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The Math of Marriage

March 27, 2009 on 9:44 pm | In Politics, Q & A, Random Stuff | 43 Comments

There was a question on the straight dope message board today that was way too interesting for me to pass up. But it took a long time to crunch the numbers for it, so this post is late!

Someone named Richard Parker wants to know whether he should get married… using math. He writes:

As most of you are likely aware, our federal income tax system imposes a marriage penalty on some couples. If both individuals are making similar income at certain levels, then the combined income will put them in a higher joint bracket (or married filing separately bracket) than if they filed a single taxpayers.

What I want to do is evaluate what potential incomes result in what penalties.

Well, after doing a bit of research on this, I’ve discovered that there are a bunch of other reasons to either get or not get married, both financial and personal, and I’m telling you now that I’m putting those aside.

All I’m looking at is the following: given a certain amount of federally-taxable income for two people, what governs whether, for income tax purposes, they should be married or single? Now, I’m not an economist, but I’m scientifically trained, I’m excellent with numbers and statistics, and I’ve got some interesting findings for you.

First off, there are only two factors that matter for how much you pay in taxes, given two people and a certain amount of taxable income.

1.) How much total income there is. More income = more taxes, and once you pass certain thresholds, the tax rate you pay continues to climb.

2.) How the income is split between the two people. If one person earns 95% of the household income and the other earns 5%, vs. if one earns 45% and the other earns 55%, you may come to two very different conclusions.

So let’s see what happens for low joint incomes, and just go up, and see what we can learn about marriage and federal taxes.

$20,000 joint income: if one person makes significantly more than the other, you should definitely get married, as you wind up in a lower tax bracket. If you make roughly even amounts, it doesn’t matter either way. What if you’re doing a little better than 20k a year?

$40,000 joint income: the disparity has to be pretty large. If one person is pulling in about 80% or more of the household income, then you save money by being married. But if not, there’s not really any difference.

$60,000 joint income: this is really the start of what I’ll call the “sweet spot” for people to get married. Again, if you have identical taxable incomes, there’s no difference between being married and single. But if there’s even a 60/40 disparity, it’s better to be married. Remember this for tax purposes: if one person works and the other doesn’t, it’s always better to be married!

$80,000 joint income: This is still part of the sweet spot for marriage. No marriage penalty, big bonuses for being married if there’s an income disparity. And this continues, but really the $60-80k range of taxable income is where it’s usually significantly better (for tax purposes) to be married.

$100,000 joint income: well, it’s much better to be married if there’s a big income disparity, as you can save thousands of dollars over being single. But unless one of you is out-earning the other by better than 2 to 1, there isn’t going to be any difference that you’ll see.

$125,000 joint income: and at $125,000 in joint income, it’s pretty much the same deal. So, so far, and in fact all the way up to a joint income of $137,050, it is never worse to be married for tax purposes. And if there’s a big income discrepancy between partners, it’s far better to be married than it is to be single. But above $137,050, you start to see something called the marriage penalty.

$150,000 joint income: pretty much the same deal, unless you and your partner bring in roughly the same income! Suddenly, if I make $75k and my partner makes $75k, we’d save $500 on our federal taxes every year by not being married! And the marriage penalty gets more significant at higher incomes:

$200,000 joint income: around $1,000 at this income level.

$250,000 joint income: around $3,000 at this level. By this point, it’s only going to get worse. The marriage penalty has been getting worse, to be sure, but have you also noticed that at large income disparities, like 95%/5% splits, you can save around $5,000 by being married? This number has also been going up, significantly, in all of our charts. Let’s go further:

$300,000 joint income: the marriage penalty starts to get more and more people, now. Unless there’s an 85/15 or more split in income (which means one of you out-earns the other by at least 6 to 1), you are looking at a penalty, just for being married, of over $5,000! But, on the other hand, if one of you doesn’t work at all, you can save over $7,000 just for being married!

$400,000 joint income: this crosses over into the highest tax bracket. Whether you’re married or single, the highest tax rate comes for those earning over $372,950. The marriage penalty is close to $10,000 here, and doesn’t go away unless one out-earns the other by 10 to 1!

$500,000 joint income: notice how the differences are pretty much the same as before. About $10,000 in “marriage penalty” for making the same incomes, but about $7,000 in savings for a one-income marriage.

$750,000 joint income: here you can see that, while the savings never gets better for one-income marriages, the marriage penalty continues to get worse for very large incomes, both in terms of who has to pay it and in terms of how much it is.

