Christians, read your Bibles

Now is a good time to think about new year's resolutions. It's an often maligned tradition, given how often they're broken or forgotten. But I do think that it's helpful to plan ahead on the time scale of about a year, and New Year's Day is as good a time as any to do that.

And I cannot think of a better resolution than to read the Bible.

It's nearly impossible to overemphasize how important this is: if you want to know God - if you want a direct line of communication with him without filters like the predilections of our culture, the distractions in our preconceptions, or the follies of our time - then go straight to the source. You want to pray more this coming year? The Bible will tell you how to pray. You want to be kinder and more spiritually attuned? The Bible will show you how Jesus treated people and what spirituality looks like. You want to be a better Christian, or grow closer to God? Reading the Bible is probably the most tangible thing you can do that will return the greatest results.

Seriously, if you believe in God, and believe that he wants to communicate with us, how could you not read the Bible? The creator of the universe wrote down the things that he wants you to know in a book, and you're NOT going to read it? How could you then call yourself a Christian? What then do you mean when you say you believe in God, or want to be in communication with him?

I realize I sound pretty legalistic there - maybe it sounds like I'm saying "you're not a Christian unless you've read a certain amount of the Bible". But you know what? I think I can live with that. I think reading the Bible is that important. For the record, I'm not a legalist (Don't fall into legalism, it's bad - like, really bad), but I'm perfectly willing to bear some false accusations if it'll better emphasize how important it is to read the Bible. Again, for the record, it's not the reading of the Bible that makes you a Christian, but God's unconditional grace working through your faith in his Son Jesus Christ. But guess how I know that, or that legalism is wrong? That's right; by reading it in the Bible. And it would be a peculiar person indeed who did have that grace working through faith and yet did not think the Bible worth reading.

I've sometimes wondered if there is a simple formula to making life work out. Like if all you had to do was wake up at 7am each morning, or just run a mile every day, and everything will just come up roses. Needless to say, I haven't found anything like that. But, I do find that reading the Bible often - daily, if possible - comes closest to this nonexistent magical procedure.

Reading the Bible in a year is a popular New Year's resolution, one that I fully endorse. There are a number of things that makes this well-suited for a New Year's resolution: first, it seems challenging, but it's actually quite doable. The overall length of the Bible is no excuse to not start. The Bible is far shorter than many other book series (Harry Potter, A song of Ice and Fire, etc). It's typically about a thousand pages long. You might've read more while cramming for a final for a single class. If you really wanted to, you can probably get it all done in a very long weekend. If you want to tackle it daily, it only takes about ten minutes a day. Think of all that time you spend before you go to sleep, reading pointless internet drivel on your phone or tablet. You can easily spare ten minutes a day out of that time. In fact, if you're in bed and you haven't read your Bible today yet, stop reading this post. Pick up your Bible and read it instead. Believe me, it's a far better use of your time. Why are you still reading this?

Well, I suppose you've already read your Bible for today. So then - here's the second reason that reading the Bible in a year is well-suited for a new year's resolution: your progress is tangible. At any point in time, you can say, "I've read this much of the Bible". On any given day, you can say "I've done my Bible reading for today". Again, this should not fuel legalistic impulses, but being able to track your progress does give you a greater likelihood of keeping to your goal and completing your resolution.

Third, the benefit is immense. There is nothing like the timeless truths in the Bible to correct the follies of our attention-deficit culture. There is no medicine like a verse that you don't understand - or better still, disagree with - to cure us of our tendency to imagine God in our own image. And finally, how else will you get to know God? Where else will you go for a direct record of what God has actually said and done?

So, read your Bible. I hope you have a happy new year - one where you grow in your relationship with God, through a deeper communication with him and a more intimate knowledge of what he has said in his word.


You may next want to read:
Key principles in interpreting the Bible
Make the most of your time and your life. Number your days.
Another post, from the table of contents

Christmas and time

I've previously discussed how long ago the universe began. Now, if the universe were purely physical, then this would be an one-dimensional question with a simple answer. But because of the depth and purpose expressed in the universe, multiple answers are possible, some more meaningful than others.

To see what I mean, let's look at a movie for an example. I take it that if you're here on my blog, you've seen Disney's "Frozen"? If not, go watch it - it's a good movie. Now, to the question: when did "Frozen" begin? One might answer that it starts when Elsa and Anna were kids, with the "Frozen Heart" song being sung by ice harvesters in the distance. Or, one might note that the oldest event referenced in the movie is the previous time someone was struck with ice powers, mentioned in the troll book. Or you can say that the movie itself was released in 2013. Or you can cite that development first began way back in 1937, when Walt Disney himself wanted to make a movie based on Hans Christian Anderson's "The Snow Queen". Or you may choose the publication date of "The Snow Queen" itself, back in 1844.

But, if I had to choose a moment in time for the "beginning" of Frozen, I would perhaps choose when "Let It Go" was composed. While this song was originally written for a villainous Elsa, it expressed such a relatable and sympathetic side to her that they had to re-think her whole character, giving us our Elsa as we know her. So it came to be that while "Let It Go" expresses Elsa's possibility for damnation within the story, it also turned out for her salvation in the story development.

This made Elsa the most memorable and human character in the movie, whose struggles and redemption infuses the whole film with that human element that makes "Frozen" what it is. Elsa, and therefore "Frozen" as a whole, cannot exist as they are without "Let It Go". That is why I say that if I had to choose a time when "Frozen" began, it began with the composition of that song.

Here's another example, this time from J.R.R. Tolkien's literary works: "The Silmarillion" tells the back-story of "The Lord of the Rings", starting with the creation story. In the beginning, Eru Ilúvatar - the One Father of All - creates the world with the great music of the Ainur. And yet, for a while, the music only remains music, or a vision, or a plan; it is not yet real, although it encodes all the events in all time for that universe. So Eru kindles the music with his Imperishable Flame, his Secret Fire, the one that is with Eru alone. It burns at the heart of the world, and that, finally, creates the World that Is. That is when that universe began.

What about our world? When did the universe begin? You can say that it started with the Big Bang, when the universe physically began about 13.8 billion years ago. You can say that it started when God breathed life into Adam, who's often thought to have lived about 6000 years ago. These are not wrong answers. But I do think that there is a more meaningful answer still.

What is the purpose of the world? The world exists by, for, and through Jesus Christ. It was created to allow Christ to be incarnated into it, so that he can carry out his eternal plan of salvation through it. Jesus truly is the Creator and the Firstborn over all creation; for without him, nothing would exist, and there is nothing that exists ontologically before him.

So that is the significance of Christmas day: it is when God himself sent his Son into the universe to make it real. All other times, all other events, and all other things - both forwards and backwards in history - orient themselves with respect to the Son of God and are made real by their connection with him. And he - the Creator, Sustainer, and the Firstborn of all creation - came in contact with us upon his incarnation, being born to Mary and Joseph in a manger.

Merry Christmas to you all - for on that day the universe was (ontologically, not temporally) created.


You may next want to read:
For Christmas: the Incarnation
The biblical timeline of the universe
Another post, from the table of contents

Two year anniversary for the blog!

The first post in this blog was made on December 12, 2013 - just over two years ago. Since then, this site has accumulated over 200,000 page views. I am not dissatisfied with this result.

At this point, one may be expected to say something like "I had no idea what this blog would become", but I don't think that's quite true for me. Even before I began, I knew many of the topics I wanted to cover. I still have a very long backlog of thing that I want to talk about, things that I've been thinking over for a long time. I honestly think I could run this blog for the rest of my life and not run out of topics. At times, my interest level and the time I have available may wax and wane, but I feel like could go on writing indefinitely about these topics. I will have period where I cut back a bit, or other periods of intense writing. But I do plan on continuing to write, God willing.

On the other hand, in matters beyond the actual text of the posts, I certainly did not know what I was doing when I started the blog. I feel like I still don't, really. I wonder about things like best layout and the best way to reach new readers. I don't actually have any good answers to these questions, although I know that they must exist. Such is the lot of small-scale bloggers like myself.

Especially because of my cluelessness, I consider myself especially blessed that I actually got a hit article out within a couple months of starting my blog - My pair of articles on Disney's "Frozen" are by far the most viewed posts, and still drive a great deal of traffic to my site. I'm not sure how I feel about that - after all, they were supposed to be "off-topic" posts. But I'm glad that people are enjoying them and that they're leading people to read my writings.

Other popular posts are clustered around these "Frozen" articles. So, the 'Gospel according to Frozen' and 'Gospel according to Tangled' articles are popular, for which I'm glad - these are posts that I'm proud of, posts that get at the truth at the heart of the Gospel. Other posts benefit from simply being close to the "Frozen" posts, such as the post on why there's so few Christians among scientists.

Other entry points to the sites are dwarfed by the "Frozen" posts, but they're still important to me; I want to have multiple streams of traffic. Some of the more popular entry points include my fractal generator, and my post on the two envelopes problem. I worked for a long time on that fractal generator, and its relative popularity is somewhat expected, but I'm surprised by how much traffic I'm getting through the two envelopes problem, for which I'm glad. I may have to add a follow-up to that post for an additional boost.

Furthermore, these two posts along with my other statistical/mathematical works on the blog have probably played no small roll in me getting a new job, for which I'm thankful.

My long series - such as the series on science as evidence for Christianity or interpreting the Genesis creation story get a steady stream of readers. It's especially gratifying to see the middle posts of these series get hits, showing that people read through the whole thing. These series include some posts that involve the most effort on my part, and they're among the ones that I most wish people would read.

So, that is the state of the blog at this point: probably over-reliant on the "Frozen" posts, but with a good number of other solid things going for it. A number of my posts are on the second or third page of their Google search results, and I feel like they just need a little bit more of a push. I still have many great things planned for the site.

I'm very thankful to all of you - my readers. Thanks for being a part of this work of mine for the past two years, and as I said, I plan to continue writing for this blog as long as God allows me to.


You may next want to read:
The Gospel: the central message of Christianity (part 1)
The role of evidence in the Christian faith
Another post, from the table of contents

How to think about the future

This post is a consolidation of a whole series of posts into one post. It's fairly long. Click on the following entries in the table of contents below to jump directly there:




Image: from Wikipedia, fair use

The future is completely unpredictable


It turns out that the future is completely unpredictable.

That may seem like a trivial statement. But most people have no idea just how true it is. A simple physics calculation may shed some light on this subject.

In the film franchise "Back to the Future", the main characters Marty McFly and Doctor "Doc" Emmett Brown travel through time and engage in various hijinks. Their travels alter the timeline in various ways, causing sometimes subtle, and sometimes drastic changes. Their goal throughout much of the films is to preserve the timeline they originally knew, with perhaps some small positive improvements.

But how likely are they to actually succeed? Can Marty, for instance, expect to return to 1985 and find things more or less as he left it, with perhaps a nicer car in his garage and an improved family? Let's say that Marty travels back in 1955, disturbs absolutely nothing by his direct contact, stays for only one second, then comes back to 1985. What can he expect to find?

Well, even if nothing is altered by his direct physical contact, Marty still exerts an additional gravitational force on his surroundings simply due to his mass. Since this is going to be an order of magnitude calculation, let's say that Marty has a mass of 100 kgs.

Now, consider the air molecules on the other side of the Earth from Marty. The Earth's diameter is 12.7e6 m. That is 12.7 million meters - I'll be using scientific notation (using e for the power of 10) and meters-kilograms-seconds throughout this calculation. Knowing that the universal gravitational constant is 6.67e-11 in mks units, we can use Newton's law of Universal Gravitation (a = Gm/r^2) to find that Marty causes an acceleration of 4.13e-23 m/s^2 to these air molecules.

Wow, that's like, nothing, right? In the one second that Marty is in 1955, that additional acceleration causes these air molecules to move an additional 2.07e-23 m that they would have otherwise not traveled. That's 0.000 000 000 000 000 000 000 0207 meters. What difference could be made by some air molecules moving such a small additional distance?

