notation Piano transpose notes down one octave

www.notation.com 8va_octaves

We can keep doing this until the notes have such a low pitch that human ears can’t detect them (although whales, elephants, and hippopotamuses could hear this.) The resulting melody would be the same as the original melody, yet undetectable to us.

Ultrasound and infrasound

This is pretty much what is happening when we print out images of data capturing UV, Infrared or Radio!

For high frequency images (like UV light) we are dropping the image by many octaves (so to speak) until we reach the visible spectrum.

For low frequency images (like radio or infrared) we are increasing the image by many octaves (so to speak) until we reach the visible spectrum.

Avoiding misunderstandings

Electromagnetic waves (light, UV, radio) are transverse waves. The direction of particle displacement is perpendicular to the direction of movement.

Sound waves are longitudinal waves.

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Lava flows

Lava is molten rock (magma) that has been expelled from the interior of a planet, like Earth, Mars, or Venus.

The interior of such planets is very hot; this heat is left over from the creation of the planet billions of years ago.

Many people ask: how the world can still be so hot on the inside? For details see Why is the Earth still hot?

When this magma erupts through the crust of a planet, we call this lava.

Lava is usually between 700 to 1,200 °C (1,292 to 2,192 °F).

A “lava flow” is a fairly common phenomenon. We see this during a mostly non-explosive eruption. The lava soon cools to form igneous rock.

Lava is far more viscous than water, yet it can flow great distances before cooling and solidifying.

Several types of lava flows on land, and several types flow underwater/ocean

Lava flows on land

a’a (pronounced ah-ah) – Rough, rubbly surface because of their high eruption rates. As the upper surface of the lava cools and becomes rock, it is continually ripped apart by the moving molten lava inside the flow.

Pieces of the rocky surface are broken, rolled and tumbled along as the lava flow moves. When finally cooled to a solid, a’a lava flows look like a jagged heap of loose rock.

Lava a‘ā flow Kilauea volcano Hawaii

pahoehoe (pronounced pah-hoy-hoy) – relatively smooth surface texture because of their low eruption rates.

Pahoehoe lava flows develop surface crusts that form thick plates with ropy and/or gently undulating surfaces.

Lava pahoehoe at Kilauea volcano Hawaii

Pyroclastic flow

Pyroclastic flow in this section is not pure lava. Pyroclastic flows are mostly made of glass, ash, pumice, tephra (misc fragmented rocky pieces,) lava chunks, and hot gas.

Some lava does get sprayed up into the air and cools down quickly into falling rocks.

So the flow is like a battering ram of hot solid and gaseous material coming at you like a freight train.

Pyroclastic flow during Mount St. Helens eruption lava volcano

From the USGS:

Pyroclastic flows move fast and destroy everything in their path. Heed evacuation warnings if a volcano is known to be active. If you witness a pyroclastic flow, run in the opposite direction as quickly as possible.

Pyroclastic flows move at very high speed down volcanic slopes, typically following valleys.

With rock fragments ranging in size from ash to boulders that travel across the ground at speeds typically greater than 80 km per hour (50 mph), pyroclastic flows knock down, shatter, bury or carry away nearly all objects and structures in their path.

The heat is between 200°C and 700°C (390 – 1300°F), can ignite fires and melt snow and ice.

Even relatively small flows that move less than 5 km (3 mi) from a volcano can destroy buildings, forests, and farmland. On the margins of pyroclastic flows, death and serious injury to people and animals may result from burns and inhalation of hot ash and gases.

This section is from Pyroclastic flows, USGS

How much lava can flow during these kinds of eruptions?

Here’s one example from Kīlauea, an active shield volcano in the Hawaiian Islands: Depth of the Halema‘uma‘u lava lake (2021)

Lava flows under the ocean

See these videos

A massive underwater volcano erupted and scientists almost missed it

Pillow lava flowing underwater off the coast of Hawaii

Undersea Volcano Eruptions Caught On Video (YouTube)

Stupendous Submarine Volcanoes (YouTube)

“Pillow” lava – forms rounded lumps that look like fat pillows. Can form piles a few to tens of meters high. Pillow lava flows can be many hundreds of meters to kilometers long.

Pillow Lava

Sheet flows – Form at much higher eruption rates than pillow flows. Rivers of lavas flow across the seafloor. These rivers can fill low areas in the seafloor and form lava ponds with very flat surfaces.

Lava in the ponds can also spread like thick pancake batter on a tilted grill, forming a long tongue-like flow. Sheet flows can have flat surfaces as well as twisted, ropy ridges all aligned in the direction that the flow moved across the seafloor.