$1,000,000 joint income: and finally, the marriage penalty bottoms out here. The marriage penalty is, maximally, about $15,000 a year for the wealthiest Americans. Which is, honestly, enough reason for many people not to marry someone with similar earning power to themselves.

So the overall conclusion? If you’re making under $137,050 of joint taxable income this year, it won’t hurt you at all to be married, and it may save you money if one of you is making more than the other. But, if you’re making more than that, being married will hurt you if you have roughly the same incomes, but will help you immensely if one of you makes virtually no money compared to the other. So feel free to use the charts all you like — and do whatever it is that respects marriage, money, and everything else that makes you happy — but now you can do it with this information in hand!

And the other obvious conclusion? I need to start making enough money so that I can start complaining about the marriage penalty!

Faith and Science: A Personal View

March 9, 2009 on 3:55 pm | In Politics, Q & A, cosmology | 17 Comments

There are a lot of people reporting, right now, on the new memo that President Obama has just signed about science, stem cell research, and his administration’s policy:

Obama said scientific decisions should be based on facts, not ideology. He said advisers should be selected based on their credentials and experience, not their politics.

Now, there are very vocal opinions on both sides of this issue, and as you would suspect, I think that in matters of scientific research, every scientist must live with their own conscience, but that science exists to serve humanity, and the research we’re doing will doubtlessly serve to have a positive impact on mankind. Once one major cure or treatment comes out of stem cell research, whether it’s for cancer, Alzheimer’s, or diabetes, I think that the debate over stem cell research will subside when it’s clear that the benefits to doing it can be so substantial.

But instead of looking at it from an economic perspective, or even from an ethical perspective (I’m still tired from doing that last week), I’d like to look at the deeper, underlying issue: whether people can come closer to realizing truths about existence from either faith or science. I also think it’s worth asking yourself, at the end, whether there’s even a right or wrong answer to this.

So rather than talk about stem cell research, I’m going to address perhaps the most interesting question of all: the very question of our Universe’s existence. My friend Brian has a cousin who is a baptist minister, and today’s question comes from him, via YouTube:

Did the Universe have a beginning? …it seems that most cosmologists do believe that the Universe had a beginning. If this is true, and you believe this, then please explain how you, in your mind, resolve the idea of something coming from nothing, uncaused.

Now, let’s start with a little scientific information about the Universe itself. We turn our eyes, telescopes, detectors, instruments, and brains towards the tiniest subatomic particles and to the farthest reaches of the heavens to learn about it, and to listen to what it tells us about itself. (Semantics: I’m going to define our Universe, for this discussion, as consisting of every single particle and every little bit of space and time ever conceivably connected to us, either visibly or invisibly.) Here’s a basic rundown:

  1. The Universe is big. It isn’t infinite, though, it’s finite in size, at about 94 billion light years from end-to-end.
  2. The Universe is old. If you took the longest-lived thing ever on Earth and gave it 10,000 lifetimes in a row, it would be only about 2% as old as our Sun and Earth are. The Universe is “only” about three times as old as our Solar System is.
  3. The Universe has a lot of stuff in it. About 1,000,000,000,000 stars in each galaxy, and about 100,000,000,000 galaxies in the whole Universe. Considering each particle of matter and energy as a separate entity, there are about 1090 particles in the entire Universe.

All of this, combined, tells us that our Universe is tremendously large, tremendously old, and full of an incredible amount of stuff. It is truly vast. However, all of it is finite, including the amount of information in it. Does that imply that there’s an intelligent force outside of it that created it?

No. It doesn’t tell us that this isn’t the case, either. But it does tell us something profound about science; specifically, it tells us something about the theoretical limits of science. Let me give you an analogy, the exploding grenade:

If you watch the individual fragments of a grenade during (or even after) an explosion, because you know the laws of physics and how a grenade works, you can figure out where the grenade exploded, how powerful the explosion was, and what the grenade was made out of just based on what you see. You can even tell, if you’re extremely careful and understand the physics of grenade explosions really well, how quickly and in what direction the grenade was moving when it exploded.

But what you can’t tell, based on looking only after the fact, is how the pin got pulled, and by whom or what.

