The Cell

Let's talk about the cell. The cell is the basic unit out of which all known life is built. It's a simple thing: a water (it's called cytoplasm, but it's 90% water)-filled membrane with a few internal parts that perform simple functions. 

onion cells

A cell is pretty simple, but if you get enough of them interacting the result can be very complicated and interesting  For example, your typical human is made of about 100 trillion cells. Each is about ten microns (0.001 mm) across. That's pretty small, but still pretty easily observed with a microscope (try it with a bit of skin or blood). Not everything in the body is made of cells, but everything you would consider living is. The enamel coating your teeth, or the keratin that makes up your fingernails are not cellular.

We are, obviously, made of many cells working together, but many living things get by as just a single cell. Bacteria, amoebas, and algae are all single-celled. The largest known single-celled organism is the xenophyophore. That's a mouthful but sorry, there isn't a laymen's name. That's because this thing is completely removed from the human experience. It's only found at the bottom of the earth's deepest oceans. In these depths, they are apparently abundant, but it's so difficult to get down there, and so much more difficult to retrieve something intact, that we know very little about them. What we do know is that the suckers can be almost eight inches across. 

That's a really big cell.

The Rule of 70

There’s a simple rule of thumb that gives the time it will take for something subject to compound interest to double in value. The time is 70 divided by the interest rate. So if the rate is 5% per year, it will double in 70/5 = 14 years.

This works because, as we discussed earlier, the effect of compound interest can be calculated by P’ = P * e^(r*t). 
In this case, P’/P = 2, 
so 2 = e^(r*t), 
ln(2) = r*t, 
t = ln(2)/r, 
which is approximately 
t = 0.69/r. 
r in that equation is in the decimal form. If we want the rate as a whole number R we can multiply top and bottom by 100 to get 69/R, 
but if you’re doing a quick mental check, 70 is close enough.

Center of Mass

The center of mass or center of gravity is the point in a rigid object at which it will always balance. It's very useful in physics and engineering because it turns out that it usually works in calculations to assume that all of an object's mass is concentrated at this point, the center of mass. This is much easier than accounting for each bit of the thing individually. For example, think of a book hanging over the edge of a desk. If you want to calculate whether it will stay put or fall, you have to consider that some of the book is solidly on the desk and contributing to stability while some is hanging over and trying to make it fall. In this case, you can either use calculus to sum up all the effects and see what prevails or you can consider a single point: the center of mass. If the center of mass is over the desk, it's stable, and if not, it falls.

There's an easy way to find the center of mass of a flat disk-like object like a plate. Hang it by some point and draw a line straight down from the hanging point. Now repeat from a different point. Those lines intersect at the center of mass. This would actually work with something that wasn't thin and flat, but you'd have to hang it three times, and you'd have to be able to draw planes instead of lines (which would not be easy)

Another trick works for things that are mostly one-dimensional. Maybe it's a hammer, or rake, or pencil, or something similar. You rest the thing on top of your hands, or preferably on just two fingers. You're not holding onto the thing. If you're successful so far, that means the center of mass must be between the two supports. Now, move your hand together. The hand farthest from the center of mass will have less weight on it, so it will have less friction, so it will move more easily. So the hand farthest away is always the one moving, so when they eventually meet it will be at the center of mass. Try it! 

Mathematically, to find the center of mass, you assign three axis to the thing (say x, y, z) at right angles from one another. Pick some arbitrary point as the origin. Now consider them one at a time. For x, sum up each bit of mass times it's distance from the y-z plane. Then divide that sum by the total mass and that's the distance of the center of mass from your origin. Repeat for the other two axis and you have the coordinates of the center of mass.

The Droste Effect

You've probably seen this before. An image contains itself, so that there’s a recursive chain of progressively smaller versions of the image until it’s vanishingly small. But maybe you didn't know that It’s called the Droste Effect, after the product depicted below.

It can also be found in the coat of arms of the Russian Federation above. Note that the eagle is carrying a scepter with itself on top.

The Categorical Imperative

In the philosophy of ethics, one of your classic heavy hitters is Immanuel Kant. This is the same fellow behind "I think, therefore I am" but today we're talking about ethics.  His take on ethics was not unlike his approach to existence; thought is the first and most important thing. He saw rationality as the most sound basis for building an ethical system. What's more, as rational creatures with free will, our first duty is to be rational and not impede the exercise of that free will. 

