The bright spot in a really pissy day

I'm not going to go into the really pissy day part because I'd probably say something that would get me arrested. Just the bright spot.

I lost my wedding ring a while ago (during the flooding stuff). Now this really upset me. It was the ring my first husband gave me. The first year we were married we had one of those fights and I took off the ring and threw it across the room. Ed retrieved it, jammed it back on my finger and said (actually yelled), "promise me you'll never take that ring off again!" I did and I never have in the 25 years since, so losing it was upsetting. But in the course of trying to deal with the problem that started of the pissy day, I found my ring!

My world will be all right again.

Knock, knock

Q: Whose there?
A: *silence*

From the San Jose Mercury News - Evolution site under fire

"Operators of a University of California-Berkeley Web site that is designed to help teachers teach evolution are being sued by a California couple who say the site improperly strays into religion."

The claim that the site strays into religion is based on the link to information provided here by the National Center for Science Education - Statements from Religious Organizations.

The rest of the story is here.

Rituals - mindless wandering because it's snowing

Every year on Thanksgiving morning I watch the Macy's parade. On Christmas Eve I usually go to a church service - candles, music, no sermonizing. New Year's Eve I watch the ball come down in Times Square. Shortly thereafter I have a birthday and whatever decorations are in the house are put away. This ritual has changed little over the years. There used to be trips to the grandparents and my godmother, but they're dead now so the visits are memories.

Rituals also exist in other ways. Our society and culture impose rituals on us. Wikipedia in its entry on ritual states that "rituals can have a more basic sociological function in expressing, inculcating and reinforcing the shared values and beliefs of a society." Weddings, graduations, and football games all include ritual.

We all have personal rituals that center on specific dates or holidays. Some of these grow out of our culture or belief systems. We also have rituals that are more private and hold an almost mystical quality such as repeating a series of actions before an exam or always wearing a particular outfit to job interviews. These type of rituals are designed by us to increase the probability of a hoped for result.

So I'm sitting here watching the snow fall and wondering if mathematics isn't one huge ritual.

Meme - my first

Sarah of That's Not Very Nice! tagged me with my first meme. I found myself having all sorts of weird reactions to this. Since most of the time I'm minimally social, I felt a little like the kid in school who is unexpectedly chosen first instead of last for a team. And then I started laughing because the first of the two class discussions I had/have to lead for the seminar was on an excerpt from Richard Dawkins 1976 book "The Selfish Gene". The title of the excerpt - Selfish Genes and Selfish Memes. This may include the first instance of the meme concept. Dawkins is writing about evolution and a new emerging replicator.

"...It is still in its infancy, still drifting clumsily about in its primeval soup, but already it is achieving evolutionary change at a rate which leaves the old gene panting far behind.

The new soup is the soup of human culture. We need a name for the new replicator, a noun which conveys the idea of a unit of cultural transmission, or a unit of imitation. "Mimeme" comes from a suitable Greek root, but I want a monosyllable that sounds a bit like "gene." I hope my classicist friends will forgive me if I abbreviate mimeme to meme."

Having bored you all with that, on to the meme itself.

1. Do you use an alarm clock to wake up in the morning?
I am so not a morning person, so what do you think? At least I haven't thrown the (expletive deleted) thing across the room lately and risked killing anything.

2. What time do you set it for?
At least an hour earlier than the latest time I can get up. There's some madness in this method.

3. Do you hit the snooze button, if so how many times?
You have to ask. Some days I beat it with my cat.

4. Have you ever abused an alarm clock?
Well let's see. When in college I threw one across the room, barely missed my way too cheerful morning person roommate, and watched it break against the concrete block walls. These days I use the remote control for the TV or the cat to beat the (expletive deleted) button into submission. (oooohhhh...this submission thing is just too too.)

5. It's time to spread some "Its Blogcess" linky love.

Rules of the game, as per Sarah:
First, copy and paste #1 - #5
(Make sure to link to: "It's Blogcess", which is the link in #5. Because it is always polite to link the one who started the linky love.)
Second, link to my site (because it's polite to link the site that tagged you)
Third, go and tag 5 other blogs, more if you like.
Fourth, Email the owner of, or post on the blogs that you have tagged, to inform them that you've tagged them.

Sarah changed the rules and picked only 3 others to harass with this. I'm following her lead and tagging:

My blog mama (forgive me?)
The Pixie who is temporarily off-line and way far away so she can't kill me
My friend Tal who may send the mole rangers after me for this.

Who am I?

Today I learned that I am an outlier.

