Neither of these things have much to do with the “Miranda warning.”  Your rights don’t disappear just because you aren’t read them.  Let me explain.

The history of Miranda warnings

The “Miranda warning” ultimately comes out of a Supreme Court case named Miranda v. Arizona (1966).  Ernesto Miranda was arrested on suspicion for kidnapping and rape.  After a few hours of interrogation by police, he signed a confession stating that he committed the crime.

Miranda’s lawyer claimed that this confession was not “voluntary,” because Miranda had not been informed of his rights.  Specifically, the United States Constitution guarantees a right that a person cannot be forced to testify against himself or herself.  From the Fifth Amendment:

No person . . . shall be compelled in any criminal case to be a witness against himself

Also, we have a right to consult with an attorney (who perhaps may be able to explain these rights better).  From the Sixth Amendment:

In all criminal prosecutions, the accused shall enjoy the right . . . to have the Assistance of Counsel for his defence.

Miranda’s lawyer claimed that the suspect, despite signing a statement saying that he waived these rights, was not fully aware of his rights.  Given the strong pressure that may be exerted in police interrogations, Miranda should have been explicitly made aware of these rights and explicitly waive them before speaking against himself.

We don’t need to get into the further details of the actual Miranda decision of the Supreme Court.  Suffice it to say that since that time, police generally verbally remind suspects of their rights immediately upon arrest and before interrogation.  Note the important fact that this is only reading rights aloud that ALWAYS exist, regardless of whether they are read aloud.

If the suspect in the Boston bombing is not “read his rights,” he still has them.  He still has a right to “remain silent” and not testify against himself in court (whether in person or by a written statement).  He still has a right to an attorney to defend him in court.  Failing to “read him his rights” does not take those rights away.

Thus, the ACLU and (mostly) liberals who claim that his rights are being taken away are grossly mistaken when they say this has anything to do with a Miranda warning.  The Miranda warning is merely a reminder of rights — it does not magically grant them when they are read aloud.  Suspects always have these rights.

Emily Bazelon over at Slate is very worried about these magical disappearing writes.  She argues:

[T]he next time you read about an abusive interrogation, or a wrongful conviction that resulted from a false confession, think about why we have Miranda in the first place. It’s to stop law enforcement authorities from committing abuses. Because when they can make their own rules, sometime, somewhere, they inevitably will.

No, no, no.  “Abusive interrogations” are generally considered to be assault.  Police who abuse suspects are often looking at a felony.  Failure to make a verbal statement does not allow police to beat up a suspect.  It does not allow them to force a “false confession,” either.  The Miranda warning exists to protect people who are ignorant of their rights, not to protect people from police abuse.  We have other laws (against assault, coercion, etc.) that protect people from such abuse.

So, if suspects don’t “lose any rights” without a Miranda warning, what exactly is it about?

When Miranda warnings matter

Simply put, a Miranda warning is only relevant for a trial.  It has nothing to do with interrogation practices whatsoever.  A Miranda warning is generally required to introduce self-incriminating testimony (like a confession) into a trial.  If a suspect has not been “read his rights,” courts will generally assume that the suspect may not have been aware of them — and therefore his testimony was not truly voluntary.

In most cases, the absence of a Miranda warning just means that any and all statements made by a suspect are thrown out of court.  They therefore cannot be used to convict the suspect.

In the Boston bomber case, the FBI and police already seem to have a lot of evidence from video tapes, eye witnesses, etc.  It seems like they may have enough to get the bomber a life sentence even without any confession or personal remarks that he might make and incriminate himself.

So, the Miranda warning is probably irrelevant.  In this case, the FBI and police could make a decision that information about possible bombs or threats to public safety are much more important than having a little bit more evidence to pile on top of the mound of evidence they already appear to have.  Isn’t this a reasonable position?

Note again that it is still completely illegal to torture the suspect.  They are not allowed to abuse him.  Police must still follow normal interrogation procedure, just as they would in any other case.  Miranda is irrelevant to this point — it would only come into play if the police wanted to report what he said in court.

The FBI has mentioned the “public safety” exception to the Miranda case, which basically allows police to ask questions about things that pose an immediate danger.  They could, for example, ask the suspect about the location of any other bombs, without necessarily making statements inadmissible in court.

However, under this rule, they could not ask random questions about things that do not pose an immediate danger.  Questions like “Did you commit this bombing?” or even things like “Where did your brother train to be a terrorist?” would not fall under this exception.  They likely would lead any answers to be inadmissible during a trial.  Again, the police and FBI might not care, because they think they have enough evidence already.  If so, Miranda is completely irrelevant to this situation (and again has absolutely nothing to do with taking away any “rights”).

(Some people — including people associated with the government and FBI — have claimed that the “public safety” exception should be read more broadly and could include more extensive questioning of a terrorist suspect.  These ideas have never been tested in court, and my guess is that such arguments would fail unless an immediate danger and justification for the specific questions could be claimed.)

To be absolutely clear: the police have NO REQUIREMENT to read the “Miranda warning.”  Whether they do so or not has no effect on anyone’s rights.  IF, however, the police seek to introduce evidence gained from interrogations without a Miranda warning, they may have a hard time convincing a judge to allow such evidence in court — because judges will protect those very rights that people are claiming are “lost.”

Conservatives, “enemy combatants,” and rights

So far, we’ve highlighted the problems with many misinformed liberal arguments about what Miranda warnings really are about.  Part of the paranoia about these rights, however, comes from statements from people on the other side of the political spectrum.  Some conservatives have gone far beyond saying not to read the suspect his rights: they want to deny him a normal trial, treat him as a wartime criminal, etc.

These are very serious proposals.  If they come into being, it will set a terrible precedent to take away the rights of American citizens.

However, whether or not this comes to pass, it has absolutely nothing to do with a Miranda warning.  Taking away rights by denying someone a trial is taking away a right to a trial, and that has nothing to do with verbal statements.  Whether you read a suspect something about what rights the suspect may or may not have is beside the point.

Why should we care about the Miranda misinformation?

The Salon article mentioned earlier is entitled “Why Should I Care That No One’s Reading Dzhokhar Tsarnaev His Miranda Rights?”  I think a better question would be “Why should I care if the media misrepresents what Miranda warnings are really about?”

We should care because there are so many other rights abuses that do matter.  Constitutional rights about searches, rights to privacy, etc. have been altered significantly in the past decade.  Invasive body scans are done on millions of people at airports everyday, while people are forced to toss drink bottles and other random items into the trash.  I’m not saying we don’t need heightened security, but these are actual situations where Constitutional rights are routinely modified or even denied.

We have situations where the President of the United States has been accused of ordering drone strikes to execute American citizens without a trial.  We have increased wiretapping and surveillance on American citizens with less oversight.

These are examples of actually denying American citizens of Constitutional rights.

Every minute we waste discussing nonsense about Miranda warnings that isn’t true is a minute in the media that we could be spending worrying about actual — and often much more severe — denials of rights.

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The previous articles in this series have dealt with considerations that should be important to every home buyer: preparing for emergencies, saving responsibly, and making informed decisions about how to prioritize debt payment.

What we haven’t yet considered, though, is the role of real estate as an investment.  For many people, the goal of getting a mortgage is ultimately to own that home.  If that is your goal, this article may not be as relevant to you.  But if you don’t necessarily plan on staying in the same area for the long term, or you plan on upgrading to a larger home at some point, your goal is NOT owning the home you are currently paying a mortgage on.

Instead, you need to consider payments on your mortgage as part of a larger investment strategy.

Seeing the investment return when you sell

If you plan to sell your home before your 30-year or 15-year mortgage (or whatever length) has come to term, your goal should be to maximize the return on your investment.  If you purchase a home with a 30-year mortgage, and you plan to sell in 10 years, it doesn’t really matter if you own 30% or 70% of the house after 10 years.  What matters most from your overall financial picture is whether you come out with a strong return on your investment.

For the moment, let’s consider a very simple case where you have a “magic” loan that requires you to pay no interest.  (This might actually happen in real life: maybe you made a deal with some family members to pay them back within 10 years.)  Also, we’re not going to consider the other costs of owning a home: taxes, home insurance, maintenance costs, etc.  Those will stay the same regardless of your mortgage payment strategy, so they’re not going to change the present analysis.  (However, they do play a role in deciding whether you should even buy a home in the first place.  In cases where you plan to own a home for only a few years, you might be better off renting rather than buying.  That’s a separate issue from what you do once you already have a mortgage, so it’s not particularly relevant here.)

We’re also going to assume, as we have in previous posts, that you have enough equity in your home so you don’t have to pay PMI (generally at least 20%).  PMI is an additional complication that can really cut into your rate of return, so often it’s best to try to achieve that level of equity as quickly as is reasonable.

Okay, so let’s take some extreme cases.  Say you buy a house that’s worth $100,000.  You put a 20% down payment on the house, i.e., $20,000.  You owe some “magic bank” or family member $80,000.  Again, we’re going to first take a really simple case where you don’t have to pay interest and don’t even make payments.  (We’ll get into the details later.)

Let’s say that over 10 years, the value of your house increases to $150,000.  You sell the home.  $80,000 of that $150,000 goes to pay off the loan.  You’re left with $70,000.

