New Zealand Day!

Our son Christian chose New Zealand for his country day. We made the national dessert, Pavlova, a cooked meringue dish. Daddy learned that egg whites don't whip into a meringue in two minutes like strongly implied in the YouTube video (more like 30 minutes of hard elbow grease), and that next time they would be better off using an egg-beater. We used the homemade whipped cream leftover from the Pavlova for the fresh strawberries and kiwis, and to give it a slightly more NZ taste supplemented it with fish.

For the movie, we wanted to watch Whale Rider, one of Rachel's favorites and considered one of the best New Zealand films. However, neither the local library, the Baylor library, Netflix, nor Amazon carried it. Ditto Hunt for the Wilderpeople, and Once Were Warriors seems a bit dark for our kids, but all three of those films are on my get-to list. We thought about watching Fellowship of the Rings, but our library didn't have a copy of that either, so we ended up watching some New Zealand All-Blacks rugby instead.

In the Beginning: The Big Bang and the Early Universe

"I could be bounded in a nutshell, and count myself a king of infinite space" - Hamlet, Act 2, Scene 2

Lesson

Where was the stuff that makes up your body before you were born? Where was it before the earth was made? Where was it before then? Eventually, if we go back far enough, before the first stars, before planets or anything else that we see in the universe, the universe was a big cloud of invisible gas and was completely dark, before then, it was filled with a glowing white hot cloud that you couldn't see through. Before then it was a tiny dot, but even if you were in that tiny dot, the universe would look infinitely large, even though outside of it only looked like a tiny dot.

Alternative approach:

About 14 billion years ago everything you see in the sky and on the earth, everything in the universe existed in a tiny point smaller than the smallest speck of dust you have ever seen. For some reason (we don't know why), it started expanding. It's not that everything was in a point in space, space itself was in that point. Also, time started at that point. Some people think that if you started now and asked somebody and kept asking "what's before that," that eventually you'd get to the Big Bang, and you could say not only that there's nothing before that, that there isn't even a before.

Because everything in the universe was crammed into such a small space, it was so hot that a special state of matter above gas happened called plasma. For about 400,000 years the entire universe was a filled with a big glowing, white-hot fog as it expanded. After 400,000 years the fog dissipated, and the earliest air was formed. These gases were invisible though, so the entire universe was completely black, there were no stars, galaxies, or planets, just a lot of invisible air floating through space. Eventually some of that gas started to pull together because of gravity, and enough gas came together that they lit on fire and became the very first stars.

The universe is expanding faster than the speed of light. Because of this, when we look at very far away galaxies, we are looking at galaxies that are very young, we are basically looking back into time. [Show them a picture of the Hubble Deep Field image with the really dull red ones in back and explain that these are some of the earliest galaxies ever]. The more powerful our telescopes, the farther back we can see, except we can see some light from the Big Bang itself called the Cosmic Microwave Background radiation [show them a map of the COBE]. This light is a color that we can't see called microwave, this is the same light we use to cook our food in microwave ovens.

However, because both time and space are expanding, space can be infinite (we have infinite galaxies, planets, and suns) within a ball, because time is different in different places in that ball. So even when the universe was the size of a room from the outside, if we were in that room-sized universe it would still look infinite to us.

Some scientists think that there are other universes besides ours, some of the math predicts that there are.

Additional activity: Blow up balloon, draw points on it representing stars and galaxies and show how they all move away from each other when the balloon is expanding, explain that that's how we found out about the Big Bang.

Recommended reading for adults

Our Mathematical Universe, Mag Tegmark (first, Big Bang-relevant parts).

Future

I don't quite get the inflation-era stuff and need to brush up on that when my kids get older. Also, I don't quite understand how the volume of the interior of an inflating sphere can be infinite while the sphere is finite from the outside. It was explained in the Tegmark book above but it's one of those things I'll need to set aside some time to really focus on.

Canada Day!

We've decided that once a week we're going to have a day dedicated to a certain country, where we eat meals from that country and watch a movie from that country (or a good movie we want them to see anyway that takes place in that country). Before we got married Rachel was heavy into international cinema, while I was a bit of an experimentalist foodie, and now our kids are old enough that we can enjoy these interests of ours with them. Hopefully this won't be something that sounds fun but dithers out after a few weeks. The rules are 1) you can't repeat the same country twice, and 2) we go in order from youngest to oldest on deciding which country we'll do. In our experience, whenever we give the kids an option it exponentially increases the fun that they derive from the activity.

So this week our youngest (3) wanted to do the "leaf flag country." We had a lunch of pancakes with real maple syrup and a few slices of Canadian Bacon from the Butcher's shop.

For dinner we found one food truck in Waco that served Poutine, the national dish of Canada: fries, cheese curds, and gravy (with mushrooms and beef in ours). It tastes a lot better than it sounds. All washed down with Canada Dry Ginger Ale (Rachel's favorite, which according to our brief Wikipedia research was in fact started in Canada).

