MathCog Idiocy

It's time to come back

2010-01-01T23:57:00.002-05:00

Last fall I joined two group son Ravelry - the Harry Potter Knit & Crochet House Cup and Fantasia. For the last three months, these groups have gotten me going on a small treasure trove of crochet projects. Several are math related.

My favorite is a mobius strip grown big and turned into a shawl/cowl (aka scowl). I've finished one and almost completed the second. The whole thing is supposed to represent something I love and is full of things to represent numbers (Fibonacci numbers, prime numbers, golden mean).

Here are a couple of pictures (the model is my gorgeous niece).

I have a second one almost completed in a beautiful silk/merion blend from Malabrigo. It's my sister's gift and she chose the yarn.

Heading back

2008-08-09T12:14:00.000-04:00

I've got a job of sorts. I've got a used notebook that works more or less. Now all I have to do is get back into the habit of writing stuff here.

Anybody have any suggestions?

Wandering into my own world to say "hi"

2007-10-09T08:30:00.000-04:00

I haven't died yet although you might think so. I've been reading, crocheting, and learning to knit, and, of course, looking for a job. The job is mega important right now since my computer is all but dead (I'm on my sister's 'puter right now).

Some extra-curricular reading for you all

2007-07-05T11:21:00.000-04:00

A comment (thank you Anonymous) on my previous post on counting included this link to an entry on the Britannica Blog: Why Math Geeks (Especially Immigrant Geeks) Rule. It's an interesting read.

I think I'm finished moving so I'll get back to all this stuff this weekend. :-)

I'm in moving hell

2007-06-15T11:02:00.000-04:00

Will this never end?

Let's start with counting

2007-06-11T18:08:00.001-04:00

In an overview of the history of mathematics, J. J. O'Connor and E. F. Robertson begin by saying that ”Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.” (MacTutor History of Mathematics, http://www-groups.dcs.st-and.ac.uk/~history/)

On the same note, I believe that the first brick in understanding mathematical cognition is counting. Fortunately (for me) there has been a great deal of research on this subject. There is a significant amount of evidence through studies done for at least the last 30 years (as far back as I looked) that show a recognition of numerosity and counting not only in people but also in a variety of animals – birds, rats, various monkeys/apes, etc. Granted the animals do not exhibit an ability to detect numerosity much above quantities of 3 – 5, but it’s there. This leads me to believe that a basic knowledge of counting is hard-wired into our brains. It’s an evolutionary trait handed down from our ancient ancestors.

There was a study reported on in SCIENCE in 1999 that sheds a little bit of light on how our brains are wired for counting. This is an illustration that appeared with the article.

DIAGRAM: Figuring out arithmetic. The principal brain regions involved in calculating exact and approximate mathematical problems. The left inferior frontal lobe is involved in verbally coded number facts that can be used in exact calculations. The intraparietal sulci of the left and right parietal lobes are implicated in estimations and approximate calculation, which are dependent on visuo-spatial representations of numbers. The intraparietal sulci are part of the circuit controlling finger movement and are likely to be crucial to finger counting, a near universal stage in learning arithmetic. (Butterworth, Brian. “A Head for Figures”. Science, 1999, 284(5416), p. 28-28-29)

subitize, v.
Psychol.
[f. L. subitus SUBITE a. + -IZE.]

intr. and trans. To apprehend immediately (the number contained in a small sample). Hence subitizing vbl. n.

1949 E. L. KAUFMAN et al. in Amer. Jrnl. Psychol. LXII. 520 A new term is needed for the discrimination of stimulus-numbers of 6 and below... The term proposed is subitize... We are indebted to Dr. Cornelia C. Coulter, the Department of Classical Languages and Literatures, Mount Holyoke College, for suggesting this term. Ibid., If no discontinuities had appeared in the results, no distinction between subitizing and estimating could have been drawn. 1971 Jrnl. Gen. Psychol. Jan. 121 The number of items in an array capable of being subitized. 1981 Nature 15 Oct. 569/2 Judgements of ‘small’ numerosities..are ordinarily attributed to subitizing.

Over the next couple of weeks, I'll review six relatively recent journal articles I've down loaded and also talk about some older studies that looked at counting in pre-verbal babies. The first article on tap is entitled "Analog Numerical Representations in Rhesus Monkeys: Evidence for Parallel Processing" - the study it reports on pretty much disputes the idea of subitizing.

Now aren't you just holding your collective breaths waiting for these?

Musical illusions

2007-06-09T18:01:00.000-04:00

I thought this article from Science News/Math Trek was very interesting - Musical Illusions

Is Mathematics language?

2007-06-06T18:22:00.000-04:00

The answer is both “yes” and “no” depending on whether you are asking if the method of communicating mathematics is a language or if you are asking whether mathematics as language defines the cognitive processes necessary to perform mathematics.

Your real question should probably be “why are you asking this?” The reason why I feel that the question of mathematics as language needs to be answered has to do with theories published in 2000 by a mathematician (Devlin, K., The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip) and a linguist and cognitive psychologist (Lakoff, G. and Nunez, R. E., Where mathematics comes from: how the embodied mind brings mathematics into being). In both cases, language becomes the underlying explanation for mathematical cognition. Devlin posits that mathematics piggy-backed on language. Lakoff and Nunez use linguistics constructs to explain the cognitive processes underlying mathematics.

So let's decide if mathematics is a language using a general definition of language. Language is a complex system so no simple definition will cover all the nuances, but we can for the time simplify as much as possible. A definition of language includes producing speech, analyzing the speech we hear, the vocabulary and its symbolic references we use, grammar, and syntax. (Deacon, 1998, p.40) Deacon offers a generic definition for language as “a mode of communication based upon symbolic reference (the way words refer to things) and involving combinatorial rules that comprise a system for representing synthetic logical relationships among these symbols.” Deacon also states that within this definition mathematics “might qualify as having the core attributes of language.” (Deacon, 1998, p.41)

Let's see what the "core attributes" of language might be. You can say that language consists of basic sound units, phonemes that combine to form morphemes. These phonemes and morphemes when combined according to predefined rules become abstract symbols which we ascribe meaning to and understand. In other words, they become words. Language also allows various combinations of these symbols by following syntactic and pragmatic rules - sentences and paragraphs. (See Matlin, 2005, p.298) The result is communication that describes an object, event, or action, which need not be present or even exist. In other words, language symbolizes and creates meaning using a series of abstract symbols (letters or sounds) which have no particular connection to a concrete object other than those connections we agree exist.

Presented in these terms, the phonemes of mathematics are the basic digits, zero through nine. These digits are combinable following a few simple rules and form mathematics morphemes, numbers such as 123 or 3.1416 or even 4/5. The branch of mathematics in question defines the particular syntax used. For example, Algebra’s syntax determines how to write an equation and the order of operations used to solve the equation. Each digit, number, or equation symbolically refers to a quantity or describes a system, event, or form. The actual quantity need not be present nor does a quantity or an equation need to refer to a concrete object or collection of objects. Many of the systems, forms, and events described by mathematics are themselves abstract concepts such as equations which describe the multidimensional shape of the universe.

Do these similarities between language and mathematics provide a sufficient condition to call mathematics language? In some instances, mathematical and language processing take place in areas of the brain that are generally similar. Experiments done on bilingual individuals indicate that exact calculations occur in the left inferior frontal lobe of the brain. This area controls linguistic representations of exact numerical values. However, approximations of numbers occur in the left and right intraparietal sulci in areas associated with visuo-spatial tasks. (Butterworth, 1999; Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999)

Given this, my answer to the question is “yes, there exists a well defined language of mathematics used to communicate mathematical knowledge.” However, I believe that it is a mistake to confuse the act of communicating mathematics with the cognitive processes taking place while doing mathematics so my answer to a mathematical language that defines the cognitive process is “no.”

References:

Butterworth, B. (May 7, 1999). A Head for Figures. Science, 284, 928-929.

Deacon, T. W. (1998). The Symbolic Species: The Co-evolution of Language and the Brain. New York: W.W. Norton and Company.

Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (May 7, 1999). Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence. Science, 284, 970-974.

Devlin, K. (2000). The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Basic Books.

Matlin, M. W. (2005). Cognition (Sixth). Hoboken, NJ: John Wiley & Sons, Inc.

Lakoff, George; Nunez, Rafael E. (2000). Where mathematics comes from: how the embodied mind brings mathematics into being. Basic Books.

World's oldest adornments

2007-06-06T11:33:00.000-04:00

This was on the Yahoo news page today. It's interesting and you'll see a little more about this in later posts from me.

RABAT (Reuters) - Perforated shells discovered in a limestone cave in eastern Morocco are the oldest adornments ever found and show humans used symbols in Africa 40,000 years before Europe, the kingdom's government said.
(Read more here.)

Origami fun for today

2007-06-04T17:12:00.000-04:00

Trisecting an Angle with Origami

2007-06-03T15:00:00.001-04:00

So the last time I sat down to write to you all, I said that I'd been at the library looking up information. And I pretty much tried to scare you away by saying that you'd see more about it. Well since then (it's been a tad busy at my house), I've decided to really scare you all.

Just about three and a half years ago I started looking for information on mathematical cognition. The search started with a book recommended to me by a high school principle, lead to a research project and rather long (one hour) presentation, and then became something of an obsession. The biggest problem I’ve been having is that the bulk of the research being done on mathematical cognition looks at arithmetic but not mathematics (geometry, algebra, and so forth). I have a couple of other problems right now. The first is that the more I’ve looked at one of the few theories of mathematical cognition that addresses “higher” mathematics, the more I think they’ve got it wrong. The other problem is my lack of access to people who study the subject which means that I can come up with all kinds of ideas, but have no way to get any feedback.

(And if I actually ever arrived at a coherent theory, I’d have no way of testing it. But I guess that’s another story.)

The lack of feedback leads directly to all of you. I decided to pretty much write papers and put them here for your comments, questions and ability to find the holes in my logic. There are a number of areas to looks at – the evolution and development of the brain and of cognition in general, the historical development of mathematics, studies of brain “use” while doing mathematics (or arithmetic), studies of mathematical learning disabilities, and possibly the effect of changes in society.

I’ll post the first of these “papers” in the next few days. Just to get it out of the way, I’ll talk about my ideas of whether or not mathematics is a language and whether or not mathematical cognition can be understood that way. (Aren’t you just way too excited?)

In the meantime, here are the definitions for arithmetic and mathematics from The Oxford English Dictionary, Second Edition (1989).

arithmetic, n.1
1. The science of numbers; the art of computation by figures.

2. Arithmetical knowledge, computation, reckoning.

3. A treatise on computation.

mathematics, n.
1. Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations. Colloq. abbreviated maths, (N. Amer.) math.

When the modern subject is studied as an abstract deductive science in its own right, it is often referred to more fully as pure mathematics (see PURE a. 2d); when applied to the modelling of physical objects and processes (e.g. in astronomy, various branches of physics, engineering, etc.) and random processes (in probability), and to the handling of data, its full name is applied mathematics (see APPLIED a.), or (in early use) mixed mathematics (see MIXED a.2 5).

