Critical Thinking

I recently came across something in a community college textbook that I found interesting. About three whole pages of this textbook was devoted to giving guidelines for intelligently reading articles of academic interest. I suppose I shouldn't be too surprised, since this is a very important skill to have for those of us in academic fields. However, I don't think there was anything included that any intelligent person shouldn't be able to figure out for himself. Here's roughly what it said:

When analyzing the claims that anyone is making, keep the following in mind:

1. Is the writer/speaker an expert in the subject on which he/she is talking about? If not, is there any reason you should trust what this person is saying? (I may be pretty picky, but when it comes to academic matters, an "expert" is someone with an advanced degree in the particular field- at least.)

2. Do the claims disagree with accepted knowledge or are outrageous for other reasons? Such claims are not necessarily false, but there has to be a reason that years of academic pursuit suggest otherwise. (This, usually along with #1, is a primary reason that you can immediately ignore crackpot theorists who make claims like "Quantum Mechanics is obviously wrong" without explaining why quantum mechanics predicts the result of every low-energy experiment ever performed.)

3. Does the writer/speaker provide evidence to support his/her claims? Does the evidence supplied hold up to the same scrutiny? (In academic papers, evidence is shown through the results of individual research, or through citing papers written by other researchers. Seriously- this should be the biggest no-brainer in this list.)

4. Could the writer/speaker have ulterior motives? There are many reasons that a person could make a certain claim, and the pursuit of truth is only one of them. The others include money, social status, political capital, embarrassment, and countless others. Don't be naive.

5. Does the argument contain logical fallacies? Here's a sample of a few:

• Circular logic
• Correlation implies causation
• Sweeping generalizations
• Bandwagon
• Arguing from ignorance
• Appeals to authority
• Slippery slope

6. Does the claim seem too simple, given the complexity of the subject matter? If someone offers a one-sentence solution to an age-old problem, that usually means that the person ignored a few factors that contributed to the problem in the first place.

To be honest, I still don't see why this needs to be outlined in a textbook. After all, in the sciences, these are rules that researchers live or die by. These are things you pick up out of necessity. You either learn to apply them or are subject to ridicule by your peers.

But when it comes to our roles in mainstream society, there's no reason not to apply these skills to the best of our ability. Take politics, for example:

Do you think Sarah Palin is an expert in health care? What qualifications does she have to decide on issues that affect Americans, besides that time that she ruined McCain's chances of getting elected? How about Glenn Beck? What kind of pedigree is required to make up stuff on TV these days? Unless Glenn Beck is really Dr. Glenn Beck, Phd., it sounds like these two fail the critical thinking check number 1.

Saying that Obama wants to put your grandma to death is a pretty outlandish claim. So are claims that compare proposed health care reform to nazi eugenics. That's check number 2. Upon two failed checks, any sane person should be looking for number 3. Give me a quote from one of the bills (with a page number), and maybe I'll listen. Otherwise, I'd rather spend my time reading up on time cube or flat earth theory. At least those sets of meaningless blabber are moderately entertaining and don't influence the well-being of 47 million people.

Before I get down from my soapbox, I'd like to mention that I really wish I could find better examples from across the aisle. As much as I hate to say it, this isn't a problem with the Republican party, but more just politics in general.

Our political system is one in which "facts" are routinely carefully selected, spun, misinterpreted, or completely fabricated just to back up one's point of view. There isn't a politician alive who doesn't have ulterior motives. They will say whatever they can, just to improve the status of their party, or get a boost in their next campaign. That sounds an awful lot like check number four.

Here's something you can do- read up on the most common logical fallacies, and try to spot them next time you're watching cable news or a debate. Some are so prevalent, that they are named after political phrases that are used when they are committed (like "slippery slope"). Maybe a harder task is to spot an argument that doesn't contain a logical fallacy.

As for check number six, I think you'll agree with me that overgeneralization is not only common in politics, but is an accepted political strategy. For example, taking a thousand-page bill and calling it a "government take-over of health care" is certainly an overgeneralization.

None of these behaviors would be tolerated in any academic field. You wouldn't even tolerate it among your coworkers. Heck, you'd probably scold your kids for some of the same behaviors that are commonplace over on capital hill. And these are the people who are running the country. Go figure.

What's the most frustrating is the fact that this isn't just a big accident. These sorts of deceitful behaviors are nothing but politics-by-design.

Eh. Fuck it.

Bored?

