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January 14, 2010

Differentials and Error Analysis

Filed under: Mathematics, Physics, Science — Administrator @ 3:48 pm

Differentials, an aspect of calculus, are important for working with errors of measurement and the propagation of error.

Dr. Donald Simanek discusses their use in Error Calculations Using Calculus. Dr. Mike Coombes discusses their use in Error Propagation Using Calculus Solutions. And Dr. Rhett Allain uses them in the interesting Error Propagation And the Distance To the Sun.

I have not read the articles/essays closely, so I don’t know if there are any mistakes in them. But they illustrate the general idea.

January 7, 2010

Atmospheric CO2 Level Constant Over the Past 160 Years?

Filed under: Physics, Science — Administrator @ 10:02 am

As with astronomy, where Ptolemy was not right because his math “worked” (mostly) and was fancy, but where Copernicus, Galileo and Newton were right because they derived their conclusions  from the facts, so also, climate science must bow to facts and evidence, not vice versa. There will be not knowledge proper in climate science until it is made scientific, i.e., until scientists and “scientists” eliminate all hypotheses, concepts, conclusions, principles and theories in their thinking that are not based on and derived inductively from facts.

There are constant reports about the invalidity of the methods and thinking of those who proclaim and push “man made global warming.” For example, ScienceDaily.com reports:

Many climate models also assume that the airborne fraction will increase. Because understanding of the airborne fraction of carbon dioxide is important for predicting future climate change, it is essential to have accurate knowledge of whether that fraction is changing or will change as emissions increase.

To assess whether the airborne fraction is indeed increasing, Wolfgang Knorr of the Department of Earth Sciences at the University of Bristol reanalyzed available atmospheric carbon dioxide and emissions data since 1850 and considers the uncertainties in the data.

In contradiction to some recent studies, he finds that the airborne fraction of carbon dioxide has not increased either during the past 150 years or during the most recent five decades.

Copyright © 1995-2009 ScienceDaily LLC  —  All rights reserved

I don’t know about the validity of the research and reasoning; I’ll have to find out more.

Recent research, e.g.,”Lindzen on Negative Climate Feedback” (be sure to also read the comments), regarding climate concludes that there is net negative feedback in our climate system, not, as presupposed by climate models that say ‘the earth is in crisis,’ a net positive feedback.

Facts must come first in science. Otherwise, our thinking is detached from reality, and our action will follow suit. Then we will be doing things like bleeding or putting leeches on people to make people healthier; or, like kingdoms of old, beating people like to make them be good; or, like some today, recommending people wear running shoes (which end up giving people back and chiropractic problems; see, for example, “Shoes, Sitting, and Lower Body Dysfunctions,”  “Running shoes may cause damage to knees, hips and ankles,” “The Effect of Running Shoes on Lower Extremity Joint Torques“); and more.

November 9, 2009

Finding Libraries At Which To Study: It’s Easy

Filed under: Logic, MGTutoring, Mathematics, Physics — Administrator @ 11:53 am

Thank goodness for the Internet — and the mathematics, physics, and reasoning that made it possible, and that continue to refine and improve it. How easy it is to find places to go to study; besides Paneras and Starbucks and home, there are nice, quiet libraries all over the place. We can see all the branch libraries in Texas at the click of a mouse.

October 15, 2009

Measuring Waves

Filed under: Mathematics, Physics, Science — Administrator @ 9:49 am

Mathematics allows us to grasp and understand things outside of the realm of perception — things like radio waves and microwaves:

Radio broadcasts use the low-frequency, long-wavelength portion of the electromagnetic spectrum. Commercial AM radio is at frequencies of 550 kHz to 1600 kHz (wavelengths of 545 m to 187 m) and commercial FM radio is at frequencies of 88 MHz to 108 MHz (wavelengths of 3.4 m to 2.8 m). Because these waves have wavelengths longer than 1 m, they are called radio waves. But the electromagnetic waves used in microwave ovens have wavelengths shorter than 1 m and are called microwaves. Microwaves extend from wavelengths of 1 m (3.3 ft) down to 1 mm (0.04 inches).

p. 433 , How Things Work (3rd ed.) by Louis A. Bloomfield, John Wiley & Sons, Inc., (c) 2006, ISBN-13: 978-0-471-46886-8.