Honor's Research project is moving forward!

Yesterday I spoke with the third professor I wanted on my project committee and she said "yes"! Woohoo, the committee is complete. On to the next step - the formal project proposal.

Jokes, Math, and Sex

In the last few days my email has included a math joke from my blog momma and a math chain mail from a friend. Both somehow someway included sex. Yes, sex and math. Who would have thought? Since you all probably don't believe me, I'm including the joke and the chain mail.

THE JOKE

A professor of mathematics sent a fax to his wife. It read:

"Dear Wife:
You must realize that you are 54 years old, and I have certain needs which you are no longer able to satisfy. I am otherwise happy with you as wife, and I sincerely hope you will not be hurt or offended to learn that by the time you receive this letter, I will be at the Grand Hotel with my 18-year-old teaching assistant. I'll be home before midnight.-- Your Husband"

When he arrived at the hotel, there was a faxed letter waiting for him that read as follows:

"Dear Husband:
You, too, are 54 years old, and by the time you receive this letter, I will be at the Breakwater Hotel with the 18-year-old pool boy. Being the brilliant mathematician that you are, you can easily appreciate the fact that 18 goes into 54 many more times than 54 goes into 18. Don't wait up."

THE CHAIN MAIL

SEX is like Math: add the bed, subtract the clothes, divide the legs, and pray you don't multiply!
You have been bumped by the Blinky
Which means you are a hottie.
You will have good sex for 2 years if you send this to 6 to 9 people. If this is sent back to you, you know you are truly a hottie.

Auctions

I love going to auctions. Sometimes I actually buy things at auctions. But I've never thought of auctions as subject to mathematical analysis. Once again, I've been proven wrong. LOL

Check out this post at Ars Mathematica. It's worth following the link to the Grimm survey and reading the pdf document.

My new favorite math quote

I followed a link from Ars Mathematica to the site to download a book (Toposes, Triples, and Theories, by Michael Barr and Charles Wells). From there I followed the link, CWRU Mathematics Department Website to the Case Western Reserve University's Department of Mathematics.

And there I found a truly wonderful quote - "Mathematicians, when they work, engage in intensely serious play. They follow their curiosity into problems that interest them and toward the smell of a solution." Richard Preston, The New Yorker, April 11, 2005

I may have to add this to my repetoire.

Stopping in to visit my own life

I've been busily trying to get school work done. So far I have two short and one long paper in the works, one short paper done and turned in, one take home exam written up, and the data analysis done for an extra credit paper (I want a 100 not a 90 for a test grade). Somewhere in there I did some database work, went to see a local production of Godspell, did the normal work and school stuff, completed all the paperwork for the honors program, and got sick.

I have the yuckys right now. You can tell I do because I didn't go to work today and paid sick time isn't part of my job. So I'm feeling sorry for myself as I go through the process of notifying professors, work, and the students in a project group when I started laughing. Why? Because I remembered that my mother used to do some self-medicating with alcohol. On occasion she'd wake up with a hangover, but my mother never had a hangover. It was always something she ate or a stomach bug. So here I am with a list of symptoms that except for the chills sound a lot like a hangover and a little ticked off that I didn't even get to have the "fun" of having a drink or two. Sheesh

8th grade math?

I'm so proud of all of you budding mathematicians with your fabulous test results!

One of my friends emailed this link. Fortunately I passed. LOL

Congratulations, you got 10/10 correct!

Could You Pass 8th Grade Math?

Retirement savings (a rant of sorts)

One of the various and sundry people who provide personal viewpoints on Sunday morning TV delivered an editorial this morning on the necessity of having personal retirement savings. Now I don't disagree with this and I'm pretty well resigned to working until I die because I no longer have any savings for retirement. Why is this? Well....

My late husband had early onset Alzheimer's disease (diagnosed in his early 50's). Neither his job nor mine provided any medical insurance let alone insurance to cover long term care. Once he could no longer be left home alone, I quit working to take care of him. The cost of home care was prohibitive - more than I was earning even with two jobs. His social security disability included Medicare, but medicare doesn't cover home health care, long term care, or prescriptions. Unfortunately he reached a point where I could no longer care for him so that both of us would be safe. Enter the long term care dilemma and using state Medicaid. This was the only way to provide him the necessary care, but excluding the house and including all monthly income, we were allowed....are you ready?.....$2500 in assests. By the time we took his social security income and the value of my car, we were at the limit. Note that any kind of insurance policy or prepaid burial was included in this assest limit. So I have no savings and will most likely not earn enough in the next ten years (theoretical retirement time) to save enough to even consider retirement. And by the way, I still have no medical insurance because I can not afford to pay for it with no access to a group policy. On the other hand I'm very healthy.

