Fun with math, part II

Yep, it's time for another installment of my (apparently) continuing series, "I've got messed up curiosities and waaay too much time on my hands."

So, a couple months ago, I looked up the formula to find the Roche limit of a given body of mass to its satellite, and asked what was perhaps the most important question of our time:

"If the Earth were to be caught in a decaying orbit around a Jupiter-sized glob of osmium (the densest natural element), how big would it be in the sky when cities started floating into space?"

And now, finally, I have the tools to answer it!

Okay, for the non-physics majors out there, let me briefly explain the Roche limit. We experience this phenomenon called "weight" (and some of us more than others) due to the Earth's massive size, gravitationally pulling us toward its center. So now, imagine you're standing on the Moon, where you'd weigh six times less:

The Moon is pulling you toward it with a certain strength, and you're too far away from the Earth for it to be able to pull you. But, as the Earth gets closer and closer to the Moon, you'll start feeling a gravitational pull from both the Moon and the Earth:

At some point, Earth's pull on you would be stronger than the Moon's, and you'd start drifting into the sky toward Earth... along with big chunks of the Moon.

So! What if the Earth were orbiting a Jupiter-sized glob of osmium? How far away would the Earth be before cities started floating into the sky?

Roche limit = (the radius of the osmium glob) x (2(density of osmium / density of Earth))^(1/3)

Roche limit = (about 69,000 km) x (2(22.59/5.15))^(1/3)

Roche limit = 139,096.4333 kilometers

Now, that's the distance from the center of the Earth to the center of the osmium glob, so we'd have to subtract the radius of the Earth (6378.1 km) to get:

And all we have to do is apply the law of sines, grab a TI-83, and we've got the answer!

sin(90) / 132,718.333 = sin(ß) / 69,000

Sin(ß) = 69,000sin(90) / 132,718.333

Sin^-1(69,000sin(90) / 132,718.333) = ß

ß = 31.32541187, or approximately 31.33

Since the angle at which we see the glob of osmium is 2ß, we get 62.66.

So, out of 180 degrees (horizon to horizon), the glob would be filling up 62.66 degrees of it, or about one third. Which, as rendered by my artistically inclined brother, means it would looks something like this:

A kind of macabre immortality.

Since I was eight years old, Carl Sagan has no longer been able to inspire us in person. It's an incredible tragedy that Sagan couldn't be here to observe the effects of dark matter on the bullet cluster, or the forthcoming results from the LHC at Cern, or any of the other astounding discoveries we've made or will make since then. And an even worse tragedy that he is no longer around to affect us with his ever-poetic gift for presentation.

In the last six months, I've been watching through his Cosmos series, idolizing him every bit as much as people did while he was still around. I feel like, across time and death, Carl Sagan is a man who really sees the universe in the same way I do. He saw, like I did, humanity's context in the universe, and we were both stunned into silent wonder.

If I had any money, I would own every piece of literature and every film he's ever made, but at the moment callumCGLP's videos on YouTube certainly suffice. If you're a YouTuber, seriously, subscribe to this guy. If you're not, here you go:

"1945-1998," by Isao Hashimoto

This is an oddly beautiful video I picked up from Phil Plait today, showing all the nuclear tests that have been conducted on planet Earth between the years 1945 and 1998. It starts out a little slow (how poignant that we would think so), but gets oddly frightening around the 3:00 mark.

If the Earth were a giant game of Rise of Nations, we'd have ended in an apocalyptic tie dozens of times over.

Predestined to rebel against predestination

Even before I played D&D, I knew I'd love it. A friend of mine had a D&D-esque game he made up which didn't use dice or paper or anything. The whole game was in his head; we'd make our characters and he'd just ad lib the whole experience.

I first played D&D a few summers ago and absolutely loved it. My friend, I'm sure, thinks D&D is too stuffy with all its rules and technicalities, but all those rules, dice, and character sheets make things, I think, more fair. After all, if the success of my attacks and my opponents attacks are both determined by the same person, my character will die when the DM wants him to, and my character will win when the DM wants him to. I don't want to die because of meta-game bias!

