Friday, December 25, 2009

Fermi Christmas (FPOTW)

There is much to read about with respect to Christmas Fermi problems.
Here are some questions to ponder while out and about today.

  • If all the wrapping paper used to wrap Christmas gifts were compressed to a ball with the average density of cardboard, how big would ball be? How much would the ball weigh?
  • How many miles of scotch tape are used to wrap all the presents?
  • How many Christmas trees are killed each year? If burned for energy, how many houses could this heat for a day?
  • Estimate how many collective years are spent listening to Christmas music in the last 30 days? The last week? Just today? (Is there a distribution?)
  •  How many times are the words "Have a merry Christmas!" used over the last 30 days? Week? Just today?
  • How much food is consumed Christmas day as compared to an average day?
  • How many calories are expended Christmas day as compared to an average day?
  • Give a rough estimate on how many gifts are given, and how many are returned, and how much gas is burned returning all those gifts to the store?
Enjoy the time you spend with family!

Wednesday, December 23, 2009

I see dumb people #5 More "Homeopathetic" nonsense.

It seems that homeopathy proponents really like to make fools of themselves.
For your viewing pleasure, and to practice your critical thinking skills, I present:

THE MECHANISM: How Homeopathy Works

Note that the ratings for this you-tube video have been disabled. Humm... I wonder why?

Did you think these homeopathetic idiots would just stand by and take all the scathing attacks by skeptics and people who actually have a scientific understanding of the world? No.
Here is a rebuttal.

A PhD! Wow! That convinces me that homeopathetic proponents may just have something...

For me to poop on!

I keed, I keed!

Friday, December 18, 2009

A randy(i) skeptic

James Randi, a well known and well respected skeptic, recently stated his opinion on the global warming debate.
He really stepped in it.

And by "stepped in it" I do not mean he screwed up, or did something wrong. He simply stepped in the steaming pile of crap the whole pro global warming and the global warming deniers have left for all of us to wade through.

Many supposed "skeptics" attacked Randi on their blogs, or in comment sections of Randy's blog. They berated him for not being an "expert" in global warming. They blasted him for using his "status and influence" to support the global warming denialists. Some crowed about how Randi's chemotherapy was destroying his critical thinking because he dared question the "reality" that global warming is caused by humans.
Others seemed to trumpet on how even a skeptic can screw up.

A couple of days later Randi posted this clarification, reiterating what he said in his prior post about not being an expert, but that he is applying some skeptical critique to the subject.

"You should keep your mouth shut unless you are an expert in global warming" shouted some people.
"Leave the science to the scientists Randi, lets listen to what the climatologists have to say about the matter rather than the general scientists signing a petition." cry others.

You know what I find most interesting while reading about the whole global warming debate and Randi's addition to the subject? The way so called skeptics seem to attack Randi for stating his opinion. It seems that many of these "skeptics" equate being skeptical with being right.

Well, I have some news for those "skeptics", and a list of what being skeptical means. A bulleted list at that!

  • Skepticism does NOT mean being correct.
  • Skepticism is asking questions, and looking for evidence rather than blindly accepting what one is told.
  • Skepticism will not always lead one directly to the right answer to any question, be it scientific, moral, political or what not.
  • Skepticism does not constrain one to stating an opinion only if one is right.
  • Skepticism allows one to change their mind in the face of evidence, not in the face of browbeating, political pressure or snarky comments and ridicule.
  • Skepticism is not being afraid to ask stupid questions, and not being afraid to seem stupid to others while asking them.
  • Skepticism about a topic does not require you to be an expert in that topic. 
  • Skepticism does not require a "science degree"
  • Skepticism is not denialism.

I think many "skeptics" would do well by understanding these realities.

Thursday, December 17, 2009

Entropy and making my bed.

I am not a neat freak.
I am not dirty per-se, I do not wallow in filth, but I am very disorganized and like to leave clutter around for my wife to trip over.

I also hate making my bed.

No, this is not my bed, nor are these my cats. (I do like cat's tho...)

I have always hated making my bed. Something about spending a few min in the morning flipping, folding and tucking just seemed wrong somehow. I mean, all that will happen later in the evening is I will mess it up again.
Of course, I cannot stand sleeping under a totally ruined set of blankets, but it takes far less effort and time to straighten those out after a few days of use. 
When my mother would tell me to make the bed however, telling her no because it will just get messed up never worked.

Then I encountered physics!

I learned about the second law of thermodynamics, or the universal law of entropy, and thought I had a well justified excuse for never making my bed. I was saving the universe!

