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Evolution of cereals and grasses
What are cereals and grains, and where do they come from?
A cereal is any grass – yes you read that correctly, grass – cultivated for the edible components of its grain.
Common grasses that produce these wonderful grains are wheat, rye, millet, oat, barley, rice, and corn.
Types of Grains found on Recipematic
Wheat is the most common grain producing grass.
(botanically, a type of fruit called a caryopsis), composed of the endosperm, germ, and bran.
The term may also refer to the resulting grain itself (specifically “cereal grain”).
Cereal grain crops are grown in greater quantities and provide more food energy worldwide than any other type of crop[1] and are therefore staple crops. Edible grains from other plant families, such as buckwheat, quinoa and chia, are referred to as pseudocereals.
From the Health happens at Home website
All of the grains that we eat have been genetically modified by thousands of years of artificial selection. This includes all wheat, barley, rye, spelt and oats.
Paper 1: “Wheat: The Big Picture”, The Bristol Wheat Genomics site, School of Biological Sciences, University of Bristol
Wheat: The Big Picture – the evolution of wheat
Figure 2. Phylogenetic tree showing the evolutionary relationship between some of the major cereal grasses. Brachypodium is a small grass species that is often used in genetic studies because of its small and relatively simple genome.
Paper 2: Increased understanding of the cereal phytase complement for better mineral bio-availability and resource management
Article (PDF Available) in Journal of Cereal Science 59(3) · January 2013 with 244 Reads
DOI: 10.1016/j.jcs.2013.10.003
Fig. 1. Phylogenetic tree of cereals and selected grasses. PAPhy gene copy numbers are given for each species and key evolutionary events are indicated.
Paper 2
Genome-wide characterization of the biggest grass, bamboo, based on 10,608 putative full-length cDNA sequences.
Peng Z, Lu T, Li L, Liu X, Gao Z, Hu T, Yang X, Feng Q, Guan J, Weng Q, Fan D, Zhu C, Lu Y, Han B, Jiang Z – BMC Plant Biol. (2010)
Figure 2: Phylogeny of grasses inferred from concatenated alignment of 43 putative orthologous cDNA sequences. (A) Tree inferred from maximal likelihood method. Bayes inference yielded the same topology. (B) Tree inferred from neighbor joining method. Branch length is proportional to estimated sequence divergence measured by scale bars. Numbers associated with branches are bootstrap percentages. Arabidopsis was used as outgroup. Subfamily affiliation of the grasses is indicated at right.
Paper 3 Evolution of corn
Figure 1: The evolutionary stages of domestication and diversification.
From Evolution of crop species: genetics of domestication and diversification, Rachel S. Meyer & Michael D. Purugganan, Nature Reviews Genetics 14, 840–852 (2013) doi:10.1038/nrg3605
http://www.nature.com/nrg/journal/v14/n12/fig_tab/nrg3605_F1.html
Paper 4 text
Brachypodium distachyon: making hay with a wild grass, Magdalena Opanowicz, Philippe Vain, John Draper, David Parker, John H. Doonan
DOI: http://dx.doi.org/10.1016/j.tplants.2008.01.007
This next image is from Setaria viridis as a Model System to Advance Millet Genetics and Genomics.
By Huang, Pu & Shyu, Christine & Coelho, Carla & Cao, Yingying & Brutnell, Thomas. (2016) Frontiers in Plant Science. 7. 10.3389/fpls.2016.01781.
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Schrödinger’s cat
Schrödinger’s cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935.
It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics when applied to everyday objects.
Here is how the Schrödinger’s cat thought experiment works:
Acat, a flask of poison, and a radioactive source are placed in a sealed box.
If an internal monitor detects radioactivity (i.e., a single atom decaying), the flask is shattered, releasing the poison, which kills the cat.
The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead.
Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead.
This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.
The Copenhagen interpretation implies that the cat remains both alive and dead – until the state is observed.
Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility.
On the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics
Since Schrödinger’s time, other interpretations of quantum mechanics have been proposed that give different answers to the questions posed by Schrödinger’s cat of how long superpositions last and when (or whether) they collapse.
This introduction has been adapted from “Schrödinger’s cat.” Wikipedia, The Free Encyclopedia, 5 Feb. 2017.
Many-worlds interpretation and consistent histories
In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process.
In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are decoherent from each other.
