The Quantum Quandary

Tuesday, 3 February 2015 20:46 by The Lunatic

I’ve discussed “The Immutable Laws of Physics” a few times in previous articles. Every shred of evidence we have indicates that the interactions between matter, energy, time, and space, are themselves the very nature of the universe, and nothing we (or anything/anyone else) can do will ever change these interactions. Whenever we’ve observed or discovered something new that we don’t understand, it reminds us that we have incomplete understanding of the laws of physics – but the physical world is still immutable.

Quantum mechanics is a “relatively new” branch of physics that was discovered roughly 100 years ago, and it has certainly enhanced our understanding of these physical interactions. It has also made things quite a bit more complicated, as quantum mechanics embodies concepts which are quite difficult to grasp. The concepts are not as elegant as the pure logic behind classical “Newtonian physics”, or the mind-bending beauty of Einstein’s discovery of relativity.

One of the problems is that quantum mechanics have a large component that has to do with randomness. Changes in quantum states are thought to be the only truly random physical interactions in the whole universe!

One question that often comes up is this: how do we account for the randomness of quantum mechanics if the fundamental laws of physics are so perfect and so immutable? Why don’t our traditional laws of physics clash with the crazy and unpredictable nature of this randomness, the particle/wave duality, and Heisenberg's uncertainty principle? And while we’re at it, what do we feed to Schrödinger’s much maligned cat?

Quantum mathematics are somewhat abstract, yet exceedingly precise. The math has been verified experimentally to within one part in many billions; the measured data agrees with the theoretical equations to the limits of our measurement technology. This is a very key point. 

As a practical example, every time a transistor switches on and off in a computer, there is a “quantum band gap” that each electron goes through. If we could somehow “see” each electron that is pushed up against the junction of a transistor, we would not be able to tell which specific electrons would make it through the gap and which ones wouldn’t. The quantum state of each individual electron is completely random. However, we can say – very, very precisely – how many in total will go through and at what energy levels.

Advancements in manufacturing technologies, resulting in less impurities (i.e. stray molecules of unwanted substances) in the silicon junction, have allowed electrical engineers and chip designers to make transistors that are smaller, faster, and more reliable.

Indeed, the processors found in most home computers have more than 4 billion transistors ... and each can turn on and off at a rate of some 3 billion times a second. If the rules of quantum mechanics were not so perfectly reliable, there is no way that any computer would run for more than a few seconds without crashing!

Even though it appears to be the basis of all randomness in the universe, we harness the power of quantum mechanics all the time. Another example is flash memory chips (such as those found in the USB stick you probably have in your pocket) which use quantum tunneling to erase their memory cells.

There are other interesting things about quantum mechanics as well. Here’s a “thought experiment” to consider:

Suppose we have two rooms, each with a bowling ball suspended from the ceiling. The rooms are absolutely identical, as are the mechanisms connected to the ceiling in each room and the wire that’s connected to the bowling balls.

If we pull both balls back exactly the same amount, and let them go at exactly the same time, their movement should be exactly the same. The more variables that we eliminate, making the two setups even more identical, the longer we can let the experiment go and get the same results in both rooms.

We can understand this scenario and the outcomes very easily. It matches our observations of “how things work”, and it follows common sense and fits our understanding of the laws of classical physics.

Let’s make the scenario a little more complicated. This time we have two identical rooms, each with a table, a fan, and a big pile of nice and fluffy goose-down feathers.

Now, when I say the two rooms are “identical”, I mean that the entire setup is identical down to the sub-atomic particles. We’ll use an imaginary “3D Printer” to lay every single atom in exactly the same position and the same quantum state – each and every molecule, including the air and any dust particles in the room, are identical at the start of the experiment. Let’s say there’s a large battery pack under the table which can run the fan. (We don’t want to bring power into the room, as we don’t want any outside influence at all.)

The question is this: if you turn on the fan for EXACTLY 30 seconds in each room, timed down to absolutely the same “Planck Time” interval, will all the feathers settle to the exact same position in each room at the end? How about if you run the fan for five minutes? A year?

You might tell me that there will always be some external influence. I agree that the passing of one stray gamma ray or neutrino through the room could change the trajectory of one air molecule ever so slightly, and the cascade affect from that would change the outcome. So let’s ensure there are no outside influences: both rooms are surrounded by 8 feet of lead and concrete, and the inner four inches of the walls of the room itself are also printed with our magical 3D printer to ensure that the interactions of the air and feathers with the surfaces of the walls are exactly the same as well.