If you wanted to think of this as a return on an investment, you put in $20,000 at the beginning of the 10 years, and you walked away with $70,000 at the end.  Your money effectively was increased 3.5 times, or an overall return of 250%.  That’s an effective annual return of 13.3% on your investment for 10 years — a rather high number.

Now, let’s say that instead of making a 20% down payment, say you made a 50% down payment.  After 10 years, the home is worth $150,000.  You sell it and pay off the other $50,000 remaining on the loan.  You walk away with $100,000.

At first this may sound better: you walk away with more money.  But you also put more money into the house to begin with.  For a $50,000 initial investment, you came away with $100,000.  You doubled your money, so your overall return is 100%, or about 7.2% annually.  That’s still a good return, but it’s significantly less than you had with a smaller initial investment.

The lower investment in your home can (under some circumstances) result in a higher effective return.  Note that in both cases the amount of money that goes in and comes out is exactly the same overall: in both cases, you eventually pay the $100,000 purchase price, and you eventually sell the house for $150,000.  Your net profit in both cases is thus $50,000.

The difference is that you put in varying amounts to get that profit.  If someone gave you a choice: (1) invest $20,000 and net $50,000 profit in 10 years or (2) invest $50,000 and net $50,000 profit in 10 years, which would you choose (assuming there was equal risk)?  You’d obviously go for the first case.

And that’s an important consideration for short-term owners.  Your goal is not to have a high percentage of equity at the end of 10 years: it’s to get away with the best return with the smallest amount of investment.

Now, of course, we made a lot of assumptions here.  In many cases, what I’ve just described may not be a great strategy.  Let’s think about some other scenarios.

Depreciating home value

The most important assumption we made above is that your house actually went up in value after 10 years.  For a well-maintained property in a desirable area to live, property values generally do gradually trend upward.  How much upward is highly variable, but I’ve seen averages over the past 50-60 years fall in the 4% annual return per year for residential property on average.  In desirable areas, it might be more like 5-8%, while in many areas it will be lower than 4%.  Only in the cases of real estate bubbles, speculation (often in previously undeveloped areas), or property neglect, do you tend to see significant decreases in value for the long term.

Nevertheless, many people have seen home values drop significantly since around 2006, so it’s important to consider the case of a depreciating home value in our calculations.

Let’s again take an extreme scenario.  Before we had a home that gained $50,000 in value; now let’s consider a loss of that magnitude.

Suppose again you buy a home that costs $100,000.  Suppose you make the $20,000 down payment.  And now suppose that after 10 years, the home has lost $50,000 in value, so it is only worth half of what it was before.

When you go to sell the home, you only get $50,000 back, but you need to pay off an $80,000 loan.  So you need to come up with $30,000 just to sell your home.  In common language these days, you were “under water” in your home loan.

Your return on your investment isn’t just zero.  It isn’t even negative 100%, because you clearly lost more than your $20,000 investment.  In this case, it’s as if you doubled-down at a casino and need to cough up even more money just to get out of the game.

Instead, suppose you initially put down a $50,000 payment, as we considered before.  In that case, when you sell the home, you get $50,000 from the sale, which you need to immediately use to pay off the remainder of the loan.  You walk away with exactly $0.

Again, in both cases, you lost $50,000.  That was your net loss.  But the lower down payment magnifies the effect of that loss, requiring you to come up with more money just to get out of your investment (obviously the least desirable situation).

What we know so far

When a home value goes up, you get a greater return per amount invested by having lower equity.  What a home value goes down, you get a greater loss per amount invested by having lower equity.

Having lower equity will, in some sense, magnify the effects on your investment.  Therefore, it generally only makes sense to deliberately keep your equity down to reap a higher investment if you’re fairly confident of an increase of property value.

This may sound a bit like gambling, and all investments are gambling to some extent.  But do remember that in these simplified cases, the NET gain or loss is the same in all cases.  You’re still gaining $50,000 at the end or losing $50,000 at the end OVERALL, regardless of the strategy.  It comes down to a question of where the best place is to put your money.  So, if your home value is going up, and if you haven’t achieved some of the goals discussed in previous posts like having an emergency fund, insurance, and retirement savings, it’s perhaps a better bet to invest more in those things before worrying about an increase in equity.

Of course, that’s not the whole story.  We haven’t factored in the interest yet.

Returns in real mortgages

When we consider the amount paid in interest to hold a mortgage, most of the returns we saw previously don’t look so good.  Nevertheless, under normal circumstances (i.e., not in a real estate bubble) with low interest rates (as we have now), lower equity still may not be a bad thing for investments.

Suppose, for example, that you have a 4% rate on a 30-year mortgage.  Suppose that you get a reasonably good (but not stellar) 5% increase in property value annually.  Suppose that you start out with a 20% down payment (to avoid PMI).

The calculations now are rather complex, but in the end, you would still see a higher effective return for a short-term sale by making the standard mortgage payments each month, rather than by overpaying.

Suppose you plan to sell your home after 10 years.

If you pay your standard payment, you would end up with a 51.7% return on the money invested over 10 years (about 4.25% annual return).

Now, suppose you overpaid your mortgage by increasing your payments by 20%.  (For example, if you had a $500 standard payment, you paid $600 every month instead.)  In that case, your effective return on your money when you sell after 10 years would be 48.2% (or about a 4.01% annual return).

If you increased your payments even further to build equity and paid double your standard mortgage payment, in this scenario you’d end up with a 39.8% return over 10 years (about 3.41% annual return).

It’s important to note again that this advice applies only to short-term ownership.  If you overpay your mortgage each month, you will eventually pay it off early.  And once you’ve paid off your mortgage, the interest no longer cuts into your returns, while your home value may continue to appreciate.  That means that eventually the overall return will in fact be better when you overpay, since you end up paying less interest overall.

For the scenarios discussed here, your return for a 20% overpayment will surpass your return for a normal payment around 24 years into your mortgage.  If you double your mortgage payment every month, the break-even point is about 15 years: after 15 years of ownership, your overall return on investment will be greater with the doubled payment versus the standard one.

This is confirmation that this the strategy we’re discussing here is only relevant when you plan to sell early.  The longer you own your home, the less relevant these ideas are.

Also, let’s emphasize the assumptions here: this was for a 4% rate on a 30-year mortgage, with a 5% gain in property value.  The returns will obviously be quite different depending on individual circumstances.  As a rule of thumb, this strategy is strongest when your expected gain in property value is at least the percentage of interest you’re paying on your loan.  You’ll still get higher effective returns on your money invested by not overpaying with your 4% interest rate if your property only gains 4% every year in value, instead of 5%.  You’ll still barely get it if your home only gains 3.75% annually.  This should be common sense, but if your house is gaining value at at significantly less than your interest rate, the additional interest you’re paying in will trump any additional returns by keeping equity lower.

Conclusion

If you plan to sell your house in the short term (5 to 10 years), building up equity is often not that beneficial just for the sake of equity.  If you are fairly confident that your home value is rising annually, there may also be good investment reasons why lower equity can actually help your overall portfolio.  Whether this is a good decision in your particular case will depend on the rising value of your real estate investment when balanced against the losses in interest that you pay on the loan.

With all of that said, keep in mind that inflation already can make the long-term difference in interest payments between payment strategies less relevant, as discussed in the first post of this series.  In the end, it comes down to a comparison among three different rates: your mortgage interest rate, the inflation rate, and the rate at which you house gains (or loses) value.  If your interest rate is below or around the inflation rate, overpayment may not be a good strategy.  As discussed here, if your interest rate is below or around your home’s appreciation rate — and you plan to sell soon — overpayment may not be a good strategy.  Making the exact call for a particular situation is difficult and requires some more complex mathematical analysis, but these overall trends are important.

Ultimately, what matters when considering an overpayment strategy is what you do with the money if you don’t use it to pay down the mortgage.  The previous posts in this series discussed some critical financial needs that may need to be addressed before paying down a mortgage.  If you have all those needs covered, though, you still need to figure out what to do with the rest of the money if you don’t put it into your mortgage.  A comprehensive investment strategy needs to take that into account, and this topic will be considered in the next post of the series.

Disclaimer: This is not intended to be professional financial advice, nor does it apply to all people in all situations.  It’s a good idea to consult a professional financial advisor before making any major changes in your finance management, because individual circumstances will often affect the choice of strategy.

The mainstream press has not reacted well to those asking why the story hasn’t been covered.  As the story spread over Twitter, there have been plenty of voices trying to excuse the situation, strenuously arguing against a “coverup.”   Of course, open letters from conservative sources asking the mainstream media to cover the story went unheeded for almost a week, as stories like the Rutgers basketball fiasco got significant coverage as a literal baby-killer went unnoticed.

Those who have read any of my other political posts (and understand the philosophy of this blog) know that I don’t tend to side with either Democrats or Republicans on issues.  Labels like “liberal” and “conservative,” in my view, tend to be rather limiting and often oversimplify underlying problems of politics and philosophy.

So, I say this as someone who is definitely NOT affiliated with any right-wing source (nor any left-wing source): Mainstream “liberal” media, you messed up bad.

Before some readers try to deny the bias of the mainstream media, realize that everyone is biased.  It’s pretty much impossible not to be to some extent.  And the reality is: most reporters at ABC, CBS, NBC, CNN, as well as newspapers like the New York Times, the Washington Post, etc. self-identify as liberals.  Pretending that such a fact has absolutely no effect on how they report or what they chose to report is simply naive.

