Why learn math?
Why learn math? When are going to use this in real life?
When students ask “when will we ever need this in real life?” they often aren’t actually being curious about their future. They are actually just unhappy with being assigned work in the present. But some students truly do want to learn the answers to this question – and teachers, one would hope – should know answers as well. And there are several answers to this question, not just one.
I. First we should recognize that this is an unfair question. Douglas Corey, at Brigham Young University, writes:
In truth, the when-will-I-use-this question is unfair for the teacher. She doesn’t know when you will (or even might) use it (except on the exam and in the next course in the sequence). She might explain how other people have used it, but, as we saw above, that response is not convincing. The difficulty in answering this question lies with an implicit assumption hidden beneath the question. The student has an idea of the kinds of situations that she will encounter in her life, and when the response from the teacher doesn’t apply to any of these situations, the mathematics seems useless. But it is fraudulent to assume that we know at a moment of reflection the kinds of situations in which we might use something. Why? Because we typically don’t know what we don’t know.
– When Will I Ever Use This? An Essay for Students Who Have Ever Asked This Question in Math Class
II. Does a football team go onto the field and lift weights? Of course the team doesn’t do that. However if they didn’t practice lifting weights then they certainly wouldn’t have a chance to win.
III. We’re actually not learning hard math that mathematicians study in university. For every subject that you think you are studying – algebra, trigonometry, calculus, etc. – you’re really just learning the introduction to these subjects! Yes, even after a year in high school calculus all you have done is scratch the surface of that field of math.
So why learn any of these math topics at all in grades K-12? Because children don’t know what they are going to be 10 or 20 years from now. So consider: If we don’t teach students how to be fluent and literate in English, then how can they read and learn anything? How can they communicate using the written word? They literally would be unable to even consider a career, right?
Now realize that the same is true for math. If we don’t teach students how to be fluent and literate in mathematics and logical thinking, then how could they ever even have a chance to consider a career in medicine, engineering, coding, chemistry, artificial intelligence, astronomy, physics, or math? No one ever would even be able to consider such a career.
IV. Here I’m excerpting some thoughts from Al Sweigart.
A math teacher is giving a lesson on logarithms or the quadratic equation or whatever and is asked by a student, “When will I ever need to know this?”
“Most likely never,” replied the teacher without hesitation. “Most jobs and even a lot of professions won’t require you to know any math beyond basic arithmetic or a little algebra.”
“But,” the teacher continued, “let me ask you this. Why do people go to the gym and lift weights? Do they all plan on becoming Olympic weight lifters, or professional body builders? Do they think they’ll one day find an old lady trapped under a 200 pound bar bell and say, ‘This is what I’ve been training for.’”
“No, they lift weights because it makes them stronger. Learning math is important because because it makes you smarter. It forces your brain to think in a way that normally it wouldn’t think: a way that requires precision, discipline, and abstract thought. It’s more than rote memorization, or making beautiful things, or figuring out someone’s expectations and how to appease them.”
“Doing your math homework is practice for the kind of disciplined thinking where there are objective right and wrong answers. And math is ubiquitous: it comes up in a lot of other subjects and is universal across cultures. And all this is practice for thinking in a new way. And being able to think in new ways, more than anything, is what will prepare you for an unpredictable, even dangerous, future.”
IV. We learn mathematics without realizing its ramifications and applications
This attitude comes partly from ignorance and partly from our faulty education system. We learn mathematics without realizing its ramifications and applications. You have been led to believe that it is useless but it is not. Look around the world in which you live. Almost everything that you experience and enjoy is possible because of mathematics.
You drive a car. A car company uses CAD software which lets it design and model components with absurd ease. Do you know how a CAD software works? It uses rigorous mathematics from geometry to matrices.
That’s one part of it. The calculation part. To display a model on your computer screen is yet another story. Processes are set, algorithms are developed and executed. But merely developing an algorithm is not sufficient. You have to optimize it. To develop and optimize an algorithm you need mathematics. Somebody has to develop the optimization algorithm. Know that the optimization algorithm is an algorithm to optimize a different algorithm. To develop such feat you would probably need to master functions, graphs and calculus. To perform stress analysis on such a component you would need yet another algorithms. To develop them you would probably need to study finite element analysis and matrices. This is true for any industry and not just for car industry.
Consider a security firm. It need to be able to identify a person’s face. They need a face recognition algorithm. Now some geeks have developed many such algorithms. Some of them are simple and less accurate while some are highly accurate but difficult to employ.
Development of each such algorithm requires extensive knowledge of matrices, probabilities, and other 100 things but do you know what is beautiful? The security firm may audit itself and using yet another mathematical process, assess exactly what type of algorithm it would need. Mathematics. Again. This is true for any forensic analysis. Fingerprint matching, face matching, pattern recognition and what not. Many private and public security firms, law enforcement agencies and spy agencies are using and developing such specialized tools thanks to mathematics.
Let’s come to gaming. You will be thrilled to know that while playing combat games, you are actually fighting with an algorithm which can ‘learn’ you. Genetic algorithm, neural networks and such things. Google it. Imagine yourself at a scene in a game. You can’t see what’s behind you in a scene, but as you look at it, the scene develops. There are special compression algorithms who use the information of the scene in compressed format when nobody is looking at it. I guess I don’t have to repeat now but still, I will. Mathematics.
Investment funds, hedge funds and other financial institutions predict the market and make decisions using mathematical software. Again, it require, number crunching, statistics, pattern recognition (which itself requires a lot of mathematics), optimization, functions and graphs and calculus (for effective predictions). Insurance companies need to use probabilistic models of customers to come up with new policies. They invest money in stock market. Now again read this paragraph just put insurance companies in place of investment funds.
Kedar Marathe, Tata Technologies, answering on Quora.
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V. Kalid Azad, of BetterExplained, writes in How to Develop a Mindset for Math
Math uses made-up rules to create models and relationships. When learning, I ask:
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What relationship does this model represent?
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What real-world items share this relationship?
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Does that relationship make sense to me?
They’re simple questions, but they help me understand new topics. If you liked my math posts, this article covers my approach to this oft-maligned subject. Many people have left insightful comments about their struggles with math and resources that helped them.
Math Education
Textbooks rarely focus on understanding; it’s mostly solving problems with “plug and chug” formulas. It saddens me that beautiful ideas get such a rote treatment:
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The Pythagorean Theorem is not just about triangles. It is about the relationship between similar shapes, the distance between any set of numbers, and much more.
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e is not just a number. It is about the fundamental relationships between all growth rates.
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The natural log is not just an inverse function. It is about the amount of time things need to grow.
Elegant, “a ha!” insights should be our focus, but we leave that for students to randomly stumble upon themselves. I hit an “a ha” moment after a hellish cram session in college; since then, I’ve wanted to find and share those epiphanies to spare others the same pain.
But it works both ways — I want you to share insights with me, too. There’s more understanding, less pain, and everyone wins.
Math Evolves Over Time
I consider math as a way of thinking, and it’s important to see how that thinking developed rather than only showing the result. Let’s try an example.
Imagine you’re a caveman doing math. One of the first problems will be how to count things. Several systems have developed over time:
fro Kalid Azad, BetterExplained
No system is right, and each has advantages:
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Unary system: Draw lines in the sand — as simple as it gets. Great for keeping score in games; you can add to a number without erasing and rewriting.
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Roman Numerals: More advanced unary, with shortcuts for large numbers.
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Decimals: Huge realization that numbers can use a “positional” system with place and zero.
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Binary: Simplest positional system (two digits, on vs off) so it’s great for mechanical devices.
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Scientific Notation: Extremely compact, can easily gauge a number’s size and precision (1E3 vs 1.000E3).
Think we’re done? No way. In 1000 years we’ll have a system that makes decimal numbers look as quaint as Roman Numerals (“By George, how did they manage with such clumsy tools?”).
Negative Numbers Aren’t That Real
Let’s think about numbers a bit more. The example above shows our number system is one of many ways to solve the “counting” problem.
