Friday, October 21, 2011


I am incapable of conceiving infinity, and yet I do not accept finity.
Simone de Beauvoir

Egyptian symbol
for 1 million or "many"
For as long as she's been talking, Clementine, five, has been asking about numbers. For years, she has asked me half a dozen times a day, every day, to tell her what time it is. I answer, knowing that she can tell time at this point and is only asking for confirmation. She let the fact that she could tell time  slip out last summer when she was taking her Kindergarten placement tests. We also discovered that she was reading well enough to answer multi-step math problems. This was only slightly surprising.

PhilosophiƦ Naturalis Principia Mathematica

Clementine has always been all about math. She gets it from her daddy. Dan is an engineer and thinks in the same terms, sees the world the same way.

This way of viewing the world is foreign to me. I am not all about the math and really have to think about it sometimes. It helps to tie math to something concrete. For me, geometry works better if I'm calculating something real, a wall to be painted, for example.How much fabric to buy to make a dress.Real stuff.

finger symbols for numbers, 
from the 16th Century

Because their thinking is foreign, I find it fascinating to watch Clementine make all these connections that don't always seem obvious at first. Dan, too. I love to listen to him explain something new. I love to observe the way these two think about the world.

the Ancient Egyptian symbol for 100,000, 
a frog or tadpole

Clementine learned to skip count by 2s recently, and the next day, she taught herself to count by 3s and 4s. 5s were easy, because they repeat a pattern of 5 & 0, but she quickly taught herself 6s and 7s, too. Clementine asked about 9s, and we taught her the rule (the "ones" number goes down by one and the "tens" number goes up up by one as you count up). The next day, she knew her 8's, figuring how to take away 2 instead of the "take away 1" from the 9 rule. On Monday, she asked about 11s, and was counting them within minutes.

Clementine asks several times a day about what will happen if you add two specific numbers. Or if you subtract them. Or what would happen if you added them to negative numbers (which she calls "minus numbers", and has understood since she was tiny). Or what would happen if one number was a minus number, and one number was a positive number.And so on. She thinks about numbers and sees patterns all day every day.

And Clemetine constantly asks about infinity. She's fascinated by the concept, and is always asking different questions about it, trying to find a way to push the idea of an endless number into a space she can handle. We've explained that it isn't a real number, but a concept, an idea about numbers. She loves that part. She wants to be reassured that you can
"always add one more".

 train tracks by DarrenHester,

Clementine seems to worry about infinity a bit sometimes. One day, I showed her the symbol for the concept. I"See, it goes around and around. It never stops." She "got" it and loved it.

This is infinity:

In math and physics, the figure-8 infinity symbol on its side is called a lemniscate. Like a Mobius Strip, it never ends.

I showed her this, from my own childhood:

There are other, similar lemniscates in math: the lemniscate of Bernoulli,^ the lemniscate of Gerono^, and who can forget the lemniscate of Booth^?


Recently, we went out and grabbed a bite after a busy day. We were given a number, an 8 on a red acrylic disk so that our food could be brought to our table.

 Einstein at the blackboard

Clementine, put the number in the holder, declaring that, "Our number isn't 8, it's infinity!"

Not an 8!

Watching her thoughts unfold is like trying to talk to someone with whom you don't share a common language. You know that they probably make sense somewhere, but not necessarily to you.

I love her so much, for so many things, including letting me see what is important and what makes sense in her world.



Thursday, October 20, 2011

Tangentially Speaking (or) How to Waste 20 Minutes In No Time Flat

I read a brief article earlier about a local man who is facing several years in prison and up to $100,00.00 in fines for picking up a Rocky Mountain Big Horned Sheep skull, possibly cougar killed, and trying to sell it without getting it "plugged". It doesn't sound like the man poached the ram. It sounds like he may not have been aware of the rules. I feel sort of bad for him. If he doesn't hunt, he may not know all the rules surrounding a specific species. I hope he's allowed to simply learn from what sounds like an honest mistake.

Bachelor Herd

Now, I had no idea what a "plugged" skull was; so of course, I spent the next 20 minutes trying to figure it out. We have some Pronghorn skulls with horns, and I want to be on the right side of the law.

Plus, I like to know what I know I don't know. And I really like minutiae - details are everything. 


/insert 20 minutes of Googling here/

A plugged skull means that the Division of Wildlife has tagged it in a way that allows the skull to be recorded with the who/what/when/where/how details. It helps assure it wasn't poached, and tells the DoW a bit about the distribution of the animal, how it died, how it lived, etc. Usually, the plug is an aluminum thingy (it's a technical term, I swear) placed in a hole drilled into one of the horns. 

Yay, knowledge!

Bachelor Herd laying in a meadow. 
They walked right past us, as if they hadn't a care in the world.

The law doesn't seem to apply to Pronghorn, not that we would sell our mounts anyway. They were earned the hard way: getting up early, standing in the cold, trying to get close enough (which is still several hundred yards away) to take a shot. Track, clean, deliver to the butcher, pick up, tada! You're in flavor country Pronghorn country.

So, good to know, but it took at least 20 minutes to figure all this out. 

Whoever said the Internet saves time/effort clearly doesn't know me at all.

There are a couple of pictures of Rocky Mountain Big Horn Sheep (and Dan) a few miles from our house in a local park in this post. Taken a few summers ago, there were dozens of rams, and they calmly walked right past us on all sides, then nestled down in the meadow uphill a bit to snooze. I think this is what is called a bachelor herd, because they are all male (see the horns?). Until a male manages to start his own a harem of females (really, it's called a harem), they live alone or in bachelor herds. We didn't make any sudden moves, and they reciprocated by not goring us or stampeding. 

Bachelor Rams and Dan

Good times.