2. The mathematical considerations or principles relating to a specified phenomenon, process, etc. With of.

What I did at work today

2007-05-20T22:01:00.000-04:00

On Sundays I'm in the library student computer lab from 1:00 to 8:30. I like the regular student computer lab better - mostly because I'm sitting at a desk with space to spread out my stuff. The library is somewhat less "user friendly." But the librarian got my laptop connected to the college Internet, so that was pretty cool. I spent a couple of hours scanning journal articles about genetics and evolution of the brain. Obviously there weren't a lot of students needing assistance. LOL

What I really started looking at (but got a tad side tracked) was information on the calculations used to determine when in the past a mutation occurred in a particular gene. I did read some interesting stuff in relation to that.

You can expect to see more about this since this is the only forum I have.

Math and Genes

2007-05-14T09:14:00.000-04:00

If you start reading about genetics, you start running into a lot of mathematics. Well, you don't usually know you have, but the math is there. Articles will appear that talk about the evolution of genes (or species) and refer to work that was done to try and determine when a gene mutated. The articles seldom (never?) actually show you the math, but here's one that does from MathTrek - A Grove of Evolutionary Trees.

What are you doing on your summer vacation?

2007-05-14T08:49:00.000-04:00

I'm moving, looking for a permanent job, and working!!!!!!!!!!!! I start a summer stint (30 hours/week for 12 weeks) in the college's student computer lab. Because of the nature of the job, there's a lot of down time so I will be making a concerted effort to read and understand H. M. Edwards' book Riemann's Zeta Function. I'm really looking forward to this.

I'm not, however, looking forward to getting everything sorted out and moved. I hope that getting my internet connection moved goes easily.

So what marvelous plans do you all have?

Still looking for a job

2007-05-07T09:52:00.000-04:00

Sometimes I wonder if I shouldn't just give it up and apply for well fare.

I was contacted by a company and went through two telephone interviews - one with HR, one with the relevant manager. Then they brought me in for four face-to-face interviews - HR again and three managers. But did I get the job? Nooooooooooooo. According to the email I received (almost a week later than they told me I would hear and after contacting them), I was an excellent candidate, but they hired some one with some unique skills (translation - younger than me).

The supervisor for the college computer lab contacted me to see if I wanted to work there for the summer (no students available for the work). So that's what I'll be doing for 12 weeks. Not a lot of money, but the basic bills starting in June will be covered.

The worst part of all this is that my lack of income means I'm losing my house. I'm trying to see if I can stave it off long enough to try and sell the house myself, but it's not looking good. See my first sentence.

This is for Rave!

2007-04-19T23:48:00.000-04:00

Back in October Rave asked me in the comments to this post what an equation was. I had no idea. But tonight an answer was provided. So Rave, go read the comments and you will have your answer. *grin*

Happy Birthday Leonard!

2007-04-15T10:12:00.000-04:00

Leonard Euler was born on this day in 1707. He produced mathematics in virtually every area of math.

Here are some of my favorites.
Typing Euler into the search box at Mathworld produces 671 results.
Typing Euler into Google produces 12,300,000 results.

A different DNA

2007-04-11T19:48:00.000-04:00

VW Bug had this on her blog. I just couldn't resist and I have to say, this is so me. *grin*

Read my VisualDNA™ Get your own VisualDNA™

Wouldn't this be a GREAT job?

2007-04-11T08:48:00.000-04:00

Still on the job hunt and still checking the various job boards. This morning's search hasn't been particularly productive, but HotJobs has the following listing. This is a job that I would absolutely love to have, but there is no way in the world I can even pretend to be qualified. Although it's pretty scary that I know what the ad is talking about. LOL

So here's the ad. Doesn't this sound like way too much fun?

Computational Research Scientist (Biomedical)
Company Name: Delta Search Labs, Inc.
Job Category: Pharmaceutical/Biotech; Technology
Location: Cambridge, MA
Position Type: Full-Time, Employee
Salary: Unspecified
Experience: 2-5 Years Experience
Desired Education Level: PhD
Date Posted: April 10, 2007

Solutions Labs (www.solutionslabs.com ) a Cambridge MA based R&D company, is recruiting one or two candidates with the following qualifications. Ph.D. or M.S. level researcher (M.S. absolutely must have several years relevant experience) with degree in Computer Science, Chemistry, Biophysics, Physics, Molecular Biology or Chemical Engineering wanted for bioinformatics, chemoinformatics, and chemometrics algorithm development. Will also consider exceptional candidates from Applied Mathematics, Statistics or related Engineering fields. Documented accomplishments in computational research and strong analytical, statistical, and numerical analysis skills required. Experience in spectroscopic data analysis (NMR is especially desirable) and mass spectrometry data analysis is prefered. We are seeking individuals whose primary background is computational and mathematical but who have experience analyzing experimental data and understand problems of preprocessing chemical data from various analytic methods. Desired background includes some of the following: pattern recognition, machine learning, multivariate statistics, numerical analysis, etc. Sufficient knowledge of biochemistry and molecular biology to interpret results of data analysis within a systems biology context (e.g. metabolic pathway analysis) would be a big plus. Experience with analysis and interpretation of Affymetrix microarray studies is also a big plus. Initial projects will be for both small molecule spectroscopic data pattern recognition (metabolomics) and DNA microarray analysis but might eventually expand to include mass spec proteomics. Position will involve both algorithm development and extensive programming. Programming may be done in Matlab and other scripting languages (e.g. Python). Position could involve collaboration with leading academic research groups. Ideal candidate will be creative with the desire and ability to help identify and aggressively pursue new opportunities in emerging fields. Strong written and verbal communication skills are a must. Prefer either US citizens, US permanent residents, or NAFTA TN applicants (but not an absolute requirement for exceptional candidates). Please send a cover letter and resume (pdf or doc file) to jobs@solutionslabs.com . Please use Research Scientist as the email subject

Okay...

2007-04-10T20:14:00.000-04:00

I have heat and hot water.

The headache is gone. (Probably because the erstwhile housemate brought me cigarettes. I was out. Have I mentioned that I don't have a working car so if I run out of something, it's just too bad so sad.)

The snow is still on the way.

Some days it doesn't pay to get out of bed

2007-04-10T15:49:00.000-04:00

I'm out of heating oil. No heat. No hot water.

Oh, and I have a headache.

And did I mention that there is a snow storm on the way?

We did the Easter dinner

2007-04-08T18:29:00.000-04:00

and I am STUFFED!

It actually was a lot of fun. Friday was the erstwhile housemate's birthday so we celebrated his birthday today. (There's a joke in there, but ... ) So besides the traditional Easter ham we had a fabulous birthday cake that my sister made with help from my youngest nephew (9 years old) on the marzipan decorations. Youngest nephew put the candles on the cake just before I took this picture.

There was also a funny birthday card with a hunky man on the front. *grin*

BTW - the cake was a carrot cake like you've never had. Sister added raisins, nuts, and pineapple. Yummy.

Sweater

2007-04-05T09:40:00.000-04:00

This is a sweater for me. It took me forever to get around to weaving in the ends. LOL
Front and back.

Greenland is closed!

2007-04-05T09:31:00.000-04:00

(At least that's what the ticker on the bottom of the TV said.)

I think the chickens want to escape and fly south. This is their world this morning. You can't really tell from the photo, but the top of the area looked like a 3-D image of a function. At least the way they look in a mathematics program. I'm such a nerd. LOL

Monday's interview

2007-04-03T10:14:00.000-04:00

If I haven't said so before, this was the second telephone interview with the company. It amuses me because I'm talking with people who are about 11 miles away. However, this is the way the company (corporate wide) does the process.

So I had the interview - lasted about 1/2 an hour. Since I had the phone on speaker, the erstwhile housemate heard the whole thing. I felt like I'd done badly, but he thought it went well. I guess it went good enough because a face-to-face interview will be scheduled this week. *crossing fingers*

Now if I could just figure out why the two people I've spoken with are both trying to point me away from the analyst position and towards a Six Sigma one.

Quote for the day

2007-04-02T10:53:00.000-04:00

from blogless friend Sue.

I discovered that nature was constructed in a wonderful way, and our task is to find out the mathematical structure of the nature itself. It is a kind of faith that has helped me through my whole life. - Albert Einstein

Friday's interview

2007-04-02T10:49:00.000-04:00

Went okay, but I felt a little like I'd been the object of a "bait and switch" ad campaign. In the first interview, HR decided to submit my resume for an analyst position. The interview was for a dead-end data entry position. I let them know that I have a second interview for an analyst position with another company and that I would get back to them after that.

So on to today's interview.

Woohoo!

2007-03-29T17:46:00.000-04:00

After 10-1/2 months of pretty much no movement, I have not one but two interviews!

The first is tomorrow morning for a company I'd really like to work for and have been trying to get a job with for some time. The job is moderately interesting, but I don't know what the pay range is. Somehow asking over the telephone today didn't feel right.

The second interview is on Monday. It's actually a second interview of sorts since the initial contact turned into a telephone interview. I was doing some mental scrambling on that one. LOL. But I must have done fairly well since they got back to me two days later to schedule the "second" interview. At any rate, it's a really interesting job, the company initiated the contact with me which I think is a major plus, and the pay range is very nice.

So we'll see what happens. Given my current disastrous financial situation, I'm inclined to go for money.

This is strange

2007-03-28T12:16:00.000-04:00

From MSNBC: Bizarre hexagon spotted in Saturn’s clouds. Astronomers can’t explain six-sided pattern at planet’s north pole. Go here for the story.

A love story

2007-03-26T21:39:00.000-04:00

Check out this YouTube video link from Gooseania - To the vector belong the spoils - the love story between a dot and a line. BTW - this is a book you can buy. I read it several years ago.

Riemann Hypothesis - Is it proved (or disproved)???

2007-03-26T20:57:00.000-04:00

So this is the current "news" making the rounds on some of the math blogs - a draft paper proving that the Riemann Hypothesis is wrong.

A rehash for all of you who get bleeding brains when I go into math mode:

There is a function (the zeta function) that predicts the distribution of the prime numbers. In 1859 this pretty neat mathematician named Riemann presented a short paper in which he conjectured that the non-trivial roots of the zeta function would all have a real part = 1/2.

Lost you, didn't I? Okay, go back to high school algebra and those equations you had to solve. The ones that looked like x² + 3x - 4 = 0. You'd do some arithmetic and find out that you could rewrite the equation as (x + 4)(x - 1) = 0 and the solution was x = -4 or x = 1. Those were, more or less, the trivial roots.

Although it's more complicated (I'm guilty of major simplification in the previous paragraph), the trivial roots of the function in the Riemann Hypothesis are all negative numbers (-2, -4, -6, .....) and the non-trivial roots are all complex numbers. The hypothesis says that the non-trivial roots will all be 1/2 + yi (y is any real number and i is the square root of -1).