Such waves are things we never see, touch, taste or smell. But because of concepts and mathematics, we can identify and control electromagnetic waves, as if they were things we could actually see or touch. Math and conceptual thought make possible all devices and inventions based on electricity and electromagnetic waves: radio, live365.com, the iPod, the iPhone, cell phones in general, GPS, the Internet, microwave ovens, AC, the automobile and more. People who say that math is useless are saying, by implication, by logical necessity, that all things logically and causally dependent on mathematics — such as those just enumerated — are useless and can and should be done away with.

But mathematics is implicit in most all the technology we use in most aspects of our lives. (That so many people don’t see this is, sadly, an indictment of the anti-conceptual nature of our culture. How I wish it were otherwise…) Mathematics and measurement are implicit in signage along the roadside and on buildings, in all recorded or amplified music we hear and enjoy, in the medical treatment we receive and depend on, in the cell phones we use to call family or friend or business associate, in the Internet we use to read news or keep up with friends, in the automobile we drive on vacation or in which we are driven to the hospital. The modern life we live is dependent on mathematics — what’s more, I’d argue that mathematics and measurement are essential to human consciousness and experience and thus to human life, and fundamentally differentiate us from all other animals.

September 16, 2009

“Introductory Physics” by Herbert Priestley

Filed under: Education, Physics, Recommended Books, Science — Administrator @ 8:30 am

Introductory Physics by Herbert Priestley (Allyn and Bacon, Inc., 1958)  has one of the best presentations of physics I’ve ever seen. (The book is, sadly, out of print and hard to find.) He presents concepts in their historical and scientific context. Priestley presents alternative viewpoints that were being used to understand phenomena such as heat or electricity, discusses why each viewpoint was held and the arguments scientists had on which position was right, and describes in some detail the experiments scientists did – especially the experiments which validated one side or the other. In showing us the development of ideas in physics, Priestley is showing us the correct view of concept formation and the formation of generalizations, Priestley is showing us that true concepts and propositions come from applying rational, objective methods to the real world.

Priestley attended the University of Leeds, receiving a B.S. in 1933 and a Ph.D. in physics in 1935. He served in the Royal Air Force as an industrial research physicist, civilian education officer, and air intelligence officer. He came to the US as RAF liaison officer in 1942, but stayed on to teach physics at Ripton College after WWII. In 1952, he became chairman of the physics department at Knox College, where he stayed until he retired in 1980.  His obituary is on Knox College’s Website.

Two caveats. Priestley makes some statements in his Chapter 1 about the philosophy of science which I do not fully agree with. He also does not give Aristotle proper credit as a scientist. People have insulted Aristotle for centuries, for things that are not Aristotle’s fault –- there have been people throughout history who blindly believed what was written in Aristotle’s corpus and who did not look at reality on their own, yes, but that is not Aristotle’s fault. Aristotle, in method, was objective, and referred to experience. If he had the evidence available to him which people did who lived 1,000 years or more after he lived, he could have arrived at the conclusions modern scientists have. He was a solid scientist, as can be seen in the work he did most: philosophy, logic and biology.

Dr. James Lennox, Professor of Philosophy and the History of Science at the University of Pittsburgh, has some good articles on his Website regarding Aristotle as scientist and philosopher of science. An article directly relevant to some of Priestley’s uninformed, unresearched accusations against Aristotle is Lennox’s “Aristotle, Galileo and the Mixed Sciences,” which discusses (1) Aristotle’s use of mathematics as a tool of explanation and (2) Galileo’s debt to Aristotle.

