MGTutoring.com. A Rational Perspective on Education.

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 13, 2010

Measurement Humor

Filed under: Humor, Mathematics, Science — Administrator @ 8:33 pm

I received this in an email from a parent of a student I have tutored:

New IEEE standard values:

Non-Conventional Units of Conversion

Ratio of an igloo’s circumference to its diameter = Eskimo Pi

2000 pounds of Chinese soup = Won Ton

1 millionth of a mouthwash = 1 Microscope

Time between slipping on a peel and smacking the pavement = 1 Bananosecond

Weight an evangelist carries with God = 1 Billigram

Time it takes to sail 220 yards at 1 nautical mile per hour = Knotfurlong

16.5 feet in the Twilight Zone = 1 Rod Serling

Half of a large intestine = 1 Semicolon

1,000,000 aches = 1 Megahurtz

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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.

January 5, 2010

Dietary Fats and Human Health

Filed under: Exercise, Health & Nutrition, Science — Administrator @ 12:27 pm

To add to our knowledge of the importance of fat (discussed, e.g., in “Real Brain Food“) to our health, to our nervous system and brain, to our body function, and hence to learning and education, we can read “Fish Oils and Oils, Fats and Trans Fats,” where the Arizona Center for Advanced Nutrition (about which center I know nothing) said:

Fats have been demonized for the last 40 years or more. And yet Americans are more overweight and more prone to chronic disease than ever before.

Today heart disease causes at least 40% of all US deaths. If, as we were told, heart disease results from the consumption of saturated fats, one would expect to find a corresponding increase in animal fat in the American diet. Actually, the reverse is true. During the sixty-year period from 1910 to 1970, the proportion of traditional animal fat consumed in the American diet declined from 83% to 62%, and butter consumption plummeted from eighteen pounds per person per year to four. During the past eighty years, dietary cholesterol intake has increased only 1%. During the same period the percentage of dietary vegetable oils in the form of margarine, shortening and refined oils increased about 400% while the consumption of sugar and processed foods increased about 60%.[2]

Butter contains many nutrients that protect us from heart disease. For starters, it has a number of anti-oxidants that protect against the kind of free radical damage that weakens the arteries. Butter has vitamin A which is needed for the health of the thyroid and adrenal glands, both of which play a role in maintaining the proper functioning of the heart and cardiovascular system. Abnormalities of the heart and larger blood vessels occur in babies born to vitamin A deficient mothers. Butter is the most easily absorbed source of vitamin A.[29]

Butter is a good source of iodine, in highly absorbable form. Butter consumption prevents goiter in mountainous areas where seafood is not available. The vitamin A in butter is essential for proper functioning of the thyroid gland.[30]

It doesn’t stop there. Butter also contains:

• lecithin, a substance that assists in the proper assimilation and metabolism of cholesterol and other fat constituents.
• butyrin, a precursor for the fuel used by intestinal cells for their normal functioning.
• selenium, a vital anti-oxidant—butter contains more selenium per gram than herring or wheat germ.
• short and medium chain fatty acid chains that have strong anti-tumor effects.[31]
• conjugated linoleic acid which gives excellent protection against cancer.[32]

[2] Enig, Mary G., PhD. Trans Fatty Acids in the Food Supply: A Comprehensive Report Covering 60 Years of Research, 2nd Edition, Enig Associates, Inc., 1995, p 4-8.
[29] Sally Fallon and Mary Enig, Ph.D; Why Butter is Better, Weston A. Price Foundation, 1999
[30] Jennings, IW Vitamins in Endocrine Metabolism, Charles C. Thomas Publisher, Springfield, Ill, pp 41-57
[31] Cohen, L A et al, J Natl Cancer Inst 1986 77:43
[32] Belury, MA Nutrition Reviews, April 1995 53:(4) 83-89

© Copyright 2007-2009. All Rights Reserved. Arizona Center for Advanced Medicine.

A plethora of resources on health and nutrition — objective, inductive, scientific health and nutrition; or at least research where they are holding those as standards, as opposed to Ancel Keys and most all that followed from him — can be found in Mark Sisson’s blog post “Stuff That I Read (Or Watch), And You Should Too.”