Fast forward to 2007 and nobody has proved or disproved the hypothesis. It's a really BIG deal for a whole lot of reasons. A draft paper has appeared on ArXiv claiming to disprove the hypothesis. Keep in mind that this is a draft and has not been peer-reviewed in any manner. Nevertheless, it's getting attention. Check the entries on Gooseania and Ars Mathematica.

Even though my interest in the zeta function has to do with that real part "y" of the non-trivial roots, I've downloaded the paper. I can tell you that 8 pages into it, I'm cross-eyed. LOL

Here's what I've been doing

2007-03-26T15:12:00.000-04:00

What have you been doing?

Today almost improved on the week

2007-03-21T16:31:00.000-04:00

Even though I woke up with a migraine, I briefly thought that all was not lost. You see after I came downstairs, the crazy kitty magically made the missing bamboo crochet hook appear. There was joy in Mudville.

The joy didn't last long. My firewall had an upgrade. I downloaded the file and ran it. Something went totally caca so with pounding head, I got to try and restore the 'puter and get the expletive deleted upgrade installed. It's done now, but the expletive deleted Norton System Works isn't recognizing the upgrade and thinks that I don't have a firewall. *banging head*

If my car was running, I'd run away from home.

The fastest turn down ever

2007-03-20T17:32:00.000-04:00

I submitted an online application today, received confirmation of receipt at 12:05, received the "thanks but not thanks" email at 12:43.

I'm pretty sure now that I am totally unemployable so the cat and I are making a list of couches we can sleep on starting April 1st. Please let me know what dates are available at your house.

And my friends think that I give them headaches

2007-03-19T18:40:00.000-04:00

From Yahoo - Brainiacs Succeed in Mapping 248-Dimensional Object

For the more mathematically inclined among you, check out what The n-Category Cafe had to say today.

New math???

2007-03-19T16:22:00.000-04:00

From Ars Mathematica - Maharishi Mathematics.

Put down your drink and your food, then follow the link to the course listings. I'm LMAO!

Is this a sign?

2007-03-19T16:00:00.000-04:00

I got up this morning, drank a cup of coffee, and started combing through job ads in the local Sunday paper and on the online job boards. This is one of those royal pains. Since the biggest "city" in this area has a population of approximately 25,000, there are a limited number of jobs. I've found that if I search for all jobs for the past week and then look through them all, I have the best chance of finding something to apply for. Today's search netted 2 on-line applications, 1 that I have to mail, and a company that I'll send a resume to in the hopes that they have something. Considering that there were only about 3 dozen ads, this isn't too bad.

So why, you might ask, am I asking if this is a sign? Well when I sat down to search I put my crochet project and the very nice bamboo crochet hook from my sister on my lap. At some point I heard the hook fall on the floor. Okay, so all I have to do is pick it up. Right? Wrong. Apparently it fell into a mini-black hole because I can't find it.

Is this a sign? Will my resume fall into the HR equivalent of a black hole?

Sunday

2007-03-18T20:16:00.000-04:00

Today the erstwhile housemate baked one of his "better than sex" chocolate cakes. It had a dual purpose - to celebrate my youngest nephew's 9th birthday (we missed that because I had a migraine) and to make my sister feel better (the oldest nephew got terminally stupid and wrecked her car). I think the cake did its job. LOL

Before the cake, my sister and BIL took me to Wally World so I could get some yarn and buttons I need to finish the two hooded sweaters for the Pixie's boys. When they're done this week, I'll post some pictures.

There's a link to this blog

2007-03-17T12:51:00.000-04:00

from this blog - Juan de Mairena [v.2.718]. From the one or two names in the posts, I'm pretty sure that it's a math related blog. I'm thinking that I should return the favor and link to his blog. I just wish that I could read it, although this makes me realize just how insular my education is.

I read, write, and speak English. That's it. Just English. (I had 6 years of French, but that was more than 30 years ago. How much do you think I remember?) A number of years ago on my first day at a new job, my new boss asked me what languages I knew. As I listed off half a dozen computer languages, he looked more and more confused. So I asked him what languages he knew. His answer - English, French, Italian, Spanish, Russian.

I've also noticed when looking at the Stat Counter data that my blog is accessed by people from other countries and I bet that they can read English and probably at least one or two languages other than their native language.

How sad is it that the average American barely speaks English? (This rambling post is a really good example of that.)

Kind of Star Trekkie (?)

2007-03-17T12:35:00.000-04:00

Once a week I receive the Science News e-Letter - brief blurbs on interesting stuff with links to the full articles. This week's featured articles for physics has the following entry.

Warming Up to Criticality: Quantum change, one bubble at a time Physicists can now observe matter as it gradually turns into a Bose-Einstein condensate--the exotic state of matter that displays quantum behavior at macroscopic scales. http://www.sciencenews.org/articles/20070317/fob3.asp

I don't have the background to understand anything that is more in depth than this article, but isn't it cool? I wonder what the mathematics that describes this system looks like?

Friday Miscellany

2007-03-16T12:06:00.000-04:00

Two links to investigate.

The first from my blogless friend Sue. She calls it "Feeding the Dark Side". I call it a really neat combination of math, crochet, and art. So, go here and check it out.

The second from blog mama, Teresa is called Romantic Math. The section starts with this quotation - "Beauty is the first test: there is no permanent place in this world for ugly mathematics." (G. H. Hardy) If nothing else it's an interesting use of functions. *grin*

Now this is potentially very cool

2007-03-15T10:28:00.000-04:00

From The n-Category Cafe, a link to what looks like a very cool paper. At least the first page caught my attention.

Mathematical knowledge: internal, social and cultural aspects

The author (Yu. I. Manin) describes the paper as follows: "I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture."

Added a couple more math blogs

2007-03-15T09:34:00.000-04:00

I realized during the fall semester when I took the complex numbers course just how much I miss doing mathematics every day. But it's difficult when you're sitting alone at home or, even worse sitting at a mind numbingly boring job, to get motivated. I'm thinking that if I go read math blogs regularly, that may get me off my ass. We'll see.

Revisiting the hometown

2007-03-10T21:43:00.000-05:00

Sort of. For reasons that escape me, I Googled "Astoria" tonight. In order to avoid any confusion, I'm talking about a part of the borough of Queens, NYC, called Astoria. The 1964 World's Fair was there, LaGuardia Airport is there, my father was born and raised there. Growing up, we visited my grandparents and then just my grandmother there. They lived on 46th off of Ditmars Blvd. I can remember walking to the end of the street. There was an IGA across Ditmars and the old Steinway building which at some point became warehousing for Sterns (I think) and now is whatever it is.

This is a picture of my grandparents in front of their house. Grandpa worked for TWA at the time this picture was taken (before 1961 when he died) and the picture is part of an article about him in an employee newsletter.

In the course of my travels, I found a blog called Queens Daily Photo. Go take a look. It's a pretty neat view of the area from someone who is "new."

Have any of you tried

2007-03-05T15:42:00.000-05:00

the Google AdSense thing? Do you actually make any money from it?

It was a dark and stormy night...

2007-03-04T17:03:00.000-05:00

Harvey tells me that I have to explain my absence. He recommends making up something dramatic and suggests that jungle adventures are always good.

Now I was trying to spare you all the gory details of my long absence, but I suspect that Harvey will not let the matter rest. So I will begin the tale.

Many moons ago in a land that existed outside of the bounds of normal time, a land of mathematical magic, beautiful princesses, and really really hot princes, an old woman crept through the trees in search of that one perfect Fibonacci flower. Or perhaps a snow flake born out of the chaos of a fractal storm. But alas, her quest was leading to the dark places where the spiders spun their webs to capture human dreams for food.

Lost within the darkness, the old woman sat down to reflect on her life. Perhaps within its tunnels she would find a way out of the spiders lair and back into the light.

(Should I really go on? LOL)

Headache inducing

2007-02-28T14:59:00.000-05:00

Reading job ads and trying to figure out how to rewrite my resume for a specific job.

With all this job stuff I don't get to do the really fun things like go over to the MIT site and check out their Open Courseware. There are some really fun math courses there.

My Dirty Little Secret

2007-02-27T18:16:00.000-05:00

I love to do things like needlepoint and crochet. The needlepoint is on hold until I can get an eye exam and have my glasses changed, but I've been doing a lot of crochet. Finished one sweater and have a second one almost complete. It's killing me right now to see all this really gorgeous yarn that I can't buy (another reason besides keeping a roof over my head for having a job).

My sister and a very good friend (she sent me the coolest row counter!) just started blogs about their knitting and needlework adventures. So I've added links to them. Go encourage them to write more. *grin*

I suppose I have to end the pity party somethime

2007-02-27T16:44:00.000-05:00

But probably not quite yet. Although I had a 3 month temp job, it's been 9 months and I still haven't found a permanent job. Off hand, I'd say that I'm totally unemployable except in low paying, unskilled jobs.

So I need to work. Any good ideas?

For what it's worth, when the temp agency called to say the assignment was ending the guy kept on saying how happy the client had been and what an excellent job I'd done. But really how hard is it to accurately query databases and enter the information into another database?

There's hope for me

2006-10-24T20:21:00.000-04:00

From the text for the complex variables course I'm taking:
Ordinarily, modern advances in the theory of complex variables for problems that are of a level comprehensible to readers of this book are extremely rare. A remarkable exception occurred in the year 1984--within the lifetime of many readers--for it was then that a relatively obscure mathematician at Purdue University, Louis de Branges, published his solution of a famous unsolved problem in functions of a complex variable: the Bieberbach conjecture...He was 54 years old at the time of his breakthrough, an age at which most mathematicians are beyond their best work...
(p. 259, Complex Variables with Applications, A. David Wunsch)

So maybe I will be able to write that proof!

I'm going to be nice and warm this winter

2006-10-24T19:56:00.000-04:00

A package, a rather large package, an unexpected package arrived on my doorstep late yesterday afternoon. My special sisters Teresa, Pixie, TOSP, Gigi, and blogless sisters Sue, Nell, Mirm, Barbara, and Joey conspired and had a fur lined coat made for me. It is the most beautiful, warm, soft, gorgeous coat. Since the temperature today was struggling to make it to 50 degrees, I wore the coat to my math class.

So even if I have no job and no way of heating my house, I can bundle up in my new coat and stay warm.

The erstwhile housemate took a picture. The house is a mess, I look like h*ll, but you can get an idea of just how nice the coat is.

Still no job

2006-10-19T19:45:00.000-04:00

I went to the interview last week. Turns out that I was one of six people being interviewed - no second interviews. Okay. Not my dream job (which I'm not qualified for anyway), but a job that I'd be good at and would really like to get. A decision was going to be made early this week and then everyone would be notified. Beyond an acknowledgement of my "thank you for the interview" communication, I've heard nothing. Looks like I'm going to continue to be unemployed.

So would some one please explain to my car that it has to stop with the mystery noise and can't break right now cause I can't afford to fix the stuff that the mechanic says needs to be done in the next 4 months or so.