Sheet flows exhibit a variety of surface textures.

Here is a lobate flow.

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How do we know how atoms are arranged in a crystal?

How do we know how atoms are arranged in a protein, an enzyme, or a fat molecule?

Each individual atom is only a few nanometers (1 x 10-10 m) wide, way too small to photograph directly.

Yet we often see images of how atoms how are arranged, like this.

Just look it this image: We see individual atoms (yellow, red, blue) connected in a precise pattern. How in the world did we see this?

Well, there’s no way to see this, in one step. Too difficult.

But there is a way to accurately visualize this, if we go through a very careful process.

The process is called X-ray crystallography.

We start with a tiny sample of whatever it is we’d like to learn about. For example, a protein or an enzyme.

First, a biochemist needs to purify cells, and extract just the one molecule that we’re interested in.

That, in of itself, is a procedure that needs to be done carefully.

Once we have a pure form of that molecule, we then crystallize it.

Of course, in order for the rest of this lesson to make sense, we need to know what a “crystal” really is. So if you haven’t already learned about this, first check out our lesson on What is a crystal?

Short version: A crystal is solid material, in which the atoms, molecules, or ions are arranged in an orderly repeating pattern.

For instance, on the left is the atom-by-atom structure of a halite crystal.

(Purple is sodium ion, green is chlorine ion.)

This crystal is so tiny, that it would take 10,000 of them to make one tiny grain of salt!

On the right is a visible salt crystal. This contains millions of such crystal units.

Well, if we have a pure chemical from a cell (protein, enzyme, fatty acid, etc.) we can slowly cool and dry this chemical until it crystallizes!

Each different kind of molecule would create a differently shaped and colored crystal.

Please understand that these crystals look tiny – maybe just 1/10 of an inch across.

Yet each crystal contains millions of repeating atomic units.

Figure 22.3. Examples of protein crystals. From left to right: β-secretase inhibitor complex; human farnesyl pyrophosphatase in complex with zoledronic acid; abl kinase domain in complex with imatinib; cdk2 inhibitor complex.

Source – Jean-Michel Rondeau, Herman Schreuder, in The Practice of Medicinal Chemistry (Fourth Edition), 2015

This crystal is then placed in front of an X-ray source.

The X-rays scatter off the atoms in a crystal.

Those X-rays fly onto either a piece of film, or a digital X-ray detector plate.

Either way, we end up with a beautiful array of dots called a diffraction pattern.

This pattern is beautiful – but doesn’t seem to look like anything?

Ah, but there’s a relationship between the placement of the atoms, and where the X-rays deflect off of them – just like there’s a relationship between a pool ball bouncing off of other pool balls.

Think about it: If you know how a pool table is set up, what balls are made of, and see how the balls move after being it, then you could use math to work backwards.

Just by seeing the results of where the balls are scattering to, you could work backwards to figure out where the balls originally where.

Billiards Pool

from Banks and Kicks in Pool and Billiards, Dr. Dave Alciatore, Billiards and Pool Principles, Techniques, Resources

The same is true here: We can use math to figure out where each individual atom in the molecule is!

Let’s follow the steps below:

On the left, we see X-rays leave a source. Some of these x-rays hit a lead screen. All those X-rays are stopped.

Only a thin, focused beam of X-rays makes it thru the slit.

Those X-rays hit our crystal sample.

The X-rays bounce off the atoms, like pool balls bouncing off of each other.

(This GIF created by Abhijit Poddar, ‘E-learning’ of select topics in solid state physics and quantum mechanics)

Some of the x-rays bounce onto a film plate. This makes an image.

We end up with a diffraction pattern on film.

DNA X-ray crystallography

Figure 11.4, Purves’s Life: The Science of Biology, 7th Edition

Once we have a diffraction pattern, we use math to work backwards:

We figure out where the atoms must have been.

The result is an electron density map.

This traces out the shape of the atoms in the molecule.

X Ray crystallography and electron density map

Left image: X-ray diffraction pattern, Wikimedia. Right upper image: electron density map. Right lower image: model fitting atoms to the density map.

Appearance of a zone of the electron density map of a protein crystal, before it is interpreted

density map peptide x ray crystallography Before interpretation

The same electron density map after its interpretation in terms of a peptidic fragment.

density map peptide X-ray crystallography

These last two images come from CSIC Crystallography

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External resources

Welcome to the world of Crystallography: The Spanish National Research Council

Cryo Electron Microscopy

Cryo-EM is an electron microscopy (EM) technique applied on samples cooled to cryogenic temperatures and embedded in an environment of vitreous water.