I’m not at all saying there was some sort of giant conspiracy to keep this story out of the news.  But I do think, particularly given some responses that reporters at these outlets have made in the past few days, that many of them consciously chose to ignore the story.  They may give excuses about how it was merely “a local matter” (which apparently led to some attempts to delete information about it on Wikipedia for lack of notability), but such excuses are nonsense.

As thoroughly documented over at The Atlantic recently, there are numerous reasons why this story should have been newsworthy.  Either all of these reporters are incompetent and/or living in a filter bubble much worse than any technology geek has imagined, or most of them actively decided NOT to cover the story, despite what their reporter friends in Philadelphia felt obligated to do.

The reasons to bury the story are obvious to any liberal.  Discussing the story brings up all those hard questions about when life actually begins (legally, if nothing else), and it risks giving further attention to conservative efforts to force all sorts of regulations onto abortion (whether or not those regulations have anything to do with preventing situations like the Gosnell case).

One thing that hasn’t been adequately discussed in the past couple days of media self-reflection is the fact that the mainstream conservative media (e.g., Fox News) also failed to report on the story.  I think this Salon piece that does note this absence fails to consider is the legitimate motivations Fox and other big conservative outlets had to wait.

It’s pretty much undeniable that any reporter at a major mainstream news outlet must have known about this trial.  It’s horrific, and it has been thoroughly covered by major media in Philadelphia, along with more limited covered in the Associated Press.  The only logical explanation for NONE of the liberal outlets covering it is hope that the story would just stay under the radar and not get the attention of those in the middle of the abortion issue (who might be swayed toward pro-life by the gruesomeness of it all).

I therefore disagree with Alex Seitz-Wald at Salon when he says: “it’s difficult to take complaints seriously from people who haven’t used their own public platforms to push a story they think others are now ignoring.”

Nope.  Alex, they played you.  You and many other reporters just wanted to ignore the story, though if you had covered it from the beginning, you would have had a chance to put your spin on it.  But instead, you ignored it.  The conservatives waited a few weeks, then they got the wacko fringe to release things like open letters to get the media to cover it, and then they waited a week more to get enough time to demonstrate bias.

And they pounced.

This is Media Relations 101: control the story by breaking it first, though it doesn’t surprise me that most reporters don’t think about media relations since they are the media.  Now they are stuck backpedaling about themselves and trying to fit their own narrative onto the story, but it’s too late.

What does the “liberal” narrative look like?  The real story is poor women, poor access to abortions, and by the way if any conservatives dare to suggest any regulation, we’re headed back to the 1960s where all abortion clinics look like this “Horror House.”

Or, in sum, we need more abortion: better access, better funding, more opportunities for women to get what they need.  I don’t necessary disagree, but all of this is beside the point.

This isn’t the time for that story — the media has to deal with their failure to report first.  I can’t help drawing a parallel with recent gun policy proposals: what we need to prevent school massacres is more guns, everywhere, with better access.  In the recent coverage, there have been comparisons to the Newtown massacre: we’ve had months of media coverage on that, but a “blackout” on the Gosnell trial.  Both involved a person who killed many children.  What’s the difference?

In reality, the cases have a lot in common.  It’s just that liberals and conservatives are on opposite sides of the issues.

Both represent a failure of regulation.  Both have caused proposals for new laws and policies — much more severe restrictions on guns or restrictions on abortion — that actually would not have prevented either of these horrific crimes.  The gun used in the Newtown shooting was already illegal; the procedures and conditions in Gosnell’s clinic were already illegal as well.   The solution is not that we need to make more things illegal — in both cases, we need to fix the regulatory system.

Nor is the solution that we just need “more” of something — more guns with better access, more abortions with better access.  In many cases, better access may be helpful, but neither of them is going to prevent people like Adam Lanza and Kermit Gosnell from doing horrific things.  These are people who exist outside the boundaries of normal societal morality.  They are actively choosing to violate our ethical codes for proper behavior.  A person like Lanza would likely have still killed a number of children before being shot himself, even if a lot of teachers had guns.  A person like Gosnell would likely have still performed a number of questionable procedures on women and babies who were particularly needy and went to him for help for privacy reasons or whatever (as opposed to more well-known clinics).  Access to more guns and more abortions would undoubtedly prevent some things, but heinous crimes committed by people who act in illegal ways are often going to be done (or attempted) by these people regardless.

The mainstream “liberal” media was stupid here.  But if they want to win the battle in turning the story back to their side (or at least having their side heard), they need to stop pretending that Gosnell’s acts are the results of conservatives forcing poor women to cheap clinics, anymore than Lanza’s acts were the results of liberals banning guns from schools.

Can we please just stop using the deaths of children for political gain?  PLEASE.

Bans on new guns that have been dubbed “assault rifles” (sometimes arbitrarily) by liberals would not have prevented Newtown, because Lanza was in possession of an illegal gun already.  Bans or restrictions on more kinds of abortion procedures (also sometimes arbitrarily) would not have prevented Gosnell’s clinic from doing what it did, since what he did was already illegal.

But sticking our heads in the sand and saying, “We just need access to more guns/abortions” is not going to solve the problem either.

As I’ve already said, we’re talking about regulatory failure to deal with situations that were already illegal in both cases.  We need to fix the regulations so that the laws are actually effective.

And even then, we’ll just have to admit that some tiny amount of people will convince themselves that it’s okay to commit murders.  Kermit Gosnell is no more a reflection of abortion doctors than Adam Lanza is of gun owners.  No matter how good the regulatory system is, sometimes these people will slip through, because they are so out of the norm.  But we can still learn lessons from both cases — just not what the extreme partisan arguments would suggest in either case.

Please, let’s stop the rhetoric.  Let’s stop the media games.  Let’s actually try to discuss things that will actually be effective at preventing these sorts of things from happening again, rather than ridiculously overreacting according to our political biases.

We’re talking about dead children here.  They deserve more respect.

While agnostic is often used today, it has a precise technical meaning that is somewhat different from the common definition.  It allows a certain kind of distinction to be made about our knowledge and beliefs that are difficult to make with other terms, so it’s useful to review the actual definitions.  Also, as we’ll see, it’s actually possible to be an agnostic atheist or even an agnostic theist.

The origins of the term “agnostic”

The word agnosticism was coined by Thomas Huxley, a biologist, in the mid-1800s.  He derived it from the Greek word gnosis, which was used in the early Christian church to refer to special knowledge about God.  Huxley personally did not believe he possessed absolute knowledge about God or the nature of any deity, and he had doubts about others who claimed to have proof or such genuine knowledge.

Agnosticism thus began for him as a methodology for understanding the world.  Without being able to rely on divine knowledge (gnosis), he was an a-gnostic.  The truth of claims about the world or the universe should therefore be evaluated on the basis of what he can actually know, not some hidden spiritual “knowledge” that could not be verified.  In short, it was a claim about epistemology, or the philosophical study of what knowledge is, what its limitations are, and how we know what we know.

As the term was adopted by other philosophers, it came to mean a systematic belief about what we can and cannot know.  In essence, to be agnostic was to believe that we cannot know whether there is a God — we lack either the information or the ability to understand or perhaps that information is not available to us in the universe we see and experience.  Any claims about the existence or nature of God are pure speculation, since we are not able to know any of those things for certain.

Note that this is very different from simply saying, “I don’t know whether there’s a God.”  Agnosticism is expressing a positive belief that “I cannot know whether there is a God” or even that “Humans cannot know whether there is a God.”  It says that we simply don’t have proper information to constitute knowledge that could be confirmed about such matters.

Varieties of atheism

Most philosophers and scholars who discuss religion have a different way of classifying people who say “I don’t know.”  The most common distinction is between so-called strong and weak atheism.  Other terms are also in use for these categories: for example, some refer to these as positive and negative atheism.

The basic distinction is that strong/positive atheism is a positive belief that there is no God.  It’s a certainty that gods do not exist.  Weak/negative atheism is merely the absence of belief in a God.  Since theism implies belief in God, weak atheism merely says, “I don’t have that belief.”  A weak atheist doesn’t know whether God exists or not, whereas a strong atheist asserts that God definitely does not exist.

Simple analogies

All of this discussion may seem somewhat technical and abstract.  It’s probably easiest to think of this in terms of beliefs about something practical.

Suppose we have a friend who is going to try to jump over a fence.  We might make some statements about our beliefs regarding that friend’s likelihood of success.

Theism: “I believe she will make that jump.” (“I’ve seen her jump fences like that many times before.”)

Strong Atheism: “I believe she will not make that jump.” (“I’ve seen her try to jump fences shorter than that one, and she’s never made it.”)

Weak Atheism: “I don’t know whether she will make that jump.” (“Honestly, I know she can jump, but I’ve never seen it, and I don’t know how high.  The fence looks pretty high, but I just don’t know.”)

Agnosticism: “I don’t think it’s possible to know whether she will make that jump.” (“All of us have seen her jump a lot of times before.  She’s consistently cleared lower fences, and she has fallen over higher ones.  This one is somewhere in the middle, and she’s wearing different shoes and clothes, so I don’t believe we have the kind of information necessary to make a solid prediction one way or the other.”)

