Book Review

The Math Gene: How Mathematical Thinking Evolved & Why Numbers Are Like Gossip by Keith Devlin

My review

rating: 2 of 5 stars
Devlin gives a hypothesis about how mathematical thinking evolved. He claims that the capacity for mathematical thinking is the same as the capacity for language (i.e., syntax), since syntactical thinking allows us to think "off-line" about objects, concepts, plans that are not in our immediate environment. Off-line thinking may be stimulated by non-environmental cues (e.g., thoughts), whereas on-line thinking is always stimulated by the immediate environment. Off-line thinking allows us to think about abstract ideas or objects, necessary for mathematical thinking.

Devlin also claims that doing math is like watching (or creating) a soap opera - it is all about relationships, but between mathematical objects instead of people. He likens mathematics to gossip.

Devlin's theories sound plausible to me, and it certainly seems that language and abstract thinking are related. It is interesting to read someone's ideas of exactly how they might be related. He gets into linguistics and archeology, too. It is also good to see someone describe, or attempt to describe, mathematical thinking for people who dislike or simply don't do math. I think this would be a worthwhile book for teachers of school math (arithmetic especially), since Devlin describes why arithmetic is difficult (his theory) and how it differs from true math. Anyone interested in math education should read it since it relates math to language and gossip, etc. Lots of good information, or at least some interesting ideas.

I don't like the way the book is written, however, neither the organization nor the writing style. For a mathematician, Devlin does not produce a neat, clean argument, although all the pieces may be there. He spends too much time saying what he will say and what he has said, and drags out what he says with extra words. Not concise. Maybe his publisher or editor wanted a long book. If one can get past the writing, organization, and repeated plugs for his other books, though, one will find an interesting, worthwhile theory.


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Finally

It is still May for a few more hours yet. Tomorrow is June, the month when the stress is supposed to all dissipate because all the reports will be in and done. It is not as clean as that, though, and everything is dragging on, so the stress continues, but it's not too bad. It helps that I finally have a non-horrible diagnosis for why I have been feeling tired, nauseated, dizzy, and tingly since before Christmas. It's not multiple sclerosis. It's not chronic fatigue syndrome. It's not a tumor. It's an inner ear disorder of unspecified everything. It might be problems actually in the vestibule. It might be damage to the vestibular-auditory nerve. It could have been caused by shoddy materials. Or my concussion 4 years ago (some gifts keep on giving). Or a virus. Or maybe it's something else. Anyway, I have been doing vestibular therapy, which consists of eye and neck exercises, and sitting up and lying down quickly. The problem is that I don't do them nearly as much as I am supposed to. The first eye exercise has really helped (or maybe it's a coincidence), so although I am still dizzy and kind of tingly, I haven't been as diligent as I should be with the exercises. And I haven't done any of them today. oops.

Here is poem, written to my friend Carol:

"Poor Toe"

A battle between wall and toe.
Wall won.
I thought of you.

That's all. Carol might understand it because she broke her toe months ago. Or she might not.

Did you hear about how cute and lovable walruses are? They are the sweethearts of the pinniped world.

Between cut-off and applause

Our concert was yesterday, and it went very well. We were all very emotional during the "Requiem" (Faure). So many singers had particular people they were singing for, people they have lost recently. One soprano lost both her sister and her brother in the past year, and she was having a hard time yesterday. Fred was performing (conducting) it in honor of both his partner's ex-wife, who passed away last year after a long, horrible battle with cancer, and his father, who died long ago. This requiem was the first big piece that Fred conducted, and that was at his father's memorial service. He cried after the last cut-off. I don't think the audience knew, but all the performers did, and so it was all more meaningful than most concerts, which are usually pretty emotional and meaningful anyway. It was a gift to be part of it, and to help people with their grieving. A gift both to us, and to them from us. It was a blessing to be part of that gift. Jennifer, our Soprano 2 vocal coach and resident soloist, performed the "Pie Jesu" (solo movement in the Requiem). She has the perfect voice for it, and put everything into it. It was beautiful. That doesn't really begin to describe it. Transcendental. I know she was working hard, but it was almost as if she just allowed it to happen, or that she was accessing some channel of perfect music that is all around us all the time, but happened to be accessible through her (and Fred and the orchestra) at that time and place. And amazingly, she did it at both dress rehearsals, too... Boy, she's good!