An aqueous sample solution is applied to a grid-mesh and plunge-frozen in liquid ethane or a mixture of liquid ethane and propane.

While development of the technique began in the 1970s, recent advances in detector technology and software algorithms have allowed for the determination of biomolecular structures at near-atomic resolution.

This has attracted wide attention to the approach as an alternative to X-ray crystallography or NMR spectroscopy for macromolecular structure determination without the need for crystallization.

Cryo-electron microscopy wins chemistry Nobel, Nature

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Mineral Identification

Mineral Identification Kit Properties

How do we distinguish one mineral from another? By any or all these properties:

Cleavage and fracture

Hit a rock with a hammer. What happens? The resulting cleavage or fracture can tell us a lot.

cleavage rocks

Crystal habit

The tendency for a mineral to grow into a special shape. This shape depends on the crystal’s structure (see next section), and also on the environment in which that mineral sample developed. (Where was it underground, how much heat, time, pressure?0

Crystal habits shapes

Crystal structure

All crystals are atoms in a three dimensional pattern. Here some examples.

Crystal structure Cubic Hexagonal

Image from Molecular and Solid State Physics, http://lampx.tugraz.at

Diaphaneity/transparency

The way that light passes through and reflects from a surface.

Diaphaneity Minerals Light

From left to right – Calcite is transparent, muscovite is translucent, and cinnabar is opaque.

Lustre

The appearance of a freshly cut mineral surface in light.

Mineral Luster Light

Magnetism

Some minerals are naturally magnetic.  These are some of the more common minerals that demonstrate magnetic properties

Hardness

The Mohs scale characterizes minerals by the ability of harder material to scratch softer material.

Mohs hardness scale minerals 2

Odor – So accustomed are we to associate odors with flowers or food that we scarcely appreciate the fact that certain minerals have a characteristic odor.

Selenium – horse-radish.

Arsenic – garlic.

Sulfides (such as pyrite) – rotten egg.

Antozonite (type of fluorite) – acid, reeking pungent smell.

Anthraconite – tar smell.

Specific gravity

How dense something is, compared to the density of water. This has to do with with how many atoms are in a unit volume (and also, with the density of those atoms themselves.)

density 3d

Streak

The streak of a mineral is the color of the powder produced when it is dragged across a flat surface.

cinnabar pyrite streak

Tenacity

Tenacity is how a rock sample responds to stress.  Put some force on it, try to crush, bend, break, or tear it. What happens to the sample? Whatever happens as a result is a way of distinguishing one sample from another.

Brittleness

If a mineral is hammered and the result is a powder or small crumbs, it is considered brittle. Brittle minerals leave a fine powder if scratched, which is the way to test a mineral to see if it is brittle.”

Broken Brittle Rock

Malleability

If a mineral can be flattened by pounding with a hammer, it is malleable. All true metals are malleable.”

Malleability malleable

Ductility

“A mineral that can be stretched into a wire is ductile. All true metals are ductile.”

Here, reddish copper is inside a steel cup, with a small hole. Pressure is applied to the copper – and a small amount is pushed out through the hole. A tool grabs this exposed copper, and slowly pulls. As it pulls, more and more copper is drawn out in a tube.

ductile draw into wire

Sectility

“Sectile minerals can be separated with a knife, much like wax but usually not as soft. An example is Gypsum.”

Many metals and some minerals can be cut with knife such as aluminum, gypsum, lead, lithium, and magnesium.

Cutting metal Lithium Knife

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What does “law” mean in “laws of nature?” ELA and Science

o-que-e-design

What does the word “law” mean in the phrase “laws of nature?” We won’t be able to understand the science until we understand the English.

In our English language arts classes we have learned about homographs – words spelled the same but have different meanings.

For instance, what is a “bow?” With the same spelling it used for 4 entirely different words.

bow – noun, the front of a boat

bow – verb, to bend at the waist.

bow – noun, a type of ribbon we used to decorate a present.

bow – noun, sporting equipment used to shoot arrows.

The same is true for the word “law.” It can refer to three different things:

Laws made up by people

City, state, or national “laws” aren’t real in any scientific sense. They aren’t part of the universe. They don’t even stay the same. They change all the time.

How old does one have to be in order to vote? How fast can you drive a car on the road? How much property tax does a homeowner have to pay on a house?