Here's something fun to do:

Browse the Flat Earth Society Forums and try to figure out which posters are actually serious. In my opinion, some of them must be serious, or else no one would have the energy to maintain that website. On the other hand, I can't believe that they can all believe that the earth is flat. I mean, some of those statements just defy too much reason for someone to actually believe in it. Then again, you just may be surprised.

By the way- I said to browse. Don't bother posting. If you think you have a chance at beating some of these people in a debate, you are quite mistaken. This isn't to say that they have good arguments or really a semblance of coherent thought. There are two specific reasons why you can't beat them in a debate, and here they are:

1. They don't listen to reason. Seriously. How else can you interpret their explanation for those NASA pictures that clearly show an Earth that is circular from all sides? Their answer- a conspiracy. Not only are the governments and scientific communities from all space-able nations involved, but so are satellite TV and GPS companies as well (they actually transmit signals via blimps and radio towers, since satellites are impossible). Those pictures taken from outer space are computer generated- 'cause everyone knows they had photoshop back in the '60s.

Some even claim that there are guards stationed along the ice sheet at the edge of the world to make sure people don't try to go over the edge. Somewhere along the way, you've got to realize that there's something not quite right in the brain with these people here.

2. They can always make up new rules to explain the discrepancies you point out.

Example- why can't you see over the horizon? Answer: Because light follows a curved path while on Earth.

Why does the sun set? Answer: Because the sun (and moon, which gives off its own light) are like spotlights- not isotropic light sources. They only shine on certain parts of the world at a time as they follow circular paths exactly 3000 miles above the surface of the Earth.

How do you explain the phases of the moon? Answer: There is another heavenly body, unknown to mainstream science, which is completely black and at times likes to obscure our view of the moon.

How do you explain gravity on Earth? Answer: There is no gravity on Earth. Instead, a "Dark Energy" continuously accelerates the Earth upward at 9.8 m/s^2. By the way, they do cede that other bodies in space have gravity, thus explaining the existence of tides (but not the fact that there are two tides a day!). As for why other bodies have gravity but not the Earth? Because the Earth is SPECIAL!

Why do distances in the southern hemisphere seem closer than what is suggested by Flat Earth geography? Answer: Remember how the GPS companies are involved in the conspiracy? GPS software intentionally sends planes in paths that make distances in the northern hemisphere seem longer than they really are.

If you come up with something else that's not right with Flat Earth theory, they'll just come up with some other new assumption that would explain the observation. If they can't come up with an explanation, they'll just give the "your a sheep who's been brainwashed by the mainstream scientific conspiracy COME ON PEOPLE WHY DON'T YOU OPEN YOUR EYES!!!" argument.

These two pieces of idiot behavior are a constant among all crackpot pseudo-scientific theories, including null science, autodynamics, intelligent design, and countless others.

I've also observed it among most ardent followers of every religious and political area of thought. Just an observation...

I said most, so don't anyone get mad at me.

Advertising

--Here's a classic:

"Did you know that 9 out of 10 people need a new mattress?"

Really? What do they sleep on? Two-by-fours? Piles of hay? I didn't think the economy had gotten that bad!

Seriously- what's the criteria for needing a new mattress? I'm pretty sure I do, but that's just because I'm moving to a new apartment. Are 90% of Americans currently relocating? Did their homes just get repossessed?

--"Drivers who switched from Geico to Allstate saved an average of $473."

You think maybe the fact that they saved money had anything to do with the fact that they switched? How many people who switched actually lost money? I have a hunch that number is close to zero, meaning the people who wouldn't have saved weren't included in the sample size. The add may as well say, "Drivers who switched from Geico to Allstate and saved at least $400 saved an average of $473!"

--"Getting the right coverage isn't just about the car, it's about who's in the back seat."

Apparently, car insurance can prevent your kids from getting hurt in a car accident. It's like magic! Oh, wait. No. They just cut you a check and then raise your premiums. Sorry. You'll have to find a witch doctor or something.

--I'm a little tired of fast food commercials where fast food chains try to tell you why their fast food is better than other fast food.

Going to a fast food chain usually isn't one of the best moments of my life. Those moments aren't exactly a good time for brand loyalty. I can't imagine how bad your life has to be in order for you to be particular about your fast food. I just know that the decision of which chain to visit is usually dependent on which one is closest. Then comes the self-hate.