So, my contention is that if we want to know about the Universe, the best source we have is to look to the Universe itself, and see what it tells us. But if we want to know what caused the Universe, although there are things we can definitely learn a number of things about it, our total amount of possible scientific knowledge is limited by the amount of information available. For instance, we are mounting evidence and may be able to someday prove that cosmological inflation caused the Big Bang to happen, and created our Universe. But then you could ask, “what caused or created the inflating Universe that gave rise to ours?” Again, we can come up with some ideas about it, and possibly some signatures to look for (although there are presently no good ideas), but at some point, you run out of information. It isn’t that something came from nothing; it’s that something came, period. We simply don’t have enough information to say that it came either from nothing or from something else. And we certainly don’t have enough information to determine what the dynamics were that caused it to come into being in the first place.

When you have no information, science is useless. And at that point, all you have left is logic and reason, and those are your only weapons against the darkness of ignorance. Science can get us far, can get us so much further than we’ve ever been before, but even science has its limits. And hence, to the many atheists that read this site, I encourage you to respect the religious beliefs of others while steadfastly standing by the scientific truths that we have discovered to be valid and factual.

We ought to all be above petty bickering here, as I think everyone is seeking to understand our Universe’s very existence, and hence we must use all of the available tools. I encourage you to recognize that religious studies can be a logical, rational pursuit as well, and that both science and religion have limits to the truths they can uncover. This one in contention here — what brought the Universe forth into existence — is still obscure to all of us.

Warp Drive: Is it Really Possible?

December 15, 2008 on 11:28 am | In Physics, Q & A, relativity | 41 Comments

Ever since we realized that our Universe extended far beyond the extent of Planet Earth, mankind has longed to travel to distant planets, stars, or even other galaxies, perhaps going as far as the edge of the known Universe.

We’ve designed spacecrafts that, in theory, can travel these great distances. The problem with all of these designs is time dilation, or the fact that while you go off on your space journey, time passes much faster for everyone who stays back on Earth, so that if you wanted to go off and return, people on Earth would age tens, thousands, or even millions of years while you were gone on your journey.

Well, reader Howard Mauch writes in and wants to know whether warp drive is really possible. Warp drive is the idea that we can bend space so significantly in front of our spacecraft that we can travel forward great distances in short amounts of time, without suffering the effects of time dilation:

This was, of course, made famous by Star Trek. But is this at all physically feasible? The quick answer is no. Why not? Because although space can be curved, and we can theoretically connect two distant points to travel instantaneously between them, nothing can safely travel through them. Take a look at this picture, where it looks like you can safely travel from one side to another through this short-cut:

The big problem is that the curvature you see here represents a gravitational field. The more curved a piece of this diagram is, the stronger the gravitational field is. And the stronger the field is, the greater the forces are on you. In the diagram above, the forces are so strong they will not only crush you, they will tear individual atoms apart. The only solution? We need some way to create stable, flat spacetime inside of this curved area. Is this possible?

Well, it’s possible in electricity; you put an electrical conductor around your ship and you block all electric fields inside the conductor. Want to do the same thing for gravity? You’d need to put a gravitational conductor around your ship. No big deal, right? Except that there’s no such thing as a gravitational conductor, because there’s only one type of mass (positive), where there are two types of electric charge (positive and negative). So either invent something with a negative mass (which doesn’t exist) and build a gravitational conductor, or everything, even in theory, will be destroyed by the gravitational forces that would allow you to travel via warp drive.

NASA is more optimistic about this. I believe they are mistaken in their optimism, but who knows what new physics will be discovered, and what new possibilities will arise from them?

And if you need a bigger fix for your space reading needs, check out the latest Carnival of Space, where many interesting space delicacies await you!

Q & A: Why don’t Woodpeckers get Brain Damage?

December 10, 2008 on 12:50 pm | In Evolution, Life, Q & A | 9 Comments

Everyone knows how much fun it is to get repeatedly hit in the head. Just ask Oscar de la Hoya after his defeat against Manny Pacquiao last weekend:

Ouch. It isn’t just boxers, either. Every animal that experiences head trauma is susceptible to the following symptoms:

  • Abnormal level of consciousness
  • Differences in pupil size
  • Rigid limbs
  • Flaccid limbs
  • Unusual eye movement
  • Bleeding from the nostril
  • Bleeding from the ear canal
  • Seizures
  • Head tilt

But the worst thing imaginable to me that results from head trauma is brain damage. It’s our minds that make us who we are, and the idea of living without mine is completely horrifying. Look at how different a normal brain can be from a damaged one:

Out of all the animals I know of, there’s only one that repeatedly slams its head into a block of wood, over and over, day in and day out, for its entire life: the woodpecker.