The Romans would consider zero and fractions strange, but it doesn’t mean “nothingness” and “part to whole” aren’t useful concepts. But see how each system incorporated new ideas.
Fractions (1/3), decimals (.234), and complex numbers (3 + 4i) are ways to express new relationships. They may not make sense right now, just like zero didn’t “make sense” to the Romans. We need new real-world relationships (like debt) for them to click.
Even then, negative numbers may not exist in the way we think, as you convince me here:
You: Negative numbers are a great idea, but don’t inherently exist. It’s a label we apply to a concept.
Me: Sure they do.
You: Ok, show me -3 cows.
Me: Well, um… assume you’re a farmer, and you lost 3 cows.
You: Ok, you have zero cows.
Me: No, I mean, you gave 3 cows to a friend.
You: Ok, he has 3 cows and you have zero.
Me: No, I mean, he’s going to give them back someday. He owes you.
You: Ah. So the actual number I have (-3 or 0) depends on whether I think he’ll pay me back. I didn’t realize my opinion changed how counting worked. In my world, I had zero the whole time.
Me: Sigh. It’s not like that. When he gives you the cows back, you go from -3 to 3.
You: Ok, so he returns 3 cows and we jump 6, from -3 to 3? Any other new arithmetic I should be aware of? What does sqrt(-17) cows look like?
Me: Get out.
Negative numbers can express a relationship:
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Positive numbers represent a surplus of cows
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Zero represents no cows
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Negative numbers represent a deficit of cows that are assumed to be paid back
But the negative number “isn’t really there” — there’s only the relationship they represent (a surplus/deficit of cows). We’ve created a “negative number” model to help with bookkeeping, even though you can’t hold -3 cows in your hand. (I purposefully used a different interpretation of what “negative” means: it’s a different counting system, just like Roman numerals and decimals are different counting systems.)
By the way, negative numbers weren’t accepted by many people, including Western mathematicians, until the 1700s. The idea of a negative was considered “absurd”. Negative numbers do seem strange unless you can see how they represent complex real-world relationships, like debt.
Why All The Philosophy?
I realized that my **mindset is key to learning. **It helped me arrive at deep insights, specifically:
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Factual knowledge is not understanding. Knowing “hammers drive nails” is not the same as the insight that any hard object (a rock, a wrench) can drive a nail.
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Keep an open mind. Develop your intuition by allowing yourself to be a beginner again.
A university professor went to visit a famous Zen master. While the master quietly served tea, the professor talked about Zen. The master poured the visitor’s cup to the brim, and then kept pouring. The professor watched the overflowing cup until he could no longer restrain himself. “It’s overfull! No more will go in!” the professor blurted. “You are like this cup,” the master replied, “How can I show you Zen unless you first empty your cup.”
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Be creative. Look for strange relationships. Use diagrams. Use humor. Use analogies. Use mnemonics. Use anything that makes the ideas more vivid. Analogies aren’t perfect but help when struggling with the general idea.
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Realize you can learn. We expect kids to learn algebra, trigonometry and calculus that would astound the ancient Greeks. And we should: we’re capable of learning so much, if explained correctly. Don’t stop until it makes sense, or that mathematical gap will haunt you. Mental toughness is critical — we often give up too easily.
So What’s The Point?
I want to share what I’ve discovered, hoping it helps you learn math:
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Math creates models that have certain relationships
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We try to find real-world phenomena that have the same relationship
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Our models are always improving. A new model may come along that better explains that relationship (roman numerals to decimal system).
Sure, some models appear to have no use: “What good are imaginary numbers?”, many students ask. It’s a valid question, with an intuitive answer.
The use of imaginary numbers is limited by our imagination and understanding — just like negative numbers are “useless” unless you have the idea of debt, imaginary numbers can be confusing because we don’t truly understand the relationship they represent.
Math provides models; understand their relationships and apply them to real-world objects.
Developing intuition makes learning fun — even accounting isn’t bad when you understand the problems it solves. I want to cover complex numbers, calculus and other elusive topics by focusing on relationships, not proofs and mechanics.
But this is my experience — how do you learn best?
This section by Kalid Azad was made under a Creative Commons Attribution-NonCommercial-ShareAlike license.
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Fraud in science
Image by Aurich Lawson, ArsTechnia, Epic fraud: How to succeed in science (without doing any)
Science is a self-correcting enterprise.
But science is about investigating nature – not about investigating the human investigators themselves. Scientists don’t assume that everyone else’s research is always correct, sure. They assume that errors might exist – so that’s why we have the peer review system. But they general presume that research is earnest and honest. When a scientist decides to engage in fraud, in some disciplines, their fake results are often harder to detect.
Topics
Lysenko, Russia, and genetics-denial
Lysenkoism was named for Russian botanist Trofim Denisovich Lysenko. It occurred in Joseph Stalin’s Soviet Union. Lysenkoism mandated that all biological research conducted in the USSR conform to a modified Lamarckian evolutionary theory. Communists wanted this to be true because it promised a biology based on a moldable view of life consistent with Marxist-Leninist dogma.
Lysenkoists employed a form of political correctness to instill terror in anyone who disagreed with their dogma. People who disagreed with them faced public denunciation, loss of Communist Party membership, loss of employment, and even arrest by the secret police. Between Lysenko’s grip on power and the “disappearances” of numerous of his opponents, it would be years until the Soviet biology program would recover. – adapted from RationalWiki.
“It was an ugly picture of what happens when science is subservient to ideology, arguable the most extreme example in history. As a result of Lysenko’s crank ideas, the famine that was already underway was worsened. Lysenkoism was also exported to other communist countries like China, who also experienced horrible famine. Millions of people starved due to Lysenko’s crank ideas, making him arguably the scientist with the largest body count in human history.” – The Return of Lysenkoism
Supposed link between personality types and cancer
A remarkable series of fraudulent papers which attempted to convince people that lung cancer wasn’t caused by cigarettes. This fake research turns out to have been funded by the cigarette lobby.
“In 1992, Anthony Pelosi voiced concerns in the British Medical Journal about controversial findings from Hans Eysenck – one of the most influential British psychologists of all time – and German researcher Ronald Grossarth-Maticek. Those findings claimed personality played a bigger part in people’s chances of dying from cancer or heart disease than smoking. Almost three decades later, Eysenck’s institution have recommended these studies be retracted from academic journals. Hannah Devlin speaks to Pelosi about the twists and turns in his ultimately successful journey. And to the Guardian’s health editor, Sarah Boseley, about how revelations from tobacco industry documents played a crucial role.”
Taking on Eysenck: one man’s mission to challenge a giant of psychology
Fake link between vaccines and autism
Andrew Wakefield, claimed that he had shown a link between vaccines and autism .
“He was found guilty of dishonesty in his research and banned from medicine by the UK General Medical Council following an investigation by Brian Deer of the London Sunday Times.” – Wikipedia
The Facts In The Case Of Dr. Andrew Wakefield, Tall Guy Investigates. The facts of the case told in graphic novel format.
Stuart Ritchie writes
By now, most people know that Wakefield’s findings have been discredited. Since 1998, there have been several large-scale, rigorous studies showing no relation between the MMR vaccine (or any other vaccine) and autism spectrum disorder. It’s also been shown that combination vaccines are just as safe as individual ones. What many aren’t aware of, though, is that the Wakefield paper, far from being an honest mistake or an understandable dead end in a tentative line of research, was fraudulent right from the beginning.
After the study’s publication and the attendant controversy, the investigative journalist Brian Deer began to dig into Wakefield’s data and, crucially, his motivations. In a series of stunning articles in The BMJ (formerly the British Medical Journal), Deer described how Wakefield misrepresented or altered the medical details of every single one of the twelve children included in his paper.
He simply invented the “fact” that all the children showed their first autism-related symptoms soon after receiving the MMR whereas in reality, some had records of symptoms beforehand, others only had symptoms many months afterward, and some never even received a diagnosis of autism at all.