Following is an excerpt from Priestley’s book. I hope this is not a copyright violation! (This post is a great advertisement for the book. This post publicizes and praises the book, which would otherwise remain largely unknown. Plus, while the quoted section is lengthy, it is a small percentage of the whole.) The book is out of print, but, I think, still under copyright. I communicated with the publisher, who said they did not have any copies of the book to sell and would not make any. This is a book that should be reprinted! It should be preserved, studied, spread far and wide, and used as a standard for how science textbooks should be.

It is impossible to grasp Priestley’s masterful and rational approach in brief one-paragraph excerpts, so the excerpt must be lengthy. Priestley does use math (only algebra; no calculus) in his textbook, but the excerpt has none. The excerpt illustrates, in context of electricity, how Priestley focuses his discussion of physics on causality, scientific method, and the development of concepts, principles and theories.

Excerpt Chp. 15, “Electricity and Chemistry,” pp. 201-205

15.1 Galvanism. Electricity and chemistry are closely inter-related. A chemical reaction can produce a supply of electricity for as long as the reaction continues. This, the first source of a continuous supply of electricity, an electric current, is the principle of the electric battery. Conversely, an electric current can produce a chemical reaction, usually the decomposition of a chemical compound into its simpler elements, the process of electrolysis. Both processes involve the conversion of energy from one form to another; in the first case, chemical energy becomes electrical energy; in the other, the reverse takes place.

Every living cell produces electricity. The functioning of living tissue today is studied through its electrical action. The study of electricity in living tissue, which began quite accidentally about one hundred and fifty years ago, led to the development of the electric battery, for many years thereafter the standard method of producing electricity

About 1750, it was noted that pieces of lead and silver placed above and below the tongue, respectively, with their outer edges in contact, produced an unpleasant and pungent taste not encountered when the metals were placed separately upon the tongue. The phenomenon was attributed to some excitation of the nerves of the tongue. By this time, various physicians and experimenters had demonstrated that electricity could be used as a muscular stimulant in man and animals. This fact had been used to distinguish between paralyzed and atrophied muscles, an electric charge producing a contraction only in a paralyzed muscle.

Before the end of the eighteenth century it was known that an electric discharge passed through the body of a freshly killed animal could cause a convulsive action in its muscles, and that the discharge of an electric eel (section 14.2) produced motion in a nearby dead fish. Identification of the origin of these effects was made by Galvani (1737-1798), a professor of anatomy at Bologna. Galvani began experimenting about 1780, using a Leyden jar [A Leyden jar was the earliest form of electric condenser, consisting of “a bottle filled with water into which was inserted a wire held in place by a cork.”  p. 191] and an electrostatic machine to test the effects of the electric discharge upon the nervous system of the frog. During these experiments he made the chance observation that nearby electrical discharge caused convulsions in a freshly prepared frog’s leg in conducting contact with the earth.

(more…)

September 2, 2009

The Integration of Biology With Chemistry and Physics: Anecdote 2

Filed under: Biology, History, Physics, Science — Administrator @ 8:11 am

Isaac Asimov tells us another fascinating, intriguing scientific anecdote in A Short History of Biology:

If a protein solution is placed in an electric field, the individual protein molecules travel toward either the positive of negative electrode at a fixed speed dictated by the pattern of the electric charge, the size and shape of the molecule and so on. No two varieties of protein would travel at precisely the same speed under all conditions.

In 1937, the Swedish chemist, Arne Wilhelm Kaurin Tiselius (1902- ), a student of Svedberg’s, devised an apparatus to take advantage of this. This consisted of a special tube arranged like a rectangular U, within which a protein mixture could move in response to an electric field. (Such motion is called “electrophoresis.”) Since the various components of the mixture moved each at its own rate, there was a gradual separation. The rectangular-U tube consisted of portions that fitted together at specifically ground joints, and these portions could be slid apart. Matters could be arranged so that one of the mixture of proteins would be present in one component of the chambers and could thus be separated from the rest.