Consider a surface of one square meter on that other side of the Earth. The air molecules within 2.07e-23 m of that surface will have then collided with that surface and bounced back, due to Marty's additional gravitational pull. One square meter with 2.07e-23 m of thickness gives a volume of 2.07e-23 m^3, and this is the volume of air we're concerned about. There is 1 mole (6.022e23) of air in 22.4e-3 m^3 of volume in typical conditions, so that amounts to perhaps 556 air molecules that have bounced back against the surface.

Now, the important point here is that these air molecules are now OUT OF PLACE. They're somewhere that they're not suppose to be. As far as anyone from 1955 is concerned, the states of these 556 air molecules are unpredictable. If Marty had not traveled back in time, they would be somewhere completely different on the atomic scale. That means that they would collide with other air molecules that they were not supposed to collide with, while missing collisions that they were suppose to make.

The focus on collisions here is important. As long as the change that Marty causes is all smooth - say, by moving everything over by 2.07e-23 m - then any predictions made from 1955 would only be off by that much. Only negligible changes would occur from moving things by a negligible distance. But collisions change all that. If an air molecule makes a collision that it wasn't suppose to make, or misses a collision that was suppose to happen, then your predictions about the trajectory of the molecules are not just slightly off, they're completely wrong. That's why we're focused on the air molecules that bounced off the surface (whose trajectories are now completely unpredictable), rather than all the other air molecules (whose positions are now just all off by 2.07e-23 m).

Now, each air molecule experiences something like 1e10 collisions with another molecule each second. Each collision changes the trajectory of BOTH molecules. That is to say, 1e10 time a second, the number of air molecules whose trajectory is now completely unpredictable DOUBLES.

If we ignore the fact that a molecules may run into the same molecule multiple times, the number of molecules whose trajectory is now completely unpredictable would be 2^1e10 in one second. This is an absurdly large number, even when you're counting molecules. For all practical purposes, you can consider the microstate of ALL the air molecules around these original 556 molecules to have become completely unpredictable, in far less than one second. This cloud of unpredictability would rapidly spread, limited only by the diffusion and mixing of the air.

Furthermore, remember that this happens to every square meter of surface on the Earth. The upshot is that, from Marty's one second stay in 1955, even if he affects nothing by his direct touch, the microstate of the Earth's ENTIRE atmosphere rapidly becomes COMPLETELY UNPREDICTABLE, completely different than how it otherwise would have been. Something similar must also happen to all the liquids on the Earth, although the calculation will of course differ in detail.

Okay, so the future trajectory of all these molecules are completely unpredictable at this point. But really, can these molecular changes actually affect anything? What does it matter whether some molecules - or all molecules, for that matter - are here instead of there?

In the short term, it won't affect much. But there would be small changes. Microscopic differences can often affect the macroscopic world. The twinkling of stars, for example, is caused by the fluctuations in the momentary, localized density of the air. Photomultiplier tubes are devices specifically designed to cause macroscopically detectable measurements from microscopic events. Cosmic rays travelling through the atmosphere can be affected by the microstate of the air molecules, and they can cause neurons to fire when they hit your brain - perhaps causing a thought or a feeling you otherwise would not have had. The microscopic collisions of the molecules with other small particles causes Brownian motion - the random, jiggling movement of small particles suspended in water. So, a pollen grain would take a different random path in water, because Marty traveled back in time, for one second.

Now, do you think these changes still can't make any real differences? Try replacing "pollen grain" in the previous paragraph with "sperm".

Each sperm carries a different genetic code. Unless a specific sperm made it to the egg at the moment of your conception, you would not have been born. And the trajectory of that sperm would have been different, because the molecular motions in the fluids would have been different, all because Marty was in 1955 for one second and exerted a little bit of extra gravity. Forget about trying to get his parents to fall in love with one another - Marty was in all likelihood doomed to not exist the moment that he popped into 1955.

If you go review the argument and the calculations above, you'll see that the situation is actually far worse, in terms of predictability, than what I have presented. For example, altering the path of a sperm is not a particularly special way of affecting the future. In general, small changes - even microscopic changes - will eventually grow to cause macroscopic differences in time. This is called the butterfly effect: the name comes from an example where a butterfly flapping its wings can cause a hurricane on the other side of the Earth some time later.

The magnitude of the initial perturbation is also unnecessarily large in the example above. Remember, this doesn't affect just Marty; similar changes would happen all over the entire Earth. As if that wasn't enough, I once carried out another calculation which showed that even at INTERSTELLAR DISTANCES, a small change at another star will easily affect the microstate of things on Earth, which will then soon grows to make macroscopic differences.

So, that is the magnitude of the future's unpredictability: your very existence hinged on small changes happening in other parts of the galaxy.

But I don't want this to be one of those "see how wrong the movies are" articles. I like the "Back to the Future" trilogy. I don't like tearing things down just for the sake of tearing them down. So I'll end this section with the following:

I think the truest thing in those movies is what Doc says at the very end: "your future hasn't been written yet. No one's has. Your future is whatever you make it. So make it a good one." That may or may not be philosophically true in the deepest sense. But what is absolutely certain is that Doc's advice is effectively true in a practical sense. What the above calculation shows is that you cannot hope to indefinitely predict the details of your future. No one can. In that sense, your future is not yet written. What you can do, however, is act in the present to control the short moments ahead, and focus on the bigger picture to extend the lifetime of our planning before the butterfly effect kicks in. We then adapt and adjust, one step at a time. That is how we make the future.




No, really, the future is COMPLETELY unpredictable


I demonstrated earlier that even if Marty McFly went back in time for just one second, just his gravitational influence would irrevocably change the future. I then claimed that this is actually overkill: that even small changes at interstellar distances will affect things on Earth. Let's see about that.

(Most of this section is a walk-through of a calculation. Jump to the end if you just want to see the conclusion. The conventions here are the same as in the last section: all numbers and equations are in mks units. The powers of 10 for scientific notation is indicated following 'e'.)

The distance to the Andromeda Galaxy is 2.5 million light-years. That's 2.4e22 meters.

Consider a single water molecule somewhere in that galaxy. Water is a polar molecule - that is, it has positive and negative parts, separated by some distance. This creates an electric dipole moment. For a single water molecule, this dipole moment has a magnitude of 6.2e-30 coulomb-meters.

Now, dipole moments exert an electric field that depends on their spatial orientation. The full equation for that electric field can be found at any number of places, but we're really only interested in how much this field can change depending on the orientation. It turns out that it can change by about 1/(4 π ε0) * p/r^3. "p" is the magnitude of the dipole moment, "r" is the distance from that dipole, and ε0 is the permittivity of free space; it's a physical constant with a value of 8.85e-12. Plugging in all these numbers, we get a value of 4.0e-87 newtons/coulomb as the electric field.

So, depending on the orientation of a single water molecule in the Andromeda Galaxy, the electric field on Earth can change by about as much as 4.0e-87 newtons/coulomb. That electric field will exert a force of 6.4e-106 newtons on an elementary electric charge here on Earth.

Now, let's take a moment to appreciate how minuscule this number is. Some mathematical tools will simply not compute a number this small, and just display it as "0". It is on the order of a millionth of a googolth of a newton. After all, what can we expect from changing the orientation of a single water molecule in the Andromeda Galaxy? How can that possibly affect us on Earth?

If this force acts on an ionized air molecule - say, a singly ionized nitrogen molecule - that would cause an acceleration of F/m = 1.4e-80 m/s^2. If this acceleration acts for 1.4e-10 seconds (0.14 nanoseconds), it will move this ion by 1.4e-100 meters. This, then, will affect the future collisions of this ion with other air molecules.

So, to review: we are changing the orientation of a single water molecule, somewhere in the Andromeda Galaxy, for 0.14 nanoseconds. We are considering how this would affect the Earth. So far, we've determined that it would move an ionized nitrogen molecule by 1.4e-100 meters (1.4 googolth of a meter), which would then influence the future collisions of that molecule.

We'll model the collisions as if they were classical collisions with hard spheres - basically, as if the molecules were billiard balls. In such collisions, changing the position of the incoming billiard ball by x causes it to bounce off at a different angle. That difference, under some simplifying assumptions, is given by 2 x/d, where d is the diameter of the "billiard balls". In our case these are air molecules, which have a diameter of about 4e-10 meters. So, after bouncing off, our original ionized molecule is now moving at a different angle - one that's 2 x/d = 6.9e-91 radians away from the direction it would have otherwise bounced to. This difference in angle will then cause it to run into the next air molecule from a different position, which will then cause another difference in bouncing angle, and so on and so forth, in an iterative fashion. Eventually, after enough bounces, the deflection will be large enough that our ionized molecule will entirely miss another molecule that it would have otherwise hit. How many collisions does this take? I wrote a small bit of code in Python to find out, using typical values for the relevant conditions for air (such as the time between collisions, or the path length that a molecule travels between collisions):
acceleration = 1.4e-80
path_length = 7e-8
time = 1.4e-10
diameter = 4e-10

n = 0
impact_parameter = 0.5*acceleration*time**2

def one_collision(incoming_d_impact_parameter):
    new_deflection = 2*incoming_d_impact_parameter/diameter
    new_d_impact_parameter = new_deflection*path_length
    return {
        "deflection":new_deflection, 
        "impact_parameter":new_d_impact_parameter}

collision = True
while collision:
    result = one_collision(impact_parameter)
    impact_parameter = result["impact_parameter"]
    n += 1
    out_string = \
        "collisions:" + "{:2d}".format(n) + \
        "  impact_parameter:" + "{:.2e}".format(result["impact_parameter"]) + \
        "  deflection:" + "{:.2e}".format(result["deflection"])
    print out_string
    if result["impact_parameter"] > diameter:
        collision = False
        print "done in " + "{:2d}".format(n) + " collisions"
Running this code gives the following output:
collisions: 1  impact_parameter:4.80e-98  deflection:6.86e-91
collisions: 2  impact_parameter:1.68e-95  deflection:2.40e-88
collisions: 3  impact_parameter:5.88e-93  deflection:8.40e-86
collisions: 4  impact_parameter:2.06e-90  deflection:2.94e-83
collisions: 5  impact_parameter:7.21e-88  deflection:1.03e-80
collisions: 6  impact_parameter:2.52e-85  deflection:3.60e-78
collisions: 7  impact_parameter:8.83e-83  deflection:1.26e-75
collisions: 8  impact_parameter:3.09e-80  deflection:4.41e-73
collisions: 9  impact_parameter:1.08e-77  deflection:1.54e-70
collisions:10  impact_parameter:3.78e-75  deflection:5.41e-68
collisions:11  impact_parameter:1.32e-72  deflection:1.89e-65
collisions:12  impact_parameter:4.64e-70  deflection:6.62e-63
collisions:13  impact_parameter:1.62e-67  deflection:2.32e-60
collisions:14  impact_parameter:5.68e-65  deflection:8.11e-58
collisions:15  impact_parameter:1.99e-62  deflection:2.84e-55
collisions:16  impact_parameter:6.96e-60  deflection:9.94e-53
collisions:17  impact_parameter:2.44e-57  deflection:3.48e-50
collisions:18  impact_parameter:8.52e-55  deflection:1.22e-47
collisions:19  impact_parameter:2.98e-52  deflection:4.26e-45
collisions:20  impact_parameter:1.04e-49  deflection:1.49e-42
collisions:21  impact_parameter:3.65e-47  deflection:5.22e-40
collisions:22  impact_parameter:1.28e-44  deflection:1.83e-37
collisions:23  impact_parameter:4.48e-42  deflection:6.39e-35
collisions:24  impact_parameter:1.57e-39  deflection:2.24e-32
collisions:25  impact_parameter:5.48e-37  deflection:7.83e-30
collisions:26  impact_parameter:1.92e-34  deflection:2.74e-27
collisions:27  impact_parameter:6.72e-32  deflection:9.60e-25
collisions:28  impact_parameter:2.35e-29  deflection:3.36e-22
collisions:29  impact_parameter:8.23e-27  deflection:1.18e-19
collisions:30  impact_parameter:2.88e-24  deflection:4.11e-17
collisions:31  impact_parameter:1.01e-21  deflection:1.44e-14
collisions:32  impact_parameter:3.53e-19  deflection:5.04e-12
collisions:33  impact_parameter:1.23e-16  deflection:1.76e-09
collisions:34  impact_parameter:4.32e-14  deflection:6.17e-07
collisions:35  impact_parameter:1.51e-11  deflection:2.16e-04
collisions:36  impact_parameter:5.29e-09  deflection:7.56e-02
done in 36 collisions
"impact_parameter" is the difference in position as our ion approaches the next molecule. You see that, after the 36th collision, this value exceeds the diameter of a molecule, causing our ion to miss a collision that would have otherwise taken place. Since air molecules make a collision about every 1.4e-10 seconds, these 36 collisions only take 5.0e-9 seconds - that is, 5 nanoseconds.