As for the motivation, Deer showed, Wakefield had two major financial interests in the research turning out the way it did. First, he was being retained, on a substantial fee, by a lawyer who had plans to sue the makers of the vaccines on behalf of the parents of children with autism. Indeed, an anti-vaccine pressure group linked to this lawyer was how Wakefield recruited the patients for his study.
Second, the year before the study’s publication, he had applied for a patent for his own single measles vaccine and would thus have profited had his research frightened people away from the combined MMR. Inexcusably, neither of these interests were disclosed in the paper:
How Fraud and a Broken Publishing System Fueled the Vaccine-Autism Myth, excerpted from Science Fictions: How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth, Stuart Ritchie, Metropolitan Books July 2020
Anesthesiology research fraud
Yoshitaka Fujii (Japan), researcher in anesthesiology, fabricated data in at least 183 scientific papers, setting what is believed to be a record. A committee reviewing 212 papers published by Fujii over a span of 20 years found that 126 were entirely fabricated, with no scientific work done. – Wikipedia
Books
Corrupted Science: Fraud, Ideology and Politics in Science
Articles
Retraction Watch: Reports on retractions of scientific papers and on related topics
Yoshihiro Sato: Researcher at the center of an epic fraud remains an enigma to those who exposed him
Yoshitaka Fujii: Epic fraud: How to succeed in science (without doing any)
Scientific Misconduct (Wikipedia)
The thinking error at the root of science denial
Excerpted from The thinking error at the root of science denial
from de.wikipedia.org, 5_characteristics_of_science_denial.jpg
By Jeremy P. Shapiro, Adjunct Assistant Professor of Psychological Sciences, Case Western Reserve University May 8, 2018, theconversation.com
As a psychotherapist, I see a striking parallel between a type of thinking involved in many mental health disturbances and the reasoning behind science denial. As I explain in my book “Psychotherapeutic Diagrams,” dichotomous thinking, also called black-and-white and all-or-none thinking, is a factor in depression, anxiety, aggression and, especially, borderline personality disorder.
In this type of cognition, a spectrum of possibilities is divided into two parts, with a blurring of distinctions within those categories. Shades of gray are missed; everything is considered either black or white. Dichotomous thinking is not always or inevitably wrong, but it is a poor tool for understanding complicated realities because these usually involve spectrums of possibilities, not binaries.
Spectrums are sometimes split in very asymmetric ways, with one-half of the binary much larger than the other.
For example, perfectionists categorize their work as either perfect or unsatisfactory; good and very good outcomes are lumped together with poor ones in the unsatisfactory category.
In borderline personality disorder, relationship partners are perceived as either all good or all bad, so one hurtful behavior catapults the partner from the good to the bad category.
It’s like a pass/fail grading system in which 100 percent correct earns a P and everything else gets an F.
In my observations, I see science deniers engage in dichotomous thinking about truth claims. In evaluating the evidence for a hypothesis or theory, they divide the spectrum of possibilities into two unequal parts: perfect certainty and inconclusive controversy. Any bit of data that does not support a theory is misunderstood to mean that the formulation is fundamentally in doubt, regardless of the amount of supportive evidence.
Similarly, deniers perceive the spectrum of scientific agreement as divided into two unequal parts: perfect consensus and no consensus at all. Any departure from 100 percent agreement is categorized as a lack of agreement, which is misinterpreted as indicating fundamental controversy in the field.
There is no ‘proof’ in science
In my view, science deniers misapply the concept of “proof.”
Proof exists in mathematics and logic but not in science. Research builds knowledge in progressive increments. As empirical evidence accumulates, there are more and more accurate approximations of ultimate truth but no final end point to the process.
Deniers exploit the distinction between proof and compelling evidence by categorizing empirically well-supported ideas as “unproven.” Such statements are technically correct but extremely misleading, because there are no proven ideas in science, and evidence-based ideas are the best guides for action we have.
I have observed deniers use a three-step strategy to mislead the scientifically unsophisticated. First, they cite areas of uncertainty or controversy, no matter how minor, within the body of research that invalidates their desired course of action. Second, they categorize the overall scientific status of that body of research as uncertain and controversial. Finally, deniers advocate proceeding as if the research did not exist.
For example, climate change skeptics jump from the realization that we do not completely understand all climate-related variables to the inference that we have no reliable knowledge at all. Similarly, they give equal weight to the 97 percent of climate scientists who believe in human-caused global warming and the 3 percent who do not, even though many of the latter receive support from the fossil fuels industry.
This same type of thinking can be seen among creationists. They seem to misinterpret any limitation or flux in evolutionary theory to mean that the validity of this body of research is fundamentally in doubt.
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Why is the Earth still hot?
How hot is it inside of our world? Well, we see that volcanoes constantly erupts – and they have been doing do for billions of years. Evidently the interior of our planet is seething hot.
If you could have a god’s eye view of the world, see right inside it, it would look something like this:
Photo by RK (c) 2019
Wow! We can clearly see that our world’s interior is full of very hot, glowing, rock! Moving in a bit closer, we’d see hot plumes of magma slowly rising towards the surface, while cooler areas at the surface are pushed mostly sideways, and then begin to descend downwards.
This is all happening slowly of course. We’d to watch for hundreds of thousands of years to clearly see the patterns.
Questions
1. Where did all of this heat energy come from?
2. And since Earth is billions of years old, why hasn’t it cooled down yet?
1. Where did all of this heat come from?
Everything in our Solar Systems – our Sun, the Earth, and the other planets – formed from the gravitational collapse of giant molecular clouds.
Atoms and dust particles are gravitationally attracted to each other, creating larger particles, then pebble-size objects. Over time those objects collided to create rocks of various types (including organic molecules, water, and metals.)
Over longer periods of time those collided to create asteroid-size objects, and then eventually planet size objects.
Big pieces orbited around the huge center of mass, which became our star, the Sun.
Over time those bigger pieces (proto planets) swept up all the material in their path – they cleared the neighborhood of their orbit.
This process created Earth and other similar worlds: Venus, Mars, and Mercury.
We think of Earth as if it were solid, but over long time scales the interior is closer to a liquid – hotter regions expand and rise, cooler regions contract and sink.
Because of this, heavier elements, like iron, would quickly have sunk to the core. In just 10 to 100 million years. This would also pull down any other elements bound to that iron. As such, most of the Earth’s interior is metal, while most of the crust is rock.
We can see this in more detail here – the formation of our solar system
2. And since Earth is billions of years old, why hasn’t it cooled down yet?
This section includes quotes from Radioactive potassium may be major heat source in Earth’s core, Robert Sanders, UC Berkeley News, 12/13/2003
When the Earth was first formed this material was not solid; some was hot enough to become viscous (like silly putty) or even liquid (like lava.)
The denser material was mostly iron and some radioactive metals.
This dense metal slowly sank towards the center, while less dense rock floated upwards.
This process itself created a lot of friction, which created a lot of heat.
“Gradually, however, the Earth would have cooled off and become a dead rocky globe with a cold iron ball at the core if not for the continued release of heat by the decay of radioactive elements like: potassium-40, uranium-238 and thorium-232, which have half-lives of 1.25 billion, 4 billion and 14 billion years, respectively.
About one in every thousand potassium atoms is radioactive.”
Heat from the decay of radioactive elements.
Most metals we know are stable. Think of Nickel, Iron, Copper and Gold. If you put them in a box so that they don’t get exposed to oxygen, then they don’t rust, and never change. Millions of years from now they will still be around.
What’s inside metal atoms? Electrons, protons and neutrons. In a metal atom, the number of these particles will normally never change.
Example: Iron-56 26 protons, 30 neutrons, 26 electrons.
But some very large atoms are special: they not stable – they do change, all by themselves. These are called radioactive elements.
Uranium-238 92 protons, 146 neutrons, 92 electrons
-> spontaneously will change into
Plutonium-239 94 protons, 145 neutrons, 94 electrons + heat
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In sum, there was no shortage of heat in the early earth, and the planet’s inability to cool off quickly results in the continued high temperatures of the Earth’s interior.
In effect, not only do the earth’s plates act as a blanket on the interior, but not even convective heat transport in the solid mantle provides a particularly efficient mechanism for heat loss.
