Things To Which Emily Listens Politely: September 2016

This short essay was originally an answer to a question on Quora asked by some anonymous student. I think it is one of the best things I've written there, and is worth saving over here in a different format.

The question and it's context were this:

Which are the best method to convince a religious person of a fact proven by science? I told my religion teacher that in the first five weeks of development of a fetus, "we are all females" but she denied everything. How can I convince her to believe in science?

PS: I know that the Y chromosome determines the sex of a person and that only the appearance of a male and a female fetus is similar in the first five weeks.

(There's a little confusion in my response and the question because the questioner added the postscript while I was writing. I then edited my answer to account for that. You'll figure it out.)

Here was my response.

Science and Persuasion

Convincing anyone of anything through a single conversation alone is nearly impossible. It almost never happens. It is even rarer when topics get controversial. Do not expect to ever find a "magic bullet" for convincing someone that you are right.

That said, let me offer you three points of advice for scientific persuasion. They won't allow you to win any argument, but I doubt you'll find much success without them.

1. Get your facts right.

First, you must get your facts right: according to Sexual differentiation in humans and everything I ever learned in school, human sex is determined immediately at conception depending on the chromosome carried by the sperm cell. Thus, in a very fundamental way we are not all female until five weeks. That five week number is just how long it takes for fetuses to start developing sexually-differentiated organs.

If your whole argument depends on getting someone to accept the authority of science but you get your facts wrong you both lower your own credibility and the credibility of the authority of science in future arguments.

(I see you have edited your question details to note that you know this bit about chromosomes. If you know this, why do you think that your interpretation of what "female" means is the correct one? Why do you think your teacher's disagreement means she "doesn't believe in science"? This is crucial, and I deal with it in my third point below. In any case, the first point still stands in general.)

2. Use scientific reasoning, not appeals to scientific authority.

Science is not a collection of facts. It is a collection of observations together with interpretations and arguments about those observations. If you aren't able to make this distinction clear you will misrepresent the scientific process and your arguments will be less convincing.

Remember that it takes a long time and a lot of arguing before anything resembling "scientific consensus" is established. Most of the "facts" we learn today in school are the result of decades or centuries of extremely smart people disagreeing about observations until they reach a mutually agreeable interpretation. And even then sometimes new observations arise that invalidate the previous interpretation and the process starts all over.

As an example, let's consider the question of heliocentrism vs. geocentrism. That the planets go around the sun is now something "everyone knows," but it took the brightest minds of the renaissance about 100 years to convince themselves of this "fact." (Not to mention that the ancient Greeks argued about the same thing and couldn't agree.) And it took another 200 years after that to make observations that finally showed conclusively that the heliocentric model is inconsistent.

Do you know why these scientists came to the conclusion that they did? Do you know the observations and arguments that they made that eventually convinced them? Do you know what the evidence that rules out the heliocentric model is? Could you explain these arguments to someone who doesn't know them? If you try to convince someone of geocentrism without knowing all of this, are you really convincing them of science?

But if you can't explain the reasoning that supports a "scientific fact" then your argument will sound like "Well my priest says your priest is wrong, so you should listen to me." Even if you are ultimately right, you won't be able to make a convincing argument.

3. Make sure you are arguing about facts, and not interpretations of facts.

This is the most difficult point, but also the most crucial.

This is more difficult than it sounds because you may be arguing for an interpretation and think you're arguing for a fact. In your example, are you trying to convince your teacher that "fetuses do not develop sexually differentiated organs until five weeks" or that "fetuses are all female until five weeks (and therefore biological sex is not fundamental to human identity)"? These are very different claims and require very different kind of arguments! If you are not clear in your own mind what you are arguing, you will have a hard time convincing anyone of anything.

And even if you are certain what you are actually arguing, the other person may not be arguing about the same thing! What we call "facts" are almost always tied up with interpretations.

Imagine that we meet someone who wants to convince you that average African American IQ scores are 15 to 18 points lower than White Americans. My guess is that you, like me, have some immediate reservations about this person. Your first thought may be something like "Okay, but why do you want to convince me of this? Next you're probably going to try to convince me that blacks are inherently inferior to whites or some other racist claim." We may or may not dispute the immediate fact, but there are a whole lot of interpretations that are closely related to the fact that you strongly disagree with, and so hearing the fact puts us on edge. You may even be tempted to argue against the fact so that you don't have to argue over the potentially racist interpretations. If you do that, won't you look like "you don't believe in science?"