In other words, when the box is opened, the observer and the possibly-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat.
But since the dead and alive states are decoherent, there is no effective communication or interaction between them. We have created parallel universes!
Decoherence interpretation
When opening the box, the observer becomes entangled with the cat.
Therefore “observer states” corresponding to the cat’s being alive and dead are formed; each observer state is entangled or linked with the cat so that the “observation of the cat’s state” and the “cat’s state” correspond with each other.
Quantum decoherence ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories.
Only the “dead cat” or the “alive cat” can be a part of a consistent history in this interpretation.
External resources
https://www.newscientist.com/article/2097199-seven-ways-to-skin-schrodingers-cat/
Learning Standards
SAT Subject Test: Physics
Quantum phenomena, such as photons and photoelectric effect
Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra
Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles
Relativity, such as time dilation, length contraction, and mass-energy equivalence
AP Physics Curriculum Framework
Essential Knowledge 1.D.1: Objects classically thought of as particles can exhibit properties of waves.
a. This wavelike behavior of particles has been observed, e.g., in a double-slit experiment using elementary particles.
b. The classical models of objects do not describe their wave nature. These models break down when observing objects in small dimensions.
Learning Objective 1.D.1.1:
The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties.
Essential Knowledge 1.D.2: Certain phenomena classically thought of as waves can exhibit properties of particles.
a. The classical models of waves do not describe the nature of a photon.
b. Momentum and energy of a photon can be related to its frequency and wavelength.
Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies
Internal reflection
Physics is a deeply conceptual class. It’s not like English or History, where everyone already knows vast amounts of content before even entering. Students entering high school already knowing what a story is, what characters are, what a theme is, and what a moral is.
The human themes discussed by Shakespeare or Homer are universal. They are intuitively understood by even the least prepared of readers. Students may not know much about Elizabethan England, or ancient Greece, but they know what it means to be happy, sad, angry, or jealous. They know what it means for a character to fall in love, or to flee from their home.
When they read about a King entering a castle, and making a pronouncement to the citizens, students get it right away. Does any student ever erroneously think that “the pronouncement” is a person? That “the King” is a large object built out of wood and stone that someone lives in? That “the Castle” is a letter to be read? Of course not.
This is not so, however, with concepts in physics. Student entering a physics class often have no meaningful understanding of conservation laws, or Newton’s laws of motion. Most don’t understand why it is essential to differentiate between conservation of energy and conservation of momentum. When someone doesn’t know if a problem requires conservation of energy concepts, or kinematic equation concepts to solve a problem, that’s a like a person not knowing the difference between a King and a Castle. It is that basic.
Outside of AP Physics we usually are teaching from the ground level upwards.
No teaching method, homework assignment, or pedagogical technique has much effect on student performance – unless that student takes time to engage in internal mental reflection.
When students review at home what we learned in class,
When students think about what happened, and why it happened,
When students compare their preconceptions to what they have observed
only they are engaging in internal mental reflection.
If a student chooses not do this, then there is little a teacher can add. We can explain it for you, but we can’t understand it for you.
This is one reason why some students struggle. Doing classwork has only limited usefulness, unless one internally reflects on the subject.
How to be a good student
Chapter 12. Learning Through Reflection, by Arthur L. Costa and Bena Kallick
Learning Through Reflection
Google Scholar Search
Math is the language of physics
Mathematics is the language of physics
Natural philosophy [i.e., physics] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written.
[The universe] cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
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Galileo, Opere Il Saggiatore p. 171
Mathematics is the language of physics. Physical principles and laws, which would take two or even three pages to write in words, can be expressed in a single line using mathematical equations. Such equations, in turn, make physical laws more transparent, interpretation of physical laws easier, and further predictions based on the laws straightforward.
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Mesfin Woldeyohannes, Assistant Professor, Western Carolina University
ἀεὶ ὁ θεὸς γεωμετρεῖ – Aei ho theos geōmetreî. God always geometrizes.
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Plato, 400 BCE, classical Greece, as quoted by Plutarch in his The Moralia, Quaestiones convivales. (circa 100 CE)
Math is so useful in the real world that it’s eerie
There is a classic paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, that it should be read even by high school students.
Wigner begins his paper with the belief, common among those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed.
Based on his experience, he says “it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.”
