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Gender is both binary and bimodal

Gender, in mammals, is binary. That’s always been taught and understood as a fact.  Yet in modern social discourse, we are hearing from people who hold that gender is not binary.

Not only does disagreement exist, but now it has become socially acceptable, among some, to demand that everyone agree with “our” views. Some even demonize those who have a different point of view.

This is an area where scientists can role-model the best public discourse: It doesn’t matter whether we are talking about forces in aerodynamics; chromosomal mutations such as Edwards Syndrome, Down syndrome; or about gender and identity.

The key is to be clear and consistent in terminology. Without clearly agreed-upon definitions we talk past each other.

image from Between the (Gender) Lines: the Science of Transgender Identity, Science In The News, Harvard U.

Science, logic, and philosophy, can sharpen our own thinking about such issues. In fact, we scientists and philosophers live by this ideal “The aim of an argument or discussion should not be victory, but progress.” – Joseph Joubert

So what can clear communication do to help us understand this issue? View gender as bimodal – and view sex as binary. Scott Barry Kaufman writes about this topic.

He notes that it is critical to distinguish between: gender identity, biological sex, and evolutionary sex.

The first, gender identity, is fluid but tends to be bimodal.

The second, biological sex, isn’t strictly binary even though it’s best thought of as a bimodal distribution.

That is to say, almost all people are male or female; that’s binary, and a scientific observation. It is not a social construct. But there are some people with differences in chromosomes and genes that are not totally male or female. (The existence of the former population does not negate the existence of the latter population)

Such variations are scientifically observable; see Other genetic and chromosomal genders.

Evolutionary sex is about the implications of biological sex. It is mostly binary in mammals or else we wouldn’t exist.

In T: The Story of Testosterone, the Hormone that Dominates and Divides Us, Carole Hooven writes

Carole Hooven

How common is it to be intersex?

There is no one, exact answer, because there is no agreed-upon definition. But there are constellation of DSDs that, when added together, can give an answer. The answer that one gets depends on which conditions one wants to include.

Anne Fausto-Sterling, professor of biology and gender studies at Brown University, has made an expansive definition of intersex in her book “Sexing The Body: Gender Politics And The Construction Of Sexuality” and in a paper, “How Sexually Dimorphic Are We?” American Journal of Human Biology.

She adds together all of the following conditions, and concludes that almost 1.7% of people could be considered intersex; her definition includes people who have some mix of male and female sexual anatomy but it also includes women and men who have incomplete development of their anatomy, but no mixing of gender.

What if we don’t include conditions such as vaginal agenesis and late-onset adrenal hyperplasia (LOCAH)? Then the percent of people who are intersex would be lower.

In “How Common is Intersex? A Response to Anne Fausto-Sterling” Leonard Sax uses a more restrictive definition of intersex and comes up with a figure of 0.018%. ( Sex Res. 2002 Aug;39(3) )

The data is clear – biological sex (which, yes, is fair to call gender) is generally binary, but not absolutely so. There is some variation.

My hope is that people will study this issue in the same way that they approach all scientific questions:

* make hypotheses with testable predictions.

* read papers from peer-reviewed scientific journals.

* do not accept or force acceptance of claims based on social or political pressure.

Learning Standards

2016 Massachusetts Science and Technology/Engineering Standards
Students will be able to:
* apply scientific reasoning, theory, and/or models to link evidence to the claims and assess the extent to which the reasoning and data support the explanation or conclusion;
* respectfully provide and/or receive critiques on scientific arguments by probing reasoning and evidence and challenging ideas and conclusions, and determining what additional information is required to solve contradictions
* evaluate the validity and reliability of and/or synthesize multiple claims, methods, and/or designs that appear in scientific and technical texts or media, verifying the data when possible.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Implementation: Curriculum, Instruction, Teacher Development, and Assessment
“Through discussion and reflection, students can come to realize that scientific inquiry embodies a set of values. These values include respect for the importance of logical thinking, precision, open-mindedness, objectivity, skepticism, and a requirement for transparent research procedures and honest reporting of findings.”

Next Generation Science Standards: Science & Engineering Practices
● Ask questions that arise from careful observation of phenomena, or unexpected results, to clarify and/or seek additional information.
● Ask questions that arise from examining models or a theory, to clarify and/or seek additional information and relationships.
● Ask questions to determine relationships, including quantitative relationships, between independent and dependent variables.
● Ask questions to clarify and refine a model, an explanation, or an engineering problem.
● Evaluate a question to determine if it is testable and relevant.
● Ask questions that can be investigated within the scope of the school laboratory, research facilities, or field (e.g., outdoor environment) with available resources and, when appropriate, frame a hypothesis based on a model or theory.
● Ask and/or evaluate questions that challenge the premise(s) of an argument, the interpretation of a data set, or the suitability of the design.


The Next Dust Bowl? Lake Powell and Lake Mead

The Dust Bowl was a period of severe dust storms that greatly damaged the ecology and agriculture of the American and Canadian prairies during the 1930s.

Could something like this happen again here in the USA?

In this unit we’ll take a look at places here in the United States, Lake Powell and Lake Mead.

Let’s start by using this map to put us in geographical perspective.

from gcdamp.com

Geography and population

Open a new Google Doc for thus unit. Title it The Next Dust Bowl? Lake Powell and Lake Mead.

Answer the questions below in this document. Share it with your teacher.

1. In what states do we find these lakes?

2. What river connects these two lakes?

3. What canyon lies in between these two lakes?

4. What major city is shown on this map (and which relies on this water)?

5. What we think of as Les Vegas is actually only a smaller part of a larger metropolitan areas, the Las Vegas Valley. What is the population of this area?

Use Las Vegas Valley to find the answer.

6. How many people, overall, depend on water from this Lake Powell/Lake Mead water system? Scroll through this till you find “rely on water from Lake Mead” – Lake Mead, National Park Service


Reading and analysis

1. Use Google Maps to find out where in the USA these lakes are, relative to the borders of the continental United States. Point them out.

2. Zoom in on the maps to show the position of these lakes relative to the states that they are in, showing the borders of the nearby states.

3. Go here: Lake Powell Reaches New Low, Earth Observatory, NASA

4. Use the interactive slider on these photos. What do we observe? Please describe in some detail.

5. We read “After two years of intense drought and two decades of long-term drought in the American Southwest, government water managers have been forced to reconsider how supplies will be portioned out in the 2022 water year.”

Let’s click the link to the referenced article:

Large contribution from anthropogenic warming to an emerging North American megadrought

By A. Park Willians et al. Science, 17 Apr 2020, Vol 368, Issue 6488, pp. 314-318

Together, let’s read and discuss the abstract here. We’ll figure out the terminology and understand the main idea.