A property of entropy is that in a system, a process that occurs will increase the entropy of the universe.

What is entropy? Well, simply put it can be thought of as a measure of disorder of a system.
Some of the properties of entropy are:
The entropy of the universe will always increase (or stay the same at best) even if in a local system the entropy can decrease.
Heat is considered to be directly related to entropy, as a value of its entropy.
Entropy is thought to set the direction of times arrow.

For instance, consider a child who has very carefully set up a toy solder army in a very specific and organized manner, with neat little rows of solders according to color, height, rank etc.

 In doing so, the child has decrease the "disorder", or entropy of the system of toy soldiers, but has also expended energy in making the arrangement. This expended energy is not 100 percent efficient at reducing the entropy of the system of toy soldiers, and some was wasted as heat. This heat increases the entropy of the child's surroundings, and consequently increases the entropy of the entire universe.

It even gets worse. Over a period of time, even if the child were to leave the soldiers alone, the state of disorder of the toy soldiers would naturally increase by itself. Dust, microbes, changes in temperature, quantum effects of decay, statistical impingement by cosmic rays would all serve to erode the plastic and over time the system becomes more disordered.

All these processes contribute to the increase in entropy of the universe!

Say a cat (I do like cats tho..) walks  by and dashes the toy soldiers into a wrecked battlefield of scattered plastic. Not only did the cat directly increase the disorder (entropy) of the system, but in doing so wasted some of its energy as heat, which increases the universes entropy. 

You can't win... or more precisely, the universe cannot win. 

Why is increasing the entropy of the universe a bad thing? 

As the entropy of a system increases, the ability to draw energy from it to do work decreases. The thermodynamic free energy decreases.

The ability of a process to draw energy from somewhere, or to use thermodynamic free energy allows for the process to decrease entropy locally (at the expense of the universe). This work can be used to create stars, planets, babies, snow flakes, and all the wonders of the universe.
However, if the entropy of the universe reaches a maximum, it will evolve toward a state known as the Heat Death

This means there is no thermodynamic free energy, and therefore no way to continue creating new stars, new life or new snowflakes. And this is a major bummer.

Every act you do sends the universe closer to heat death. Every act of creating and kindness, of hatred and havoc increases the disorder of the universe. Nothing can be done to stop this, but why not spend that energy, and waste some heat doing good? Create, be kind!

So, to extend the time till the heat death of the universe by just a little bit, I claim that I should put the energy of making my bed to better use!
I am saving the universe! (Take that you environmentalists you!)

My wife is not buying this...

Saturday, December 12, 2009


I need to vent. There is a little bit of physics in this post, but this is more about how arguments start.

I always like to talk about using critical thinking as a way make decisions or draw conclusions without being ruled by one's emotions. I try and paint a picture of dispassionate analysis, and clear logical thinking.
In the real world emotions can run high, cloud ones judgment, and can lead one to draw erroneous conclusions even if one is very good at critical thinking.
It is really hard to think critically during an argument.

Here is an example of how discussions can degenerate to arguments between two well educated critical thinkers.

The other day I was working with some colleagues on taking temperature measurements of an object. The object was made from stainless steel and delrin, and we had an RTD temperature sensor mounted in a small air gap in side the object.
Our plan was to immerse a small area of the metal part of the object in ice water, and measure the time it took to equilibrate to the ice water, then remove the object to air and measure the time it took to equilibrate back to room temperature.

One of my friends said that the two equilibration times would be nearly the same, and that we would not be able to measure the difference within experimental limits of our measurement system, and that at most the difference would be a couple of seconds.

I was pretty darned sure that the difference would easily measurable. The moment he said that the difference would be two seconds, I was wary.
Our RTD sensor is pretty accurate, and has a good response rate. But due to some limitations of the sensor suite we can only sample the temperature every two seconds.
Lets assume that the time it takes for a tennis ball sized hunk of stainless steel partly immersed in ice water and attached to a solid plastic pipe to equilibrate in a few minutes. Lets say 5 min, even though that would probably be an understatement.
If the difference in equilibration times are indeed 2 seconds, that represents 0.7% difference. That would indicate that there would be a very small difference in the thermal conductivity of air and water. Plus a .7% difference just smelled very very wrong to me.

All this went through my head, and I decided to argue the point, and with a smirk/grimace I tactlessly blurt out: "I don't agree, I think there will a signifigant difference it in the two times."

My friends eyebrows rise and he responds:  "Really, why's that?"

