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Teaching three dimensional geometry in high school
Most school districts still make students master a one-size-fits all sequence of geometry topics and skills that is largely unchanged since the 1800s. Does this inspire students to love math, become mathematicians, engineers, or physicists? Does it provide the mathematical literacy necessary for people to function in society?
The endless system of curriculum reforms over the last century (*) hasn’t helped achieve either goal. Some students do fall in love with math and science, but usually in spite of curriculums, not because of them.
School districts are pressured to have standardized state exams. Some pressure is from parents who think that good education means doing it the same way that it always has been done. (And to be sure, it is important to have mastery of some basic geometry topics.) Yet most pressure is from politicians. How? Textbook publishing companies give campaign donations to politicians; they want them to enact a constant stream of new curricula so they can sell new learning materials and tests. Students are stuck in a system in which the voices of expert math and science teachers are minimized.
How does this issue relate to geometry in specific? Students are relentlessly drilled on two dimensional geometry, and how to construct proofs. Many students dread this; they find it disconnected from daily life, devoid of fun, and not instilling any sense of wonder.
Yet when we talk to actual mathematicians we learn that they they investigate interesting and fun problems in geometry; they find almost mystical connections between the laws of math and laws of the universe itself; and they use geometry not in two dimensions, but in three.
They use geometry for engineering and building; machining and 3D printing parts, metalwork, and tools; they use 3D polygon design for computer programming and making video games.
Where is all of this in our schools? It is time to listen to math teachers, mathematicians, and people who use these ideas for work or art. We should reduce the amount of time we spend on geometry proofs, and increase the use of fun, interesting and practical 3D geometry.
– Robert Kaiser
(*) Left Back: A Century of Battles over School Reform, Diane Ravitch
Presented below is an example of transforming two dimensional geometry into three dimensional geometry, which has applications in sports, engineering, and videogames.
First, consider regular, convex polygons Mathsisfun.com Regular polygons
Here are the basic regular and irregular polygons.
Now consider shapes in three dimensions: A polyhedron (plural polyhedra or polyhedrons) is a 3D shape with flat polygonal faces, straight edges and sharp corners or vertices.
The five convex examples have been known since antiquity and are called the Platonic solids:
The triangular pyramid or tetrahedron, cube, octahedron, dodecahedron and icosahedron:
Look at 2D pentagons and hexagons – consider: Do they tile together without gaps or overlaps?
If so then show us…. But if not then how can we get such tiles to fit tightly without overlap or gaps?
We need to assemble them together into a 3D structure. What do we mean by 3 dimensional?
Questions: How many tiles of each type will we need? How do we arrange them? Is there more than way to do this, or just one way?
Procedure
Give students hexagon and pentagon templates (on heavy card stock.)
They will trace multiple copies of each one onto card stock or construction paper.
Carefully cut out all of these pieces. Assemble them together into a 3D structure with a regular, repeating pattern. The resulting shape should have no gaps or overlap.
How do we use geometry in real life
Geometry in real life: careers and at home
Related readings
The (Math) Problem With Pentagons.
“Three pentagons at a vertex gives us 324 degrees, which leaves a gap of 36 degrees that is too small to fill with another pentagon. And four pentagons at a point produces unwanted overlap. No matter how we arrange them, we’ll never get pentagons to snugly match up around a vertex with no gap and no overlap. This means the regular pentagon admits no monohedral, edge-to-edge tiling of the plane.”
The (Math) Problem With Pentagons. Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives? Patrick Honner, Quanta Magazine, 12/11/2017
Two-Dimensional Math In a Three-Dimensional World, Marjorie Senechal & George Fleck, Education Week, 2/6/1985
Week Five: Make Something Big, Daniel B. Rosenberg
Building a buckyball, PBS NOVA
Learning Standards
Common Core Math – Geometric Measurement and Dimension
• Explain volume formulas and use them to solve problems
• Visualize relationships between two-dimensional and three-dimensional objects
CCSS.MATH.CONTENT.HSG.MG.A.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*
Appendix A Common Core Math, Unit 3: Extending to Three Dimensions
Visualize the relation between two dimensional and three-dimensional objects.
Apply geometric concepts in modeling situations.
National Council of Teachers of Mathematics, Standards and Positions
Grades 9–12 Expectations: In grades 9–12 each and every student should – Analyze properties and determine attributes of two- and three-dimensional objects; Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.
Influenza vaccine
“Flu” is short for “influenza virus”.
How are influenza vaccines made?
The US CDC and other labs partner with the World Health Organization (WHO) to choose certain virus strains to send to private vaccine manufacturers.
The flu can mutate and strains can change each year, meaning new vaccines are needed for every flu season.
The selected virus is injected into a fertilized hen’s eggs, where it incubates and replicates for a few days — just as it would do inside a human host.
Scientists then harvest fluid containing the virus from the egg.
They inactivate the virus so it can no longer cause disease, and purify it, leaving scientists with the virus antigen.
The antigen is the crucial element — it’s a substance released by the virus that triggers your immune system to respond. That’s how the vaccine prepares your immune system for a real infection.
The entire process, from the arrival of the egg to the publicly available vaccine, takes at least six months, according to the CDC.
Why does the flu vaccine seem to make some people sick?
Vaccines merely stimulate our immune system, which temporarily creates non-specific responses. For example, redness, swelling, small increase in body temperature.
These are not a sign of infection. Rather, they are the normal signs that your body is developing defenses against the antigen.
How effective is the influenza vaccine?
How effective are influenza vaccines?
No one claims that vaccines are 100% effective. No medical technique is 100% effective. Most vaccines are very effective, usually over 90% effective.
However, that is not yet the case for flu vaccines. The flu virus evolves through natural selection, like all viruses and life, and it happens to evolve very quickly.
“CDC conducts studies each year to determine how well the influenza (flu) vaccine protects against flu illness. While vaccine effectiveness can vary, recent studies show that flu vaccination reduces the risk of flu illness by between 40% and 60% among the overall population during seasons when most circulating flu viruses are well-matched to the flu vaccine. In general, current flu vaccines tend to work better against influenza B and influenza A(H1N1) viruses and offer lower protection against influenza A(H3N2) viruses.”
Vaccine Effectiveness – How Well Does the Flu Vaccine Work? CDC (Centers for Disease Control)
So if it isn’t perfect, why use this vaccine at all?
Excerpted from the CDC article:
Keeps you from getting sick with flu.
Reduces risk of flu-associated hospitalization, including among children and older adults.
Flu vaccination lowers rates of some cardiac (heart) events among people with heart disease
Reduces chances of being hospitalized among people with diabetes (79%) and chronic lung disease (52%).
Helps protect women during and after pregnancy. Getting vaccinated can also protect a baby after birth from flu. (Mom passes antibodies onto the developing baby during her pregnancy.)
Vaccination reduced the risk of flu-associated acute respiratory infection by about one half
Significantly reduces a child’s risk of dying from influenza.
It can make your illness milder even if you do get sick.
Most importantly, it protects people around you, including those who are more vulnerable to serious flu illness, like babies and young children, older people.
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Why don’t we yet have a vaccine for HIV/AIDS?
Intro – What is HIV?
HIV (human immunodeficiency virus) is a virus that attacks cells that help the body fight infection, making a person more vulnerable to other infections and diseases.
It is spread by contact with certain bodily fluids of a person with HIV, most commonly during unprotected sex (sex without a condom or HIV medicine to prevent or treat HIV), or through sharing injection drug equipment.