The rest of the story is similar to how they occurred in the last section. A missed collision means that the states of the two molecules that would have been involved are now completely different, completely changed from what they would otherwise be. Then each of their future collisions also completely changes the states of these new molecules they run into. This means that with each round of collisions, the number of affected air molecules doubles. In far less than a second, all of the molecules around the original ion are affected. Furthermore, this is happening starting from every single ionized molecule in Earth's atmosphere - so in no time at all, the microstate of Earth's entire atmosphere is completely changed. This then leads to macroscopic changes (like Marty McFly never being born) soon enough.

So, that is the magnitude of the future's unpredictability. That is the degree of the universe's inter-connectivity and complexity. A SINGLE WATER MOLECULE, located in ANOTHER GALAXY, changing its orientation for a FRACTION OF A NANOSECOND, will completely alter the microstate of the Earth's atmosphere nearly instantly (after accounting for the speed-of-light delay), and change our macroscopic future in short order. Your life, brain, and very existence is the result of all these effects combining to create you in your current state. "Subtle is the LORD" indeed.




The future will be like the past, and therefore "predictable"


And now for something completely different: It's easy to predict the future. It'll be basically like the past.

How could that be? Didn't I just explain how unpredictable the future is? Isn't everything changing all the time? Are we not living in an era of unprecedented growth and technological advancement? Isn't the world not only changing, but changing faster and faster? I mean, just look at the graph of the world population: look at that absolute explosion in recent years. And similar graphs can be made for technological progress as well. Isn't it absolutely clear that the present is completely different than the past, that we are on the cusp of something disastrous or transcendent, and that the future will be far more different still?

Well, in a sense, I guess that's true. But that's pretty much always been true. That's what I mean by saying the future will be like the past. All those hyperbolic things said about the future could have been said at most other times in the past - A hundred, two hundred, or perhaps even thousands of years ago. And they would have been about as right then as we are now in saying these things. That is simply the nature of exponential growth.

Here's what I mean: if we assume that humanity's growth - whether it's measured in population or in technological development - follows an exponential curve, then the future can always be exactly mapped onto the present, or the past, through some simple transformations. Let me demonstrate: consider the following graph:


That exponential graph may represent world population or technological growth or whatever. Isn't it clear that there are two distinct regions in that graph, the flat region and the rapid rise before the end? Let's zoom in to the transition between the two regions:


Isn't that where we are in history? At that unique and crucial point where we leave off being "flat" to where everything blows up and goes off the scale?

Well, let's not do anything hasty based on that line of thinking. After all, I can make any other region of the graph look exactly like that "unique and crucial point" by simply focusing on that new point and re-normalizing the y-axis. The following is a graph of the exact same function as before at a different x-value, viewed according to the treatment I just prescribed:


Note that the view window is now focused around -400 instead of +200, and the y-axis has been re-scaled. But the shape of the function is exactly the same as it was before. You can try this for yourself  - desmos is a good online graphing calculator - and see that it's true, starting with any exponential growth function. Algebraically, this is because if you
1. take any exponential function (e^kx),
2. and translate it horizontally by any amount (e^k(x+x0)),
3. and vertically scale it to re-normalize things so that the new y-value becomes the new normal ( 1/e^kx0 * e^k(x+x0))
4. then you get back your original function. (e^kx)
This means that if you transport yourself to any time in history, and get used to your environment so that this new time period becomes your new "normal", then the pace of the changes around you will look the same as it does now. In fact, it'll look the same at any other time in history. There is therefore nothing new under the sun, and the future will be like the past.

You can even test this with events within living memory. Consider that archetypal example of modern progress: the advancements in computers. Back when I first started to really look at computers, a "gigabyte" was an unheard amount of storage for a computer to have. If you had told me then of a future of such rapid progress where a computer's storage increased by many gigabytes in a couple of years, I might have marveled at this hyper-technological future where such wonders were possible. I might have thought that everything I knew would be thrown out and be completely changed in this new world. But of course, this is the future we live in now, and the increase from 64 to 128 GB between iPhone 5 and 6 is not some world-shattering news.

Now, one may argue that the pace of growth has actually been even faster than merely exponential growth - there may be something to be said for that. Certainly, this graph of the world's population has distinct regions, and the growth is not only exponential, but there are period where the exponential growth rate itself increases. But I think it's too much to conclude that this is the definitive, continuous pattern in human progress. I think that the graph can be best interpreted by saying that human growth rate is usually exponential, but that at the rate of growth jumps to a new value at certain moments in history (the beginning of civilization, the industrial revolution, etc). We may be in such a moment in history, but even so, the rate of change would not be fundamentally different than they were during the industrial revolution. It's exciting, to be sure, but it's not the end of the world, and the future will continue to be more or less like the past.




The future contains both good and bad extremes from all possible worlds


What I am about to say here is less certain than what I have said in the previous sections; it's a half-formed thought, which I only post because I think it may be more important than my other thoughts, especially regarding the future of human society. In short, this section will more nebulous compared to the others in the series.

The thought here is simple:

I wonder if humans only learn through experiments.

That doesn't seem important? Let me rephrase that:

I wonder if humans only learn through experiences. Or, to put in a little bit more detail: I wonder if humans only learn through experiencing mistakes.

Note that I intend for this to apply to human societies as a whole rather than to just individuals. You see, when we start talking about the future, we sometimes have this idea that we'll reach some kind utopia, where all our social problems will be solved. We just have to learn to treat each other as fellow humans, right? Surely with the right education and policies, and with our ever increasing powers of science and technology, we'll eventually reach that eternally perfect society?

If there were some cap to the amount of beauty in the universe, or a limit to human potential, perhaps. Then we will eventually reach that maximum and stay there. Then we could maybe be like those space-faring aliens whom I mentioned before, who are fated merely to rule the stars then perish with the universe.  But I don't think that this is the case. I don't think that we are bounded in that way.

So, if we have infinite potential, and we can only learn though experiencing mistakes, what will the future be like? Well, here is one possible future history:

One thing that it's popular to wonder about nowadays is whether we should make a computer that's smarter than a human (whatever that means). Now, this is a question of immense importance, but if we can only learn through experiencing mistakes, the only way to settle the question would be to try it, then see the results: there is no historically analogous previous situation to draw on. And getting the question wrong may be disastrous.

So then, after the disastrous Skynet wars of 2050, humanity might finally agree on what kind of artificial intelligence to build. This will allow us to colonize the other planets in the solar system - and we'll then ask questions like "how should we share the resources between the different planets?" This type of question has never been asked on a planetary scale, so there will be no historically analogous previous situation to draw on. Even a super-intelligent AI might not be able to reason with no data. So again, we'll just have to try out different models of planetary economics, and learn by trial and error. So, Mars and Jupiter may prosper, but then the citizens of Mercury and Earth may suffer for generations under an oppressive system of planetary trade.

But eventually, that will get sorted out, after a great deal of human suffering. But at this point, the differences between the haves and the have-nots, at the planetary scale, subject to different planetary conditions, combined with the genetic tinkering that's been going on, may threaten to tear apart our conception of "the human race". What should we do about this? Should we allow a portion of humanity to evolve separately from the rest? Again, this will be the first time in history where we can meaningfully ask this question, and the only recourse may be to try different policies and make our mistakes. And given the momentous nature of the question, the consequences for getting them wrong will be correspondingly tragic.

Of course, these scenarios are only projected from the mind of an early 21st century human. More likely, the kinds of issues faced by these future people will be completely incomprehensible to us; just as, say, the 20th century's nuclear ideology of Mutually Assured Destruction would be unimaginable to a prehistoric human. And each time, because of this unimaginable newness and lack of historical precedence, it may be that mistakes may have to be made in order to learn from them. And each time, because of humanity's increased power and the larger scale and scope of the problem, the mistakes will be more costly, even as the benefits of getting it right propels us further into the future.

What kind of future is this? It's actually a strangely hopeful but tragic one. Our powers and glory will perpetually increase - but with many steps being paid for with ever more costly mistakes. You think that slavery or the killing fields were bad? The instances of such tragedies will only increase in enormity. On the other hand, you think that modern democracies and smartphones are good? The overall trajectory for history as a whole will continue to be upwards, as all these things will perpetually be superseded by something better.

As I said, I'm unsure about all this; but it seems likely, as it's been the case thus far in history.



Conclusion


Trying to predict the future is a good way to put your foot in your mouth. It's hard enough to just think about the future, let alone predict it. Even in this series of posts, all I have done is provide some rules of thumb: the future is impossible to predict. The future will be like the past. The future will have both good and bad in it, in ever increasing measure.

Some of these rules are vague, and may even seem contradictory. How could the future be unpredictable yet still be like the past? But the possibilities concerning the future are rich enough that such superficial paradoxes can be easily resolved. And when we harmonize these rules, a coherent pattern does seem to emerge: the future cannot be predicted in detail, and ever larger events are considered "details" as we consider times further into the future. However, there are real patterns that repeat themselves in time. The details get averaged out if you consider them in aggregate. So in these ways, at a sufficiently broad level, the future can be predicted from the past. As far as humans are concerned, this means that our history will grow in both glory and tragedy in ever larger degree. We will continue to grow, yet the inevitable, unpredictable, fluctuating "details" will cause disasters in correspondingly larger degrees.

So what should we do? What can we predict or plan for? I really don't know. I don't know how right I am in my thoughts about the future. So, in the end, as it often happens, all I can say is what has already been said in the Bible:
Now listen, you who say, "Today or tomorrow we will go to this or that city, spend a year there, carry on business and make money." Why, you do not even know what will happen tomorrow. What is your life? You are a mist that appears for a little while and then vanishes. Instead, you ought to say, "If it is the Lord's will, we will live and do this or that."
I am indeed only a mist - a "detail" that's here by accident and whose affect will be averaged out by other similarly fluctuating detail. That is why I can only say, "If it is the Lord's will, I will live and do this or that." But in that Divine will, I believe that I am a positive part of the pattern that's woven throughout time, a pattern that continues into eternity.


You may next want to read:
Christian predictions on the future of science (part 1)
The biblical timeline of the universe
Another post, from the table of contents

How to think about the future (Conclusion)

Trying to predict the future is a good way to put your foot in your mouth. It's hard enough to just think about the future, let alone predict it. Even in this series of posts, all I have done is provide some rules of thumb: the future is impossible to predict. The future will be like the past. The future will have both good and bad in it, in ever increasing measure.

Some of these rules are vague, and may even seem contradictory. How could the future be unpredictable yet still be like the past? But the possibilities concerning the future are rich enough that such superficial paradoxes can be easily resolved. And when we harmonize these rules, a coherent pattern does seem to emerge: the future cannot be predicted in detail, and ever larger events are considered "details" as we consider times further into the future. However, there are real patterns that repeat themselves in time. The details get averaged out if you consider them in aggregate. So in these ways, at a sufficiently broad level, the future can be predicted from the past. As far as humans are concerned, this means that our history will grow in both glory and tragedy in ever larger degree. We will continue to grow, yet the inevitable, unpredictable, fluctuating "details" will cause disasters in correspondingly larger degrees.