At night we finished it off with another of Rachel's favorites--the first episode of the Anne of Green Gables 1985 Canadian miniseries. With all boys Rachel wants them to get at least some exposure to girlish things.

Organizing the Univese: Base Ten and Zero

"God created the integers. All the rest is the work of man." -Leopold Kronecker

 

Introduction

The base ten concept is necessary for knowing how to add, subtract, multiply, and divide large numbers. When I was younger I was only taught the steps necessary to do these operations without really appreciating the concepts behind them, and it's easy to take for granted the power of places to compress so much information into few numerals. It's rather simple, but the development of places and zero is the doorway to being able to access everything interesting about mathematics above the basic business-oriented functions it was used for anciently like measuring out land and pyramid dimensions (with a few, limited exceptions such as Pythagoras above). This lesson is part utilitarian--they do need to have this down solid to do more than basic arithmetic, but I also hope to convey the power that human constructs have in organizing and making sense of the universe. The concept of "carrying the one" may be a bit difficult to grasp for younger children. My 7-year old almost has it down. Mileage may vary.

Lesson Plan

One way of counting is to make one mark for each item you have. In this way, if we wanted to show one hundred, we would have one hundred tally marks (show them how this might look). As you can see, this would take a long time to both make and count every time you saw it. Some early cavemen did numbers this way, often by putting notches in bones or counting out pebbles, but they usually didn't have to count very high, so it was okay. Some ancient societies would only have numbers up to four, and then every number after that was " a lot." Ancient Romans would only name the first four children, then all of the ones after that became "the fifth," "the sixth," etc. Some people think that this group of four rule is because that's as many as you can count to before you get to all the fingers on the hand. V for five is almost as universal as I for one.

Another way might be to have a different symbol for every numbers. But here you would have to memorize every single symbol, so to memorize all the numbers up to 100 you would need 100 different symbols. Also, it would be very hard to add these symbols together. Some ancient languages would use letters as symbols for numbers, so in Hebrew the first letter equals 1, the second equals 2, and so on. People could then use groups of letters to show numbers. Some religions would believe in sacred numbers because they would add up to the name of God, or something like that. In the Bible it says that the mark of the devil is 666, so some people think that a bad person's name near the end of the world will have letters that add up to 666. This shows you how powerful numbers could be for religions.

The way most ancient societies counted things is groups of symbols. They would have a few symbols that would represent certain numbers. This way, they would only have to memorize a few symbols, it was easy to add, and it didn't take long to count up the number of symbols.

[Show examples from Roman numerals, Ancient Egyptian]

However, for really big numbers it was still hard to add a lot of numbers together, and still took a long time to write. The ancient Babylonians started to use places, so instead of having lots of symbols showing groups of different amounts, the Babylonians made each place equal sixty of the earlier place. They needed to do this because they were one of the first empires in the world, and had to figure out how much money they could get from the people they ruled, so they needed to use big numbers.  Some Indian groups used places as well, but they would use it on a knot of cords, and wouldn't write it down, so people would have to bring the knot with them wherever they went to show people a certain number. Being able to just write down the number made things a lot easier.

Nowadays each place is ten of the place to the right of it, this is how most number systems today work. However, they had to somehow show if there was one place that was missing, so for example 406 is different from 46, so they came up with a symbol that meant that showed that four is four groups of one hundred, even though there are no groups of ten.

[Those color-coded blocks of 1, 10, 100, and 1000 are very helpful here to show them the idea of groups of ten]

The Babylonians came up with a placeholding symbol, but it wasn't the same as zero. Zero had not been invented yet. At first they used a space to show the gap, but it was sometimes confusing because the spaces often weren't big enough, so a sign that represented a space, or nothing became very useful.

[At this point an abacus is useful to show them the idea of groups represented by different symbols/colors, with a space equaling a space in the groupings].

The Greeks and Hebrews didn't like the idea of nothing, so they never used zero. Eventually the Indians used zero, and it caught on fast because with zero they were able to do very large calculations. The Mayans on the other side of the world invented zero independently.

With zero you have a lot of tricks for adding and subtracting large numbers [show them carrying the one, subtraction, etc.]. It would be very hard to do this without zero or places (try it with Roman numerals).

With the base ten system that we have today, you can do large calculations with very big numbers, like 10 billion, 543 million... + [another big number--for kids used to adding 3 +5 this blows them away]. Because it's 10 groups of a billion, 500 groups of a million, 40 groups of a million, 3 groups of a million.... So if you add the same groups together you get the two numbers added together.

We still do use a base one system though for computers, because one means a switch is on and zero means a switch is off. So for a computer 100 is four.

Future Lesson Development

The real significance of zero kicks in when we get to calculus. I'll use Xeno's paradox and  the Greek's inability to solve it without zero as a launching point for the discussion of calculus, and how mathematics stalled for almost two thousand years because people didn't see the full implications of zero.

Reading for Parents

There are a lot of "history of numbers" books that are worthwhile reads. For zero, Zero: A Biography of a Dangerous Idea does an excellent job of describing the implications of place notation and zero in a non-mathematician, reader-friendly way.