The planet does lose some heat through the processes that drive plate tectonics, especially at mid-ocean ridges. For comparison, smaller bodies such as Mars and the Moon show little evidence for recent tectonic activity or volcanism.
We derive our primary estimate of the temperature of the deep earth from the melting behavior of iron at ultrahigh pressures.
We know that the earth’s core depths from 2,886 kilometers to the center at 6,371 kilometers (1,794 to 3,960 miles), is predominantly iron, with some contaminants.
How? The speed of sound through the core (as measured from the velocity at which seismic waves travel across it) and the density of the core are quite similar to those seen in of iron at high pressures and temperatures, as measured in the laboratory.
Iron is the only element that closely matches the seismic properties of the earth’s core and is also sufficiently abundant present in sufficient abundance in the universe to make up the approximately 35 percent of the mass of the planet present in the core.
The earth’s core is divided into two separate regions: the liquid outer core and the solid inner core, with the transition between the two lying at a depth of 5,156 kilometers (3,204 miles).
Therefore, If we can measure the melting temperature of iron at the extreme pressure of the boundary between the inner and outer cores, then this lab temperature should reasonably closely approximate the real temperature at this liquid-solid interface.
Scientists in mineral physics laboratories use lasers and high-pressure devices called diamond-anvil cells to re-create these hellish pressures and temperatures as closely as possible.
Those experiments provide a stiff challenge, but our estimates for the melting temperature of iron at these conditions range from about 4,500 to 7,500 kelvins (about 7,600 to 13,000 degrees F).
As the outer core is fluid and presumably convecting (and with an additional correction for the presence of impurities in the outer core), we can extrapolate this range of temperatures to a temperature at the base of Earth’s mantle (the top of the outer core) of roughly 3,500 to 5,500 kelvins (5,800 to 9,400 degrees F) at the base of the earth’s mantle.
The bottom line here is simply that a large part of the interior of the planet (the outer core) is composed of somewhat impure molten iron alloy.
The melting temperature of iron under deep-earth conditions is high, thus providing prima facie evidence that the deep earth is quite hot.
Gregory Lyzenga is an associate professor of physics at Harvey Mudd College. He provided some additional details on estimating the temperature of the earth’s core:
How do we know the temperature? The answer is that we really don’t–at least not with great certainty or precision. The center of the earth lies 6,400 kilometers (4,000 miles) beneath our feet, but the deepest that it has ever been possible to drill to make direct measurements of temperature (or other physical quantities) is just about 10 kilometers (six miles).
Ironically, the core of the earth is by far less accessible more inaccessible to direct probing than would be the surface of Pluto. Not only do we not have the technology to “go to the core,” but it is not at all clear how it will ever be possible to do so.
As a result, scientists must infer the temperature in the earth’s deep interior indirectly. Observing the speed at which of passage of seismic waves pass through the earth allows geophysicists to determine the density and stiffness of rocks at depths inaccessible to direct examination.
If it is possible to match up those properties with the properties of known substances at elevated temperatures and pressures, it is possible (in principle) to infer what the environmental conditions must be deep in the earth.
The problem with this is that the conditions are so extreme at the earth’s center that it is very difficult to perform any kind of laboratory experiment that faithfully simulates conditions in the earth’s core.
Nevertheless, geophysicists are constantly trying these experiments and improving on them, so that their results can be extrapolated to the earth’s center, where the pressure is more than three million times atmospheric pressure.
The bottom line of these efforts is that there is a rather wide range of current estimates of the earth’s core temperature. The “popular” estimates range from about 4,000 kelvins up to over 7,000 kelvins (about 7,000 to 12,000 degrees F).
If we knew the melting temperature of iron very precisely at high pressure, we could pin down the temperature of the Earth’s core more precisely, because it is largely made up of molten iron.
But until our experiments at high temperature and pressure become more precise, uncertainty in this fundamental property of our planet will persist.
— end quote —
What will happen when the Earth finally cools?
When the Earth’s core finally does cool – billions of years from now – then Earth will solidify and there will be no more plate tectonics. Therefore there will be
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No more earthquakes
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No more volcanic eruptions
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no more island building
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No more mountain building
The Earth’s surface will eventually be eroded down to a flatter surface, marred only by new impact craters.
Earth will then be a geologically dead planet, like the Moon.
Some scientists estimate that “The planet is now cooling about 100°C every 1 billion years, so eventually, maybe several billions of years from now, the waning rays of a dying sun will shine down on a tectonically dead planet whose continents are frozen in place.”
How do we know what lies at the Earth’s core?
How we know what lies at the Earth’s core. BBC
Addressing misconceptions
If the Earth’s core is radioactive why is there no radiation at the surface?
Click the link to read the article, but short version, there indeed is radioactivity here on the Earth’s surface!
External resources and discussions
What percent of the Earth’s core is uranium? earthscience.stackexchange.com
Claim: Radioactive decay accounts for half of Earth’s heat, and related, What Keeps the Earth Cooking? Berkeley Lab scientists join their KamLAND colleagues to measure the radioactive sources of Earth’s heat flow
A fascinating although somewhat controversial article, Andrault, Denis & Monteux, J. & Le Bars, Michael & Samuel, H.. (2016). The deep Earth may not be cooling down. Earth and Planetary Science Letters. 443. 10.1016/j.epsl.2016.03.020.
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Teaching science with augmented reality
Using virtual reality in the classroom
We learn through lectures and reading. We especially learn through illustrations, photographs, diagrams, and animations. But a limitation is that so many of these images are flat, two-dimensional. Not surprisingly, many folks have trouble visualizing what a system is really like, if they only have two dimensional pictures.
An obvious practical solution is to make a lesson hands-on: Students can take a field trip to see gears and machines in a power plant; see ancient ruins on site; travel to a valley and fly over a vast ecosystem to see different parts of the environment. But there’s only so much that a school can do in practice: we can’t purchase every manipulative and lab, or travel to see every place that we talk about.
Yet with today’s technology we can actually model machines, cells, valleys and volcanoes, ecosystems, distance cities, and archaeological sites, in three dimensions – and then bring all of this into the classroom. We bring these models in to a virtual space that students can explore.
And that’s what we are already doing in our classrooms! First, let’s learn a few terms: XR, AR, and VR.
XR- Extended Reality
the emerging umbrella term for all immersive computer virtual experience technologies. These technologies AR, VR, and MR.
Augmented Reality (AR)
When virtual information and objects are overlaid on the real world. This experience enhances the real world with digital details such as images, text, and animation. This means users are not isolated from the real world and can still interact and see what’s going on in front of them.
CRISPR enzyme floating in three dimensions.
Photo by RK (c) 2019
Virtual Reality (VR)
Users are fully immersed in a simulated digital environment. Individuals must put on a VR headset or head-mounted display to get a 360 -degree view of an artificial world. This fools their brain into believing they are walking on the moon, swimming under the ocean or stepped into whatever new world the VR developers created.
A team of researchers at ESA’s mission control centre in Darmstadt, Germany, are investigating new concepts for controlling rovers on a planet and satellites in orbit. Image from the ESA, esa.int/ESA_Multimedia/Images/2017/07/Reality_check
Mixed reality (MR), aka Hybrid Reality
Digital and real-world objects co-exist and can interact with one another in real-time. This experience requires an MR headset… Microsoft’s HoloLens is a great example that, e.g., allows you to place digital objects into the room you are standing in and give you the ability to spin it around or interact with the digital object in any way possible.
Image from Microsoft
Excerpts of these definitions from Bernard Marr, What Is Extended Reality Technology? A Simple Explanation For Anyone, Forbes, 8/12/2019
Augmented reality in Ecology & Environmental Science
When students actively participate in augmented reality learning, the class is effectively a lab, as opposed to being a lecture. Here we are studying ecosystems with an app from the World Wildlife Foundation, WWF Rivers.