So what should we do? What can we predict or plan for? I really don't know. I don't know how right I am in my thoughts about the future. So, in the end, as it often happens, all I can say is what has already been said in the Bible:
Now listen, you who say, "Today or tomorrow we will go to this or that city, spend a year there, carry on business and make money." Why, you do not even know what will happen tomorrow. What is your life? You are a mist that appears for a little while and then vanishes. Instead, you ought to say, "If it is the Lord's will, we will live and do this or that."
I am indeed only a mist - a "detail" that's here by accident and whose affect will be averaged out by other similarly fluctuating detail. That is why I can only say, "If it is the Lord's will, I will live and do this or that." But in that Divine will, I believe that I am a positive part of the pattern that's woven throughout time, a pattern that continues into eternity.


You may next want to read:
How to think about the future (Consolidation post for this series)
Sherlock Bayes, logical detective: a murder mystery game
The biblical timeline of the universe
Another post, from the table of contents

How to think about the future (Part 4)

What I am about to say in this post is less certain than what I have said in the previous posts; it's a half-formed thought, which I only post because I think it may be more important than my other thoughts, especially regarding the future of human society. In short, this post will more nebulous compared to the others in the series.

The thought here is simple:

I wonder if humans only learn through experiments.

That doesn't seem important? Let me rephrase that:

I wonder if humans only learn through experiences. Or, to put in a little bit more detail: I wonder if humans only learn through experiencing mistakes.

Note that I intend for this to apply to human societies as a whole rather than to just individuals. You see, when we start talking about the future, we sometimes have this idea that we'll reach some kind utopia, where all our social problems will be solved. We just have to learn to treat each other as fellow humans, right? Surely with the right education and policies, and with our ever increasing powers of science and technology, we'll eventually reach that eternally perfect society?

If there were some cap to the amount of beauty in the universe, or a limit to human potential, perhaps. Then we will eventually reach that maximum and stay there. Then we could maybe be like those space-faring aliens whom I mentioned before, who are fated merely to rule the stars then perish with the universe.  But I don't think that this is the case. I don't think that we are bounded in that way.

So, if we have infinite potential, and we can only learn though experiencing mistakes, what will the future be like? Well, here is one possible future history:

One thing that it's popular to wonder about nowadays is whether we should make a computer that's smarter than a human (whatever that means). Now, this is a question of immense importance, but if we can only learn through experiencing mistakes, the only way to settle the question would be to try it, then see the results: there is no historically analogous previous situation to draw on. And getting the question wrong may be disastrous.

So then, after the disastrous Skynet wars of 2050, humanity might finally agree on what kind of artificial intelligence to build. This will allow us to colonize the other planets in the solar system - and we'll then ask questions like "how should we share the resources between the different planets?" This type of question has never been asked on a planetary scale, so there will be no historically analogous previous situation to draw on. Even a super-intelligent AI might not be able to reason with no data. So again, we'll just have to try out different models of planetary economics, and learn by trial and error. So, Mars and Jupiter may prosper, but then the citizens of Mercury and Earth may suffer for generations under an oppressive system of planetary trade.

But eventually, that will get sorted out, after a great deal of human suffering. But at this point, the differences between the haves and the have-nots, at the planetary scale, subject to different planetary conditions, combined with the genetic tinkering that's been going on, may threaten to tear apart our conception of "the human race". What should we do about this? Should we allow a portion of humanity to evolve separately from the rest? Again, this will be the first time in history where we can meaningfully ask this question, and the only recourse may be to try different policies and make our mistakes. And given the momentous nature of the question, the consequences for getting them wrong will be correspondingly tragic.

Of course, these scenarios are only projected from the mind of an early 21st century human. More likely, the kinds of issues faced by these future people will be completely incomprehensible to us; just as, say, the 20th century's nuclear ideology of Mutually Assured Destruction would be unimaginable to a prehistoric human. And each time, because of this unimaginable newness and lack of historical precedence, it may be that mistakes may have to be made in order to learn from them. And each time, because of humanity's increased power and the larger scale and scope of the problem, the mistakes will be more costly, even as the benefits of getting it right propels us further into the future.

What kind of future is this? It's actually a strangely hopeful but tragic one. Our powers and glory will perpetually increase - but with many steps being paid for with ever more costly mistakes. You think that slavery or the killing fields were bad? The instances of such tragedies will only increase in enormity. On the other hand, you think that modern democracies and smartphones are good? The overall trajectory for history as a whole will continue to be upwards, as all these things will perpetually be superseded by something better.

As I said, I'm unsure about all this; but it seems likely, as it's been the case thus far in history.


You may next want to read:
How to think about the future (Conclusion) (Next post of this series)
The biblical timeline of the universe
The lifetime of evil (part 2)
Another post, from the table of contents

On becoming a good person

I don't care much about the recent terrorist attacks in Paris.

I mean, it's hard to care, given some perspective. It happened half a world away. The death count at the moment stands at 136, according to Wikipedia. That's nothing. The world's mortality rate is about 0.8% per year - or about 100 persons per minute. That's six thousand people in the last hour. About a hundred of those are due to malaria - a cheaply preventable disease.

If I started to care about the Paris attacks, I'd have to start caring about all these other deaths too. And who can actually care about a hundred people every minute? Who can handle a death toll of a 9/11 happening every half-hour? And if I actually cared about all those people, I might have to start donating money to prevent malaria, where it's estimated that it only costs $3,300 per life saved. You say you value human life? Well, there's your value, right there.

So I think that I value human lives at less than $3,300 a pop. Otherwise, I would actually spend that $3,300 and actually save a life. My value may be higher for a Frenchmen than for a sub-Saharan malaria victim, because of my shared Western culture with the French. It would be higher still for an American, and even higher for the people I actually know. But at the end of the day, the death of these 136 people in Paris upsets me less than the loss of a couple of thousand dollars.

And that's not even the end of it. If I started to care about all these things - if I got worked up about this Paris attacks - I'd not only have to care about all the other deaths in the world, but also smaller things that are closer to me. I'd have to deeply care about my co-workers kids' Halloween costumes and the break-up an acquaintance is going through and the health of my server at a restaurant. And I can't do that. I don't have the emotional bandwidth. Some people seem to care about all these things and genuinely empathize with everyone. I am not one of these people. I'm bad enough at caring for the people that I'm actually close to. It's not possible for me to care about everyone. For someone to actually care about literally everything, they'd have to be God-like.

But I want to care.

I don't like the fact that I don't care. I want to change, to be different. I want to be more like those people who somehow manage to always genuinely care. In becoming more like these people, I would become more like God.

And that is the ultimate meaning of what it means to become a good person. You see, we, in our society, have many measures of worth we assign to individuals: wealth, fame, status, intellect, political power, physical strength or beauty, etc. These are all somewhat useful metrics, but we're all somehow agreed that these are not the ultimate measure of a person. We've all heard aphorisms like "beauty is only skin deep" or "money can't buy happiness". But if these are not the ultimate measure, then what is?

The answer is Love. Our worth is precisely that degree to which we channel the God who is love though our lives. All other measures of worth are merely substitutes or enablers for this ultimate measure. You want to become rich and famous? You think that'll make you a better person? Well, it might: what will you do with that money and fame?

In caring for one another, we channel God's love for us through our lives. We improve the other person's lives and draw them closer to God, while improving ourselves by becoming more loving, more worthy, and more godly. I want all these things. That is why I want to care. I want to care more than I do now.

How do I go about this? How do I care more in the future, when I actually don't care now? As with everything, through practice. I start by pretending, by imitating those who are better than me. As I have already confessed, I haven't gotten very far on this path of Love. So I look at the others on the path, and imitate those who are further along. Like a baby learning to walk and talk, or like a student learning to solve problems, that is how we start. We watch and imitate those who do it better - these may be our parents, our pastors, saints from long ago like apostle Paul, and ultimately, Christ himself.

Meanwhile, as I'm getting better, God can even use cold, calculating, heartless people. He can even change and improve someone like me. My peculiarities may even serve a purpose in his kingdom.

I talked with a French co-worker about the attacks on the day that it happened. It's something that I had to fight with myself to do. I offered my condolences, but being relatively unpracticed in the way of Love, I'm not sure how much good I did. But I think I care a little bit more now, than before I had that conversation.


You may next want to read:
I am a sinner.
The lifetime of evil (part 2)
Another post, from the table of contents

How to think about the future (Part 3)

It's easy to predict the future. It'll be basically like the past.

How could that be? Isn't everything changing all the time? Are we not living in an era of unprecedented growth and technological advancement? Isn't the world not only changing, but changing faster and faster? I mean, just look at the graph of the world population: look at that absolute explosion in recent years. And similar graphs can be made for technological progress as well. Isn't it absolutely clear that the present is completely different than the past, that we are on the cusp of something disastrous or transcendent, and that the future will be far more different still?

Well, in a sense, I guess that's true. But that's pretty much always been true. That's what I mean by saying the future will be like the past. All those hyperbolic things said about the future could have been said at most other times in the past - A hundred, two hundred, or perhaps even thousands of years ago. And they would have been about as right then as we are now in saying these things. That is simply the nature of exponential growth.

Here's what I mean: if we assume that humanity's growth - whether it's measured in population or in technological development - follows an exponential curve, then the future can always be exactly mapped onto the present, or the past, through some simple transformations. Let me demonstrate: consider the following graph:


That exponential graph may represent world population or technological growth or whatever. Isn't it clear that there are two distinct regions in that graph, the flat region and the rapid rise before the end? Let's zoom in to the transition between the two regions:


Isn't that where we are in history? At that unique and crucial point where we leave off being "flat" to where everything blows up and goes off the scale?

Well, let's not do anything hasty based on that line of thinking. After all, I can make any other region of the graph look exactly like that "unique and crucial point" by simply focusing on that new point and re-normalizing the y-axis. The following is a graph of the exact same function as before at a different x-value, viewed according to the treatment I just prescribed:


Note that the view window is now focused around -400 instead of +200, and the y-axis has been re-scaled. But the shape of the function is exactly the same as it was before. You can try this for yourself  - desmos is a good online graphing calculator - and see that it's true, starting with any exponential growth function. Algebraically, this is because if you
1. take any exponential function (e^kx),
2. and translate it horizontally by any amount (e^k(x+x0)),
3. and vertically scale it to re-normalize things so that the new y-value becomes the new normal ( 1/e^kx0 * e^k(x+x0))
4. then you get back your original function. (e^kx)
This means that if you transport yourself to any time in history, and get used to your environment so that this new time period becomes your new "normal", then the pace of the changes around you will look the same as it does now. In fact, it'll look the same at any other time in history. There is therefore nothing new under the sun, and the future will be like the past.

You can even test this with events within living memory. Consider that archetypal example of modern progress: the advancements in computers. Back when I first started to really look at computers, a "gigabyte" was an unheard amount of storage for a computer to have. If you had told me then of a future of such rapid progress where a computer's storage increased by many gigabytes in a couple of years, I might have marveled at this hyper-technological future where such wonders were possible. I might have thought that everything I knew would be thrown out and be completely changed in this new world. But of course, this is the future we live in now, and the increase from 64 to 128 GB between iPhone 5 and 6 is not some world-shattering news.

Now, one may argue that the pace of growth has actually been even faster than merely exponential growth - there may be something to be said for that. Certainly, this graph of the world's population has distinct regions, and the growth is not only exponential, but there are period where the exponential growth rate itself increases. But I think it's too much to conclude that this is the definitive, continuous pattern in human progress. I think that the graph can be best interpreted by saying that human growth rate is usually exponential, but that at the rate of growth jumps to a new value at certain moments in history (the beginning of civilization, the industrial revolution, etc). We may be in such a moment in history, but even so, the rate of change would not be fundamentally different than they were during the industrial revolution. It's exciting, to be sure, but it's not the end of the world, and the future will continue to be more or less like the past.


You may next want to read:
How to think about the future (Part 4) (Next post of this series)
How to think about the future (Part 2) (Previous post of this series)
How to make a fractal
Another post, from the table of contents

How to think about the future (Part 2)

In the last post, I demonstrated that even if Marty McFly went back in time for just one second, just his gravitational influence would irrevocably change the future. I then claimed that this is actually overkill: that even small changes at interstellar distances will affect things on Earth. Let's see about that.