Furthermore, by the use of appropriate cylindrical lenses, it became possible to follow the process of separation by taking advantage of changes in the way light was refracted on passing through the suspended mixture as the protein concentration changed. The changes in refraction could be photographed as a wavelike pattern which could then be used to calculate the quantity of each type of protein present in the mixture.

pp. 155-156, A Short History of Biology by Isaac Asimov, American Museum Science Books, the Natural History Press, Garden City, New York, (c) 1964 Isaac Asimov.

The integration of physics, chemistry, technology, and biology is awe-inspiring and beautiful.

Mr. Asimov presents some of the discoveries and ideas in biology that led up to Tiselius’ work (such as the discovery of organic compounds and proteins), and then discusses in his book what happened after this. He focuses on the biology and chemistry. Mr. Asimov teaches correctly: the reader gets to see what basic evidence and reasoning led to the concepts, principles and theories of modern biology. The reader gets the skeleton of induction needed to grasp a concept, etc.

Most students now-a-day are trained in a mash that amounts to confusion, memorized words (like a parrot), and obedience of authority, not to understanding proper. Students are not being trained in reasoning and objectivity.

To properly understand Tiselius’ work, one would need to learn that which Mr. Asimov presented, but one would also need to learn some of the scientific work of Michael Faraday (The Laws of Electrolysis) and Willebrord Snellius (Snell’s Law of Refraction). What’s more, Tiselius’ work has to be clearly rooted in the work of Galileo and Newton, who studied telescopes and light, studied motion and gravity, and started modern science. There are also ideas developed in the 1600s, 1700s, and 1800s that are essential to achieving a real, inductive, objective understanding.

Update (9-4-09, 8:15 AM):  And, of course, none of this would have been possible without the development of mathematics, Aristotle’s development of logic, and the integration of mathematics and the physical and biological sciences.

September 1, 2009

More on the Death — the Murder — of Science Education

Filed under: Culture, Education, Physics, Science — Administrator @ 12:23 pm

In “Science Workshop: Building a Lifelong Love of a “Boring” Subject” (Core Knowledge Blog, August 30, 2009), Robert Pondiscio quotes a newspaper article:

The Future of Science: ‘Science Workshop’ Approach Lets Students Learn What They Want

The New York Times  
By Motoko Rich
   August 30, 2009

JONESBORO, Ga. — For years Lorrie McNeill loved teaching chemistry.  She taught her students the periodic table of elements, the ubiquitous classroom staple that many Americans regard as a scientific rite of passage.

But last fall, for the first time in 15 years, Ms. McNeill, 42, removed the periodic table from her classroom.  Gone, too, were assigned lab partners–and even the laboratory tables themselves, bunsen burners and all. Instead she turned over all the decisions about what science to learn to the students in her seventh- and eighth-grade science classes at Jonesboro Middle School in this south Atlanta suburb.

Among their choices: building model volcanoes, setting off smoke bombs, making sundials from modeling clay and popsicle sticks, and creating “geysers” by dropping Mentos candies into 2-liter bottles of Diet Coke.

The approach Ms. McNeill uses, in which students choose their own science projects, discuss them individually with their teacher and one another, and keep detailed journals about their observations, is part of a movement to revolutionize the way science is taught in America’s schools. While there is no clear consensus among science teachers, variations on the approach, known as science workshop, are catching on.

John Dewey rears his corrupting head and raises his cognition-destroying hand. Again.

Without induction, integration, and hierarchy, it is not science. It’s just a Feynmanian cargo cult (Feynman’s speech is also on GasResources.net, UIowa.edu, and elsewhere on the Internet).