Wigner then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms “very scanty observations” to describe the motion of the planets, where it “has proved accurate beyond all reasonable expectations”.
Another oft-cited example is Maxwell’s equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell’s death.
Wigner sums up his argument by saying that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it”. He concludes his paper with the same question with which he began:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences. (2016, September 11). In Wikipedia, The Free Encyclopedia
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Math is different from physics
Mathematics does not need to bother itself with real-world observations. It exists independently of any and all real-world measurements. It exists in a mental space of axioms, operators and rules.
Physics depends on real-world observations. Any physics theory could be overturned by a real-world measurement.
None of maths can be overturned by a real-world measurement. None of geometry can be.
Physics starts from what could be described as a romantic or optimistic notion: that the universe can be usefully described in mathematical terms; and that humans have the mental ability to assemble, and even interpret, that mathematical description.
Maths need not concern itself with how the universe actually works. Perhaps there are no real numbers, one might think it is likely that there is only a countable number of possible measurements in this universe, and nothing can form a perfect triangle or point.
Maths, including geometry, is a perfect abstraction that need bear no relation to the universe as it is.
Physics, to have any meaning, must bear some sort of correspondence to the universe as it is.
Why-is-geometry-mathematics-and-not-physics? Physics StackExchange, by EnergyNumbers
Related articles
What is mathematics, really? Is it made by humans or a feature of the universe? Math in art & poetry.
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Thanks for reading. While you’re here see our articles on astronomy, biology, chemistry, Earth science, physics, the scientific method, and making connections to science through reading, books, TV and movies.
Ancient mesopotamian science
Here we examine the development of astronomy, math, and science in ancient Mesopotamian science.
Akkadian era – 3000 – 2000 BCE.
Sumerian city-state kings fought over land from 3000 to 2000 B.C.
Sargon of Akkad was powerful leader, creator of worldʼs first empire – took over northern and southern Mesopotamia around 2350 B.C. – empire—many different peoples, lands controlled by one ruler (emperor) The Akkadian Empire
Sargonʼs empire was called the Akkadian Empire. This included the Fertile Crescent—lands from Mediterranean Sea to Persian Gulf
Known for rich soil, water, and good farming
Sargonʼs conquests spread Akkadian ideas, culture, writing system. Empires encourage trade and may bring peace to their peoples. Peoples of several cultures share ideas, technology, customs.
Babylonian mathematics
As early as 2000 BCE, Babylonians used pre-calculated tables to assist with arithmetic such as:
This became useful for their early astronomy.
Babylonians developed advanced forms of geometry, some of which was used in astronomy.
Info above comes from Houghton Mifflin Historical-Social Science: World History: Ancient Civilizations: Eduplace Social studies review: LS_6_04_01. This historical overview is brief, and by necessity, highly simplified.
Metallurgy
Chemistry connections
http://www.anvilfire.com/21centbs/stories/rsmith/mesopotamia_1.htm
“[People in ancient mesopotamia] made substantial advances in crafting higher quality bronze tools and weapons. It took trade to relatively distant places – because tin ore caches are sparse – to create tin-alloy bronze. This was the standard to aim for in the ancient world – and also prevented metal-smiths from developing limps and dying of gradual arsenic poisoning. (not joking)”
Babylonian era
First Babylonian dynasty – Amorite Dynasty, 1894–1595 BCE
Early Iron Age – Native Rule, Second Dynasty of Isin, 1155–1026 BCE
Assyrian rule, 911–619 BCE
Let’s look at this same area. in its larger geographical context:
This empire was very similar to the Akkadians. 1792-1749 BCE.
King Hammurabi of Babylon is a major figure.
• Akkadian Empire lasted about 200 years
• Amorites invaded Sumer about 2000 B.C., chose Babylon as capital
• Hammurabi—powerful Amorite king who ruled from 1792 to 1750 B.C.
– extended empire across Mesopotamia, Fertile Crescent
– appointed governors, tax collectors, judges to control lands
– watched over agriculture, trade, construction
Babylonians recognize that astronomical phenomena are periodic (e.g. the annual cycle of the Earth-Sun system)
The motion of the moon, and tides, are more examples of periodic phenomenon
Although they did not know the physical reasons why such patterns existed, they discovered the mathematical periodicity of both lunar and solar eclipses.