Anyway, I absolutely love D&D for several reasons, but one reason really shines above all the rest:

Versatility.

If the players are marching through a town and one decides he/she wants to light his/her staff on fire and use the burnt end to tag "Defy the system!" on the wall of a local store, he/she can. Try doing that in a video game!

Which is why I prefer to host D&D sessions rather than play them. I love crafting a world for the players to explore and experience. I love keeping track of NPCs the players have met, and I love imagining the consequences of the players' actions as they ripple through the world I've created. The players, in my sessions, are the most important part.

I create a world, put the players in it, put some characteristic NPCs in it, and set it off, like a violent chemical reaction. What would this NPC do, now that his house was burned to the ground because a PC decided he/she wanted to tag "Defy the system!" on the side of it? How would the town generally react to adventurers after this event? Will the players meet up with this now-homeless NPC in the future? What's happening on the other side of the world? What are the Significant Event NPCs doing now, and what big events are probably going to happen?

But, after playing in a few D&D sessions hosted by several different friends of mine, I've discovered that D&D is something quite different to most people. It's a frighteningly linear experience with god-like town guards, where the players hack-and-slash their way to level 30. Want to tag "Defy the system!" on the wall? Tough luck. Your character gets jailed by the town guards, whose purpose isn't to preserve peace or promote order but to rigidly force the players down a plot which has been set in stone.

In these kinda games, I'm always a rogue, and I'm always jailed. I think it's a pure expression of myself in real life, actually, that I rebel against this restrictive, totalitarian micromanagement. My hapless rogue throws himself at the system in defiance, earning in-game mockery at best and death at worst.

"Come on, Peter," they say. "Quit dicking around and play the game."

"I am playing the game," I say. "My rogue isn't Fate's bitch."

The world just doesn't feel real if I can't stretch out a little, and the freedom to give up a quest and do something else &mdash "No, I don't care about saving the princess. She can die for all I care. Let's go help this beggar dude steal from the store instead!" &mdash makes for a much more human experience. I mean, if I want to throw immersion to the wind and hack and slash my way to level 30, I can just buy any video game on the market and skip the dice rolling all together.

And this lack of immersion is also why I can never seem to talk to anyone about D&D. The conversations usually go this way:

Me: "Oh, you played D&D this weekend? How'd it go?"

Him: "Dude, I totally rolled a Sorc build that didn't suck!" (Proceeds to list spells, weapons, etc.)

Me: "Yeah... but what happened? What's your sorceror like? Meet any interesting characters?"

Him: "Oh shit, man. You're one of those gay RPers. Look, I don't care. I made my Sorc's eyes glow-in-the-dark purple for teh lolz."

At which point we both smh and part ways.

I'm afraid, though, that my games will get more convoluted as I take more and more physics classes. My players will say, "I command my squad of archers to release a volley" and I'll be like, "Wait, lemme calculate that real quick; I'm not sure if they can actually hit, given the difference in elevation." And then I'd break and try to figure out how high the arrows are off the ground at any specific second, given that they'd have to fire in an arc in order to hit their targets... so, if a shortbow has a range of 60 feet, how much would its range be if you were indoors with a low ceiling?

Oh my god, I can't wait to take physics!

Atheist straw men

Welcome to the Atheist straw men page! This page will be a (hopefully infrequently updated) collection of counterarguments for all the simplistic rebuttals people use to "refute" the Atheist position, inspired by an interview I saw of S.E. Cupp by Sean Hannity.

Table of contents:

• Atheists believe something can come from nothing
• Atheists claim to know for certain there is no God

Atheists believe something can come from nothing.

The simple answer to this goes something like, "No we don't; we have no idea what started or preceded the Big Bang, and we're not claiming it popped out of nowhere. We're saying 'I don't know'."

The complex answer is exactly that: more complex. The entire concept of causality (philosophical shorthand for "cause and effect") rests inside time. There is an interval of time between, say, my dropping an apple and that apple hitting the floor.