The Integration of Biology With Chemistry and Physics: An Anecdote

Filed under: Biology, History, Physics, Science — Administrator @ 10:14 am

Isaac Asimov writes, in A Short History of Biology:

Meanwhile, those steps in the breakdown of glycogen that lay beyond lactic acid and that did require oxygen could be studied by means of a new technique developed by a German biochemist, Otto Heinrich Warburg (1883- ). In 1923, he devised a method for preparing thin slices of tissue (still alive and absorbing oxygen) and measuring their oxygen uptake. He used a small flask attached to a thin U-shaped tube. In the bottom of the tube was a colored solution. Carbon dioxide produced by the tissue was absorbed by a small well of alkaline solution within the flask. As oxygen was absorbed without being replaced in the air by carbon dioxide, a partial vacuum was produced in the flask and the liquid in the U-tube was sucked upward toward the flask. The rate of level change of the fluid, measured under carefully controlled conditions, yielded the rate of oxygen uptake.

The influence of different compounds on this rate of uptake could then be studied. If a particular compound restored the rate after it had fallen off, it might be taken to be an intermediate in the series of reactions involved in oxygen uptake. The Hungarian biochemist, Albert Szent-Gyorgyi (1893- ) and the German-British biochemist, Hans Adolf Krebs (1900- ), were active in this respect. Krebs had, indeed, by 1940, worked out all the main steps in the conversion of lactic acid to carbon dioxide and water, and this sequence of reactions is often called the “Krebs cycle.” Earlier, during the 1930s, Krebs had also worked out the main steps in the formation of the waste product, urea, from the amino acid building blocks of proteins. This removed the nitrogen and the remainder of the amino acid molecules could, as Rubner had shown almost a half-century earlier (see page 89), be broken down to yield energy.

Hand in hand with this increase of knowledge concerning the internal chemistry of the cell came in increase of knowledge concerning the fine structure of the cell. New techniques for the purpose were developed. In the early 1930s, the first “electron microscope” was built. … Particles no larger than very large molecules could be made out and the protoplasm of the cell was found to be an almost bewildering complex of small but highly organized structures called “organelles” or “particulates.”

pp. 146-148, A Short History of Biology by Isaac Asimov, American Museum Science Books, the Natural History Press, Garden City, New York, (c) 1964 Isaac Asimov.

This work depended on the work of prior scientists in, for example, the discovery, isolation, and characterization of oxygen and carbon dioxide by Van Helmont and Priestley; the work in chemistry of Lavoisier and Cavendish and others; Lavoisier’s idea that the process of life was the same as that of combustion; the study of “vacuum” above a fluid; the laws of gases as developed by Boyle, Charles’, and others; the fundamental work of Galileo and Newton.

The way biology is presented by Mr. Asimov is close to how science should be taught. As science is taught today, ideas come out of nowhere, like flotsam and jetsam, with no induction, integration, rationale, or cause-effect relationships. It is no wonder that the state of science education and people’s knowledge of science is impoverished. And it is no wonder that they have the idea that science is detached from everyday life and thought!

Update (4:15 PM): FYI, Mr. Asimov, writing a “short” history, does not discuss physics, or at least not much. He focuses mainly on the history of biology as such, with some discussion of chemistry.

Update (9-4-09, 8:15 AM):  And, of course, none of this would have been possible without the development of mathematics, Aristotle’s development of logic, and the integration of mathematics and the physical and biological sciences.

August 18, 2009

One Step in the Historical Development of the Concepts of Life and Energy

Filed under: Biology, History, Physics, Science — Administrator @ 9:11 am

Isaac Asimov writes, in A Short History of Biology:

Since a candle and an animal both produce carbon dioxide and consume oxygen, it seemed reasonable to Lavoisier to suppose that respiration was a form of combustion and that when a particular amount of oxygen was consumed, a corresponding quantity of heat was produced whether it was a candle or a mouse that was involved. His experiments in this direction were necessarily crude (considering the measuring techniques then available) and his results only approximate, but they seemed to bear out his contention.