HIV leads to the disease AIDS (acquired immunodeficiency syndrome).
The human body can’t get rid of HIV and no effective HIV cure exists. So, once you have HIV, you have it for life.
from HIV.Gov
HIV/AIDS vaccine: Why don’t we have one after 37 years, when we have several for COVID-19 after a few months?
Ronald C. Desrosiers writes
HIV has evolved an ability to generate and to tolerate many mutations in its genetic information. The consequence of this is an enormous amount of variation among strains of the virus not only from one individual to another but even within a single individual.
Let’s use influenza for a comparison. Everyone knows that people need to get revaccinated against influenza virus each season because of season-to-season variability in the influenza strain that is circulating.
Well, the variability of HIV within a single infected individual exceeds the entire worldwide sequence variability in the influenza virus (*) during an entire season.
What are we going to put into a vaccine to cover this extent of strain variability?
HIV has also evolved an incredible ability to shield itself from recognition by antibodies. Enveloped viruses such as coronaviruses and herpes viruses encode a structure on their surface that each virus uses to gain entry into a cell.
This structure is called a “glycoprotein,” meaning that it is composed of both sugars and protein.
But the HIV envelope glycoprotein is extreme. It is the most heavily sugared protein of all viruses in all 22 families. More than half the weight is sugar.
And the virus has figured out a way, meaning the virus has evolved by natural selection, to use these sugars as shields to protect itself from recognition by antibodies that the infected host is trying to make. The host cell adds these sugars and then views them as self.
These properties have important consequences relevant for vaccine development efforts. The antibodies that an HIV-infected person makes typically have only very weak neutralizing activity against the virus.
Furthermore, these antibodies are very strain-specific; they will neutralize the strain with which the individual is infected but not the thousands and thousands of other strains circulating in the population.
Researchers know how to elicit antibodies that will neutralize one strain, but not antibodies with an ability to protect against the thousands and thousands of strains circulating in the population. That’s a major problem for vaccine development efforts.
HIV is continually evolving within a single infected individual to stay one step ahead of the immune responses. The host elicits a particular immune response that attacks the virus. This puts selective pressure on the virus, and through natural selection a mutated virus variant appears that is no longer recognized by the individual’s immune system. The result is continuous unrelenting viral replication.
Life cycle of HIV
Source: HIV/AIDS vaccine: Why don’t we have one after 37 years, when we have several for COVID-19 after a few months? By Ronald C. Desrosiers, TheConversation.com, 5/17/2021
(*) Evolutionary and immunological implications of contemporary HIV-1 variation
Bette Korber, Brian Gaschen, Karina Yusim, Rama Thakallapally, Can Kesmir, Vincent Detours
British Medical Bulletin, Volume 58, Issue 1, September 2001, Pages 19–42, https://doi.org/10.1093/bmb/58.1.19
Learning Standards
Massachusetts Comprehensive Health Curriculum Framework
Students will gain the knowledge and skills to select a diet that supports
health and reduces the risk of illness and future chronic diseases. PreK–12 Standard 4
8.1 Describe how the body fights germs and disease naturally and with medicines and
immunization
8.2 Identify the common symptoms of illness and recognize that being responsible for individual health means alerting caretakers to any symptoms of illness.
8.5 Identify ways individuals can reduce risk factors related to communicable and chronic diseases
8.6 Describe the importance of early detection in preventing the progression of disease.
8.7 Explain the need to follow prescribed health care procedures given by parents and health care providers.
8.8 Describe how to demonstrate safe care and concern toward ill and disabled persons in the family, school, and community.
8.13 Explain how the immune system functions to prevent and combat disease
Interdisciplinary Learning Objectives: Disease Prevention and Control
8.a. (Law & Policy. Connects with History & Social Science: Geography and Civics &
Government) Analyze the influence of factors (such as social and economic) on the treatment and management of illness.
Benchmarks for Science Literacy, AAAS
The immune system functions to protect against microscopic organisms and foreign substances that enter from outside the body and against some cancer cells that arise within. 6C/H1*
Some allergic reactions are caused by the body’s immune responses to usually harmless environmental substances. Sometimes the immune system may attack some of the body’s own cells. 6E/H1
Some viral diseases, such as AIDS, destroy critical cells of the immune system, leaving the body unable to deal with multiple infection agents and cancerous cells. 6E/H4
Vaccines induce the body to build immunity to a disease without actually causing the disease itself. 6E/M7** (BSL)
This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
§107. Limitations on Exclusive Rights: Fair Use. Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include: the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; the nature of the copyrighted work; the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)
How to be an ally to Jewish students and families
Over the last decade antisemitism has increased dramatically in the United States. An increasing number of students in public schools and colleges report being made to feel unwelcome or unsafe; violent attacks and death threats have been on the rise.
Jews in America are the target of 60 percent of all religiously motivated hate crimes in the US. This is despite Jewish people constituting a mere two percent of the population, newly released FBI statistics for 2020 have shown.
“New data analysis of the just-released FBI hate crime statistics uncovers a disturbing trend in the United States: Jews are at least three times more likely to experience a hate crime in America than any other ethnic group.
The Federal Bureau of Investigation recently released its Hate Crime Statistics Report highlighting troubling trends related to hate crimes against Jews. According to the report, Jewish people were the targets of over 60% of religious bias-related hate crimes. Jews were targeted at significantly higher rates than any other religious group.
This data indicates an increase of 41% since 2015. Over the past decade, hate crimes targeting Jews topped the charts every year, with rates ranging from 52% to 67% of the total religious bias crimes.
Factoring in the relative proportion of Jews from the total US population, this analysis highlights an alarming result: A Jewish person is three times more likely to experience a hate crime than African Americans and thirteen times more likely than Hispanic Americans.
These comparisons are not intended to diminish anyone’s suffering; however, these numbers are alarming and require deep evaluation. Antisemitic rhetoric, vandalism, and intimidation have become normalized in the US in recent years. Whether it takes place on social media, in the public square, or even in Congress. It is no wonder that such trends would escalate to violent hate crimes against Jewish people on the streets, in our places of worship, and even in our homes.”
Jews are top target for hate crimes in US, FBI data shows
As teachers we have an obligation to insure that all of our students and their families are safe and welcome in our schools.
Teachers of all backgrounds work to understand students of all backgrounds, and we learn to recognize bigotry so that we can keep that out of our schools.
An important point in being an anti-racist is listening to voices. Make space to learn from the lived experiences of our Jewish students and their families.
A Jewish Resistance to antisemitism
Antisemitism Stories
Antisemitism Today
ChallahBackGirls – perspective from Jewish teens
Jewish On Campus
Stop Antisemitism
This Modern Jew
“You Don’t Look Jewish”
Being anti-racist includes being an anti-antisemite.
No one is born racist or antiracist; these result from the choices we make. Being antiracist results from a conscious decision to make frequent, consistent, equitable choices daily. These choices require ongoing self-awareness and self-reflection as we move through life. In the absence of making antiracist choices, we (un)consciously uphold aspects of white supremacy, white-dominant culture, and unequal institutions and society. Being racist or antiracist is not about who you are; it is about what you do.
– Talking About Race. Being Antiracist. National Museum of African American History and Culture, Smithsonian
“To be antiracist is a radical choice in the face of history, requiring a radical reorientation of our consciousness.”