I feel very fortunate to be part of this group. It demands a lot of time and energy, and there were many times this winter and spring when I wanted to quit because I was just so tired, but I am glad that I didn't. Something magical happens at the concerts. We are singing the same music we have been singing all along, but until the audience is there (and we can't stop to correct mistakes), we are singing for ourselves alone. With the audience, we are singing for them. We are giving them a gift. But we are also singing for ourselves and for Fred and for the orchestra, much more than in rehearsal. Lately, Fred has been showing his emotions more at concerts, or maybe I have just started noticing. He goes to a different spiritual plane during concerts. He is with us absolutely, and is connected to each singer and each instrumentalist, but he is also in some higher realm. Some of us are there with him, or near him, I think. It's not that we don't make mistakes, or that Fred makes no mistakes, or that we are not worried or tense about making those mistakes. We make brand new mistakes during the concerts, mistakes that we would never have imagined making. But it doesn't matter (usually), because the audience (usually) doesn't know, and the energy in the room takes us past it. That energy is part of what has always drawn me to choir. My high school chorus teacher always talked about positive energy, and it sounds a little hokey, but it's true. There is something about working in concert (literally and figuratively) with many other people, all toward one end and all together, that produces a magical energy. "Magical" isn't quite the right word. Maybe "transcendental" again. It takes us out of ourselves, and maybe onto that plane of Fred's, except that I don't think we are quite where he is. And it's odd, because I don't always recognize that transcendental energy at the time, and sometimes I wonder how it is that other singers noticed it or that the audience noticed it when I didn't. But I notice it afterwards. I notice that it was there at the time. And that it is now gone, and so I am now a little bummed. But the memory of it is still here. It doesn't hit you over the head. If you don't want to notice it, you won't. But if you are open to it, it will be there during the concert, and especially between the last cut-off and the start of the applause. Maybe I notice it then because Fred reflects it most in those moments. I think it is strongest in those moments of transition between our giving to the audience, and the audience giving to us. Typically, those moments are filled with coughing from the audience. A cough will take you right out of that transcendental space - grr! That was the case during most of the concert yesterday, until the end of the Faure, when even the coughers were spell-bound. Or maybe they had just gotten their cough drops down by that time. I'm glad they did; we needed that moment. Fred needed that moment. And later, when I am annoyed with Fred, I will remember his moments during the silences of the concert, and I will be kind. I hope.

All our soloists right now are wonderful, and I hope they stay with us. We were all a little worried when Lisa, our previous Soprano 1 soloist and vocal coach, left us to move to Chicago with her husband, the new bishop. Lisa is a wonderful singer and teacher, and so warm and helpful and kind, and some of us couldn't imagine that anybody could take her place or that we could continue in the same way without her. Well, no one has taken her place and we are not quite the same without her, but Jennifer is also a wonderful singer and teacher, and she is what we need right now. She is positive but honest and reasonable and not snotty or cliquish, as some soloists can be (especially the altos, for some reason). Linda is our Soprano 1 soloist. I don't think she has the teaching experience that Jennifer and Lisa have, but that's okay because Jennifer has it. Linda's voice is achingly beautiful. She claims that it is just hitting high notes (a common claim among the high-voiced soloists), but it is much more than that. She also accesses the channels of perfect music. And our male soloists did that, also. I hope they all stay with us!

My friend Lisa (Alto 1 section leader and all around great person) won the Inspiration Award this year, and I'm so happy for her. Congratulations, Lisa! I'm thrilled that people other than the Alto 1's recognize her greatness! And also that someone I voted for finally won. :-)

Avian Junior High

see more crazy cat pics

You didn't know this was a cat pic, did you? And of course, you can't see it all because blogger's default settings are silly and I don't know how to change them, and don't plan on wasting my programming energy on it. Nyeh. So there. Here's what the caption says:
"well u can tell her i'm not speaking to her either."

Nyeh.

Where Should You Live?

I just took a test that matches personality and geographic location. If you want to know where you would be happiest, go here. Maybe Eric Weiner should take this test.

Here are my results:

Your personality type is RLOAI

You are moderately reserved, moderately moody, moderately organized, moderately accommodating, and intellectual, and may prefer a city which matches those traits.

The largest representation of your personality type can be found in the these U.S. cities: Oklahoma City, Albuquerque/Santa Fe, Indianapolis, Reno, Greenville/Spartanburg, Cincinnati, Memphis, Chicago Area, Pittsburgh, Orlando, Louisville, Providence and these international countries/regions Czech Republic, Guam, Austria, Luxembourg, Philippines, Iceland, Indonesia, Portugal, Taiwan, Hungary, Israel, France, New Zealand, Slovenia, Canada

What Places In The World Match Your Personality?
City Reviews at CityCulture.org

The Purfuit of Happineff

I just finished reading a book on happiness/unhappiness around the world, The Geography of Bliss by Eric Weiner. Weiner is a grump who wants to know who the happy people are and where they live, and why they are happy. What is happiness? So he studied up on Happiness Studies, and went to a bunch of different countries that are well-known to be either very happy or very unhappy. The happy countries were the Netherlands, Switzerland, Iceland, Thailand, and Bhutan. The unhappy one was Moldova, a very unhappy place. India and Qatar were mixed, but India seemed happier than Qatar. Great Britain was fairly unhappy, although they are beginning to think about trying to be happy, to the dismay of many people. America is not the unhappiest country, but not near the top of the happy spectrum. I hope I haven't forgotten any.

Weiner's conclusion is that happiness is multifaceted. A certain amount of money is involved, but it isn't much. Human connections are necessary, and trust. Envy is the enemy to happiness. That all makes sense. After that, you're on your own. That's what he found, anyway. That makes sense, too. Different people find different things that bring them happiness. Most people in the happy countries do not spend time wondering about happiness, perhaps because they are too busy being happy. If you've got it, you don't miss it or wonder where it is.

