A Comment on Winter in NH

For those of you who don't know, New Hampshire's state motto is "Live Free or Die." I was behind a truck tonight with a bumper sticker that read, "Live, Freeze and Die." I hate winter. I love this bumper sticker.

I am now officially brainless

Well...not quite. I finally sat down and made all the changes to my project proposal. This was not in actuality difficult since all the changes were in formatting. This was the first paper that had to be strictly within APA format and I messed up in a few places. There is this one paragraph though that I want to rewrite and expand, but my brain is shut down. I've been trying to write the blasted thing for over two weeks. Do you think that this diet the doctor put me on (for high blood pressure not weight loss), has destroyed my little gray cells?

So, your job Mr./Mrs./Ms. Phelps is to attack the (very short) paragraph. This communication will self-destruct when the universe begins to collapse.

A test to show evidence of the containment schema and containment as class metaphor will be created for this study and will include a study of its reliability and validity during the spring 2006 semester. The basis for the test includes, but is not limited to, information from previous testing of metaphor and containments as reported by Jones and Estes (2005), Low, 2003; Graham (2003), Hampe (2005), Drodge and Reid (2000), and Langston (2002).

Good luck. Aren't you glad I didn't copy the whole paper? *grin*

Very cool math stuff

Following a link from Ars Mathematica, I found a seriously cool math blog - Philosophy of Real Mathematics. I'm adding it to my side bar. But that's not the point of this note. The point is this entry - Why Do People Get Ill? The following quote is from the second paragraph.

I was talking last summer to Niels Birbaumer, who worked in the early days on conditioning the autonomic nervous systems of rats, with psychsomatic theories in mind. He didn't need any convincing that our immune system may be significantly affected by our mental states. Niels is in charge of a brain imaging unit in Tübingen, and has done work on imaging musicians while they imagined they were playing. We discussed the possibility of doing similarly for mathematicians.

Now, how cool is this? If they do the brain imaging on mathematicians, I so want to be able to follow the study.

I'm an alternative energy source!

Stolen from Contagion because I just couldn't resist (and I don't feel like doing the rewrite on my project proposal).

Ten Top Trivia Tips about MathCog Idiocy!

1. MathCog Idiocy can drink over 25 gallons of water at a time.

2. Olympic badminton rules say that MathCog Idiocy must have exactly fourteen feathers!

3. Ostriches stick their heads in MathCog Idiocy not to hide but to look for water.

4. It takes more than 500 peanuts to make MathCog Idiocy.

5. Carnivorous animals will not eat another animal that has been hit by MathCog Idiocy!

6. Abraham Lincoln, who invented MathCog Idiocy, was the only US president ever granted a patent.

7. The water in oceans is four times less salty than the water in MathCog Idiocy.

8. If every star in the Milky Way was a grain of salt they would fill MathCog Idiocy!

9. MathCog Idiocy can only be destroyed by intense heat, and is impermeable even to acid!

10. Two grams of MathCog Idiocy provide enough energy to power a television for over twenty-three hours.

I am interested in - do tell me aboutherhimitthem

The email version of a meme

Every couple of months I get one of these emails. You all know the kind I mean where you have to answer a bunch of questions and then forward it to all your friends (many of whom promptly block you from their email). According to the instructions - "The theory is that you will learn a lot of little known facts about those who know you." The end result is that you get a lot of emails back from people you don't know telling you that you're pretty normal (a state that I work hard at avoiding). So I got one yesterday from a co-worker and decided to inflict it on all the innocent parties who are so foolish as to visit this blog.

If you read further, you will learn 38 things you never wanted to know about me. If you're obnoxious, you'll follow the instructions at the end and send these questions with your answers to all your soon to be former friends. If you're really really obnoxious, you'll answer me (at which point, I will post at least one esoteric proof from mathematics).