Ibram Kendi, “How to be an Antiracist”
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Include Jews in your activism
Antisemitic Incidents: Being an Ally, Advocate and Activist, ADL
Include Jews in Your Activism
An unheard hatred: how anti-Semitism is dangerously ignored
It’s Time for Intersectionality to Include the Jews
Start Including Jewish People In Your Activism, Her Campus
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Best Practices When Teaching About Native American Peoples
Some helpful links:
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Indigenous peoples of the Americas, the pre-Columbian peoples of North and South America and their descendants
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Native Americans in the United States
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Indigenous peoples in Canada, the indigenous peoples of Canada
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First Nations, indigenous Canadians who are neither Inuit or Métis
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Inuit, indigenous peoples inhabiting the Arctic region
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Métis in Canada, people who trace their descent to indigenous First Nations peoples and European settlers
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Learning Standards
Toward Responsibility: Social Studies Education that Respects and Affirms Indigenous Peoples and Nations, National Council for the Social Studies, 3/2018
The National Council for the Social Studies recognizes the responsibility of social studies education to respect and affirm Indigenous peoples, nations, and sovereignty. NCSS supports the creation and implementation of social studies curricula that explicitly present and emphasize accurate narratives of the lives, experiences, and histories of Indigenous Peoples, their sovereign Nations, and their interactions—past, present, and future—with Euro-American settlers and the government of the United States of America.
Glycans (polysaccharides and oligosaccharides)
Glycans are polymers of individual sugar molecules (monosaccharides)
Here’s a glucose, a simple sugar monomer (single unit.) Note that there are also many other types of sugars.
What’s the difference between monomers and polymers?
Living things can link many sugars together into a polymer – a glycan.
Here’s one example:
Glycans are made by all living things and by many viruses.
Glycans can be free (not bonded to anything else.) In this state they are often used to store chemical energy, or as building blocks for plant cell walls.
Glycans can be bonded together with a protein or a lipid. In such cases they have specific jobs.
• When bonded with a protein they’re called glycoproteins.
• When bonded with a lipid they’re called glycolipids.
Types of glycans
Cellulose – glucose monosaccharides linked to one another in a long, linear chain.
Used for structural support in cell walls of plants and algae.
Trees and plants use these glycans as building blocks.Here we see them linking together until they build the structure of a leaf, a stem, or branch.

From Direct evidence for α ether linkage between lignin and carbohydrates in wood cell walls, Hiroshi Nishimura et al, Scientific Reports volume 8, Article number: 6538 (2018)
Starch is made in plants. This molecule is used for energy storage.
Glycogen – used for energy storage in fungi and animals.
Comparison of cellulose, starches, and glycogen
Uses of glycans in the body
In breast milk
Human milk oligosaccharides are found in breast milk.
Human milk oligosaccharides(HMOs)
On cell membranes
They are found in cell membranes (lipid bilayers) as glycans attached to proteins – glycoproteins.
Immune system
I don’t know if any glycoproteins evolved to be part of the immune system, but I do know that they became a part of the immune system – various pathogens can recognize some glycans and use them as part of a pathway to infect a cell. Some antibodies interact with them.
Uses in bacteria
We find peptidoglycan in bacterial cell walls.
Medical uses
They are valuable diagnostic and therapeutic targets.
How to draw glycans, the exact way
On the left we see a skeletal drawing of a single sugar molecule, glucose. In the middle we see two sugars bonded together to make a sucrose molecule. (disaccharide, i.e. a molecule with 2 sugars.)
On the right we see a starch, which is a more complex structure of several sugars covalently bonded.
On the bottom we see a much more complex assembly of sugar molecules bonded together N-Glycan, in this case mostly a bunch of sucrose molecules bonded together.
The advantage of drawing glycans this way is that we see their exact structure.
The disadvantage of of drawing glycans this way is that it is super difficult to do when drawing freehand, it ain’t that even easy when using an app, and finally – being “exact” isn’t always an advantage! Look at that last molecule. Yes, if you look at it long enough you might figure out that it is a bunch of sugars.
But what about complex molecules like this that are made of many different types of sugars? It would be very difficult to interpret a drawing. Thus we have developed an easier way to visually represent them!
How to draw glycans: the easier way
There is a standard Symbol Nomenclature for Glycans (SNFG).
It is from the National Center for Biotechnology Information, U.S. National Library of Medicine.
Super easy to read, each color and shape represents a different sugar.
On the top is an example of a glycan in which we draw the name of each sugar. Technically correct but hard to read.
So below it we show the easier way to draw and color the glycan, so we can see which sugars it is made of.
Another example: Here are seven sugars (monosaccharides.)
And here they are linked together. The atom by atom details are not necessary.
Articles
Recent Advances in Nutritional Sciences: An Overview of Glycans and miRNAs, Marcello Menapace
Mathematics in science fiction
Mathematics in science fiction
The three leading Mathematicians in contemporary American Science Fiction are:
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- Professor Vernor Vinge – recently retired from teaching Mathematics in a major San Diego, California, university so as to write full-time;
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- Professor Rudy Rucker – Ph.D. in Mathematical Logic; taught at San Jose State University, in the heart of Silicon Valley;
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- Professor Jonathan Vos Post : also known as Your Humble Webmaster, in the 2nd semester as part-time professor of mathematics at Woodbury University, in Burbank, California; with a B.S. in Mathematical Logic from Caltech, and 4 Mathematics papers written in the first 4 weeks of 2004 and submitted to journals and international conferences.