January 4, 2010

Violating the Laws of Statistics is Bad For Health

Filed under: Exercise, Health & Nutrition, Science, Statistics — Administrator @ 11:19 am

Many in education offer advice on diet and nutrition to help students in school and on tests. But most of their advice (eat candy or a grain-based breakfast before a test, etc.) is rubbish based on pseudo-science (e.g., the ungrounded, unproven (and false) cholesterol-heart health hypothesis of Ancel Keys — who violated the laws of statistics in doing his ‘research’ and reporting his results — and which hypothesis has led to the recommendations that we eat more grains and sugars), hasty generalization (e.g., drawing conclusions about proper human diet without considering the American Indians’ (and other peoples’!) decay in health when put on a high-sugar, high-grain diet instead of a hunter-gatherer-type diet), and failure to integrate (e.g., failing to understand and assess results of a ’scientific experiment’ in terms of our evolutionary history).

Statistics is the science that studies the quantitative, numerical attributes of groups. It is by nature grounded in induction and classification. Hence, when doing statistics, to fail to generalize properly, to fail to classify properly, and to fail to integrate a conclusion with the rest of human knowledge — i.e., to fail to induce properly — is to fail to follow the laws and presuppositions of statistics. Statistics do not lie and cannot be made to say anything whatsoever; people lie. In such cases, statistics is being abused, not used.

Violating the laws of statistics (and, more generally, the laws of logic) has led to more obesity in America, more diabetes, more heart disease. And to American students eating a diet that adversely affects their memories, ability to learn, brain function, nervous system function, synapse growth and repair, etc.

In Scott Smith’s interview with Gary Taubes (”Gary Taubes on Cold Fusion, Good Nutrition and What Makes Bad (and Good) Science,” posted on 11-22-09), Mr. Taubes identifies some objective, scientific, integrated principles of a healthy diet:

1. Dietary fat, whether saturated or not, is not a cause of obesity, heart disease or any other chronic disease of civilization.

2. The problem is the carbohydrates in the diet, their effect on insulin secretion and so the hormonal regulation of homeostasis — the entire harmonic ensemble of the human body. The more easily-digestible and refined the carbohydrates, the greater the effect on our health, weight and well-being.

3. Sugars – sucrose and high fructose corn syrup specifically – are particularly harmful, probably because the combination of fructose and glucose simultaneously elevate insulin levels while overloading the liver with carbohydrates.

4. Through their direct effect on insulin and blood sugar, refined carbohydrates, starches and sugars are the dietary cause of coronary heart disease and diabetes. They are the most likely dietary causes of cancer, Alzheimer’s Disease and the other chronic diseases of civilization.

5. Obesity is a disorder of excess fat accumulation not overeating and not sedentary behavior.

6. Consuming excess calories does not cause us to grow fatter any more than it causes a child to grow taller. Expending more energy than we consume does not lead to long-term weight loss; it leads to hunger.

7. Fattening and obesity are caused by an imbalance – a disequilibrium — in the hormonal regulation of adipose tissue and fat metabolism: Fat synthesis and storage exceeds the mobilization of fat from the adipose tissue and its subsequent oxidation. We become leaner when the hormonal regulation of the fat tissue reverses this balance.

8. Insulin is the primary regulator of fat storage. When insulin levels are elevated – either chronically or after a meal – we accumulate fat in our fat tissue. When insulin levels fall, we release fat from our fat tissue and use it for fuel.

9. By stimulating insulin secretion, carbohydrates make us fat and ultimately cause obesity. The less carbohydrates we consume, the leaner we will be.

10. By driving fat accumulation, carbohydrates also increase hunger and decrease the amount of energy we expend in metabolism and physical activity.

To do well in school and on tests, we should put fat in our diet, and we should remove sugars and grains, which injure and wreck havoc upon our bodies, nervous systems, and brains. Our brains and our nervous system needs fats, omega-3s, and cholesterol to function properly. See, for example, my posts “Real Brain Food” and “Insulin, Obesity, and Exercise.”