One thing that Weiner doesn't address is the temporal aspect of happiness, or the essence of happiness. He wrote about what makes people happy, but not about what it is to be happy. Is it joy? If so, is it constant joy? Or do scattered joyous moments equate to overall happiness? Is a person's happiness level their average state of being, and if so, is that necessarily where they are on the happiness meter during the majority of their life (or day, or week, or hour), or can it be the average of extreme joy and extreme misery? Is not hating your life the same as being happy? I think I am fairly happy, although there are many things I would like to change about my life. It could be better. But it is what it is, for now. (I think that was a message from one of the happy countries, actually.) But it's not constant or even frequent joy.

Another question: Why should we expect to be happy? In America, we are told that we must be happy, and that if we are not happy, then it must be our own fault. But I don't think that it is the human norm to be happy, not actively, consciously happy. I also don't think it's the human norm to be actively miserable. I think that in general, people just go along and do what they have to do to get by, and if they are happy, that's great, and if they are not, well, then, that's the way it is because they don't have any choice in the matter. Granted, I am thinking of serfs and subsistence farmers and all, but most people in the world have been at that level of society and have had little choice in their lives. (The Bhutanese, pretty happy people but they don't admit to it, have had little choice in their lives until now, when they are getting democracy by decree of the king; they don't want it, but they all voted because the king told them to. I don't think they really get this democracy thing.) It is all Thomas Jefferson's fault, this fixation on happiness that Americans have. Not that he promised us out and out happiness. He just promised the right to pursue happiness. With that right, then if we are not happy, then it must be our own damn fault. Jerk. Also, the American public is too stupid to distinguish between the right to pursue happiness and happiness itself. We feel so entitled to everything. If we are not happy, then it must be the government's fault that we are not happy. The government owes us!

So, it's either our own fault that we are unhappy, or it's the government's fault that we are unhappy. The book implies that it is both, in the sense that some countries are generally happy because of the system of government, and others are happy because of the cultural and societal attitude, which of course defines the government, as well. It could be our ancestor's fault, if it is all genetic. Or perhaps happiness is just a modern marketing ploy, and it really means nothing. I think that part of it is that, and that the choices that we make will not necessarily lead to either happiness or unhappiness. They may lead to comfort or discomfort, but not necessarily change our happiness level. (Happiness researchers agree.) On the other hand, some choices are definitely better than others. If only they were easy to identify.

This book did not address anything like depression or PTSD or the effects of war or trauma or other bad things. Weiner has spent time in Iraq and other places that have been going through horrible times, and he purposely avoided these places and issues for this book. He himself is not a happy person, which is why he was curious about it. He seems to be a little happier after writing the book (certainly after getting it done). One thing he says at the end: many people find it more important to have full and meaningful lives rather than empty and happy lives. The implication is that having full, meaningful, and happy lives may not be an option - so you may not get to pick. In which case, perhaps we should just stop worrying about it, and get on with our lives.

So there are lots of contradictions here, and in the interest of my happiness and yours, dear reader, I am not going to try to smooth them all out. I liked this book, and I recommend it.

It's About Time

As usual, it is Sunday. Always Sunday here at the FFP. It is a short Sunday, with one hour missing. This is just cruel. Sunday is a day crammed with things to do, so why must it be the day that gets shorter? What should I not do because of that missing hour? Sleep? Laundry? Clean? Cook? Surf the Web and Post on my Neglected Blog? Talk to my Neighbor? Walk? Obsess about MS/Gluten Intolerance/Celiac Disease/Body-on-own-Body Attacks That May Continue Until I can Eat Nothing AT ALL? Read? Work? I vote for cleaning, as I usually do on Sundays, even those of normal length. But this place really needs cleaning. And work really needs to be done, along with the laundry and the cooking and the neighboring and the walking. The obsessing just comes along for the ride. I plan to obsess about gluten as I eat the remaining Girl Scout cookies. After all, I have to get them out of the house, right? They haven't been here long.

I have made progress on my book problem: I have finished two books, and now have only 6 to read before I can get any more. It has taken me a long time to finish these books, partly because of work and partly because I keep trying to read too many at once. For one thing, it's hard to hold them all. Weight Watchers has an article about how to save time, and talks about learning to speed-read. My reading of their article slowed down considerably on those 3 sentences about speed-reading. I don't think I am made for that. Also, even though I would like to not be buried under a pile of unread books, and I like buying new books, I don't want to just get through the books I have as fast as possible. Why bother reading them if you don't plan to enjoy them? I like reading slowly. But it does make it hard to stay up-to-date with the current crop of books, let along catch up to the rest of the reading population. I will never catch up, and will never be up-to-date. But I don't really want to be. For one thing, it's more expensive. If you keep buying books when they first come out, then you spend extra money on hardbacks and extra money on the extra bookshelves needed to house the hardbacks. If you wait a few years or decades, then the books come out in paperback, and they are smaller and easier to store. And if they don't ever come out in paperback, then maybe they weren't worth reading in the first place. But you will be out of touch. Not necessarily a bad thing.