Ethics really just comes down to "what should you do." One approach is to target good outcomes. If what you do results in "good" things, it's a moral action. But this has dangers. Who decides what is good? And it seems like sometimes good results come from clearly immoral actions and vice versa. Kant figured it was better to judge ethical behavior by how well it adheres to ethical rules (this is called Deontology). And how do we judge whether the rule is ethical? We ask if it is rational, which we can take to mean logically consistent in a universal way. So you can follow whatever rule you choose as long as it would still make sense applied to everyone universally. For example, "Always pay your debts in a timely fashion." If everyone followed this rule that would be great, so feel free to adopt it as a guide for your own actions. On the other hand "A bit of littering is no big deal" fails the test. That may be okay as long as everyone else behaves better than you, but if everyone thinks littering is no big deal you quickly spoil your environment. This duty to live by universally consistent rules what what we call the categorical imperative. 

At this point you may say, "Uh, Kant, that's basically the Golden Rule. We've had that about since the origin of the species." There is definitely truth to this. The Golden Rule: "Do unto others as you would have them do unto you," seems very similar. A defender of Kant would point out that the similarity suggests we're on the right track, since the Golden Rule is one of our best common-sense ethical principles, but there are critical differences. The Golden Rule seems to be founded on a desired outcome. IF you want people to pay back their loans, THEN you should pay back yours. This takes us back to the outcome-based ethics and the associated weaknesses. The Categorical Imperative is founded only on logic and is thus thought to be more sound. 

The biggest consequence of the categorical imperative, to Kant, is that lying is always immoral. Lying is a prime example of something that only works if it is not universally taken advantage of. If everyone felt free to lie, we couldn't trust one another and lying would cease to be effective. Lying would seem to be doubly evil because it corrupts the other's free will. If you give someone false information, than their resulting actions are no longer entirely their own; you have taken some of that agency and pushed them to think and do what you wanted them to think and do. 

Like most ethical systems, you may find that it is less than helpful for some of life's more subtle and thorny problems. Most people judge it moral to lie under certain circumstances. And how specific can your proposed ethical law be? Could you say "It's okay for anyone listening to this awesome song and driving on this fun road in this sweet car to go way over the speed limit."? In any case, maybe it gives us a glimpse into how ethics and morality might work.

Chekhov's Gun

Chekhov's Gun is the name given to a certain storytelling trope. Coined by the playwright Anton Chekhov, in can be stated as "if a gun is shown on the mantle in the first act, it must be used in the second."

The idea is that in good, economical storytelling, everything is important. If something with large potential significance is presented (like a gun), that should be foreshadowing the later significant use of that thing.

Sometimes the rule is deliberately violated to throw the audience off track and surprise them later, but generally it holds.

"Excuse me, Egon, you said crossing the streams was bad."

Longer Words to the Right

Here's a memory aid I've found useful. Observe: The longer word always indicates the one on the right.

Left vs. Right 
Port vs. Starboard
Red vs. Green lights on a boat or plane
Fork vs. Knife and Spoon 
Hot vs. Cold water tap

The Wobbling Table

There is a very simple fix for a wobbling table: rotate it.

Sometimes a table needs to keep the orientation it has, but if you're free to rotate it, give it a try. It's amazing how often it works. In fact, under certain conditions (all legs equal, table symmetrical, no steps in ground) it has been mathematically proven to always work.

My favorite intuitive proof that this works goes like this:
Think of how a four-legged table wobbles: Two diagonally opposite legs are in contact with ground and it wobbles between the other two. Call the legs a, b, c and d. To start with the table is wobbling between a and c. now rotate the table 90 degrees. Now b and d are where a and c were, so it’s wobbling between b and d. At some point between these two states, it had to transition between the two wobbles, so at that point there was no wobble at all.

Zeno

I'm a great fan of paradoxes. A paradox uses a rational argument to arrive at an impossible conclusion. The point, I think, is not to prove that the conclusion is wrong. The wrongness of the conclusion is a requirement to be called a paradox. The point is to find the flaw in the seemingly rational argument, to think deeply about the subject, and maybe in a way you haven’t before. The result may expose flaws in our assumptions and improve the rigor and depth of our science and philosophy.