The comment after the interview I must disagree with vehemently. In saying:

We tend to believe – and this is NOT an opinion we have arrived at through any kind of numerical or scientific analysis – that the entire Western scientific culture has been perverted by the endless amounts of money cast at it by governmental entities at the behest of a small coterie of individuals with great wealth and a generational agenda. This goes to the heart of the Daily Bell’s ongoing analysis, which is all about the growing efforts by the monetary elite to impose dominant social themes on the West’s increasingly harried masses.

Money is the motivating factor in all this. The amount of public money thrown at science today is infinitely corrupting. If you are a researcher, where are you going to go? Universities in the West are on the public dole and private institutions for the most part are linked in some form or other to governmental entities as well – or at least share stated agendas.

the author is driven, implicitly or explicitly, by Marxism. (Or, possibly, some related false theory of man and money.)

It is not money as such that is the problem; nor is the problem some “elite” “oppressing” the “masses.”

The problem is bad ideas and bad philosophy governing the use of some money — as well as of some people’s time, effort, and cognition. We can see this by encompassing the whole of history and the whole of human experience. The kings of old were not held in power by money possessing some magic power breathed into it by Marx; they were held in power by wrong ideas about morality and the metaphysics of man, ideas held volitionally, not deterministically, by each individual man and by the driving minds of the era. Ancient Athens was neither raised up nor thrown into decay by magic Marxist money; it was affected by the fundamental ideas governing people’s thinking: the idea of man as a self-sovereign rational animal making Athens great; the idea of man as a helpless, irrational pawn of unknowable forces bringing its decline. America did not go from the Founders’ Republic to the Federal Reserve because of magic money imposing Marxism on the structure of the universe and on human nature; it decayed because the dominant ideas influencing people’s thought and action went from the ideas of man as self-sovereign, individual, independent and rational to the ideas of man as dependent on the state, servant to the state, and irrational/arational.

December 21, 2009

Statistics and Current Events

Filed under: Mathematics, Science, Statistics — Administrator @ 8:48 am

In “Fables of the Reconstruction (Or, How to Make Your Own Hockey Stick),” the blogger Iowahawk says:

What follows started as a comment I made over at Ace’s last week which he graciously decided to feature on a separate post (thanks Ace). In short, it’s a detailed how-to-guide for replicating the climate reconstruction method used by the so-called “Climategate” scientists. Not a perfect replication, but a pretty faithful facsimile that you can do on your own computer, with some of the same data they used.

A good read. And fun with stats. Check it out.  (HT: Geoffrey K.)

On a related note, read “The ‘Science’ of Global Warming” (Macleans.ca, Thursday, December 3, 2009 10:00am) by Mark Steyn. He writes:

Yet perhaps the most important revelation is not the collusion, the bullying, the politicization and the evidence-planting, but the fact that, even if you wanted to do honest “climate research” at the Climatic Research Unit, the data and the models are now so diseased by the above that they’re all but useless. Let Ian “Harry” Harris, who works in “climate scenario development and data manipulation” at the CRU, sum it up. Mr. Harris was attempting to duplicate previous results—i.e., to duplicate all that science that’s supposedly settled, and the questioning of which consigns you to the Climate Branch of the Flat Earth Society. How hard should it be to confirm settled science? After much cyber-gnashing of teeth, Harry throws in the towel:

“ARGH. Just went back to check on synthetic production. Apparently—I have no memory of this at all—we’re not doing observed rain days! It’s all synthetic from 1990 onwards. So I’m going to need conditionals in the update program to handle that. And separate gridding before 1989. And what [#%] happens to station counts?

“OH [#&] THIS. It’s Sunday evening, I’ve worked all weekend, and just when I thought it was done I’m hitting yet another problem that’s based on the hopeless state of our databases. There is no uniform data integrity, it’s just a catalogue of issues that continues to grow as they’re found.”

You cannot do good statistics with bad data. Nor can you do science.   (HT: Harry B.)

In stats and science, reality must come first.

December 18, 2009

What I Already Knew

Filed under: Education, Logic, Science — Administrator @ 12:32 pm

Writing in “Cognitive Scientists Debunk Learning-Style Theories” (Inside School Research Blog on Education Week, December 17, 2009, 9:47 AM), Debra Viaderosays:

Writing in the journal Psychological Science in the Public Interest, cognitive scientists Hal Pashler, Mark McDaniel, Doug Rohrer, and Robert Bjork argue that, of the thousands of articles published on learning styles in recent decades, few really put the theory to an adequate test.