Video Resources

The Story of One is a BBC documentary on the history of numbers that looks promising, but I haven't watched it yet so I don't know if it's age appropriate.

Where We Came From: Human Evolution

“In the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.”- Genesis 3:5 King James Version

Introduction

This is a subject where the forest can easily get lost in all the trees of the technical debates about the different possible evolutionary lines and species. Consequently, I try to focus on the big picture climate and evolutionary changes, and only mention the most major species (e.g. Homo Erectus). Presumably later iterations of this lesson will get into more detail about the other species.

Throughout the lesson I refer to other hominids as “our ancestors” or “your great, great, great… grandparent or grand uncle” I’ve found that the idea the idea that our ancestors were different animals naturally peaks children’s interest.

Also, I refer to the other hominids as “other kinds of humans.” This is technically correct, and once again the connection to “other humans” peaks children’s interest more than just “other animals” does.I'll sometimes use dogs as a touchstone("just like there are different types of gods, there used to be different types of humans").

Lesson Plan

A long time ago our great great… grandparents and monkey’s great great… grandparents lived in trees in Africa. At some point, however, some of the trees started to die off and there were a lot of fields and bushes instead. Our ancestors moved into those forests with lots of fields and bushes, while another group stayed in the trees. The group that stayed in the trees became chimpanzees, and the group that left the trees eventually became us.

The group of monkeys that left the trees eventually started to walk on two legs, some scientists think that this is because the ones that walked on two legs were better able to survive in the fields because they were able to look over the tall grass, and maybe protect their bodies from sunburns.

These monkeys looked like monkeys, only they walked on two legs (show them a picture).

Eventually, because they walked on two legs, they could use their hands for gathering things and creating sharp rocks and other things to hunt. They could not have done this without walking on two legs because their hands would not have been free.

Once their hands were free, the smartest ones survived and had more children because they were able to figure out how to use their hands to make stone weapons and tools, so their brains started to get bigger.

At this point there were some humans that were able to make tools, but they still weren’t as smart as us, they couldn’t talk a lot to each other, and they still looked like monkeys walking on two feet.  

Because the brains started to get bigger, women had to deliver babies earlier because their heads were getting too big to fit through their legs. Because babies were getting delivered earlier they had to spend more time with them. They couldn’t just have them and then leave them after a short time like some animals. They also had to he social and like families and groups, so that their groups and families could help raise their children. Because they had to protect their babies for a long time they formed groups. Usually women die after they’re too old to give birth, but in humans women keep living, and we think that it’s so that they can help with their grandchildren.

Eventually, some of these humans started to take care of their older people and weaker people. They also started to use fire to cook food so that they could hunt bigger animals and not get sick from their meat. Up to this point all of the humans were in Africa, but some started to leave and search for living areas elsewhere. One type of human that came out of this was Homo Erectus. Homo Erectus is the longest living type of human, they were on the earth 9 times as long as we’ve been. Homo Erectus went to South Asia (show them migration routes on a map). Some of them must have crossed oceans, so maybe they had early boats. Another human was Homo Heidelbergensis that was the first to live in really cold areas (Northern Europe). We think that they were the ancestors to Homo Neanderthals, which were a species of human that lived next to us in Europe. Also, some scientists think that Neanderthals and us had babies together, and that some of our ancestors were both Homo Sapiens and Homo Neanderthals. Homo Neanderthals may have had white skin and red and blond hair.

Eventually, since we were getting smarter and formed groups, some of our ancestors invented language and started talking. We don’t know if it was our own species or one of the earlier ones that first started talking. Eventually all of the different humans but us died off. The last two to die off were the Neanderthals in Europe, and a dwarf species of humans that lived in Indonesia that only died out about 10,000 years ago. Some scientists think that we killed them off.

Future Lesson Development

The Smithsonian National Museum of Natural History has some lesson plans for Jr. High-level students. I’ll look into those when my children are older. Also, I’ve taken them to the exhibit before, but the Smithsonian’s Human Origins exhibit in Washington D.C. is incredible.

Reading for Parents

The Third Chimpanzee: By far the most readable, enjoyable work on human evolution out there.

Also, from a more spiritual perspective, Hugh Nibley’s “Before Adam” is a good discussion from a Mormon perspective (although sometimes he’s a little too skeptical about the science).

Web Resources

Human Evolution Interactive Timeline

http://humanorigins.si.edu/evidence/human-evolution-timeline-interactive

Video Resources

BBC’s excellent Walking With series has some good episodes that involve early hominids. Specifically, they have the four-part Walking with Cavemen series, as well as the latter half of the Walking with Beasts series.

Material Resources

The classic charts that show a linear progression from earlier forms to Homo Sapiens can be misleading as they imply a higher level of certainty about relationships than we have--and possibly will ever have. The particulars about who descended from who is fiercely debated in human anthropology, and most of the details about the “family tree” type charts are highly arguable. Posters that take the overlapping timeline approach may be useful.