Photo by RK (c) 2019
This student has their head in the clouds 😉
Photo by RK (c) 2019
Here we are using the Google Expeditions app, on a Pixel 3A smartphone. The plug-in is “Earth Geology” by Vida systems. For more details see Google Expeditions – Education in VR.
AR in Earth Science
As we walk around the room, we see the Earth and all of it’s layers in a realistic 3D view. Here we stood above the arctic circle, and took screenshots as we moved down latitude, until we were above the antarctic.
Photo by RK (c) 2019
Photo by RK (c) 2019
AR in Physics & Engineering
A simple machine is a mechanical device that changes the direction or magnitude of a force. They are the simplest mechanisms that use mechanical advantage to multiply force.
Here we are examining gears, including bicycle gears.
Photo by RDK (c) 2019
Related Special Education topics
If you can’t visually imagine things, how can you learn?
If someone can’t visually imagine things, how can you learn? We know some people can’t conjure up mental images. But we’re only beginning to understand the impact this “aphantasia” might have on their education.
A discussion of an inability to form mental images , congenital aphantasia. This is believed to affect 2% of the population.
by Mo Costandi, Jun 2016, The Guardian, UK
Learning Standards
What kind of learning standards will students address when using augmented reality science lessons?
NGSS Cross-Cutting Concepts
6. Structure and Function – The way an object is shaped or structured determines many of its properties and functions: Complex and microscopic structures and systems can be visualized, modeled, and used to describe how their function depends on the shapes, composition, and relationships among its parts; therefore, complex natural and designed structures/systems can be analyzed to determine how they function
Massachusetts Digital Literacy and Computer Science (DLCS) Curriculum Framework
Modeling and Simulation [6-8.CT.e] – 3. Select and use computer simulations, individually and collaboratively, to gather, view, analyze, and report results for content-related problems (e.g., migration, trade, cellular function).
Digital Tools [9-12.DTC.a] – 2. Select digital tools or resources based on their efficiency and effectiveness to use for a project or assignment and justify the selection.
American Association of School Librarians: Standards Framework for Learners
1. Inquire: Build new knowledge by inquiring, thinking critically, identifying problems, and developing strategies for solving problems
Advanced Placement Computer Science Principles
AP-CSP Curriculum Guides
LO 3.1.3 Explain the insight and knowledge gained from digitally processed data by using appropriate visualizations, notations, and precise language.
EK 3.1.3A Visualization tools and software can communicate information about data.
EK 3.1.3E Interactivity with data is an aspect of communicating.
MCAS Classification
MCAS Classification questions
32. The table below shows the classifications of three different sea lions.
a. Identify which two of the sea lions are most closely related.
b. Justify your answer to part (a).
c. Describe and explain two types of evidence scientists would have used to determine the proper classifications of these three sea lions.
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2016.
5. A scientist concludes that two organisms belong to the same species within the
class Mammalia. Which of the following observations most likely led the scientist
to conclude that the organisms are the same species?
A. The organisms move in the same way.
B. The organisms live in the same habitat.
C. The organisms are nocturnal and carnivorous.
D. The organisms mate and produce fertile offspring.
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24. The brush mouse and the northwestern deermouse are both classified in the
genus Peromyscus. Which of the following conclusions can be made from this information?
A. The two types of mice live in the same habitat.
B. The two types of mice have the same fur color.
C. The two types of mice are closely related to each other.
D. The two types of mice can successfully interbreed with each other.
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32. The table below gives the common names, scientific names, and known geographic locations of several wild cats.
a. Using their common names, identify all the wild cats listed in the table that belong to the same genus.
b. Identify and explain one type of evidence scientists could have used to classify these wild cats.
The three kinds of tigers listed in the table are all classified as one species.
c. Based on the information in the table, identify which kind of tiger has the greatest chance of becoming a separate species. Explain your answer.
d. Describe how scientists could determine if one of the kinds of tigers becomes a separate species.
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33. The table below shows taxonomic information for the gray wolf and four other species.
Based on this information, which of the following lists the species in order from most closely related to least closely related to the gray wolf ?
A. 1, 2, 3, 4
B. 1, 2, 4, 3
C. 2, 1, 3, 4
D. 2, 1, 4, 3
31. All organisms classified in kingdom Animalia must also be classified as
which of the following?
A. Archaea
B. Eubacteria
C. Eukaryota
D. Protista
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45. A student researching bears found the chart below in a textbook. The chart shows the
classifications of several types of bears.
Which of the following conclusions is best supported by the data given in this chart?
A. Modern bears evolved from species that are now extinct.
B. The short-faced bear was the ancestor of the Asiatic black bear.
C. Present day bear species are more closely related than their ancestors were.
D. Natural selection favored the brown bear over the American black bear. .
MCAS Plants
MCAS Plant questions from the Biology MCAS
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31. A plant species growing along a coast produces seeds with fluffy hair-like
fibers on one end. A seed from one of the plants is shown below:
Some of these seeds were dispersed by the wind to islands off the coast, where new plants grew. Within 10 years, the seeds of the island plants were different
from the seeds of the mainland plants. Compared to the mainland seeds, the
island seeds were heavier and had shorter hair-like fibers. Which of the following statements best explains why heavier seeds with shorter fibers were favored in the island environment?
A. These seeds carried more genes than the mainland seeds did.
B. These seeds were less likely to be blown off the island by wind.
C. The island plants needed to prevent animals from eating the seeds.
D. The island plants used more energy to produce heavy seeds than to grow.
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33. Students investigated the effect of acid rain on photosynthesis. Several plants
were given water with a pH of 4 each day for two months. The results showed
that the plants had a reduced rate of photosynthesis.
How did the acidic water most likely reduce the plants’ rate of photosynthesis?
A. by storing excess oxygen produced by the plants
B. by changing the effectiveness of enzymes in the plants
C. by causing root hairs to grow on the roots of the plants
D. by increasing the amount of carbon dioxide taken in by the plants
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34. Waxes form a waterproof coating over the stems and leaves of many terrestrial plants. The waxes are composed of fatty acids linked to long-chain alcohols. Based on this information, waxes are which type of organic molecule?
A. lipids . B. nucleotides . C. polysaccharides . D. proteins
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37. Maltose is a carbohydrate molecule that provides energy to plants early in their
life cycle. Which elements are most common in a molecule of maltose?
A. carbon and hydrogen
B. copper and nitrogen
C. iron and phosphorus
D. magnesium and sulfur
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Algae, and the scientific method
The rate of photosynthesis in organisms depends in part on the wavelength of visible light. In the late 1800s, Thomas Engelmann demonstrated the relationship between the wavelength of light and the rate of photosynthesis. His experiment is described below.
• Engelmann used a prism to produce a visible light spectrum of violet, blue, green, yellow, orange, and red light.
• He shined the light spectrum onto cells of the algae Spirogyra.
• Once the light was shining on the Spirogyra cells, Engelmann added aerobic bacteria to the system. Aerobic bacteria need oxygen to live and grow.
• After adding the bacteria, Engelmann observed the regions of the light spectrum where the bacteria concentrated around the Spirogyra cells.
The setup and results of Engelmann’s experiment are represented by the diagram below:
Mark your answers to multiple-choice questions 8 through 11 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet, but you may work out solutions to multiple-choice questions in the test booklet.
8. Why are the greatest numbers of aerobic bacteria found at the 400–500 nm and 600–700 nm wavelengths of light?
A. Photosynthesis rates are highest there, producing large amounts of water.
B. Photosynthesis rates are highest there, producing large amounts of oxygen.
C. Photosynthesis rates are lowest there, producing small amounts of glucose.
D. Photosynthesis rates are lowest there, producing small amounts of carbon dioxide.
9. What is the role of visible light when Spirogyra cells perform photosynthesis?
A. It provides the energy for the photosynthesis reaction.
B. It concentrates the photosynthesis products for export.
C. It activates the DNA that directs the photosynthesis reaction.
D. It transports photosynthesis reactants across the cell membrane.
10. What is exchanged between the Spirogyra and the bacteria in
Engelmann’s experiment?