Traditional Newtonian physics says that yes, the rooms will act the same way and all the feathers will end up in exactly the same position at the end. Of course it would be practically impossible to calculate all the force vectors, collisions, micro-air currents, etc (admittedly, the idea that we could actually build such an experiment is practically impossible in the first place) – but Newtonian physics say that if we have identical rooms without any external influence, all the feathers in both rooms will all follow the exact same paths and end up in the exact same places at the end.

It’s hard to conceive of such an outcome. This concept does not obey common sense, and our skepticism is well founded. It is an example of how the “randomness” of quantum mechanics will interfere with the traditional laws of physics as described by Newton.

Usually, quantum randomness of an enclosed system will “average out” and have no fundamental effect on larger objects. With the swinging bowling ball in our first example, there are quantum movements of the sub-atomic particles that make up the air molecules in the room – but the large, single contained object of the bowling ball isn’t really affected by it, as the number (and trajectories) of air molecules on one side of the ball are always balanced out by the number (and trajectories) of molecules on the other side. The net force on the ball will, on average, always be zero when viewed from a classical physics standpoint.

(Similarly, as tumultuous as the weather patterns are here on Earth, the weather patterns on each side of the planet “cancel out” and don’t affect the Earth’s orbit around the sun, or the gravitational interactions with other planets. But hold that thought for a moment ...)

In the two rooms with the fans and pile of feathers, the randomness of quantum movements can alter the outcome of the experiment. Just one molecule of air that gets bumped into a slightly different trajectory due to a different quantum state of one electron will change the trajectory of each subsequent molecule that it bumps into. And soon you have a cascade effect in the air molecules. This becomes a big enough change to alter the position of one feather, which in turn has a cascade effect on the other feathers. With a vastly larger number of smaller/lighter objects (rather than a single large bowling ball) it is far more likely that any individual quantum fluctuation will alter the outcome.

Indeed, it is believed that this is the primary reason why weather patterns on Earth are so difficult to predict. It doesn’t matter how carefully you project the current atmospheric forces today, you won’t get an accurate prediction of what will happen ten days from now. You may have heard of the “Butterfly effect”; it is an idea that the wind generated from the wings of one butterfly can have a cascade effect which may trigger a hurricane on the other side of the planet. So we cannot predict what the weather will be like in ten days ... but we CAN predict where each planet in our solar system, the sun, and all the stars in the Milky Way galaxy will be in a million years! (Like the bowling ball, the stars and planets will be immune to the “self-cancelling” forces within each enclosed system)

Current understanding of modern physics says that quantum mechanics is the only true “randomness” in the universe. That’s fine and dandy. However, I can conjure up a random thought. How about “elephant snot”? Is that random enough?

There’s the rub. We have no explanation, from a physics standpoint, of how or why we have creativity and randomness in our thoughts. It’s not just human thought either. Although other animals don’t have advanced reasoning capabilities, they certainly have creativity and decision making abilities. In fact, every biological organism has some “randomness” in their response to stimulus.

Now, before we go down the path of taking the easy way out and saying “god made it that way”, I will say that the entire idea of ‘god’ is just another random thought that someone came up with, as a way to explain something that – with the evidence available at the time – couldn’t be answered any other way. Throughout human history, we’ve continuously asked questions about things we didn’t understand, and over time we’ve found answers to many (but not all) of these puzzling questions. Saying ‘god made it that way’ is a cop out. The only consequence of that statement is that it keeps people from looking for the real answers. It stifles curiosity and is disruptive to our persistent desire to understand the true nature of our universe.

So back to our puzzle. Here’s an interesting hypothesis. I’m not saying that this is “the truth”, or that it has any scientific basis – it’s just another creative idea that we can explore:

What if we think of neurons, and the synaptic exchange of electrical or chemical signals between the neurons in our brain, as a type of “quantum amplifier”?

If quantum mechanics are truly the basis of all randomness in the universe, then that should be the basis of random thought and creativity.

The implications of this are interesting. We may accept the idea that within a single “closed system”, quantum effects cancel out and can’t affect anything externally ... but by amplifying quantum randomness such as creative thought, we can direct the muscles in our bodies to do things and build things and create civilizations. For example, my mind is now amplifying many quantum interactions, turning them into thoughts, directing my muscles to move my fingers on the keyboard, typing on a computer with technology that evolved from the scientifically creative ideas of many people over many millennia.