To really determine if a theory is valid, the researchers write, a study would have to first classify students based on the theory being tested and then randomly assign them to one of several different learning methods. Students would also have to be tested before and after the instruction. If the theory is correct, the researchers said, then students would learn best when taught with the teaching methods that mesh with their individual learning styles.

Yet few studies use that or any kind of experimental method to test learning-style theory. And, among those that did, the authors found, several yielded results that contradicted the theory. The authors write:

We conclude therefore, that at present, there is no adequate evidence base to justify incorporating learning-styles assessments into general educational practice.”

That’s not to say learning-style theory would never work, the authors add. Dozens of such theories have been identified and some have never been tested at all.
What many of these theories give a name to may actually be a learning preference. And it’s a long way from preferring to be taught one way to actually learning more when taught by a compatible instructional method.

Besides which, it is we humans who must adjust to the world, to reality and all its modalities: visual, auditory, kinesthetic, etc. — it is not the world which will bend to us. Education is about preparing a child to live independently in the world and amongst other self-sovereign people; it is not about training children to stomp their feet at the world and other people in demand that their “learning styles” be pandered to.

Update (3:30 PM): (1) I should point out that, at this time, I have not yet read the article. (2) I wrote a bit about “learning styles” in my blog post Two Points of Pedagogy.

November 24, 2009

The Periodic Table of Elements

Filed under: Science — Administrator @ 1:01 pm

The Dynamic Periodic Table is interesting. You can click on an element, and you will be taken to a Wikipedia article about that element. The table also has tabs to give you the properties, orbitals, and isotopes of each element.

November 23, 2009

Science, Sugar, and Life Span

Filed under: Biology, Exercise, Health & Nutrition, Science — Administrator @ 11:19 pm

Charles Washington said in “Spoonful Of Sugar’ Makes The Worms’ Life Span Go Down“(Zeroing in On Health – The Blog!,  11-12-09):

By adding just a small amount of glucose to C. elegans usual fare of straight bacteria, they found the worms lose about 20 percent of their usual life span. They trace the effect to insulin signals, which can block other life-extending molecular players.

Although the findings are in worms, Cynthia Kenyon of the University of California, San Francisco, says there are known to be many similarities between worms and people in the insulin signaling pathways.

“In the early 90s, we discovered mutations that could double the normal life span of worms,” Kenyon said. Those mutations effected insulin signals. Specifically, a mutation in a gene known as daf-2 slowed aging and doubled life span. That longer life depended on another “FOXO transcription factor” called DAF-16 and the heat shock factor HSF-1.

Although we do not fully understand the mechanism by which glucose shortens the life span of C. elegans, the fact that the two mammalian aquaporin glycerol-transporting channels are downregulated by insulin raises the possibility that glucose may have a life-span-shortening effect in humans, and, conversely, that a diet with a low glycemic index may extend human life span,” the researchers write. Kenyon also points to recent studies that have linked particular FOXO variants to longevity in several human populations, making the pathway the first with clear effects on human aging.

© Zeroing In On Health – The Blog!.

Update (11-24-09, 8:20 AM):  See also Worms and Stress: Live Long and Prosper by Petro Dobromylskyj, at his blog Hyperlipid. An excerpt:

This is how this research group view the impact of their work on diabetes management:

“In light of our findings, the current body of evidence tentatively calls into question the efficacy of increasing cellular glucose uptake in diabetics and suggests that other methods of lowering blood glucose (Isaji, 2007; Wright et al., 2007) may be preferable to achieve normal life expectancy in human type 2 diabetes patients.”

The two refs cited refer to techniques for extracting glucose through the kidneys or possibly reducing its uptake through the gut. No consideration seems to be given to not actually putting quite so much glucose in to the system in the first place!

Read his post and the comments, and follow the links. Good stuff.