Probably the most famous set of paradoxes are the three known as Zeno’s paradoxes.

1. Achilles and the Tortoise - Achilles and a Tortoise have a footrace. Obviously, Achilles is going to give it a head start, but then he’s off! Soon he’s reached the spot where the tortoise was when he started, but by then the tortoise is farther along, and by the time Achilles reaches that spot the tortoise has gone further still! It seems he can never catch up!

2. The Dichotomy Paradox - A similar situation: in order for you to go from point A to point B, you must first go half way. Then you must traverse half the remaining distance, then half of that distance and so on forever. It seems you can only approach, not reach, your destination.

In fact, can you ever get started? to make it to that first half way point, you’d have to go half-way there...

See Meg Ryan in IQ.

3. The Arrow Paradox - Pick a point in time where an arrow is flying through the air. At that moment, the arrow is not moving. Well, we could pick any moment of the arrow’s flight and observe the same. If at every point in time the arrow is not moving, how can it get from point A to point B?

These have been very stubborn and resisted satisfactory explanation for thousands of years. We've since developed mathematical tools like calculus to deal with infinite quantities of infinitely small things and get results that make sense, but providing an alternate explanation that works is not quite the same as showing what was wrong with the original paradoxical explanation.

It may be that relatively new ideas in physics show us something that may be wrong with Zeno’s assumptions. It looks like space can not be divided into arbitrarily small pieces.

For example, the idea of the Planck length. If the distance in the Dichotomy paradox is one meter, after about 116 half-way trips, the distances you would be traversing would be so small that the type of Newtonian  linear motion we’re talking about isn't valid anymore and quantum effects dominate. 

Also It looks like an arrow, on a quantum level (you may notice philosophy often vaguely waves it's arms and mutters something about quantum when it's in trouble), can not be said to be frozen in place with no motion at a point in time - you run into the Heisenberg Principle. At a point in time, there’s a limit to how precisely you can know the position and speed of a thing, so maybe Zeno can’t assume that it’s not moving at that point in time.

Monty Hall

The Monty Hall Problem, sometimes called the Monty Hall Paradox, is a fascinating demonstration of how counter-intuitive statistics can be.

As the name suggests, the scenario plays out something like a game show. Say, with thanks to Frank Stockton, an eccentric ruler has arranged for you a game a chance and wit. You must pick and open one of three doors. behind one is a fair maiden to marry, behind the others, tigers. Pick one. But before opening it to discover your fate, the ruler indicates one of the doors you didn't pick that hides a tiger and asks if you would like to change your guess now that you've seen one of the tiger doors. Switch or stay?

Intuitively, it seems that whether you stay or switch, your chance is the same. Two doors and two fates: 50/50. But in fact that's not the case.

As it happens, switching as a strategy is twice as likely to be successful. Think of it this way: the only way to lose by switching is if your initial guess was correct, 1/3. Therefore, the odds of winning by switching are 2/3.

The Bechdel Test

The Bechdel Test is a tool we can use to think about how women are (or aren't) represented in movies. It sets some simple bare minimum requirements that should be easy to fulfill and leaves it to the reader to think about how many of their favorite movies manage to fail it.

The questions:
Does it have two or more named female characters.
Do they talk with each other at some point.
Do they talk about something other than a man.

For example, here are the ten top grossing movies and how far they make it though the above questions:

1. Avatar - Only talk about men 
2. Titanic - Pass 
3. The Avengers - They don’t talk 
4. Harry Potter and the Deathly Hallows - Don’t talk. 
5. Transformers: Dark of the Moon - Iffy pass (this can be a bit subjective) 
6. Lord of the Rings: Return of the King - Don’t talk 
7. Skyfall - Iffy pass 
8. The Dark Knight Rises - Don’t talk 
9. Pirates of the Caribbean: Dead Man’s Chest - Barely talk, and about man 

Toy Story 3 - Barely Pass So, if you're being generous, that's 4/10. Easy as the test is, you may not be feeling very charitable. In that case it's 1/10.

Of the AFI Top 100 films, it comes out to 32/100.

See also the Finkbeiner test for science journalism. Stories about female scientists tend to focus a bit too much on the fact that they are female.

