Friday, March 31, 2006

Friday Miscellany

It's been a weird week - very busy at work, a meeting with my honors' advisor which actually went very well, and a mini-spending spree. I took out the plastic and went on Amazon. Today my purchases arrived - more music. I now have Belafonte at Carnegie Hall (1959) which has what I think is the best ever recording of Danny Boy. And just to further confirm that I'm an aging hippie, the rest of the music purchase was the 4 CD set of the Woodstock 25th anniversary collection. (Peace and love, baby)

I was going to tell you all a little about the fundamental theorem of arithmetic, but I've decided to save it for later this weekend when the psychology stuff begins to drive me around the bend. Instead I have for you more of my favorite poetry.

In my junior and senior years of high school, I had an English teacher who (probably inadvertently) taught me to learn about the things I love and do it with passion. He loved poetry. He'd act out a poem as he recited and get incredibly excited. One day he got a little carried away. He had one of those old wooden office chairs that twirled around and was on wheels. In a fit of excitement, he threw himself into the chair, pushed off from the desk, and flew across the room, through the open door, and slammed across the hall almost taking out the principal. In the spring, he read e.e. cummings' poem "in Just-" and jumped in imaginary mud puddles.

So, to celebrate the arrival of spring (finally), here is the poem I most associate with spring.

in Just-

in Just-spring
when the world is mud-
luscious the
little lame baloonman

whistles far and wee

eddyandbill come
running from marbles and
piracies and it's

when the world is puddle-wonderful

the queer
baloonman whistles
far and wee
and bettyandisbel come dancing

from hop-scotch and jump-rope and


baloonMan whistles

e.e. cummings

taggy taggy: ,

Saturday, March 25, 2006

Friday Miscellany on Saturday

Because I was tired last night and really couldn't think of anything to say. And Carmen tagged me, but I'll get to that in the next day or two.

Lately I've been thinking about number theory, Hilbert's program, and arithmetic. And I've been wondering if the axioms of arithmetic constitute a mathematical description of the cognitive processes underlying arithmetic. Hilbert's program was simply (although it wasn't simple) an effort to formalize mathematics in axiomatic form and to show the consistency of the system. Godel threw a bomb into the effort with his Incompleteness theorem.

A more thorough and better description of Hilbert's program is available at The Stanford Encyclopedia of Philosophy - Hilbert's Program.

Today's tags: ,

Saturday, March 18, 2006

It's real (sort of)

I filed my intent to graduate last week. In an amazingly fast turn around, the college has already completed the academic audit and sent it to me. No surprise in the audit. I have one more course to take (the honors research is a separate entity). The down side? The last course - Sensation and Perception - isn't available until the Spring 2007 semester. *sobbing*

taggy taggy:

Friday, March 17, 2006

Friday Miscellany

This week's miscellany ... hmm ... a little bit of science and a little bit of poetry.

First the science (see I don't always torture my gentle readers with math).

Take a look at this explanation of why we have so much trouble with the concept of evolution as presented at Mixing Memory: Thinking About Evolution: Cognitive Factors That Get in the Way. I'd call this a definite "must read."

Then there is poetry. I grew up in the Northeast at the end of the 60s. It seemed that we were all either writing poetry, writing songs, or writing both. When the theme wasn't the evils of war, the poetry was pretty self-consciously arty. You can, however, breath a sigh of relief. The poetry is not mine, but William Blake's. This is just one of my favorite poems and has been rattling around in my head all week.

The Tyger
William Blake

Tyger Tyger. burning bright,
In the forests of the night;
What immortal hand or eye.
Could frame thy fearful symmetry?

In what distant deeps or skies.
Burnt the fire of thine eyes?
On what wings dare he aspire?
What the hand, dare seize the fire?

And what shoulder, & what art,
Could twist the sinews of thy heart?
And when thy heart began to beat.
What dread hand? & what dread feet?

What the hammer? what the chain,
In what furnace was thy brain?
What the anvil? what dread grasp.
Dare its deadly terrors clasp?

When the stars threw down their spears
And watered heaven with their tears:
Did he smile His work to see?
Did he who made the lamb make thee?

Tyger Tyger burning bright,
In the forests of the night:
What immortal hand or eye,
Dare frame thy fearful symmetry?

On that note, Happy St. Patty's Day and enjoy your weekend.

Monday, March 13, 2006

dislike math majors

My first time on google. hehehe

Pass the cheese please

I woke up this morning feeling too old and too stupid to ever get into a graduate program and learn and do the things I want to do.

So pass the cheese, please. I'd prefer either Liederkranz or Stilton if you don't mind.

Sunday, March 12, 2006

What is closure?