This should make the distinction between weak atheism and agnosticism more clear.  Agnosticism is not just “I don’t know” — it’s a recognition that the current state of knowledge is not sufficient to make a determination.

To offer another example:

Theism: “I believe it will snow next Wednesday.”

Atheism: “I believe it will NOT snow next Wednesday.”

Weak atheism: “I don’t know whether it will snow next Wednesday.”

Agnosticism: “I believe we cannot determine whether it will snow next Wednesday” (due to inherent problems in predicting weather, lack of good forecast data, etc.).

As mentioned above, we can combine agnosticism with other statements about belief.  Agnosticism is a statement about our certain knowledge, whereas theism/atheism are statements about beliefs (which believers may or may not believe can be proved with certainty in an objective scientific fashion).  Thus, we could have:

Agnostic theism: “We don’t have enough solid scientific data to make an accurate prediction, but I nevertheless believe it will snow next Wednesday because it always snows on Aunt Tilly’s birthday.”

Agnostic atheism: “We don’t have enough solid scientific data to make an accurate prediction, but I nevertheless believe it will NOT snow next Wednesday because it never snows on Uncle Ted’s anniversary.”

In these cases, we have beliefs that do not follow from any logical or scientific rigor.  There’s no scientific reason to associate snowfall with someone’s birthday or anniversary.  Nevertheless, one may still have faith in something (or deny the possibility of something) on the basis of “beliefs” (rational or irrational) while still acknowledging that ultimately we just don’t have proper evidence to make a determination.

Note that I do not at all mean to trivialize any religious beliefs (or even atheistic beliefs) by comparing them to the statements here about jumping or snowfall.  I’m merely trying illustrate the distinction made between claims about what we are able to know (gnostic/agnostic) versus what we believe (atheist/theist).

Many theists would state that they not only “believe” but that they “know” that God exists for certain.  Those religious persons believe that actual knowledge (gnosis) about a deity is possible, which would be the opposite of agnostic.

What about those who “just don’t know” but don’t want to be called “atheists”?

As I mentioned at the beginning, there seems to be a stigma associated with the term atheist.  This is probably the reason why many people have adopted the term agnostic when they really are referring to a category of weak atheism.

In common language today, most people will understand agnostic to mean “weak atheist,” unless you are talking to a philosopher, a religious scholar, or someone who is pedantic about word meanings.  To use agnostic in that sense is incorrect from a historical and etymological standpoint, however, and some people might misunderstand you or even correct you.

This leaves a conundrum for people who aren’t quite certain about religion (they aren’t really believers or “theists”) but don’t want to be associated with the term atheist.  For those people, I would propose you adopt the term skeptic.

A skeptic merely questions the validity of commonly accepted beliefs, whether those beliefs are in a theist’s God or a strong atheist’s certain (but ultimately unprovable) assertion that there is no God.  A skeptic just doesn’t know.  A skeptic also is generally not ready to make the agnostic claim that we can’t know.  A skeptic is hesitant to make any certain claims about knowledge or beliefs.

Being a skeptic probably the best middle ground, and it’s more accurate than claiming to be “agnostic” unless you want to make a specific philosophical assertion about the nature of knowledge.

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In previous articles, we identified two of the highest priorities in financial planning that should generally be addressed before making extra payments on a mortgage — high-interest debt and employer matches to retirement funds.  There is one further high priority that should take precedence over most other investments: preparing for disaster.

Build up an emergency fund

Everyone should have at least 3 to 6 months (and preferably 12 months) of income saved up somewhere in case of some sudden financial need: job loss, major home repair, uncovered medical expenses, whatever.  At least 3 months of income should be kept in a relatively liquid state (such as a savings or money market account), so you can access them without a huge amount of trouble when a sudden need arises.  The rest of the emergency fund can be put into low-risk investments with guaranteed returns, if you like.  A CD may have an early withdrawal penalty, and it may not be a high return, but it gives a little growth in your funds while still guaranteed not to lose value when the market crashes and you just happen to be out of a job and need the money the most.

If you pay down your mortgage before building up your emergency fund, you may find yourself in greater trouble when disaster strikes.  You may think the extra equity you have in your home will help you, but it’s not going to be easy to get a home equity loan when you don’t have a job or you have sudden huge expenses that the bank can see which may prevent you from even making regular payments on your original mortgage.

With the emergency money in a savings or investment account, you are free to do with it as you wish, including, for example, continuing to make payments on your mortgage for a year or more when you’re out of work.  If all of that money has already gone into your house, and you have no cash reserve, you may end up in a default instead.

That’s not to say that you shouldn’t work toward equity in your home, but after paying down very high interest rate debt (like credit cards), the next priority should usually be establishing a emergency fund in reserve.  That will allow much more flexibility in down times than any equity locked up in your house.

Have adequate insurance

Emergency funds are great for dealing with minor disasters, but for serious situations that will cost you more than about 6 months’ worth of income to deal with, you probably need insurance.  People with mortgages will already have homeowners insurance, but they may not be adequately insured for other major catastrophes.  Life insurance, disability insurance, and long-term care insurance will be incredibly important for covering financial gaps when a spouse or parent dies or is unable to work.

Particularly for parents, a life insurance policy for a few thousand or even a hundred thousand dollars is usually not enough.  Be sure that your life insurance and disability insurance are sufficient to keep the household running until children are grown.  Most people never need to use term life insurance, and that’s the best-case scenario: you get to be with your kids as they grow up.  But what happens if you don’t?  It may seem expensive, depending on your age, sex, and health, but it will do a lot more to help your family in the event of a true disaster than just about any other investment.

One important money-saving note about insurance with deductibles: go for a high deductible in most cases.  That’s what your emergency fund is for.  And that’s why emergency funds and insurance go hand-in-hand.  It’s ridiculous to pay to have a $250 deductible for your car insurance instead of a $1,000 or $2,000 deductible when you have tens of thousands in an emergency fund.  You can afford better insurance with higher deductibles, and you can afford to have higher deductibles if you have a strong emergency fund.  In this case, saving your emergency money will actually help you to afford better insurance at a cheaper rate.

Conclusion

We’ve now identified the three main items you MUST do before even considering paying down your mortgage: (1) pay down higher-interest debt, (2) take advantage of major retirement opportunities like employer matches and significant tax-advantaged accounts, and (3) be prepared for disaster with emergency money and insurance.

If you’ve paid off those high-interest credit cards, you’ve got at least 6 months of emergency money in the bank, and you’re doing at least the full employer match for retirement, it may be time to consider whether overpayment is a good option.  However, as we’ll explore in the next couple of posts, there are still other factors to consider.

Disclaimer: This is not intended to be professional financial advice, nor does it apply to all people in all situations.  It’s a good idea to consult a professional financial advisor before making any major changes in your finance management, because individual circumstances will often affect the choice of strategy.

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As detailed in the previous post of this series, excess savings in your budget should not automatically be used to pay down principal on a mortgage loan.  Aside from paying off higher interest loans first, another better option is often investment in retirement accounts.

The employer match: Always the best option

Many employers offer some sort of matched funds for investment in a retirement account, whether that takes the form of a 401(k), a 403(b), or some other type of account.

If you are lucky enough to be in that situation, you should generally take advantage of that as much as your financial situation allows.  Sometimes employers will even have a 1:1 match up to a certain amount: be sure to take that.  Can you think of a single other investment where you are guaranteed an instant 100% return on your money?

Even if your employer only matches a portion of your retirement investment, you should contribute the maximum that you can to take advantage of that match.  Retirement may seem a long time away, but a 50% return or whatever on your money instantly should not be dismissed.  The value of a real estate investment or a stock portfolio may go up or down — as may your retirement account — but starting out with 50% or 100% more in it is a huge financial gain.  And generally it requires little more than a bit of paperwork.

Other retirement accounts

Once you get beyond the matched funds, further investment in IRAs (Roth or traditional) or in 401(k) or 403(b) accounts is a riskier proposition.  Here you have to balance the guaranteed return on your mortgage versus variable returns on retirement investments.  This is a difficult question and will be considered in more detail in a future post.

For now, I would say that the situation depends on your overall financial condition.  If you have enough money in an emergency fund and no high interest debt (like credit cards), you can start to consider these options.  If you’re younger, all things being equal, you might lean toward retirement investments, since you have time to take some bigger risks rather than depending on the guaranteed return of the mortgage.  If you’re older, it may depend on how much retirement money you already have put away.

The other factor to consider is that annual investment in some of these types of accounts is capped.  For example, the Roth IRA provides tax-free growth, but annual contributions are capped.  This creates difficulties for investment strategy.

Suppose you have a 4% fixed-rate mortgage.  Assuming you have a large mortgage or other deductions, you might have an effective after-tax interest rate of slightly less.  But right now, there are few options (such as CDs) that could give you a guaranteed return on a retirement investment that is 3-4%.  So, it seems that paying the mortgage is clearly the winner, if you’re risk-averse.

But wait a minute.  Let’s say that the interest rate situation changes in a couple years, and now there are CDs or bonds or other guaranteed investments with a higher rate of return.  If you had socked away a few thousand each year in your Roth IRA, you could now take advantage of those tax-free returns with a large balance in your IRA, but if you don’t have that money in the Roth IRA to begin with, you are limited to the annual caps in getting your money into the account in the first place.