The Globe

Some interesting things about a sphere, like the Earth (approximately¹)

• The "Hairy Ball"² theorem tells us that for something that can be modeled as a continuous³ vector⁴ field, like the wind, there must be a point on the globe where the value of that field is zero. Which is to say: somewhere, at this moment, there is no wind.

• For a scalar⁵ field on a globe, like temperature, there must be two antipodal⁶ points with the same value. So somewhere, two points on direct opposite sides of the earth have the same temperature.
• For any five points on the globe, there is some view of the globe that shows four of them.

¹ The Earth is a slightly "squashed" sphere, and not perfectly smooth, but close enough.
² Great name, right? Think of a ball densely covered with hair all over, no matter how you comb it, at some point it's sticking straight up.
³ Continuous meaning no "jumps" from one geometric point to another. Note that these points are infinitely close together, so you can still get some very dramatic changes from place to place. It's reasonable to assume the wind is continuous.
⁴ A vector is a magnitude and a direction at a point. Like, "At this spot the wind is blowing 10 mph south-west."
⁵ A scalar is a name for something that just has a magnitude and no direction at a point, as opposed to a vector.
⁶ Antipodal, points on a sphere across the center from one another.

Learning to Walk - 2

When walking with a group, consider that others may need to pass (in either direction) and don't take up the whole sidewalk.

Like these guys

Energy

Energy is one of the most powerful concepts in physics and can often be a simple and basic way to understand a phenomenon because of the following:

1. Damn near everything can be expressed in terms of energy, so it can be used as a currency to compare and equate very different things. 
2. The total amount of energy never changes. If one thing loses energy, something else must have gained it. 

Consider a classic example:
it takes energy to lift a ball some height against gravity, and the amount of energy required can be calculated (e = m * g * h).
It also takes energy to change something’s velocity (e = 1/2 * m * v²)

So, knowing these two things you can both determine how high a moving thing will rise before coming to rest and determine how fast a thing will be moving once it falls a certain distance.

Suppose that falling ball bounces. You’ll see that it does not rise quite to the height from which it fell. This way we know that there’s energy to be found somewhere. What you’ll find is that the ball and the surface it bounced off of both heated up a very small amount. (that's why this works) Maybe the surface dented, that took energy. There’s also the sound of the impact and some stirring of the air. These all have an energy equivalence and together account for the ball eventually coming to a rest.

So when you walk, don’t scuff your feet. You are using extra energy to generate the scuffing sound and to wear off bits of sole.

Dirt

How much do you really know about the dirt beneath your feet?

First, when in a scientific or engineering context, we call it soil - just one of those things.

Second, soil can behave in some interesting and complicated ways, mainly because it is a mix of solid, liquid, and gas: minerals and organic materials, water, and air.

The mineral (rock) portion of soil is generally broken down by particle size, because particle size has the biggest effect on how they behave. How big the particles are is just how finely the original rock mass has been weathered down by erosion and other forces.

Boulders	On the scale of a refrigerator	Unsurprisingly, behaves much like solid rock
Cobbles	Think softball or melon	Mostly found in transition zones mixed with other types. What types they are will mostly determine behavior.
Gravel	About an inch, like you see on a path	Relatively strong and stable. Large void spaces between grains makes it very easy for water to flow though. Good for drainage.
Sand	About a millimeter, like on a beach or sandbox or sandbag	Similar to gravel, but smaller size makes it susceptible to acting like a liquid when saturated and under certain conditions
Silt	Micron scale, think milled flour	Like clay, but not as extreme
Clay	Very small, around smoke particles	At this scale, things act in strange ways. When dry, it could float in the air heedless of gravity, or be part of a hard mass of stone or pottery-like material. At various levels of liquid content it can dramatically shrink or swell. It can be sticky, but it can also be very useful as a lubricant. It will aggressively soak up water, but once filled can serve as an impervious barrier.

Clay will shrink dramatically when it dries and swell again, with water.

Typically, the coarsest soils will be deepest, with finer soils closer to the surface. So, if you were to drill down, you will likely find a series of layers of similar material.