None of those rules are part of the universe. These “laws” are just things that people agree on. Nothing more. People get together in communities, clubs, or governments, and decide upon rules so that (hopefully) their society runs safely and smoothly.

Writing Laws Legal Books

Natural law

The idea of natural law is a somewhat controversial idea in philosophy, ethics, and religion. The idea is that there are universal moral laws in nature that mankind is capable of learning, and obligated to follow.

This idea is held by some religious groups and some schools of philosophy.

It isn’t necessarily related to religion; there are many non-religious people who believe in the necessary existence of natural law.

ethics-morality

image from commons.wikimedia.org

Laws of nature

In physics, a law of nature is something scientists have learned about how things in our physical world actually work.

A law of nature is a precise relationship between physical quantities, and is expressed as an equation.

Laws of nature are relationships universally agreed upon – but not agree upon because we want this relationship to exist. Rather, the law is only accepted because repeated experiments show us that this relationship exists.

People don’t decide what nature’s laws are. People can only investigate and discover what they are.

Here’s an example: Electrical charge is conserved. The total electric charge in an isolated system never changes. People can’t pass a law that says “positive charges can now be created.” That won’t work. Nothing humans say changes the way that the universe works,

Conservation of charge

Laws of nature are true for every time and every place.  They are just as true in Michigan, Moscow, or Miami, just as true on the Moon or on Mars. They are just as true 10,000 years ago as today, and as next year.

We explore the concept of laws of nature in more detail here – What are laws of nature? What are theories?

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Thanks for reading. While you’re here see our other articles on astronomybiologychemistryEarth sciencemathematicsphysicsthe scientific method, and making science connections through books, TV and movies.

Great physics discussion questions!

Great physics discussion questions! These were written by Physicist Dr. Matt Caplan, who used to run the QuarksAndCoffee blog.

That blog no longer exists, links to archived copies exist.

If everyone was Kung fu fighting, and their kicks really were fast as lightning, what would happen?

How many calories do superheroes burn using their powers?

What would happen if a 10 meter plasma sphere was transported from the Sun to Earth?

Dyson Sphere: Is there enough material in the solar system to build a shell to enclose the sun?

If it was cold enough for the atmosphere to condense, how deep would the ‘liquid air’ be?

Does my phone weigh more when the battery is charged?

How loud would a literal ‘shot heard round the world’ be?

Why are there seven colors in the rainbow?

Math

What are the odds of solving a Rubik’s cube by making random moves?

 

Maslow’s hierarchy of needs – claims and reality

Maslow’s hierarchy of needs is a theory in psychology proposed by Abraham Maslow. His first discussion of this idea was in his 1943 paper “A Theory of Human Motivation” in Psychological Review. This was was developed further in his 1954 book Motivation and Personality.

Maslow's hierarchy of needs

Created by FireflySixtySeven, CC BY-SA 4.0, Wikimedia

Yet contrary to popular belief, Maslow never created a pyramid to represent these needs. Nor did he conclude that in order for motivation to arise at the next stage, each stage must be satisfied. Much that teachers have heard about Maslow’s hierarchy of needs isn’t what he taught.

How his ideas were changed, incorrectly claimed as scientifically proven, and then became the basis of profitable seminars in business and education, is the subject of these papers:

Who Built Maslow’s Pyramid? A History of the Creation of Management Studies’ Most Famous Symbol and Its Implications for Management Education, by Todd Bridgman, Stephen Cummings and John Ballard, Academy of Management Learning & EducationVol. 18, No. 1, 3/1/2019

“Who Created Maslow’s Iconic Pyramid?” by Scott Barry Kaufman Scientific American, 4/23/2019

A modern packaging of Maslow’s work is popular in management training and secondary and higher psychology and education instruction.

Saul McLeod points out that

Maslow continued to refine his theory based on the concept of a hierarchy of needs over several decades. Regarding the structure of his hierarchy, Maslow proposed that the order in the hierarchy “is not nearly as rigid” as he may have implied in his earlier description. Maslow noted that the order of needs might be flexible based on external circumstances or individual differences. For example, he notes that for some individuals, the need for self-esteem is more important than the need for love. For others, the need for creative fulfillment may supersede even the most basic needs.

Maslow’s Hierarchy of Needs, 3/20/2020, Saul McLeod, Simply Psychology

In Scientific American, Scott Barry Kaufman writes

Abraham Maslow’s iconic pyramid of needs is one of the most famous images in the history of management studies. At the base of the pyramid are physiological needs, and at the top is self-actualization, the full realization of one’s unique potential. Along the way are the needs for safety, belonging, love, and esteem.