There’s no clear answer here.  The best choice will depend on the details of your finances, the economic conditions, various tax advantages, your risk tolerance, and how lucky you might be about predicting the future.  Nevertheless, saving for retirement is not necessarily a lesser goal than paying your mortgage, so keep options open.

In general, taking advantage of tax-free retirement growth (e.g., Roth IRA) and tax-deferred retirement plans (many other retirement accounts) is a better option for long-term financial gain.  Paying down the mortgage should only be a priority in particular situations where that equity or guaranteed return are necessary for your specific portfolio.

Summary

If your employer offers a match for retirement contributions, definitely take advantage of that over just about any other possible investment opportunity.

For retirement savings beyond the employer match, there are a lot of variables, but a balanced investment strategy should generally consider retirement as a priority at least on par with mortgage investment.  That means that a tax-advantaged retirement plan with a possible high rate of return will usually be better than worrying about tax-deductible mortgage interest.  However, this is a general statement that may not apply to every situation.

Disclaimer: This is not intended to be professional financial advice, nor does it apply to all people in all situations.  It’s a good idea to consult a professional financial advisor before making any major changes in your finance management, because individual circumstances will often affect the choice of strategy.

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For many years, making extra payments on your mortgage was generally viewed as an excellent investment.  If you want to own your home “free and clear,” there’s no better feeling than seeing that principal number go down on your loan.

However, with mortgage rates at historical lows, it may be time to reconsider the value of making early payments or extra payments on your mortgage.  If you have extra cash that you can do something with, mortgage payments are just one of many options.  At a minimum, there are generally other financial steps you should consider before putting the money into a mortgage.

In a previous post, I considered the need to evaluate long-term inflation effects when evaluating payment strategies.  But before you even worry about complexities like that, there are other more basic issues to consider.

Pay down expensive debt first

This should be obvious, but if you have high-interest loans or debt, you should start with the those debts with the highest rates.  If you have a credit card you’re paying 25% interest on, it makes little sense to overpay on a mortgage that you’re only getting charged 5% on.

Similarly, if you have auto loans, student loans, or any other debts that have a rate higher than your mortgage, put your extra cash toward them before even considering an extra mortgage payment.

Some people might be tempted to still make payments on a mortgage over other debts because the mortgage value is so much greater.  If you owe $100,000 on your house, shouldn’t you worry about that large balance over $5,000 on your credit cards?

Let’s consider that scenario in more detail, with a few simplifying assumptions.  Suppose your mortgage rate is 4% (not uncommon these days), while your credit card rate is 15% (a middle-of-the-road rate, unfortunately, but very few are below 10%).  And let’s assume you have $8,000 per year to devote to payments on your house and credit card debt.  At these rates, you’ll need at least $4,750 per year just to keep up the interest.

Furthermore, just to simplify things further, suppose that beyond paying the interest on both the mortgage and credit cards, you use the rest of the money to pay principal down on only one of them.  This is not a typical situation: most loans don’t allow “interest-only” payments, where you effectively never pay the principal down.  But it’s the simplest assumption for our calculations.  (For simplicity, I’ve also assumed here that interest compounds annually, so that the math is easy to follow.)

First, let’s look what happens when you put all your excess money toward paying down the mortgage debt, which has a higher principal.

• Starting Balances: $100,000 on mortgage, $5,000 on credit card
• Year 1: $4,000 interest on mortgage, $750 interest on credit card, $3,250 to pay principal down on mortgage
• Balances at end of Year 1: $96,750 on mortgage, $5,000 on credit card, total interest paid: $4,750
• Year 2: $3,870 interest on mortgage, $750 interest on credit card, $3,380 to pay principal down on mortgage
• Balances at end of Year 2: $93,370, $5,000 on credit card, total interest paid: $9,370

If we continue this pattern for ten years, you end up with a mortgage principal of $60,980, and our initial $5,000 remaining on our credit card.  You thus owe a total of $65,980.  Over the 10 years, you’ve paid $40,980 in interest.

Now, suppose we reverse the strategy and instead put all the excess money toward the credit card debt, with the higher interest rate (but lower balance).

• Starting Balances: $100,000 on mortgage, $5,000 on credit card
• Year 1: $4,000 interest on mortgage, $750 interest on credit card, $3,250 to pay down credit card
• Balances at end of Year 1: $100,000 on mortgage, $1,750 on credit card, total interest paid: $4,750
• Year 2: $4,000 interest on mortgage, $263 interest on credit card, $1,750 to pay OFF credit card, $1,987 to pay principal down on mortgage
• Balances at end of Year 2: $98,013 on mortgage, $0 on credit card, total interest paid: $9,013

Already, by the end of 2 years, we can see a significant decrease in the amount of interest paid.  But suppose you continue the pattern for 10 years.  Since you already paid off the credit card, you now continue paying down the mortgage principal.

At the end of 10 years, you end up with a mortgage principal of $60,423, and no balance on the credit card, so the mortgage is your total debt.  Over the 10 years, you’ve paid $35,423 in interest.

There’s simply no comparison here.  By paying down your credit card first, you would end up paying over $5,000 LESS in interest AND owing over $5,000 LESS in debts at the end of 10 years.

Obviously this example is oversimplified, but the strategy would be the same for loans in the real world.  In general, you should always pay down the debt with the highest interest rate first, regardless of what has a higher principal.  So, start with credit cards, student loans, car loans, whatever — as long as their interest rate is higher than your mortgage, pay them off first.  If your mortgage does happen to have a higher rate than one of those other loans, you should perhaps start paying your mortgage.  However, if this is true, you might also consider whether refinancing is a good option, which might be able to bring your mortgage rate down further and below the interest rates for other debts.  (Whether refinancing is a worthwhile strategy can be a rather complicated thing to determine, which really depends on the individual terms of your loan: consult a financial planner to figure out whether this is a good option in your situation.)

One last comment: if you take no other lesson from this section, realize how ridiculously bad it is for your finances to carry credit card debt.  Paying your credit cards off every month will likely have a much greater impact on your financial future than any overpayment you might make on mortgages or other loans.  Make that the highest priority, and if you don’t have the discipline to keep zero balances on your cards, stop using credit cards as much as possible and use cash, checks, or debit cards.

An exception to the rule: Possible tax benefits

Even if the rates for another loan are equal or slightly less than your mortgage rate, it may still make sense to pay the other loan first.  Why?

Consider the tax benefit of mortgage interest, which is deductible.  For people with relatively small mortgages and little else to deduct, there may be little tax advantage in mortgage interest.  But for those with large amounts of mortgage interest each year, it can provide a significant tax advantage, perhaps making your 4% mortgage rate effectively into a 3% rate.  In such a case, you might still want to start by paying on other loans with rates greater than 3%.

The tax benefits of mortgage interest deductions are something to discuss with a tax accountant or a financial planner, and the advantages will depend on your specific financial situation and loan terms.  But keep in mind that mortgage debt is often the last loan to overpay, even if it has a slightly higher rate than some other debt.

A final complicating factor: low equity or PMI

The previous analysis assumes that you have at least 20% equity in your home and aren’t paying for private mortgage insurance (PMI).  Most of the time, PMI is based on a percentage of the mortgage principal.  For very low equity in a house and bad credit, you might be paying 1% or more of your loan value in PMI.

As a general rule, you should add in the percentage of your principal paid annually to PMI to your interest rate.  So, for example, if you have a 4% interest rate on your mortgage, but are paying 1% for PMI each year, that’s effectively a 5% loan rate.  That’s the rate you should use when comparing it to interest rates on your other debts.

This is an oversimplification, but in some cases the PMI cost may a significant factor to consider.  Also, if you know that you can reduce or eliminate the cost for PMI by paying down the mortgage slightly in the near future, it may be better to dedicate some money toward that goal before tackling higher rate debts.  In general, credit cards are still the first thing to pay off, but if you don’t have credit card debt, an approaching PMI threshold might argue in favor of paying on the mortgage versus car loans, student loans, etc.  However, this is really a question for a financial planner.

Summary

If you have excess money in the bank to pay down debts, congratulations!

But before you start a plan to donate an extra $100 or more automatically to your mortgage each month, first make a list of all of your loans and their interest rates.  In general, devote your overpayments to the highest interest rate loans first, which often will NOT be your mortgage.  However, if you are paying PMI or taking a mortgage interest tax deduction, you will need to factor that in your decision.

Disclaimer: This is not intended to be professional financial advice, nor does it apply to all people in all situations.  It’s a good idea to consult a professional financial advisor before making any major changes in your finance management, because individual circumstances will often affect the choice of strategy.

When I first stumbled on this story, I was intrigued by the use of mathematics to solve a common problem: how many decorations do you need to buy for a Christmas tree of a given size?  But the more I looked at the University of Sheffield page, the more disturbed I became.  The formulas may be the creation of a couple 20-year-old students in a math club, but they are being effectively endorsed by a university, a major retailer, and a number of news sources.  Yet anyone with an 8th-grade knowledge of math should realize that what is being presented is absolute nonsense.  The students are clearly either far less intelligent than we should expect from university math students, or they have attempted to perpetrate a subtle hoax (which has now been spread by a university press office and some media sources).

Before we even get to the formulas themselves, I should note that even the press release itself has ridiculous errors.  The University of Sheffield includes some “Christmas Tree Facts” on its website, including the following:

The world’s tallest Christmas tree would, at 2,600ft tall, need more than 16,000 baubles, over 4,000 meters of tinsel, almost 2,500 meters of lights, and an 80 meter tall star.