People talk about getting closure all the time. I have some issues with this concept. For starters, why do you only need closure for a “bad” thing? If the idea is to find closure for an event that makes a major impact on a person, shouldn’t a major “good” event also need closure? But more importantly, what do we mean by closure? Is it looking at the event, determining what we’ve learned from it, applying those lessons, and then getting on with our lives? You read or hear people saying that catching and convicting the person responsible for a crime will provide the victim with closure. Will it really? Personally, I’d rather take the responsible person into a back alley and do onto as had been done unto me.

But I’ve digressed.

In mathematics, there is a concept for closure that is common across most (possibly all) branches of mathematics. As near as I can tell from Katz’s A History of Mathematics, closure appears in the mathematical literature early in the twentieth century.

Outside of the psycho-babble closure, this is the first place where I learned about closure. The idea is similar across all maths, but the definition with which I am most familiar is from algebra. It’s a pretty simple to state – a set is closed under an operation if applying the operation to two members of the set results in another member of the set. (Huh?)

Example – if you take the set of natural numbers (your counting numbers), the set is closed under addition and multiplication, but not subtraction or division. All that means is that if I add two natural numbers, I get another natural number - 5 + 11 = 16 (all natural numbers). The same happens if I multiply two natural numbers (2 x 3 = 6). But if I subtract or divide two natural numbers, I can get a negative number (in the case of subtraction) or a fraction (in the case of division). Negative numbers and fractions do not belong to the set of natural numbers.

For a number of examples across mathematics, check out the Wikipedia entry I’ve quoted below.

Now it’s time to get to closure in psychology because that’s where (believe it or not) this ramble started from. In the history & systems class, we just finished the chapter on Gestalt psychology. Not the Gestalt therapy that you might have heard of, but a psychological theory that attempts to explain how we perceive the world.

The theory developed in Germany at the beginning of the twentieth century and traveled to the US in the 1930s. You all know that quote – “the whole is greater than the sum of its parts.” That’s Gestalt in 10 words.

In explaining perception, Gestalt includes a number of principles one of which is closure. This closure is nothing more than our tendency to complete (at least internally) an incomplete picture. We organized pieces into a whole in order to understand our physical perceptions. This works really well for artists – a few lines and we recognize a famous face.

At the start of the twentieth century mathematicians and psychologists were studying closure. I wonder if they talked to each other.

If you type “closure” into the search box at Wikipedia, you will get links to:

· closure (computer science), an abstraction binding a function to its scope
closure (mathematics), the smallest object that both includes the object as a subset and possesses some given property
closure (philosophy), a philosophical description of the world put forward by Hilary Lawson
closure (psychology), the state of experiencing an emotional conclusion to a difficult life event
Closure (Nine Inch Nails VHS), a Nine Inch Nails video set
Closure (band), a Canadian rock band
cloture, a motion in parliamentary procedure to bring debate to a quick end

For closure in Gestalt theory's Law of Closure, see
Gestalt psychology.

For closure in music, see:
resolution (music)
consonance and dissonance
Pretty cool how many disciplines are concerned with this idea.

If you’re interested, closure (mathematics) From Wikipedia, the free encyclopedia

In mathematics, the closure C(X) of an object X is defined to be the smallest object that both includes X as subset and possesses some given property. (Thus, an object is, among other things, a set.) An object is closed if it is equal to its closure. Typical structural properties of all closure operations are:

· The closure is increasing or extensive: the closure of an object contains the object.
· The closure is
idempotent: the closure of the closure equals the closure.
· The closure is monotone, that is, if X is contained in Y, then also C(X) is contained in C(Y).

An object that is its own closure is called closed. By idempotency, an object is closed if and only if it is the closure of some object.

These three properties define an abstract closure operator. Typically, an abstract closure acts on the class of all subsets of a set.


· In topology and related branches, the topological closure of a set.

· In linear algebra, the linear span of a set X of vectors is the closure of that set; it is the smallest subset of the vector space that includes X and is a subspace.

· In matroid theory, the closure of X is the largest superset of X that has the same rank as X.

In set theory, the transitive closure of a binary relation.

In algebra, the algebraic closure of a field.

· In algebra, the closure of a set S under a binary operation is the smallest set C(S) that includes S and is closed under the binary operation. To say that a set A is closed under an operation "×" means that for any members a, b of A, a×b is also a member of A. Examples: The set of all positive numbers is not closed under subtraction, since the difference of two positive numbers is in some cases not a positive number. The set of all positive numbers is closed under addition, since the sum of two positive numbers is in every case a positive number. The set of all integers is closed under subtraction.

· In commutative algebra, closure operations for ideals, as integral closure and tight closure.

· In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset.

· In the theory of formal languages, the Kleene closure of a language can be described as the set of strings that can be made by concatenating zero or more strings from that language.