This was a powerful stroke on the side of the mechanistic view of life, for it seemed to imply that the same chemical process was taking place in both living and nonliving matter. This made it that much more reasonable to suppose that the same laws of nature governed both realms as the mechanists insisted.

Lavoisier’s point was strengthened as the science of physics developed during the first half of the nineteenth century. In those decades, heat was being investigated by a number of scientists whose interest was aroused by the growing importance of the steam engine. Heat, by means of the steam engine, could be made to do work, and so could other phenomena, such as falling bodies, flowing water, air in motion, light, electricity, magnetism, and so on. In 1807, the English physician, Thomas Young (1773-1829), suggested “energy” as a word to represent all phenomena out of which work could be obtained. It comes from the Greek words meaning “work within.”

The physicists of the early nineteenth century studied the manner in which one form of energy could be converted to another, and made increasingly refined measurements of such changes. By the early 1840s, at least three men, an Englishman, James Prescott Joule (1818-89), and two Germans, Julius Robert von Mayer (1814-78) and Hermann Ludwig Ferdinand von Helmholtz (1821-94), had advanced the concept of the “conservation of energy.” According to this concept, one form of energy might be freely converted into another, but the total amount of energy could neither be decreased nor increased in the process.

It seemed natural for such a broadly general law, based on a wide variety of meticulous measurements, to apply to living processes as well as nonliving. The mere fact that no living animal could continue living without obtaining energy continuously from its food made it seem that life processes could not create energy out of nothing. Plants did not eat and breathe in quite the same way animals did, but, on the other hand, they could not live unless they were periodically bathed in the energy of light.

pp. 48-49, A Short History of Biology by Isaac Asimov, American Museum Science Books, the Natural History Press, Garden City, New York, (c) 1964 Isaac Asimov.

June 2, 2009

Foolish at Physics

Filed under: Culture, Education, Physics — Administrator @ 2:12 pm

A science textbook tried to explain the fact that a shower curtain (unweighted and without magnets) will push toward you by applealing tp the Bernoulli principle.

This claim is shown to be ignorant in “Fun in the Tub” by Howard P. Lyon:

Over the past few years, a half-page article called “Attack of the Shower Curtain” has been printed again and again in middle-school books published by Prentice Hall. It first appeared in the 1993 version of Motion, Forces, and Energy, one of the books in the Prentice Hall Science series. Since then it has been used in later versions of Motion, Forces, and Energy and in several successive versions of Prentice Hall Exploring Physical Science.

In their pedagogic note, Prentice Hall’s writers tell the teacher that this concept explains a shower curtain’s aggressiveness:

[The "Attack" article] helps students relate Bernoulli’s principle about pressure in fluids to a real-life situation. . . . The pressure exerted by the fast-moving fluid (water inside the shower) is less than the pressure in the surrounding fluid (air outside the shower). The greater outside pressure pushes the shower curtain into the shower . . . .


In an effort to find out why shower curtains sometimes attack showerees, I observed the action of the curtain that adorns my own bathtub.

Clearly, the “Attack of the Shower Curtain” is a response to temperature. When the water falling from the showerhead is hot, it warms the air inside the shower enclosure and induces convection. The warmed air rises, escapes from the enclosure by flowing over the top of the curtain, and is replaced by cooler air that flows into the bottom of the enclosure. As this cooler air enters the enclosure, it pushes the lower margin of the curtain ahead of it, causing the lower part of the curtain to swing inward.

As Galileo would say, one needs to ‘make the experiment.’ And as Galileo said of Aristotle: “[F]or I am sure that he never took [the belief that there is no change in the heavens and celestial sphere, that things are perfect, timeless, and indestructible in the heavens and the celestial sphere] to be as certain as the fact that all human reasoning must be placed second to direct observation.” (p. 118, Discoveries and Opinions of Galileo, trans. Stillman Drake, Doubleday Anchor Press, Garden City, NY, (c) 1957 Stillman Drake.)

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