Aside from basic fact checking, does anyone at this university’s press office have a clue about what numbers mean?  A 2600-foot Christmas tree would be nearly a half of a mile high, almost twice the height of the Empire State Building!  For the record, the tallest giant sequoias in California are less than 400 feet tall.

What this “Christmas Tree Fact” is referring to is not a tree at all, but rather a giant lighting decoration on the side of a mountain near the Italian city of Gubbio.  True, the lights go up the mountain in a shape that looks like a sort of “drawing” of a Christmas tree, but that hardly counts as an actual “tree.”  And it makes no sense to apply a formula made for a 3-dimensional tree to an effectively 2-dimensional mountain surface decoration.

Unfortunately, the errors in the “facts” are only the beginning of the problem.  Here are the formulas given for decorating a tree:

The first odd thing about the formulas is their complexity.  What is the need for square roots of numbers?  Why use √17/20 in the first formula, when you could just use 0.2?  The exact value of √17/20 is an irrational number, 0.206155…, but the results given by the formulas cannot be accurate to more than a digit or two (as will be explained below), so what is the reason for this complicated looking use of square roots and fractions?  Similarly, why 13×π/8, when one could just say 5 or 5.1?  (Again, the exact value is the irrational number 5.105088….)  The use of pi at least seems to be more relevant than the arbitrary inclusion of a square root of 17, since most trees have a roughly circular shape when viewed from above.

But if these formulas are meant to be used by average people, why not make them as easy-to-use as possible?  It’s much easier for someone to plug in 0.2 × height into a calculator, or even 0.206 × height, rather than taking a square root of some random number.  What does the square root of 17 have to do with the shape of trees?  Its value is about 4.1.  Is there some reason that approximation is inadequate here?

Now if this were the only problem with the formulas, the students would at best be guilty of not understanding significant digits or failing to make their formulas user-friendly.  It certainly is possible that they performed some calculations that ended up with a square root or some factors of pi in deriving these expressions.  On the other hand, these mathematical expressions might also be an attempt to hide the simplicity of a rather mundane model.  Which looks more “complicated” (and therefore requiring the expertise of university math students): the above expressions or the following ones, which are reasonable approximations to them?

• Number of baubles = tree height ÷ 5
• Length of tinsel = 5 × tree height
• Length of lights = 3 × tree height
• Height of star = tree height ÷ 10

All those square roots and fractions and factors of pi don’t appear to do much.  Now, you might say that they could provide additional accuracy to the expressions.  Maybe there is a reason why the length of the lights is closer to 3.14159… than to 3.  But that level of accuracy would require a rather accurate model of the tree shape.

And yet the tree shape is not modeled well at all by these expressions.  The only measurement is the height of the tree.  Even if the wacky constants used are roughly accurate, the relevant variable for amount of lights, ornaments, etc. is the surface area.  To estimate that, you’d need at least one (and preferably two or more) radius/diameter/circumference measurements to take into account the shape of the tree (conical, full with a bulge in the middle, very thin, etc.).

But the biggest issue is that the formulas say that amount of lights, etc. should vary linearly with the height of the tree.  That is, if you have a tree that is twice as tall, their formulas would require twice as many lights, twice as many ornaments, etc.  However, the surface area of the tree will increase roughly with the square of the height (assuming that the general shape of the tree remains the same).  That is, for a tree that is twice as tall, the surface area will be about 4 times as much; for a tree three times as tall, the surface are will be about 9 times as much.

Let’s say, for example, that the Sheffield formula is accurate for a tree that is 9 feet tall.  If we then tried to use the same formula for a 3-foot desktop tree, we’d end up tripling the density of lights, ornaments, and tinsel on the tree’s surface.  It would clearly look overdecorated, particularly given that a smaller tree would likely be easier to see through at spots, thereby increasing the apparent density of lights in particular.  On the other hand, if the Sheffield formula were calibrated to a 3-foot desktop tree, it would recommend rather sparse decorations for a taller tree in a living room.

I do imagine the numbers might stay roughly accurate for a giant outdoor tree compared to an indoor one, since you’d use larger lights and larger ornaments on a giant outdoor tree, and therefore would need fewer of them.  But if you’re trying to decorate a 3-foot tree on your desk vs. a 9-foot tree in your living room with similar ornaments, these formulas will produce vastly different results, even with trees of the same shape.

I think the absolute minimum for a reasonably accurate formula would be three measurements: (1) height, (2) radius at the widest point of the tree, and (3) the height of the widest point.  Or, alternatively, (1) height, (2) radius halfway up, and (3) radius at lowest large branches.  A set of three measurements would allow an extrapolation of surface area, which would be an estimate of “fullness.”  Of course, there will still be trees with odd shapes, and different kinds of trees may require different lighting (e.g., thin pine needles don’t hide lights as much as a thick spruce).  But at least such a formula could aim for consistency in a variety of scenarios.

One might challenge the validity of the question posed to the Sheffield students.  Is it reasonable to come up with a formula for the number of ornaments and the length of strings of lights without knowing anything about the size of the ornaments, the brightness of each light, how close the lights are on the string, etc.?  In a way, the problem is difficult to solve without standard “components” for decorating, not to mention the inherent subjectivity in the “proper” amount of decorations.

Nevertheless, when such formulas are announced with authority by a university and a large commercial chain, they could at least give some rough guidelines that make some sense.  As we’ve seen, however, the proposed “solutions” to this problem not only lack appropriate information to solve it (i.e., the shape of the tree, specifically the surface area), but also make little sense even if we assume a consistent tree shape.

My guess is that university math students are not that dumb.  They probably started by making some very rough approximations: “the star on top should be about 1/10 of the height of the tree.”  Relating the height of one prominent ornament to the height of the tree makes some sense.  But then, rather than considering surface area, they just began to estimate other decorations for a “normal” height tree: “the amount of tinsel might take roughly 5 times of the height of a ‘normal’ tree to cover it, but we need fewer lights, maybe only 3 times the height of the tree.”  And then someone thought: “Hey, 3 is close to pi, and pi is related to round things, so we could just use pi for the light formula!”  Pretty soon, there were fractions and more uses of pi and even square roots, making it all look very cumbersome.

I can’t say for sure that this is what happened, but it seems rather unlikely that the students would use complex methods resulting in these odd irrational numbers and yet not consider the need to incorporate surface area factors rather than simply height.  It also is mildly suspicious that the three complex-looking formulas effectively amount to multiplying or dividing by 5 or 3.

While I wouldn’t expect any editor in the mainstream media or the University of Sheffield press office to do the detailed analysis I’ve done here, I would hope that anyone with any basic numerical intuition would question formulas that claim to scale to various sizes yet clearly don’t contain enough information to perform the necessary calculation.  It should be intuitively obvious that formulas that only take height into account wouldn’t recognize the difference between a thin tree and a full and bushy one.  The former might not even need half of the decorations of the latter to appear full of ornaments and lights.  And once that question comes up, the next one presents itself: how does this formula actually scale?  If you just begin to plug numbers in, they immediately seem rather crazy for very small or very large trees.

For example, in the theoretical “2,600-foot tree” referenced above, it is claimed that only 16,000 ornaments would be required.  That’s an average of only 5 ornaments per foot of tree height — do 5 ornaments really seem sufficient to encircle a foot-high band around a 2,600-foot tree, except near the very, very top??  Similarly, the formulas predict that if I had a tiny rosemary bush that is 1-foot tall on my desk, I would need about 3 feet of lights to decorate it, which seems rather excessive, no?

Just a minimum of common sense should have shown the university, Debenhams, and any other media that picked up this story that it makes no sense.  But because the formulas contained complicated-looking square roots and Greek letters, it must be the product of deep thought and analysis, right?

To the students at the University of Sheffield: congratulations.  You’ve not only got a lot of attention for a well-played hoax, but you’ve also demonstrated the complete and utter mathematical illiteracy of a huge number of people.  This is an important lesson.

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Over there, over there
Send the word, send the word over there,
That the Yanks are coming, the Yanks are coming,
Their drums rum-tumming everywhere.
So prepare, send a prayer,
Send the word, send the word to beware—
We’ll be over, we’re coming over,
And we won’t come back till it’s over over there.

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Have you ever wondered why we celebrate Veterans Day on November 11 every year?  Most other federal holidays, including birthdays of historical figures, get moved to Mondays.  Aside from New Year’s Day, which obviously can’t be moved, and Christmas, which has a very strong tradition for a specific date, all other holidays generally float around to create a convenient long weekend.

But Veterans Day does not.  It is always celebrated on the 11th day of the 11th month of the year, and those who are involved in ceremonies may know that they generally begin at the 11th hour (11:00 in the morning) on Veterans Day.  Hmm — 11:00 on 11/11.  This year is 2011, which made it 11:00 on 11/11/11.  Perhaps, given the special form of the date this past week, it is time to recall why we celebrate at such an unusual time on such a specific date.

There is another reason why this year is a particularly special time to remember the significance of Veterans Day: the last original veteran died this year, or at least the last U.S. veteran.  There is only one remaining in the rest of the world, a 110-year-old woman in England.