Update (11-24-09, 10:50 AM):  Here are some cookie recipes; cookies wheat-grainless and sugarless (or at least capable of being made so):

1.  Chocolate chip cookies and more from Elena’s Pantry

2.  Assorted cookies from This Primal Life

3.  “Caveman Cookies” from Son of Grok

4.  Almond cookies from Mark’s Daily Apple

Search through those Websites and you’ll find more good eating.  See also RecipeZaar and Paleofood (like their cookie recipes).

Update (11-24-09, 2:190 PM): Forgot to give a hat tip to Mark’s Daily Apple for bringing the Charles Washington post to my attention. And to Marnee D and Valda R for bringing the Dobromylskyj post to my attention.

November 17, 2009

Induction, Economics and More

Filed under: Economics, Logic, Quotes, Science — Administrator @ 8:31 am

In the Introduction to A Treatise on Political Economy the author, Jean-Baptiste Say (1767-1832), makes some insightful comments on all science:

I.1
A SCIENCE only advances with certainty, when the plan of inquiry and the object of our researches have been clearly defined; otherwise a small number of truths are loosely laid hold of, without their connexion being perceived, and numerous errors, without being enabled to detect their fallacy.

I.5
The wide range taken into the field of pure politics, whilst investigating the subject of political economy, seemed to furnish a much stronger reason for including in the same inquiry agriculture, commerce and the arts, the true sources of wealth, and upon which laws have but an accidental and indirect influence. Thence what interminable digressions! If, for example, commerce constitutes a branch of political economy, all the various kinds of commerce form a part; and as a consequence, maritime commerce, navigation, geography—where shall we stop? All human knowledge is connected. Accordingly, it is necessary to ascertain the points of contact, or the articulations by which the different branches are united; by this means, a more exact knowledge will be obtained of whatever is peculiar to each, and where they run into one another.
I.6
In the science of political economy, agriculture, commerce and manufactures are considered only in relation to the increase or diminution of wealth, and not in reference to their processes of execution. This science indicates the cases in which commerce is truly productive, where whatever is gained by one is lost by another, and where it is profitable to all; it also teaches us to appreciate its several processes, but simply in their results, at which it stops. Besides this knowledge, the merchant must also understand the processes of his art. He must be acquainted with the commodities in which he deals, their qualities and defects, the countries from which they are derived, their markets, the means of their transportation, the values to be given for them in exchange, and the method of keeping accounts.
I.7
The same remark is applicable to the agriculturist, to the manufacturer, and to the practical man of business; to acquire a thorough knowledge of the causes and consequences of each phenomenon, the study of political economy is essentially necessary to them all; and to become expert in his particular pursuit, each one must add thereto a knowledge of its processes. These different subjects of investigation were not, however, confounded by Dr. Smith; but neither he, nor the writers who succeeded him, have guarded themselves against another source of confusion, here important to be noticed, inasmuch as the developments resulting from it, may not be altogether unuseful in the progress of knowledge in general, as well as in the prosecution of our own particular inquiry.

I.8
In political economy, as in natural philosophy, and in every other study, systems have been formed before facts have been established; the place of the latter being supplied by purely gratuitous assertions. More recently, the inductive method of philosophizing, which, since the time of Bacon, has so much contributed to the advancement of every other science, has been applied to the conduct of our researches in this. The excellence of this method consists in only admitting facts carefully observed, and the consequences rigorously deduced from them; thereby effectually excluding those prejudices and authorities which, in every department of literature and science, have so often been interposed between man and truth. But, is the whole extent of the meaning of the term, facts, so often made use of, perfectly understood?
I.9
It appears to me, that this word at once designates objects that exist, and events that take place; thus presenting two classes of facts: it is, for example, one fact, that such an object exists; another fact, that such an event takes place in such a manner. Objects that exist, in order to serve as the basis of certain reasoning, must be seen exactly as they are, under every point of view, with all their qualities. Otherwise, whilst supposing ourselves to be reasoning respecting the same thing, we may, under the same name, be treating of two different things.
I.10
The second class of facts, namely, events that take place, consists of the phenomena exhibited, when we observe the manner in which things take place. It is, for instance, a fact, that metals, when exposed to a certain degree of heat, become fluid.
I.11
The manner in which things exist and take place, constitutes what is called the nature of things; and a careful observation of the nature of things is the sole foundation of all truth.

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