A. DNA and RNA
B. starch granules and spores
C. chlorophyll and cytoplasm
D. oxygen and carbon dioxide
11. A scientist used Engelmann’s data to predict how the concentrations of different substances in and around Spirogyra cells will change when the cells are exposed to different wavelengths of light. A graph for one substance is shown below.
What is represented on the y-axis?
A. chlorophyll concentration . B. hydrogen concentration
C. oxygen concentration . D. water concentration
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3. All corn plants contain the ZmLA1 gene. Some corn plants contain a certain mutation in the ZmLA1 gene. The graph below shows the amount of ZmLA1 RNA produced in plants with the normal gene and in plants with the mutated gene.
Based on the graph, what most likely happens in corn plant cells as a direct result of the mutated gene?
A. DNA replication increases.
B. Lipid production decreases.
C. Glucose synthesis increases.
D. Protein production decreases.
____________________
4. The growth of plants in many ecosystems is limited by the supply of
nitrogen. Which of the following groups of organisms plays the largest role in
moving nitrogen between the atmosphere and plants?
A. bacteria . B. earthworms . C. insects . D. protists
____________________
7. Lithops are multicellular organisms found in sandy soil in deserts. They
have large, central vacuoles in their cells that store water. Which of the following best classifies lithops?
A. They are bacteria because they store water.
B. They are animals because they are multicellular.
C. They are fungi because they are found in sandy soil.
D. They are plants because they have large, central vacuoles.
____________________
14. There are many fungus species that live inside plant tissues. What determines
whether the relationship between a fungus and a plant is commensalism,
mutualism, or parasitism?
A. where the fungus is located in the plant
B. how long the fungus survives in the plant
C. whether the fungus reproduces in the plant with spores, seeds, or runners
D. whether the effect of the fungus on the plant is neutral, positive, or negative
____________________
37. Plants in floodplains often get covered by water during floods. Some
plants survive the floods because they can continue photosynthesis
underwater. However, the plants’ rates of photosynthesis are much lower
underwater than above water.
Which of the following helps to explain why the rates of photosynthesis are
lower underwater than above water?
A. There is too much oxygen in the water.
B. There is no carbon dioxide in the water.
C. The chloroplasts do not function underwater.
D. The available light is less intense underwater.
____________________
17. Carbon fixation is an important part of the carbon cycle. Carbon fixation is the conversion of carbon dioxide into organic compounds such as glucose. Which of the following organisms cannot fix carbon?
A. grass
B. green algae
C. mushrooms
D. oak trees
____________________
3. A botanist studied two groups of rice plants to determine how they are related. Both groups of plants have similar shapes, but one group has longer stalks. When the botanist cross-pollinated plants from one group with plants from the other group, the seeds produced did not sprout or grow.
Which of the following conclusions is best supported by this information?
A. The two groups are the same species because the plants have similar shapes.
B. The two groups are different species because they have differently sized stalks.
C. The two groups are different species because the seeds produced cannot sprout or grow.
D. The two groups are the same species because the plants were cross-pollinated and produced seeds
____________________
20. A partial food web is shown below. Which organisms in the food web are both primary and secondary consumers?
A. bluegills
B. cattails
C. coyotes
D. snakes
____________________
28. A student looks at a cell under a microscope. Which of the following
observations would indicate that the cell is from a plant rather than an animal?
A. a nucleus located inside of the cell
B. numerous cilia on the outside of the cell
C. chloroplasts in the cytoplasm of the cell
D. a thin membrane around the edge of the cell
____________________
30. Prolonged periods of drought in an area cause decreases in plant population
sizes. Which of the following statements describes how the decreases in plant
population sizes then affect other populations in the area?
A. Omnivore population sizes increase, and herbivore population sizes increase.
B. Omnivore population sizes decrease, and carnivore population sizes increase.
C. Herbivore population sizes increase, and carnivore population sizes decrease.
D. Herbivore population sizes decrease, and carnivore population sizes decrease.
Pseudoscience
Resource under construction
Introduction
Pseudoscience is a belief system which tries to gain legitimacy by wearing the trappings of science, but fails to abide by the rigorous methodology and standards of evidence that are the marks of actual science.
Pseudoscientists adopt the vocabulary of science, describing conjectures as hypotheses, theories, or laws, providing “evidence” from observation and “expert” testimonies, or developing what appear to be mathematical models of their ideas. However, in pseudoscience there is no attempt to follow the scientific method, provide falsifiable predictions, or develop double blind experiments.
Intro adapted from RationalWiki
Pseudoscience is characterized by:
contradictory, exaggerated or unfalsifiable claims
reliance on confirmation bias rather than rigorous attempts at refutation
lack of openness to evaluation by other experts
absence of systematic practices when developing hypotheses
continued adherence long after the pseudoscientific hypotheses have been experimentally discredited.
(list here adapted from Wikipedia)
Examples
Facts and fiction of the Schumann resonance
If ANY of these claims were actually workable then…
Image from xkcd.com/808/
How to identify red flags
Below are red flags that a supposedly “scientific” claim is in fact pseudoscience.
These essays are from Graham Coghill’s ScienceOrNot. He has articles on indicators of good science (Hallmarks of Science) and indicators of bad science (Science Red Flags).
These are covered by a Creative Commons License.
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The ‘scientifically proven’ subterfuge. |
Scammers and deniers use two forms of this tactic:
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Persecuted prophets and maligned mavericks: The Galileo Gambit. |
Users of this tactic will try to persuade you that they belong to a tradition of maverick scientists who have been responsible for great advances despite being persecuted by mainstream science. |
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Empty edicts – absence of empirical evidence |
This tactic shows up when people make claims in the form of bald statements – “this is the way it is” or “this is true” or “I know/believe this” or “everybody knows this” – without any reference to supporting evidence. |
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Anecdotes, testimonials and urban legends |
Those who use this tactic try to present stories about specific cases or events as supporting evidence. The stories range from personal testimonials, to anecdotes about acquaintances, to tales about unidentifiable subjects. |
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Charges of conspiracy, collusion and connivance |
Conspiracy theorists usually start by targeting weaknesses in an accepted model, then propose a conspiracy that explains why their ‘better’ model has been suppressed.Although there can be overwhelming evidence favouring the accepted model, they claim that this simply means the conspiracy has been successful. |
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Stressing status and appealing to authority |
People who use this tactic try to convince you by quoting some ‘authority’ who agrees with their claims and pointing to that person’s status, position or qualifications, instead of producing real-world evidence. The tactic is known as the argument from authority. |
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Devious deception in displaying data: Cherry picking |
In cherry-picking, people use legitimate evidence, but not all of the evidence. They select segments of evidence that appear to support their argument and hide or ignore the rest of the evidence which tends to refute it. |
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Repetition of discredited arguments – parroting PRATT |
In this tactic, people persist in repeating claims that have been shown over and over to have no foundation. Look for slogans, sweeping statements or claims that look as though they could easily be refuted. |
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Duplicity and distraction – false dichotomy |
In this tactic, people assert that there are only two possible (and usually opposite) positions to choose from, when in fact there are more.They try to argue that if one position is shown to be false, then the other must be correct. |
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Wishful thinking – favouring fantasy over fact |
We all fall victim to this tactic because we use it on ourselves. We like to believe things that conform with our wishes or desires, even to the extent of ignoring evidence to the contrary. |
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Appeals to ancient wisdom – trusting traditional trickery |
People who use this tactic try to persuade you that a certain explanation, treatment or model must be correct because it’s been around for a long time. |
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Technobabble and tenuous terminology: the use of pseudo scientific language |
In this tactic, people use invented terms that sound “sciencey” or co-opt real science terms and apply them incorrectly. |
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Confusing correlation with causation: rooster syndrome |
This is the natural human tendency to assume that, if two events or phenomena consistently occur at about the same time, then one is the cause of the other.Hence “rooster syndrome”, from the rooster who believed that his crowing caused the sun to rise. |
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Straw man: crushing concocted canards |
When this tactic is used, it’s always in response to an argument put up by an opponent. Unable to come up with a reasoned response, the perpetrator constructs a distorted, incorrect version (the “straw man”) of the opponent’s argument, and then proceeds to tear it to shreds. |