What is often forgotten these days is that Veterans Day is actually Armistice Day.  On the 11th day of the 11th month at the 11th hour in the year 1918, the armistice—the agreement to end all hostilities—was signed to mark the official end of the First World War, which at that time was known as simply the Great War, or even the War to End All Wars.

Armistice Day was not a celebration of the war.  It was not a time for patriotism or for the cheering of veterans for their service.  Instead, it was a celebration of peace, of thanksgiving that some veterans did make it home to their families after a senseless war.

The origins of World War I are complex, but people at the time and today agree that the alliances and agreements that forced all of Europe into a total war also escalated the crisis and the subsequent carnage.  This war was the worst meeting of old styles of war against machines.  Tanks, poison gas, and improved machine guns coexisted with traditional lines of charging men and horses.  Trenches, which previously had been an element of siege warfare because of the long duration of such campaigns, became a permanent home on battlefields as the traditional lines of soldiers sought refuge from the automatic weapons.  Disease, poor supply lines, and weather contributed to the horror.

As Wilfred Owen, a poet in the lines in World War I, described it, the old platitude about how sweet and fitting it is to die for one’s country (Dulce et decorum est pro patria mori) seemed very strange in the conditions of the trenches:

Bent double, like old beggars under sacks,
Knock-kneed, coughing like hags, we cursed through sludge,
Till on the haunting flares we turned our backs
And towards our distant rest began to trudge.
Men marched asleep. Many had lost their boots
But limped on, blood-shod. All went lame; all blind;
Drunk with fatigue; deaf even to the hoots 
Of tired, outstripped Five-Nines that dropped behind.
Gas! Gas! Quick, boys! – An ecstasy of fumbling,
Fitting the clumsy helmets just in time;
But someone still was yelling out and stumbling,
And flound’ring like a man in fire or lime . . .
Dim, through the misty panes and thick green light,
As under a green sea, I saw him drowning.
In all my dreams, before my helpless sight,
He plunges at me, guttering, choking, drowning.
If in some smothering dreams you too could pace
Behind the wagon that we flung him in,
And watch the white eyes writhing in his face,
His hanging face, like a devil’s sick of sin;
If you could hear, at every jolt, the blood
Come gargling from the froth-corrupted lungs,
Obscene as cancer, bitter as the cud 
Of vile, incurable sores on innocent tongues,
My friend, you would not tell with such high zest 
To children ardent for some desperate glory,
The old Lie; Dulce et Decorum est
Pro patria mori.

Is it any wonder that, following a war that escalated to encompass most of the world, everyone would want to celebrate the peace?  Armistice Day was not like the later V-E Day and V-J Day that would celebrate victories over Germany and Japan in World War II.  The Armistice was hardly a triumphal victory following an unconditional surrender: it was a peace deal that ended a long and bloody war.

The hope of an annual celebration of Armistice Day was that the world would never again be plunged into such a horrific conflict.  In 1928, many countries made this an official policy with the passage of the Kellogg-Briand Pact, a treaty that effectively outlawed war.  Not just aggressive war, but all war used by governments as a policy.  The U.S. Senate ratified the treaty almost unanimously (with only one dissenting vote), and to this day it remains the official law of the U.S.  Of course, the pact barely lasted a few years, as the build-up to World War II saw numerous invasions and ultimately the escalation into another total war.

But in these early days between the wars, Armistice Day stood not as a monument to patriotism or to cheering troops, but as a reminder of the destruction of the Great War, the War to End All Wars.  Armistice Day did not celebrate veterans: it stood for the hope that we might never need more of them.

This year, the last U.S. veteran of that war died.  Frank Buckles was 110 years old when he died on February 27, 2011, and in his last years, he lobbied for the construction of a national monument to those who served in World War I.  There was perhaps some hope in him and the few other veterans of that conflict who remained in recent decades that we might recall the terrible things that led to Armistice Day, the Kellogg-Briand Pact, and the hope that we might never need another veteran to go off to war.  (Now, only one veteran remains—Florence Green, from the U.K., also 110 years old, who never served in combat, but served as an officers’ mess steward.  Buckles, too, never saw combat, but the last veteran who did also died earlier this year.)

This year marked the first Veterans Day without any of those original veterans.  In the years following World War II, which had been viewed as a conflict against the evils of Hitler rather than a senseless war brought about alliances, the millions of new veterans sought their own recognition.  World War II was felt to have been a more just war for a just cause, even a defensive war fought against powers that threatened to take over the world.  Evil had been vanquished, and the victors were proud of it.

So, it was proposed to change the meaning of Armistice Day, which by then was merely a memory of a long-gone conflict where World War I veterans might form a parade, into a celebration of the warriors who came home from all wars. Unlike Memorial Day, which honored the dead, Veterans Day would exalt the living soldiers, the ones who came back in honor and glory.

Armistice Day, the celebration of peace and the hope that the last veteran had served in 1918, became (under President—formerly Supreme Commander—Eisenhower) Veterans Day, a celebration of nationalist pride for our warrior heroes.

Now that the last veteran has passed, it is perhaps time to remember the meaning of Armistice Day.  Of course, we should honor the character of the many men and women who have served, and the dynamics of our world today demonstrate that there is a lot we would have to resolve before achieving a new peace.  I am not hopelessly idealistic, but I do think we could do better.

Therefore, for Armistice Day, let us also recall the hope that the world might be better if we didn’t need veterans at all, if the last veteran who died this year might have been the last veteran of all, because the War to End All Wars might have actually convinced us to end them.  Whatever happened to: “We won’t come back till it’s over over there.”  The “it” was obviously the Great War, but Armistice Day was the hope that “it” might be the end of all war.

What would it be like to have a Veterans Day without veterans?

Wouldn’t that be the ultimate way to honor the dead of World War I, to celebrate the Armistice, to hope for peace?  As you reflect on last week’s holiday and on future Veterans Days that cause us to stop and reflect in the middle of the week on that strange but exact time of the 11th hour of the 11th day of the 11th month, remember the last U.S. veteran of that Great War is gone.  What would those old soldiers say?

In Flanders fields the poppies blow
      Between the crosses, row on row,
   That mark our place; and in the sky
   The larks, still bravely singing, fly
Scarce heard amid the guns below.

We are the Dead. Short days ago
We lived, felt dawn, saw sunset glow,
   Loved and were loved, and now we lie,
         In Flanders fields.

Take up our quarrel with the foe:
To you from failing hands we throw
   The torch; be yours to hold it high.
   If ye break faith with us who die
We shall not sleep, though poppies grow
         In Flanders fields.

—Lieutenant Colonel John McCrae, May 3rd, 1915

While McCrae’s final stanza is often seen as an incitement to war after the somber beginning, perhaps we can see also see the “quarrel with the foe” as a better alternative to a true war.  We all have arguments, and sometimes we say and do things that we shouldn’t have, but when the quarrel is over, we move past it by recognizing the wrongs and trying to prevent the quarrel from happening again.  We seek peace, rather than childishly thumping our chests in victory.  After the quarrel was over, the torch that Armistice Day celebrations carried for those veterans was a promise to sue for peace when possible, to avoid another wasteful war.

We should be thankful our veterans have returned home safely, and we should honor their service, but perhaps now is the time to reinvigorate hope for the ending of conflicts, for the quest for peace, and for those World War I dead finally to sleep.

We were faithful, we made peace, and now let it finally be over . . . not just over there, but everywhere.

Would it surprise you to know that when decisions aren’t unanimous, they frequently divide the justices into groups that don’t fit partisan stereotypes?

To become a justice on the Supreme Court, you generally can’t just be a partisan hack.  Take some time and read some Supreme Court decisions.  Listen to some oral arguments.  The people who sit on this Court are very intelligent.  Very intelligent people tend to have their own opinions, particularly on such nuanced issues as the Law.

Nevertheless, in the lead-up to the decisions on health care and immigration which should be coming out in the next week or so, there has been a frankly inexcusable tendency for the media to act as though these nine people are like typical partisan idiots who walk into a voting booth and simply check the box next to “Republican” or “Democrat” based on their affiliation.  According to this gross distortion of the Court, Kennedy is some sort of wildcard, swaying back and forth as the breeze takes him to “conservative” and “liberal” quarters.

This is, frankly, insulting to the Court.  It is insulting to the justices.  And it speaks volumes about the ignorance of the media in propagating such a myth.

It takes a certain level of ignorance to post a story about Supreme Court statistics on a day when the Court’s behavior actually shows those statistics to be meaningless.  Yet John Hudson over at The Atlantic apparently aspires to a higher standard of ignorance.

Decrying polarization is the everyone’s favorite game in Washington, but in the case of the Supreme Court, it’s statistically measurable.  On Monday, the high court handed down three 5-4 split decisions in its four most recent cases. Considering the outcome, and the fact that a likely five-four split will be on its way for the health care reform ruling, The New York Times Juliet Labidos was curious if the court is more divided than it has been in history. Turns out: There’s a strong case that it is.

That would be one way of reading Juliet Labidos’s blog post over at The New York Times.  Unfortunately, it’s a rather ignorant one, and one that is incredibly deceptive.  There’s not a “strong case” for polarization, and even if we could argue that there is a weak case for one, Monday’s 5-4 decisions are certainly not a good example of it.  (Labidos does give a little more nuance to the arguments with a few more caveats, but the general discussion is still misleading.)

