Homeschooling Corner: Erdos, Fibonacci, and some Really Big Numbers

One of the nice things about homeschooling is that it is very forgiving of scheduling difficulties and emergencies. Everyone exhausted after a move or sickness? It’s fine to sleep in for a couple of days. Exercises can be moved around, schedules sped up or slowed down as needed.

This week we finished some great books (note: I always try to borrow books from the library before considering buying them. Most of these are fun, but not books you’d want to read over and over):

The Boy who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heligman, was a surprise hit. I’ve read a bunch of children’s biographies and been consistently disappointed; the kids loved this one. Improbable, I know.

I suppose the moral of the story is that kids are likely to enjoy a biography if they identify with the subject. The story starts with Erdos as a rambunctious little boy who likes math but ends up homeschooled because he can’t stand regular school. My kids identified with this pretty strongly.

The illustrations are nice and each page contains some kind of hidden math, like a list of primes.

Professor Astro Cat’s Frontiers of Space, by Dominic Walliman. This is a lovely book appropriate for kids about 6-11, depending on attention span and reading level. We’ve been reading a few pages a week and recently reached the end.

Minecraft Math with Steve, by Steve Math. This book contains 30 Minecraft-themed math problems (with three sub-problems each, for 90 total.) They’re fairly simple multiplication, subtraction, division, and multiplication problems, probably appropriate for kids about second grade or third grade. A couple of sample problems:

Steve wants to collect 20+20 blocks of sand. how much is that total?

Steve ends up with 42 blocks of sand in his inventory. He decides that is too much so drops out 12 blocks. How many blocks remain?

A bed requires 3 wood plank and 3 wools. If Steve has 12 wood planks and 12 wools, how many beds can he build?

This is not a serious math book and I doubt it’s “Common Core Compliant” or whatever, but it’s cute and if your kids like Minecraft, they might enjoy it.

We are partway into Why Pi? by Johnny Ball. It’s an illustrated look at the history of mathematics with a ton of interesting material. Did you know the ancient Greeks used math to calculate the size of the Earth and distance between the Earth and the moon? And why are there 360 degrees in a circle? This one I’m probably going to buy.

Really Big Numbers, by Richard Evan Schwartz. Previous books on “big numbers” contained, unfortunately, not enough big numbers, maxing out around a million. A million might have seemed really good to kids of my generation, but to today’s children, reared on Numberphile videos about Googols and Graham’s number, a million is positively paltry. Really Big Numbers delivers with some really big numbers.

Let’s Estimate: A book about Estimating and Rounding Numbers, by David A. Adler. A cute, brightly illustrated introduction. I grabbed notebooks and pens and made up sample problems to help the kids explore and reinforce the concepts as we went.

How Big is Big? How Far is Far? by Jen Metcalf. This is like a coffee table book for 6 yr olds. The illustrations are very striking and it is full of fascinating information. The book focuses both on relative and absolute measurement. For example,  5’9″ person is tall compared to a cat, but short compared to a giraffe. The cat is large compared to a fly, and the giraffe is small compared to a T-rex. My kids were especially fascinated by the idea that clouds are actually extremely heavy.

Blockhead: The Life of Fibonacci, by Joseph D’Agnes. If your kids like Fibonacci numbers (or they enjoyed the biography of Erdos,) they might enjoy this book. It also takes a look at the culture of Medieval Pisa and the adoption of Arabic numerals (clunkily referred to in the text as “Hindu-Arabic numerals,” a phrase I am certain Fibonacci never used.) Fibonacci numbers are indeed found all over in nature, so if you have any sunflowers or pine cones on hand that you can use to demonstrate Fibonacci spirals, they’d be a great addition to the lesson. Otherwise, you can practice drawing boxes with spirals in them or Pascal’s triangles. (This book has more kid-friendly math in it than Erdos’s)

Pythagoras and the Ratios, by Julie Ellis. Pythagoras and his cousins need to cut their panpipes and weight the strings on their lyres in certain ratios to make them produce pleasant sounds. It’s a fun little lesson about ratios, and if you can combine it with actual pipes the kids can cut or recorders they could measure, glasses with different amounts of water in them or even strings with rock hanging from them, that would probably be even better.