(Most of this post is a walk-through of a calculation. Jump to the end if you just want to see the conclusion. The conventions in this post are the same as in the last post. All numbers and equations are in mks units. The powers of 10 for scientific notation is indicated following 'e'.)

The distance to the Andromeda Galaxy is 2.5 million light-years. That's 2.4e22 meters.

Consider a single water molecule somewhere in that galaxy. Water is a polar molecule - that is, it has positive and negative parts, separated by some distance. This creates an electric dipole moment. For a single water molecule, this dipole moment has a magnitude of 6.2e-30 coulomb-meters.

Now, dipole moments exert an electric field that depends on their spatial orientation. The full equation for that electric field can be found at any number of places, but we're really only interested in how much this field can change depending on the orientation. It turns out that it can change by about 1/(4 π ε0) * p/r^3. "p" is the magnitude of the dipole moment, "r" is the distance from that dipole, and ε0 is the permittivity of free space; it's a physical constant with a value of 8.85e-12. Plugging in all these numbers, we get a value of 4.0e-87 newtons/coulomb as the electric field.

So, depending on the orientation of a single water molecule in the Andromeda Galaxy, the electric field on Earth can change by about as much as 4.0e-87 newtons/coulomb. That electric field will exert a force of 6.4e-106 newtons on an elementary electric charge here on Earth.

Now, let's take a moment to appreciate how minuscule this number is. Some mathematical tools will simply not compute a number this small, and just display it as "0". It is on the order of a millionth of a googolth of a newton. After all, what can we expect from changing the orientation of a single water molecule in the Andromeda Galaxy? How can that possibly affect us on Earth?

If this force acts on an ionized air molecule - say, a singly ionized nitrogen molecule - that would cause an acceleration of F/m = 1.4e-80 m/s^2. If this acceleration acts for 1.4e-10 seconds (0.14 nanoseconds), it will move this ion by 1.4e-100 meters. This, then, will affect the future collisions of this ion with other air molecules.

So, to review: we are changing the orientation of a single water molecule, somewhere in the Andromeda Galaxy, for 0.14 nanoseconds. We are considering how this would affect the Earth. So far, we've determined that it would move an ionized nitrogen molecule by 1.4e-100 meters (1.4 googolth of a meter), which would then influence the future collisions of that molecule.

We'll model the collisions as if they were classical collisions with hard spheres - basically, as if the molecules were billiard balls. In such collisions, changing the position of the incoming billiard ball by x causes it to bounce off at a different angle. That difference, under some simplifying assumptions, is given by 2 x/d, where d is the diameter of the "billiard balls". In our case these are air molecules, which have a diameter of about 4e-10 meters. So, after bouncing off, our original ionized molecule is now moving at a different angle - one that's 2 x/d = 6.9e-91 radians away from the direction it would have otherwise bounced to. This difference in angle will then cause it to run into the next air molecule from a different position, which will then cause another difference in bouncing angle, and so on and so forth, in an iterative fashion. Eventually, after enough bounces, the deflection will be large enough that our ionized molecule will entirely miss another molecule that it would have otherwise hit. How many collisions does this take? I wrote a small bit of code in Python to find out, using typical values for the relevant conditions for air (such as the time between collisions, or the path length that a molecule travels between collisions):
acceleration = 1.4e-80
path_length = 7e-8
time = 1.4e-10
diameter = 4e-10

n = 0
impact_parameter = 0.5*acceleration*time**2

def one_collision(incoming_d_impact_parameter):
    new_deflection = 2*incoming_d_impact_parameter/diameter
    new_d_impact_parameter = new_deflection*path_length
    return {
        "deflection":new_deflection, 
        "impact_parameter":new_d_impact_parameter}

collision = True
while collision:
    result = one_collision(impact_parameter)
    impact_parameter = result["impact_parameter"]
    n += 1
    out_string = \
        "collisions:" + "{:2d}".format(n) + \
        "  impact_parameter:" + "{:.2e}".format(result["impact_parameter"]) + \
        "  deflection:" + "{:.2e}".format(result["deflection"])
    print out_string
    if result["impact_parameter"] > diameter:
        collision = False
        print "done in " + "{:2d}".format(n) + " collisions"
Running this code gives the following output:
collisions: 1  impact_parameter:4.80e-98  deflection:6.86e-91
collisions: 2  impact_parameter:1.68e-95  deflection:2.40e-88
collisions: 3  impact_parameter:5.88e-93  deflection:8.40e-86
collisions: 4  impact_parameter:2.06e-90  deflection:2.94e-83
collisions: 5  impact_parameter:7.21e-88  deflection:1.03e-80
collisions: 6  impact_parameter:2.52e-85  deflection:3.60e-78
collisions: 7  impact_parameter:8.83e-83  deflection:1.26e-75
collisions: 8  impact_parameter:3.09e-80  deflection:4.41e-73
collisions: 9  impact_parameter:1.08e-77  deflection:1.54e-70
collisions:10  impact_parameter:3.78e-75  deflection:5.41e-68
collisions:11  impact_parameter:1.32e-72  deflection:1.89e-65
collisions:12  impact_parameter:4.64e-70  deflection:6.62e-63
collisions:13  impact_parameter:1.62e-67  deflection:2.32e-60
collisions:14  impact_parameter:5.68e-65  deflection:8.11e-58
collisions:15  impact_parameter:1.99e-62  deflection:2.84e-55
collisions:16  impact_parameter:6.96e-60  deflection:9.94e-53
collisions:17  impact_parameter:2.44e-57  deflection:3.48e-50
collisions:18  impact_parameter:8.52e-55  deflection:1.22e-47
collisions:19  impact_parameter:2.98e-52  deflection:4.26e-45
collisions:20  impact_parameter:1.04e-49  deflection:1.49e-42
collisions:21  impact_parameter:3.65e-47  deflection:5.22e-40
collisions:22  impact_parameter:1.28e-44  deflection:1.83e-37
collisions:23  impact_parameter:4.48e-42  deflection:6.39e-35
collisions:24  impact_parameter:1.57e-39  deflection:2.24e-32
collisions:25  impact_parameter:5.48e-37  deflection:7.83e-30
collisions:26  impact_parameter:1.92e-34  deflection:2.74e-27
collisions:27  impact_parameter:6.72e-32  deflection:9.60e-25
collisions:28  impact_parameter:2.35e-29  deflection:3.36e-22
collisions:29  impact_parameter:8.23e-27  deflection:1.18e-19
collisions:30  impact_parameter:2.88e-24  deflection:4.11e-17
collisions:31  impact_parameter:1.01e-21  deflection:1.44e-14
collisions:32  impact_parameter:3.53e-19  deflection:5.04e-12
collisions:33  impact_parameter:1.23e-16  deflection:1.76e-09
collisions:34  impact_parameter:4.32e-14  deflection:6.17e-07
collisions:35  impact_parameter:1.51e-11  deflection:2.16e-04
collisions:36  impact_parameter:5.29e-09  deflection:7.56e-02
done in 36 collisions
"impact_parameter" is the difference in position as our ion approaches the next molecule. You see that, after the 36th collision, this value exceeds the diameter of a molecule, causing our ion to miss a collision that would have otherwise taken place. Since air molecules make a collision about every 1.4e-10 seconds, these 36 collisions only take 5.0e-9 seconds - that is, 5 nanoseconds.

The rest of the story is similar to how they occurred in the last post. A missed collision means that the states of the two molecules that would have been involved are now completely different, completely changed from what they would otherwise be. Then each of their future collisions also completely changes the states of these new molecules they run into. This means that with each round of collisions, the number of affected air molecules doubles. In far less than a second, all of the molecules around the original ion are affected. Furthermore, this is happening starting from every single ionized molecule in Earth's atmosphere - so in no time at all, the microstate of Earth's entire atmosphere is completely changed. This then leads to macroscopic changes (like Marty McFly never being born) soon enough.

So, that is the magnitude of the future's unpredictability. That is the degree of the universe's inter-connectivity and complexity. A SINGLE WATER MOLECULE, located in ANOTHER GALAXY, changing its orientation for a FRACTION OF A SECOND, will completely alter the microstate of the Earth's atmosphere nearly instantly (after accounting for the speed-of-light delay), and change our macroscopic future in short order. Your life, brain, and very existence is the result of all these effects combining to create you in your current state. "Subtle is the LORD" indeed.

Next week, we'll discuss a different way of thinking about the future.


You may next want to read:
How to think about the future (Part 3) (Next post of this series)
The dialogue between two aliens who found a book on Earth
How physics fits within Christianity (part 1)
Another post, from the table of contents

How to think about the future (Part 1)

Image: from Wikipedia, fair use
It turns out that the future is completely unpredictable.

That may seem like a trivial statement. But most people have no idea just how true it is. A simple physics calculation may shed some light on this subject.

In the film franchise "Back to the Future", the main characters Marty McFly and Doctor "Doc" Emmett Brown travel through time and engage in various hijinks. Their travels alter the timeline in various ways, causing sometimes subtle, and sometimes drastic changes. Their goal throughout much of the films is to preserve the timeline they originally knew, with perhaps some small positive improvements.

But how likely are they to actually succeed? Can Marty, for instance, expect to return to 1985 and find things more or less as he left it, with perhaps a nicer car in his garage and an improved family? Let's say that Marty travels back in 1955, disturbs absolutely nothing by his direct contact, stays for only one second, then comes back to 1985. What can he expect to find?

Well, even if nothing is altered by his direct physical contact, Marty still exerts an additional gravitational force on his surroundings simply due to his mass. Since this is going to be an order of magnitude calculation, let's say that Marty has a mass of 100 kgs.

Now, consider the air molecules on the other side of the Earth from Marty. The Earth's diameter is 12.7e6 m. That is 12.7 million meters - I'll be using scientific notation (using e for the power of 10) and meters-kilograms-seconds throughout this calculation. Knowing that the universal gravitational constant is 6.67e-11 in mks units, we can use Newton's law of Universal Gravitation (a = Gm/r^2) to find that Marty causes an acceleration of 4.13e-23 m/s^2 to these air molecules.

Wow, that's like, nothing, right? In the one second that Marty is in 1955, that additional acceleration causes these air molecules to move an additional 2.07e-23 m that they would have otherwise not traveled. That's 0.000 000 000 000 000 000 000 0207 meters. What difference could be made by some air molecules moving such a small additional distance?

Consider a surface of one square meter on that other side of the Earth. The air molecules within 2.07e-23 m of that surface will have then collided with that surface and bounced back, due to Marty's additional gravitational pull. One square meter with 2.07e-23 m of thickness gives a volume of 2.07e-23 m^3, and this is the volume of air we're concerned about. There is 1 mole (6.022e23) of air in 22.4e-3 m^3 of volume in typical conditions, so that amounts to perhaps 556 air molecules that have bounced back against the surface.

Now, the important point here is that these air molecules are now OUT OF PLACE. They're somewhere that they're not suppose to be. As far as anyone from 1955 is concerned, the states of these 556 air molecules are unpredictable. If Marty had not traveled back in time, they would be somewhere completely different on the atomic scale. That means that they would collide with other air molecules that they were not supposed to collide with, while missing collisions that they were suppose to make.

The focus on collisions here is important. As long as the change that Marty causes is all smooth - say, by moving everything over by 2.07e-23 m - then any predictions made from 1955 would only be off by that much. Only negligible changes would occur from moving things by a negligible distance. But collisions change all that. If an air molecule makes a collision that it wasn't suppose to make, or misses a collision that was suppose to happen, then your predictions about the trajectory of the molecules are not just slightly off, they're completely wrong. That's why we're focused on the air molecules that bounced off the surface (whose trajectories are now completely unpredictable), rather than all the other air molecules (whose positions are now just all off by 2.07e-23 m).

Now, each air molecule experiences something like 1e10 collisions with another molecule each second. Each collision changes the trajectory of BOTH molecules. That is to say, 1e10 time a second, the number of air molecules whose trajectory is now completely unpredictable DOUBLES.