And what if all the collective quantum amplification in a large civilization put together a rocket, which carried enough explosives to blow up the planet Mars, or push the Earth into a different orbit? That would certainly qualify as a quantum effect that – through amplification – has an influence on something outside of its closed system!

Some modern physicists have taken the position that all objects obey the laws of quantum mechanics, and classical physics is just an approximation of quantum mechanics as it is applied to a large system of objects. Wow. Think about that for a minute.

This is a fascinating idea. It would certainly fit with the Third Law of Thermodynamics, which describes “entropy” and the statistical basis of molecular motion. One of the most common examples of entropy is calculating how probable it is, at any given moment, that all the air molecules in an enclosed room will be on one side of the room. It’s not impossible that it would happen – but it’s so improbable that it’s not likely to happen even once in hundreds of trillions of years. The Third Law of Thermodynamics isn’t about the randomness, it’s about the statistical probability that results from randomness ... but it certainly fits neatly into this idea of “quantum mechanics as applied to a larger system of objects”.

Almost every physical interaction that can be easily described in general terms can get very complex when looking at the extremes. A gas engine for example – the more gas you give an engine, the faster it goes. It’s a linear relationship of more gas equals higher RPM, you just need to find the slope of the line to describe it. However, if you slow it down too much (to the point of where it begins to stall) or you hit the maximum speed that the engine can go (due to the mechanical parts that just can’t move any faster), then you’re in trouble. Precisely defining the exact shape of the gas/RPM curve at either extreme can get difficult.

So if the above statement is true and “all objects obey the laws of quantum mechanics, and classical physics is just an approximation of quantum mechanics as it is applied to a large system of objects” ... then we have to adjust our thinking a little bit:

Instead of saying “All matter obeys the immutable laws of physics, except in the very small quantum sized interactions where it gets more complicated” we would say ...

“The movement of all the matter in the universe can be described by quantum mechanics, but on the ‘normal’ scale (not looking at the quantum extremes), we can use the simplified equations of classical physics which give a good enough approximation as to be considered immutable.”


Ok, I think we have it all figured out now. Unless we finally crack open some credible evidence to support this whole “string theory” idea ... then everything will certainly get much more interesting again!

Categories:   Science
Actions:   E-mail | Permalink | Comments (4) | Comment RSSRSS comment feed

An Overview of the U.S. Patent System

Wednesday, 30 July 2014 13:07 by The Lunatic

(Note: This was a term paper I wrote for an MBA class in 2012. I recently ran across it in my files and thought it would be a good addition to my blog. Enjoy!)

An Overview of the U.S. Patent System
David M. H. Workman


A Patent is a form of legal protection for an invention, allowing the patent holder to have exclusive rights to make, use, or sell the invention for a specific period of time (typically either 14 or 20 years in the U.S., depending on the type of patent).

To secure a patent, a Patent Application is submitted to the U.S. Patent and Trademark Office (USPTO); the application consists of two major elements: a description of the invention, and certain claims (which define the scope of protections desired under the patent application). The USPTO may grant the patent for the invention, but allow or disallow each of the claims individually. “Broad” claims mean that the applicant is asking for the invention to be protected in a wide range of uses, and are more likely to be rejected (and if allowed, are more likely to be challenged by competitors). “Narrow” claims mean that the invention has very focused and well defined commercial applications, which are less likely to be challenged.

For a patent application to be approved, it must meet a certain bar for (1) Novelty, (2) Non-Obviousness, and (3) either Utility, Distinctiveness, or Ornamentality (depending on whether it is a “Utility”, “Plant”, or “Design” patent, respectively). The USPTO reviews the patent application to ensure that the patent, and each of the claims, meets the bar for each criterion.

During the application process, the patent may be rejected if “prior art” (i.e. any published diagrams or descriptions which show that the invention is not original) is found by the USPTO, or if any aspect of the invention was publicly disclosed by the inventor before the filing date. Even after the patent has been granted, others may challenge the validity of the patent (or any of the individual claims) if prior art is presented which is proven to have been publicly available before the application date.

Patents cover an amazingly diverse range of ideas – from describing the optimal radius of the bend in a wire paper clip, to More...