1. What time is it? 9:34pm
2. What's your full name? MathCog Idiocy (you all didn't think I'd give you another name, did you?)
3. What are you most afraid of? Fire and airplanes
4. What is the most recent movie that you seen in a theatre? Harry Potter and the Goblet of Fire
5. Place of birth? New York City
6. Favorite food? sushi, chocolate, pasta
7. What's your natural hair color? I've pretty much forgotten
8. Ever been to Alaska? No
9. Ever been toilet papering rolling? a really long time ago
10. Love someone so much it made you cry? Yes
11. Been in a car accident? Yes
12. Croutons or bacon bits? Bacon bits
13. Favorite day of the week? Friday
14. Favorite Restaurant? had favorites in CT, but not around here
15. Favorite Flower? Day lilies and black-eyed susans
16. Favorite sport to watch? Dog agility
17.Favorite sport to play? Dog agility
18. Favorite Drink? Earl Grey tea
19. Favorite ice cream? chocolate
20. Disney or Warner? Warner
21. Favorite fast food restaurant? none of them
22. What color is your bedroom carpet? sort of beige
23. How many times you failed your driver's test? None (I should have the first time)
24 . Before this one, from whom did you get your last e-mail? Sue
25. What do you do most often when you are bored? read
26. Bedtime? 11:30-12:00
27.Who will respond to this e-mail the quickest? Since I'm gonna cheat and blog it, probably no one.
28. Who is the person you sent this to that is least likely to respond? See above
29. Who is the person that you are most curious to see their responses? Refer to question 27.
30. Favorite TV shows? NUMB3Rs, Charmed, NOVA
31.Ford or Chevy? Ford I guess since I like Mustangs better than Camaros (and assuming that I got the make/model right)
32. What are you listening to right now? the geese making geesy noises
33. What are your favorite colors? Black, blue, red
34. How many tattoos do you have? none
35. How many pets do you have? One dog, one cat, one pigeon (There are also 2 other cats that are my housemates and a gaggle of geese, ducks and chickens that aren't pets)
36. Which came first the chicken or the egg? chicken
37. What would you like to accomplish before you die? turn the whole world into math nerds 3
8. How many people are you sending this e-mail to? see question 27

And the original email return directions:
Now, here's what you're supposed to do... and please do not spoil the fun. Hit forward, delete my answers and type in your answers. Then send this to a whole bunch of people you know INCLUDING the person who sent it to you. The theory is that you will learn a lot of little known facts about those who know you. Remember to send it back to the person who sent it to you.

Life is good!

Classes started today. The start of a new semester means two things -

1) I restart adding license plates. First I have to get two sums in consecutive order which didn't happen today. That's a first. But I did see one license plate that I sincerely hope is a last name and not a philosophical statement. The plate read "WARMAN".

2) I bought my books. Right now the favorite is Sniffy, the Virtual Rat. I get to play computer games for a class. Hehehe.

Of course things did not go smoothly. The professor for the Honors Research Seminar was changed and the class is delayed for a week. This delay included, according to the announcement posted by the new professor, a "brain fart" that apparently rescheduled the class from Tues to Mon morning. Watch 9 women, 6 with conflicts between work and other classes, reading that the class will be on Monday mornings! Not a pretty sight.

Just in case anyone really cares, classes are
Psychology of Learning (with Sniffy)
History and Systems (a core requirement that is mostly psychoanalytic stuff, yuck)
Honors Research Seminar
and my Independent Honors Research Project

And because the oil company and the electric company, and the phone company, and.....won't provide me with free service, there is work. Any one know a really rich old man who will marry me, die quickly, and leave me a trust fund?

Peano and the (we are not) Chimps Act III, in which we are left with a question

Do Peano's Axioms as stated in Act I provide a model of the process we utilize when counting?

Peano and the Chimps: Act II, Where we first witness a temper tantrum

The relevant primates are loudly proclaiming that they are not the clown-like cousins human so love, but are MONKEYS! Specifically, rhesus macaques. So my erstwhile readers, your narrator admits to a failure of language and begs your forgiveness.