The sort of rant? We need to find a way around this kind of idiocy. I don't particularly want to lose half my income to taxes to cover health care and retirement, but the current situation is disastrous for many people. I'm lucky since I'm healthy, prefer working over sitting around getting old, and own my home. But what about the people who aren't as fortunate as I am? Are we going to end up with lots of homeless elderly people who have limited or no access to medical care? There are a lot of people who work hard all their lives, but are not in a position to save for retirement. They're called the working poor. Technically these days, I'm one of them.

That's all. And probably the only time I'll go political here. I much prefer math.

Mathematical "proof" of the existence of God?

Via Bayesian probability here

Is this a sign?

It's raining again - a nor' easter. There are flood watches and high wind warnings out. On my way to school and work this morning the radio played Creedence Clearwater's Bad Moon Rising. Do you think this might be a sign? *snicker*

Tidbits from Ars Mathematica

This past week my favorite math blog, Ars Mathematica, has had two posts that relate to the seminar (Nature & Origins of Consciousness) I'm taking this semester. I doubt the mathematician intended this, but stuff happens. So now I can entertain you with information you never wanted to know about.

On October 19th, this notice appeared: Week 222 of This Week’s Finds in Mathematical Physics is up. If you go to this link, #2 - #5, talk about the idea of singularity - not the black hole math singularity thing, but a point where technological development goes beyond us.

2) Charles Stross, Accelerando, Ace Books, New York. Also available at http://www.accelerando.org/book/

This is one of the few tales I've read that does a good job of fleshing out Verner Vinge's "Singularity" scenario, where the accelerating development of technology soars past human comprehension and undergoes a phase transition to a thoroughly different world. This is a real possibility, and it's been discussed a lot:

One of the things we've discussed fairly extensively in class is what constitutes consciousness and whether an AI machine or a robot is truly conscious. Since I'd never read about this particular idea (singularity), I followed the links to learn some more. Kind of scary when I'm reading that this point in technology is predicted to occur by 2030.

October 23rd's post says "According to a new paper on Arxiv, Goedel’s theorem is false. There you have it." I haven't read the paper, but I'm assuming that it refers to Goedel's incompleteness theorem. One of the more interesting books I've read on consciousness was written by a mathematician (Shadows of the Mind by Roger Penrose, 1994). In the book, Penrose uses Goedel's incompleteness theorem to refute the possibility of creating a conscious machine. Does this mean Penrose isn't buying the singularity idea?

Math and psychology meet on the horizon of physics.

Counting and negative numbers question for all.

In mathematics there is a set of axioms called "Peano's Axioms" which are the basis for proof by induction. These axioms also build the set of natural numbers (1, 2, 3, .......) or counting numbers. There are some interesting studies by psychologists that seem to show that these axioms exist at an unconscious level in children and primates. The psychologists aren't referencing the axioms, it's just something I noticed when reading the papers. It's pretty cool and gives me something to think about when I'm driving.

So....here I am driving down the road and thinking about how we learn to count and when different number concepts were incorporated into arithmetic and mathematics. Which gets me to negative numbers. You can conceptualize the natural numbers and fractions (rational numbers), but how do you conceptualize a negative number? When numbers are thought of as quantities, what is a negative quantity? Any ideas out there?

If you have some uncontrollable desire to read about Peano's axioms, there is a good description here at Wikipedia.

Happy Happy Joy Joy

My road is open in both directions! There's still paving and guard rails to go, but I can drive through the much much shorter way. I'm hoping the paving is done before the weekend since the local weather is forcasting heavy rains this weekend.

That's all.

Hypothesis, Theory, and Proof (very long)

One of the classes I'm taking this semester is a senior seminar entitled "Nature and Origins of Consciousness." We've looked at and discussed different historical explanations for consciouness and have now wandered into a discussion of intelligent design vs evolution. Which leads me to the concepts of hypothesis, theory, and proof (and a rant).

I'm finding that scientists, psychologists, mathematicians, and the general population use each of these terms in somewhat different ways. Everyone seems to use hypothesis to denote an unproved idea. A scientific or mathematical hypothesis appears to be a complete idea. It's the theory and proof concepts where problems occur.