6. Click back to our main article (“Lake Powell Reaches New Low”) Look at the graph showing water levels in the lake from 1999 to 2021. What is the main point here?

7. What do experts expect to see here over the next five years?

8. Why is the Colorado River basin so important?

9. Go here: Earth Observatory, NASA

Lake Mead drops to a record low

10. Use the interactive slider on these photos. What do we observe? Please describe in some detail.

11. Look at the graph showing water levels in the lake from 2000 to 2021. What is the main point here?

Related article

First-Ever Colorado River Water Shortage Declaration Spurs Water Cuts in the Southwest


Pitfalls on Multicultural Science Education

This classic essay is from Emeritus Professor Bernard Ortiz de Montellano. Wayne State University, Anthropology.

I have been appointed to a State Department of Education committee to recommend materials that could be used to train teachers on including gender and multiculturalism in teaching science. At the first meeting, one of the members who works at a gender and equity program at the U, of Michigan passed around one of their publications that included claims about the Dogon, the usual post-modernist critique of “Western science,” and recommended Aronowitz and Helen Longino for theory.

I prepared the following to try to educate the members of the committee, who are primarily out of education rather than science. It is short, elementary, and covers too much. Please keep that in mind and the intended audience when you critique it.


Comments on Pitfalls on Multicultural Science Education
Bernard Ortiz de Montellano
Anthropology Department
Wayne State University

As a group that is going to be in charge of recommending materials for the instruction of teachers on how to best introduce gender and equity considerations we need to be clear about what is valid science and what is not. I was concerned at our first meeting when materials were distributed that included a reference bibliography and a critique of “Western” science that are very troublesome.

Every member of the committee should read Higher Superstition [Gross, P. R. and N. Levitt. 1994. Higher Superstition. The Academic Left and its Quarrels with Science. Baltimore: Johns Hopkins Univ. Press.], but in its stead I have prepared this brief paper for our consideration.

First, we need to get a fuller sample of what the multicultural-post-modernist claims that are being made are. Hunter Havelin Adams is the author of the Portland Baseline Essay in Science that is widely used including in the Detroit School District and was quoted in the University of Michigan publication distributed here.

What follows comes from his article in Blacks in Science [Adams, H. H. 1983. “African Observers of the Universe: The Sirius Question.: In Ivan Van Sertima, ed. Blacks in Science. Ancient and Modern. 27-46. New Brunswick: Transaction Books.]

p. 31 “[Citing Carl Spight on the tenets of Western science]:

1. science is fundamentally, culturally independent and universal.
2. The only reliable and completely objective language is scientific knowledge.
3. Science is dispassionate, unemotional, and anti-religious.
4. Logic is the fundamental tool of science.
5. The scientific method leads systematically and progressively toward the truth.

[This is a straw-man as we will see below]

… (citing Wade Nobles) “Science is the formal reconstruction or representation of a people’s shared set of systematic and cumulative ideas, beliefs and knowledge (i.e. common sense) stemming from their culture.”

Thus science cannot always spring from a universal or culturally independent base. It must be consistent with the essentials of its people’s “common sense.”

[B O. de M.–no scientist would agree with this definition.]

p. 41 “Nobody has a monopoly on truth. There is no one correct way of knowing: there are ways of knowing. And Western conceptual methodology cannot discover any more basic truths to explain the mysteries of creation than can a symbolic/intuitive methodology.”

p. 43 [citing the mystic R. A. Schwaller-Lubicz who characterized Western science as “a research without illumination.”

“…Eastern societies, such as those of India and Africa, do not have this problem because there is no distinct separation between science and religion, philosophy and psychology, history and mythology. All of these are viewed as one reality and are closely interwoven into the fabric of daily life. Astronomers, biologists and physicists are gradually coming around to accepting that there is something transcendental behind the empirical. They are realizing that, despite the exponential increase in information about the universe and about life, they are no closer to the truth they so passionately seek, than when the Greek philosopher Democritus, speculated about the atom 2000 years ago…”

[This is patently ridiculous on its face, do we really know as little about atoms today as Democritus did? In our daily life we can see the results of science and technology at work in real life.]

Before there can be a different science in the West, there first must be a transformation of values: a revolution in paradigms. As Jan Houston director of the foundation for Mind Research,[This a foundation set up by R. Houston to prove the validity of Laetrile as a cure for cancer.] observes, “we may now be in the early stages of a qualitative and quantitative departure from the dominant scientific and social paradigms.” This change may bring science into a more creative dialogue with other ways of knowing, other intuitive models and methodologies which are synthesized with the empirical mode in the science of early blacks. “

“This science was such a synthesis. It was a sacred science, whose fundamental paradigm was based on a spiritual principle: a principle which implicitly acknowledged the existence of One Supreme Consciousness or Force pervading the Universe, expressing itself in an infinite variety of transformations, from atom to stars, from plants to moon.”[This sentence is New Age science babble, mystical, and religious but not science.]

Feminist philosophers of science like Sandra Harding or Helen Longino and critics such as Stanley Aronowitz make similar critiques claiming that science is a set of conventions produced by the particular culture of the West at a particular historical period and not a body of knowledge and testable conjecture concerning the “real” world. The agenda, methodology, and conclusions of science are determined by the interests of the male dominated capitalistic system.

This approach has been called “strong cultural constructivism” by Gross and Levitt. Because science is just a “situated” mode of discourse and not reflective of the real world, other modes of discourse (feminist, African, Aztec) are equally valid “ways” of knowing (including intuition, magic, and religion), and may even be superior to “Western” science.

All of these critiques claim that the advent of quantum physics and particularly of the Heisenberg Uncertainty Principle has created a crisis in science because physics can no longer provide reliable information about the world and science has lost its claim to objectivity. Much is made of Heisenberg, Thomas Kuhn’s, The Structure of Scientific Revolutions, Paul Feyerabend, and Chaos theory.

The first question that arises, is why in the world are we getting into questions of epistemology, quantum mechanics and chaos theory with grade school teachers? As we will see, the valid questions that arise from Heisenberg’s Uncertainty Principle have little to do with the types of topics dealt or the level of presentation in K-8 or even K-12.

Henry Bauer [Bauer, H. H. 1992. Scientific Literacy and the Myth of the Scientific Method. Urbana: Univ. of Illinois Press.] makes a very useful distinction between “Frontier Science” which is necessarily volatile, unstable, and proceeds by stages, and “Textbook Science” (such as Kepler’s Laws of Planetary Motion or the Laws of Thermodynamics) which is well established and almost surely correct. In schools we are dealing with “Textbook Science” and it is not in crisis.