Centuries of Babylonian observations of celestial phenomena are recorded in the series of cuneiform tablets known as the Enûma Anu Enlil
Astronomical studies of the planet Venus
Writing of the “Mul Apin” clay tablets, catalogs of stars and constellations, heliacal rising dates of stars, constellations and planets
Babylonian cosmology
They developed a view of the universe in which our Earth was essentially flat, with several layers of heavens above, and several layers of underworlds below.
This diagram roughly shows their view of the universe – but note that this image is not meant to be geocentric. They didn’t imply that our world is the center of the universe; this was just what the universe was imagined to be like, locally.
The idea that our Earth is literally the center of the entire universe (geocentrism) didn’t develop until the later Greek era, circa the time of Aristotle.
“A six-level universe consisting of three heavens and three earths:
two heavens above the sky, the heaven of the stars, the earth, the underground of the Apsu, and the underworld of the dead.
The Earth was created by the god Marduk as a raft floating on fresh water (Apsu), surrounded by a vastly larger body of salt water (Tiamat).
The gods were divided into two pantheons, one occupying the heavens and the other in the underworld. ”
– History of cosmology, from Astronomy 123: Galaxies and the Expanding Universe
Assyrian empire 850 – 609 BCE
• Assyrian Empire replaced Babylonian Empire
• Located in hilly northern Mesopotamia
– built powerful horse and chariot army to protect lands
– soldiers were the only ones in the area to use iron swords, spear tips
– used battering rams, ladders, tunnels to get past city walls
• Assyrians were cruel to defeated peoples
• Enemies who surrendered were allowed to choose a leader.
Enemies who resisted were taken captive, and killed or enslaved.
• Enemy leaders were killed, cities burned
• Captured peoples were sent into exile
• Assyrian Empire fell in 609 B.C.
– defeated by combined forces of the Medes and Chaldeans
– victors burned the Assyrian capital city of Nineveh
Science
Astronomers of their day discovered a repeating 18-year Saros cycle of lunar eclipses
(data for this GIF is from http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros101.html)
Chaldean Empire/Neo-Babylonian empire 625 – 539 BCE
• Chaldeans ruled much of former Assyrian Empire
– sometimes called New Babylonians because Babylon was capital
• Chaldean empire peaked from 605 to 562 B.C. under Nebuchadnezzar II
– took Mediterranean trading cities, drove Egyptians out of Syria
• Nebuchadnezzar seized Jerusalem when the Hebrews rebelled in 598 B.C.
– destroyed the Jewish people’s Temple in Jerusalem, and held many captive in Babylon for about 50 years. (Many Jews returned to their homeland under Cyrus the Great.)
At the height of their wealth and power, the Chaldeans:
• Nebuchadnezzar built Babylonʼs Ishtar Gate, Tower of Babel ziggurat
• Built the Hanging Gardens of Babylon, one of Seven Wonders of the World
– an artificial mountain covered with trees, plants
The Empire Fades
• Weak rulers followed Nebuchadnezzar II
• Internal conflicts over religion divided Chaldean people
– made it easy for Cyrus The Great, King of Persia to conquer land
Post-Chaldean Babylonians
Jesse Emspak, in the Smithsonian, “Babylonians Were Using Geometry Centuries Earlier Than Thought” 1/28/16
As one of the brightest objects in the night sky, the planet Jupiter has been a source of fascination since the dawn of astronomy.
Now a cuneiform tablet dating to between 350 and 50 B.C. shows that Babylonians not only tracked Jupiter, they were taking the first steps from geometry toward calculus to figure out the distance it moved across the sky.
Obliquity of the Nine Planets http://solarviews.com/eng/solarsys.htm
Mathieu Ossendrijver of Humboldt University in Berlin found the tablet while combing through the collections at the British Museum.
The written record gives instructions for estimating the area under a curve by finding the area of trapezoids drawn underneath.
Using those calculations, the tablet shows how to find the distance Jupiter has traveled in a given interval of time.
The distance travelled by Jupiter after 60 days, 10º45′,
computed as the area of the trapezoid whose top left corner is Jupiter’s velocity over the course of the first day, in distance per day, and its top right corner is Jupiter’s velocity on the 60th day.
In a second calculation, the trapezoid is divided into two smaller ones,
with equal area to find the time in which Jupiter covers half this distance.