If we ignore the fact that a molecules may run into the same molecule multiple times, the number of molecules whose trajectory is now completely unpredictable would be 2^1e10 in one second. This is an absurdly large number, even when you're counting molecules. For all practical purposes, you can consider the microstate of ALL the air molecules around these original 556 molecules to have become completely unpredictable, in far less than one second. This cloud of unpredictability would rapidly spread, limited only by the diffusion and mixing of the air.

Furthermore, remember that this happens to every square meter of surface on the Earth. The upshot is that, from Marty's one second stay in 1955, even if he affects nothing by his direct touch, the microstate of the Earth's ENTIRE atmosphere rapidly becomes COMPLETELY UNPREDICTABLE, completely different than how it otherwise would have been. Something similar must also happen to all the liquids on the Earth, although the calculation will of course differ in detail.

Okay, so the future trajectory of all these molecules are completely unpredictable at this point. But really, can these molecular changes actually affect anything? What does it matter whether some molecules - or all molecules, for that matter - are here instead of there?

In the short term, it won't affect much. But there would be small changes. Microscopic differences can often affect the macroscopic world. The twinkling of stars, for example, is caused by the fluctuations in the momentary, localized density of the air. Photomultiplier tubes are devices specifically designed to cause macroscopically detectable measurements from microscopic events. Cosmic rays travelling through the atmosphere can be affected by the microstate of the air molecules, and they can cause neurons to fire when they hit your brain - perhaps causing a thought or a feeling you otherwise would not have had. The microscopic collisions of the molecules with other small particles causes Brownian motion - the random, jiggling movement of small particles suspended in water. So, a pollen grain would take a different random path in water, because Marty traveled back in time, for one second.

Now, do you think these changes still can't make any real differences? Try replacing "pollen grain" in the previous paragraph with "sperm".

Each sperm carries a different genetic code. Unless a specific sperm made it to the egg at the moment of your conception, you would not have been born. And the trajectory of that sperm would have been different, because the molecular motions in the fluids would have been different, all because Marty was in 1955 for one second and exerted a little bit of extra gravity. Forget about trying to get his parents to fall in love with one another - Marty was in all likelihood doomed to not exist the moment that he popped into 1955.

If you go review the argument and the calculations above, you'll see that the situation is actually far worse, in terms of predictability, than what I have presented. For example, altering the path of a sperm is not a particularly special way of affecting the future. In general, small changes - even microscopic changes - will eventually grow to cause macroscopic differences in time. This is called the butterfly effect: the name comes from an example where a butterfly flapping its wings can cause a hurricane on the other side of the Earth some time later.

The magnitude of the initial perturbation is also unnecessarily large in the example above. Remember, this doesn't affect just Marty; similar changes would happen all over the entire Earth. As if that wasn't enough, I once carried out another calculation which showed that even at INTERSTELLAR DISTANCES, a small change at another star will easily affect the microstate of things on Earth, which will then soon grows to make macroscopic differences.

So, that is the magnitude of the future's unpredictability: your very existence hinged on small changes happening in other parts of the galaxy.

But I don't want this post to be one of those "see how wrong the movies are" articles. I like the "Back to the Future" trilogy. I don't like tearing things down just for the sake of tearing them down. So I'll end this post with the following:

I think the truest thing in those movies is what Doc says at the very end: "your future hasn't been written yet. No one's has. Your future is whatever you make it. So make it a good one." That may or may not be philosophically true in the deepest sense. But what is absolutely certain is that Doc's advice is effectively true in a practical sense. What the above calculation shows is that you cannot hope to indefinitely predict the details of your future. No one can. In that sense, your future is not yet written. What you can do, however, is act in the present to control the short moments ahead, and focus on the bigger picture to extend the lifetime of our planning before the butterfly effect kicks in. We then adapt and adjust, one step at a time. That is how we make the future.

The next post will walk though the calculation I mentioned earlier, about how this all works even at interstellar distances.


You may next want to read:
How to think about the future (Part 2) (Next post of this series)
An analysis of "Let It Go" in Disney's "Frozen"
The dialogue between two aliens who found a book on Earth
Another post, from the table of contents

On martyrdom (Part 1)

We're going over the book of Acts in my Bible study group. We recently went over the stoning of Stephen in Acts 7, and did a related study looking at the concept of martyrdom. Here are some relevant quotes on that topic, from various persons:

If a man has not discovered something that he will die for, he isn't fit to live.
 - Martin Luther King Jr.

When Christ calls a man, he bids him come and die.
 - Dietrich Bonhoeffer

Cheap grace is the deadly enemy of our Church. We are fighting today for costly grace.
 - Dietrich Bonhoeffer

He is no fool who gives what he cannot keep to gain what he cannot lose.
 - Jim Elliot

Those willing to die will live, and those willing to live will die.
 - Yi Sun Shin

Whoever wants to be my disciple must deny themselves and take up their cross and follow me. For whoever wants to save their life will lose it, but whoever loses their life for me will find it.
 - Jesus, in Matthew 16:24, 25

Large crowds were traveling with Jesus, and turning to them he said: “If anyone comes to me and does not hate father and mother, wife and children, brothers and sisters—yes, even their own life—such a person cannot be my disciple. And whoever does not carry their cross and follow me cannot be my disciple.

Suppose one of you wants to build a tower. Won’t you first sit down and estimate the cost to see if you have enough money to complete it? For if you lay the foundation and are not able to finish it, everyone who sees it will ridicule you, saying, ‘This person began to build and wasn’t able to finish.’

Or suppose a king is about to go to war against another king. Won’t he first sit down and consider whether he is able with ten thousand men to oppose the one coming against him with twenty thousand? If he is not able, he will send a delegation while the other is still a long way off and will ask for terms of peace. In the same way, those of you who do not give up everything you have cannot be my disciples."
 - Jesus, in Luke 14:25-33

Do not be afraid of what you are about to suffer. I tell you, the devil will put some of you in prison to test you, and you will suffer persecution for ten days. Be faithful, even to the point of death, and I will give you life as your victor’s crown.
 - Jesus, in Revelations 2:10

In fact, everyone who wants to live a godly life in Christ Jesus will be persecuted
- Paul, 2 Timothy 3:12

If the world hates you, know that it has hated me before it hated you. If you were of the world, the world would love you as its own; but because you are not of the world, but I chose you out of the world, therefore the world hates you.
 - Jesus, in John 15:18

Blessed are those who are persecuted because of righteousness, for theirs is the kingdom of heaven.
Blessed are you when people insult you, persecute you and falsely say all kinds of evil against you because of me. Rejoice and be glad, because great is your reward in heaven, for in the same way they persecuted the prophets who were before you.
 - Jesus, in Matthew 5:10-12

My next post will explore the ideas in these quotes.


You may next want to read:
On martyrdom - a parable (Part 2) (Next post of this series)
"Simon, son of John, do you love me?"
The Gospel: the central message of Christianity (part 1)
Another post, from the table of contents

Religious freedom and religious accommodations

This post is a consolidation of a whole series into one post. It's fairly long. Click on the following entries in the table of contents below to jump directly there:




Introductory case: A Muslim flight attendant who won't serve alcohol


There is a news article about a Muslim flight attendant who is in danger of losing her job. She refuses to serve alcohol on flights, as such service would go against her faith.

This story seems to be a decent initial test case for evaluating our positions, without the usual political cheerleading getting in the way of our thinking. So we'll start out here, and later consider other similar cases, using the principles we use in this case.

As for me, I think that we are doing something very wrong if the structure of our society requires people to violate their sincerely held religious beliefs. If we do so, we impoverish the diversity, tolerance, and freedom in our world while making it more dogmatic and tyrannical. This is so obvious, and already expressed so clearly by the first amendment, that it's actually a little embarrassing to have to write it out. Yet, here we are.

This is doubly true when a simple shifting of duties can so easily accommodate the religious conviction in question. Seriously, someone else can't take over for her when a passenger requests a drink, while she does extra work elsewhere? If we can't figure out this trivially simple logistics problem because we're all too busy taking sides, then we really are in trouble. What do we gain by forcing this woman to serve alcohol? More importantly, what do we lose?

Now, one possible objection to my view is that having a job requirement is not discriminatory. I fully agree. Nobody is arguing that she be allowed to keep a job as a bartender. But serving alcohol is a very minor part of being a flight attendant. Whatever other duty this woman performs instead of serving alcohol can easily make up for her inability to perform this one minor task, whether that is measured through customer satisfaction, the airline's bottom line, or her co-worker's work load.

This is an important condition: that she MUST take up extra duties elsewhere to make up for her inability to serve alcohol. Whether or not this is possible is where the line gets drawn in deciding if the airline ought to fire her. In this case, there's no question that it is possible, as serving alcohol is a minuscule part of a flight attendant's duties. (If this somehow turns out not to be the case, then I have no problem with the airline firing her.) Implementing this reassignment of duties is a trivially simple matter.

At this point, some people go off the deep end and say that if an employee cannot perform ANY PART of their job duties, no matter minor that part is, then the business has an absolute right to fire her. But this position is simplistic, one-sided, and concerned only with preserving the power of the business. It would allow a business to fire any imperfect employee - which is of course any employee, period. Instead, we must consider both sides - the business has the right to operate without undue interference or obstacles, but an employee also has the right to protect herself from being forced to violate her identity. These concerns must be evaluated and weighed. The above-mentioned condition is where these concerns meet: the employee must take up extra duties to make up for the trouble to the business, and if this accommodation is not possible she should be fired. In the case of our flight attendant, it's pretty clear that the accommodation is easily possible.

So then, the choice here is simple. The airline can simply shuffle some duties around - something so trivially easy that even a five-year-old can understand it - with no loss. Or, it can fire her. If we can't make the right choice here because we're too busy getting wrapped up in political cheerleading, we're in deep trouble.

Another possible objection would be to claim that firing the flight attendant has nothing to do with religious freedom: the flight attendant would not be fired for being Muslim (which would be discriminatory), but for refusing to serve alcohol (which is just a part of her job). Anyone else making the same refusal would also be let go. But line of thought fails on multiple levels. First, if the airline were to fire a non-Muslim with a genuine conviction against serving alcohol, it would still be making the wrong choice, even if it's only concerned with its own profits: note the cost of firing, hiring, and training, compared to no loss for the airline in making the accommodation. Accommodation is better even in the case of non-Muslims. Our Muslim flight attendant is therefore not pleading for some special privilege associated only with religion. She is simply appealing to the universal principles of common sense and basic decency.