We don't really know what causes time, what time really is, nor why immense gravity seems to have an effect on it. What we do know, however, is that time started with the Big Bang, so trying to discuss what caused it is really just a nonsense question at the moment

Really though, I shouldn't have to defend that fact that we don't know. The theist making this claim is really just saying, "The God I worship, which I haven't yet proven or demonstrated exists, can simplistically explain this problem, therefore It must exist." Or, in logical form:

1. The Flying Spaghetti Monster exists.
2. Part of the definition of the Flying Spaghetti Monster is that He can do X.
3. X has been done.
4. Therefore, the Flying Spaghetti Monster exists.

Even if you prove point 1, you'll still have to add a point in between 2 and 3 which reads: "X can only be done by the Flying Spaghetti Monster, exclusively."

Sorry theists, the burden of proof's on you. Logic's is a bitch, isn't it?

Atheists claim to know for certain there is no God.

No, actually, we don't. We believe there is no God. There's a difference.

Let's use Santa Claus as an example. Parents across the U.S. raise their kids with this pleasant and harmless idea that there is a chubby old man, dressed in red, who flies all around the world delivering presents to children, all in one day, who are good. He knows which kids are good, of course, because he's been watching them &mdash each and every one &mdash for the entire year, grading them with a remarkably simple "naughty or nice" system.

Kids always buy this story completely. After all, they're hearing it from their parents, who seem to know absolutely everything, and they keep hearing about it in commercials and storybooks.

As they grow up, however, they start accumulating extra evidence. Mom and Dad seem really tired on Christmas morning, Santa's handwriting looks like Mom's, they saw Mom putting presents under the tree, etc., and start to think, "You know? I don't think Santa Claus exists. I think it's much more likely that Mom and Dad made up Santa Claus just to make me be good."

Atheists know God doesn't exist in the same way that we all know Santa Claus doesn't exist; they've heard the arguments for and against the God hypothesis, and it seems infinitely more likely that God was made up to explain stuff that Bronze Age intellects didn't understand (like Zeus was for lightning) and to make people be good.

Comments

So I moderated my first comment today. Not because it conflicted with my worldview, not because it was hostile, not because it was random and off-topic... but because it was mindless copypasta. That being said, I guess I'll lay out my terms.

I am wholeheartedly against censorship, and that wholeheartedness extends even to views I don't agree with. I, in fact, love reading and hearing views that are very different from mine (and love arguing with them even more), so I would never censor someone strictly because I didn't like their opinion.

What's more, I wouldn't even censor myself if I looked like a fool while I was arguing with the person whose view I disagreed with. What you say is here to stay, and what I say is here to stay.

Unless, of course, your comment is just spam or copypasta. And, actually, even that isn't absolute. If David Mabus left his obnoxiously lengthy copypasta on my blog, I'd probably write a post rebutting it. Unless, of course, he kept posting it, even after I'd rebutted it; then I'd start moderating him.

So, to sum up everything: Censoring ideas you don't like is heinous, but censoring blatant and obvious spam is a-ok.

Science vs. Religion

The Daily Show With Jon Stewart	Mon - Thurs 11p / 10c
Marilynne Robinson
www.thedailyshow.com
Daily Show Full Episodes Political Humor Tea Party

I've just decided that I loathe Marilynn Robinson. Yes, I've written about her before and yes, I still like the "bones and feathers" quote. I don't know how long the Daily Show will keep the video up, so I'll blockquote the parts I want to complain about.

Jon starts off with the statement that, it seems, "science and religion are exclusive and at odds," which I think is absolutely true. Science observes and creates testable hypotheses about the nature of our world, while religion sits on the sidelines, makes shit up, and claims it's "contributing to our spiritual well-being," whatever that means. Anyone claiming that science and religion can coexist don't understand either one; science whittles away at the vacuous claims of religion with reason, debate, peer-review, discussion, testing, and, well, science, while religion only puffs its chest out and proclaims, "I don't know, therefore God."

Says Marilynn Robinson:

People on one side of the argument have claimed the authority of science, but they have not construed an argument that actually satisfies the standards of science. It tends to be part of a history of a certain kind of thinking that, since early in the 20^th century has, for some reason, minimized the complexity and the importance of the human mind. And so, for the sake of good Atheism, for the sake of good religion —

(Jon and Marilynn laugh.)