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Indelible initial impressions: the anchoring effect |
Anchoring is the human tendency to rely almost entirely on one piece of evidence or study, usually one that we encountered early, when making a decision. |
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Perceiving phoney patterns: apophenia |
This happens when you convince yourself, or someone tries to convince you, that some data reveal a significant pattern when really the data are random or meaningless. |
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Esoteric energy and fanciful forces. |
This tactic is easy to pick because people who use it try to convince you that some kind of elusive energy or power or force is responsible for whatever effect they are promoting. |
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Banishing boundaries and pushing panaceas – applying models where they don’t belong |
Those who use this tactic take a model that works under certain conditions and try to apply it more widely to circumstances beyond its scope, where it does not work. Look for jargon, sweeping statements and vague, rambling “explanations” that try to sound scientific. |
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Averting anxiety with cosmic connectivity: magical thinking |
Magical thinking is present when anyone argues that everything is connected: thoughts, symbols and rituals can have distant physical and mental effects; inanimate objects can have intentions and mystical influences.Often, the connectivity is supposedly mediated by some mysterious energy, force or vibration and there is much talk of holism, resonance, balance, essences and higher states. |
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Single study syndrome – clutching at convenient confirmation |
This tactic shows up when a person who has a vested interest in a particular point of view pounces on some new finding which seems to either support or threaten that point of view. It’s usually used in a context where the weight of evidence is against the perpetrator’s view. |
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Appeal to nature – the authenticity axiom |
You are expected to accept without question that anything ‘natural’ is good, and anything ‘artificial’, ‘synthetic’ or ‘man-made’ is bad. |
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The reversed responsibility response – switching the burden of proof |
This tactic is usually used by someone who’s made a claim and then been asked for evidence to support it. Their response is to demand that you show that the claim is wrong and if you can’t, to insist that this means their claim is true. |
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The scary science scenario – science portrayed as evil. |
The perpetrators try to convince you that scientific knowledge has resulted in overwhelmingly more harm than good.They identify environmental disasters, accidents, human tragedies, hazards, weapons and uncomfortable ideas that have some link to scientific discoveries and claim that science must be blamed for the any damage they cause.They may even go so far as claiming that scientists themselves are generally cold, unfeeling people who enjoy causing harm. |
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False balance – cultivating counterfeit controversy to create confusion |
This tactic is promoted by peddlers of bad science and pseudoscience and is often taken up by journalists and politicians. In discussing an issue, they insist that “both sides” be presented.Many journalists routinely look for a representative of each “side” to include in their stories, even though it might be inappropriate.Groups or individuals who are pushing nonsense or marginal ideas like to exploit this tendency so that their point of view gains undeserved publicity. |
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Confirmation bias – ferreting favourable findings while overlooking opposing observations |
This is a cognitive bias that we all suffer from. We go out of our way to look for evidence that confirms our ideas and avoid evidence that would contradict them. |
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Crafty contrarians and wily watchdogs – donning the mantle of shrewdness |
This is an attitude adopted by a person – and it’s usually an older male – who has achieved success within his profession. This person feels entitled to make pronouncements about areas in which he has no competence.He believes he has developed a knack for making good judgements based on ‘intuition’ or ‘gut feeling’ and you are expected to respect his opinions because of his reputation for astuteness. His opinions are usually at odds with the accepted science. |
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The appeal to common sense – garbage in the guise of gumption |
The perpetrator tries to persuade you to accept or reject a claim based on what’s supposedly “common sense”.Look out for key words such as “Obviously, …”, “Naturally, …”,
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Ostensible oppression of opposing opinions – claims of rights violated. |
In this tactic, people insist that their right to express their opinion, or their right to free speech, is being denied. This is their reaction to having their opinions dismissed, rejected or ignored by mainstream scientific forums.They refuse to accept that their opinions fail because they do not meet the standards for publication in those forums. |
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The alarmism accusation – claims of crises created to funnel funding. |
Those who use this tactic insist that the current scientific consensus on some issue is corrupt. This, they claim, is because a group of scientists has colluded to hype the position which favours its own interests.The purported motive is to attract funding for their research. Look for derisive terms such as “follow the money” or “pal review”. |
Consilience: Converging lines of evidence
One of the biggest misunderstandings about science is the idea that scientists reach conclusions by “consensus.” This sounds dangerously like democracy:
Sure, while democracy is great for a free nation, one can’t vote on reality. Scientists can’t, and don’t, vote on “Should Earth have one moon or two moons? Should the Earth be thousands of years old or billions of years old?” There’s no voting to create a consensus in science.
In reality the process goes in the other direction: the appearance of consensus among scientists isn’t caused by voting. Consensus only appears if all evidence, from different people, in different situations, always leads towards the same conclusion.
Michael Crichton says it well:
I want to pause here and talk about this notion of consensus, and the rise of what has been called consensus science. I regard consensus science as an extremely pernicious development that ought to be stopped cold in its tracks. Historically, the claim of consensus has been the first refuge of scoundrels; it is a way to avoid debate by claiming that the matter is already settled. Let’s be clear: the work of science has nothing whatever to do with consensus. Consensus is the business of politics. Science, on the contrary, requires only one investigator who happens to be right, which means that he or she has results that are verifiable by reference to the real world. In science consensus is irrelevant. What is relevant is reproducible results. …
Michael Crichton, Caltech lecture, 2003
Richard Feynman says the same thing:
If [a consensus] disagrees with experiment, it’s wrong. In that simple statement is the key to science. It doesn’t make any difference how beautiful your guess is, it doesn’t matter how smart you are who made the guess, or what his name is … If it disagrees with experiment, it’s wrong.
We may draw highly certain conclusions when we have many converging lines of evidence.
Consilience is the principle that evidence from independent, unrelated sources can converge on strong conclusions.
Examples: Is the tooth fairy real?
How do children get money from the supposed tooth fairy?
Lines of evidence that one might present as being for the existence of said tooth fairy:
(Get ideas from the students – what stories did they hear from their parents when they were young?)
(Then discuss, did anyone as a kid ever try to see if their parents were honest about this? How did they investigate?)
Lines of evidence that the money actually comes from parents:
(Again, ask for ideas from the students)
Result: the converging lines of evidence suggests that tooth fairy money really does comes from the parents.
Big point: Even if we do not have perfect knowledge we can still come to reasonable conclusions when all of the evidence points in the same direction.
Example: Ancient age of the Earth
Some people say that the planet Earth is only thousands of years. Others say that it is billions of years old.
How do we decide? Consilience.
A. There are only divergent lines of evidence for young Earth claims
B. All lines of evidence converge on the ancient Earth claim
Example: Life evolved through evolution
Some people say that life was created all at once, recently, and has had almost no changes. Others say that life developed through evolution by natural selection, and that much change has occurred over billions of years.
How do we decide? Consilience.
A. There are only divergent lines of evidence for creationism.
B. All lines of evidence converge on the slow development of life over billions of years.
Additional reading
Established scientific models are supported by multiple independent lines of evidence.
Multiple lines of reasoning in support of one claim
Evolution’s web of evidence
The logic of scientific arguments
How science lets us analyze competing ideas.
Example of consilience in Astronomy, evidence for the Big Bang
Could there be a shadow biosphere?
Could there be a shadow biosphere here on Earth?
I. Life on Earth, but not as we know it?
This section excerpted from Life on Earth… but not as we know it,
Robin McKie, The Guardian (UK), 4/13/2013
These researchers believe life may exist in more than one form on Earth: standard life – like ours – and “weird life”, as they term the conjectured inhabitants of the shadow biosphere.
All the micro-organisms that we have detected on Earth to date have had a biology like our own: proteins made up of a maximum of 20 amino acids and a DNA genetic code made out of only four chemical bases: adenine, cytosine, guanine and thymine,” says Cleland.
“Yet there are up to 100 amino acids in nature and at least a dozen bases. These could easily have combined in the remote past to create lifeforms with a very different biochemistry to our own. More to the point, some may still exist in corners of the planet.”
