Infinity

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.

Newton's 

Philosophiæ 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.

solid figures by ppdigital,
by permission of MorgueFile^

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.

Six 6's by alvimann, 
by permission of MorgueFile^

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.

 peeling numbers by chelle,
by permission of MorgueFile^

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,

by permission of MorgueFile^

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:

lemniscate

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^?

Pythagoras

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!

Infinity!

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.

Namaste

deena

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. 

So...

/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.

Namaste. 


deena

The First Snow of Autumn

We woke up Saturday to cold weather and snow. Clementine was almost impossible to get moving. She complained about the cold and didn't want to get out from under the covers on our bed after I finished putting her hair up.

After ballet, we ran a few errands. Even after the snow stopped down here, we could see a storm up on Pikes Peak. Here are a few photos from around town...

From the parking lot on the way to the tire store. Dan needed new tires and I'd promised myself that we'd carve out time to get them by the end of the week. There is a snow storm on top of the mountain, and the snow is blowing from the top toward the north.

Snow storm with blowing storm at the top of Pikes Peak. It was dry, sunny and cold down here as we watched the storm. After 11 years here, I still find all of this simply fascinating and love to watch it unfold. 

What looks like the top of the mountain in the previous picture is really the top of the storm, as seen here. 

Later in the day, the sun is beginning to set. Taken at the end of Academy Blvd, in the parking lot of the grocery store. I think that we probably have the best view in the world from this grocery store.

Pikes Peak as the sun sets, with Academy Blvd. in view.

America The Beautiful was written after Katherine Bates in 1893. Bates was an English professor at Wellesley College, and was inspired after a trip to the top of Pikes Peak. She was spending the summer locally, teaching at Colorado College. You can certainly see where the line about purple mountain majesties came from, can't you?

I've lived all over the United States, and the sunsets out west, and particularly over the Rockies, stand out for their beauty and breathtaking color.

The last few moments of daylight... time for us to go home, have dinner, and happily snuggle together against the cold autumn night.

Namasté 

deena

Amused...

Just when I think I have a handle on the simplest things, Clementine cheerfully shows me that I'm not even close. She always manages to think of things I couldn't have predicted in a million years and I end up like this: 

Earlier today, we were reviewing her math lesson...

Me: So, remember talking about symmetry? How some shapes have symmetry, like hearts, squares, and circles? You can divide symmetrical shapes to get two identical parts. The parts will always be the same size and shape.

Things in nature have symmetry, like leaves and flowers on many plants.
(shows picture)

Me: Nature seems to like symmetry. Many insects have symmetry. They are the same on both sides. They are balanced so that they can fly. If they were unbalanced, heavier on one side, it would be hard to fly, wouldn't it?
(shows picture)

from here^, used with permission

Clementine: Yes. Ladybugs are the same on both sides, too.
Me: Yes! You're right. Many things we make have symmetry, like buildings and spoons. This is the Taj Mahal, in India. Look at the symmetry. Both sides are the same.
(shows picture of the Taj Mahal, and a spoon)

 from here, used with permission^

Me: People have a lot of symmetry. We have two eyes, one on each side. Two ears, one on each side. And our paired features are usually the same size, are in the same place, and are usually the same color. We usually have two eyes the same color and shape, right? We have two feet. Animals have two pairs of feet.

Clementine: Yes. except some people and some cats have different colored eyes. Like Dustbunny.

Background: Dustbunny was our cat, who passed away a few years ago. She had one blue eye and one golden eye. She was deaf and had a neurological malformation called CH - Cerebellar Hypoplasia^, which made her stagger and stumble). CH happens when the mother cat gets sick when she is carrying kittens. Distemper is a common cause.

Me: Right. Exactly. Most people and most animals have at least some symmetry. People and four-legged animals have an invisible middle line and mirrored features on either side of that line. That line is called the line of symmetry^. Your line of symmetry runs from the top of your head, through the middle of your nose, through your belly button, and between your feet. One side looks like the other in reverse.

Can you show me the line of symmetry here? Some of these figures have it, some don't. Ask me if you have questions. Okay?

Clementine: Okay. (draw draw draw)

Clementine's lines of symmetry

Me: Awesome! You got them all! Now, some figures have more than one line of symmetry. Squares, for example. You can go top to bottom, or side to side and get the same shapes which will be the same size. Can you find all of the lines of symmetry here? There may be more than just two.

Clementine: Okay. (draw draw draw, quickly finding all four lines of symmetry).

Clementine's four lines of symmetry in a square

Me: Awesome! Yay! There is a picture that people think of when they think of symmetry. It's called the Vitruvian Man by Leonardo da Vinci. Leonardo was was thinking about a book when he drew it, which is how the picture gets its name. The guy who wrote the book was Vitruvius, who lived in Ancient Rome.He wrote a book about using the measurements and symmetry in the human body to build buildings. Vitruvius is who the Vitruvian Man is named for.
(shows picture of Vitruvian Man)

Vitruvian Man, by Leonardo da Vinci

Clementine: (looks briefly at Leonardo's drawing): But he's not symmetrical, Mommy. One of his eyes is different from the other.

Me: (looking closely) I think he's drawn with a shadow that...

Clementine: He's like Dustbunny. Was he deaf? Did he wobble when he walked? Did his Mommy have bad tempers like Dustbunny's mommy? Do you think he was really moody?

Me: o.0

At this point, the questions are piling up and I have no answers. This is me, in cat form:

Huh?

After a few minutes, we get everything straightened out and we finish the review and move on.

• It's just a shadow, he does not have different eyes (at least, that's what I'm going with).
• I'm sure his Mommy was fine. Please don't worry. 
• He probably did not wobble because he looks really strong and healthy. 
• It's distemper, not bad temper. People don't get it (at least I hope not). Probably ought to look it up. She'll hold me to the answer.
• He is supposed to represent the perfect human, so he probably was not deaf.  

What a smarty pants cat might look like.
Image from an antique postcard

So, I survived another day with my little smarty pants and will live to be befuddled by her another day. 

And Clementine knows a lot about symmetrical shapes and cats with CH.

Not bad for a Monday.

Namasté

deena

We Shall Find Peace

photo by dpawatts^

  We shall find peace. 

We shall hear angels, we shall see the sky sparkling with diamonds.

Anton Chekov, Uncle Vanya

Namasté

deena

Sunday morning...

Sometimes the questions are complicated and the answers are simple.

Dr. Seuss

Namasté,
deena

This week is...

So much better.

Much less stress, so much more peace.

I want to thank everyone who sent a note or an email or called about Petey last week. It made a bad week not-nearly so bad.

Thank you so much.

I was looking through some photos tonight and wanted to share these, from a city park near our house. We go here for picnics sometimes, and always take out-of-town guests, as it is a great place to see wildlife.

These were taken after a heavy rainstorm, and sort of typify the past week for me. 

Namaste,

deena