There is plenty of Fantasy and Science Fiction about Mathematics, including:
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- “Socrates and the Slave”, by Plato [date?] : Reprinted in Fantasia Mathematica;
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- “The Tachypomp”, by Edward Page Mitchell [18xx] : Originally published in a New York newspaper; arguably the first story ever about computer-enhanced human intelligence; idiot has what we would call a computer implanted in his skull, making him a genius; likely influenced the classic “Flowers for Algernon” and the botched film “Lawnmower Man”; Reprinted in Fantasia Mathematica;
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- “The Plattner Story”, by H.G. Wells [1896] : 4-D rotation makes 3-D object mirror-reversed;
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- “Peter Learns Arithmetic”, by H.G. Wells [18xx]: Reprinted in Fantasia Mathematica;
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- “Young Archimedes”, by Aldous Huxley [1924]: Peasant prodigy discovered by couple vacationing in Italy; explicitly shows boy rediscovery of a theorem of Pythagoras; warning: tragic ending. Reprinted in Fantasia Mathematica;
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- “The Captured Cross-Section”, by Miles J. Breuer, M.D. [1929] : A multi-dimesnional geometry fiction, where the Mathematician hero has to save his mathematician finacee; starts with some Linear Algebra, and quickly moves to a 4-D creature manifesting in our 3-D world; Reprinted in Fantasia Mathematica; has a sort of sequel by Greg Bear {to be done};
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- “The Death of Archimedes”, by Karel Capek [19xx] : Historically, we think that Archimedes was killed by an ignorant Roman soldier. In this tale, the soldier knew very well who Archimedes was, and the murder stems from the great Mathematician refusing to work for the Roman Army, after some fascinating discussion about the use of Mathematics in military science. Karl Capek wrote the famous Science Fiction play “R.U.R.” which introduced the word “robot”, and the SF novel “War with the Newts.” Reprinted in Fantasia Mathematica;
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- “Jurgen Proves it by Mathematics”, by James Branch Cabell [19xx] : Reprinted in Fantasia Mathematica;
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- “A. Botts and the Mobius Strip”, by William Hazlett Upson [19xx] : Reprinted in Fantasia Mathematica;
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- “God and the Machine”, by Nigel Balchin [19xx] : Reprinted in Fantasia Mathematica;
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- “Misfit”, by by Robert A. Heinlein [1939] : math prodigy Libby;
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- “And He Built a Crooked House–“, by Robert A. Heinlein [1940] : tesseract-projected-into-3D house folds into 4-D in California quake, with occupant inside; considered one of the most cited Mathematics story in modern fiction;
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- “Inflexible Logic”, by Russell Maloney [1940] : Old theory that enough monkeys typing on enough typewriters would eventually type all the books in the British Museum. In this story, six chimpanzees are put at six typewriters, and start typing flawlessly. The Mathematician has to decide whether or not to intervene, to save the Laws of probability. Reprinted in Fantasia Mathematica;
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- “No-sided Professor”, by Martin Gardner [1946] : First published in Esquire. A Mobius strip is a strip of paper with a half-twist, that has only one side. Is there a way to keep going and get no sides? And what if you could fold a person that way? Reprinted in Fantasia Mathematica; reprinted in Mathenauts; has a sequel “The Island of Five Colors”;
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- “Wall of Darkness”, by Arthur C. Clarke [1949] : topological weirdness;
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- “The Incomplete Enchanter”, by L. Sprague de Camp and Fletcher Pratt [1942] : in this novel, which had sequelae, a mathematical logic equation when read aloud as if a magical spell, is the key to travel to alternative universes, mostly ones inside what are fictions from our world;
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- “Pythagoras and the Psychoanalyst”, by Arthur Koestler [19xx] : Reprinted in Fantasia Mathematica;
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- “Mother and the Decimal Point”, by Richard Llewellyn [19xx] : Reprinted in Fantasia Mathematica;
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- “Superiority”, by Arthur C. Clarke [19xx] : Reprinted in Fantasia Mathematica;
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- “Expedition”, by Fredric Brown [19xx] : Reprinted in Fantasia Mathematica;
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- “The Universal Library”, by Kur Lasswitz [19xx] : Reprinted in Fantasia Mathematica; probably influenced Jorge Luis Borges’ “The Library of Babylon”;
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- “Postscript to The Universal Library”, by Willy Ley [19xx] : Reprinted in Fantasia Mathematica;
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- “John Jones’s Dollar”, by Harry Stephen Keeler [19xx] : The power of Compound Interest; clearly influenced “Door into Summer” by Robert Heinlein, and “Age of the Pussyfoot” by Frederick Pohl. Reprinted in Fantasia Mathematica;
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- “A Subway Named Mobius”, by A. J. Deutch [1950] : Boston’s transit authority (MBTA) build a new train line, and the network becomes some complicated that train vanishes, disappearing into multidimensional network topology, or something like that. The math is not correct, but the story is fun. Reprinted in Fantasia Mathematica; allegedly adapted to a movie;
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- “The Mathematical Voodoo”, by H. Nearing, Jr. [1951] : a collection of short stories (not a novel as claimed on the cover) originally printed in the Magazine of Fantasy & Science Fiction
[Curtis Books, paperback, number 123-07051-075, cover price 75 cents, 224 pages; contains these stories among others: “The Mathematical Voodoo”, “The Hyperspeherical Basketball”, “The Factitious Pentangle”, “The Malignant Organ.” Cleanth Penn Ransom is the math Professor protagonist, although his name is obviously a composite of three famous poet/critics. Title story reprinted in Fantasia Mathematica;
- “The Mathematical Voodoo”, by H. Nearing, Jr. [1951] : a collection of short stories (not a novel as claimed on the cover) originally printed in the Magazine of Fantasy & Science Fiction
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- “The island of Five Colors”, by Martin Gardner [1952] : sequel to “The No-sided Professor.” Characters try to solve the Four Color Theorem in Topology (which has been solved recently by a computer-assisted proof that few people can follow).
It gives a good summary of the Theorem, and then launches into a story about an imaginary African island divided into five simply-connected districts each of which borders the other four as well as the ocean. Professor Slapenarski is about to explain all, before he is kidnapped via a Klein Bottle by some sort of giant bug. Reprinted in Fantasia Mathematica;
- “The island of Five Colors”, by Martin Gardner [1952] : sequel to “The No-sided Professor.” Characters try to solve the Four Color Theorem in Topology (which has been solved recently by a computer-assisted proof that few people can follow).
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- “The Last Magician”, by Bruce Elliott [1952] : Magician with Klein Bottle baffles extraterrestrials. Reprinted in Fantasia Mathematica;
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- “FYI”, by James Blish [1953] : transfinite arithmetic;
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- “The Devil and Simon Flagg”, by Arthur Porges [19xx] : A deal-with-the-devil story with a unique twist: the Devil is challenged to prove Fermat’s Last Theorem. By the story’s end, he and the human are collaborating with enthusiasm, to the disgust of the man’s wife. Reprinted in Fantasia Mathematica; a short and somewhat different version was published under the title “The Devil a Mathematician Would Be”;
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- “Fantasia Mathematica”, edited by Clifton Fadiman [1956] : essential anthology;
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- “Occam’s Razor”, by David Duncan [1959] : explains Calculus of Variations;
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- “The Mathematical Magpie”, edited by Clifton Fadiman [1962] : essential anthology;
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- “Euclid Alone”, by William F. Orr [1975; in Orbit 16 anthology] : author is also a mathematician;
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- “Sorority House”, by Frederick Pohl (19zz) ;
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- various stories, by Norman Kagan [19zz] ;
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- “Solid Geometry”, by Ian McEwan [1976] : sort of a sequel to “No-sided Professor” [1946]
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- “Cosmos”, by Carl Sagan [19xx] : the novel (but not this film) has a particularly absurd subplot near the end, where the digits of “pi” are calculated to an immensely large distance, and a 2-D image of a circle appears, as if as the signature of God. This is absurd for several reasons, including: God has no reason to prefer Base 10; and Pi is Pi in any universe, regardless of the physics;
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- “Mathenauts”, by Rudy Rucker [19zz] : anthology;
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- various other books, by Rudy Rucker [19zz] ;
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- “Kandelman’s Krim”, by J. L. Synge [19zz] ;
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- “Luminous”, by Greg Egan [19zz]
- “Division by Zero”, by Ted Chiang [19zz]
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- others
: {to be done}
There are also Fantastic or Science Fictional MOVIES about Mathematics, most notably:
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- “A Subway Named Mobius”, by A. J. Deutch [1950]
: Reprinted in Fantasia Mathematica; allegedly adapted for film;
-
- Goodwill Hunting [1997]
: Directed by Gus Van Sant; screenplay by Matt Damon and Ben Affleck; starring Robin Williams as Sean Maguire, a janitor at MIT who has a natural gift for Mathematics;
-
- Pi [1998]
: Kabbalists and Wall Street goons chase a mathematician who has been going insane while earching for a pattern in the digits of Pi; the actual Greek lower case letter for “pi” is the official title of the film;
-
- A Beautiful Mind [2001]
: Directed by Ron Howard; adapted to screenplay by Akiva Goldman from the book by Sylvia Nasar; starring Russell Crowe as John Forbes Nash, the brilliant Game Theorist who redirected Economics with his discoveries at Princeton, and then was captive of hallucinatory schizophrenia for decades;
-
- Hypercube [2003]
: sequel to “Cube”, where 4-D geometry and a kind of time travel complicate things for a motley assortment of people trapped in a Military Industrial Complex deadly super-secret project;
-
- others
: {to be done}
And there are movies that have fragments of Mathematics:
-
- Return of the Pink Panther
: in the Lugash National Museum, we see the Star of Lakshmi, also known as the Star Polygon {8/2} which the Hindus use to symbolize Ashtalakshmi (the 8 forms of wealth); this figure is also widely used in traditional Mexican art;
-
- Last Year in Marienbad [1961]
: as Margherita Barile points out, Alain Resnais’ film has two players in the Game of Nim, alternately taking counters from one of 4 heaps of 1, 3, 5, and 7 counters at the start, with the player winning who moves last;
-
- The Avengers [date?]