This sort of thing happens all the time! I highly recommend reading this blog post/research paper [1] about how often conversations and surveys that look like they are about science knowledge are actually about religious belief (or the lack thereof). It examines some large scale surveys of science literacy/religious belief, especially about evolution, and concludes that

"That work shows that there isn't relationship. What people say they “believe” about evolution is a measure of who they are, culturally. It’s not a measure of what they know about what’s known to science."

and

When subjects who are highly science literate but highly religious answer “False” to the NSF Indicator’s Evolution item, their response furnishes no reason to infer that they lack knowledge of the basic elements of the best scientific understanding of evolution.

and

For respondents who are below average in religiosity, a high score in “science literacy” predicts a higher probability of “believing” in “Naturalistic Evolution”—and so does a low score!

That is, when it comes to certain subjects, even if you think you are talking about "science facts" other people are talking about what they believe about religion. Even people who give the scientifically correct answer about these topics may not actually know anything about the science, but are telling you that they have low religiosity. (These, I suppose, are people who were convinced of scientific authority, but not scientific reasoning.)

This is very, very difficult to overcome. If you really want to convince someone of a scientific fact, leaving interpretation alone, you will have to put in tremendous effort to convince them of that. You must convey to them "I am not trying to attack your fundamental values. I recognize that there are many possible interpretations of this data. I really do just want to point out this scientific observation. I respect your values and interpretations, even if I disagree with some of them. If I can get you to agree to this scientific fact, I am not then going to use it against you to make your other beliefs look foolish."

This is hard. Maintaining trust in conversation when interpretations get controversial is one of the hardest tasks there is. It requires trying to really understand your conversational partner and their values. It requires asking lots of questions, and listening sincerely. If you assume that because someone disagrees with you that means they "don't believe in science" you have failed at this, and you will not find success until you can overcome this bias.

But it is possible. People can come together and learn from each other, and we should never stop trying. When we succeed, it is one of the peaks of human achievement. It is worth spending your life cultivating this skill, and I commend you trying to learn it.

Footnotes

[1] cultural cognition project - Cultural Cognition Blog - How religiosity and science literacy interact: Evolution & science literacy part 2

Boston Haikai 82 -- Seagulls fighting

A mid-air gull fight
Over a washed up oyster;
Autumn at the beach.

September 24 2016 -- Revere Beach

Boston Haikai 81 -- Island

The view from the shore
Makes a distant cargo ship
Look like an island

September 24 2016 -- Revere Beach

23 September 2016

Boston Haikai 80 -- Asphalt

Smells of the season,
Barbecues, freshly cut grass,
New asphalt baking.

September 23 2016 -- Mass Ave Bridge

21 September 2016

Boston Haikai 79 -- Food truck

Before the lunch rush,
A cook waits by his food truck,
Stretching on the curb.

September 21 2016 -- MIT campus

18 September 2016

Boston Haikai 78 -- Learn to code

In just thirty days,
According to this bus ad,
I can learn to code

Sept 18 2016 -- ?

16 September 2016

Boston Haikai 77 -- Sidewalk weeds

Up through the cement
The weeds have claimed some sidewalk;
Small yellow flowers.

September 16 2016 -- Sidewalk near a truck lot

Why is North North? Part 2, The Hairy Ball Theorem

A few days ago I wrote too many words about how north, south, east, and west are defined.

The purpose then was to answer the question of why you can't walk north forever, but you can walk east forever. The answer was that the definition of north/south has a "coordinate singularity", a point where the definition breaks down and can't uniquely name different directions, and also that walking north by definition leads you to the singularity.

We also saw that the east/west scheme has a coordinate singularity at the poles, but that east/west was conveniently designed to never lead you to the singularity like north and south were.

Then at the end I raised a question: can we do better? Is there a directional scheme we can choose for the earth so that there are no coordinate singularities anywhere? If so, what would that scheme look like?