In 1927, Werner Heisenberg studying the behavior of electrons concluded that it was not possible to simultaneously know exactly the position and the momentum of an electron. This became known as the Heisenberg Uncertainty Principle. It was certainly important in the development of quantum physics, but it is not an important factor in the daily practice of science except for nuclear physicists. In my fifteen years of research in organic chemistry, I never had to consider the Heisenberg Uncertainty Principle in planning or interpreting my results.

A somewhat simplified explanation is that Heisenberg is only important in the case of very small particles (atoms and smaller) that are moving very fast. The uncertainty in these cases comes from the fact that the size of the instrument (let’s assume a photon of light) used to try to determine the position of an electron is in the range of the electron itself. The moment the photon hits the electron to determine its location; the collision of the photon pushes the electron changing its momentum.

Thus another name for the Heisenberg Uncertainty Principle is the “observer effect.” Imagine trying to determine the position of billiard balls on the table using the cue ball as an instrument.

However, when we are dealing with the kind of experiments or sizes that teachers and students would be dealing with there is no problem (and no crisis). A photographer could take a strobe photograph of a baseball pitch in the World Series and we would be able to calculate both its momentum and position at any time accurately even though it is “being observed” by countless photons and thousands of observers.

The reason is that the mass of baseball is enormous compared to the mass of the photons and they bounce off without changing it motion. Similarly, the uncertainty about the location of the desk in your classroom is zero because it is not moving and therefore its momentum is zero.

The Uncertainty Principle has been a victim of the suggestive nature of its name, of physicists dabbling in philosophy, and of English professors who are illiterate in science.

Gross and Levitt (p. 51-52) provide an appropriate summary.

“Once obscurantism has been stripped away, we recognize that the uncertainty principle is a tenet of physics, a predictive law about the behavior of concrete phenomena that can be tested and confirmed like other physical principles.”

“It is not some brooding metaphysical dictum about the Knower versus the Known, but rather a straightforward statement, mathematically quite simple, concerning the way in which the statistical outcomes of repeated observations of various phenomena must be interrelated. And, indeed, it has been triumphantly confirmed.”

“It has been verified as fully and irrefutably as is possible for an empirical proposition. In other words, when viewed as a law of physics, the uncertainty principle is a very certain term indeed. It is an objective truth about the world (If that were not so, there would never have been so much fuss about it).”

Similarly, post-modernists make much of Thomas Kuhn and Paul Feyerabend, but again they are off the mark. Kuhn [Kuhn, T. S. 1970. The Structure of Scientific Revolutions. 2nd ed. Chicago: Univ. of Chicago Press,] described the process by which a “normal” science paradigm (a commonly held theory of a group scientists and an exemplar about how to solve scientific puzzles) becomes increasingly unable to explain observations.

A “revolution” occurs by which it is replaced by a new paradigm, which in turn is accepted by the scientific community and becomes a new “normal” science.

The most recent example would be the replacement of the classical physics of the 19th century by quantum physics. Several points need to be made. A paradigm is not just discarded or overthrown; it is replaced by a paradigm that has wider explanatory powers. A scientific revolution does not change the fundamental characteristics of science as described below. Quantum mechanics still functions in the natural world without supernatural explanations; it still uses the experimental method; makes predictions and attempts to verify them; and depends on acceptance by the scientific community.

Kuhn, in a postscript to his 2nd edition, diplomatically pointed out that his concept had been extended to social sciences and to the humanities but that,

“the sciences, at least after a certain point in their development, progress in a way that other fields do not… Consider, for example, the reiterated emphasis, above, on the relative scarcity of competing schools in the developed science. Or remember my remarks about the extent to which members of a given scientific community provide the only audience and only judges of that community’s work (pp. 208-209).”

Kuhn [Kuhn, T. S. 1977. The Essential Tension. Chicago: Univ. of Chicago Press, p. 312.] also points out the characteristics that both an existing normal science paradigm and one that is proposed as a replacement must meet.

“First, a theory must be accurate: within its domain, that is consequences deducible from a theory should be in demonstrated agreement with the results of existing experiments and observations. Second, a theory should be consistent, not only internally or with itself, but also with other currently acceptable theories applicable to related aspects of nature.”

“Third, it should have broad scope: in particular, a theory’s consequences should extend far beyond the particular observations, laws, and subtheories it was initially designed to explain. Fourth, and closely related, it should be simple, bringing order to phenomena that, in its absence would be individually isolated, and as a set, confuse.”

“Fifth– a somewhat less standard item, but one of special importance to actual scientific decisions– a theory should be fruitful of new research findings: it should, that is, disclose new phenomena or previously unnoted relationships among those already known.”

This certainly does not support the idea that new “scientific” paradigms would include “symbolic\ intuitive methodologies” or religion.

Paul Feyerabend, who is quoted almost as much as Kuhn by post-modernist critics of science, and whose work eventually led to the cultural constructivist view of science now feels that things have gone too far.

“How can an enterprise [science] depend on culture in so many ways, and yet produce such solid results? Most answers to this question are either incomplete or incoherent. Physicists take facts for granted. Movements that view quantum mechanics as a turning point in thought– and that include fly-by-night mystics, prophets of a New Age, and relativists of all sorts– get aroused by the cultural component and forget predictions and technology.”

[Feyerabend, P. 1992. “Atoms and Conscience,” Common Knowledge 1(#1): 157-168.]

That is, we have to remember that science makes predictions that can be verified, and further that we have evidence in our daily lives that science works.

Science is not independent of culture, but we must define and explore what that implies and distinguish it from the post-modern definition.

[Much of what follows comes from Gross and Levitt, pp. 43-45.]

It is clear that certain kinds of research get more encouragement (funding, prestige, recognition) in society depending on perceived priorities. For example, cancer, AIDS, and high temperature superconductivity are high scientific priorities both because they are scientifically interesting and because they are clearly important to society. In this sense it is clear that “Western” science is influenced by culture. It is also clear than in the past science was dominated by white males and excluded and discouraged women and minorities, and that, to a large extent, this continues to be the pattern.

This is clearly an egregious fault, and feminist and minority critiques are justified in this aspect of science. It may well be that, if many more minorities and women became scientists, the agenda and the problems considered interesting and important in science would change. However, critics of science have not provided a clear and specific list of what these different scientific priorities would be, but it could be done. Clearly science is culturally dependent in this sense.

At another level, called “weak cultural constructivism” by Gross and Levitt, it is claimed that scientific debate and how one paradigm is chosen over another is to some degree influenced by social, political, or ideological preconceptions.

For example, Stephen J. Gould [Gould, S. J. 1992. “The Confusion over Evolution,” New York Review of Books, November 19: 47-54.] has argued that Darwin’s view of sexual selection as an important evolutionary mechanism was slow to win acceptance because it went against the Victorian prejudice, that females are by nature passive and lack enough energy to choose mates as Darwin’s extended-model required.