: Uma Thurman descends a Penrose Stairway, and ends where she began. A Penrose Stairway famously appears in M. C. Escher’s prints “Ascending and Descending” and “House of Stairs”;
-
- The Man Without a Face [1993]
: Mel Gibson (as Justin McLeod) demonstrates the Perpendicular Bisector Theorem to Nick Stahl (as Chuck Norstadt);
-
- It’s My Turn [1980]
: as Margherita Barile points out, The Snake Lemma is explained in the first scene of this film by Claudia Weill, starring Michael Douglas and Jill Clayburgh;
- others : {to be done}
For illustrations of some of the above, see: Mathematics in Film For some examples of Mathematical concepts in stories not promarily about math, see: Mathematics in Literature For a "geneology" of my teachers' teachers' teachers, including many of the most famous Mathematcians in History, see: My Teachers' Teachers' Teachers For a web page about the Mathematics of "The Four Nines Problem", see: The Four Nines Problem I am not automatically assuming that all Computer Scientists are Mathematicians, although some are. Your Humble Webmaster is also in the Faculty Pool of the Computer Science Department of California State University, Los Angeles, but not teaching there this semester (state budget crisis). But there is a plethora of quasimathematical content in Computer-oriented Science Fiction: see the section on Cyberpunk in this web page.
Ecology and Biology in Science Fiction
Ecology and Biology in Science Fiction
Copyright 1996, 1997, 1998, 1999, 2000 by Magic Dragon Multimedia. All rights reserved Worldwide. May not be reproduced without permission. May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge.
We examine both works of fiction and important contemporaneous works on non-fiction which set the context for ecological Science Fiction and Fantasy. Some questions that we study include:
- How do living organisms grow and reproduce? (Tribbles, TV: Star Trek)
- What forces shape the evolution of species, including our own? Could humans evolve into something very different? (novel: Galapagos, by Kurt Vonnegut)
- What kind of planet is needed for living things and ecosystems to evolve? (novel: Red Mars, by Kim Stanley Robinson)
- What would a desert planet look like? (novel: Dune, by Frank Herbert)
- How does genetics create us–and recreate living things? (novel: Jurassic Park, by Michael Crichton)
- Could genetics make us immortal? (novel: The Children Star, by Joan Slonczewski)
- What if an alien invader tried to do us in–from within? (novel: Andromeda Strain, by Michael Crichton)
- What if the aliens decide they like us–too well? (novel: Dawn, by Octavia Butler)
Biology in Science Fiction: Syllabus by Prof. Joan Slonczewski. Prof. Joan Slonczewski describes her required reading list as follows (the hotlink shows the color art for each book):
- Barlowe’s Guide to Extraterrestrials, by Wayne Douglas Barlowe [New York: Workman Publishers, 1979] “In his classic guide, Wayne Douglas Barlowe’s brilliant portraits bring to life 50 aliens from science fiction literature: Larry Niven’s Thrint and his Puppeteer, Arthur C. Clarke’s Overlord, Frank Herbert’s Steersman, Robert Silverburg’s Sulidor and more. Humanoids, insectoids, reptillians-even protoplasmic, gaseous, and crystalline life forms-are all faithfully and naturalistically depicted so that you can now visualize what could only before be imagined.”
- The Time Machine, by H.G. Wells [New York: Bantam Books, 1895] “When the Time Traveler courageously stepped out of his machine for the first time, he found himself in the year 802,700 — and everything had changed. In another, more utopian age, creatures seemed to dwell together in perfect harmony. The Time Traveler thought he could study these marvelous beings — unearth their secret and then return to his own time-until he discovered that his invention, his only avenue of escape, had been stolen.”
- Galapagos, by Kurt Vonnegut [New York: Dell Publishing, 1985] “Galapagos takes the reader back one million years, to A.D. 1986. A simple vacation cruise suddenly becomes an evolutionary journey. Thanks to an apocalypse, a small group of survivors stranded on the Galapagos islands are about to become the progenitors of a brave new, and totally different human race. Here, America’s master satirist looks at our world and shows us all that is sadly, madly awry-and all that is worth saving.”
- Dune, by Frank Herbert [New York: Ace Books, 1965] “Set on the desert Planet Arrakis, a world more awesome than any other in literature, Dune begins the story of the man known as Muad’dib-and of a great family’s ambition to bring to fruition humankind’s most ancient and unattainable dream…”
- The Children Star, by Joan Slonczewski [Analog magazine serial; New York: Tor Books, 1999] “The Children Star — A world so alien that only children can be lifeshaped to live there. The Children Star features mind-bending genetic engineering, and tire-shaped creatures that evolved with triplex DNA and exotic amino acids. And which of the many circular- shaped life forms is actually an intelligent species with its own plans for the human colonists?”
- Dawn, by Octavia Butler [New York: Warner Books, 1987] “Xenogenesis: The birth of something new-and foreign. Lilith Iyapo awoke from a centuries long sleep…and found herself aboard the vast living spaceship of the Oankali. Alien creatures covered in writhing tentacles, the Oankali had saved every surviving human from a dying, ruined Earth. They healed the planet, cured cancer, increased human strength and disease resistance, and were now ready to help Lilith lead her people back to the Earth. But for a price. For the Oankali were genetic engineers. DNA manipulators. Gene traders. They planned to give us their alienness. They planned to take our humanity. They planned to interbreed. And there was no way to stop them.”
- Red Mars, by Kim Stanley Robinson [New York: Bantam Books, 1993] “For eons, sandstorms have swept the barren, desolate landscape of the red planet. For centuries, Mars has beckoned to mankind to come and conquer its hostile climate. Now, in the year 2026, a group of one hundred colonists is about to fulfill that destiny. John Boone, Maya Toitovna, Frank Chalmers, and Arkady Bogdanov lead a mission whose ultimate goal is to give Mars an Earth-like atmosphere. They will place giant satellite mirrors in Martian orbit to reflect light to the planet’s surface. Black dust sprinkled on the polar caps will capture warmth and melt the ice. And massive tunnels, kilometers in depth, will be drilled into the Martian mantle to create stupendous vents of hot gases. Against this backdrop of epic upheaval, rivalries, loves, and friendships will form and fall to pieces — for there are those who will fight to the death to prevent Mars from ever being changed.”
- Jurassic Park, by Michael Crichton [New York: Ballantine Books, 1990] “An astonishing technique for recovering and cloning dinosaur DNA has been discovered. Now, one of mankind’s most thrilling fantasies has come true. Creatures extinct for eons now roam Jurassic Park with their awesome presence and profound mystery and all the world can visit them-for a price. Until something goes wrong…”
- The Andromeda Strain, by Michael Crichton [New York: Ballantine Books, 1969] “What if there was a virus so lethal, it could kill people as quickly as they took a breath? What if it spared some people from instant death…but drove them hopelessly insane instead? What if the swiftest acting, deadliest, virus ever known to humankind could be spread, by no more than a gust of wind, from the remote desert site of its first massacre to the busiest cities in America…and the world? What, if anything, could stop it?”