This act takes place in the laboratories of major research universities. It’s main character being a cognitive scientist investigating numerosity in animals and humans. Enter our monkeys (still yelling that they are not CHIMPS!). Some of them learn quantity pictures of 4 numbers in the order 1->2->3->4, others learns 4->3->2->1. But when they are presented with the 5, 6, and 7 quantities something odd happens. The 1->2->3->4 monkeys can place the new quantities in order, but the 4->3->2->1 monkeys can not. How strange.

Perhaps if they learn 4->5->6 and 6->5->4, they will do better? Or perhaps the monkey Peano has been to see them? Alas, it appears that monkey Peano snuck into the lab late one night and explained the principle of a first number and its successors. His 4->5->6 children know what to do with 7, 8, and 9 but not 1, 2, and 3. But while the 6->5->4 progeny are stumped by 7, 8, and 9, they can order 1, 2, and 3.

What is going on here? Do Peano’s Axioms actually explain the cognitive process of counting? Will the answer appear in Act III? Or will we be left with questions?




Note: The relevant journal articles on the studies with the rhesus macaques are available here along with a number of other interesting papers on numbers in animals and humans.

The monkeys (we are not CHIMPS!) have their stories told in:

Brannon, E. M., & Terrace , H. S. (1998). Order of the Numerosities 1 to 9 by
Monkeys. Science, 282, 746-749

Brannon, E. M., & Terrace , H. S. (2000). Representation of the Numerosities 1-9 by
Rhesus Macaques (Macaca mulatta). Journal of Experimental Psychology, 26(1),
31-49

Brannon, E. M., & Terrace , H. S. (2002). The Evolution and Ontogeny of Ordinal
Numerical Ability In M. Bekoff, C. Allen, & G. M. Burghardt (Eds.). The
Cognitive Animal (pp. 197-204). Cambridge, MA: The MIT Press

Terrace, H. S., Son, L. K., & Brannon , E. M. (2003). Serial Expertise of Rhesus
Macaques. Psychological Science, 14(1), 66-73

Peano and the Chimps: Act I, Where we meet our hero Peano.

Peano makes his entrance during a class at a rather small (enrollment approx. 5,000) institution of higher learning in an equally small (pop. approx. 24,000), but with a large attitude, town. It is a grand entrance with all due pomp and circumstance. Then with a nod to the professorial staff as they immortalize his impeccable logic and their love of dominoes, Peano leaves. Years later he will enjoy an unacknowledged cameo appearance (along with dominoes) on the television show NUMB3RS.

Peano will return to this same school several years later when older, and more subdued, students are learning how to create number sets using his axioms.

But what is Peano’s motive? The pamphlet describing these axioms (Arithmetices principia, nova methodo exposita, 1889) is in Latin! For the benefit of these untutored rubes taking up valuable educational space, the axioms are proffered in English with explanations by the harried professor.

P(1) There is a natural (counting) number * (the first number which
the students may think of as 1).
P(2) For each natural number n, there is a natural number n’ (called the successor of n and which the students may think of as n + 1).
P(3) There is no natural number n that has a successor equal to *.
P(4) If m and n are both natural numbers and m is not equal to n, then the successor of m does not equal the successor of n..

P(1) and P(2) starts the sequence of counting numbers. P(3) gives the it a beginning and P(4) makes sure that each number in the sequence has a distinct successor (otherwise 4 could be the successor to 3 and another number – maybe 2?)

To complete the axioms, there is the most perplexing of all, but oh so important if the student is going to count properly.

P(5) If A is a subset of the set of all the natural numbers and if * is in subset A and n’ is in subset A for every n in subset A, then A is the set of all the natural
numbers.(1)

Ah such confusion reigns. Is our hero really a hero? And who (or what) are the chimps? Perhaps Act II will provide the insight we desperately search for.

(1)This is a rather lose translation of Peano’s Axioms from class notes for Intro to Abstract Math (2002).