Categories:   Economics | Miscellaneous
Actions:   E-mail | Permalink | Comments (0) | Comment RSSRSS comment feed

I Believe That Belief Is Irrelevant

Tuesday, 15 April 2014 11:44 by The Lunatic

In a previous article titled I’m a believer!, I proposed we should swap the traditional definition of who’s a believer and who isn’t – I suggested that a believer is someone who believes that the laws of physics are immutable and a non-believer is someone who doesn’t.

In this post, I’ll take a little different approach. I’ll go on record and say that what people believe in is irrelevant. I don’t care what you believe in. Heck, I don’t even care about what I believe in myself! Simply having a belief in something does not make it true.

What if I go around the world and convince everyone that the universe is governed by a Grand Orange Duck. And what the Grand Orange Duck really wants is for everyone to donate their ear wax to the famed Diamond Crucible. I know it sounds crazy, but hear me out ... I really believe this is the truth! Once we have ear wax from every person on Earth, and the Diamond Crucible is full to the brim, the Grand Orange Duck will reveal himself to us and we will be allowed to marvel at his magnificent wings. It will be a glorious day indeed!

Even if I can get everyone to believe in the Grand Orange Duck (let’s just call it “GOD” for short), and convince every single person on Earth that they need to contribute some ear wax to the Diamond Crucible, that still doesn’t make it the truth.

Is this scenario really that far-fetched? How about this: The Mormons are very good at getting people to believe that there were white people on Earth before black people (Mormon scripture says that Cain, who killed his brother Abel, was so evil that God "cursed" him with black skin), and that More...

The Lunatic’s take on Daylight Savings Time

Sunday, 4 November 2012 04:24 by The Lunatic

Twice a year, once in the spring and once in the fall, we move our clocks either forwards or backwards to accommodate the change in Daylight Savings Time.

And twice a year, there are the requisite news articles written about Daylight Savings Time, explaining to everyone why we go through all this hassle. Then there are the cutesy and often misguided Facebook posts with statements like: “only the government would believe that you could cut a foot off the top of a blanket, sew it to the bottom, and have a longer blanket.” (which is what prompted me to write this particular article in the first place!)

So let’s get to the bottom of what Daylight Savings really is. First of all, however, we have to understand what midnight is. That’s right: midnight, the time that we’ve decided each day should start.

Technically, midnight is the time that is halfway between sunset and sunrise. It’s simple enough, but that definition needs some clarification. As the Earth revolves around the Sun, the Earth’s tilt causes daylight hours to shift with the seasons.

A better definition is that midnight is the time that is halfway between sunset and sunrise, at the equator, on either the fall or spring equinox (the only two days of the year when the sun is directly overhead at the equator).

Now we’re getting somewhere, but there’s one more wrinkle in this definition.

You see, the Earth is just over 24,000 miles around and More...

Raising Kids To Be Good Eaters

Thursday, 3 May 2012 20:00 by The Lunatic

When my kids were born, in 1999 and 2000, I decided to conduct some scientific experiments on them.

Oh, don’t worry, it wasn’t anything too gruesome; all their limbs and internal organs are still intact. I just wanted to put some personal child-rearing philosophies to the test and see if I could turn them into healthy and conscientious eaters without any odd phobias or irrational dislikes of certain foods.

Fundamentally, I believe that kids’ eating habits are mostly formed between the ages of two and five, and having a pro-active methodology to respond to the typical food related tantrums that every kid goes through would help get through those critical years and make them better eaters.

Primarily, my belief was that all kids naturally go through short cycles of not wanting to eat certain foods, not liking certain flavors or spices, and that many times (not always) this is due to external influences – not being hungry, tummy upsets, a particular mood, or just being enamored with something that tasted good last week and not wanting anything else. One of the key ideas is that these usually are “short” cycles of likes and dislikes, but having an inappropriate response can extend the cycles or even artificially create a lifelong dislike of one certain food.

What I wanted to avoid was the typical parental response of coming to the conclusion that “my kids don’t like ... xxx”, when “xxx” really isn’t the problem.

When parents come to the conclusion that “my kid doesn’t like xxx”, they usually stop giving their child that particular food and let everyone know at school and at play dates that their kid won’t eat it – or they make a big deal about it at home and try to forcefully cajole their kid to eat the food in question. Both responses perpetuates the cycle and just makes it worse. Furthermore, I truly believe that it gives positive reinforcement and the child realizes that they get extra attention when they don’t like something.