But much more importantly, this idea of divorcing identity from action is fundamentally misguided, and fails on any other application. So, our flight attendant is allowed to BE Muslim, but she's not allowed to ACT Muslim? Behold the catalog of fails this leads to, in a multitude of analogous cases:
A Jewish holocaust survivor works as an artist in a graphics design firm. His identity doesn't matter much for his job, until his firm is commissioned by a Buddhist temple to draw some swastikas for a brochure. Due to his past trauma, he asks his boss to shift around the project assignments so that he can work on something else instead. But his boss replies, "Look, being an artist is your job. You must draw what the customer wants. To accommodate you may negatively affect the firm's bottom line. I know that you ARE a Jew, and I have no problem with that, but you're not allowed to ACT Jewish, by bringing up your past history or your people's past history. If you insist on ACTING Jewish, you're fired." 
A female P.E. instructor is working at a school, and for the new school year, they're bringing back a swimming class. Unfortunately, all previous swim instructors were male, so they don't have any female swimsuits for adult teachers. As part of the school's dress code, all articles of clothing - including swimsuits - must be provided by the school. When she goes to the principal to ask for a female swimsuit, she is told, "Look, I know that you ARE a woman, and I have no problem with that. But you're not allowed to ACT like a woman if that will hurt your job performance. Wearing a swimsuit is part of your job. You'll just have to wear one of the past instructor's male swimsuits we have available. Ordering another swimsuit would definitely impact the school's budget in a negative way. If you insist on ACTING like a woman and demand a woman's swimsuit, you'll be fired." 
A gay man works as a general handy-man around the school in a small, conservative town. He does gardening, plumbing, cleaning, and other such jobs after school is out. His work doesn't involve much interaction with the students or the parents - except at the annual "Back to School Night", for which he represents the school by serving as the greeter. He plans to marry a man that he loves, but doesn't want to create drama in his small, conservative town. So he goes to the principal and asks to be let off this one duty, with a corresponding pay cut. There he is told, "Look, I have no problem with the fact that you ARE gay. But I do have a problem with you ACTING gay by getting married. I'm not being discriminatory, because even if you were straight, I wouldn't want you to marry a man, and we would not be having this discussion if you would just marry a woman instead. Representing the school is part of your duties, and your effectiveness there would obviously decrease if you married a gay man in a town like ours. I don't want to have to look for another greeter, therefore you are forbidden to marry. Otherwise, you're fired." 
A transsexual woman starts at a new job, and runs into the usual problems with the bathrooms. Fortunately, the building has many single-occupancy bathrooms, but unfortunately they're all currently labeled as either for male or female. Not wanting to cause a stir at her new job, she asks the building supervisor to simply designate some of them as unisex bathrooms so that she doesn't have to bother anyone. The supervisor replies, "Look, I know that you think that you ARE a woman, and I have no problem with that. But working in this building is obviously a part of your job description, and you are not allowed to ACT like a women if that would disrupt the building and the use of its facilities. Furthermore, ordering new bathroom signs would undoubtedly impact the company's bottom line negatively. So, you must use the men's bathrooms. Otherwise you lose your job." 
A Muslim is working as a flight attendant, and on rare occasions a passenger requests alcohol, which her religion forbids for her to serve. So she asks for a simple reassignment of duties - she'll do some other work while being excused from having to serve alcohol. But the airline replies, "I know that you ARE a Muslim - in fact, you can call yourself whatever you'd like - but you're not allowed to ACT Muslim. That would interfere with your duties as a flight attendant. We furthermore deny your request for a different set of responsibilities, as that may be detrimental to our business. Violate your conscience, or face termination."
Who among us thinks any of this is okay? Identity without actions is meaningless. It's absurd to say things like "you can BE gay, as long as you don't ACT gay". The solution to these problems does NOT involve dictating what is allowed to someone with a marginalized identity, and it does NOT involve the ones in authority trampling everything to get their way. The solution in these cases consists of making a simple choice between two options:
Option A: Force the employee to perform an action that would profoundly violate their identity, by threatening them with the loss of their livelihoood. Or,  
Option B: Accommodate the employee's simple request, which has no significant negative effect for the employer.
This is not a hard choice. It is, as I said before, actually trivially simple. It is so easy that even a five-year-old can understand it and get it right. If you can't figure out something this easy because of some preconceived notions, you need to reject those notions and rethink your life.



Enumerating the general principles at work


Now, we want to extract the core principles involved in cases like this.

Let's begin by summarizing my position: the flight attendant's sincerely held religious beliefs ought to be protected, but the airline also has a right to operate without undue hardship. This calls for a careful consideration of the claims of each party, to see whether both concerns can satisfactorily addressed. The solution I proposed was this: the flight attendant ought not to be forced to serve alcohol, but she must make up for this in taking up other duties, so that the net effect on the airline is negligible. Whether or not she CAN make up for it determines whether this accommodation ought to be accepted: for instance, if she were a bartender instead of a flight attendant, clearly she would not be able to make up for not serving alcohol, therefore the accommodation would not work out, and I would fully support the business in firing her. However, since serving alcohol is a minuscule part of a flight attendant's job, it would be trivially simple to shuffle around the duties so that she does something else while another flight attendant serves the drinks. Thus, she should be accommodated.

I was furthermore against the simplistic idea that "if she can't do her job, she ought to be fired". To say that the business has an absolute power to fire an employee for not doing a part of her job - even if that part is a minuscule portion of the job description - would mean that the business could fire any imperfect employee. That is to say, it could fire any employee, period. That would simply be a case of the business trampling over the employee with its power, with no regard for balance, fair play, or the rights of the employee.

So, let's explicitly state the general principles involved here:
I believe that people have a right to the free exercise of their religion. This is actually only a small slice of a broader principle: that people have a right to live according to their identity. 
Conversely, it is wrong to require people to violate their conscience, their gender, their sexual orientation, their people's history, or other such categories that form one's core identity. 
I believe that the many - whether it be a large corporation, a governmental institution, a school, or simply "society" - also has a right to impose order and insure its own smooth operation. 
Conversely, it is wrong for an individual or a minority group to disrupt the workings of the majority to satisfy their own needs. 
I believe that, in case of a conflict, a balance should be struck. We should take the concerns of all parties into account and weigh them together to achieve a fair solution. 
Conversely, I am against one side simply imposing its will on the other. I will oppose any actions whose chief goal is to forcefully restrict the freedom of others, whether it comes from the minority or the majority. 
I believe in cooperative, common-sense solutions characterized by nuance and empathy. 
Conversely, I am against ham-fisted, absolutist, or antagonistic decision making processes. 
Of course, we will not always find perfect solutions that perfectly satisfy all these principles. But especially in such cases, I believe that we should take extra care not to favor the strong over the weak, the large corporation over the individual employee, the majority over the minority, or profits over personal rights.
I believe that my position on the issue of the flight attendant embodies all of these principles. I sincerely hope that these principles are things we can all agree on. It's only common sense and basic decency.

Also note that I'm not particularly concerned about the law of the land. Human laws derive their legitimacy from natural laws - in our case, from what is right and wrong as established by moral principles. If we understand the principles well, the implementation of their particulars in our laws will be straightforward. That is why I'm primarily concerned with the principles.

With these principles, we are now ready to tackle other similar cases where religious freedom, societal power, minority rights, and government authority intersect.



A Muslim student's home-engineered clock is taken for a bomb


Ahmed Mohamed is a 14-year old Muslim student who was arrested for bringing in a home-assembled digital clock to school. If you haven't heard this story already, please read up on it. The remainder of this post will assume your familiarity with the story.

Now, because this is a recent event, new facts may emerge that changes the character of the story. Of course, I am all for taking into account any new relevant information, and for people always digging deeper for more facts. However, since I have to apply the above principles to SOMETHING, and because I cannot read every single article out there about Ahmed, I have decided to take the story, as it appears on Wikipedia today (9/21/15), as canon. Remember that my chief concern is the application of the above principles: I am confident that, regardless of any additional information, the principles can be applied to arrive at a correct conclusion. That will be true even if that conclusion changes based on the new information.

Now to the matter at hand: first, Ahmed has the right to live according to his identity - that of being a Muslim student interested in engineering. He is free to put together digital clocks and bring them to school to show to people.

But the school also has a right to ensure its smooth operation and a duty to ensure the safety of its students and staff. At this point, I should point out that the appearance of Ahmed's clock is a legitimate cause for concern. This is true completely independent of any questions about Islamophobia or racism. Imagine that you're a teacher, and you came across this device with nobody nearby. It's been left behind beneath a random student's desk, and it's making beeping sounds. Would that not cause at least a small bit of concern? You would certainly be derelict in your duties if you simply shrugged your shoulders and walked away.

So, now we have a conflict between the student and the school. The principles stated above says that we should look for a balance. Neither party should get an absolute final say in restricting the freedom of the other: the school ought not to treat the student as a terrorist, but the student also ought not to be allowed to bring dangerous-looking device to school and flaunt it. Instead, we should seek a balanced solution that maximally preserves the rights of both parties. In my view, Ahmed's engineering teacher comes closest to striking this balance: upon looking at the clock, the teacher told Ahmed, "that's really nice", but also advised him to keep the device in his backpack the rest of the day. In this interaction, Ahmed is praised and validated for his achievement, but is also gently told that the appearance of his clock is problematic. The student's rights and the school's concerns are both taken into account and adequately protected.

The one additional thing that the engineering teacher could have done is to ask Ahmed to leave the clock with him until the end of the school day, so that he can to show it off to his other students. This would have enhanced both the recognition of the student's achievement, and also the security of the school. Of course, we can't fault the engineering teacher for not coming up with this solution on the spot - it's something that I came up with only due to perfect hindsight and the benefit of sitting calmly at my desk. But it is this kind of win-win solution, which takes the interests of all parties into account, that we always ought to be looking for.

Unfortunately, the story from this point veers off in the opposite direction, to a one-sided lose-lose scenario. The school acts in a unilateral, antagonistic manner, trampling over the student's concerns while only looking out for its own rights: the clock later beeped in Ahmed's English class, and the teacher requested to see it. Ahmed was then reported to the principal's office (up to here, I think things are okay - if you disrupt class with beeping from a scary-looking device, it's not unreasonable for that to merit a report to the principal's office). From there, the police got called in, and Ahmed is interrogated, handcuffed, and sent to a juvenile detention center. He was denied contact with his family, threatened with expulsion, and suspended for three days.

Clearly, the school massively overreacted. At some point in this chain of events - probably pretty early on - it must have become clear that the clock was not a bomb. At that point the school should have turned back from its course, acknowledged its error, and apologized to Ahmed. It should have upheld his right to make clocks and bring them to school, while gently reminding him to be careful about the threatening appearances of his devices. Instead, it plowed ahead on its one-sided course, and the story was then reported all over the news.

Fortunately, once the story hit the news, American society as a whole reacted to restore the balance by coming to Ahmed's support. He has been invited to the White House by President Obama, along with receiving a great deal of other opportunities and expressions of support. So Ahmed has been greatly wronged by his school, but society as a whole restored the balance by compensating him for that wrong. That is as it should be. The only thing I might wish to have gone differently is if President Obama's invitation was delivered through Ahmed's school or the local police department, instead of over Twitter. That might have done more to directly compensate for the harm caused to Ahmed from these institutions, and allowed them to apologize to Ahmed gracefully. But of course, I can't fault Obama for not implementing that particular solution, which again only comes to me through hindsight and calming distance.

So in the end, the story appears to have come to an acceptable ending. I just can't help but think that all this would have been unnecessary if more authority figures around Ahmed had been able to see things from multiple perspectives, like his engineering teacher had. But instead, so much of our society seems to be driven by a simplistic, antagonizing, ham-fisted, one-sided narrative. It's not hard to imagine that the school administrators were driven by a safety-first, zero-tolerance policies that says "anything that compromises the safety of the school must be stopped". Conversely, the reaction to Ahmed's plight seems to be driven in part by an equally one-sided "LOL, Americans are racist Islamophobes" narrative. Sometimes we get lucky, and these one-sided narratives collide in such a way as to restore balance, as it did in Ahmed's case. But I still worry about what happens when we don't get lucky.



A Christian cake shop that doesn't cater same-sex weddings


Sweet Cakes by Melissa is a cake shop that was heavily penalized for refusing to cater a same-sex wedding, which they felt was against the principles of their religion. The rules here are the same as in the previous section: I will assume familiarity with the story. I will take only the Wikipedia article as it appears today (9/28) as canon. I care more about what is right rather than what is legal. And lastly, my chief concern is the application of the principles governing the interaction between the majority and the minority.

Let's get right to it: first, the owners of the cake shop have a right to free religious exercise. They should not be forced to participate in an activity that violates their sincerely held beliefs.

But the State of Oregon also has a right to enforce its 'equal accommodation' law, and the same-sex couple has a right to walk into any public business and expect and receive that equal accommodation.

So that is the conflict. How can we resolve it? As before, it would be wrong to simply allow one party to unilaterally impose its will upon the other. That is to say, it would be wrong to simply allow the owners of the cake shop to refuse service, and it would also be wrong to simply force them to violate their conscience and cater the same-sex wedding. Both sides must be taken into account in our solution.

So how can we balance the rights of both parties? Is there a way to protect both the cake shop's free exercise of religion, and the same-sex couple's equal accommodation? I believe there is. In fact, there are multiple, simple ways to preserve the rights of everyone involved in a live-and-let-live fashion, without antagonizing anyone.