While waiting for the story of Peano and the Chimps

I thought I'd share other stories with you. Although the green piggies are interesting, I offer you the following for your immediate entertainment.

From space.com - Space Tornado! Cosmic Front Packs a Punch. If you were picked up by this tornado, would you say "I don't think we're in Kansas anymore?"

And from livescience.com - Researcher: Early Man Was Hunted by Birds. Do you think Hitchcock knew about this?

Have a happy Friday the 13th!

Coming Attractions (hehehe)

Peano and the Chimps!

(Are you intrigued?)

And you thought math was a serious business!?

How many ways can you catch a lion? Here are the answers from Bjorn’s Maths Blog - How to catch a lion in the Sahara Desert. Link courtesy of Ars Mathematica.

Could I build a mathematical model?

For the past year I've been considering whether or not mathematics could be used to model the evolution/emergence of human cognition and wondering if this could tell me anything new about the development of the cognitive processes necessary to mathematics. Since I fell asleep last night and woke up this morning with my mind connected to this problem, here it appears for your comments and/or ideas.

So here's a very short version of what I have from 2 years of reading books and journal articles. About 6 million years ago there was an evolutionary split between hominids and apes. As you look at the various ancestors to homo sapiens, brain size increases although the time intervals are not equal nor are the volume increments.

There is a significant amount of literature describing the emergence of activities (wearing of jewelry, burials, art, etc.) associated with the development of modern cognitive capabilities. These activities do not appear in any straight time-line fashion, but arise in different places at different times with varying periods between their appearances. One all purpose tool sufficed for thousands of years. Development of multiple special purpose tools, once it began, was relatively rapid (at least in evolutionary terms) and continues today.

There are some studies by evolutionary biology/genetics people that attempt to determine when particular genes relating to the brain mutated. These studies give date ranges for when the mutations might have occurred. We share 96-98% of our genetic structure (I've read both numbers recently) with chimps.

In the cog psych literature the development of cognition appears to be equated with the development of language, but there does not appear to be a consensus on when language development occurred. I noted this in a paper I wrote last winter/spring - Dates for the advent of language, or symbolic references, range from 200,000 years ago with the expansion of the brain to modern human size and concurrent changes in vocal apparatus to five to seven million years ago during a period shortly after hominids and chimpanzees branched from a common ancestor.

If anyone is foolish enough to want to see the ever growing list of references, let me know.

The largest prime number?

I don't think so. A friend emailed me a link to a Yahoo article headlined Mo. Researchers Find Largest Prime Number. Since this friend is a wonderful writer but not even a wannabe mathematician, I refrained from answering with the very simple proof of the infinity of primes and went off to read the article. At least the first sentence is "Researchers at a Missouri university have identified the largest known prime number, officials said Tuesday. " (Emphasis mine) It would have been nice if the headline was written with a little more care. I wonder how many people read the headline but not the article and now think that there is a finite amount of prime numbers and the largest (translate last) has been found?

Math Ed in the elementary grades - a question

For the record, math teachers in the US are certified for grades 7 - 12. In the elementary grades (K - 6) there is no specific math certification. This means that the majority of teachers who are responsible for providing the foundation needed to learn math have little or no background in the subject. Before the holidays a friend asked me how I would change this. I have a number of thoughts running around in my head, but before I once again prove my ability to cause a comatose state in most people I'd like to know if anyone out there has a thought or two on this subject.

So.....

Part Deux

What types of things do you think we should be teaching in elementary school math?

More useless fascinations

After an email discussion with blog mama Teresa, I loaded a counter on the blog. I was kvetching about not knowing if anyone actually read this thing - the stat counter answers that question or at least indicates who has arrived. This counter lets me find out all sorts of things (most of which are not particularly interesting to me at this time). However, the chart that shows which countries visitors are from fascinates me. So tonight I looked at the chart and found out that someone from Denmark had stopped by (at least briefly). Why did this catch my eye? My maternal grandparents emigrated to the US from Denmark at the beginning of the 20th century. So this was today's useless fascination.