I should have really really hated the job because then I would have gotten it and the car-car would get lots of tender loving care.

I have an interview...

2006-10-09T11:35:00.000-04:00

this Wednesday. Woohoo!

Course I'm convinced that by telling you all this, it guarantees that I'll not get a job out of it. But at least someone wants to talk to me.

Just so Harvey doesn't have to sadly shuffle off

2006-10-03T19:20:00.000-04:00

In two weeks I'll have been unemployed for five months. I'm just a little bit depressed. Apparently I'm too old, too stupid, and too uneducated (or over educated around here) to get a job.

There has been a bright spot the last month. I'm taking a course in complex variables. But it's also kind of sad because I've been realizing how much I've missed math courses. Maybe I should sell the house and my furniture, pack my books, computer, and cat in the car, then live homeless in the car and sneak into math courses at various and sundry universities. I can take a drudge job at Micky D's to buy gas, books, and food for the cat. Does that sound like a plan?

How long does it take...

2006-06-29T17:41:00.000-04:00

to read a resume and then email/mail a note that says, "you're stupid as sh*t and we're not even going to bother considering you for the job." I'm tired of reading job ads and responding and never hearing anything back.

Friday miscellany is global warming

2006-06-23T16:51:00.000-04:00

By now you've probably all seen some variation on the theme - planet warmest in 400 years. The media is going on about this in various places, but I know that most of you see this as "spin" so here is a link to the National Academy of Sciences press release. Note that this release includes a link to the actual study. It will cost you for the full report, but a brief version (pdf file) is available here.

Link to the NAS courtesy of The Scientific Activist.

Global warming

Riemann and non-trivial zeroes

2006-06-18T21:36:00.000-04:00

I was reading about Riemann Zeta Function Zeros on Mathworld. A non-trivial zero for the Riemann Zeta Function looks like this: a + ti, where a, according to the hypothesis equals 1/2; i is the imaginary number - the square root of -1, and t is a real number.

This is the part that I think is interesting."ZetaGrid is a distributed computing project attempting to calculate as many zeros as possible. It had reached 1029.9 billion zeros as of Feb. 18, 2005. Gourdon (2004) used an algorithm of Odlyzko and Schönhage to calculate the first 10 x 10¹² zeros (Pegg 2004, Pegg and Weisstein 2004)...All known values of t corresponding to nontrivial zeros appear to be irrational (Havil 2003, p. 195; Derbyshire 2004, p. 384)."

So for the billions of non-trivial zeroes calculated to date, the real part, t, appears to be irrational. I have to tell you that if I had the necessary knowledge, I wouldn't want to prove the hypothesis but rather I'd like to prove that the real part, t, is irrational for all non-trivial zeroes.

In the meantime, here is a rather interesting article about the Riemann Hypothesis and the number 42 (the answer to everything *grin*) - Marcus du Sautoy, "Prime Numbers Get Hitched", Seed Magazine" (03/27/2006). I found the link to this while reading about the Riemann Zeta Function on Wikipedia. It's a really cool paper talking about the link between the Riemann Hypothesis and physics. Go take a look.

Math

Update to Honor's Research blog

2006-06-18T15:50:00.000-04:00

I've posted the next installment here. Enjoy or not as the case may be.

I have to say that at times I really hate Blogger. I had the whole bloody thing formatted so that it looked right (done in NoteTab Light and previewed), but when I copied it into Blogger the formatting went all to hell. sheesh

Special request. Support future mathematicians!

2006-06-18T09:02:00.000-04:00

For all of the 2 or 3 people who read this blog, I've got a request that you do something for me that I think is very important. I can't do this right now because yesterday's mail brought the "pay by or we turn you off" electric bill (which I can't pay at the moment *sigh*). So, please think about going over to ScienceBlogs, specifically Good Math, Bad Math and donate for me.

"Donate to what?" you ask.

Here's the deal. From Help the SB gang help schools -

What we're doing is trying to get people to donate to DonorsChoose.org. That's an organization where teachers who's classrooms lack the supplies that they need can submit proposals, and donors can select specific proposals that they want to support. Each of the participants from SBs has picked a bunch of proposals that we think are valuable, and we're asking you guys, our readers, to look at those proposals, and donate some money to whichever ones you think are worth supporting.

So go on over to the Good Math, Bad Math donor site and GIVE! GIVE! GIVE!

ScienceBlogs is matching donated funds up to $10,000! As of yesterday (6/17/06), $8498.73 had been raised and will be matched.

Thank you.

Math, Math Education

Friday miscellany

2006-06-16T16:01:00.000-04:00

This is a long miscellany for a Friday.

Off and on for awhile, I've been wondering what would happen if I wrote a post full of names of people like Oprah and Angelina Jolie, or concepts like global warming and evolution, or the ever popular sex. Would people who googled on those come here and take the time to read my idiot ramblings, or would they just be pissed off at the mis-direction? What would happen if I used somewhat less mundane phrases like "theory of mind" or "calculating rate of decay?"

What do you think? Who will be the first to verbally "kick my ass?" Or will someone, for reasons unknown, get interested and maybe even wander over to my Honor's Research blog?

Instead, I could share something with you - The Paradox of Science by Edward L. Thorndike, from the Proceedings of the American Philosophical Society, Vol. 75, No. 4 (1935), pp. 287-294. This is a really interesting paper and is available on JSTOR. (I'd give you the link to the paper, but your can't download it unless you happen to be accessing through a subscribing entity like my college.)

The Paradox of Science
by Edward L. Thorndike
(read April 18, 1935)

Intelligent men who know the facts of science have relinquished most of their hopes of supernatural control of the forces of nature. No matter how devotedly they worship their God, they do not ask him to turn men into animals, or send rain for the just and lightning against the unjust. No devil is blamed for sending a plague of infantile paralysis, and no deity is expected to remove it. Where bullets, blessed or unblessed, go is determined by the laws of ballistics. Whether a gift to a beggar will benefit or injure him is determined by facts of psychology and the social sciences, not by the blessing of the church. With few or no exceptions, nature takes its course undisturbed by vows, sacrifices, and prayers.

Science, studying the ways of nature, finds them to be so regular and reliable that the assumption that they are perfectly so has gradually become almost an axiom in science and its applications. In the faith that nature will not change her ways (or customs, or habits, or laws, or behavior in the frame of space and time, or whatever the reader likes to call them) bridges are built, trains are run, diseases are treated or prevented, crops are grown, children are taught. We no longer fear, as men once did, that the sun may not bring summer again. We do not pay sacrifices to control the seasons, but trust the uniformity of nature and our predictions of the earth's path for thousands of years. We have abandoned prayers to the goddess of fertility to bring the seed to harvest, believing that the same seed in the same soil with the same climate will always produce the same result.

Supernatural forces were often irregular and capricious. In spite of one's best efforts to induce them to act in a certain way, one might be outbidden; and sometimes all bids were rejected in favor of some darling of the gods. But the forces known to science always produce the same result under the same conditions.

In human affairs precisely the same conditions rarely, if ever, recur. Perhaps no two typhoid infections ever were absolutely alike; almost certainly no two cases of typhoid infection studied have been absolutely alike. But pathology is confident that if identical bacilli invaded identical human bodies and were treated identically, the results would be identical.

There has never been another depression just like the depression of 1929- ?; there has never been a war identical with the World War. The situation of the world on January 1, 1935 never existed before and never will again. There probably has never existed a single village the conditions of which were identical at any two moments; nor any two villages which were identical in nature. Science cannot roll identical villages down a depression again and again to test the laws of economics as it rolls ivory balls down an inclined plane to test the uniformity of the laws of motion. But it has confidence that if the same human elements could be subjected to the same conditions, they would display the same outcome. It believes that the same brain or mind acted upon by the same stimuli will give forth the same thoughts, feelings and acts. Physiology and psychology use that belief just as physics used the belief that the same mass at the same distance from the earth's center will, other things being equal, fall toward it with the same speed.

Nature's ways are not only regular; but to the best of science's knowledge and belief they are also immutable. Nature may add new customs if new things and conditions develop, but it does not change its customs of behavior with the same things and conditions. Science expects the combination of oxygen and hydrogen to make water a million years from now if conditions remain the same. If a certain equipment of genes under certain conditions of environment made John Doe born in 1900 a murderer, that same equipment of genes in that same environment will make Richard Roe born in 1950 a murderer except for supernatural or extra-natural forces.

In proportion as power is taken from personal deities and lodged in the uniform and stable ways of nature, man abandons all appeals, bribes, and inducements such as might move a super-man who enjoyed material gifts, praise, submission, respect, or affection. It is more reasonable to find out the course of nature and make the best of it. Propitiation gives way to observation and prediction. Science aims to learn nature's ways so as to know what will result from any concantenation of events. The present goal of science is to understand and predict every event in the world as it can now understand and predict the movements of familiar heavenly bodies or the swings of a pendulum.

But, by a unique paradox, science, which finds nature's ways invariable and unchangeable, changes nature as the personal appeals of religion never could. Science, which accepts the course of nature, controls it to an extent and degree far beyond the powers of priests or magicians. Science can make lightning and direct its course; can stop plagues; can double a harvest; can breed new strains of animals (and of men, if human laws and customs would permit).

In proportion as we treat the world as regular and resistant to outside influences we influence it. If science in the next hundred years should describe the ways of human nature and behavior as accurately as it has by now described the nature and behavior of the planets and stars, so that man could predict what men would do as he now predicts eclipses, he would increase his power to control the fate of men. Every immutable "law" of human physiology and psychology would turn into an instrument to change human life. By the same token, if, by science, I could prophesy exactly what I would think or feel or do in every conceivable situation that life could offer, and knew that my thoughts and feeling and actions in each case were as inevitable as the pull of the magnet on steel, I would thereby enormously increase my power to change my fate. Every fact of the universe which science takes from the realm of fortuity, miracle and caprice, and puts under the rule of the regular and changeless ways of nature, means one more addition to control over nature. The more the world is determined, the more man can work his will upon it.

The explanation of this paradox should be instructive and comforting to men and women who are disturbed because the march of science seems to reduce the world to a mere machine, to abolish the freedom of the will and eliminate human responsibility.

They have thought that the paradox was a dilemma - that if the ways of nature including human nature were invariable and immutable, then no acts of man could change nature - that one must choose between science and freedom.

The paradox is not a dilemma. Science does not necessitate fatalism. The uniformity of nature is consistent with changes in nature made by human thought and action, especially as guided by science itself. This is possible because science is a part of nature, because knowledge is a natural force, because human ideas, wants, and purposes are part and parcel of the stream of natural events. Your consideration of whether to say yes or no in certain situations is an event in nature. Your decisions yesterday to say No and today to say Yes are events in nature. Both have their consequences in perfect accord with the ways of nature. but your "No" of yesterday may have changed the world by the death of a prisoner whom you refused to pardon, and your "Yes" of today may have changed you from a bachelor to a husband and been a link in a chain of causation resulting in the birth of a child who in 1983 will discover a cure for cancer.