These ideas are reasonable in principle, but the areas of science in which such direct intrusion of ideology is possible are few, and primarily in the life sciences. In this sense, also, “Western” science is culturally constructed.

However, Adams, Aronowitz, Harding and others claim that the very methods (logical\experimental) of science and the answers it gets are “culturally constructed.” This is not acceptable.

The base sequence of a DNA will be the same regardless of the culture of the person performing the analysis.

The trajectory and momentum of a rocket will not change with the amount of testosterone in the blood or the amount of melanin in the skin of the scientist in charge.

The Second Law of Thermodynamics does not have a supernatural component.

It is not true that science is unemotional and does not use intuition.

The process of formulating hypotheses and questions to be investigated is described by physicist J. T. Davies [Davies, J, T. 1973. The Scientific approach, NY: Academic Press, p. 12.] as ” [it] comes from an intuitive leap of the imagination, from inspiration, from induction, or from a conjecture.”

Science starts with imagination and creativity

Jacob Bronowski [Bronowski, J. 1956. Science and Human Values. New York: Harper & Row, pp. 27, 35.] compares the creativity of artists and scientists as “finding unity in diversity.”

It took a leap of the imagination for Copernicus to ask himself, “What would the solar system look like if I stood on the sun as the center?”; or for Newton to ask, “what would be the effect if the attraction, that makes the apple fall to the ground, extended out beyond the solar system?”

Popper [Popper, K. R., 1959 The Logic of Scientific Discovery. New York: Basic Books, p. 32.] cites Einstein on “the search for those highly universal laws from which a picture of the world can be obtained by pure deduction.”

“There is no logical path,” Einstein says, “leading to… these laws. They can only be reached by intuition, based upon something like an intellectual love (“Einfuhlung”) of the objects of experience.”

The difference with pseudoscience or with non- science is that a scientist will then take the next steps which are to see what predictions result from the hypotheses and attempt to verify or falsify those predictions in the real world, whereas other “ways” of knowing will not continue the sequence.

Why do Afrocentrists espouse “strong cultural constructivist” critiques of science. In my opinion, it comes from a misguided need to inflate the achievements of ancient Egyptians or Africans. If “other ways” of knowing including magic, are equal or superior to “Western” science, because they both are “culturally constructed modes of discourse” and “Western” science is in crisis, then ancient Egypt can be proclaimed to be equal or superior to modern science.

What must be made clear is the difference between magic, religion, and science. Malinowski [Malinowski, B. 1954. Magic, Science, and Religion. New York: Doubleday Anchor, pp. 1-87.] provided a useful distinction for our purposes. Both science and magic are attempts to control the world, but they differ in that science only deals with the natural world and natural causes while magic recognizes both natural and supernatural causes.

Religion resembles magic in recognizing the existence of the supernatural, and differs from both magic and science in that the role of humans is that of suppliants rather than actors. Non-Western societies and the West until approximately 1500 do not make a distinction between magic, science, and religion.

A crucial step was the gradual separation of science from religion and magic between 1500 and 1700, i.e. the Scientific Revolution. Before this revolution, the hand of God was seen in all the operations of the Universe, and after it, the operations on the universe became subject to natural forces, and God became the ultimate cause setting these forces into motion. God established the physical laws and then stepped out of the way.

[Marks, J. 1995. Human Biodiversity. Genes, Race, and History. New York: Aldine de Gruyter, p. 228-230.]

Contrary to Adams science is not anti-religion. It is areligious. There are other “ways” of knowledge, but they are not science. They function in other important areas where science has nothing to say.

Science has nothing to say about religion, about forms of government, about ethics, about standards of beauty, or about the ultimate causes of the universe. Science can talk about the evolution of humans but not about why or for what purpose we are here.

This separation of science and the supernatural is crucial and a defining characteristic of science.

The key question is whether children in public schools are going to be taught that religion (under the guise of “Egyptian science”) equals science. This is the same question which was roundly forbidden by both lower courts and the United States Supreme Court in the case of so-called “scientific creationism.”

The essence of the decision of Judge Overton in McLean vs. Arkansas [McLean vs. Arkansas Board Of Education. 1982. “Creationism in the Schools: The Decision in McLean versus the Arkansas Board of Education.” Science 215: 934-943.] was that science does not allow an appeal to the supernatural for explanations. He outlined the essential characteristic of science as:

(1) It is guided by natural law;
(2) It has to be explanatory by reference to natural law;
(3) It is testable against the empirical world;
(4) Its conclusions are tentative; i.e., are not necessarily the final word;
and (5) It is falsifiable.

It is perfectly feasible to teach what I call “culturally relevant” science. The Arabs, the Egyptians, the Chinese, the Aztecs, American Indians, the peoples of Africa, and other non- Western peoples all have agricultural practices, mathematics, and technology that can be used to teach science and to illustrate scientific principles. All that has to be done is to strip away the religious motivation. Religion in the past was a powerful motive to seek knowledge. Newton’s motivation for much of his work was his deep religious conviction that he cold glorify God by showing the beauty and harmony of the arrangements in the cosmos. What distinguished Newton is that he did not invoke supernatural explanations for his work in optics and mechanics.

Similarly, the motivation for the Maya intensive study of the skies was their religious conviction that they had to be able to predict astronomical events in order to survive and prosper. I teach Maya religion as social studies. Maya astronomical, calendric, and mathematical achievements can be taught as science separate from the motivation that impelled them just as we study Newton’s mechanics with no concern for his deep religious motivation.

We are now ready to propose a definition of science that is different that the straw man set up by Adams which may reflect perception of the layperson. Science does not claim to be the ultimate, or the final truth. Science is both a special kind of information and a method.

Strahler [Strahler, A. N. 1992. Understanding Science. Buffalo: Prometheus Books, pp. 27-28.] defines it thus,

“Scientific knowledge: the best picture of the real world that humans can devise, given the present state of our collective investigative capability. By “best” we mean (a) the fullest and most complete description of what we observe, (b) the most satisfactory explanation of what is observed in terms of interrelatedness to other phenomena and to basic or universal laws, and (c) description and explanation that carry the greatest probability of being a true picture of the real world… “

“scientific knowledge is imperfect and must be continually restudied, modified and corrected it will never reach static perfection. Scientific method: the method or system by which scientific knowledge is secured. It is designed to minimize the commission of observational errors and mistakes of interpretation. The method uses a complex system of checks and balances to offset many expressions of human weakness, including self-deception, narrowness of vision, defective logic, and selfish motivation.”

To this must be added the scientific community; the worldwide group of people engaged in science. This community is a key component of the scientific method because it is what serves as the self-correcting and error minimizing component.