--Around in this area there is a college that airs commercials called 4-D College. First of all, I don't know anything about this college apart from what's on the commercials. Despite this fact, it may very well be a good place to study, but I'm not convinced. So, what does 4-D stand for? No, it's not the average report card of their top students. 4-D stands for the following:

1: Determination
2: Desire
3: Drive
4: Deliver

What? Now, I'm not sure where they make the rules for these mnemonic-driven bullet-point list things, but I'm pretty sure you're not allowed to start it with three nouns and end it with a verb. Plus, the first three are close enough to synonyms to discount the whole list in the first place. Once again, this college may very well be perfectly sufficient in preparing its students for the workplace, but if the commercial is indicative of the education you'll get there...

What I'm just saying is it's usually a good idea to put your best foot forward. And hopefully you've got a good one to show.

Heisenberg Uncertainty

One of the things that just about everyone knows about quantum mechanics is that it is a theory that only predicts probabilities. In other words, even if you know everything about a particle there is to know, you still may not be able to say where it is. The only thing quantum mechanics can tell you is the probability of detecting the particle in any given location. This fact does not have a famous name, but is often referred to as the indeterminacy of quantum mechanics. What it is not called, however, is the Heisenberg uncertainty principle. I've heard everyone from John Stewart to cult-recruitment movies get this little bit of terminology wrong. This post is about what the Heisenberg uncertainty principle actually is.

The Heisenberg uncertainty principle is something much more specific, and much more interesting. It is a piece of the weirdness of quantum mechanics all wrapped up in simple mathematics. In case you are wondering why I never mentioned it in the definition of quantum mechanics that I wrote in the previous post, the answer is that I didn't have to. The Heisenberg uncertainty principle can be derived explicitly from what was written there. Thus, any evidence that violates this principle in turn violates all of quantum mechanics. Luckily (or unluckily), no one has ever found any such evidence (despite the efforts of many, with none other than Albert Einstein at the head).

So what does the Heisenberg uncertainty principle say?

Well, in quantum mechanics, there are many observable quantities, like position, momentum, angular momentum, energy, etc. The Heisenberg uncertainty principle states that certain pairs of observable quantities are incompatible, which means that it is impossible to know both quantities of a particular particle simultaneously to a certain level of certainty. There are many such incompatible pairs, the most famous of which is position and momentum. Other pairs include time and energy, and orthogonal components of angular momentum. The position-momentum uncertainty principle is mathematically represented like this:

The left side of the inequality is the product of the standard deviations of the position and momentum distributions, while the right hand side is a constant. This constant is so small, that it does not affect the observations that we make here in the macroscopic world.

Heisenberg showed evidence for this principle by asking what would happen if one were to try and measure either of these quantities. For example, imagine you have a particle inside a box, and you wish to measure its precise location.

So, to find the location of the particle, you might open a window and shine a light inside, and then study the light that is scattered off of the particle. In this way, you can know where the particle was at the instant you shined the light on it to arbitrary accuracy. However, the light you shine on the particle, by scattering off of it, can impart a wide range of possible momentum into it. As a matter of fact, if you would like to decrease the uncertainty behind your position measurement, you would have to use light of shorter wavelength, which has higher momentum and would produce a wider spread in the particle's resulting momentum distribution (by the way, to those of you who are familiar with the collapse of the wave function, this is one illustration of how it could actually happen- no sentient beings necessarily involved).

Measurements that would determine the momentum of a particle would similarly produce spreads in the position distribution in very real and concrete ways.

However, some would say that this argument is not entirely satisfactory, since it only shows how the position and momentum of a particle cannot both be known to arbitrary certainty. The Copenhagen interpretation insists that these values cannot even exist simultaneously. To even guess at the values would be in violation of the laws of physics.

In other words, a particle with perfectly defined position has momentum in all magnitudes simultaneously. A particle with perfectly defined momentum exists in all places in the universe.

However, another way to look at things might make this principle seem completely ordinary. In quantum theory, all particles are described by wave functions, not points. A particle's position is described by the position distribution of its wave function. The particle's momentum is described by the frequency distribution of the wave function.

Therefore, a particle with perfectly-defined position has a wave function that is a single spike- in mathematical terms, a Dirac delta function. A delta function has a frequency distribution that stretches to infinity in both directions, meaning that the momentum would have no definition at all.

On the other side, a particle with perfectly defined momentum would have a wave function that is an infinitely long sine wave. This function gives a spike in the frequency distribution, but extends to both sides of infinity in position-space.

This argument makes perfect mathematical sense (at least if you've taken a course in Fourier analysis). However, it is only valid if you assume that the wave function describes the entire state of the particle. Hidden variable theories claim that there is another piece to the puzzle- therefore, to prove the existence of a hidden variable, one would just have to show a situation with Heisenberg uncertainty violation. (Once again, Einstein himself tried and failed. Do you think you've got a shot?)