"Because the thermal conductivity of water is huge compared to that of air." I respond smugly.

I was saying this with a bit of a smug attitude. It is common in physics culture to act a bit cocky and smug and self assured when arguing theory or such with your colleagues. It is commonly done, but it is not taken very personally, and in the end one is always ready to change their opinions in the face of evidence.
This may not be true in chemistry culture, but one data point cannot let me be certain.

My friend shakes his head and replies: "Don't assume I am stupid, I know that it will take longer to equilibrate in air than water, all I am saying is that it will not be measurable with our system. And anyway, the heat capacity of air is huge, and greater than water."

I again smirk: "Actually, water has a greater heat capacity than air. But that does not matter, because at my old job when I did similar experiments we saw large differences, greater than 20% in some cases, and..."

"I don't care what you did at you old job!" He interrupts. "That was a different experiment, and not the same situation!"

Now I was getting pissed, and I retort:
 "Of course it is not the exact same experiment, but from experience and extrapolation the differences will be large!"

"Prove it!" He demands.

Now, know that heating and cooling of bodies is a very non-trivial problem. It is difficult to develop exact models in arbitrary shapes, and even in simple models such as spheres there are difficulties such as volume to surface area ratios, turbulent flow of convection.
Our system was made of various odd shaped materials, so the situation was difficult.

Knowing this, I tried to argue from authority and "common sense".

"I don't have to prove anything. It is common sense that it will take longer to come back to room temperature in air than it took to cool down." I say heatedly.

At this point my other friends interjects: "Hey guys, umm... let's just agree to disagree... OK?"

I round on the poor guy and say: "That is such a cop-out to say that."  (I really do think that, but the reasons are for another blog)

"Look, say I drop a ball here from this height and measure its acceleration. Then I move it two feet over to that part of the floor and do it again... the two values will be nearly the same! Then if I were to tell you that if I moved it to a third spot that the value would again be the same, you would not tell me to prove it. My experience and ability to extrapolate and predict would..."

"What..." he interrupts again: "Are you telling me that there is no difference in the gravity from that point to that other point?"

"Yes... " I start to reply

"Aha!" He triumphantly shouts, "Gravity is not the same, because the Earth is round and there are other masses around..."

"Don't tell me about gravity!" I yell back, "I did thesis work on the topic! Science is predictive, not just something done to verify every freaking propisition! Science can help us avoid testing every case by allowing us to extrapolate and predict from theories we create from observation..."

At this point the argument went way down hill.
He kept insisting that my prior experience was useless in this case, since I had not done "exactly" the same thing.
I kept inisting that my experince was good enough that I could predict the value of the difference. In the end he kept going back to "prove it" and "lets do the experiment".

And truthfully, he had a point. We were arguing about something that could be settled by simple experiment.
He was pissed off at my smugness, and I was pissed that he would not accept my conclusions based on my experience.

I really dislike having my opinion questioned. I know, I should be able to defend my position, and accept questioning with grace. But sometimes I don't want to always be defending what I say. I feel that the time and effort I have spent educating myself should confer a bit of acceptance of my ideas among my peers.
I always say not to blindly acept what someone says. But questining every little thing is pointless and a waste of time.
If I asked a native speaker of Tagalog to teach me the word for water, and then argued with him and ask him "How do you know that is the word for water", I am certain the teacher would give up in disgust.
And this is how I feel when someone questions my about my experience or expertise.
I knew I was right, as both theory and experience coulded with the predictive powers of science were on my side. And probably I could have convinced him if I did not cop to the attitude I had. (Or perhaps not.)

The argument ended with I asserting that the effect would be 20%-25% while he asserting there would be no measurable difference.

At the end of the experiment, the time it took the object to heat back up to room temperature was 30% greater than it took to cool to ice water.

After showing him the data, all I got was a grunt and a shaking of the head. All that arguing for nothing it seems.

So, I was close to right. But, how I approached the discussion was wrong.

Neither of us used much critical thinking. Both of us were talking past each other. My friend could just as easily been in the right, but our tempers did not allow us to discuss the problem rationally and constructively.

It was a case of "I had to be right" for both of us.

What a useless and fucking stressful waste of time.

What I need to take from this is that in future situations like this, I need to chill, and not always have to prove I am right.

Friday, December 11, 2009

Mountain of Meat! (FPOTW)

I must say, I like cows.

Braised, roasted, grilled... you name it.
While eating a nice steak this evening, a friend and I were discussing how nice it was of the vegetarians to leave more meat for us, and that we should come up with a nice Fermi problem to show our appreciation. The basic theme is the number of cattle slaughtered to fill our collective stomachs.