Older than Dirt: A Wild but True History of Earth, by Don Brown. I was disappointed with this book. It is primarily an overview of Earth’s history before the dinosaurs, which was interesting, but the emphasis on mass extinctions and volcanoes (eg, Pompeii) dampened the mood. I ended up leaving out the last few pages (“Book’s over. Bedtime!”) to avoid the part about the sun swallowing up the earth and all life dying at the end of our planet’s existence, which is fine for older readers but not for my kids.

Hope you received some great games and books last month!

Creativity and Psychoticism

I was discussing the research for the AIDS and California post with a friend the other day, and they reacted with what I recall as shock and horror, protesting that San Francisco was home to Silicon Valley, Steve Jobs (formerly,) and all kinds of fabulous innovations. I thought about this for a moment, and replied something to the effect of, “Creatives are Psychotic.”

Now, I do not mean that creative people are stark raving bonkers and lost connection with reality, nor that they are violent, dangerous, malicious, or anything like that. I do mean that their minds do not function the same as everyone else’s.

Normal people, as I’ve mentioned before, (seem to have) neurological feedback loops that make them imitate other people. This is deep in the wiring of the brain; it’s crucial for things like learning to talk. People who imitate other people are normal, functional humans; people who fail to imitate others generally have severe life impairments. Understanding how these feedback loops work and influence our decision-making processes is crucial, IMO, to understanding the vast majority of humans.

But creative people, by definition, are not imitating others.

There are two obvious ways to be creative:

  1. Not know what other people know/think about something. Therefore, you are completely unable to have any conformist thoughts about it.
  2. Not care what other people know/think about something.

Most people who don’t know what other people know/think are small children, and small children are wonderfully creative. To get the same effect in an adult, in any useful sort of way, your best bet is to look for outsiders. Outsiders aren’t deeply tied into and invested in your way of thinking and doing things, and so can easily see things you’ve overlooked. I tend to think of Jayman’s creativity, for example, as springing at least partially from his semi-outsideriness, giving him a perspective other people lack. (Jay, if I’m wrong, forgive me.)

Creatives who don’t care what other people know see past what everyone else sees. They see new ways to combine things, new ideas, new stuff other people haven’t tried yet.

Normal people either cannot see this stuff, or when they do see it, their neuro feedback loops punish them for having deviant wrongthought.

The normal person experiences reality like a fish experiences water. A creative person is a fish with wings.

A normal person cannot escape from reality. They struggle to produce novelty because their brains only like doing things that are already being done. Normal is their programming.

Creatives lack some aspect of this programming. The normal feedback loops aren’t there. They are disconnected from reality. Not totally, of course–if they were totally disconnected, they’d probably just walk in front of a car and then we’d never hear from them again. They are usually connected enough to function, to eat and sleep and not get run over, but to be frank, all of that normal stuff is often a struggle for them.

Paul Erdős comes immediately to mind. Yes, mathematicians are creatives. This is obvious.

From the Wikipedia:

“Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life as a vagabond, traveling between scientific conferences, universities and the homes of colleagues all over the world. He earned enough in stipends from universities as a guest lecturer, and from various mathematical awards to fund his travels and basic needs; money left over he used to fund cash prizes for proofs of “Erdős problems” (see below). He would typically show up at a colleague’s doorstep and announce “my brain is open”, staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom to visit next.”

Just one case; you may provide many others. Artists who cut off their ears or seem obsessed with vaginas; rock stars with their fiery careers and often spectacular ends; scientists or engineers obsessed with tiny, obscure bits of the world that no one else pays attention to, like eels or gyroscopes.

For San Francisco to be both the source of great technological breakthroughs and improvements, and a place where a good percentage of the population decides to just throw social norms out the window, heh, norms, who needs the damn things? seems entirely sensible. Sometimes not caring what other people think leads to good ideas, sometimes to bad ideas, sometimes to really strange but ultimately neutral ideas.

Therefore:

  1. If you want creativity and innovation in your society, you have to tolerate some crazy, socially-deviant behavior from your creatives.
  2. A certain percentage of “outsiders” will probably help maximize society’s creative output.
  3. Creatives are not always very good at taking care of themselves. If a peripatetic mathematician arrives suddenly on your doorstep, it’s probably best for humanity if you let him sleep on your couch and do math on your table. Society at large may want to keep this in mind, as well.
  4. Don’t believe *everything* creatives say. Sometimes they have great breakthroughs; sometimes they just don’t see the underlying logic for doing things the normal way.

 

This was not originally my idea–I think it was Bruce Charlton‘s. If not, I apologize.