The essential facts are as follows: The course of nature is partly repetitive or cyclical, as in the movements of the planets or the turn of a motor, and partly original or creative, as in the development of a new species of animals, or the construction of the Panama Canal. The distinction is not, however, sharp. Even the most repetitive parts may change. Indeed they must if conditions change. Even the most novel events consist of old elements in new combinations. The net total is a universe changing very little in some respects and very much in others, but surely changing from 100000 B.C. to now, and equally surely from now till tomorrow. Within the brains of men, the changes are so numerous and rapid that a year's crop within New York City alone could not even be listed by a thousand chroniclers in a life time.

Parts of the world change other parts. So changes in the moon will cause changes in the tides; the birth of a baby changes the habits of a household. Notable among changes of one part of nature by another are those initiated by changes in human brains. To them are due buildings, mines, farms, tools, and all the material paraphernalia of civilization; laws, customs, creeds, and all present forms of social institutions; schools, libraries, laboratories, and all the apparatus of science and letters.

The changes initiated in human brains are on the whole serviceable in satisfying human wants. Those which are outcomes of impartial scientific observation and inference discovering nature's ways, have been specially successful in satisfying human wants. They operate by changing his own behavior into forms more suitable to obtain satisfaction from the rest of nature, and by changing the rest of nature into forms that suit man's needs better. They work within nature, as regularly as any of its habits. Man is creative, not because he is in part supernatural or extra-natural and imposes a super- or extra-natural will on nature, but precisely because he is, in part or altogether, a natural object, linked in the chain of natural causation, and playing a role in nature's long drama. The fundamental basis of that drama may be very simple, nothing but moving electrons and protons which perhaps have always been and always will be the same, but its actual course is anything but the same from moment to moment. It constantly creates new forms for itself, and parts of it known as men share in that creation.

One need not be in despair because science teaches that the world is a great self-contained machine whose operation no god or devil can alter. If so, it is a peculiar sort of machine which alters itself and has produced the Divine Comedy, Paradise Lost, Beethoven's symphonies, and all the truth, goodness and beauty that man knows. If so, man is a part of it and is constantly altering it. His duty and his pleasure in respect of it will be much the same whether deities outside it are or are not active to help or hinder him.

No one should feel that nay zest will be lost from life if science proves all of nature to operate according to regular customs so that an omniscient historian at the end of the world could honestly say that never had the same set of conditions failed to produce the same result. The zest of life does not consist in fortuity and ignorance of what will happen. It would not be increased, for example, if days and nights come by chance like the red and black of a roulette series. It is increased rather than lessened by the possibility of predicting what will happen in new situations from knowledge of the regular behavior of their components, provided there is enough novelty and surprise. There will be enough, surely, for the next thousand years, and probably forever. The discovery of nature's uniformities by science leads to creative action that increases the amount and proportion of novelty, surprise, and new discovery.

The threat of a universe without hope because the forces in it must inevitably determine every item of its future and produce results which an omniscient observer a billion years ago could have foretold is an idle threat. In the nature of the case there could not have been any such observer then or now. But if there could have been, and if he had left a record of what could happen until A.D. 10000, and if his record had been found in A.D. 1935 and verified as correct by the occurrences say to A.D. 1975, it would include the fact that science profited by it from 1935 to 1975 to increase man's control over the rest of nature and inaugurated the era about 1940 since known as the "Era of Hope" when man could foretell the future and control his fate as never before. The best hopes we have are those got by the predictive power of science. Every advance in prediction means a gain in valid hope and a loss for disappointments.

No one need fear that science will diminish human freedom. On the contrary it greatly increases the only freedom that any reasonable being can desire. The freedom of the will has meant and still means different things, some of which are of no consequence whatever to human welfare, and some of which are highly undesirable. It sometimes means simply that there is a small margin of sheer chance or fortuity in the universe. For example, electrons might vary slightly one from another in unknown and unpredictable ways, but the total or average behavior of any atom composed of them might be perfectly regular and dependable. All our chemistry and physiology would remain true in spite of such uncertainty about the behavior of single electrons (or indeed of single atoms). A margin of fortuity in the behavior of electrons would be of no consequence in relation to the question of whether persons have a freedom of will lacked by dogs and cats (or to any question about persons, dogs, or cats).

Another meaning locates this undetermined margin in the higher animals, especially man, asserting that human choices are occasionally or in part unpredictable, unaccountable. If this be so, it is regrettable, since it would be a cause of confusion and error. Occasionally the best of men might choose the worst of courses, or the worst of men upset reasonable expectations. Freedom is a bad name for it, for it would really be bondage to chance.

The doctrines of theology and of intelligent people in general are wisely not concerned with margins of fortuity or unpredictability, but with the freedom of a person from domination by circumstances, or with the freedom of some core or kernel of a person from domination by circumstances or by some more superficial and temporary features of him. There are many possible variations on this general theme. Thus some would say that men are not the creatures of temporary circumstances, but bear, each within his own nature, tendencies to favor and cherish certain courses of thought and action and to reject or discard others. By birth and training, a man acquires a core of personality or should which can dominate circumstances and change their consequences. Nothing in science denies this. It might deny that nay extra-natural force implanted these souls in babies, crediting rather the genes in their chromosomes. Others would mean by the freedom of the will the power of a man's deeper self to direct his life with or against the pull of external influences, or superficial motives, or casual enticements. "I am the captain of my fate, I am the master of my soul." Nothing in science denies this. On the contrary, the more fully man knows the ways of nature, including human nature, the better able will his deeper self be to rule the external, casual, transient, and superficial.

Everywhere it is the same. Science transforms a world of fairies, demons, magic, charms, and luck into the dependable world of "natural law." Every addition it makes to its catalog of nature's changeless habits helps man to change nature, including himself. The uniformity of nature does not take power away from man, but from fortuity or chance and from alleged forces which operate partly or wholly by chance.

misc musings

I think this is so funny

2006-06-15T16:12:00.000-04:00

This was the subject on an email that went into my junk mail. I just think it's too funny.

delusion kwashiorkor spleenwort bluet greenwich posterior hiram henequen adrian
...

I've already trashed the email, but I wonder if the message was as "creative" *grin*

Did I miss something?

2006-06-14T20:41:00.000-04:00

From Yahoo News - Panel recommends firing Colo. professor

The fifth paragraph finally gets past the bs and tells the why of the recommended firing - "The school's investigation focused on allegations that Churchill committed research misconduct and plagiarism."

Now it's the last paragraph that confuses me. "Churchill's case has been cited by conservatives as an example of how universities have overstocked their faculties with leftists. Others raised concerns about academic freedom."

What does research misconduct and plagarism have to do with his political views (they are pretty obnoxious) or academic freedom?

The next Honors Research post

2006-06-14T19:14:00.000-04:00

I've posted part I of a two part post - this one is the mathematical description of sets here.

Math, MathCog

I need some math

2006-06-13T18:14:00.000-04:00

I'm really feeling math deprived, like no one even wants to hear the word. So help me out here. Is there something in math that sounds interesting (or weird) to you that I could blog about. Otherwise you might get something like odd and unusual facts about Reimann's Zeta Function. *grin*

Math

I think I need to toss school and move...

2006-06-13T11:04:00.000-04:00

someplace with more people and hopefully more jobs.

Stupid census facts. The population of the town I live in was 1,832 in the 2000 Census. The 2005 estimate for the county is 77,287.

Life whine

This just pisses me off

2006-06-11T11:20:00.000-04:00

Earth as the center of the universe? Only if you use bad math from Good Math, Bad Math.

If you want to believe that the universe and the earth were created by some supernatural being some time in the (relatively) recent past, that's your choice. If you refuse to understand the scientific process and that evolution is a fact, that's your choice. But please don't try to use mathematics to prove it! Math and mathematicians get a bad enough rap as it is.

Math, bad Science

Another post on my honors research project

2006-06-09T22:00:00.000-04:00

Post is here. Have fun.

I just made a correction to the post so that the three hypothesis showed up properly. I have continuing problems with less than (<) and greater than (>) signs.

Friday miscellany

2006-06-09T17:34:00.000-04:00

I really need a job or something that reasonably approximates a regular income! I'm close to the panic stage where I just grab the first thing that comes up even when I know it's a mistake. But for tonight, I'm ignoring that and hoping that all the resumes that went out this week will get me something other than silence or a "thanks, but no thanks" letter.

Just to add to the noise in my house, the erstwhile housemate got some chicks. Here are the babies right after they went into their "growing up" pen. When they get big enough, they'll go outside with the other chickens. Baby chicks are noisy and make a mess. It's only been 24 hours, but I can't wait. Sort of like the kid in the car asking every 5 minutes, "are we there yet?"

And here are all the ducklings after a week. They're growing like weeds. LOL I like the ducklings better than the chicks - they're cleaner and they actually shut up once in the while.

I have to change a couple of links on the blog since two of my favorites (Mixing Memory and Science & Politics) have moved over to the SEED ScienceBlogs. Science & Politics is now A Blog Around The Clock. I'm adding ScienceBlogs to my links as well. Lots of very good science blogs now residing there. I have a habit of landing there for ridiculously long periods of time. Really, go check them out.

Misc

Just in case you're interested

2006-06-05T21:26:00.000-04:00

I've done my first post on my honor's research project. It's just an introduction/explanation of where the project came from. The post is here.

Math and God

2006-06-05T20:30:00.000-04:00

Who was it who said "God created the natural numbers. All else is the work of man."??? There is no connection at all from that to the two radically different things I read today. Or maybe there is. You all will have to decide.

First was the math courtesy of Teresa - an entry on Slashdot, Chinese Mathematicians Prove Poincare Conjecture. The last I'd read was that the Russian mathematician, Perelman, had a proof that was being verified. It seems that I'm not the only one on that track judging by the question on Ars Mathematica.

Second were several blog entries at ScienceBlogs referring to this story from Reuters - Lioness in zoo kills man who invoked God

Mon Jun 5, 2006 9:37 AM ET
KIEV (Reuters) - A man shouting that God would keep him safe was mauled to death by a lioness in Kiev zoo after he crept into the animal's enclosure, a zoo official said on Monday.
"The man shouted 'God will save me, if he exists', lowered himself by a rope into the enclosure, took his shoes off and went up to the lions," the official said.

I have way too much time on my hands with no job.

Math and Misc

Here come the ducks!

2006-06-03T17:06:00.000-04:00

UPDATE: It's been raining for a couple of days and the temperature has really dropped. It's friggin' cold! So the erstwhile housemate moved the Muscovy babies inside with the baby Runners. You should have seen those little guys dive into the food. LOL.

Here are the four Indian Runner babies. When these guys grow up they are the silliest looking things - almost like cartoon ducks. The white ones look the most like cartoons. I found a site once where Indian Runners were described as "bowling pins on legs." The white ones really look like that. *grin* These runners will probably be a little less upright.