So I would never say “My kids don’t like xxx”.  In fact, in their entire lives, they have never heard me say that to anyone. Instead, I would say “My kids eat everything, but I didn’t cook the xxx right the last time. I’ll make it better next time.”

The next time I’d make the offending dish, I’d change it a little bit and do something different.  I’d ask More...

I'm A Believer!

Friday, 27 April 2012 02:39 by The Lunatic

There is a pervasive and somewhat lopsided tendency in our society to separate fellow humans into the categories of being either “believers” or “non-believers”. The not-so-subtle implication is usually that there is something wrong with you if you are a “non-believer”.

Let’s play a little game; I’ll take the position that there really is something wrong with non-believers. But first, let’s swap the traditional idea of who is a believer and who is a non-believer.

For example, if I have a ball in my hand and I hold my arm straight out from my body and I drop the ball, I believe that the ball will always fall “down” – towards the ground. In our game, non-believers are the people who will say that god can make the ball go up, or sideways, or turn into a flying cheeseburger and flap its wings at the moon.

If we get all the non-believers on Earth to PRAY really hard, and ask god to make the ball go “up” when I let go of it, I still believe it will go down.

If you ask a believer why the ball will go down instead of up, the typical explanation you will get is that “gravity is a force that attracts two objects proportional to their mass”. In general, the answers that believers give you will have something to do with gravity, and the answers will be relatively consistent on average. Without some external physical force (a blast of air, or someone swatting it with a tennis racket for example), believers will say that the ball will drop “down” even if you conduct the experiment hundreds of billions of times, as long as the Earth and the ball have mass.

However, if you ask all the non-believers why praying to god doesn’t ever change the fact that the ball goes down when dropped, you will get a bunch of different, inconsistent, and largely contradictory answers.

One of the answers you might get is that ‘god doesn’t work that way’. I love that answer, I hear it all the time. I keep asking all the non-believers how god does work, and no one really seems to know. The fallback response, however, is this: “you have to have faith.”

Ok, I’ll accept that. I am a person of absolute unwavering faith, and I will gladly put the full conviction More...

Categories:   Religion | Science | Social Issues
Actions:   E-mail | Permalink | Comments (12) | Comment RSSRSS comment feed

Black-Scholes’ Dirty Little Secret

Tuesday, 6 September 2011 01:35 by The Lunatic

Back in 1973, two mathematicians named Fischer Black and Myron Scholes wrote a paper entitled "The Pricing of Options and Corporate Liabilities".  This became known as the “Black-Scholes option pricing model”, which earned them a coveted Nobel Prize in economics in 1997 (technically, Myron Scholes shared the prize with Robert Merton, another collaborator, since Fischer Black had passed away by that time).

The Black-Scholes option model serves as the benchmark for setting the price of a common stock option. All you need to know is the stock price, the strike price of the option, the time left to expiration, the current interest rate, and this tricky little thing called the volatility of the stock.

Ahhh, the volatility. There’s the rub. The volatility of a stock is calculated using an iterative process called a “cumulative normalized distribution function”. Basically, it looks at the variations of a stock’s up and down movement over a certain time period and offers up a percentage of the average movement. The volatility is an absolute measurement, which is different from a stock’s “beta” – the beta is a ratio of that particular stocks’ volatility as compared to the rest of the market, which is actually much easier to measure.

In my definition of volatility, I said that it relies on the variation of a stock price over a certain period of time. But what period of time should you use? One week? A month? Three months? Six months? A year? Maybe two years? The time period that you use can make a huge difference in the value of the option, but there’s no general recommendation for what period to use.

All of the other factors (stock price, strike price, time to expiration, etc.) are quantifiable values that can be specifically defined. The volatility, however, requires a bit of artistic interpretation.  If the stock was highly volatile nine months ago, but is more stable now, then measuring the historic volatility over the last six months is probably a good choice. Or not. More...

Categories:   Economics
Actions:   E-mail | Permalink | Comments (0) | Comment RSSRSS comment feed

An Apology to Mother Gaia

Tuesday, 12 July 2011 07:42 by The Lunatic

For the past billion years or so, every animal on Planet Earth has been in danger of being eaten by some other animal at one time or another.