The prevailing ethic is honesty as Bronowski [Bronowski, 1956, pp. 65-94.] put it “We OUGHT to act in such a way that what is true can be verified to be so.”

Truth in science is particularly truth in the process of carrying out research. The scientific community will attempt to verify claims, hypotheses, and observations made by others, and therefore the ethic in science is for members of the community to be independent, and original in thought and to communicate fully and openly.

The more important or unexpected the faster and more thoroughly will the claim be investigated. The recent case of cold fusion is a good example of the speed with which a claim can be falsified when it is both unexpected and potentially very important. As in all human institutions, there will be scientists who will fail to act according to the ideal, but to a greater extent than other professions, violation of standards such as honest reporting of data will lead to professional death.

The scientific community is worldwide, and includes Chinese, Japanese, Nigerians, Egyptians, Argentineans, people of all races, ethnic groups, and sexes. Anyone can become a member by agreeing to function according to he same ethos and approach.


By Bernard Ortiz de Montellano. This was originally published on bit.listserv.skeptic in March 1995, and directed at teachers nationwide.

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Topics: History, pseudohistory, archaeology, pseudoarchaeology, skeptic

Rotating space stations with counter rotating segments

Big idea: Building a rotating space station with artificial gravity isn’t a far-out sci-fi idea. The idea has its roots in firm, realistic engineering & science.

Let’s start here Rotating space stations in fact and science fiction.

This is an image of a Rotating O’Neill cylinder space station, see the animation here.

Rotating O'Neill cylinder space station by SolCommand

Next we see a fictional space ship from the classic sci-fi TV series, Babylon 5. This is an Omega class destroyer. As you can see, the main engines are in back as one would imagine in a typical spaceship.

When the main engines are not on there is no acceleration, so everyone inside would be in zero-gee.  That is why there is a rotating section. People living in the rotating elements far from the axis would feel something like gravity (depending on the diameter of the ship, likely only a small fraction, such as 025 gee.

Babylon 5 – EAS Charon Omega Class Destroyer

The rotating sections simulate gravity. This would be useful for people spending long periods of time in a spaceship or space stations

But are they controllable? They have counter-intuitive physics. They can become stable easily

Consider the tennis racket theorem, aka Dzhanibekov Effect, aka intermediate axis theorem.

See it demonstrated here, with a (you guessed it) tennis racket! Tennis racket theorem GIF demo

It is named after Soviet cosmonaut Vladimir Dzhanibekov who noticed one of the theorem’s logical consequences while in space in 1985 – although the effect was already known for at least 150 years before that.

The theorem describes the following effect: rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not.

Dzhanibekov effect, Intermediate axis theorem, Tennis racket effect (NASA)

In many situations spaceships or space stations would demonstrate such behavior.

In theory such motion is completely predictable and deterministic; the motions follow from a standard analysis of classical mechanics. But in practice, a human making the station or ship move wouldn’t be able to do this physics in their head. We might want the ship to speed up and move right, but when thrust is applied this counter-intuitive motion would likely occur.

There are two solutions:

One solution is to use a layer of computer control between the navigator/pilot and the actual thrusters.  The pilot inputs the path desired, and the computer works backward from the desired path, figuring out which directions thrust should be applied (and which ways gyroscopes should be spun)

Another solution is to have two separate rotating sections, aka counter rotation.  This reduces the likelihood of counterintuitive motion and makes it easier for a human to engage in manual control. It increases the stability of the design overall.

This is the same reason that helicopters have two counterrotating rotors.

This does introduce some engineering costs. Torsional stresses exist at every place where sections rotate. So two such sections would double the maintenance and associated costs.

Here is an example of a hypothetical rotating space station with counterrotating rings. This GIF from a Reddit user at  Reddit Kerbal Space Program

Quote II

Now, one would think that such a centrifuge would act as a titanic gyroscope, doing its best to prevent the ship from changing its orientation. The obvious solution is to have two counter-rotating centrifuges, so their torque cancels out. Just like contra-rotating propellers on an airplane.

Alternatively you can use one centrifuge plus a monstrous counter-rotating flywheel with the same mass.

Aerospace Engineer Bill Kuelbs Jr points out that if the centrifuge is a sufficiently large percentage of the ship’s total mass, it will not prevent turning. What it will do is alter the axis of any turning force by ninety degrees. The technical term is gyroscopic precession. Rev up a toy gyroscope and try to turn it and you’ll see what I mean.

The solution to that is fairly simple. The turning thrusters will have to be effectively at ninety degrees to where you’d expect. In reality, this means that when the centrifuge is spinning, the “pitch the nose downward” control button will actually fire the “yaw to the left” thruster.

Very few helicopters have two counterrotating rotors. It’s much easier to manage the problem through adding a thruster – a tail rotor – than to build the complex mechanics and the blade angle control required from double rotors (in a smaller helicopter – if it needs two rotors anyway things change).


External Links

The Bizarre Behavior of Rotating Bodies – Veritasium – The Dzhanibekov Effect or Tennis Racket Theorem

Artificial gravity/Atomic rockets


Halema‘uma‘u lava lake depth compared to Empire State Building

Halemaʻumaʻu (six syllables: HAH-lay-MAH-oo-MAH-oo) is a pit crater within the much larger Kīlauea Caldera.

This is located at the summit of Kīlauea, an active shield volcano in the Hawaiian Islands.

How much lava can pour out of it during an eruption? Let’s find out.

This is part of that volcano erupting back around 2020.

Lava fountain of the Pu`u `O`o cinder and spatter cone on Kilauea Volcano, Hawai`i. https://spaceplace.nasa.gov/volcanoes2/en/

A caldera is a large cauldron-like hollow that forms shortly after the emptying of a magma chamber in a volcanic eruption

Image from Teacher’s Guide to Valles Caldera: The Science

A caldera collapse would look like this:

So how much lava poured out of it from 2020 to 2021? We find out from this USGS (U.S. Geological Survey,) U.S. Department of the Interior press release:

Halema‘uma‘u lava lake depth compared to Empire State Building

On September 29, 2021, fissure vents opened in Halema‘uma‘u crater.

A new lava lake began to form on the one previously active from December 2020–May 2021.

How much lava has filled Halema‘uma‘u crater?

If the Empire State Building, in New York City, was placed at the bottom of Halema‘uma‘u crater, we estimate the lava lake level could already be as high as the 70th floor!

USGS graphic by J. Bard.

For reference, the base of Halema‘uma‘u crater after the 2018 collapse was 517.4 m/1698 ft above sea level (asl). A water lake occupied the base of the crater from July 2019–December 2020, to a depth of 50.9 m/167 ft (equal to an elevation of 568.3 m/1865 ft asl).