- The Cartoon Guide to Genetics, by Larry Gonick and Mark Wheelis [New York: Harper Perennial, 1991] “Have you ever asked yourself: Are spliced genes the same as mended Levis? Watson and Crick? Aren’t they a team of British detectives? Plant sex? Can they do that? Is genetic mutation the name of one of those heavy metal bands? Asparagine? Which of the four food groups is that in? Then you need “The Cartoon Guide to Genetics” to explain the important concepts of classical and modern genetics.”
- Brain Plague, by Joan Slonczewski [New York: Tor Books, 2000] “What if alien microbes could give us whatever our brains imagined–at a price? ‘Brain Plague’ gives new epic meaning to hearing voices inside your head. Tune in or you’ll be sorry.” — Eva, Fantastica Daily
Joan Slonczewski's Book List
The following list is selected, permuted, and edited from: Themes/Genres in Science Fiction: An idiosyncratic and woefully incomplete list, by Kay Fowler ©All the material in this website is copyrighted to Kathleen L. Fowler unless explicitly indicated otherwise. Permission is granted to use and distribute this material freely but please attribute properly by retaining the full header information. 11/16/99 "This list has been constructed over time based on a list and categories originally constructed by the late Professor Ted Michelfeld and owing debts to a number of other sources including The Encyclopedia of Science Fiction. It is still under construction and by no means complete but it is a starting place. The categories are by no means as distinct as is suggested here. Most every one of these works could appear in multiple categories and in many cases I have assigned them rather arbitrarily to one of the many choices they might occupy."
Plagues/Disease/Epidemics:
- Mary Shelley. The Last Man (1826)
- Jack London. The Scarlet Plague (1915)
- George Stewart. Earth Abides (1949)
- Michael Critchton. The Andromeda Strain. (1969).
- Sherri Tepper. Grass (1989); Raising the Stones (1990) Sideshow (1992). Earth has become “Sanctity” controlled by fundamental relgionists. Rich exploration of themes of religion, ecology, social relationships, etc.
Agricultural/Ecological/Population Disasters:
- George Griffith. Olga Romanoff (1894) comet strike and alien invasion.
- M. P. Shield. The Purple Cloud (1901). poisonous gas.
- Arthur Conan Doyle. The Poison Belt (1913) the Earth passes through a poisonous ether
- J. J. Connington. Nordenholt’s Millions (1923) agricultural disaster
- S. Fowler Wright. Deluge (1928). flood.
- Philip Wylie. When Worlds Collide (1932). dying sun on collision course with Earth. Film: When Worlds Collide (1951).
- John Wyndham. The Day of the Triffids (1951) Venomous Plants.
- Isaac Asimov. Caves of Steel (1954) overpopulation — and a great mystery story
- John Christopher. The Death of Grass (a.k.a. No Blade of Grass) (1957)
- Robert Silverberg. Masters of Life and Death (1957). overpopulation.
- J. G. Ballard. “Billenium” (1961) population
- J. G. Ballard. The Drowned World. (1962). flood
- Kurt Vonnegut, Jr. Cat’s Cradle (1963) Ice-9
- J. G. Ballard, The Drought (aka The Burning World) 1965.
- Harry Harrison. Make Room! Make Room! (1966). Film: Soylent Green (1973).
- William F. Nolan and George Clayton Johnson.Logan’s Run (1967). Film: Logan’s Run (1967) Overpopulation; destruction of those over 30.
- Lee Tang. The Wind Obeys Lama Torus. (1967). From India. Overpopulation.
- John Brunner. Stand on Zanzibar. (1968). Young adult novel on overpopulation.
- James Blish. A Torrent of Faces (1968)
- Fred and Geoffrey Hoyle. The Inferno (1973). Cosmic radiation
- Nancy Bond. The Voyage Begun (1989). Young Adult. In a near future Cape Cod, dwindling resources, unemployment, and ecological damage combine to make the Cape a dangerous, and forlorn world.
- David Brin. Earth. (1990). Black hole.
- Karen Hesse. Phoenix Rising (1994). Young adult. A young girl on a farm in Vermont copes with the consequences of a nuclear accident in Massachusetts. Dedicated to the children of Chernobyl.
- Monica Hughes. Invitation to the Game. 1996. Young Adult. overpopulation and shrinking resources leave most unemployed and without hope — unless they can get into “the game”
- Jack McDevitt. Engines of God. (1997) Alien artifacts related to ancient mass destructions on a number of planets. Should we be worried?
- Mary Sullivan. Earthquake 2099. (1997) Young adult.
Using Science Fiction to Understand Biological Concepts by Tamsen K. Meyer and Cheryl H. Powers ©1994 Woodrow Wilson Biology Institute "Integration of disciplines that involve science, social issues, and literature is an increasingly attractive alternative in curriculum development today." "Science fiction has great appeal to many students who do not necessarily think of themselves as readers nor as the stereotypical 'math/science student.'" "The following is a resource list of science fiction short stories and novels that might be used either as an interdisciplinary teaching unit for teachers, an enrichment exercise in your biology course, or possibly a summer reading list for students entering your course the following year." "It also can serve as a starting point for students to create their own science fiction stories if only selections from these novels or short stories are read. "Students can demonstrate their understanding of complex biological concepts by writing their own short science fiction stories on topics such as 'The Day Diffusion Stopped.' What a difference a gene makes: food in the future, medicine in the future, eugenics revisited, and restoring extinct species are possible genetics ideas that could be developed." "Readings are listed by title rather than author because titles seem more useful. Titles were submitted by several Woodrow Wilson participants. A content summary is included for most of the selections and if there is a film version of the book, the notation FVA (film version available) is added in the following bibliography.
- Andromeda Strain, Michael Crichton. 1969. New York: Knopf, Random House. A returning space capsule releases an alien virus on the earth. FVA
- The Beast, Peter Benchley. 1991. New York: Random House. Coral reef ecology is disturbed and a giant squid picks man as his new prey.
- Blade Runner, The, Alan E. Nourse. 1974. New York: D. McKay & Co. In a future of increased human longevity, doctors struggle to cope with problems of overpopulation, hereditary disorders, and virulent new diseases. FVA [The Ultimate Science Fiction Web Guide says: actually, the title is used in a film based on Philip K. Dick’s ‘Do Androids Dream of Electric Sheep”; see below]
- Boys from Brazil, The, Ira Levin. 1976. New York: Random House. Dr. Mengele attempts to produce cloned copies of Adolf Hitler, but in order to do so he must reproduce the environmental factors which made Hitler the evil genius that he was; deals intelligently with the fashionable subject of cloning. FVA
- Brave New World, Aldous Huxley. 1946. New York: Harper and Bros. Reproductive technology as imagined in the 30’s – this famous satire about a technologically stratified world six centuries in the future helped define 20th-century humanity’s view of itself. FVA
- Clan of the Cave Bear, The, Jean Auel. 1980. New York: Crown. Human evolution at the level of the Cro-Magnon/Neanderthal junction. FVA
- Congo, Michael Crichton. 1980. New York, Knopf: Random House. Animal behavior, primate evolution: near future thriller of African exploration involving a tribe of talking gorillas.