Here are the Muscovies. Well eight of the babies came out in the rain with momma. A ninth was in the nice dry house.

ducklings

More ducklings and dreams of duck a l'orange

2006-06-03T10:09:00.000-04:00

What a great way to start a rainy Saturday. We woke up this morning to more ducklings. Woohoo! One of the muscovies hatched the clutch she'd been sitting. There are either 7 or 8 fluffy yellow babies. Getting close to the little peepers is dangerous right now. The erstwhile housemate faced down a hissing, pecking momma when he put food and water by by her.

We also have two geese sitting on eggs and another duck that wants to but she's trying to sit on chicken eggs. LOL

life

Friday miscellany

2006-06-02T18:41:00.000-04:00

The erstwhile housemate brought home four new black Indian Runner ducklings today. They're itty bitty ducklings. Somehow I forget every year how much noise baby birds make. Ducklings, goslings, chicks - they all peep continuously. But they're soooooo cute. *grin*

Even though it looks like I'll have to take the NH state motto rather too seriously, I've got a few links for your weekend edification.

Since the subject of channeling our inner beach bunnies has arisen in the great email sister conversation today, your first link is from Yahoo - Top Ten Beaches. Pick your favorite and get ready to rock and roll with your inner beach bunny or inner surfer dude.

I just love it when people have fun with math. Now if you combine statistics (the brunt of many math jokes) with the environment and feminism, you get Feminism: Destroying the Planet. Thanks to Science and Politics for highlighting this. (BTW, S & P is about to go big time over at the SEED ScienceBlogs. If you're into science, check out the site. It's very cool.)

This article was on Yahoo News yesterday. I'm fascinated whenever scientist discover new species, or extinct species that are living, or anything to do with evolution. If I ever get bored with the math and psychology stuff, I'll just have to go after another degree in whatever is required to do this kind of research.

Scientists discover 8 new species AP - Thu Jun 1, 4:34 PM ET
JERUSALEM - Israeli scientists have discovered an ancient ecosystem containing eight previously unknown species in a lake inside a cave, where they were completely sheltered from the outside world for millions of years.

Finally we have this, also from Yahoo - Mona Lisa's voice finally heard. This may be even too weird for me.

So that's it for tonight. Enjoy your weekend. (Billy Holiday is playing on my mp3 right now. What a way to start the weekend. *grin*)

Misc

The new kitty

2006-06-01T20:16:00.000-04:00

This kitty has a story of sorts. He moved in under my front porch the end of last summer. Cats and kittens get dumped here all the time. There's a dairy farm down the road and we have chickens, ducks, and geese so I guess people think that it's an appropriate place to toss out their unwanted kitties. I usually bribe the kitties with food to get them on the porch and then call the local humane society. But this guy was like a ghost. No way was he showing his face. We put water and food out every day, but the minute anyone even looked out the door he ran away. This went on until late fall when we had a really bad cold snap - below zero weather at night. The first cold night, he still wouldn't come on the porch. The second cold night he slept inside the little shelter we put on the porch. The next morning he let us pick him up and take him to the vet. This was the first time I got a good look at the boy. Skinny, but very pretty. The vet checked for a microchip (none) and gave him all his shots and a worming. I called the humane society to see if someone was looking for the boy - no one was. So, we kept him. Well actually one of my housemates did. (Poor boy got neutered shortly thereafter.)

After old kitty died, this guy started spending a lot of time with me and sleeping in my bed. And here I thought that I'd finally get to have the larger part of the bed to myself. LOL Last week my housemate told him that I was his mother, so I guess I now have a kitty. A blue-eyed kitty. A not overly bright kitty. But he sleeps in my bed and tries to bite my toes! It could be worse.

life stuff

How stupid is this?

2006-05-31T11:01:00.000-04:00

There's a job opening. The only way to apply is online. The site bombs halfway through the process. There is no contact info for HR. After trying multiple times over a 24 hour period, do I really want to apply for the position?

Memorial Day 3

2006-05-29T11:28:00.000-04:00

As the weekend ends and you get ready to return to work, spend a few minutes to remember the families that the soldiers left behind.

Memorial Day

Memorial Day 2

2006-05-28T08:16:00.000-04:00

Instead of another beer, here is some more reading for your weekend. Go over to HeoCwaeth, read this, and remember the vets who are as much a casualty of war as those who died.

Memorial Day

Memorial Day

2006-05-27T12:21:00.000-04:00

Something, other than hamburgers and hotdogs on the barbeque, for your Memorial Day weekend - WWII hero Donald Rudolph Sr. dies at 85.

Memorial Day

Friday miscellany

2006-05-26T20:08:00.000-04:00

I almost forgot that it was Friday. Not working and not having classes has me all mixed up. I'm trying to change the "not working" part, but I just have to wait until the end of August for the "not having classes" part to be fixed.

The job market around here is the pits unless I want to do what is euphemistically referred to as "light assembly." I have nothing against doing this, but my royally screwed up back does. I don't think that getting a job that would leave me pretty much disabled within 6 months is a good career choice. And I passed on a part-time job through the temp agency. It seemed wiser not to lock myself into something with no defined end date, but to wait for something better. I think I started second-guessing and regretting that as soon as I got off the phone. I did manage to get my resume in on a couple of jobs, but I'm not holding my breath. (Well, I am holding my breath. Just not in expectation of getting an interview for either job.)

I have been reading a lot this week. And I've set-up a separate blog for my honor's research stuff - not that there's anything to see there yet. Zephyr came over with The Other Sister Person yesterday. TOSP brought lunch. Zephyr cut my hair.

No links this week since the time I've spent on-line has been mostly job searches and psychology stuff.

That's all, folks.

Putting my fields in order

2006-05-23T17:08:00.000-04:00

I'm back to reading Analysis With an Introduction to Proof, 4th Ed. by Steven R. Lay. This is the book with the proof of the proof by the method of induction that I mentioned the other day. So I've made it through chapter 3, section 11: Ordered Fields relatively quickly largely because this is pretty much all review.

The interesting thing about ordered fields is that all of you are familiar from high school algebra with the things that determine whether something is a field and whether the field is ordered. It's just that nobody bothered to tell you this. An oversight I'm about to correct.

"What," you ask, "are these ordinary things that define fields?" Axioms. The very same axioms you learned in high school. And, yes, I'm going to tell you what they are, but first you need to learn a couple of mathy symbols. ℝ - The set of real numbers, and -the symbol meaning "is a member of" so x ℝ reads "x is a member of the set of real numbers. That's all you need to know.

On to the axioms.

There are 5 axioms for addition.

A1: For all x, y ℝ, x + y ℝ andif x = w and y = z, then x + y = w + z

A2: For all x, y ℝ, x + y = y + x

A3: For all x, y, z ℝ, x + (y + z) = (x + y) + z

A4: There is a unique real number 0 such that x + 0 = x for all x ℝ

A5: For each x ℝ there is a unique real number -x such that x + (-x) = 0.

There are also five axioms for multiplication that will look pretty much like the addition axioms.

M1: For all x, y ℝ, x ^. y ℝ andif x = w and y = z, then x ^. y = w ^. z

M2: For all x, y ℝ, x ^. y = y ^. x.

M3: For all x, y, z ℝ, x ^. (y ^. z) = (x ^. y) ^. z

M4: There is a unique real number 1 such that 1 ≠ 0 and x ^. 1 = x for all x ℝ.

M5: For each x ℝ with x ≠ 0, there is a unique real number 1/x such that x ^. 1/x = 1. You can write 1/x as x^-1.

Now for the last 5 axioms. You should recognize the first of these since it is the distributive law. This is pretty cool because it shows how addition and multiplication are related to each other.

D1: For all x, y, z ℝ, x ^. (y + z) = x ^. y + x ^. z

Then you have the 4 axioms that define order.

O1: For all x, y ℝ, exactly one of the relations x = y, x > y, or x < y holds (trichotomy law)

O2: For all x, y, z ℝ, if x < y and y < z, then x < z

O3: For all x, y, z ℝ, if x < y, then x + z < y + z

O4: For all x, y, z ℝ, if x < y and z > 0, then x . z < y . z

Actually, any set of numbers or mathematical system where the first 11 axioms are true is a field. If all 15 axioms are true, you have an ordered field. The set of rational numbers makes up an ordered field, but the set of integers does not (do you see why?).

Reference: Lay, S.R. (2005). Analysis With an Introduction to Proof, 4th Ed. Pearson-Prentice Hall: Upper Saddle River, NJ. pp 108 - 112.

Math

Just a test of sorts

2006-05-20T13:59:00.000-04:00

I've been thinking that I'd like to have an editor where I could create and edit entries off-line (because I have dial-up) and then publish later. But I want to see what they'll look like for real. It's a pain to copy, past, and correct a Word doc. So this is a test of one editor. I'll take suggestions on any others out there that you all know about, but I have to tell you that until I'm working again I can only do free.

Technorati Tags : blogging stuff

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Friday miscellany

2006-05-19T18:50:00.000-04:00

Today was my last day at the company I've temped at for a year. I made some new friends working there - I'll miss seeing them every day. The temp agency said that they would be in touch the beginning of next week about a new job, but I'm thinking I should hit the streets on Monday and spread my resume around. I really have to get myself revved up for that one.

I like to check stat counter to see where people have come from on their way to my blog. When I did that tonight, I found my way to an interesting blog - A Sweet, Familiar Dissonance. And I got as close to a rave review as I'm ever going to get. *grin*

Two links for tonight.

The first is about the "discovery" of a possibly habitable planetary system at MSNBC. It's really cool how planets are found - lots of math.

The second (which is really three) is at Science and Politics - Teaching the bare bones of Biology and Teaching Update. I wish I'd had this guy for a biology teacher. He also has a really interesting post about Lyme Disease here.

If any of you think that I've run out of things to say about order and mathematics, think again. There will be more order coming to you. *hehehe*

Misc

Nothing special

2006-05-17T21:04:00.000-04:00

Two more days and the job from hell is finished. Unless something pops, I'll be unemployed. So what did I do about this today? I read a proof of the method of proof by induction. Do you think that mathematicians may be a tad anal if they feel the need to prove that a method of proof is valid?

Misc

What do you really think of NUMB3RS?

2006-05-16T21:35:00.000-04:00

Or more to the point, what do mathematicians think of NUMB3RS? For a partial answer, see the discussion on Ars Mathematica.

sorta Math

Rain and more rain and more...

2006-05-14T19:32:00.000-04:00

It's raining.

Blog mom talks about the rain by her here and Yahoo has the AP story here. We're lucky this time around with only a flood watch, but no warning for the county I live in. The New Hampshire TV station spent an hour tonight on flood news. It was nice to hear towns with evacuations telling residents to bring their pets because arrangements had been made for them. Frustrating to hear that people were out "sight seeing" when the they're being told to stay home because of the danger with roads washed out.

I know it's selfish, but I'm glad that the probability of repeating last fall's washout is relatively slim.

