I tutored a fifth grader on 11-17-09. We did some work on numbers and the decimal system.
Me: “So do you understand this about the way decimals work?”
Student: “I do the way you explain it.”
Logic. Gotta love it. Theory and practice unite.
November 30, 2009
November 17, 2009
“These Are A Few Of My Favorite Things”
One of my favorite phrases is “Q.E.D.” It means:
which was to be shown or demonstrated (used esp. in mathematical proofs).
1810–20; < L quod erat dēmōnstrandum
QED. Dictionary.com. Dictionary.com Unabridged. Random House, Inc. http://dictionary.reference.com/browse/QED (accessed: November 16, 2009).
November 14, 2009
Breakfast Informed By Math and Science
Breakfast (October 30th) at 10:45 AM: a pound of shrimp sauteed in lots of butter (then sprinkled with chipotle powder and black pepper) and some homemade guacamole. I ate 30 to 45 minutes after 15 to 30 minutes of “hunting and gathering:” a little kettlebell work, some sit-ups, jumping up the stairs, and crawling (bear, crab, and push-up).
Exercise that week: made it to the gym Tuesday for a good half hour, then went for a mile to mile and a half walk outside (without a shirt, to get some good vitamin D; and barefoot, to maintain a good posture and reinforce good body dynamics); Wednesday I rode my horse for an hour and a half; Thursday I went to the gym for a good half hour.
November 9, 2009
Finding Libraries At Which To Study: It’s Easy
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.
November 5, 2009
A Three-question Quiz
In “Clever fools: Why a high IQ doesn’t mean you’re smart” (New Scientist, 02 November 2009), Michael Bond said:
When Shane Frederick at the Yale School of Management in New Haven, Connecticut, put [these] counter-intuitive questions to about 3400 students at various colleges and universities in the US – Harvard and Princeton among them – only 17 per cent got all three right (see “Test your thinking”). A third of the students failed to give any correct answers (Journal of Economic Perspectives, vol 19, p 25).
© Copyright Reed Business Information Ltd.
Here are the questions (click on the link for the answers):
1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?
2) If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of it?
© Copyright Reed Business Information Ltd.
Yes, I got all three right. And it didn’t take very long. Note that they are all math questions.
Another question (more “logical” than “mathematical”) asked in the article is:
Jack is looking at Anne, and Anne is looking at George; Jack is married, George is not. Is a married person looking at an unmarried person?
October 28, 2009
Theoretical Statistics Is Practical and Life-Giving
In “The Median Isn’t the Message,” Stephen Jay Gould (evolutionary biologist who taught at Harvard University) wrote:
My life has recently intersected, in a most personal way, two of Mark Twain’s famous quips. One I shall defer to the end of this essay. The other (sometimes attributed to Disraeli), identifies three species of mendacity, each worse than the one before – lies, damned lies, and statistics.
Many people make an unfortunate and invalid separation between heart and mind, or feeling and intellect. In some contemporary traditions, abetted by attitudes stereotypically centered on Southern California, feelings are exalted as more “real” and the only proper basis for action – if it feels good, do it – while intellect gets short shrift as a hang-up of outmoded elitism. Statistics, in this absurd dichotomy, often become the symbol of the enemy. As Hilaire Belloc wrote, “Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.”
This is a personal story of statistics, properly interpreted, as profoundly nurturant and life-giving. It declares holy war on the downgrading of intellect by telling a small story about the utility of dry, academic knowledge about science. Heart and head are focal points of one body, one personality.
Mr. Gould also goes on to discuss how the Platonic view that the type or kind is (most) real is false; what is true is the Aristotelian view that the individual (“variation”) is real. He says:
We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous “beginning of life” or “definition of death,” although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation.
But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.
Notice how Mr. Gould is talking about kinds of things as being separate from variation, shadings, and continua. I don’t know if he’d say everything was like that, even individuals, but if so, I’d have to disagree: individuals are distinct and separate; this is given clearly (by real, immutable cause-effect relationships) in perception. Kinds of things, conceptual categories, come about only by recognizing things in their reality- and perceptually-given background of variation: tables grasped as related to but contrasted with furniture and other items in a house; trees grasped as related to but contrasted with grass and bushes; people grasped as related to but contrasted with other animals; engineers grasped as related to but contrasted with other human professions.
Concepts are only ways of categorizing individuals based on cause-effect and explanatory relationships. Individuals are most real; types or kinds are real, but have a “secondary, dependent existence” to individuals.
October 15, 2009
Measuring Waves
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.
October 13, 2009
Minerals and Mathematics
How explosives have shaped our world:
In order to maintain our standard of living in the United States, every day 187,000 tons of cement are mixed, 35 million paper clips are purchased, 21 million photographs are taken using millions of ounces of silver…80 pounds of gold are used to fill 500,000 cavities and 3.6 million light bulbs are purchased.