Going abstract

To be able to answer this question we first need to think clearly about what constitutes a direction scheme. This concept may not be obvious, but it's pretty simple when you think about it. A direction scheme is a rule that points out a direction at every point on a sphere. Imagine arrows painted on every point of the sphere. When you stand at a point, wherever the arrow points is the direction associated with that scheme.

The direction scheme called "north." At every point there is an arrow pointing north. If you walk along the arrows you are heading north.

A hypothetical direction scheme called "crazynorth." Wherever you are on the sphere, if you walk along the red line there then you are heading crazynorth. We'd never actually use this scheme, but we want to consider all possibilities in general.

We'll also require that a direction scheme be smooth, that is it doesn't change abruptly at any point, because it would be confusing for your directions to suddenly switch just because you moved a millimeter.

A rule that assigns an arrow like this to every point on a surface is called a "vector field" by mathematicians.

One way to picture vector fields is to imagine that the surface in question has hair growing out of it that you then comb. Every hair has a corresponding arrow that represents whose size and direction represents how parallel to the surface the hair is. If the hair is completely flat against the surface then we draw an arrow with length 1. If the hair is sticking straight out of the surface we draw no arrow.

Hairs on a surface and how they correspond to arrows (or vectors) on that surface.

Singularities (again)

What does a coordinate singularity mean in the context of vector fields? In the last post we said a coordinate singularity is a point where directions are not defined. When we interpret arrows from a vector field as directions, we can see that the directions are undefined when the arrows have zero length (so you can't tell which way they point), or they have infinite length (because that's just not defined), or when the surrounding vector field isn't smooth and changes abruptly at a point (because at the point of change there are multiple definitions for the direction).

Two kinds of singularity. In (a) there is a point with a zero length arrow. In (b) there is a point of discontinuity, where the vector field changes abruptly. In both cases we can't use the vector fields to uniquely distinguish directions. (a) is the kind of singularity east/west has, while north/south has the type in (b)

Thus, the our question about finding singularity-free direction schemes becomes "can we find a smoothly varying vector field on a sphere that such that all the arrows are finite and not zero at every point?"

In terms of the hairy surface, a coordinate singularity then corresponds to a place where the hair sticks straight up.

Golly!

The Hairy Ball Theorem

(Try not to laugh too hard.) Now the best part. It turns out there is a definite answer to the question I just asked. The answer is no, it is not possible. Every smooth vector field on a sphere has at least one point where the the arrow has zero length. In terms of hairy balls, every time you arrange the hair on a sphere there will be a point where the hair stands straight up.

An attempted vector field with singularities that look like hairy cowlicks at the poles.

This means that any direction scheme we try to devise on the surface of a sphere will have a point where the direction is not defined! We will always have the same problem we had with the north/south, east/west direction schemes. There will always be points where our direction scheme isn't defined. The usual north,south,east,west scheme is the best system we can get.

I'm not going to explain how you prove this theorem, but it is very general. The Hairy Ball Theorem applies to spheres, but also any shape that is sphere-like (in the sense that you can squeeze it into a sphere shape without tearing any holes). So you also can't find a singularity-free direction scheme for an egg, or a banana, or any simple 3D object. It doesn't apply to other shapes though: it's easy to find good direction schemes on a donut, or on an infinite plane.

And the Hairy Ball Theorem doesn't just apply to maps and globes. It implies that it is impossible to design a radio antenna that doesn't have a blind spot. It implies that there is always at least one wind cyclone on the earth (because there must be a point with no wind).

The center of a cyclone is a zero singularity in a surface wind pattern

Electrical radiation acts like vectors on a sphere, so every antenna has a point with zero signal. Image courtesy https://de.wikipedia.org/wiki/Datei:Felder_um_Dipol.jpg

Math is cool, man.

Boston Haikai 76 -- I've got that pizza smell

The smell of pizza,
Pans clanging through a window,
Just before dinner

September 16, 2106

15 September 2016

Why is North North?

Why is north North?

My cousin recently asked an interesting question:

Why can you travel east indefinitely but you can only travel north until you reach the north pole?

As with all good questions, there are actually a bunch of good questions here all packed in together. As is my wont, I'm going to go way too deep, and hopefully come out the other side of this question with some answers. Chalk this up under the dangers of asking Luke a question.