Friday miscellany

2006-05-12T19:37:00.000-04:00

Last week I got shifted from the temp job I've had since May '05 to a different temp job at the same company. I HATE it! I'm spending 6 - 8 hours a day on the telephone. This is hell for me - after all, I'm the person who when she needed to cut expenses got rid of her phone for over a year and DID NOT miss it. If it wasn't for the fact that I have to support myself.... *sigh*

That said, some linky stuff to annoy, amuse, or inform you.

From Mixing Memory: an interesting post on a study of about how Craving a Cigarette Warps Your Sense of Time. Having sat through all the speeches at a college graduation (which by themselves warp time), I can confidently say that craving a cigarette when you have to pee and can't do either really warps time. I swear it took at least 5 or 10 minutes for the speaker to utter a one syllable word. You can imagine how long the bigger words took. *grin*

From Science and Politics: a link to a letter to the editor about faith vs. ethics. Love this part of the letter - "The irrational mind knows no boundaries and has no tolerance for self-restraint. It is the rational mind that can set boundaries and control impulses."

And a new blog to check out - Heo Cwaeth. You'll have to read it to find out what the blog is all about. I found it via Mixing Memory.

I could rant for months on this story on Yahoo - No States Meet Teacher Quality Goal.

And check out blog daughter Zephyr's post about being a student at a beauty academy.

Misc and life woes

More order

2006-05-11T18:47:00.000-04:00

Since math and order have arisen here and here, it's time that I introduced you to the Well-Ordering Property. This is one of those incredibly simple statements, but its important particularly when you are talking about sets.

The Well-Ordering Property: Every non-empty set of positive integers has a least element.

That's it. Notice that it says nothing about the numbers being in order (ie., 1, 2, 3, 4). Only that a set with at least one element (non-empty) will have a least or smallest element.

Before you ask, this property addresses only positive integers because the set of negative integers has no least element. Rememeber that the negative integers go -1, -2, -3, and that -1 is greater than -2 which is greater than -3 and so forth. So while the set of positive integers is well-ordered, the set of negative integers is not.

Math

I am so good (LOL)

2006-05-09T21:48:00.000-04:00

Grades were posted today.
Psych of Learning - A
History & Systems - A
Honors Research - pass (pass/fail only)
Honors Research Seminar - pass (pass/fail only)

GPA is now at ~~5.67~~ 3.547.

(I was trying so hard to be "smarter" than I am, but I have no idea where the 5.67 came from. This time I copied/pasted so it's the correct number. *grin*)

I am just so good. ROFLMAO

Odd and even numbers - answers for VW

2006-05-09T20:13:00.000-04:00

VW asked some questions about odd and even numbers in her comment to this post and since I live to torture you all, here are the questions and the answers. *grin*

1. Why does adding two even numbers give an even number?
2. Why does adding two odd numbers give an even number?
3. Why does adding an odd and an even number give an odd number?
4. Why aren’t there more even than odd numbers?

I’ll answer each one for you although the last is going to take the most explaining. *grin* So, here goes.

To start with, the answers to these questions are referring only to integers (…, -3, -2, -1, 0, 1, 2, 3, …).

There are several things to keep in mind.
When you add two integers, the answer is always another integer (this is a property of the set of integers called closure).
The associative property – for any integers m, n, p; m + n + p = (m + n) + p = m + (n + p).
The distributive property – for any integers a, b, c; ab + ac = a(b + c).

Now onto the first three questions.

1. Why does adding two even numbers give an even number?

Let’s start with a definition. We are defining an even number as a number that when divided by 2 has no remainder. We can write any even number as 2k where k is any integer. It doesn’t matter if it’s even or odd since multiplying by 2 immediately makes the result (2k) even.

Now add two even numbers. By the definition above, we can choose any two even numbers. Let’s call them 2k and 2m where k and m are integers.

Do the arithmetic: 2k + 2m = 2(k +m) by the distributive property. (k + m) is an integer because adding two integers always results in another integer. Since 2(k + m) is divisible by 2 with no remainder (see our original definition), adding 2k + 2m results in an even number.

2. Why does adding two odd numbers give an even number?

First we’ll define an odd number as a number that when divided by 2 results in a remainder of 1. We know that for any n = 2k, n is even from above. What we want is an n that is odd. By our definition of an odd number, n = 2k + 1 is odd because when we divide n by 2 we end up with a remainder of 1.

Now add two odd numbers. As above, we can choose any two odd numbers. Let’s choose n = 2k + 1 and m = 2r + 1 where k and r are integers.

Next the arithmetic: n + m = (2k + 1) + (2r + 1) = 2k + 2r + 2 (combining like terms).
2k + 2r + 2 = 2(k + r + 1) by the distributive property. Since k, r, and 1 are integers, (k + r + 1) is also an integer. So we now have an even number by our previous definition of an even number.

3. Why does adding an odd and an even number give an odd number?

Choose any odd number m = 2k + 1 (by our previous definition of an odd number) and any even number n = 2p (by our previous definition of an even number) where m, k, n, and p are integers. Now do the addition.

m + n = (2k + 1) + (2p) = 2k + 2p + 1 = (2k + 2p) + 1 (by the associative property) and
(2k + 2p) + 1 = 2(k + p) + 1 (by the distributive property). Since k and p are integers, k + p is an integer, and so we have by definition an odd number.

Now for the last question – why aren’t there more even than odd numbers?

I need to start by talking about infinite sets and how we tell their “size” or cardinality in math speak. The set of natural numbers (counting numbers – 1, 2, 3, …) is an infinite set. It’s a countably infinite set because (at least in theory) you could count all the members of the set. Of course, since there is no “largest” natural number, you’d never actually count to the end. Georg Cantor, when he described infinite sets, said that the set of natural numbers has a cardinality (size) of aleph-0. All countably infinite sets have this cardinality of aleph-0. So all countably infinite sets are the same size. Got that?

In order to show that a set is countably infinite, I have to find a way to match each member of the set to each member of the set of natural numbers. This is a one-to-one correspondence between the two sets. The good thing is that I can rearrange the numbers in the set I’m trying to put into one-to-one correspondence with the set of natural numbers – order, in the every day sense, doesn’t matter in this case.

Let’s start with the even numbers. The set of even numbers (I’m using integers) is (…, -6, -4, -2, 0, 2, 4, 6, …). This is a problem because the even numbers go on forever in the negative and in the positive direction. But I can reorder the set and end up with (0, -2, 2, -4, 4, -6, 6,...).

With this reordering, I can make the match to the set of natural numbers like this (my one-to-one correspondence) by lining up the natural numbers under the even numbers.

0	-2	2	-4	4	-6	6	and so forth (the even numbers)
1	2	3	4	5	6	7	and so forth (the natural numbers)

Since there is a one-to-one correspondence between the set of even numbers and the set of natural numbers, the set of even numbers is countably infinite and has the same cardinality (size) as the natural numbers – aleph-0.

The odd numbers work the same way.

Reorder the set of odd numbers (…, -5, -3, -1, 0, 1, 3, 5, …) to (0, -1, 1, -3, 3, -5, 5, …).
Now you can make a one-to-one correspondence to the natural numbers in the same way as for the even numbers. With this one-to-one correspondence, the set of odd numbers is countably infinite and so has a cardinality (size) of aleph-0.

Since the set of odd numbers and the set of even numbers both have a cardinality of aleph-0, they are the same size.

Tada!

BTW – the set of rational numbers (your fractions – ½, ¼) is also countably infinite which makes it the same size as the set of integers, the set of even numbers, and the set of odd numbers. The set of real numbers (includes the integers, the rationals, and the irrational numbers) though, is uncountably infinite and has a different cardinality. Proofs are here. I think the proof for the rational numbers is pretty slick.

Math

College graduation

2006-05-07T17:06:00.000-04:00

Today I watched two college friends graduate. I'm feeling a little bit like the mother hen who has just ushered the chicks out of the nest. And I'm so proud of these two young women. Let me tell you a little about them. We'll call them Chick1 and Chick2 (the numbers are the order I met them in).

When I returned to college to complete my math degree, I had tons of math, science, and programming courses, but virtually none of the dreaded general education courses. As a result I took way more gen ed courses than math courses and met a lot of freshmen students who weren't math majors. Most of them were and are totally not memorable, but two became something very like little sisters to me.

My first semester I met Chick1. We were assigned to the same team for a major presentation. Chick1 was terrified of public speaking to the point that she'd pass out. Not good when a large chunk of your grade is dependent on one presentation. So the erstwhile housemate and I practiced with Chick1 until she knew her part of the presentation so well that nothing could shake her. And I kept on giving pep-talks, lots and lots of pep-talks. We aced the presentation and somehow Chick1 became the person I most wanted to see succeed in college. She's funny, smart, energetic, caring, and so much more. She was also having a tough time with her school work. The story of how she dealt with that is hers, but by the end of her second year she was on the dean's list every semester and graduated with membership in two honors societies. At today's graduation, Chick1 told me that she'd gotten accepted to grad school for her masters. I am so proud of her.

I met Chick2 my second semester. We might never have gone past the surface conversations between two people who are in the same class except that I needed to interview someone whose work was unusual in some way for a cultural anthropology class. I have to side track a bit here and tell you that I run screaming from anyone who tries to preach to me or shove their religion down my throat. As a result, I tend to avoid people who appear to be openly religious. (And I am NOT discussing this with anyone here.) In one of our earlier conversations, Chick2 had told me that she wanted to be a missionary. There were a few more conversations about this where I learned that she spent her school breaks doing missionary work. Okay, this pretty well covers unusual work in my book. Chick2 was nice enough to agree to be the subject of the paper. That interview lead to a friendship which I value deeply. Chick2 is one of the most giving people I know. She is also one of the few people I know who lives her religion rather than preaches it. The world needs more good people. I think Chick2 is one of these good people (even if she doesn't entirely approve of my often raunchy humor).

So the chicks left the nest today. Next year as I finish up the last couple of classes for my psych degree will feel very strange without these two young women on campus.

student and life woes

Does order matter?

2006-05-06T18:44:00.000-04:00

It’s time to return to those mathy things that I know you all hold your breath in anticipation of. In the comments to this post, Teresa asked if the order mattered since multiplication is commutative. The idea that multiplication is commutative follows fairly naturally when you think of multiplication as a sister to addition. Multiplying 3 by 2 is the same as adding 3 two times - 2 x 3 = 3 + 3 = 6. By the same process, 3 x 2 = 2 + 2 + 2 = 6. So she’s right that in the case of the set of integers (and I've used integers in these examples), multiplication is commutative and order doesn't matter. But multiplication is not always commutative.

A matrix, as opposed to the matrix of movie fame, is an array of numbers. You will often see a matrix referred to as an (m x n) matrix where m and n denote the number of rows and columns, respectively. Matrix multiplication is not commutative.

Here's your math lesson for the day.