For scientists and mathematicians, a theory (or theorem) is an hypothesis that has been proven. For psychologists, a theory is a logically organized set of statements that include definitions of various events or concepts, contain information about relationships between these events, explain the causes of the events where the hypothesis is simpler and more tentative. (I just had to memorize this for a test.)

Psychologists and scientists consider a theory proved when they can show significant evidence for it and when the theory exhibits good predictive validity. Einstein's theory of relativity was considered proven once phenomena predicted by the theory was shown to exist and when phenomena behaved in ways the theory predicted. In psychology proofs of theories are really statistical analyses of experimental data showing that the hypothesis based on the theory has a good probability of being true.

Since people (and the larger world in general) aren't particulary tidy, proof is not a 100% probability, true in all cases, concept for psychologists or scientists. This is also one of the reasons why theories are changed (or thrown out completely). As we learn more and gain more evidence, theories are modified. Sometimes the modifications become so unwieldy that science is forced into rethinking the whole idea. This is how science grows, but this does not automatically invalidate science.

Mathematicians (who are anal retentive) define a proof as a logical and rigourous mathematical argument. Unfortunately exhaustive evidence is not a proof. The mathematician must show that the hypothesis is true for all instances. For example, if I want to show that the sum of the numbers from 1 to n (n is any counting number greater than 1) = n(n+1)/2, just summing all the numbers from 1 to n=2, 1 to n=3, 1 to n=4, and so on for however long I want to go doesn't constitue proof. I could have done the sums a million times and all equaled n(n+1)/2, but that's not a proof. The proof involves an argument that shows this is true for all values of n. (BTW - this has been proved.)

The nice thing about this? Once a theorem is proved in mathematics, it stays proved. Euclid showed a proof of the PythagoreanTheorem that is still valid. The not so nice thing? Hypothesis that appear to work and for which there is a lot of evidence, but no proof. My personal favorite is the Riemann Hypothesis - unproven, but over a million solutions have been calculated and all agree with the hypothesis.

Remember what I said about people not being as tidy as numbers? I have to remind myself of this on a regular basis. Otherwise, I can't look at any psychological theory as proven. I learned the concept of proof in terms of mathematics.

Looking at the arguments "against" Darwin's theory of evolution, it seems that the general population defines both hypothesis and theory as an unproven idea and expects proof to be similar to a mathematicians - 100% true in all cases. The fact that evolutionary theory has significant amounts of evidence and excellent predictive value doesn't appear to convince people of its validity. I end up with a problem though when the counter proposal involves an unknown intelligence for which no evidence is available and a theory with no apparent predictive value.

Of course I also have a problem with the definition of a transcendental number - a number which is not algebraic. Hello, tell me what it is not what it isn't.

Mathematics and Arithmetic

Contagion asked, "What exactly is the difference between mathematics and arithmetic." There's a short answer and a longer answer. Since I live to ramble on about math, this is the longer answer.

Arithmetic is simply the calculation/computational discipline. In terms of my particular interest in mathematical cognition, I consider arithmetic one of the building blocks necessary to mathematics.

Mathworld (a really great online source for short answers to math questions and just fun reading) defines arithmetic as "the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. " (http://mathworld.wolfram.com/Arithmetic.html)

Balancing your checkbook is arithmetic. Having a degree in mathematics does not mean that I'm any better (probably significantly worse) at that than the average person.

Mathematics is more difficult for me to define because it covers many areas so back to Mathworld for a definition. "Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined." (http://mathworld.wolfram.com/Mathematics.html) Things like logic, which is essential to proofs, figure prominently in the study of mathematics.

Mathworld's main index lists the following topics and serves as a fairly good example of what is included in mathematics: Algebra, Applied Mathematics, Calculus and Analysis, Discrete Mathematics, Foundations of Mathematics, Geometry, History and Terminology, Number Theory (my personal favorite), Probability and Statistics, Recreational Mathematics, and Topology. No arithmetic. The foundations of mathematics section includes axioms, logic, set theory, and theorem proving. Again, no arithmetic.

If you look at the history of mathematics, different maths were developed to serve the needs of people. All mathematics through calculus were application driven and strongly tied to arithmetical calculations. Early in the 19th century, math went crazy (probably too much math happy juice) and new maths were developed for their own sake. It happens that many of these "pure" maths have applications in today's world, but the applications came later and are only of interest to applied mathematicians (or scientists, engineers, etc.) using them.

Have I put you to sleep yet? LOL If not, here's one of my favorite math quotes - A mathematician is a machine for converting coffee into theorems.

The Bad Example Family has a black sheep

Check out my welcome -

It's a Girl