A woodpecker moves so quickly that its tiny, 50 gram head absorbs 1,300 pounds of force every time it smashes into a tree! So why don’t woodpeckers get brain damage? There has to be something that prevents its brain from rattling around in its head and slamming against the skull around it, right? No, there isn’t. The woodpecker’s brain does rattle around in its head and smash into its skull. Yet it still emerges brain-damage-free. There are three special adaptations of a woodpecker that allow this to happen; let’s take a look.

1. Spongy skull bones — while humans have spongy bones mostly on the interior of large bones, woodpeckers’ skulls are extremely spongy. This means they can compress and help absorb the impact of the brain jostling around. It’s like smashing a brain into memory foam instead of into solid bone, and it reduces the force on the brain tremendously.

2. Large surface area — a woodpecker’s brain is tiny. This is actually a positive thing, because the smaller something is, the larger its surface-area-to-volume and surface-area-to-weight ratios are. If something has a bigger surface area, it means that even if the force is large, the pressure gets smaller, and this helps protect the woodpecker’s tiny bird-brain.

3. Woodpeckers peck in a straight line — this one is hugely important. If everything’s in a straight line then there’s no rotating or torquing of the brain, and therefore no tearing of the nerves in the brain. Hence, no brain damage the way that car crash victims experience it.

And those three things combined allow a woodpecker to escape from all their daily pecking activities without so much as a hint of head trauma. Isn’t evolution neat?

What, you were expecting some astronomy/physics today? Go check out the latest Carnival of Space to get your fix, done by Dave Mosher in a new video format, and I’ll see you all next time!

Q & A: The Speed of Light

November 24, 2008 on 3:25 pm | In Physics, Q & A, relativity | 37 Comments

It’s 103 years after Einstein first formulated his Theory of Special Relativity, which explains what happens to objects near the speed of light. But SWAB reader Jacinth wants to do one better, and asks:

What will happen if we can actually travel at the speed of light?

It’s a great question, and provides a lot of learning opportunities. First off, let’s take a look at what happens to regular matter when we bring it close to the speed of light. There are three major things:

1. Lengths contract. This works for everyone. If I move close to the speed of light, then anyone who sees me sees that my length is smaller. But from my point of view, everything that I see is moving towards my rear close to the speed of light, and also looks like it has a smaller length.

2. Time slows down. We call this time dilation, and again, it works for everyone. It means that if I’m moving close to the speed of light, everyone who sees me sees that time is traveling more slowly for me: my clocks run slower, I age slower, my heart beats slower, etc. But I see the same thing: everyone else looks like their clocks are running slower, they’re aging slower, etc. But if I go away close to the speed of light and then come back to Earth at Earth’s speed, we find out that on my journey, although I’ve aged normally, much more time has passed on Earth. (Incidentally, this is what Paris Hilton was worried about.)

3. It takes more energy to accelerate your speed. Some of you who know a little physics know that the rest energy of a particle is E=mc2. Some of you also know that Kinetic Energy = 1/2 mv2. But when you get close to the speed of light, it takes more and more energy to move quickly. In the graph above, the purple line is the old formula for kinetic energy, but the red line is the real (relativistic) energy. Notice that you never quite get up to the speed of light, but that the energy it takes approaches infinity.

So that’s what happens when something made of normal matter approaches the speed of light: it sees lengths contract, times slow down, and it requires more energy to change its speed. Alternatively, things that have no mass (like photons, or perhaps gravitons), have to move at the speed of light.

But let’s say you had a spaceship, and decided to actually go at the speed of light, somehow. What would happen?

Well, if you used all the energy in the Universe for your spaceship, you could probably get up to speeds incredibly close to the speed of light. How close? The speed of light is exactly 299,792,458 meters/second. And you could get to within about 1 x 10-30 meters/second of that value — pretty good. If you got that fast, though, what would happen? First, the entire Universe would contract to appear to only be a few billion kilometers across — less than one light year! Second, time would slow down so much, that as you would only age a few seconds, the Universe would age literally trillions of years. Galaxies would merge, stars would be born and explode in the blink of an eye. And finally, you may get to see the fate of the Universe firsthand; if the Universe has an end, you would slow down time for yourself so much that you might not only see it, you might do it in just a few seconds.

So, in conclusion, not only can’t you move at the speed of light, there’s good reason not to!

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