The water lake was evaporated when an eruption began in Halema‘uma‘u crater in December 2020. That eruption created a lava lake that reached a depth of 158 m/518 ft (equal to an elevation of 675.4 m/2216 ft asl) by December 23, 2020. By the end of that eruption in May 2021, the lava lake had reached a depth of 223 meters/732 ft (equal to an elevation of approximately 741 meters/2431 ft above sea level).

The eruption that began on September 29, 2021, continues to fill the bottom of Halema‘uma‘u crater and by October 6, had reached a depth of 256.6 m/842 ft (equal to an elevation of 774 m/2539 ft asl) above the former base of the crater after it collapsed in 2018. For comparison, the height of the Empire State Building is 443.2 m (1454 ft).


Analyzing the science of San Andreas (2015 movie)

Analyzing the science & physics in films: San Andreas.

San Andreas is a 2015 American disaster film directed by Brad Peyton and written by Carlton Cuse. The film stars Dwayne Johnson, Carla Gugino, Alexandra Daddario, Ioan Gruffudd, Archie Panjabi, and Paul Giamatti. Its plot centers on an earthquake caused by the San Andreas Fault devastating Los Angeles and the San Francisco Bay Area.


The San Andreas Fault is a strike-slip fault. It marks the boundary between the North American Plate on the east and the Pacific Plate on the west.
It was the cause of the 1906 San Francisco earthquake.

It developed about 20 million years ago. It extends roughly 1,200 kilometers (750 miles.)

A great view of the fault.

Another great view.

Slippage along the Imperial fault caused an offset in this orange grove, east of Calxico CA.

Earth Science, Tarbuck & Lutgens, Chapter 8


Back to the Future on the San Andreas Fault, USGS

Extreme Science: The San Andreas Fault. How California is predicting and preparing for the inevitable.
Mary Beth Griggs, 8/19/2015

How scientifically accurate is San Andreas? Rock solid or a bit faulty?

San Andreas – The Scientific Reality, RMS, Justin Moresco May 29, 2015

“To figure out what could realistically happen when the Big One finally strikes, a team of earthquake experts sat down several years ago and created the ShakeOut scenario. Seismologists modeled how the ground would shake and then other experts, including engineers and social scientists, used that information to estimate the resulting damage and impacts. The detailed report examines the effects of a hypothetical 7.8 quake that strikes the Coachella Valley at 10 a.m. on November 13, 2008. In the following minutes, the earthquake waves travel across California, leveling older buildings, disrupting roads and severing electric, telephone and water lines. But the quake is only the beginning.”

What Will Really Happen When San Andreas Unleashes the Big One? Sarah Zielinski, May 28, 2015

The ShakeOut Scenario, U.S. Geological Survey Open File Report 2008-1150

This is the initial publication of the results of a cooperative project to examine the implications of a major earthquake in southern California.


Open this Word file: San-Andreas-movie-analysis

Why use clips from sci-fi and disaster movies in the classroom?

C. Efthimiou and R. Llewellyn write

Over the past year and a half we have developed an innovative approach to the teaching of Physical Science… [it] uses popular movies to illustrate the principles of physical science, analyzing individual scenes against the background of the fundamental physical laws. The impact of being able to understand why, in reality,

 • the scene could or could not have occurred as depicted in the film,

 • what the director got right and what he got wrong,

 • has excited student interest enormously in a course that, when taught in the traditional mode, is usually considered to be ‘too hard and boring’.

The performance of students on exams reflected the increased attention to and retention of basic physical concepts… Following the first offering of the revitalization of the Physical Science course, in which action and sci-fi films were the primary source of the scene clips used in class, the instructors have demonstrated the versatility of the approach by building variations of the course around other genres, as well – Physics in Films: Superheroes and Physics in Films: Pseudoscience.

“Physics in Films” A New Approach to Teaching Science, C. Efthimiou and R. Llewellyn

Also see Intuitor.com, Insultingly Stupid Movie Physics by Tom Rogers.

Learning Standards

Next Generation Science Standards: Science & Engineering Practices
● Ask questions that arise from careful observation of phenomena, or unexpected results, to clarify and/or seek additional information.
● Ask questions that arise from examining models or a theory, to clarify and/or seek additional information and relationships.
● Ask questions to determine relationships, including quantitative relationships, between independent and dependent variables.
● Ask questions to clarify and refine a model, an explanation, or an engineering problem.
● Evaluate a question to determine if it is testable and relevant.
● Ask questions that can be investigated within the scope of the school laboratory, research facilities, or field (e.g., outdoor environment) with available resources and, when appropriate, frame a hypothesis based on a model or theory.
● Ask and/or evaluate questions that challenge the premise(s) of an argument, the interpretation of a data set, or the suitability of the design

Next Generation Science Standards

7.MS-ESS3-2. Obtain and communicate information on how data from past geologic events are analyzed for patterns and used to forecast the location and likelihood of future catastrophic events.

8.MS-ESS2-1. Use a model to illustrate that energy from Earth’s interior drives convection that cycles Earth’s crust, leading to melting, crystallization, weathering, and deformation of large rock formations

Appendix III Disciplinary Core Idea Progression Matrix – Plate tectonics is the unifying theory that explains movements of rocks at Earth’s surface and geological features.

College Board Standards for College Success: Science

Objective ES.1.3 Tectonism – Students understand that tectonic plates interact along their boundaries, resulting in folding, faulting, earthquakes and volcanoes.

ESM-PE.2.3.2 Analyze earthquake and volcano location data on a map or a globe to find global patterns and to relate these patterns to tectonic plate boundaries, interactions and hot spots.

Objective ES.3.2 Rock and Fossil Records

Essential Knowledge: Changes in Earth’s environment occur in both short and long time intervals. Large changes are relatively infrequent, and small changes are relatively frequent. Infrequent global catastrophic events, such as impacts from bolides or periods of widespread volcanic activity, leave evidence in the geologic record.

ESM-PE.5.2.2 Use a geologic map of the world to predict areas that are at risk due to geologic hazards such as earthquakes, volcanoes and tsunamis.

We Are What We Eat

“You are what you eat.” We hear that all the time. And it is literally true. Today we’re going to consider exactly what it is in food that we need, and what our body does with it. Let’s start with a classic PSA that was shown on TV in the 1980s. Let’s view

You Are What You Eat animated PSA

Alrighty then, we clearly need to eat in order to get organic molecules.

What molecules do we need to eat? Here’s a brief overview – Molecules that cells need

Now let’s look at what we need in more detail.


We of course need oxygen gas – but we get that from breathing. What exactly are oxygen atoms and molecules? – Oxygen atoms and molecules


Our body requires several types of salts in order to function. Sodium chloride (table salt) as well as magnesium chloride, calcium chloride, and potassium chloride.