As the graph cited by Hudson notes, there have been a higher percentage of 5-4 decisions in the Roberts Court than under previous Chief Justices.  But there are a number of reasons that such an observation tells us nothing about political polarization on the Court.

To begin with, we need to take into account whether the Court actually splits 5-4 along supposed ideological lines — with Ginsberg, Sotomayor, Kagan, and Breyer in the “liberal” camp, Scalia, Thomas, Alito, and Roberts in “conservative” camp, and Kennedy drifting back and forth as the mood takes him. Hudson is smart enough to mention this:

Now, it’s worth noting that the Roberts court isn’t always divided by partisan lines. As Lapidos notes,  ”Chief Justice Roberts wrote today’s dissenting opinion in Salazar v. Ramah Navajo Chapter. He was joined by Justices Ginsburg, Breyer, and Alito.” That’s quite an ideologically diverse group. Still, we know by the legal opinions of the court, that this sort of split isn’t the norm.

While “this sort of split” may not happen all the time, these sorts of non-partisan divisions actually do occur rather frequently.  In fact, it might be good to mention that such supposedly abnormal divisions happened in not one but two of the three decisions on Monday.  Hint to the media: if you want to prove that the Court is ideologically divided along 5-4 lines, try not to publish about it when 2/3 of the decisions are 5-4 NOT along supposed ideological lines.  And, by the way, in the fourth decision issued on Monday, the ruling was 8-1, with Sotomayor dissenting.  Clearly that isn’t along partisan lines, so 75% of the decisions which came out on Monday do NOT support the thesis of the New York Times and The Atlantic.

Let’s recap those decision splits.  In Christopher v. SmithKline Beecham Corp., the Court actually split 5-4 along the supposed “partisan” lines.  But in Salazar v. Ramah Navajo Chapter, we saw a 5-4 split with Sotomayor writing the opinion for the majority, joined by Scalia, Thomas, Kagan, and Kennedy.  The decision had to do with money Congress had allocated to pay for police services and other governmental duties for Native Americans, but which Congress later capped below the levels it had originally agreed on.  Essentially, it left the Native Americans footing the bill for something when they were told that someone else was paying.  You might think that conservatives (with their “small government, less tax” leanings) might all gang up and say the federal government is better not spending more, and spending caps are good, even if they cause a few problems administratively.  Yet the arch-conservatives Thomas and Scalia (along with Kennedy) came to the opposite conclusion.  Meanwhile, if you were the simplistic ideological sort, you might think that liberals (with their “bleeding heart” sympathy for Native Americans and lack of care for federal spending) might rush to give the money to tribes.  But, alas, Ginsberg and Breyer seem to buck that trend too.  What the heck is going on?

It seems to get even more puzzling when we look at the other 5-4 ruling of the day, Williams v. Illinois.  If you saw, for example, the Boston Globe’s coverage of the story, you might think that the evil conservatives headed by Clarence Thomas (with his dour face) were spearheading a fight to take away defendants’ rights:

Justice Clarence Thomas provided the margin of difference in the case to uphold conviction in the rape case.

Amidst all the talk of “factions” on the Court, a mildly intelligent reader of this story might start to wonder: “What?! I thought Kennedy was that yellow-bellied scoundrel who flits back-and-forth!  How could Clarence Thomas be the deciding vote?”

Well, first off, Thomas was hardly “writing only for himself, but controlling the outcome of the case.”  All nine justices controlled the outcome of the case.  The fact that they happened to split into two groups rather than three or four or nine is irrelevant information.  One could just as well say that one of the justices in the other groups of four “controll[ed] the outcome of the case,” since any of them could change the outcome by switching their vote.

Note the desperate attempt to portray the idea of warring factions, 4 on one side, and 4 on the other.  Except… wait a minute — what’s crazy liberal Stephen Breyer doing over there with Roberts and Alito and Kennedy?  And why is arch-conservative Scalia siding with arch-liberal Ginsberg, along with Kagan and Sotomayor?  These aren’t the four-against-four battle lines we’re supposed to have, with Clarence Thomas, arguably the most conservative justice of them all, flitting back-and-forth to decide things in the middle.  Scalia lines up for defendants, while Breyer wants to cast them into jail?  What is going on here?

The answer is rather simple.  The justices’ vote based on legal reasoning, not based on simplistic partisan nonsense.  They sometimes do line up roughly with conservative and liberal stereotypes, just because they were chosen because their nuanced legal perspectives often happened to serve the President who appointed them.  But these are law scholars — they will vote based on their opinion of the law, which may (and often does, if you pay attention to opinions) conflict with partisan ideology or personal opinion.  In the end, they have complex perspectives on the law which are much, much more intelligent and rational than any party platform, which is generally made up to pander to the most people.

Here’s the reality — even in these supposedly political polarized 5-4 decisions, about 1/3 of the time, the split does not have the “four liberals” lined up against the “four conservatives.”  That’s pretty significant: about 1 out of 3 cases decided 5/4 is not actually “polarized” by these supposed boundaries.  Hudson is right that 5-4 decisions split differently aren’t the most common occurrence, but they’re fairly common.

Well, actually, they would be if in fact polarized decisions were that common anyway, which they’re not.  As the official SCOTUSblog statistics show, the Court has ruled unanimously in about half of the cases this term.  (For more details and charts, scroll down to the “StatsPack,” which contains analysis of this term and the previous 10 years of Court history, up through the end of May this term — it does not include the most recent rulings.)  Daniel Fisher noted this over at Forbes earlier this month.

In fact, for all of this talk about partisan divisions, the Roberts Court has one of the highest unanimous decision rates in history (if not the highest), with roughly 40% of its decisions being 9-0.  Another 10% or so tend to be 8-1, where we can’t really see “ideological divisions,” since it’s just one loan person in dissent, not clearly representing a “faction.”

What about the other possible divisions: 7-2 or 6-3?  Do they always fall along partisan lines?  The answer, as can quickly be seen from the SCOTUSblog stats is a clear NO.  In this term alone, “conservative” Alito and “liberal” Breyer teamed up in dissent in Golan v. Holder, while the supposedly more polarized justices further to the “left” and “right” all agreed in the 6-2 decision (Kagan recused herself).  It gets even weirder.  In this year’s Reynolds v. United States concerning sex-offender registries (not to be confused with Reynolds v. United States decided in 1878, which effectively outlawed bigamy when dealing with the common Mormon practice), which decided 7-2, the dissent was written by Scalia, joined only by arch-liberal Ginsberg.

So, 2 of the 5 decisions this term which came out with only 2 justices in dissent showed combinations of justices that did not split along ideological lines.  What would we expect, if justices’ opinions were randomly distributed?  There are 36 possible combinations of two justices, and 20 of them would classify as “ideological” divisions (according to the traditional 4 against 4 rhetoric, with Kennedy qualifying for both sides).  Thus, we’d expect apparent ideological decisions in roughly 56% of cases, even if justices chose sides by chance.  What did we actually see?  60% this term, with 40% “non-ideological.”  That’s not even a significant showing for decisions with 2 justices in dissent.

As for the 6-3 decisions, they might seem slightly more partisan, except it’s rarely predictable which justice will bolt from the dissent to the majority.  From the liberal side, for example, it’s rarely Ginsberg (who tends to be the most ideological justice, according to stats, beating even Thomas and Scalia).  But it could be Kagan or Sotomayor or Breyer or… sometimes both Kagan and Sotomayor will join the conservatives, with Kennedy coming into the dissent.  This hardly sounds like a well-defined set of clear “liberals” against clear “conservatives.”

Yes, it is true that some of the 7-2, and 6-3 divisions, along with the 5-4 decisions, do tend to group ideologically.  But this is not always the case.

Let’s be perfectly clear about all of this: The Roberts Court has ruled unanimously or 8-1 (where there is no meaningful ideological division) at least 50% of the time.  In the 7-2 decisions, at least in the past year, it’s hard to see any partisan alignment above chance.  That leaves us with only about 35% of decisions that could even be considered partisan in any way.  And in those remaining decisions, roughly 1/3 of the time, the divisions do not fall on meaningful “partisan” lines.

All of this stupidity in the media about a partisan Court follows weeks of commentary about how Americans are supposedly losing faith in the Court, with only 44% of Americans “approving” it.

Let’s contrast that with an actual partisan body, namely the U.S. Congress, whose approval rating has been in the 10-20% range for the past YEAR (and, frankly, I’m not sure approval of Congress has ever been up as high as 44%, except perhaps in the “patriotic” days after 9/11).

If there is are any lessons from these statistics, perhaps we should correlate disapproval with real partisanship.  In that case, the Supreme Court, which has tended to float between 45% and 60% approval over the years, is actually a model to imitate, while Congress, which struggles to get above 25% approval even in good years, is uniformly dysfunctional.

Perhaps the American public is actually smarter than the yahoos over at The Atlantic and The New York Times.  Maybe they actually can tell the difference between simplistic partisan divisions and actual intellectual debate.

The Supreme Court may be trending toward stronger divisions due to the politicized appointment process in the past few decades.  But, so far, the actual statistics show that the Court is frequently unanimous, and when it does split, it is quite frequently in ways that are not “predictable” according to party politics.

That’s exactly what you’d expect from nine people who actually have the ability to think for themselves.