In order to multiply 2 matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. If you have an (m x n) matrix multiplying an (r x s) matrix, you must have n = r. The funny thing is that if you switch the order so that you're multiplying the same (r x s) matrix by the same (m x n) matrix, then you need s = m.

Here's an example: if matrix A is a (3 x 3) matrix and matrix B is a (3 x 1) matrix, you can multiply A by B – a (3 x 3) multiplying a (3 x 1), where n and r both equal 3. But you can’t commute the two matrices. Multiplying B by A is undefined since you have a (3 x 1) multiplying a (3 x 3) and n = 1 while r = 3.

But what if you have two matrices with the same number of rows and columns? Shouldn't they be commutative? First, you need to know how matrix multiplication is performed. The simple (text book) definition looks like this:

For a matrix A = (a_ij) and a matrix B = (b_ij), the product AB is defined as

In math speak that makes very little sense. It looks something like this.

Nasty! Let’s try an example with numbers. I’m going to use (2 x 2) matrices A and B where

and

When you multiply AB, you get

And when you multiply BA, you get

So, for this example, you can see that AB is not equal to BA. There are occasional instances where AB will equal BA, but this is not generally true.

Just to briefly return to the Fundamental Theorem of Arithmetic where this started. The theorem orders the prime factors. This is important within the proof - order matters - but I think we’ll get to that tomorrow.

Reference: Johnson, L.W., Riess, R.D. & Arnold, J.T. (2002). Introduction to Linear Algebra (5th ed.). Boston, MA: Addison-Wesley.

Math

The semester is over

2006-05-04T20:02:00.000-04:00

If you watch Iron Chef America, in my mind I'm hearing "the semester is over" in the same voice.

I'll know next week what my grades are. The honors project is pass/fail and that has already been posted - pass. 4 credits. Nothing that counts towards my GPA. What's really sad is that I'll be working on the blasted thing this summer without earning credit, but what the heck I don't have to pay for credits either.

Tomorrow I'll get back to all the fun stuff (like math) that got dropped while in the end of semester crunch. BTW - that fit learning theory into 4 page paper was an A. hehehe.

Revision 6? 7?

2006-05-01T19:18:00.000-04:00

I've lost count. Major revisions get a new number, small changes might get a letter designation. Confused? They're just changes in the file name. I start with paper, go to paper1, paper2, and so forth when the revisions are major. A small change to paper2, but one where I want to keep the original paper becomes paper2a. Got it? I'm on paper6 which was a major revision of paper5a. Swear to god if I ever get this thing finished, I'm posting the whole paper on this blog. You all might want to run away while you still can.

Like the terminator, I will be back. LOL

student woes

I'm exhausted, about to be unemployed, and...

2006-04-27T19:52:00.000-04:00

relatively happy. I had a meeting with my advisor for my honors research project today. He's happy with the paper, but asked if I would add some more stuff. Fortunately, I have most of the "more stuff" in another paper and, yes, I can take that stuff and reuse it. *stuff, stuff, stuff, la dee da dee da, stuff, stuff stuff*

My favorite comment from Gary - "maybe go the ontogeny/phylogeny route --> become rich, famous!" (yeah, right)

Now I have to put together all of the various and sundry things needed for submission to the IRB (Institutional Review Board - the people who tell me whether or not I can actually run the study). And add the *stuff* and review for finals next week and find another job.

Well, sh*t.

student woes and life woes

What are they looking for?

2006-04-25T20:40:00.000-04:00

Recent searches that landed here.

sister incest
dog die graph pie
biased math bar graph

Some people have too much time on their hands.

Sunday Science

2006-04-23T12:55:00.000-04:00

I'm finishing up a paper for the History & Systems class - compare and contrast the learning theories of Thorndike, Kohler, and Tolman in 4 pages. It's the 4 page limit that causes the problems. So I needed a break and found this on Yahoo News.

Scientists find brain cells linked to choice

Interesting enough to warrant a trip to the library to read the paper.

Misc, Choices and brain

The other twin has arrived!

2006-04-22T19:22:00.000-04:00

My gorgeous, charming, funny niece who is now my other blog daughter has arrived. Check out her description of herself - this is so the niece. You can find her at Zephyr's Place.

And remember all you dirty old men out there that I may be gun deficient, but I'm handy with a knife. *hehehe*

Friday Miscellany

2006-04-21T18:16:00.000-04:00

Yesterday when I went outside on a break some of the guys were tossing around a softball. In the random way that thoughts go, this reminded me of playing baseball with the neighborhood kids. I'm a total loss at sports, but that didn't matter. Usually the two oldest boys made up one team and all the rest of us were the other team. When it was my turn at bat the oldest boy in the neighborhood (he was 4 or 5 years older than me) would stand behind me and help me hold the bat and swing. Okay he swung and I just followed along for the ride. I was about 10 and had such a crush on this boy.

The random thoughts rambled on. We played outside a lot. This was in the days before computers and video games and a gazillion TV channels. Every Sunday we watched The Wonderful World of Disney (or whatever it was called then). Which leads to my first TV character/actor crush. In 1964 Disney ran a show that was 3 episodes (I know cause I looked it up) called The Scarecrow of Romney Marsh. I was soooooo in love with the Scarecrow and with Patrick McGoohan who it turns out was born in Astoria, Long Island, New York 16 years after my father was born there. Go figure.

Because it's been on my mind this week, a little bit of history from 1971. This was the year I turned 18 and registered to vote. My mother took me down to the town hall to register. Now, this was a Republican town and my parents were registered Republicans. I wanted to register Independent, but the town clerk got all fussy about primaries and stuff. So, in an act of rebellion, I said that I'd register Democratic. The town clerk actually asked my mother if that was all right with her.

26th. Amendment to the U.S. Constitution

Section 1. The right of citizens of the United States, who are eighteen years of age or older, to vote shall not be denied or abridged by the United States or by any State on account of age.

Section 2. Congress shall have power to enforce this article by appropriate legislation.

Proposal and Ratification

This amendment was proposed by the Ninety-second Congress by Senate Joint Resolution No. 7, which was approved by the Senate on Mar. 10, 1971, and by the House of Representatives on Mar. 23, 1971. It was declared by the Administrator of General Services on July 5, 1971, to have been ratified by the legislatures of 39 of the 50 States.

This amendment was ratified by the following States: Connecticut, March 23, 1971; Delaware, March 23, 1971; Minnesota, March 23, 1971; Tennessee, March 23, 1971; Washington, March 23, 1971; Hawaii, March 24, 1971; Massachusetts, March 24, 1971; Montana, March 29, 1971; Arkansas, March 30, 1971; Idaho, March 30, 1971; Iowa, March 30, 1971; Nebraska, April 2, 1971; New Jersey, April 3, 1971; Kansas, April 7, 1971; Michigan, April 7, 1971; Alaska, April 8, 1971; Maryland, April 8, 1971; Indiana, April 8, 1971; Maine, April 9, 1971; Vermont, April 16, 1971; Louisiana, April 17, 1971; California, April 19, 1971; Colorado, April 27, 1971; Pennsylvania, April 27, 1971; Texas, April 27, 1971; South Carolina, April 28, 1971; West Virginia, April 28, 1971; New Hampshire, May 13, 1971; Arizona, May 14, 1971; Rhode Island, May 27, 1971; New York, June 2, 1971; Oregon, June 4, 1971; Missouri, June 14, 1971; Wisconsin, June 22, 1971; Illinois, June 29, 1971; Alabama, June 30, 1971; Ohio, June 30, 1971; North Carolina, July 1, 1971; Oklahoma, July 1, 1971.

Ratification was completed on July 1, 1971.

The amendment was subsequently ratified by Virginia, July 8, 1971; Wyoming, July 8, 1971; Georgia, October 4, 1971.

Certification of Validity Publication of the certifying statement of the Administrator of General Services that the amendment had become valid was made on July 7, 1971, F.R. Doc. 71 099691, 36 F.R. 12725.

Created by Martin Luther King, Jr., National Historic Site Interpretive Staff

Last week's poem generated some comments not at all related to the poem (or anything else for that matter). So this week I'm going to try some song lyrics that ought to really get out the crazy comments. This song is actually what got me to go and look for the dates of ratification on the 26th Amendment.

Eve of Destruction
by P.F. Sloan
Recorded by Barry McGuire (1965)

The eastern world, it is explodin’.
Violence flarin’, bullets loadin’
You’re old enough to kill, but not for votin’
You don’t believe in war, but what’s that gun you’re totin’
And even the Jordan River has bodies floatin’

But you tell me
Over and over and over again, my friend
Ah, you don’t believe
We’re on the eve
of destruction.

Don’t you understand what I’m tryin’ to say
Can’t you feel the fears I’m feelin’ today?
If the button is pushed, there’s no runnin’ away
There’ll be no one to save, with the world in a grave
[Take a look around ya boy, it's bound to scare ya boy]

And you tell me
Over and over and over again, my friend
Ah, you don’t believe
We’re on the eve
of destruction.

Yeah, my blood’s so mad feels like coagulatin’
I’m sitting here just contemplatin’
I can’t twist the truth, it knows no regulation.
Handful of senators don’t pass legislation
And marches alone can’t bring integration
When human respect is disintegratin’
This whole crazy world is just too frustratin’

And you tell me
Over and over and over again, my friend
Ah, you don’t believe
We’re on the eve
of destruction.

Think of all the hate there is in Red China
Then take a look around to Selma, Alabama
You may leave here for 4 days in space
But when you return, it’s the same old place
The poundin’ of the drums, the pride and disgrace
You can bury your dead, but don’t leave a trace
Hate your next-door neighbor, but don’t forget to say grace
And… tell me over and over and over and over again, my friend
You don’t believe
We’re on the eve
Of destruction
Mm, no no, you don’t believe
We’re on the eve
of destruction.

Misc

One out, another on the way

2006-04-20T20:13:00.000-04:00

One down (or out as the case may be) and one to go. The first of my twin blog daughters is MY SISTER! (More bloggy incest) After months of sending her links to interesting blog stuff and having her send me the comments, Easter Sunday I got her to register on the blogspot place. Then....well you can go here and check it out. Our little test posts are still there - an extra virtual chocolate cigar to anyone who gets them. *grin*

I could tell you lots about the other sister person, but I'll be good. I'm hoping that she'll post pictures of some of her needlework. I just saw her newest piece - an original design for one of those pretty purses brides carry (a friend's daughter is getting married). What you won't know from any pictures she might post is that the reverse side of her needlework is just about as perfect as the front. She also quilts - one year she was one of the Hoffman Challenge winners. She sings. She cooks (one of us has too). She loves colors like orange. The other stuff you'll have to learn from her.

So with no further ado, my first baby girl - The Other Sister Person

Spring has sprung

2006-04-16T16:24:00.000-04:00

The grass has rizz
I wonder where the birdies is.

And in good spring fashion I am pleased to announce that I'm pregnant with not one but two blog children. The births should occur later this week at which time formal announcements and chocolate cigars will appear. *grin*

(And you thought all I did was math. hehehe)