1. First, perhaps some soil with lots of organics in it. This is usually dark in color. At the extreme, you'd call it potting soil. Contains things useful for life: decaying plant and animal matter, bugs and worms, roots, etc. This is what people really think of as "dirty." This is usually rather shallow, some feet, or nonexistent.
2. Next silts and clays. Often mixed with sand. This layer can be over a hundred feet deep, but is usually much less, or nonexistent.
3. There is almost always a layer of sand and gravel, usually with some clay and silt content. Could be anything from zero to hundreds of feet thick.
4. Then a transition mix from sand, gravel, and cobbles to boulders and solid rock mass. This is always down there somewhere. In the mountains it's often the surface.

Remember there is space between all these particles of rock of whatever size. Water can reside in and flow through these spaces. Almost anywhere you are standing over water. The depth where you can find it is called the water table. That depth is not uniform, so the water underground is always flowing from higher to lower areas. Think of a surface river. Much of that water is flowing over the surface, which is what you see and think of, but much is also soaking down into the ground. So at the edge of the river the water table is at zero depth, and water is flowing down toward deeper areas. Also water in the ground at high elevations (say in hills or mountains) is flowing down toward the valleys, rivers and oceans. 

Have you ever wondered how a river continues to flow so long after a rain? It would seem that all that water hits the ground at the same time and should rush off down the hill in a torrent and be gone. Well, most of it actually goes down into the ground. Then, underground, flows very slowly toward the river and downhill. The rain soaks the soil, and the soil feeds the river over days and weeks.

Wells work on a similar principal. You send a shaft down below the water table and the water in the surrounding soil flows into this hole you've created until it's full up to the level of the table. Then you can take water out of the hole and it will refill. 

Compound Interest

One bit of math that everyone must reckon with is compound interest.

You have some money, you earn some interest, that interest gets added to your money, then you earn interest on your money and your previous interest. Good news if you're lending, bad news if you're borrowing. Either way, you should know what you're in for. This is how you calculate it.

P' = P * (1+r/n)^(t * n)
Where
P is the principal, what you start with
P' is how much you end up with after interest has accrued
r is the interest rate, expressed as a decimal, so 4% would be 0.04
t is the amount of time you're considering
and n is where this gets interesting

n is the number of times the interest will be compounded per unit time. So if the interest rate is 4% per year, and you're compounding twice per year, n is 2. If n is assumed to be infinite, the equation turns into

P' = P * e^(r * t)
where e is Euler's Number, 2.718...
I find that form easiest to remember 'cause it spells Pert.

It may seem absurd to take such a thing to infinity, but as you can see above, the result is actually a simpler equation. It also makes sense when you consider that in a real account deposits and withdrawals may be made at any moment. Continuous compounding works on the moment scale.

Einstein may have called compound interest the most powerful force in the universe. But it really is a force of nature. Consider population growth. If the population grows at some rate, the added members of the population will soon be contributing to the growth. This is compound interest. Obviously death, availability of resources and age of maturity temper the effects, but the concept applies.

Irreducible Complexity

One popular argument in favor of intelligent design is the idea of irreducible complexity. The idea is that certain biological systems are so complicated and interdependent that a piece-wise  incremental development of the type evolution suggests is not possible. The most common example given is that of the eye. The eye is a fantastically sophisticated sensory organ and we with all our industry have not yet matched it, but is it irreducible? No, of course not.

The short argument is that you probably know people with less complicated eyes: the colorblind. Colorblindness is an example of what happens when you remove one of the parts of the eye (in this case one of the three types of cones). These eyes work just fine and have been reduced in complexity.

We can take it much further though.

• Suppose we removed all cones. Now you see in black and white - still very useful.
• Remove the ability to swivel the eye. Now you must move your head around to look - fine.
• Now we remove the ability of the iris to adjust the pupil size. Now you don't see as well in low or very bright light, but that's not bad.
• Remove the ability to adjust focal depth. Now things near or far are fuzzy, but these are still eyes you would be glad to have.
• Remove the lens entirely. Now everything is fuzzy, but you can still tell if a predator is pouncing toward you.
• Remove the eyeball itself, leaving rod sensors in a depression on your face. You now collect less light and lose more focus, but some sight remains.
• Remove the indentation. Now it's just light sensors on skin. The sensors are less shaded so you get more noise and less sensitivity and protection, but they still work.
• Simplify the rods to just cells slightly reactive to light. You still know if it's daytime - that's something.

Learning to Walk - 1

Let others out before you go in. This applies to: elevators, train cars, buildings, and anything else with a finite capacity.