However, many people may not realize that during the last few years of his life Maslow believed self-transcendence, not self-actualization, was the pinnacle of human needs. What’s more, it’s difficult to find any evidence that he ever actually represented his theory as a pyramid.

On the contrary, it’s clear from his writings that he did not view his hierarchy of needs like a video game– as though you reach one level and then unlock the next level, never again returning to the “lower” levels. He made it quite clear that we are always going back and forth in the hierarchy, and we can target multiple needs at the same time.

If Maslow never built his iconic pyramid, who did? In a recent paper, Todd Bridgman, Stephen Cummings, and John Ballard trace the true origins of the pyramid in management textbooks, and lay out the implications for the amplification of Maslow’s theory, and for management studies in general. In the following Q & A, I chat with the authors of that paper about their detective work.

Question: Why did you set out to answer the question: Who built “Maslow’s Pyramid”?

My colleague Stephen Cummings and I have long been interested in how foundational ideas of our field, management studies, are represented in textbooks. Textbooks often present ideas very differently than in the original writings. We’re interested in understanding how and why this happens. We’ve taught Maslow’s hierarchy of needs for many years and were aware the pyramid did not appear in his most well-known works, so were interested in delving deeper. We contacted John Ballard, who knew Maslow’s work better than we did and who shared our concern about Maslow’s theory being misrepresented. Thankfully, he agreed to join us on the project.

Question: Do you think the popularity of Maslow’s hierarchy of needs is due in part to the iconic appeal of the pyramid that became associated with it?

Yes, absolutely. Maslow wasn’t the first psychologist to develop a theory of human needs. Walter Langer presented a theory with physical, social and egoistic needs that appeared alongside Maslow’s in an early management textbook. And Maslow’s theory generally hasn’t performed well in empirical studies (although I’m aware of your recent research which challenges this).

In fact, this lack of empirical support is one of the main criticisms of the theory made by textbook authors. So why do they continue to include it? The pyramid. We know from having taught management courses for 20 years that if there’s one thing that students remember from an introductory course in management, it’s the pyramid. It’s intuitively appealing, easy to remember and looks great in PowerPoint. Students love it and because of that, so do textbooks authors, teachers, and publishers.

Question: So what’s your problem with the pyramid?

It’s described as ‘Maslow’s pyramid’ when he did not create it and it’s just not a good representation of Maslow’s hierarchy of needs. It perpetuates unfair criticisms of the theory. For example, that people are only motivated to satisfy one need at a time, that a need must be 100% satisfied before a higher-level need kicks in, and that a satisfied need no longer affects behavior.

Another is the view that everyone has the same needs arranged and activated in the same order. In his 1943 article in Psychological Review Maslow anticipates these criticisms and says they would give a false impression of his theory. Maslow believed that people have partially satisfied needs and partially unsatisfied needs at the same time, that a lower level need may be only partially met before a higher-level need emerges, and that the order in which needs emerge is not fixed.

Question: How did this inaccurate interpretation of the hierarchy of needs become established in management textbooks?

It’s a complicated story and one we address fully in the paper. Douglas McGregor is a key figure, because he popularized Maslow within the business community. McGregor saw the potential for the hierarchy of needs to be applied by managers, but for ease of translation he deliberately ignored many of the nuances and qualifications that Maslow had articulated. To cut a long story short, McGregor’s simplified version is the theory that appears in management textbooks today, and most criticisms of Maslow’s theory are critiques of McGregor’s interpretation of Maslow.

Question: Did McGregor create the pyramid? Or if not, who did?

No pyramid appears in McGregor’s writing. Keith Davis wrote a widely-used management textbook in 1957 that illustrated the theory in the form of a series of steps in a right-angled triangle leading to a peak. The top level shows a suited executive raising a flag, reminiscent of the flag-raising at Iwo Jima. But this representation of the theory did not catch on.

We traced the pyramid that we associate with the hierarchy of needs today to Charles McDermid, a consulting psychologist. It appeared in his 1960 article in Business Horizons ‘How money motivates men’ in which he argued the pyramid can be applied to generate “maximum motivation at the lowest cost”. We think McDermid’s pyramid was inspired by Davis’ representation, but it was McDermid’s image that took off. If there is an earlier pyramid, we did not find it.

Question: Is it right that you actually found no trace of Maslow framing his ideas in pyramid form? Where did you look, and how comprehensive was your search?

