Thalweg sent me a canister of freshly-made peanut butter from the Safeway at the corner of Taft and Drake in Fort Collins, CO. She sent it priority in case it could go bad. It is the most incredible peanut butter I have ever eaten. She wrote an ode to it, and after I tasted it I wrote an ode back.

I will reproduce the odes here:

Thalweg:

Though your brown cast is at first unappealing
Deep pleasure is your color concealing
If a synesthete were I
My spirit would fly
For a seraphic concerto I'd be hearing

Zanzibar:

In the mail did treasure fly,
"Ambrosia!" was the Herald's cry
To kitchen's tower she made her haste
To pleasure her tongue with love's first taste
And at once the nectar did her senses besot
Skippy and JIF her soul forgot
Such joy and rapture could not be relayed
If the Heavens were of peanuts made!
Such luscious truth the prophet bespake
Of the holy corner of Taft and Drake.

Srsly. Go there. Honey-roasted peanut butter. You will never be the same.

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"Print out this page for me," he instructed.
I printed out the page and he fetched it from the copy room. He set the paper down on the table and pulled up a chair, brandishing his red pen. I could hear the scritch-scratching of the marker on the paper. For a long time. Much too long. I glanced at him out of the corner of my eye.

"I'm not writing a novel," he said, reading my thoughts. He brought the paper over. A small change, and a long sentence tacked on the end of the conclusions that snaked across the page and sideways down the margin. I read the sentence and rejected it, explaining why. He frowned and started scribbling out the handwritten red sentence. Then he grabbed the paper and violently crumpled it up. Almost as quickly he put the paper on the table and smoothed it out again. He handed it to me.

"I still want you to make this small change."

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Life is difficult. Life is mostly difficult because there are so many possibilities and you only have a limited amount of time to explore them.

For example, what am I going to do in the next two years?

Should I take a bunch of classes and try for the Engineering Masters?
Should I try and study in France for a semester?
If I weren't going to Antarctica, I could probably do both... but I'd much rather go to Antarctica!
Should I write about radar or water coming out of volcanoes?
Induration hypotheses or lava properties?

After I graduate, (aged 27) the road forks again:
Post-doc in Paris studying Martian climate models?
Post-doc in Maryland studying brand new images coming down from the Mercury mission?
Job paying me lots of money at Exxon?
Post-doc studying volcanoes at the New Zealand Volcano Observatory?
Post-doc at the Smithsonian in Washington D.C. studying Mars?
Post-doc at the Southwest Research Institute studying Mercury?
Post-doc at the Desert Research Institute in Reno studying wind?
Fellowship studying desert processes at some Asian university?
Peace Corps/Michigan Tech program fighting volcanic hazards in poor nations?
Post-doc in Southern France dividing time between studying volcanic ash and going to Antarctica to collect it?
Move to New Zealand with no plan for employment at all?
Work at a hostel in northern France, learning French?
Teach English in South Korea?
Or my newest plan: Write a grant to study inverted topography at the University of �r�mqi!!!

The post-doc positions are each 1-2 years, so after that (aged 29) my path would branch again:

Space Research Institute Staff Scientist
University Professor
NASA Scientist
Exxon Scientist
DARPA!?!?!
Astronaut!
National Oceanographic and Atmospheric Administration Scientist
Museum Curator
National Center for Atmospheric Research Scientist
--Something having to do with fluid mechanics or engineering--

An old advisor of mine used to say:

"Some geologists study the Northern Shield of Canada, horrible, cold, mosquito-infested places.... me? I study the Galapagos Islands. Why? Because somebody has to study paradise, and it might as well be me."

This has been my philosophy for everything since. After all, somebody has to do my dream job..... it might as well be me.

And then there is the whole question of settling down in the Midwest and getting married and having a bunch of kids...

How many eligible bachelors are there in �r�mqi?

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The journey of water molecules from snow to ice is not always a linear one.

Imagine a stack of spheres. You drop all of the spheres haphazardly into a pile, and then shake them around a little bit until they settle into their lowest energy state-- that is, they achieve "perfect packing". Perfect rhombohedral packing, to be exact.



The story is much more complicated with snow, you see, because a snowflake is about the furthest shape you can get from a sphere.



As snow falls into a pile, the snowflakes on the bottom are put under pressure from the ones above. They are also insulated from the cold surrounding atmosphere by their mates. At their spindly edges, the snowflakes begin to buckle, break and deform, becoming more like spheres. They settle slightly due to gravity, eliminating large empty spaces. They also start to melt just slightly, especially at the pointed edges. They call it "cintering". Over time the snowflakes are cintered and deformed until they form a kind of snowflake lattice, where all of the snowflakes form the walls of cavities filled with air. Eventually these cavities break or shrink, putting greater and greater pressure on the air. Air is a gas and eminently compressible, so it shrinks and shrinks in volume along with its shrinking cavity. As the layers of snow build up above, the layers at the bottom are under so much pressure that the air pockets close.