Jon: "For the sake of good Atheism." You don't hear that enough.

Marilynn: Yes, I agree. I certainly agree.

As a person who is quite strongly on that "one side of the argument," I do claim the authority of science, and we have construed an argument that actually satisfies the standards of science:

1. Any evidence that has been fronted in support of a Creator God has been refuted, leaving only the empty claims from personal, anecdotal experience.
2. People can believe things which aren't true, making personal experience an unreliable source of evidence if offered as the only evidence.
3. With this incredible lack of evidence for God (and in light of the indoctrination of children), a universe run by natural processes becomes indistinguishable from a universe run by an omnipotent Magic Man in the Sky.
4. Occam's Razor slices the Creator God hypothesis out of the picture, in favor of current scientific models.

And Marilynn, science and Atheism don't "minimize the complexity and the importance of the human mind." What on Earth made you think they do?

Anyway, she continues:

I don't think, frankly, that it's scientific to proceed from the study of ants to a conclusion about the nature of the cosmos. I don't think that the argument that has been made is leveraged against anything that actually ought to appropriately be called science. I love science. I think that the new cosmologies and so on are among the most beautiful things that people have conceived. They don't need to be interpreted as religious or anti-religious. They're beautiful in their own right, and another demonstration of what the human mind is.

Given that ants exist in the cosmos, any study of them will give us at least some insight into the nature of the cosmos, at least as it applies to ants. But beyond that, scientists actually aren't looking at ants to explain the cosmos; they're looking at the cosmos to explain the cosmos!

And whether you like it or not, the new cosmologies are anti-religious; the literal interpretation of Genesis, for example, has been completely and utterly destroyed by them. Science, every day, is destroying the claims that religious people have invented about the nature of the universe, and their only survival method is to bash science or make their claims as non-disprovable as possible... which, I might add, is exactly what they're doing. The Bible is no longer literal and God is now an abstract, all-powerful, invisible being who, it seems, has been made that way to hide from science.

Science is a beautiful demonstration of the power of the human brain. Every scientific or mathematical achievement is a testament to its creativity, ingenuity, and its capacity for devious and clever workarounds. It is absolutely awe-inspiring that we can actually know what we know about the universe.

And it is a testament to the flaws of our brains that religion still exists. When presented with evidence which contradicts our cherished worldviews, our brain doesn't change its worldview to adapt to the new evidence; instead, it either ignores it or rationalizes it away.

Then Jon makes a little blunder:

Jon: I've always been fascinated that, the more you delve into science, the more it appears to rely on faith. You know, when they start to speak about the universe they say, "Well, most of the universe is actually antimatter." "Oh really? Where's that?" "Well, you can't see it." "Well, where is it?" "It's there." "Well can you measure it?" "We're working on it."

He's actually referring to dark matter, not antimatter. The universe is actually mostly matter; in order to use antimatter we have to create it ourselves.

I, too, thought dark matter was stupid, but have since been proven wrong. We can actually see dark matter because it distorts the light from stars behind it. We can even see its gravitational effects by analyzing, say, the Bullet Cluster and how the clouds of gas are reacting with each other.

However, Jon, I'll agree with you a little on this. I'm actually majoring in physics precisely because Einsteinian relativity (especially concerning black holes) looks exactly like your "antimatter" does. But, rather than sit back on a TV show and say, "Eh, they're taking it on faith," I'm actually researching it.

Marilynn: Until quite recently, many great scientists, like Isaac Newton and so on, were profoundly religious people. The division is something that has come late and I don't think it was ever necessary.

Funny how ignorant that statement is, Marilynn.

And now, the part that made me both laugh and rush to my blog. Marilynn shows that she's actually a talented comedian:

At this point in time, we need the best insights from science and the best insights from religion...

HAHAHAHAHAHAHA!!! "Best insights from religion!" Let's get the best insights from alchemy and ghost hunting, too, while we're at it!

Now I know why PZ hated you so much.

EDIT: Lookit, PZ said the same thing as me, just better and more concise.

Piracy

If you have an opinion regarding the piracy of music, movies, and such, it is irrational.