Humans aren’t immune from the risk, of course; just because we’re at the top of the food chain doesn’t mean we wouldn’t be a tasty treat to something else. A hiker was eaten by a bear in Yellowstone park just last week, and a few times a year we hear about sharks that feed on an unlucky swimmer.

So I get a little perturbed by folks who tell me I shouldn’t eat meat because it’s unethical, or because we’re “exploiting” animals for our personal gain. Frankly, if every animal on the planet stopped eating other animals, all species would die out. The “Circle of Life” would come to a complete halt.

Someone asked me if I’m a vegetarian and I said, “No, but I mostly eat vegetarian animals!”

Granted, in our modern society, homo sapiens (especially the ones living on the North American continent) should cut back on meat consumption. But from a health standpoint, completely eliminating meat from our diet is going too far in the other direction.  We are omnivores and always have been, and we require a balanced diet. Unfortunately, some people balance their diet about as well as they balance their checkbooks and they end up overweight AND broke!

Even though I’m certainly not a vegetarian, I do have many issues with our “factory farmed” meat production. Not just because it might be considered “cruel” to animals, but because we are getting increasingly isolated from our food supply.  In the past 100 years, we’ve become the very first humans in history where the majority of the population doesn’t know where our food comes from, or how it’s grown and processed. As long as the grocery store is fully stocked and the local restaurant can serve a hot dinner plate in a timely fashion, we’re happy.  We don’t want to think about where it comes from – and if we watch a video of a butcher at work, it’s considered “gross” for some reason. Why is that?  For thousands of years, More...

Americans and their Guns

Wednesday, 8 June 2011 06:20 by The Lunatic

I’m really tired of seeing these news stories, pretty much every single week lately, about some kid (usually under age ten) who gets their hands on a gun and accidentally shoots themselves, a parent, sibling, or their best friend.

It’s not so much that I’m against guns; but I’m certainly against the American attitude towards guns.

Everyone is so concerned about their “right” to own a gun. But with rights come responsibility. The question shouldn’t be “do I have the right to own a gun?” – the question we should ask is “am I willing to bear the responsibility of owning a gun?”

Pro-gun advocates often invoke references to Switzerland as a country where gun ownership is high and crime is low. I lived in Switzerland for a year and just recently moved back to the USA. In Switzerland, every adult male must serve in the armed forces for at least two years, and those that have received combat training are considered “reservists” – and as such, they are required by law to keep their military issued service arms at home in case of an attack by a foreign country.

The difference is the Swiss attitude towards the firearms. Gun ownership is for the protection of the country; it’s not for personal protection, not an item that is brought out and shown off to all your friends, not something that is brought along to the bank or grocery store, not something that you can buy and sell at a flea market or local shop, and certainly not something that is left lying around for kids to pick up and play with. It is not a “right” to own a gun in Switzerland, it is a responsibility, which they take very seriously.

The Second Amendment to the US constitution states:

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

I know the issue has been bashed to death by the courts, and everyone has very strong opinions on More...

Categories:   Politics | Social Issues
Actions:   E-mail | Permalink | Comments (12) | Comment RSSRSS comment feed

Government Debt and Rising Interest Rates – A Dangerous Combination

Tuesday, 17 May 2011 00:41 by The Lunatic

Everyone knows that our national debt is completely out of control. But there’s an important issue that the press seems to be ignoring: the potentially devastating effect of rising interest rates.

The Federal Reserve is responsible for implementing our fiscal policy, but the Fed can not “set” interest rates – the overall market does that, based on supply and demand.  However, the Fed can influence rates by increasing or restricting money supply.  At the moment, just like in Louisiana and Mississippi, the floodgates are wide open. The bond market is awash in “virtually free” money, which is artificially keeping interest rates at historic lows.

But here’s the crux of the issue: with the floodgates open, the reservoir will eventually run dry – and the expectation is that interest rates will then rise. What happens to our federal budget when rates go up?  It could get really ugly really quickly.

Here’s why:

If you look at the chart in my earlier post, Trying to Make Sense of the Federal Budget, (the second chart, with the Social Security and Medicare numbers removed), you will see that interest payments on the federal debt clocked in at $218 billion in 2010, or 11% of our federal budget:


The weighted average interest rate of all the US debt currently runs about 2.07%.  Shorter term debt has a lower interest rate – less than .25% – and longer term debt has a higher interest rate – approaching 4.375%. When longer term debt is more expensive than short term debt, we have what is referred to as More...