So, for those of you who are not yet entirely clear on this whole thing, lets look at what I think is the simplest example- spin states.

So, as you may know, certain particles like electrons and protons are called spin-1/2 particles. You may have heard that these particles have two spin states, commonly called spin-up and spin-down. Well, this picture omits a few details, so let's start over.

So, spin is a vector quantity that describes the innate angular momentum of certain particles. The fact that it is a vector quantity means that it has three components which we'll call the x-, y-, and z- components. What's special about spin is that for any particle, the magnitude of this vector is a constant, though each of the components is not.

Another interesting thing about spin is the fact that for spin-1/2 particles, there are exactly two stationary states corresponding to each spin component. So, for the z-component of spin, there are two stationary states, commonly called spin-up and spin-down. Likewise, looking at the x-component of spin, there are two different stationary states, which we'll agree to call spin-right and spin-left- for sake of the argument I'll present in a minute.

Now here's where things get interesting. It turns out that the three components of spin are incompatible in the Heisenberg sense. Therefore, if you know that an electron is in a spin-up state, the x- and y- components necessarily are undefined.

Imagine that you're on a plane, and you ask the flight attendant which direction you happen to be flying. She says, "We're headed in the eastern direction. As to whether we're headed north-east or south-east is undefined".

Bewildered, you ask the flight attendant if she could go to the cockpit and confer with the pilot whether they are headed north or south. The flight attendant returns, and says, "We're headed north, but now we don't know if we're headed north-east or north-west".

Now, let's imagine we're in a physics lab with an electron in a box. We measure the z-component of spin of this electron (let's not worry about how), and measure it to be in the spin-up state. Heisenberg comes by and says, "Now that the z-component is defined, the x-component is undefined and therefore has no value".

You say, "Poppycock! The x-component must be defined, or none of this makes sense! Why can't I just measure the x-component and find its value?"

So, you do the measurement along the x-axis, and now find that it is in the spin-right state.

You grin and exclaim, "Heisenberg, you're a fraud! This electron is spin-up and spin-right, thereby invalidating your uncertainty principle!"

Heisenberg responds, "Well, the particle was spin-up until you measured the spin along the x-axis. Now that the x-component is defined, the z-component is no longer. By making the second measurement, you caused the wave-function to collapse, thereby invalidating the first measurement."

You say, "Well, I never understood the wave-function collapse thing anyway. You'll have to provide another argument."

"Well, why don't you just measure the z-component once again?"

At this point two things could happen:

1: There is a 50% chance that you measure the particle to be spin-up again, in which case, you grin at Heisenberg until he convinces you to flip the coin again by measuring the x-component once more.

2: There is a 50% chance that the particle will now be spin-down. Now there's egg all over your face, since it is clear that the particle ceased to be spin-up as soon as you measured it to be spin-right. Otherwise, subsequent measurements of the z-component would always reveal it to be spin-up.

There's still one little caveat in this Heisenberg uncertainty business. That is, we still haven't really established what the cause of all this observation is. On the one hand, it could be an innate property of the particles involved. A particle known to be in a specific location just doesn't have a well-defined momentum. On the other hand, it could be a product of the effects of measurement. Strange mathematical coincidences regarding wave-function collapse make it impossible for the momentum to be known, but it may nevertheless exist. These two interpretations happen to be represented by two sides of the old quantum mechanics debate. On the one side is Niels Bohr with the Copenhagen interpretation- on the other, Albert Einstein and the hidden variables approach. Maybe I'll write more on that if this little girl in my lap will let me.

Maybe.

Quantum Mechanics

Quantum Mechanics is one of the most popular yet misunderstood physics topics out there. There are many myths around quantum mechanics that I run into from time to time, and I thought I'd devote some posts to the topic.

Perhaps the biggest myth surrounding quantum mechanics is the idea that it doesn't make sense. This idea is absurd. Quantum mechanics describes how our world works- if it doesn't make sense, then you just don't understand it. Or at least you haven't thought about it in the right way.