Actually, I can't quite say that. All I can say is that I'm pretty sure it's irrational, and not just because I'm pretty sure your opinion is different from mine. I first seriously considered my stance on the piracy issue when Jeff Dee of the The Atheist Experience made the same argument that Joe Biden did a while ago:

"This is theft, clear and simple. It's smash and grab, no different than a guy walking down Fifth Avenue and smashing the window at Tiffany's and reaching in and grabbing what's in the window."

I used to hold an opinion as rigid and uncompromising as Biden's, but I've since graduated from the simplistic "if you didn't pay for it, you stole it" dogma. Piracy, in my opinion, is okay if:

1. You purchased a CD a while back and it has since gotten irreparably scratched.
2. You cannot obtain said object by paying for it (like, for example, if the CD or game was discontinued, out of print, etc.). If the company isn't going to, or even trying to, make money off it anymore, why would pirating it be bad?
3. You're cracking a game you own for which you've lost the CD key. Yes, I know, CD keys are so five years ago and gaming companies prefer the "you can only play if you have an internet connection" route now, but that's beside the point. I bought that game, and can't use it because their piracy protection is preventing me from reinstalling it.

Jason Robert Brown, an evidently reputable composer that I've never heard of, crafted a post which Eric Whitacre snatched up, which then went viral all over my Facebook news feed. Whitacre, Brown, and all my music major friends are evidently hopping on the "smash and grab" bandwagon.

However, pirating isn't such an easy, clear-cut issue. Unlike the simplistic analogy Brown used, pirating music isn't like stealing someone's screwdriver:

Friend of mine is building a house. He drew up the plans, he chopped down all the trees, he's got it all together. He doesn't have a screwdriver. He calls me up, says, "Dude, I need a screwdriver." I happen to have a screwdriver, so I give it to him, but I say, "Hey, I need that back later today, I have some work to do." He looks incredulous. "I have to build a house, my man. I'm not going to be done in a day. And what if someone likes my house and wants me to build one for them? I'll need the screwdriver to build their house too, yo." So I suggest he get his own screwdriver. "Why can't I just use yours?" he says. I tell him he can use mine, but then I need it back, it's my screwdriver, after all. He insists that he has the right to take my screwdriver, build his house, then keep that screwdriver forever so he can build other people's houses with it. This seems unfair to me.

Yeah, borrowing someone's screwdriver forever isn't exactly fair. However, I imagine it would be a little more fair if you could lend him your screwdriver and still use your screwdriver, too. (i.e. "Dude, I need a screwdriver." *Brown takes his screwdriver, duplicates it exactly, and hands the guy one of them* "Thanks, man.")

We can't make dramatic, hyperbolic, Biden-esque analogies with music sharing because it's a very different beast. If I burn a copy of my recording of Beethoven's 9th, for example, and give it to a friend, I have not stolen a CD and neither has my friend. I have not destroyed anything, nor have my friend and I taken property from anyone. What we have done, only in an abstract sense, is reduced the potential, hypothetical income that would've been made had my friend intended to buy the CD himself.

And this abstraction is the problem. Piracy is NOT stealing. Piracy diminishes record sales, yes, but pirates aren't stealing from the record companies, and it's an important distinction to realize. And also, lamentably, a distinction that Biden, Brown, and Whitacre don't see.

If you look at it from an evolutionary standpoint, the music industry is losing its ability to restrict who uses its material because of the internet, computers, and the other technological wonders of the 21^st century, and is trying to legislate its way back to environmental success. But I'm betting we're going to see some changes in the entertainment industry as younger artists adapt to the internet. A bigger focus on theatre-going, concerts, and online gaming perhaps, all of which are essentially pirate-proof. Just try to imagine it: A band writes some songs, posts them on their website, advertises their website at gigs, then people download those songs and pass them around on merit, and the band gets more fans, concert attendance, and money!

I don't think legislating media sharing into oblivion is going to work; piracy is just too damn easy. Without a horrific amount of censorship and regulation, people will always be able to download whatever media they want for free. And isn't a sharp dip in entertainment quality better than the Orwellian "imminent infringement" thought-crime legislation being proposed?