---- Start Fermi Problem ---

How much beef is consumed in the United States each day?

How much in the world each day?

How many cows have to be slaughtered to provide this much beef, for the US and the world respectively?

If you stuffed all the cows in a big cube, what would the dimensions be for the amount slaughtered in the US and the world respectively?

How long until there would be a "mountains" worth of cows slaughtered?

How many cattle are slaughtered each second for the US and the world?

From these numbers can you estimate how many slaughter houses there are?

---- End Fermi Problem ----

Where is the beef?

Friday, December 4, 2009

Liquid Sugar (FPOTW)

A friend and I were walking around the mall waiting for the movie theater to open. We were lamenting how much the tickets would cost, and formulating plans to smuggle food into the theater. Why in the hell should we spend more on the snacks than on the tickets? Like a flash out of the blue a Fermi problem presented itself to help us while away the time:

---- Start Fermi Problem ----

How much soda pop do Americans drink each day?

If you could put all that soda into a cubic container, what would the containers dimensions be?

How much sugar energy is represented?

How long would that energy power an average home?

---- End Fermi Problem ----

As is usual for a Fermi problem, we are only concerned with accuracy of an order of magnitude.
You can look up certain numbers such as kilo calories per gram of sugar if you don't know it, but in a Fermi problem one should use common sense and reasonable guesses rather than looking up numbers. And since most of you do not carry a calculator around everywhere, you should be facile with numbers.

Sunday, November 29, 2009

Fat of the Land (FPOTW)

Ugg... I am stuffed! All that turkey, all that food. =(   =)

I was reading an article in CNN about the percentage of overweight and
obese people in the good old USA. The pundits and experts agree that 65%
of Americans are overweight, and 30% are obese.

---- Start Fermi Problem ----

If you were to liposuction the excess fat off of Americans, estimate how much you would get.

If you could burn the fat for energy, for how long could you power an average home?

---- End Fermi Problem ----

The radical Muslims could now say: "Kill all Americans, and burn them for electricity!"

Sunday, November 22, 2009

I see dumb people #3. Sinister LHC

I have to wonder what makes seemingly normal, semi intelligent people believe stupid things and fear what they do not understand?
For instance, there is a blog I have recently read who's followers believe that the scientists at the Large Hadron Collider at CERN are up to no good, that they are up to something "sinister".
These outwardly normal seeming people truly believe that the LHC could end humanity as we know it.
Some of them believe that the physicists are doing this on purpose, that they want to destroy the world they live on. Other readers believe that the physicists are doing this because they don't know what they are doing.

This is just a projection. The readers do not understand the physics and science invololved, and so project their inadiquacies on the scientists at the LHC.
As for those who think the physicists are doing sinister things, I have to wonder what projection that represents.
But in general, these people simply fear what they do not understand. They seem no better than hooting primates (oh... wait... am I insulting primates?) faced with fire. They scream and hurtle feces.

However, fear is natural. It is hardwired into our physiology. For instance there is something I fear, and I admittidaly do not understand it very well, and that is stupidity. Oh yes, I understand that there are those who through brain damage or natural selection are simply stupid. But I am speaking of "stupidity" in the form of willful ignorance. Willful ignorance is where a person, even after being show massive amounts of evidence actively chooses to ignore said evidence. A side effect of willful ignorance is that those who chose to be "stupid" often want to spread their stupidity to others.
This form of stupidity can lead to injury to me or my loved ones. Stupidity can lead to death and destruction on many scales. Stupidity is something to be feared.

These people scare me. They are the types who hold back medical progress. They are the ones who enforce their ignorance on others by legislating bans on teaching evolution. These are the type of people who kill people to protect animals, or threaten the families of those who do animal based medical research.
These are the type of people who burned Giordano Bruno at the stake.
These are the type of people who, not content to live their lives as they want to, instead want to spread their fear and ignorance to others, and want to force others to live in the same intellectually decrepit state as they.

Yes, when I see such willful ignorance, I get a small thrill of fear.
Perhaps I should be more scared?

Friday, November 20, 2009

The Days, Months and Years of Our Lives (FPOTW)

Small moments... that is what our life is comprised of. 

We all see the reports of how much time the average person sits in front of a television, or how much of our lives are spent sleeping, or driving to work. But the most mundane and trivial aspects of our existence pile up to large numbers.
How much time do you spend on the toilet? How about brushing your teeth? Picking your nose?
Here are a few ponderables to while away some of the time left over in your life. After considering these, spend some time coming up with some of your own.