- Deathworld Trilogy, Harry Harrison. 1974. Garden City: Nelson Doubleday. Coevolution and adaptation: mysteries of a planet where every life-form appears to be implacably hostile to human colonists.
- Do Androids Dream of Electric Sheep? Philip K. Dick. 1968. Garden City: Doubleday. After World War Terminus, the Earth is an underpopulated wasteland where people keep electronic animals as pets; killer androids come from off-Earth where most economic activity takes place. Filmed as The Blade Runner.
- Dorsai, Gordon R. Dickson. 1976. New York: Dow Books. Themes of human development and the purpose of life; originally published as The Genetic General.
- Dragonflight, Anne McCaffrey. 1968. New York: Ballantine. A well crafted tale of a planet threatened by spores from space which can only be defeated by taming fire-breathing dragons; first of Dragons of Pern series.
- Dune, Frank Herbert. 1965. Philadelphia: Chilton. Planetary environment and system of cultures much like that which would be present on Earth if Earth had no water. FVA
- Earthclan: Startide Rising, David Brin. 1987. Garden City, NY: Nelson Doubleday. Genetic manipulation, origin of man: intelligent dolphins and chimpanzees cooperate with man in the exploration of space.
- Ender’s Game, Orson Scott Card, 1985. New York: Tor, A Tom Doherty Association Book. Interstellar war, aliens and genocide.
- Fantastic Voyage, Isaac Asimov. 1988. New York: Doubleday and Co. Microminiaturization is used to explore the human body; written originally as a screenplay for the movie of the same name. FVA
- Frankenstein, Mary Shelley. 1980 (1818). James Kinsley and M.K. Joseph eds., Oxford, New York: Oxford University Press. Gothic horror story about a medical student who creates an artificial man; first English science fiction novel. FVA
- Galapagos, Kurt Vonnegut. 1985. New York: Delacorte Press/Seymour Lawrence. An observant ghost haunts the Galapagos Islands for a million years and watches as the descendants of a few marooned humans devolve into a new species – furry, finned, and small of brain; a sadly funny Darwinian fable.
- Genesis Quest, Donald Moffitt. 1986. New York: Ballantine. A species of intelligent starfish in another galaxy use genetic engineering to recreate the extinct human race.
- Human Error, Paul Preuss. 1985. New York: Tor. Scientists produce a biochip or living microcomputer.
- Jurassic Park, Michael Crichton. 1990. New York: Alfred A. Knopf. This fictional account of a theme park featuring dinosaurs cloned from DNA in mosquitoes fossilized in amber lends itself to many interesting discussions of genetic engineering, ethical issues, and chaos. FVA
- “Last Question, The,” Isaac Asimov. 1959. in: Nine Tomorrows: Tales of the Near Future. Garden City, NY: Doubleday. Themes of artificial intelligence and definition(s) of intelligence.
- Mortal Fear, Robin Cook. 1988. New York: G.P. Putnam and Sons. Eyedrops accelerate the aging process.
- Mutants: Eleven Stories of Science Fiction. Robert Silverberg, ed. 1974. Nashville: Thomas Nelson. Anthology of collected works.
- Plague Dogs, The, Richard Addams. 1977. London: Allen Lane, Rex Collings. Issues of animal experimentation, epidemics.
- “Rendevous with Rama,” from 2001: A Space Odyssey, Arthur Clarke. 1985. London: Octopus. Ecosystems necessary for terraforming are described.
- Ringworld, Larry Niven. 1970. New York: Ballantine. Complex artificial world is the main focus of this popular book.
- Science Fiction Adventures in Mutation, Groff Conklin, ed. 1956. New York: Vanguard Press. An anthology of collected works. [the referenced site misspell’s Groff’s name]
- “Sound of Thunder, The,” Ray Bradbury. 1966. in: Science Fiction for People Who Hate Science Fiction, Terry Carr, ed. New York: Doubleday. Ecology, human impact on the environment.
- Sphere, Michael Crichton. 1987. New York: Alfred A. Knopf. The discovery of an ancient spacecraft deep in the ocean is the focus of a scientific probe. [FVA]
- Time Machine, The, H.G. Wells. 1931 New York: Random House. Ecological splitting of society leads to human evolution. FVA
- 20,000 Leagues Under the Sea, Jules Verne. 1908. London/New York: J.M.Dent. Underwater adventures with sea creatures, technology of sea exploration.
- Watchers, The, Dean Koontz. 1987. New York: G.P. Putnam’s Sons. Ethics of genetic engineering and issues of animal welfare.
- West of Eden, Harry Harrison. 1984. New York: Bantam Books. Imagine a world where dinosaurs did not die but survived to develop their own civilization; their culture comes into conflict with an emergent human race.
"An excellent resource for short summaries of works of science fiction is:
The Ultimate Guide to Science Fiction,
David Pringle. 1990. Grafton Books, London; Collins Publishing Group."
"Numerous anthologies of science fiction short stories are available in libraries and science fiction magazines have many interesting
short pieces. Omni, Amazing Stories, Fantasy in Science, and Analog Science Fiction/Science Fact are four that are recommended."
This is by no means a comprehensive list of science fiction that could be used at the secondary level. Hopefully, teachers will use this as a
springboard to generate their own annotated bibliographies that might also include favorite biological literature (books, poems, stories, and essays)
and film resources that are not science fiction."
"A sample writing exercise that might be done after students have read 'The Andromeda Strain':
Support the truth of these quotes as demonstrated by events in the book:
"The survival value of human intelligence has never been satisfactorily demonstrated."
"Increasing vision is increasingly expensive."
In the acknowledgments Crichton states, "We can expect more crises on the pattern of Andromeda." How much truth exists in the novel?
What evidence do you see to support his prediction? (Thanks to Susan Terry for these questions.)
Miscellaneous ecological novels:
BLOOM by Wil McCarthy [New York, Del Rey, 1998, paperback, 303 pages, cover art by Rick Berry] [A New York Times Notable Book] A science fiction book featuring nanotechnology. Reporter John Strasheim, Captain Wallich, bioanalyst Renata Baucum, and the rest of the small crew of the space ship Louis Pasteur travel on a dangerous mission from Jupiter's moon of Ganymede and the Immunity, visiting the Gladholders in the asteroid belt, to the inner solar system, including Earth, which has been taken over by the feared Mycosystem. From the back cover: "Mycora: technogenic life. Fast-reproducing, fast-mutating, and endlessly voracious. In the year 2106, these microscopic machine/ creatures have escaped their creators to populate the inner solar system with a wild, deadly ecology all their own, pushing the tattered remnants of humanity out into the cold and dark of the outer planets. Even huddled beneath the ice of Jupiter's moons, protected by a defensive system known as the Immunity, survivors face the constant risk of mycospores finding their way to the warmth and brightness inside the habitats, resulting in a calamitous 'bloom'" But the human race still has a trick or two up its sleeve: In a ship specially designed to penetrate the deadly Mycosystem, seven astronauts are about to embark on mankind's boldest venture yet -- the perilous journey home to infected Earth. Yet it is in these remote conditions, against a virtually omnipotent foe, that we discover how human nature plays the greatest role in humanity's future." Denver Science Fiction & Fantasy Book Club SCIENCE FICTION BOOK SELECTION
Miscellaneous Biological novels/films:
- Fantastic Voyage, film based on novel by Isaac Asimov, where an (impossibly) miniaturized submarine explores the interior of a living human body.
- Them, film: radiation makes ants grow (impossibly) large.