Few people know that 42 different minerals are used to make a telephone and 35 are used to make a color television. Even everyday products such as talcum powder, toothpaste, cosmetics and medicines contain minerals, all of which must be mined using explosives.
And where there are explosives, there is a great need for math — no arguing with that!! Oh, how important math is in context of explosives; we need math to measure and control their destructive power. Some uses of explosives — canon, old guns — we might not need math for; but many uses — building demolition, bombs, mass production of cartridges — we do need math for.
The quote is from a Website called “The World of Explosives,” which says about itself:
This site was developed for the general public by the Society of Explosives Engineeers, Inc. to show the important role explosives have played in the
development of our society. Explosives have had a profound influence on every individual. Their use in the extraction of materials (metals, rock, coal) and application in the building of roads, dams, foundations, tunnels and railroads have made our standard of living what it is today.
One page on the site is a long list of “The Many Uses of Explosives.”
HT: Michael S
October 9, 2009
Health, Flu, Vitamin D, Diet and More
I’m convinced that vitamin D3 and a change in diet has improved my health, immunity, and biochemistry. Well, as convinced as one can be without running scientific experiments on oneself, or doing some rough controlled experiments. I’m basing my conviction on personal experience, friends’ experience, and the science I’ve read on Dr. Eades’ Website, Dr. Harris’ Website, Dr. Guyenet’s Website, and others.
Note how this all demonstrates the practicality and pro-human-life nature of science and mathematics, without which I could never know what I do about health.
Here are some personal anecdotes (which, while not reaching the status of scientific experiment, are still informed by principles of induction):
1. I used to get sick (catch a cold or feel like I was coming down with one; I don’t mean sick to my stomach) if I’d work out at the gym after skipping lunch, even if I had a good breakfast. I recall one time when I worked out under those conditions, then sat down at my computer to do some work until I became hungry. After an hour, I was not hungry yet. But after an hour and a half or two, my vision started to black out in the center, so that I couldn’t see what I was typing. At that point, I made dinner!!
But since I changed my diet and started taking vitamin D3, this no longer happens. I can skip breakfast and lunch, then work out, and be fine for hours — no blacking out of vision, no getting sick. What’s more, I can fast for 24 hours, but stay energetic and clear-headed. Once upon a time, I never would have thought I could fast that long, and never would have tried. And I used to hate, hate, hate to go to bed hungry. Now sometimes I *want* to go to bed hungry.
2. In tutoring students, I am around students who are sick, of course. But, recently, I have not come down with anything. I know I have picked stuff up from some students because one weekend I had two periods lasting about half hour to an hour where I was sneezy and feeling like I was coming down with something. But I never did. This was a shocker; in years of prior experience, feeling like I had those two times always had led to being sick. The only/major differences between now and then are vitamin D3 and diet. On the recent days when I was around students who were sick, by they way, I increased my dosage of vitamin D3 to 6,000 to 10,000 IU. (I recently bought some vitamin C, with 1,667% of the “recommended” daily amount; I save it only for days when I’m around someone who is sick.)
In other words, that’s “not getting sick, courtesy of science and mathematics.”
I take 2,000-5,000 IU per day of vitamin D3, unless I’m going horseback riding, in which case I don’t take any — I get plenty of vitamin D made by body + sunshine. (In a prior blog post, I linked to a vitamin D calculator, which you can check out, if you are interested.)
Danica McKellar: A Quote
In the course of reviewing a math book written by Danica McKellar, Math Doesn’t Suck, Denise at Let’s Play Math Blog posted a good quote from Mrs. McKellar:
But now Danica McKellar’s second book is out, and the first one has been released in paperback. A friendly PR lady emailed to offer me a couple of review copies, so I gave Math Doesn’t Suck a second chance.
…
Danica McKellar knows far more about math than I do. She majored in mathematics at UCLA and graduated summa cum laude in 1998.
…
As McKellar writes:
Working on math sharpens your brain, actually making you smarter in all areas. Intelligence is real, it’s lasting, and no one can take it away from you. Ever.And take it from me, nothing can take the place of the confidence that comes from developing your intelligence — not beauty, or fame, or anything else “superficial.”
Math isn’t easy for anyone. It takes time and persistence to understand this stuff, so don’t give up on yourself just because you might feel frustrated. Everyone feels like that sometimes — everyone. It’s what you do about those feelings that makes you who you are.
It’s in those moments when you want to give up but you keep going anyway that you separate yourself from the crowd and build the skills of patience and fortitude that will allow you to excel throughout your entire life — no matter what you choose as a career.
Danica McKellar is an actress (an intelligent one!!). Check out her interview on NPR.