The easiest way is to simply outsource the job. Make some arrangements with another cake shop that does not mind catering same-sex weddings, then simply let all customers know that any personalized cake order may be filled by that shop. The owners of the original cake shop would then take the order from the same-sex couple, and hand off the job to the other shop. The customers won't even have to know why this happened. The cake shop wouldn't have to cater a same-sex wedding, and the same-sex couple gets their cake without a hitch.

What if the same-sex couple were to insist on the order being filled by the original cake shop? I think this is an unreasonable demand, for multiple reasons. First, it seems likely that the motivation behind such a demand is "We want to violate your conscience", and not "we want equal accommodation". I am against motivations like these, which seeks to forcefully restrict the freedom of others. As long as the service and the customer experience is not meaningfully different between homosexual and heterosexual couples, the customer's rights have been satisfied and they do not get to furthermore demand that the inner workings of the business itself must conform to their ideology. In addition, such a demand would suggest that the cake shop is not really a public accommodation - that they are more like an artist with a unique, singular talent whom the couple is commissioning for a new project. And of course, the artist is free to accept or reject any new projects in such cases.

On the other hand, what if the cake shop were adamant in not serving the same-sex couple, in any way? This, too, is unreasonable. This position may look like they're saying "we want to make your wedding difficult" rather than "we want to obey our conscience". The fact of the matter is that the cake shop, by refusing to serve the same-sex couple, did cause them some amount of actual inconvenience. They wasted their customer's time and nullified their efforts. This is an actual, material harm that they caused to the couple, and it must be compensated for.

What would be the right amount of compensation in such cases? This, too, can be framed in terms of the previously listed principles: the cake shop has the right to free exercise of their religion and the same-sex couple has the right to equal accommodation. So, if the cake shop has not made any previous outsourcing arrangements, or if their beliefs are so rigid that they cannot even bear to take an order from the same-sex couple, what should happen? The answer is straightforward, at least in theory: the couple should receive enough compensation to restore their experience to be on par with "equal accommodation".

Note that this is a second-best solution, after the "outsourcing" solution mentioned above. Because it is a second-best solution, where the cake shop's demands are higher, the implementation will be much messier and the compensation to the couple must be correspondingly higher. To determine the appropriate level of compensation - enough to make up for the couple's time and effort and achieve "equal accommodation" - let's consider these two scenarios:
Scenario 1: you walk into a cake shop, then order a cake without any problems. 
Scenario 2: you walk into a cake shop, receive X dollars, and are turned away. You then order the cake from elsewhere.
The value of X that makes us equally likely to choose either scenario is the proper compensation. My gut feeling on this is that about $60 should be sufficient to cover most cases. Of course, that value is subject to refinement pending further consideration.

It's important to note that the same-sex couple doesn't simply get to choose their own value of X, as that obviously has a massive potential for abuse. X should therefore be based on what the population, as a whole, would choose in such scenarios. Also note that this solution assumes a civil business-customer interaction: words like "bigot", "abomination", or "homophobe" are assumed to have not been thrown around. If they were, that could be handled separately. Lastly, the same-sex couple here is being compensated for their lost time and energy, and not for their hurt feelings beyond simply being turned away. They do not receive any compensation for being offended at the beliefs of the cake shop owners, no more than the cake shop owners receive any compensation for for being offended that two people of the same sex should be getting married. Each party believes the other is wrong; but neither gets to impose their beliefs on the other, and both get to preserve their core identities. Truly, each may say to the other, "we're here, we're queer (from your perspective), get used to it".

If I were the dictator of Oregon and this case came before me, I would rule in favor of the same-sex couple, and order the cake shop to pay about $600 to the couple as compensation for damages (the tenfold increase from $60 is due to the fact that the state had to step in and force the transaction). I would then expand the scope of this decision by turning the case into a class-action suit, allowing any same-sex couple who can demonstrate that they had been similarly discriminated against to receive their $600 from their respective cake shops. Lastly, I would force such cake shops to implement the "outsourcing" solution. Alternatively, these cake shops may issue coupons for $60 off on wedding cakes from other nearby shops to any same-sex couple they turn away. The original cake shops would be responsible for negotiating and implementing this coupon system with the other shops.

The details of that "$60" solution can certainly be improved with more input from better businessmen and lawyers than I. However, the main point is that for both the "outsourcing" and the "$60" solution, the rights of both the cake shop and the same-sex couple can be preserved. The "outsourcing" solution is simple and fair. Even if it comes to the "$60" solution, the two parties can get along with minimal antagonism and with their core identities and rights intact. Both solutions achieve balance, and are vastly to be preferred over any scenario where one party simply imposes its will on the other.

As a final test, let's think about how these solutions work when the identities have been switched around. What if a Christian organization asked a gay-owned cake shop to put a Bible verse - say, Leviticus 20:13 - on a cake? Or what if an interracial couple asked a racist cake shop to make their wedding cake? How about if a white supremacist couple asked a black cake shop owner to write "for the propagation of the superior Aryan race" on their wedding cake? What about when a Buddhist temple wants a swastika-shaped cake from a Jewish cake shop? Can my proposed solutions above handle these cases equally well?

Think through these test scenarios, and consider how the two solutions would be implemented in each case. You'll see that the "outsourcing" solution handles all these cases with no conflict and protects the core identities of all involved parties. It's important to note that it does so completely independent of the moral correctness of any of the parties, which is a good sign. Even the "$60" solution minimizes antagonism and prevents one party from simply trampling over the rights of the other - again independent of the moral correctness of the parties involved.

Of course, nothing like my solutions happened in real life. The same-sex couple was simply turned away from "Sweet Cakes by Melissa" (sigh...), then the court hit the business with a crushing $135,000 fine (arg!). The cake shop then raised over $100,000 in an online campaign before that campaign was shut down (what?), and the owners have stated that they will contest the decision against them. I still have hope that all these one-sided efforts might cancel out to restore balance in our society, but real life continues to worry me.



A county clerk refuses to issue marriage licenses


Kim Davis is the county clerk of Rowan County, Kentucky, who was jailed for some time for refusing to issue marriage licenses. Her rationale was that issuing them to same-sex couples would violate her religious beliefs.

The rules here are again the same as before: I will assume familiarity with the story. I will take only the Wikipedia article as it appears today (10/4) as canon. I care more about what is right rather than what is legal. And lastly, my chief concern is the application of the principles governing the interaction between the majority and the minority.

If you've read this far, you likely know what I'm going to say about Kim Davis: we should seek balance. We cannot allow one clerk to simply deny marriage licenses to a whole county, but we also must not force an individual to violate their religious convictions. A simple, reasonable accommodation for the clerk should be sought. If such accommodation is not possible, we may have to go to second-best solutions, which require more complicated accommodations and therefore more cost to all involved parties, as in the "$60" solution in the previous post. If all attempts fail, then as the last resort, the county clerk may have to be removed from office, or be otherwise compelled to issue the licenses.

The problem in this story is that it's unclear how much accommodation Kim Davis requires. The story essentially starts off from the beginning with her refusing to issue marriage licenses. Now, if that's the end of the issue for her - if there is absolutely no way for same-sex couples to get their licenses while she's in office - then no accommodation is possible. She must resign, or be somehow compelled to issue the licenses.

However, if Davis is only asking for her name to not be on the marriage licenses, then that seems to be a simple matter. We just have to ask, "is this possible? Is it feasible? Is this costly, beyond what can be made up for by Davis?" If it turns out that this is a reasonable accommodation (which seems likely), then it should be made.

But, if this is what Davis wanted, why did she not start off her protest in that way? She could have issued licenses with her name manually crossed out. She could have changed her own name - perhaps to something like "Matthew 19:4-5". There are several different ways for her to circumvented her name appearing on the licenses. Then if she were challenged, she could legitimately say that she was only protecting her own religious freedom, with no intent to restrict the freedom of others.

What if Davis had only been asking that she herself not handle same-sex marriage licenses? Well, she has several deputy clerks. One of them could issue licenses in her stead. There should be no problems with providing that kind of accommodation to Davis - in fact, it seems likely that she could have implemented it herself without any trouble.

Failing all that, Davis might have offered the couples a monetary compensation for them to go to another county clerk, as in the "$60" solution in the previous post. However, this is a distinctly worse solution, even moreso than in the previous post. The differing nature of a cake shop and a government office would dramatically increase the required compensation, to the point where this scheme would likely become unworkable. But at least it would be something - anything to show that there was some way for some kind of arrangement where Davis' religious freedom could be accommodated.

But in starting her protest by simply turning couples away, Davis seemed to be saying that her office will not issue any marriage licenses while she was the county clerk. Under those circumstances, it is entirely appropriate to call for her resignation, or to jail her to force her to act. Fortunately, after the usual legal and media circus, it turned out that it was acceptable for all parties for the marriage licenses to be issued without her name, through a deputy clerk. And that is how things are now done in Rowan County.

So this story seems to come to a reasonable conclusion - everyone wins, or at least doesn't lose. Same-sex couples get their licenses, and Kim Davis keeps her job and her clear conscience. A simple, reasonable accommodation allows for everyone to more or less get along. The "system" seems to have worked.

But as in the previous cases, I see several worrisome things. I wonder about our ability, as a society, to come to these reasonable conclusions. There seems to be a strong tendency for us to become polarized, line up on opposite sides, then cheer for whomever is on our side. Could Kim Davis not have simply started by implementing the reasonable accommodation herself? Why begin by turning people away? The opinions of many people reacting to this issue also seems to be entirely one-dimensional: in the Wikipedia article it says "When asked what Davis should do, 65% said that Davis should resign from office; 23% said that Davis should stay in office and continue to refuse to issue marriage licenses to same-sex couples; and 4% said that Davis should remain in office but issue licenses to all persons legally entitled to one." NONE of those three options come close to the solution they eventually settled on, the one that actually maintains balance among the rights of all parties.

Furthermore, apparently there are some people who are calling into question the validity of the newly issued marriage licenses, the ones without Davis's name that are issued by a deputy. Seriously? What good could come of this? You would invalidate the licences of couples that have already received them, so that you can imperil Davis's religious liberty? That's the lose-lose solution. The only thing it accomplishes is to further antagonize the other side by blowing everything up. It is perhaps the worst way for this story to continue, for pretty much everyone involved.



Conclusion


Once again, here are the general principles involved in these cases:
I believe that people have a right to the free exercise of their religion. This is actually only a small slice of a broader principle: that people have a right to live according to their identity. 
Conversely, it is wrong to require people to violate their conscience, their gender, their sexual orientation, their people's history, or other such categories that form one's core identity. 
I believe that the many - whether it be a large corporation, a governmental institution, a school, or simply "society" - also has a right to impose order and insure its own smooth operation. 
Conversely, it is wrong for an individual or a minority group to disrupt the workings of the majority to satisfy their own needs. 
I believe that, in case of a conflict, a balance should be struck. We should take the concerns of all parties into account and weigh them together to achieve a fair solution. 
Conversely, I am against one side simply imposing its will on the other. I will oppose any actions whose chief goal is to forcefully restrict the freedom of others, whether it comes from the minority or the majority. 
I believe in cooperative, common-sense solutions characterized by nuance and empathy. 
Conversely, I am against ham-fisted, absolutist, or antagonistic decision making processes. 
Of course, we will not always find perfect solutions that perfectly satisfy all these principles. But especially in such cases, I believe that we should take extra care not to favor the strong over the weak, the large corporation over the individual employee, the majority over the minority, or profits over personal rights.
I sincerely hope that these principles are things we can all agree on. It's only common sense and basic decency. We have, as a society, seem to have not done too poorly by these principles. But too often that only seems to happen through dumb luck, and the one-sided extremist voices often seem to be the loudest and get the most press.

So... "God bless America". At the end of the day, that is perhaps the only thing that may be said here. He has done so abundantly up till now, and we'll surely need his continuing blessing into the future.


You may next want to read:
Basic Bayesian reasoning: a better way to think (Part 1)
History, moral progress, and moral perfection (part 1)
Another post, from the table of contents