Photo credit: Trustees of the British Museum/Mathieu Ossendrijver
http://www.space.com/31765-ancient-babylonians-tracked-jupiter-with-math.html
Until now, this kind of use of trapezoids wasn’t known to exist before the 14th century.
“What they are doing is applying it to astronomy in a totally new way,” Ossendrijver says. “The trapezoid figure is not in real space and doesn’t describe a field or a garden, it describes an object in mathematical space—velocity against time.”
Scholars already knew that Babylonians could find the area of a trapezoid, and that they were quite familiar with the motions of planets and the moon. Previous records show that they used basic arithmetic—addition, subtraction, multiplication and division—to track these celestial bodies.
By 400 B.C. Babylonian astronomers had worked out a coordinate system using the ecliptic, the region of the sky the sun and planets move through, Ossendrijver says. They even invented the use of degrees as 360 fractions of a circle based on their sexagesimal, or base 60, counting system. What wasn’t clear was whether the Babylonians had a concept of objects in abstract mathematical space.
The trapezoid method involves learning the rate at which Jupiter moves and then plotting the planet’s speed against a set number of days on an x-y graph. The result should be a curve on the graph. Figuring out the area of trapezoids under this curve gives a reasonable approximation of how many degrees the planet has moved in a given period.
Babylonians Were Using Geometry Centuries Earlier Than Thought, Smithsonian Magazine
External references
https://en.wikipedia.org/wiki/Babylonian_astronomy
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Understandings about the Nature of Science: Science knowledge has a history that includes the refinement of, and changes to, theories, ideas, and beliefs over time.
Science Is a Human Endeavor: Scientific knowledge is a result of human endeavor,
imagination, and creativity. Individuals and teams from many nations and cultures have contributed to science and to advances in engineering.
Massachusetts History and Social Science Curriculum Framework
Mesopotamia: Site of several ancient river civilizations circa 3500–1200 BCE
7.10 Describe the important achievements of Mesopotamian civilization.
Next Generation Science Standards
HS-ESS1 Earth’s Place in the Universe
Construct an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. (HS-ESS1-2)
Apply scientific reasoning to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. (HS-ESS1-6)
Engaging in Argument from Evidence: Use appropriate and sufficient evidence and scientific reasoning to defend and critique claims and explanations about the natural and designed world(s). Arguments may also come from current scientific or historical episodes in science.
Connections to Nature of Science:
Science Models, Laws, Mechanisms, and Theories Explain Natural Phenomena.
A scientific theory is a substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment, and the science community validates each theory before it is accepted. If new evidence is discovered that the theory does not accommodate, then the theory is generally modified in light of this new evidence. (HS-ESS1-2),(HS-ESS1-6)
The nature of reality
What is the ultimate nature of reality? This the core questions of physics, as well as of classical, rationalist philosophy. We now know that this question relates to interpretations of quantum mechanics.
“Those are the kind of questions in play when a physicist tackles the dry-sounding issue of, “what is the correct interpretation of quantum mechanics?” About 80 years after the original flowering of quantum theory, physicists still don’t agree on an answer. Although quantum mechanics is primarily the physics of the very small – of atoms, electrons, photons and other such particles – the world is made up of those particles. If their individual reality is radically different from what we imagine then surely so too is the reality of the pebbles, people and planets that they make up.”
The Many Interpretations of Quantum Mechanics, Graham P. Collins, Scientific American, November 19, 2007
To what can we compare our knowledge of the universe?
The allegory of Plato’s cave
The Allegory of the Cave was presented by the Greek philosopher Plato the Republic (380 BCE) He retells an analogy created by Socrates, about people who think that they know the true nature of reality – however, as the analogy progresses, we find that they have no idea what the real world is like at all.
The idea is that most people don’t actually understand our own real world – and that we never will without philosophical and scientific inquiry.
Socrates says to imagine a cave where people have been imprisoned from childhood. They are chained so that their legs and necks are fixed, forcing them to gaze at the wall in front of them, and not look around at the cave, each other, or themselves
Behind the prisoners is a fire, and between the fire and the prisoners is a raised walkway with a low wall, behind which people walk carrying objects or puppets “of men and other living things”
The masters walk behind the wall – so their bodies do not cast shadows for the prisoners to see. But the objects they carry cast shadows. The prisoners can’t see anything behind them : they only able see the shadows cast on the cave wall in front of them. The sounds of people talking echo off the wall, so the prisoners falsely believe these sounds come from the shadows.