Hothersall, D. (2004). Gestalt Psychology in Germany and the United States. In History of Psychology, 4th edition (pp. 207-247). Boston: McGraw Hill

Katz, V.J. (1998). Aspects of the Twentieth Century. In A History of Mathematics: an Introduction, 2nd edition (pp. 805-855). Reading, MA: Addison-Wesley.

Wikipedia contributors (2005). Closure (mathematics). Wikipedia, The Free Encyclopedia. Retrieved 23:56, March 9, 2006 from

Wikipedia contributors (2006). ‘Closure’. Wikipedia, The Free Encyclopedia. Retrieved 17:11, March 12, 2006 from

How shall we tag this one?

Saturday, March 11, 2006

A little organization is a good thing

The piles of books, magazines, notebooks, CDs, and other miscellaneous junk that collect on the back of my couch got really out of control this semester. One of my housemates took an old wooden shutter and put it up as a shelf over the couch. All the stuff that was piling up and falling down is now semi-neatly stacked on the shelf. Woohoo! I feel so organized. See.....

Tag anyone?

The mathematician meets the psychic

My favorite, must watch, TV show is NUMB3RS. (That the show is on Friday nights at 10pm probably tells you a lot about my social life. LOL) If you've never seen the show, it's your basic solve a crime show. But wonder of wonders, the main characters are - an FBI agent and his brother who is a mathematician and an FBI consultant. One of the major minor characters is a physicist. This is like hog heaven - a prime time TV show with a mathematician using math. (No comments from mathematicians about how good or bad the math may be, that math in any form has made it to prime time is just too good to be true.)

Last night's episode featured a psychic. Huh? How did this guy get involved? The math brother spent most of the show trying to figure that one out. He spent the program railing at the fact that supposedly rational adults were buying into the psychic stuff. When all else failed, he'd just chalk it up to coincidence. The writers wimped out and solved the crime through "good old-fashioned" police work. I guess they didn't want to take a position on either mathematical logic or psychic phenomena.

So...would you have wimped out? If not, who should have solved the crime - the mathematician or the psychic?

And a tag?

Tuesday, March 07, 2006

Personality Tests

Over at vw bug's, is a link to another online personality test. It seems that the net is over run with various long, short, and in between personality tests. Everything you may want to know about your personality, or any facet thereof, is available. What these tests don't come with is an explanation of how the test was created and verified. However, there is usually a disclaimer that the test if "for entertainment purposes only."

What I find most interesting is that I generally test relatively high on the masculinity scale and low on the feminity scale. I also scored high on masculinity on the MMPI. Now the MMPI is a well documented psychological test so maybe, at least in this area, these amateur personality tests are accurate. The question is, of course, does the "high" masculinity rating reflect a societal view that makes someone with a more analytic frame of mind masculine while someone who is more emotional feminine? If one is a geek and, horror of horrors a math geek, must that person by definition be masculine?

So, here's my personality report - respectful creator - as reported on the PersonalDNA test. Those of you who know me can decide how accurate this test is. LOL

You may have noticed that I'm trying something new - Technorati tags. woohoo

Friday, March 03, 2006

Friday miscellany while climbing another rung on the project ladder

I was able to get out of work today and go to the weekly math seminar. Today's seminar was a trial run for students making presentations at a math conference and the college's Academic Excellence Conference. Some really interesting stuff. Some of the work these kids are doing is truly amazing.

Now how does this relate to my honors project? Well, I took the time afterwards to talk to the department chair and the relevant professor about my project. They've both given their permission for me to use the Intro to Abstract Algebra class as guinea pigs. (Really, all I'm going to do is give the class a test before and after they complete the section that introduces set theory.) Now if I can just get all the official approvals on the project proposal paper, I can submit the study to the IRB for approval and actually start. Woohoo!

Totally unrelated - the one seminar I really wanted to go to this semester ( Permutations, Trees, and the Cantor Set), I couldn't make. Talked to the professor who did that one and he's emailed me his presentation. At least I'll have a little light reading while I study for the next exam in History & Systems.

If you've gotten this far, here are some of the one word descriptions of me courtesy of my friends. LOL

From sister: Big-sis (ummm.....)
From my oldest friend: unpredictable but fun - ok it's three but what the hell (this says it all)
From blog-sis, Irish: Survivor (well I did bury two husbands. LOL)
From my squirrelly friend: Friend (this is good)
From the southern belle: Dedicated (okay? wonder what I'm dedicated to other than making everyone miserable by rambling on about math)
From the picky one: intellebabe (I love this one!)

Wednesday, March 01, 2006

This is just wrong!

I don't do politics or religion here, but this is neither. This is just wrong! Check out Blackfive's post Help Protect Fallen Soldier's Funeral. I don't care if your political view is anti-war or your religious view is anti-gay, the disrespect this shows to the soldier and his family is disgusting.

Thank you to blog mom, Teresa, for posting this link.