What is North?

First, what is North, and why? How is that particular direction defined, and why is it useful?

The answer begins with a cool fact about rotations. Any constant rotation in three dimensions leaves an axis, or a line through space, fixed in place while everything else moves around it. Try rotating a few objects to see what this means. It's a law of geometry that this is so, and a law of physics that spinning objects prefer this kind of motion.

When objects experience constant rotation there is always a line through the object that doesn't move.

The earth spins (surprise!) and so there is an axis that is left fixed in space that passes through the center of the earth and picks out two special points where it intersects the surface. These two points are called poles, and we can use them to define directions.

Here's how the system works (it may be obvious, but I wouldn't be writing this if it weren't for pedantry): First name the two poles North and South. This is arbitrary as long as you keep them straight, which you can do using the fact that the stars look different in the northern hemisphere than in the south. Now at any arbitrary point on the earth, you can draw lines that directly connect that point and the two poles. Draw arrows on the lines that point towards the North pole. Now when you are walking towards the North pole on the most direct line you are walking North, and likewise for South. This is the definition.

How North is defined: at every point on earth, draw the most direct line to the north pole. The direction of the resulting lines is called North.

You might ask "how can I tell if I'm moving towards the pole if it is far away from me?" Good imaginary question! The answer goes back to the rotation of the earth. That fixed axis that has been useful also ensures that we can orient ourselves to a pole no matter where we are on the earth as long as we can see the night sky. If you look at the stars over a long period they appear to move because of the rotation of the earth. And the stars nearest the axis move the least. If you face the spot in the sky where the stars don't move at all then you are facing one of the poles. Useful!

A time lapse showing the rotation pole in the night sky. Courtesy http://www.eso.org/public/images/potw1534a/ via Creative Commons.

Even better, you can measure how far away you are from the pole with a pretty simple measurement.
Since the earth is a sphere you can measure locations with angles instead of miles or whatever. In particular, you might want to know the angle between your location and the pole. The diagram below hows how you can measure this angle simply by measuring the angle between the horizon and the pole spot in the sky.

You can find your latitude (how far you are from the North pole) by finding a pole star and measuring the angle it makes from the horizon.

All together, this is how North is defined, and why it is defined that way. (And I haven't even mentioned how the earth's magnetic field also runs North/South.)

Singularity (is a cool word)

If you've been practicing your pedantry you may have already noticed slight problem with the definition of North. There are two points on the earth where the definition fails. Since we defined North as the direction towards the North pole, North doesn't mean anything when you are standing at the pole! Also, since South is the shortest direction towards the South pole, every direction is South when you're at the North pole, so it's not defined either. Both poles have this problem.

A singularity is where a system of directions stops working. North and South both have singularities.

A point where a direction scheme fails like this is called a coordinate singularity. But note these singularities are not problems with the earth! You can cross the poles all you want. The problem is with the scheme we've defined for describing directions. You can go any direction from the poles or walk over them just fine, you'll just have problems describing what you're doing in the standard North/South scheme.

We'll come back to singularities later. But at least now you feel cool for reading something that legitimately uses the word singularity.

East!

Now that we've defined North, East is pretty easy. Face North, then point to the right at a 90 degree angle to the North/South line. That's it.

The direction East is defined at a point to be at a right angle relative to North at that point.

If, for some reason, you can't distinguish right and left, wait until night. When the sun rises in the morning, East is the direction that is perpendicular to North and points towards the sun.

Of course, this definition also has singularities. Because it is defined relative to the direction North, it fails anywhere that definition fails. So you can't go North at the North pole, and you can't go East either.

Are we done yet?

Now the original question, at long last! Both North and East have singularities where the directions become undefined. The difference between North and East is that North by definition leads you towards the singularity, while East by definition keeps you the same distance away. You can't go North forever because you will always eventually reach a point where North is meaningless. You can go East forever because you will never reach the singularity.

Can we do better?

One might ask if there is a better system, one that doesn't have confusing singularities so that all directions are defined everywhere. The answer is no, not really, because of something called the hairy ball theorem (seriously). But I'll leave that for another time.