The shadows constitute reality for the prisoners – because they have never seen anything else. They do not realize that what they see are shadows of objects in front of a fire, much less that these objects are inspired by real living things outside the cave
The philosopher (or scientist) is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, for he can perceive the true form of reality – rather than the mere shadows seen by the prisoners.
Plato then supposes that one prisoner is freed: he turns to see the fire. The light would hurt his eyes and make it hard for him to see the objects that are casting the shadows. If he is told that what he saw before was not real but instead that the objects he is now struggling to see are, he would not believe it. In his pain the freed prisoner would turn away and run back to what he is accustomed to, the shadows of the carried objects.
Plato continues: “suppose…that someone should drag him…by force, up the rough ascent, the steep way up, and never stop until he could drag him out into the light of the sun.” The prisoner would be angry and in pain, and this would only worsen when the light of the sun overwhelms his eyes and blinds him.” The sunlight represents the new knowledge that the freed prisoner is experiencing.
Slowly, his eyes adjust to the light of the sun. First he can only see shadows. Gradually he can see reflections of people and things in water, and then later see the people and things themselves. Eventually he is able to look at the stars and moon at night until finally he can look upon the sun itself (516a). Only after he can look straight at the sun “is he able to reason about it” and what it is.
- adapted from “Allegory of the Cave.” Wikipedia, The Free Encyclopedia. 29 May. 2016. Web. 3 Jun. 2016
Another illustration of Plato’s cave.
Are the laws of physics really absolute?
One of the major goals of physics is to emerge from the relative ignorance of the cave, and venture out into an understanding of the real world – how our universe really works.
We have made remarkable progress in doing so – everything we have learned in classical physics over the last two millennia is part of the human adventure.
What we have learned is, in an important sense, “real.” Physics lets us ask specific questions and then use math to make specific answers. We then compare our predictions to the way that universe really works.
Yet we need to be careful – we could make the mistake of using physics equations as if they are absolutely true. Yes, they certainly are true in the sense that they work. But are these math equations the absolute truth themselves – or are they really emerging from a deeper phenomenon? See The laws of physics are emergent phenomenon.
Is nature a simulation?
The simulation hypothesis proposes that our reality is actually some kind of super detailed computer simulation. This hypothesis relies on the development of a simulated reality, a proposed technology that would seem realistic enough to convince its inhabitants. The hypothesis has been a central plot device of many science fiction stories and films.
Simulation hypothesis (Wikipedia)
Video Why Elon Musk says we’re living in a simulation: YouTube, Vox
Elon Musk thinks we’re characters in a computer simulation. He might be right.
Is the Universe a Simulation? Scientists Debate
Nick Bostrom: Are you living in a computer simulation?
Is the universe a hologram?
The holographic principle is a principle of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region—preferably a light-like boundary like a gravitational horizon.
First proposed by Gerard ‘t Hooft, it was given a precise string-theory interpretation by Leonard Susskind who combined his ideas with previous ones of ‘t Hooft and Charles Thorn.
As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. In a larger sense, the theory suggests that the entire universe can be seen as two-dimensional information on the cosmological horizon. – Wikipedia
Our Universe May Be a Giant Hologram
Study reveals substantial evidence of holographic universe
Space’The Holy Grail for Physicists’: First Evidence Universe is a Hologram Uncovered
To learn more about quantum mechanics
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.
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…
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.”
External links
The Many Interpretations of Quantum Mechanics, Scientific American
Tom’s Top 10 interpretations of quantum mechanics
Learning Standards
SAT Subject Test: Physics
Quantum phenomena, such as photons and photoelectric effect – Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles.
AP Physics Curriculum Framework
Essential Knowledge 1.D.1: Objects classically thought of as particles can exhibit properties of waves.
a. This wavelike behavior of particles has been observed, e.g., in a double-slit experiment using elementary particles.
b. The classical models of objects do not describe their wave nature. These models break down when observing objects in small dimensions.
Learning Objective 1.D.1.1:
The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties.
Essential Knowledge 1.D.2: Certain phenomena classically thought of as waves can exhibit properties of particles.
a. The classical models of waves do not describe the nature of a photon.
b. Momentum and energy of a photon can be related to its frequency and wavelength.
Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies
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