That’s correct. It was a comprehensive search. Maslow was a prolific writer. We examined all of his published books and articles that we could identify, as well as his personal diaries, which are published. John immersed himself in the Maslow archives at the Centre for the History of Psychology at the University of Akron in Ohio and examined many boxes of papers, letters, memos, and so forth. We found no trace of the pyramid in any of Maslow’s writings. Additionally, John went through pre1960 psychology textbooks for any discussions of Maslow. Most psych books in those times did not even mention Maslow.

Question: Why didn’t Maslow argue against the Pyramid once he saw it? He could have criticized it, right? I heard from someone who knew Maslow that he actually thought the pyramid on the back of the $1 bill was a fair representation of his theory.

Also, one of his students who took his course at Brooklyn College told me he would include a slide of the pyramid when he described his theory in class. So perhaps he was pleased with the iconic pyramid even if he didn’t invent the depiction himself?

Answer: Those are interesting questions. Maslow lived for 10 years after McDermid presented the pyramid. We found no evidence of Maslow challenging the pyramid at any time. We don’t think that’s because he regarded pyramid as an accurate representation. A more plausible explanation, which comes from our analysis of his personal diaries, is that aspects of his professional life were unravelling.

He felt underappreciated in psychology. The major research journals in psychology had been taken over by experimental studies, which depressed Maslow for their lack of creativity and insight. He also had more pragmatic concerns, suffering periods of ill health and financial difficulties. Key figures in the management community saw him as a guru and rolled out the red carpet. They gave him the recognition he felt he deserved. Furthermore, through speaking engagements and consulting, he could generate additional income. Seen in that light, it’s not surprising he went along with it.

Question: You wrote: “Inspiring the study of management and its relationship to creativity and the pursuit of the common good would be a much more empowering legacy to Maslow than a simplistic, 5-step, one-way pyramid.” I agree! It seems like Maslow’s original thinking about self-actualization is at odds with how business leaders treated the concept, right?

Definitely. Following the publication of Motivation and Personality in 1954, Maslow emerged as one of the few established psychologists to challenge the prevailing conformism of the 1950s. He spoke out on how large organizations and social conformity stifled individual self-expression. At times he was frustrated that the business community treated his theory of human nature as a means to a financial end–short-term profits–rather than the end which he saw, a more enlightened citizenry and society.

It would be great if students were encouraged to read what Maslow in the original. Students would better understand that motivating employees to be more productive at work was not the end that Maslow desired for the hierarchy of needs. He was concerned with creativity, freedom of expression, personal growth and fulfillment – issues that remain as relevant today in thinking about work, organizations, and our lives as they were in Maslow’s time.

State of the theory today

William Kremer and Claudia Hammond write

There is a further problem with Maslow’s work. Margie Lachman, a psychologist who works in the same office as Maslow at his old university, Brandeis in Massachusetts, admits that her predecessor offered no empirical evidence for his theory. “He wanted to have the grand theory, the grand ideas – and he wanted someone else to put it to the hardcore scientific test,” she says. “It never quite materialised.”

However, after Maslow’s death in 1970, researchers did undertake a more detailed investigation, with attitude-based surveys and field studies testing out the Hierarchy of Needs.

“When you analyse them, the five needs just don’t drop out,” says Hodgkinson. “The actual structure of motivation doesn’t fit the theory. And that led to a lot of discussion and debate, and new theories evolved as a consequence.”

In 1972, Clayton Alderfer whittled Maslow’s five groups of needs down to three, labelled Existence, Relatedness and Growth. Although elements of a hierarchy remain, “ERG theory” held that human beings need to be satisfied in all three areas – if that’s not possible then their energies are redoubled in a lower category. So for example, if it is impossible to get a promotion, an employee might talk more to colleagues and get more out of the social side of work.

More sophisticated theories followed. Maslow’s triangle was chopped up, flipped on its head and pulled apart into flow diagrams. Hodgkinson says that one business textbook has just been published which doesn’t mention Maslow, and there is a campaign afoot to have him removed from the next editions of others.

The absence of solid evidence has tarnished Maslow’s status within psychology too. But as a result, Lachman says, people miss seeing that he was responsible for a major shift of focus within the discipline.

“He really was ground-breaking in his thinking,” Lachman says. “He was saying that you weren’t acting on the basis of these uncontrollable, unconscious desires. Your behaviour was not just influenced by external rewards and reinforcement, but there were these internal needs and motivations.”

Abraham Maslow and the pyramid that beguiled business, William Kremer and Claudia Hammond, BBC World Service 9/1/2013

Links

Maslow’s Hierarchy: Separating Fact From Fiction