Tuesday, January 31, 2006
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*
Friday, January 27, 2006
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.
Wednesday, January 25, 2006
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.
Saturday, January 21, 2006
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.
Tuesday, January 17, 2006
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?
Monday, January 16, 2006
Sunday, January 15, 2006
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),
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
Saturday, January 14, 2006
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 whichAh 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.
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
(1)This is a rather lose translation of Peano’s Axioms from class notes for Intro to Abstract Math (2002).
Thursday, January 12, 2006
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!
Tuesday, January 10, 2006
Saturday, January 07, 2006
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.
Wednesday, January 04, 2006
What types of things do you think we should be teaching in elementary school math?