The nerves in our brain, and throughout our body, absolutely require dissolved salt ions in order to work. If we didn’t have these ions in our body then life would cease instantly. For details you could look at Action potentials.

Most of the salts that we need are obtained from eating plant and animal based foods.

We could also ingest salt right from solid salt crystals. While cooking people often add these to the foods being prepared.

Salt dissolved in water – Salt molecules dissolved in water


Our body uses fats in two ways:

Some fats are building materials for many parts of all our cells

Fats are used as a source of energy. Fats store chemical energy in their molecular bonds.

Here are some common fats found in many foods, and in healthy people.

Important: Fat, in of itself, is not bad for you. Never was. Rather, too much fat, or the wrong kinds of fat, become bad for you.

Here are some healthy sources of fats.

(Note the red meat: Most doctors believe that it is healthy for us to get some fats from a diet with small amounts of red meat. Larger amounts of meat present a problem; processed meats present a problem.)

from doctorkiltz.com


Why do we need “protein?” Protein is a chemical found in all plants and animals. We eat the food, digest it, and the protein breaks down into small pieces – amino acids.

Our cells pick up these individual, digested amino acids – and then stitch them together into a new, three dimensional shapes.

These shapes aren’t just interesting or pretty: They are literally machines.

Consider your muscles. Here we look at a muscle, and keep zooming in with higher magnification.

GIF made by SSACC and hosted on imgur.com

How do we contract our muscles? When we look deep inside them, we see fibers moving past each other.

What makes these fibers move?

This unit of muscles fibers is called a sarcomere.


Image from Mohammad Attari and Hossein Khadivi Heris at the McGill Univ Bio Active Materials (BAM) Lab

Or consider the mitochondrial in our cells. Details aside, mitochondria also have proteins that are basically little machines.

What foods are good sources of protein? Not just meat.

Meat itself can also be a good source of protein.



Carbohydrates are found in all plants and animals. We eat part of a plant (or plant based food,) digest it, and break the carb down into smaller pieces – sugars.

Our cells pick up these individual, digested sugars. They break them down to release the chemical energy stored inside them.

There are many sources of carbs but some are healthier than others. Complex carbs have a low impact on our blood sugar level. Simple carbs have a large impact on our. blood sugar level.


DNA bases

Humans, like all life, need DNA. Our chromosomes are made of DNA.

These chromosomes are in turn made of smaller units called nucleotides bases. There are four types. (Shown here.)

Does our body use DNA like the other nutrients?

When we build proteins, we first need to eat food with protein. We break it down into monomers and then rebuild those into human proteins. Is that true for DNA?

Sure, DNA is in every food we eat. Strawberries, apples, chicken, tuna, green beans, blueberries, all of these are living organisms with DNA. We eat them, and our intestines digest all of that DNA.  Those digested DNA parts them circulate in our body, and can be taken up by other cells.

Does our body then

(a) salvage those solitary DNA pieces, and stitch them together into human DNA?

(b) create new DNA bases from scratch (de novo synthesis), and then stitch those together into human DNA?

(c) Or a bit of both?

Turns out that in a healthy person it is mostly (b.) Our cells usually take small molecule fragments and synthesize those directly into DNA bases.

Although we can do (a) when necessary.

Learning standards


MS-LS1-3. Use argument supported by evidence for how the body is a system of interacting subsystems composed of groups of cells. Emphasis is on the conceptual understanding that cells form tissues and tissues form organs specialized for particular body functions. Examples could include the interaction of subsystems within a system and the normal functioning of those systems.

MS-LS1-7. Develop a model to describe how food is rearranged through chemical reactions forming new molecules that support growth and/or release energy as this matter moves through an organism. Emphasis is on describing that molecules are broken apart and put back together and that in this process, energy is released.

DCI – LS1.C: Organization for Matter and Energy Flow in Organisms

As matter and energy flow through different organizational levels of living systems, chemical elements are recombined in different ways to form different products. (HS-LS1-6),(HS-LS1-7)

Massachusetts Science and Technology/Engineering Curriculum Framework

HS-LS1-6. Construct an explanation based on evidence that organic molecules are primarily composed of six elements, where carbon, hydrogen, and oxygen atoms may combine with nitrogen, sulfur, and phosphorus to form monomers that can further combine to form large carbon-based macromolecules.
Clarification Statements:
• Monomers include amino acids, mono- and disaccharides, nucleotides, and fatty acids.
• Organic macromolecules include proteins, carbohydrates (polysaccharides), nucleic acids, and lipids.
State Assessment Boundary:
• Details of specific chemical reactions or identification of specific macromolecule structures are not expected in state assessment.

National Science Education Standards

Most cell functions involve chemical reactions. Food molecules taken into cells react to provide the chemical constituents needed to synthesize other molecules. Both breakdown and synthesis are made possible by a large set of protein catalysts, called enzymes. The breakdown of some of the food molecules enables the cell to store energy in specific chemicals that are used to carry out the many functions of the cell.

National Research Council. 1996. National Science Education Standards. Washington, DC: The National Academies Press. https://doi.org/10.17226/4962.


One-page notes/posters

Idea: Students show what they learn by creating a large, colorful single page poster with graphics and text. Why? One-pagers are visually attractive; help students organize their thoughts; give students an opportunity to show originality & creativity.

Materials: Large pieces of paper (art pads/newsprint pads.) e.g. 18”x12” or 18”x24”; colored pencils, markers, pastels, pens, etc.

Who this project typically appeals to: Students comfortable with art. They want to create their own unique layout and drawings from scratch. Challenges: Some students don’t feel comfortable with their artistic skills. These students will benefit from us providing templates to choose from.

This kind of project will be new to many students: we need to show them a few examples.

Rubrics/parameters (possible ideas)

English Language Arts/Literature

• Create a drawing or icon which represents the theme.

• Create a sketch (or decoupage a photo) showing the setting (location/time period.) Have a couple of sentences describing this.

• Include quotations

• Describe main characters; info about a character arc.

• Describe themes; questions that the author is asking us; responses.

• Write something that they personally connected with.

History/Social Studies

• Create a drawing or icon which represents the theme.

• Make connections between the text and current events

• Create a sketch (or decoupage a photo) showing the setting (location/time period.) Have a couple of sentences describing this.

• Include quotations from related primary sources.

• Examine several historical figures in this unit and their impact on history

• Write something that they personally connected with.


• Create a drawing or icon which represents the main ideas

• If about the discovery of a law of physics or chemistry, create a sketch (or decoupage a photo) showing the setting (location/time period.) Have a couple of sentences describing this.

• Relevant equations

• Examples of how this scientific principle operates in the real world.