---- Start Fermi Problem ----

How much time does one spend picking their nose?

How much time is spent brushing ones hair.

Brushing teeth?




What is the total percentage of your life that your eyes are closed?

Sitting on the crapper?

Doing Fermi problems?

---- End Fermi Problem ----

Damn... my nose itches...

Sunday, November 15, 2009

The 10 weirdest physics facts bull$hit

Seems to me a way of mindlessly parroting what thousands before you think is cool and trendy. Heaven forbid you actually pause and think for a second about what you read.

Take the latest #physics re-tweets about an article called The 10 weirdest physics facts, from relativity to quantum mechanics.

My god... for the last week this has been re-tweeted numerous times. Don't any of these people actually read the comments to this article pointing out the obvious factual errors? Do they even stop for a millisecond and perform a sanity check?

OK people, here is a small tutorial on how to think critically about such an article.

1. Approach everything you read with a modicum of skepticism.

Any article that states weirdest physics facts causes my bullshit meter to twitch. "Facts" is a term most physicists like to avoid writing down, even if they secretly believe in those facts. All facts are open to the possibility of being disproved. Just design an experiment to test the "fact".

2. Check the authors credentials.

When I read in the opening paragraph the following, my bullshit meter starts to really twitch:

"The humanities-graduate writer of this piece would like to stress that this is his work, so any glaring factual errors he has included are his own as well. If you spot any, feel free to point them out in the comment box below"

A humanities graduate writer is writing a piece on physics? Humm... it is a pretty good bet they don't know enough to write cogently about the subject, but that is ok, they are simply going to write an article for mass consumption to promote science as cool and interesting.  Thanks for the help Mr. Humanities-graduate writer.

And don't give me any crap about Einstein being a patent clerk etc etc. Crackpots use this argument in support of their bullshit physics assertions. Einstein had the training and the credentials. For every Ramanujan out there, who literally came from nowhere (but still had the training) there are a million others who put in vast time and effort to learn the subject. Don't pander to the exceptions. 99% of the time it is safe to be very skeptical of anything a humanities-graduate writer will write about physics.

WTF? Are we, the readers supposed to correct the writers misconceptions? Whatever happened to checking your facts before posting? The writer is making the assertion, and in science it is up to the asserting person to make his case.

3. Perform a Sanity Check on one of the topics.

Lets make this easy, and lets look at the very first one:

If the Sun were made of bananas, it would be just as hot
"The Sun is hot, as the more astute of you will have noticed. It is hot because its enormous weight – about a billion billion billion tons – creates vast gravity, putting its core under colossal pressure. Just as a bicycle pump gets warm when you pump it, the pressure increases the temperature. Enormous pressure leads to enormous temperature."

Wow, where to start? Oh yeah, how about starting where he states that the sun is hot because of its enormous weight.

It is very easy to calculate the amount of energy the sun produces. This number was pretty well determined over a hundred years ago. This number is about 4E26 J/s.

We can trivially calculate the gravitational energy of our "banana sun" by assuming that the sun was assembled via self gravitation of bananas falling toward a central point from a very large distance.
The potential energy of a sun's mass of bananas falling from infinity to the radius of the sun is: gives us some facts about the sun:

M ~ 2E30 kg
R ~ 7E8 m

G ~ 7E-11 m^3/(kg s^2)

E_G ~ 4E41 J

Therefore the gravitational energy of the bananas can produce the energy radiated by the sun for a total of 31  million years. Considering that the sun has been shining for about 5 billion years so far, we can see that the authors statement is the monkey digested remains of all those bananas.

The sun is powered by nuclear fusion. The banana's are made of the intergalactic vomit spewed by a dying star, in other words what the star could not consume. Chances are a banana sun would not last comparatively as long.

4. Don't waste your time.

At this point we have direct empirical evidence that the article will be bullshit. If the very first entry on the 10 "facts" is trivially disproved, then you have better things to do than waste any more time with the article. Go crack a book on physics. There are literally thousands of good texts or even popular accounts out there. Hell, even Scientific American is better than some random article on a internet news site.

And please stop re-tweeting this bullshit.

Friday, November 13, 2009

Balloon Boy and the Spherical Cow (FPOTW)

Sorry, no balloon boy here, at least in the popular media sense... sorry.
Rather than my usual Fermi problem, today I would like to present a physics thought experiment.

