Mr. Lincoln was a peculiar man, having a peculiar mind; he was gifted with a peculiarity, namely, a new look-out on nature. Everything had to be newly created for him – – facts newly gathered, newly arranged, and newly classed. He had no faith, as already expressed. In order to believe he must see and feel, and thrust his hand into the place. He must taste, smell and handle before he had faith, i.e., belief. Such a mind as this must act slowly, must have its time. His forte and power lay in his love of digging out for himself and hunting up for his own mind its own food, to be assimilated unto itself; and then in time he could and would form opinions and conclusions that no human power could overthrow. They were as irresistible as iron thunder, as powerful as logic embodied in mathematics.

– – William Herndon as quoted in Abraham Lincoln and the Structure of Reason by David Hirsch and Dan Van Haften, p. 235.

]]>Also from show description: “There’s no way around it, we’re being bombarded by an insane amount of information when it comes to COVID-19, and not all of it makes sense. As vaccines make their way across the country, the questions are only increasing and it can feel overwhelming to find answers from expert sources. While we don’t have all the answers, we are learning more every day. We’ve seen that for people 15 and older, COVID-19 can double our risk of dying this year. And while we know chronic disease puts us at an increased risk for severity and death, we don’t know why some perfectly healthy people still can’t fight this virus off. We’re seeing that vaccines will be a dramatic help for this virus, helping to reduce the risk of severe symptoms and death, but that they won’t stop transmission.”

]]>We need to know what logic really is so we can better structure and sequence curriculum, as well as education overall, and we need to know what it really is so we can teach more effectively and efficiently, and so we can make it matter. We need to bring in clarity of explanation and love of life.

And every human who thinks conceptually needs to know what logic is so they can improve their thinking to improve their life: physically, socially, cognitively, emotionally, and in every way.

Also available on many, many podcast apps.

]]>“Compliance, following instructions: those don’t serve us very well in the 21st century. If that’s all you can do, and you show up to a job interview, your employer is going to look at you, and just say, ‘Well, I really don’t need people like that, because I’ve got a computer, or an algorithm, or a piece of software, that is compliant or follows instructions. I need somebody that can come here and think critically, and not just problem-solve, but detect problems. I want you to point out to me problems that I’m not even aware of and solve them.’ That’s what employers in the 21st century are looking for. It’s what life is looking for.”

In the article, they also say: “[Whitley’s] film excavates the roots of our current education system, argues for how the world is changing in a way that make this form of education obsolete, and looks for answers for the future of education.”

Agreed — though I have not seen his documentary, so I do not know if I’d agree with his ideas or not! And thinking conceptually and independently is not a “21st century skill ” — it’s a skill for all humans in all times and all places.

]]>Blurb: “Too much sun exposure isn’t a good thing, but not enough may be even worse. Read this to find out why.”

Excerpt: “These guidelines were based on the observation that light-skinned people of European ancestry living in Northern Australia had the highest risk of malignant melanoma, the deadly form of skin cancer, in the world. However, as you’ll see below, applying guidelines that were originally developed for people living in an area with a high ultraviolet (UV) index, such as Northern Australia, to areas with limited sunshine and a much lower UV index (such as many parts of North America and Europe) is not only unnecessary, it may be harmful.

“In a new study, researchers tracked the sun exposure habits of 30,000 Swedish women for 20 years. They found that the women who strictly avoided the sun during that period had a two-fold greater risk of early death than women who received normal amounts of sun exposure.

“What’s more, they found that women with normal sun exposure habits were not at significantly increased risk for malignant melanoma or melanoma-related death. This is consistent with the results of a previous Swedish study that followed 38,000 women for 15 years and found that sun exposure was associated with reduced risk of both cardiovascular and overall death.

“I’d like to emphasize that these studies are observational in nature, and thus do not prove causality.”

]]>On the website for the book, they say:

“Body Physics sticks to the basic functioning of the human body, from motion to metabolism, as a common theme through which fundamental physics topics are introduced.

and

Body Physics was designed to meet the objectives of a one-term high school or [a college] freshman level course in physical science, typically designed to provide non-science majors and undeclared students with exposure to the most basic principles in physics while fulfilling a science-with-lab core requirement. The content level is aimed at students taking their first college science course, whether or not they are planning to major in science. However, with minor supplementation by other resources, such as OpenStax College Physics, this textbook could easily be used as the primary resource in 200-level introductory courses.

The book is “Creative Commons Attribution NonCommercial ShareAlike,” so you can read, study, and download Body Physics for free.

]]>And How and Why.

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Method Concerning Mechanical Theoremsdescribes a process of discovery in mathematics. It is the sole surviving work from antiquity, and one of the few from any period, that deals with this topic. In it Archimedes recounts how he used a “mechanical” method to arrive at some of his key discoveries, including the area of a parabolic segment and the surface area and volume of a sphere. The technique consists of dividing each of two figures into an infinite but equal number of infinitesimally thin strips, then “weighing” each corresponding pair of these strips against each other on a notional balance to obtain the ratio of the two original figures. Archimedes emphasizes that, though useful as a heuristic method, this procedure does not constitute a rigorous proof.