Science’s failure to date to spot this weird life may seem puzzling. The natural history of our planet has been scrupulously studied and analysed by scientists, so how could a whole new type of life, albeit a microbial one, have been missed?
Cleland has an answer. The methods we use to detect micro-organisms today are based entirely on our own biochemistry and are therefore incapable of spotting shadow microbes, she argues. A sample of weird microbial life would simply not trigger responses to biochemists’ probes and would end up being thrown out with the rubbish.
That is why unexplained phenomena like desert varnish are important, she says, because they might provide us with clues about the shadow biosphere. We may have failed to detect the source of desert varnish for the simple reason that it is the handiwork of weird microbes which generate energy by oxidising minerals, leaving deposits behind them.
The idea of the shadow biosphere is also controversial and is challenged by several other scientists.
Biological Dark Matter
This section is originally from ‘Dark Matter’ in Biology, Ian Dunn, Biopolyverse, 3/21/2011.
That website no longer exists, so we present this here as a resource for our students.
… All current examples of ‘biological dark matter’ cited in the literature are, in essence, uncharacterized manifestations of known types of entities. Consider the issue of ‘dark’ products of complex genomes, in the form of numerous transcribed RNAs with unknown functions. However exotic the biological roles of certain non-coding RNAs, the general chemical nature of any RNA molecule is very familiar …
A strict analogical extension of cosmic to biological dark matter would then be the discovery of a biological effect that cannot be accounted for by ‘ordinary’ biological mediators or processes. And just as dark matter in the universe is a recent finding, such a hypothetical biological effect might itself be long unrecognized, rendering the agency involved truly obscured.
… there are levels and levels of ‘darkness’ in any area of investigation, not least of which is biology. In other words, a hierarchy of novelty / unfamiliarity / strangeness can be readily constructed when we consider new biological discoveries, and speculate upon their ‘outer limits’...
Some discoveries may provide interesting precedents for processes or structures hitherto unreported, but without causing too many eyebrows to be raised.
This image from Illuminating the dark matter in metabolomics, Ricardo da Silva, PNAS. http://www.pnas.org/content/112/41/12549
Still other findings may indeed cause considerable supra-ocular hair elevation, yet fall short of seriously challenging key biological principles.
With these considerations in mind, it is not difficult to categorize the experimental input of new biological information as a spectrum of sorts:
‘Dark Matter’ in Biology http://biopolyverse.com/2011/03/21/dark-matter-in-biology/
Extremely hypothetical dark life from actual, cosmological dark matter
This section excerpted from Could Dark Matter Spawn ‘Shadow Life’?
By Ian O’Neill, 2/7/2018, HowStuffWorks
The vast majority of mass in our universe is invisible, and for a while, physicists have been trying really hard to understand what this elusive “stuff” is.
Assumed to be some kind of particle, there are hopes that the Large Hadron Collider might produce a dark matter particle or that a space telescope might detect the obvious gamma-ray telltale signature of dark matter particles colliding. But so far, hints have been few and far between; a problem that’s forcing theoretical physicists to think up new ideas.
In a mind-bending 2017 op-ed for Nautilus, famed theoretical physicist Lisa Randall delved into one of the more extreme possibilities for dark matter. Rather than thinking of dark matter as one type of particle, might dark matter be composed of an entire family of particles that create dark stars, dark galaxies, dark planets and, perhaps, dark life?
This dark universe’s chemistry might be as rich and varied as our “ordinary chemistry.”
…Astrophysicists have hypothesized in the past that “dark stars” — stars made of dark matter — may have existed in our primordial universe and may persist to this day. If this is the case, Randall argues, perhaps “dark planets” may have formed, too.
She then takes this idea a step further: If there’s a family of dark matter particles, governed by forces only accessible in the dark sector, might this realm also have complex chemistry? If so, might there be life? If there is “shadow life” living out its days parallel to our universe, you can forget any hopes of detecting it, however.
Does Dark Matter Harbor Life?
Excerpted from Does Dark Matter Harbor Life? An invisible civilization could be living right under your nose. By Lisa Randall
… The Standard Model contains six types of quarks, three types of charged leptons (including the electron), three species of neutrinos, all the particles responsible for forces, as well as the newly discovered Higgs boson. What if the world of dark matter—if not equally rich—is reasonably wealthy too?…
If we were creatures made of dark matter, we would be very wrong to assume that the particles in our ordinary matter sector were all of the same type. Perhaps we ordinary matter people are making a similar mistake.
Given the complexity of the Standard Model of particle physics, which describes the most basic components of matter we know of, it seems very odd to assume that all of dark matter is composed of only one type of particle. Why not suppose instead that some fraction of the dark matter experiences its own forces?
In that case, just as ordinary matter consists of different types of particles and these fundamental building blocks interact through different combinations of charges, dark matter would also have different building blocks—and at least one of those distinct new particle types would experience non-gravitational interactions….
Ordinary matter’s many components have different interactions and contribute to the world in different ways. So too might dark matter have different particles with different behaviors that might influence the universe’s structure in a measurable fashion.
When first studying partially interacting dark matter, I was astonished to find that practically no one had considered the potential fallacy—and hubris—of assuming that only ordinary matter exhibits a diversity of particle types and interactions….
… Perhaps nuclear-type forces act on dark particles in addition to the electromagnetic-type one. In this even richer scenario, dark stars could form that undergo nuclear burning to create structures that behave even more similarly to ordinary matter than the dark matter I have so far described. In that case, the dark disk could be populated by dark stars surrounded by dark planets made up of dark atoms. Double-disk dark matter might then have all of the same complexity of ordinary matter.
- Lisa Randall is the Frank B. Baird, Jr., Professor of Science at Harvard University, where she studies theoretical particle physics and cosmology.
Tags
#shadowbiosphere #shadowlife #darklife #exobiology
Further reading
Hypothetical types of biochemistry, Wikipedia
Purple Earth Hypothesis, Wikipedia
‘Dark Matter’ in Biology
http://biopolyverse.com/2011/03/21/dark-matter-in-biology/
Paradigms and Biological ‘Dark Matter’
http://biopolyverse.com/2011/03/28/paradigms-and-biological-%E2%80%98dark-matter%E2%80%99/
‘Dark Matter’ in Biology: Great Expectations and Biological Limits
http://biopolyverse.com/2011/04/05/%E2%80%98dark-matter%E2%80%99-in-biology-great-expectations-and-biological-limits/
A Dark Shadow Biosphere with Unorthodox Orthogonality?
http://biopolyverse.com/2011/04/12/a-dark-shadow-biosphere-with-unorthodox-orthogonality/
A Dark Shadow Biosphere with Unorthodox Orthogonality?
Does ‘Dark’ Biology Have Its CHARMs?
http://biopolyverse.com/2011/05/03/does-%E2%80%98dark%E2%80%99-biology-have-its-charms/
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
MA 2016 Science and technology
Appendix I Science and Engineering Practices Progression Matrix
Science and engineering practices include the skills necessary to engage in scientific inquiry and engineering design. It is necessary to teach these so students develop an understanding and facility with the practices in appropriate contexts. The Framework for K-12 Science Education (NRC, 2012) identifies eight essential science and engineering practices:
1. Asking questions (for science) and defining problems (for engineering).
2. Developing and using models.
3. Planning and carrying out investigations.
4. Analyzing and interpreting data.
5. Using mathematics and computational thinking.
6. Constructing explanations (for science) and designing solutions (for engineering).
7. Engaging in argument from evidence.
8. Obtaining, evaluating, and communicating information.
Scientific inquiry and engineering design are dynamic and complex processes. Each requires engaging in a range of science and engineering practices to analyze and understand the natural and designed world. They are not defined by a linear, step-by-step approach. While students may learn and engage in distinct practices through their education, they should have periodic opportunities at each grade level to experience the holistic and dynamic processes represented below and described in the subsequent two pages… http://www.doe.mass.edu/frameworks/scitech/2016-04.pdf
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