Lensyl Urbano – Page 162 – Montessori Muddle

Jam algebra

I’d like to minimize the sugar content of the jam in order to see the most of the currant’s tartness. According to the FAO, you need to have about 60% sugar concentration in the final jam for good preservation. I’ve squeezed the currants and produced quite a bit of juice. I need to find out how much sugar to add.

To figure out how much sugar we need to add, based on the mass, we need to define our terms. Let’s say the amount of sugar is s, the amount of jam is j and the total mass, the sugar plus the jam, is t.

So the total mass is going to be:

(1) t = s + j

Since the amount of sugar needs to be 60% then:

(2) s = 0.6 t

If we substitute the first equation (1) into the second (2) we’ll have just one equation we can solve to find the amount of sugar:

(3) s = 0.6 (s + j)

Now we solve for the amount of sugar, s. Start by expanding the right hand side of the equation (distributive property):

(4) s = 0.6 s + 0.6 j

Next, isolate s on the left hand side of the equation by subtracting:

(5) s – 0.6 s= 0.6 s + 0.6 j – 0.6 s

Which gives:

(6) 0.4 s= 0.6 j

Now, get rid of the coefficient on the left hand side by dividing through:

(7) 0.4 s / 0.4 = 0.6 j / 0.4

To get:

(8) s = 1.5 j

So to have the right amount of sugar, I need to add one and one half times as much sugar as I have juice. So, if I have 2.0 kg of juice, then:

s = 1.5 (2.0 kg)
s = 3.0 kg

3.0 kg of sugar is a lot of sugar! However, if we boil the jam, some of the water in the juice will evaporate. Therefore, if we know how much sugar we want to add in we should be able to calculate how we need to evaporate to get the right ratio. More evaporation should also lead to a more concentrated flavors in the jam. Hmmm …

Jam tectonics

Boiling jam will often create a froth that floats on top, much like the granitic continental crust floats on the Earth’s mantle. Also like the boiling jam, the mantle convects (even though the mantle is not liquid).

The darker red areas in the image are where the convection cells in the boiling jam reach the surface and push the froth away. It’s a bit like the bulge in the Earth’s crust that occurs beneath hot-spots and the mid-ocean ridges.

Convection-snapshot — Model of convection in the Earth's mantle (image from Wikipedia)

Origin of life lab

ENSI has a set of great labs that can be used all the way from the middle school to the university level. They deal with the nature of science, the origin of life, evolution and genetics/DNA. (Thanks again Anna Clarke for the link.)

mid-Amoeba_movement.ogv — Amoeba (image from Wikipedia). This image is part of a neat video of amoeba movement.

I’m thinking that the Creating Coacervates lab, the only one on the origin of life section, might fit into my orientation cycle plans. Coacervates are small, microscopic blobs of fat (lipids) that look like, and have many of the same properties as cells, amoebas in particular. They can be produced with simple chemicals. One of the key things I’d like to start the year with, is the idea that:

complex life-like cell-like structures can be produced naturally from simple materials with simple changes. Flammer, 1999.

These abiotic blobs can be compared to the protozoans in a water droplet sample while we learn how to use the microscopes. It also ties into the Miller–Urey experiments that produced amino acids using electricity and simple compounds: water, methane, ammonia and hydrogen gas. The Miller-Urey experiments will pop up later when we read Frankenstein.

Oil does not come from dinosaurs.

phytoplankton — Phytoplankton (image from NASA).

There’s a nice article in the New York Times on the fact that oil, petroleum, did not come form dead dinosaurs, but rather from the microscopic plankton that died and fell to the ocean floor.

The idea that oil came from the terrible lizards that children love to learn about endured for many decades. The Sinclair Oil Company featured a dinosaur in its logo and in its advertisements, and outfitted its gas stations with giant replicas that bore long necks and tails. The publicity gave the term “fossil fuels” new resonance. – Broad, 2010

It’s easy to forget how pervasive is the idea that oil comes from dinosaurs. Broad’s article is a nice reminder that:

Today, a principal tenet of geology is that a vast majority of the world’s oil arose not from lumbering beasts on land but tiny organisms at sea. It holds that blizzards of microscopic life fell into the sunless depths over the ages, producing thick sediments that the planet’s inner heat eventually cooked into oil. It is estimated that 95 percent or more of global oil traces its genesis to the sea. – Broad, 2010

How do we know?

[I]n the 1930s. Alfred E. Treibs, a German chemist, discovered that oil harbored the fossil remains of chlorophyll, the compound in plants that helps convert sunlight into chemical energy. The source appeared to be the tiny plants of ancient seas. – Broad, 2010

phyto-bloom — Phytoplankton bloom off the Carolina coast. (Image from NASA).

We tend to find a lot of oil in the deltas of the great rivers because the rivers provide nutrients for the microorganisms to survive and layers of sand and clay sediments that trap the oil and natural when they’re produced.

The article also ties the location of oil production to the geography of plate tectonics.

[W]hen Africa and South America slowly pulled apart in the Cretaceous period, forming the narrow beginnings of the South Atlantic. Big rivers poured in nutrients. A biological frenzy on the western shores of the narrow ocean ended up forming the vast oil fields now being discovered and developed off Brazil in deep water. – Broad, 2010

Went fishing

We went fishing yesterday and one of us caught our first fish. I tend to dislike dissection for dissection’s sake, at least with middle schoolers, but I believe that cleaning fish is a practical life exercise everyone should have that accomplishes the same thing. There is also an ethical dimension for anyone who eats meat. I have no opposition to cleaning anything else if we’re willing to eat it.

So we’ll probably be cooking fish this year. There aren’t many places to purchase whole fish in Memphis so we’ll probably end up doing it during our immersions. An article on the ethics of vegetarianism might also make a good basis for a Socratic dialogue.

10,000 hours of deliberate practice

10,000 hours of deliberate practice is what it takes for great achievement. That’s a lot of time to put in on anything, especially if you’re constantly pushing yourself to improve, which is necessary for the 10,000 hour rule to work. You’d better be really interested in what you’re working on.

Michael Nielson has a slightly different take. He points out a number of people, like Werner Heisenberg who discovered quantum mechanics, who did not spend that much time on the specific subject. Instead, they had focused on broad background in subjects that they were interested in and were able to apply that expertise in one specific domain. So instead of dedicating 10,000 hours to on subject:

[P]ick a set of skills that you believe are broadly important, and that you enjoy working on, a set of skills where deliberate practice gives rapid intrinsic rewards. Work as hard as possible on developing those skills, but also explore in neighbouring areas, and (this is the part many people neglect) gradually move in whatever direction you find most enjoyable and meaningful. The more enjoyable and meaningful, the less difficult it will be to put in the time that leads to genuine mastery. – Nielson, 2010

However, he does point out that if you were really interested in a particular subject, like being a concert pianist, you should probably put in the hours.

cat-box — Heisenberg also came up with his famous uncertainty principle. (Image by Kahoun on Wikimedia Commons).

On having good conversations

Pissarro_Conversation — Conversation, c. 1881. by French Impressionist Camille Pissarro. (Picture from Wikimedia Commons).

[A]s a general rule, conversations about how people have or will interact are interesting, and conversations about objects are dull. So steer toward topics that involve human perceptions and feelings, and away from objects and things. – Scott Adams, 2010.

Scott Adams, the cartoonist behind Dilbert, has some good thoughts on having a good conversation and active listening.

You’ve heard of the Kevin Bacon game, where every actor is just a few connections away from Kevin Bacon. Likewise, you almost always have something interesting in common with every other person. The trick is to find it. As with the Kevin Bacon game, you’d be surprised at how few questions it takes to get there.