On Floating Bodies(in two books) survives only partly in Greek, the rest in medieval Latin translation from the Greek. It is the first known work on hydrostatics, of which Archimedes is recognized as the founder. Its purpose is to determine the positions that various solids will assume when floating in a fluid, according to their form and the variation in their specific gravities. In the first book various general principles are established, notably what has come to be known as Archimedes’ principle: a solid denser than a fluid will, when immersed in that fluid, be lighter by the weight of the fluid it displaces. The second book is a mathematical tour de force unmatched in antiquity and rarely equaled since. In it Archimedes determines the different positions of stability that a right paraboloid of revolution assumes when floating in a fluid of greater specific gravity, according to geometric and hydrostatic variations.…

Given the magnitude and originality of Archimedes’ achievement, the influence of his mathematics in antiquity was rather small. Those of his results that could be simply expressed—such as the formulas for the surfacearea and volume of a sphere—became mathematical commonplaces, and one of the bounds he established for π,

^{22}/_{7}, was adopted as the usual approximation to it in antiquity and the Middle Ages. Nevertheless, his mathematical work was not continued or developed, as far as is known, in any important way in ancient times, despite his hope expressed inMethodthat its publication would enable others to make new discoveries. However, when some of his treatises were translated into Arabic in the late 8th or 9th century, several mathematicians of medieval Islam were inspired to equal or improve on his achievements. That holds particularly in the determination of the volumes of solids of revolution, but his influence is also evident in the determination of centres of gravity and in geometric construction problems. Thus, several meritorious works by medieval Islamic mathematicians were inspired by their study of Archimedes.The greatest impact of Archimedes’ work on later mathematicians came in the 16th and 17th centuries with the printing of texts derived from the Greek, and eventually of the Greek text itself, the

Editio Princeps, in Basel in 1544. The Latin translation of many of Archimedes’ works by Federico Commandino in 1558 contributed greatly to the spread of knowledge of them, which was reflected in the work of the foremost mathematicians and physicists of the time, including Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642). David Rivault’s edition and Latin translation (1615) of the complete works, including the ancient commentaries, was enormously influential in the work of some of the best mathematicians of the 17th century, notably René Descartes (1596–1650) and Pierre de Fermat (1601–65). Without the background of the rediscovered ancient mathematicians, among whom Archimedes was paramount, the development of mathematics in Europe in the century between 1550 and 1650 is inconceivable. It is unfortunate thatMethodremained unknown to both Arabic and Renaissance mathematicians (it was only rediscovered in the late 19th century), for they might have fulfilled Archimedes’ hope that the work would prove useful in the discovery of theorems.

]]>Archimedes was, arguably, the world’s greatest scientist – certainly the greatest scientist of the classical age.

He was a mathematician, physicist, astronomer, engineer, inventor, and weapons-designer. As we’ll see, he was a man who was both of his time and far ahead of his time.

Archimedes was born in the Greek city-state of Syracuse on the island of Sicily in approximately 287 BC. His father, Phidias, was an astronomer.

Archimedes may also have been related to Hiero II, King of Syracuse.

In the 3rd Century BC, Archimedes:

• invented the sciences of mechanics and hydrostatics.

• discovered the laws of levers and pulleys, which allow us to move heavy objects using small forces.

• invented one of the most fundamental concepts of physics – the center of gravity.

• calculated pi to the most precise value known. His upper limit for pi was the fraction 22⁄7. This value was still in use in the late 20th century, until electronic calculators finally laid it to rest.

• discovered and mathematically proved the formulas for the volume and surface area of a sphere.

• showed how exponents could be used to write bigger numbers than had ever been thought of before.

• proved that to multiply numbers written as exponents, the exponents should be added together.

• infuriated mathematicians who tried to replicate his discoveries 18 centuries later – they could not understand how Archimedes had achieved his results.

• directly inspired Galileo Galilei and Isaac Newton to investigate the mathematics of motion. Archimedes’ surviving works (tragically, many have been lost) finally made it into print in 1544. Leonardo da Vinci was lucky enough to see some of the hand-copied works of Archimedes before they were eventually printed.

• was one of the world’s first mathematical physicists, applying his advanced mathematics to the physical world.

• was the first person to apply lessons from physics – such as the law of the lever – to solve problems in pure mathematics.

• invented war machines such as a highly accurate catapult that stopped the Romans conquering Syracuse for years. He may have done this by understanding the mathematics of projectile trajectory.”

“Archimedes.” Famous Scientists. famousscientists.org. 1 Jul. 2014. Web. 1/19/2021 <www.famousscientists.org/archimedes/>. Revised 18 Jul. 2018.

]]>As I engage in the so-called “bull sessions” around and about the school, I too often find that most college men have a misconception of the purpose of education. Most of the “brethren” think that education should equip them with the proper instruments of exploitation so that they can forever trample over the masses. Still others think that education should furnish them with noble ends rather than means to an end.

It seems to me that education has a two-fold function to perform in the life of man and in society: the one is utility and the other is culture. Education must enable a man to become more efficient, to achieve with increasing facility the ligitimate goals of his life.

Education must also train one for quick, resolute and effective thinking. To think incisively and to think for one’s self is very difficult. We are prone to let our mental life become invaded by legions of half truths, prejudices, and propaganda. At this point, I often wonder whether or not education is fulfilling its purpose. A great majority of the so-called educated people do not think logically and scientifically. Even the press, the classroom, the platform, and the pulpit in many instances do not give us objective and unbiased truths. To save man from the morass of propaganda, in my opinion, is one of the chief aims of education. Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal, and the facts from the fiction.

The function of education, therefore, is to teach one to think intensively and to think critically. But education which stops with efficiency may prove the greatest menace to society. The most dangerous criminal may be the man gifted with reason, but with no morals.

Maroon Tiger(January-February 1947): 10.