- The Thing, film (and remake of film) from short novel “Who Goes There” by John Campbell; an alien creature terrifies antarctic expolors with its ability to change shape. How do you know that your partner is not an alien morphed to resemble a human?
- Film: It Came from Beneath the Sea
- Film: Jaws
MANY MORE: {to be done}
Academic Papers on Ecology and Science Fiction "From Earth to Ecosphere: Science Fiction, spaceships, and ecology", by Mark Rich pages 373-93 of: "Science et science-fiction", Actes de 4eme colloque international de science-fiction de Nice, 3-6 Apr 1991, Ed. Denise Terrel, Metaphores, #20-21-22 (sep 1992), 2 vols., 653 pages, 180 ff. Order from J. Emiliana, UFR Lettres, BD Herriot, 06007 Nice Cedex, France
What is chaos? The butterfly effect explained
Chaos theory is a branch of mathematics focusing on chaos.
Chaos is a behavior of any dynamical systems which appear to have random change and irregularities, but which actually follow simple underlying patterns and deterministic laws.
The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. There is nothing random or mysterious – just a very sensitive dependence on initial conditions.
A metaphor for this behavior is that a butterfly flapping its wings in one place can eventually cause a hurricane someplace else.
The discovery of the butterfly effect comes from the work of mathematician and meteorologist Edward Lorenz. He discovered that the details of a tornado (exact time of formation, exact path taken) is very influenced by minor perturbations, such as, just say for example, a distant butterfly flapping its wings several weeks earlier.
Lorenz discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.
Basic idea: Whenever we look at something in the real world – or even in a computer simulation! – we always have either errors in measurements, or problems due to rounding errors in numerical computation.
This leads, over time, to widely diverging outcomes of these systems, making long-term specific prediction of their behavior impossible.
This is true even though such systems are deterministic and is fully determined by their initial conditions, with no random elements involved.
In other words, the deterministic nature of these systems does not make them predictable.
Explainer: What is chaos theory?
Chaos Theory, The Butterfly Effect, And The Computer Glitch That Started It All
What is Chaos? a five-part online course for everyone
Chaos is something that shows up in any complex, classical system.
We can never know the initial conditions of an object (position, speed, momentum, etc.) with complete accuracy.
So small uncertainties over time lead to large uncertainties as time goes by.
This is an animation of a double compound pendulum showing chaotic behaviour.
The two sections of the pendulum have the same length and mass. The mass is distributed evenly along the length of each section, and the pivots being at the very ends.
Here we see that even planetary orbits are not stable forever.
Chaos orbit of 6Q0B44E orbit around Earth data from NASA’s Horizon’s system.
Prof. Rory Barnes animations of chaos in planetary orbits
See What defines a stable orbit?
History of the field
Joshua Sokol writes
The story of chaos is usually told like this: Using the LGP-30, Lorenz made paradigm-wrecking discoveries. In 1961, having programmed a set of equations into the computer that would simulate future weather, he found that tiny differences in starting values could lead to drastically different outcomes.
This sensitivity to initial conditions, later popularized as the butterfly effect, made predicting the far future a fool’s errand. But Lorenz also found that these unpredictable outcomes weren’t quite random, either. When visualized in a certain way, they seemed to prowl around a shape called a strange attractor.
About a decade later, chaos theory started to catch on in scientific circles. Scientists soon encountered other unpredictable natural systems that looked random even though they weren’t: the rings of Saturn, blooms of marine algae, Earth’s magnetic field, the number of salmon in a fishery.
Then chaos went mainstream with the publication of James Gleick’s Chaos: Making a New Science in 1987.
Before long, Jeff Goldblum, playing the chaos theorist Ian Malcolm, was pausing, stammering and charming his way through lines about the unpredictability of nature in Jurassic Park.
… Yet two women programmers played a pivotal role in the birth of chaos theory. Their previously untold story illustrates the changing status of computation in science. Ellen Fetter and Margaret Hamilton were responsible for programming the enormous 1960s-era computer that would uncover strange attractors and other hallmarks of chaos theory….
The Hidden Heroines of Chaos, Quanta Magazine
Videos
Chaotic Solar System
Chaotic Planets MinuteLabs.io
Apps
Gravity Simulator TestTubeGames
Chaotic Planets app MinuteLabs.io
Articles
The Butterfly Effect: Everything You Need to Know About This Powerful Mental Model
When the Butterfly Effect Took Flight, MIT News Magazine
Chaos Theory, The Butterfly Effect, And The Computer Glitch That Started It All
Edward Norton Lorenz, biography, University of St Andrews, Scotland
The Hidden Heroines of Chaos, Quanta Magazine
How to draw elliptical orbits lab
Here’s an easy to do lab that just requires paper, a pencil, some string, thumbtacks, and cardboard to lay the paper on. With this we can demonstrate the path of objects around the sun.
Basic idea: A circle is just a special case of an ellipse!
How to draw elliptical orbits
The next few paragraphs are from “Science Curriculum by Aaron Keller”
Pictures of the Solar System tend to show all the orbits of the planets as circles centered on the Sun [but] no orbit in the solar system is perfectly round.
In reality, the planets orbit the Sun traveling along an oval path. The mathematical term for this shape is an ellipse.
Notice that the Sun in this picture is not right in the center. The Sun is at one of the two ‘centers’ of the ellipse. These are called foci (plural for focus). The closer these foci are together, the more circular the orbit. The orbit of Venus is the closest to a circle of any planet in the Solar System.
Scientists have a name to describe just how much like an ellipse an orbit is. This is called eccentricity and is a measure that uses numbers between 0 and 1.
If an orbit has an eccentricity close to 1 then the ellipse is so long as to be more cigar-shaped than round.
Comets tend to have very elongated, high-eccentricity orbits.
The closer the eccentricity is to zero, the more circular the orbit.
Ellipse = the big oval shape.
Has a major axis (the longer axis) and a minor axis (the shorter one).
Has two foci: in the case of planetary orbits one focus is the Sun.
All the points in an ellipse are defined in relation to the foci.
The sum of the distances from each point on the ellipse to both foci is constant for all points on the ellipse.
Point on an orbit nearest the Sun is called perihelion.
Point farthest from the Sun is called aphelion.
Here is a similar image from a different source.
External links
Introductory Astronomy: Ellipses
Learning Standards
Massachusetts Curriculum Frameworks for Mathematics
Expressing Geometric Properties with Equations G-GPE Translate between the geometric description and the equation for a conic section.
3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
MA.3.a. (+) Use equations and graphs of conic sections to model real-world problems.
Expressing Geometric Properties with Equations G-GPE Translate between the geometric description and the equation for a conic section. 3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. MA.3.a. (+) Use equations and graphs of conic sections to model real-world problems.
Analytic geometry. The branch of mathematics that uses functions and relations to study geometric phenomena, e.g., the description of ellipses and other conic sections in the coordinate plane by quadratic equations.
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
8.MS-ESS1-2. Explain the role of gravity in ocean tides, the orbital motions of planets, their moons, and asteroids in the solar system.
HS-ESS1-4. Use Kepler’s laws to predict the motion of orbiting objects in the solar system. Describe how orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system.
ESS1.B Earth and the solar system – The solar system contains many varied objects held together by gravity. Solar system models explain and predict eclipses, lunar phases, and seasons.

















