External resources

We Are Teachers – One-pager-examples ELA

cultofpedagogy.com – One pagers

Colonialsd.instructure – Sample instructions and rubric

Alvord Schools – Sample one pager instructions (PDF)

Learning Standards

Common Core ELA Science

Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text.

Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.

NGSS Science and Engineering Practices

O​​btaining, Evaluating, and Communicating Information

Communicate scientific and technical information (e.g., about the process of development and the design and performance of a proposed process or system) in multiple formats (including oral, graphical, textual and mathematical).

NGSS Evidence Statements – Observable features of the student performance by the end of the course: Students use at least two different formats (including oral, graphical, textual and mathematical) to communicate scientific and technical information, including fully describing the structure, properties, and design of the chosen material(s). Students cite the origin of the information as appropriate.

Essential Knowledge and Skills Statements (ESS)

National Association of State Directors of Career and Technical Education Consortium (NASDCTEc) 2008

Communications: Use oral and written communication skills in creating, expressing and
interpreting information and ideas including technical terminology and information.


High effectiveness of covid-19 vaccines, breakthrough cases and the base rate fallacy

How effective are the mRNA covid-19 vaccines? Don’t some vaccinated people nonetheless get covid-19? Doesn’t that mean that vaccines don’t work?

Not at all. This is a logical error known as the base rate fallacy.  What is the base rate fallacy?

Consider a soldier going out into battle against an army armed with bows & arrows. Doctors and experts say, “Protect yourself as best you can! Wear a suit of armor!”

This soldier went to the battlefield. Later he returns, complaining about pain in his shoulder. Here he is:

Should we conclude that a suit of armor is useless? If we look at this one person, alone, without comparing him to anyone else, it might seem that way.

But that’s illogical: there is no way to tell the effectiveness of wearing armor versus not-wearing armor by looking only at the people wearing armor.

We need to compare the rate of wounds from people in armor to the rate of wounds from people refusing to wear armor. When we do so we come to a very different conclusion:

Wow, it now is clear that when we take all the data into account, wearing armor makes one far safer.

Let’s see how this helps us understand the effectiveness of vaccines, and what it really means about breakthrough cases.

Tom Buytaert writes

The more people in society are vaccinated, the more of the deaths will be among vaccinated people. Imagine a scenario where 95% is vaccinated, with a vaccine that is 90% effective, in a target group where IFR is 10% (80+).

In reality, as we now know, covid-19 vaccines are a lot more effective than 80%. So the infographic below even understates the advantage of being vaccinated!

In that scenario the total number of deaths among vaccinated people will be 2x higher, but their individual chance is 10x lower than that of people who are unvaccinated.

So that might sound like the vaccines are not working?

Well, that the total number is higher among the vaccinated is thus normal – it is a result of the fact that there are simply more vaccinated people around.

Similarly, if there are more red cars driving around on the roads, more red cars will crash. That doesn’t mean that the color red makes driving less safe.

You can see the actual (individual) protection provided by the vaccine on the right side, which shows the odds of dying* for vaccinated and non-vaccinated groups.

* For this fictional scenario of only 90% protection. In reality protection is a lot higher.

The vaccines do not offer 100% protection against heavy illness or death (although it is very close) .

So sometimes a (small!) part of the vaccinated people will still end up in hospital. It’s much less likely than if you are not vaccinated, but sometimes still possible.

In my infographic you see two views of the same situation: absolute numbers and odds.

left box:
– 10 unvaccinated, of which 1 died
– 190 vaccinated, of which 2 died

right box:
– 1 out of 100 vaccinated people died
– 10 out of 100 unvaccinated people died

The left box corresponds to “the numbers” that you will see in the news and on dashboards published by CDC, Worldometer, RIVM,…

But the right box is the one that counts. That one indicates that the vaccines do make a big difference.

So if you might hear about vaccinated people still ending up in hospital, keep this in mind. This is an example of the ‘Base Rate Fallacy’:

If someone is throwing percentages at you, a good reflex is to ask yourself: “exactly WHAT is this a percentage of?”

Or you could draw an example: “If I have 100 people in this group and 100 in the other, what happens to those percentages then?”

This infographic clearly shows us what group we should be comparing with what other group.

Related articles

“Israel, 50% of infected are vaccinated, and base rate bias”

Katelyn Jetelina writes

The statistic that’s concerning most (and that’s in the news) is a detail the Director General of the Health Ministry of Israel (Professor Chevy Levy) said during a radio interview. When asked how many of the new COVID19 cases had been vaccinated, Levy said that, “we are looking at a rate of 40 to 50%”. This must mean the Delta variant is escaping our vaccines, right? When I started digging into the numbers, though, this might not be as alarming as it seems.

This is likely an example of base rate bias in epidemiology (it’s called base rate fallacy in other fields). Professor Levy said that “half of infected people were vaccinated”. This language is important because it’s very different than “half of vaccinated people were infected”. And this misunderstanding happens all. the. time.

read more here Covid, breakthrough infections data – Your Local Epidemiologist


Kristen Panthagani writes

People are looking at the percent of vaccinated hospitalizations and getting alarmed. But by itself, this number can’t tell you much about how the vaccines are working, as it’s highly dependent on the rate of vaccination in a community. Here’s some maths to show what I mean

Learning Standards

Common Core Math – Statistics & Probability

Making Inferences & Justifying Conclusions

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Evaluate reports based on data.

Mechanical equilibrium lab

This introduction comes from  Being Brunel: Notes From a Civil Engineer

What is mechanical equilibrium? Why do we study it?

This introduction comes from  Being Brunel: Notes From a Civil Engineer

If civil engineering was religion (and in a way it is; institutionalised by men in funny hats), the first commandment would be: “Thou shalt always have static equilibrium”

The principle is easy: the sum of all the actions acting on a structure should come to zero….

The logic goes as such:

  • Structures neither move, nor do they accelerate

  • Therefore the ‘velocity’ of the structure, and all of the components that make it, is always zero.

  • That means that the net force on the structure is zero (Newton’s first law)

  • All forces applied to a structure are due to accelerating masses (Newton’s second law)

  • At a global level these actions on the structure are resisted by the reactions of its supports (Newton’s third law)


This is going to have to be true with anything we safely build, for instance:

In this lab we will see that the Σ F (the sum of all forces) equals 0.

Mechanical equilibrium lab


Meter sticks, spring scales

table clamps, rod clamps, collar hooks, metal rods (crossbars)


More about this and related labs

Inertia and Mechanical Equilibrium labs

An elegant experiment in mechanical equilibrium, J N Boyd and P N Raychowdhury, Physics Education, Volume 20, Number 5, 1985

Walking the plank lab

Concept Development Practice Page Static Equilibrium

Equilibrium and Statics, The Physics Classroom