Unable to escape, the air is forced to somehow become a part of the molecular lattice of the ice. One way to do this is to dissolve, sometimes splitting into component atoms and existing in the empty spaces between atoms in the ice lattice. The other way is to squeeze into cage-like molecular structures called "clathrates". Clathrates in this case are a collection of water molecules that form a cage around an empty space. All kinds of molecules can find their way here such as methane, sulfur species, or air.

Climate scientists often attempt to use the bubbles trapped in the ice as a measure of what the atmosphere was like when the bubbles were closed off from the environment way back when the ice was still made of snow. In this technique you are limited to snow that hasn't completely become ice yet (it is called "firn"). In order to get at the climate of times long long ago, climate scientists investigate the atmospheric gases trapped in the clathrate structures.

Both of these techniques are very clever, but the fact that air comes in and out of the firn quite a lot during its compaction into ice means that the resolution on the exact date of that atmospheric composition can sometimes be shockingly bad. After all, it can take 80-90 years for snow to become ice, and all that time the firn is interacting with the atmosphere and smearing out the atmospheric signal. In one case at the Russian base in Antarctica (Vostok), the date at which the atmosphere was trapped has an error bar of up to 490 years! The exactness of the ice dates is directly dependent on the accumulation rate of snow at the site. If new snowflakes and atmospheric bubbles are buried very quickly, they will turn to ice more quickly and the smearing effect will be less. If the accumulation rate is slow, the snow and firn will sit there circulating atmosphere in and out of pore space for hundreds of years, smearing out all of the climate signal during that time.

For more information, see the awesome book by Paterson, 1981 The Physics of Glaciers

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"Yes"
"No"
"Yes"
"No"
"Yes yes yes!"
"No No No!"
"Yes times infinity!"
"No times infinity to the infinity!"

Have you ever had this argument? Probably most of us has. It is possible that at the time we sat and pondered exactly how much infinity times infinity was, and if it were really possible to add infinities together or take infinities to the power of other infinities. What does infinity really mean, anyway, and can we ever hope to wrap our minds around it?

It is also possible that some hitting and kicking and punching and pulling of hair ensued, though whether this was an outgrowth of the fundamental frustration of the human mind to conceive of infinity, I cannot say.

So there are several different kinds of infinity.

Imagine the natural numbers, let's say, "1, 2, 3, 4, 5...etc." They go on into infinity, non?

But let's imagine the rational numbers, that is, numbers that can be represented using fractions, like 1/2, 1/3, or 7/22. How many of those are there? Also an infinite number!

But despite the fact that the rationals and the naturals are infinite in number, we say that they are also "countable". How can something be infinite and yet countable? Well that depends on your definition of "countable". Sure, you could never count to infinity in your lifetime or an infinite number of lifetimes. But on the other hand, everyone can start counting to infinity in the natural numbers and be absolutely certain that they aren't missing any. 1, 2, 3, 4... there aren't any natural numbers between 1 2 3 or 4 that you would be missing. In the same way you could count the rationals, making a grid where you had 1/1, 2/1, 3/1, etc. going horizontally and 1/1, 1/2, 1/3, etc. going vertically and you could ostensibly get all of the rational numbers in existence, because after all, the rationals are just combinations of the naturals. You would probaby get an infinity on the order of infinity times infinity. It would still be countable: you could start counting up rationals and be sure you aren't missing any.

However, if you made it your goal to count the real numbers, you would immediately run into a big problem. What problem is this? Well imagine we wanted to begin by counting up all the real numbers between 0 and 1. We could start with 0.01, and then go up to 0.02. But if we did that, we'd be missing all the numbers like 0.001 or 0.0000001 or 0.0000023343434 that lie between 0.0 and 0.01 and 0.02. In fact, between any two real numbers, there exists an infinite number of real numbers, because you could just extend those decimal places out as far as you like, in whatever combinations you can imagine, making however many numbers as you like between 0 and 1. This, to be sure, is a new kind of infinity. This is an uncountable kind of infinity, and as you may have guessed, its magnitude is far greater than the normal kind of infinity that you just imagined when we were counting natural numbers or rational numbers.

Mathematicians, thinking of this idea for the first time, decided to differentiate between different magnitudes of infinity. They called infinity after the Hebrew letter "aleph". For the regular old type of countable infinity, they chose the term Aleph-Zero. Most types of infinity that one encounters fit into this term. Even if someone made some kind of proclamation like, "Infinity times infinity" or "infinity to the infinity", they would all still fall under the countable kind of infinity of Aleph-Zero.
Even when we discuss the number of real numbers, we can say that the number of digits available to use for each number is Aleph-Zero, because we can say that there is one digit, there are two digits, three, four, and not be missing any in between. But each one of an infinite number of numbers can have Aleph-Zero digits, so we know we are dealing with a much larger form of infinity.

The number of real numbers fits under the term Aleph-One.

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A geologist friend of mine got to actually go to Zanzibar. How unfair is that?

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Now that I had become suddenly sensible of the fatuity of the hopes I had begun to cherish, I suffered not merely what another lover might, but in addition a desolate loneliness, an utter forlornness, such as no other lover, however unhappy, could have felt.

---Looking Backwards, by Edward Bellamy

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