Quantum mechanics is baffling yet incredibly simple. You can literally write down all of quantum mechanics on a half-sheet of paper. As a matter of fact, here it is:

- The state of a system is entirely represented by its wave function, which is a unit vector of any number of dimensions (including infinite) existing in Hilbert space. The wave function can be calculated from the Schrodinger equation:

- Observable quantities (like position, momentum) are represented by Hermitian Operators, which function as linear transformations that operate on the wave function.
- The expectation value (in a statistical sense) of an observable quantity is the inner product of the wave function with the wave function after being operated on by the observable's hermitian operator.
- Determinate States, or states of a system that correspond to a constant observed value, are eigenstates of the observable's hermitian operator, while the observed value is the eigenvalue. (ex. energy levels that give rise to discrete atomic spectra are eigenvalues corresponding to energy determinate states.)
- All determinate states are orthogonal and all possible states can be expressed as a linear combination of determinate states.
- When a measurement is made, the probability of getting a certain value is the square root of the inner product of that value's determinate state with the wave function.
- Upon measurement, the wave function "collapses", becoming the determinate state corresponding to the value that was measured.

So how bad was that?

Okay, so this is probably confusing to those of you who haven't had a class in quantum mechanics or an advanced course in linear algebra. Getting passed the math, it really isn't that hard conceptually. The important thing to note, though, is the fact that it can be defined so concisely. I think I've actually included more than necessary, so it probably can be even more concise than what I've written. Quantum mechanics is pretty complex in application, but is simple at its core. All of the best theories have this quality.

I'll probably post some stuff later that will (hopefully) clear up some of the details.

Another myth I run into is around the term "Quantum Physicist". There isn't such thing- at least in the professional sense. The reason why is the fact that there isn't a physicist in the world who doesn't use quantum mechanics. If the term "Quantum Physicist" represents a scientist who uses quantum mechanics in his/her research, we can probably just agree to just use the term "Physicist". Likewise, it is impossible to go to college and major in "Quantum Physics". Any respectable university would require its physics majors to learn quantum mechanics, so there is no reason to create a new major around it. I'm saying this in reference to the nerdy characters in movies and TV shows who are described using these terms. If you know anyone who writes screenplays, let them know.

I was going to get into some of the misunderstandings around actual quantum mechanics, but maybe I'll get into it later. Most of these misunderstandings involve the indeterminacy of the statistical interpretation, the Heisenberg uncertainty principle, and the collapse of the wave function. I'll try to get to all these issues later. For now, I'm hungry.

Cartoons

My eight year old brother-in-law's 'Spongebob Squarepants' watching has made me nostalgic for old cartoons of my childhood. If only I could find a single episode of 'loony tunes' on TV somewhere.

But now that 'loony tunes' is off the tube, there are some questions that I find myself asking- like "where are kids these days going to get the introduction to classical music that I had?" 'Loony Tunes' was how kids of my generation got to hear great pieces like Tchaikovsky's "Romeo and Juliet" and Wagner's "Ride of the Valkyrie". Of course, I learned them under the titles "Shot-by-Cupid's-arrow Theme" and "Kill the Wabbit", but I learned them nonetheless. When I just got started listening to classical music, it was nice to hear something familiar. Kids these days don't even recognize these pieces.

Of course, 'loony tunes' is considered by today's standards to be too 'violent'. But to put things in perspective, lets look at a cartoon that is readily watched by kids on TV today called Pokemon.

So, the basic idea behind Pokemon is that a bunch of kids go romping through the woods in search of certain creatures. When they find a creature they want, they beat it up, and trap it inside a tiny ball- where it will stay night and day for just about the remainder of its life. In fact, the only time these creatures are allowed to come out is when they are forced to battle each other for the praise of their owners.

Wow. That sounds like an activity that Micheal Vick would find enjoyable. I'm surprised PETA isn't more involved.

Okay, so maybe my point isn't that clear, but here's what I think: Let's not get into a tizzy fit over what kids watch on TV. Seeing some cartoonish violence isn't nearly as harmful as the effects of being ignored and inactive for long periods of time. Give them attention and something to do with their time, and your kids'll be just fine.

'Fatherhood'

The next time you know someone who just had his first baby and you want to ask a question like, "so how does it feel to be a father?"- just wait a little while. Wait until after the first few sleepless nights and diaper changes. Maybe he'll have a better idea by then.

The answer: "Tired".

Or maybe you want to ask after the moment that the little stinker opens her eyes and seems to take in her surroundings for the first time. She can only see about a foot in front of her, so she'll gaze at your face incessantly before falling asleep/crying for mommy.

I still don't know how to answer the question in that case. Just look at the picture. See what I'm talking about?

There are some things that I have learned within these first few days with my daughter.

People don't grow up just because they grow older. It's the experiences we have and hardships that we endure that make us better people. People have an amazing ability to live up to expectations. Nowhere are these expectations greater than in the eyes of a child who looks to you for all aspects of her livelihood. Generation after generation of us have risen up to the challenge and everyone has benefited as a result. I suppose it's my turn now.