Real life physics is not a textbook exercise. This is because reality rarely gives you all the variables. It is up to you, as a scientist, a physicist and as a critical thinker to determine what is germane to the solution of a real life problem.

A common joke among physicists is as follows:

One day a physicist was asked by a friend of his, a dairy farmer, to help design a better milking machine for her business. The physicist readily agreed, and asked for a couple of days to think about it, after which he would present his results and design to his friend.
Sure enough, a couple of days later the physicist come over to the farm with his laptop and a beautiful power-point presentation titled: "Explorations towards a better milking machine."

After setting up the projector and gathering his notes, the physicist presents his findings:

"After much though and calculation, I have come up with a workable solution to the cow milking problem. First, let us assume that the cow is a sphere of radius r, homogeneously filled with milk..."


Although the following problem is not meant to be solved exactly, it can be explored to any depth you wish, by any method you choose! You can solve a simple rule of thumb Fermi type problem, and have plenty left to explore by adding an udder to a spherical cow. ;)

The situation is thus:

A helium balloon as shown above is at neutral buoyancy a distance above the ground. Attached a given distance below the basket is a bucket. In the basket is an identical bucket filled to the brim with b-b's. In the bottom of the basket is a hole.
At time t=0 the b-b's are poured through the hole at a given rate, where they fall straight down and into the bucket hung below.

Describe the subsequent motion of the balloon.

That's it.

Ask yourself if the color of the spots on the "spherical cow" have an effect on the solution?
Have fun!

Wednesday, November 11, 2009

I see dumb people #2. Cell phone danger!

Come on people... simple physics indicates that cell phone radiation cannot ionize a molecule and is not a source of ionizing radiation.

"The jury is out" is bullshit, considering that science is not done by jury, or its validity in a court of law.
Dr. Ronald Herberman is now appealing to our genetic tendency to want to protect children in his latest warnings on the dangers of the "harmful electromagnetic radiation from cell phones".

But of course, you should read the article for yourself, and apply some critical thinking skills.

Friday, November 6, 2009

Power to the People (FPOTW)

Incandescent light bulbs are very inefficient. Use a google search engine to find out just how inefficient.
Compact florescent bulbs are much more efficient in the percentage of watts producing visible light.
This information is also on google. "how to use google" is a good place to start. =)

---- Start Fermi Problem ----

Estimate how many incandescent 100 Watt light bulbs there are in the United States.

Estimate how much power is used to power the light bulbs.

Estimate how much power is saved by switching all the light bulbs to equivalent lumen compact florescent.

Assume that the old light bulbs are thrown away. How much landfill space is taken up if the bulbs are not broken?

How about if the bulbs are broken?

What is the mass of the broken bulbs?

Some Physics: What is the weight of the broken bulbs compared to the weight of the unbroken bulbs? Remember, I said "weight" here.

---- End Fermi Problem ----

Estimate how many Poles it takes to screw in all those light bulbs. (old POLEitically incorrect ethnic joke here)

Tuesday, November 3, 2009

Project Tuva, Feynman Lectures online!

On nearly every physicists bookshelf you will find three particular books. These books may be in hard cover, or they may be in soft cover. Sometimes they are published with an additional book in order to sell the set to a new generation of physicists. This set of books are collectively known as the red books, the physics bible, or The Books.

They are The Feynman Lectures on Physics.

It is not all that uncommon to hear students quote from the Feynman Lectures in biblical fashon, quoting book and verse:

"Oh, you want to know how I did that least action problem? Check out Feynman, Book 2, 19-5."

Students use the red books to study for qualifiers, or for their GRE's (and perhaps that is a mistake).
Other physicists make a once a decade pilgrimage to spend a significant portion of their free time reviewing the red books cover to cover.

Why this devotion? Because the Feynman Lectures on Physics is perhaps one of the greatest collection of books on general physics that exists!

The classes the lectures were based on were by all accounts a nightmare for most of the regularly admitted students. The courses were an experiment, and a work in progress. However, the classroom where the lectures were given was always full, as in standing room only. Most of those in the class were grad students or other professors auditing the lectures. You see, the lectures are best appreciated after one has already made it through the gauntlet of an undergraduate physics curricula. The books are not good for learning physics for the first time, but are wonderful to come back to and font of wonderful insight and nuggets of wisdom.

Ahh the internet! What a wonderful resource! The generation before widespread use of the web were lucky indeed if they ever had a chance to view a Feynman lecture. It was a special treat when someone would bring a reel to reel or a VHS of a Feynman lecture. I heard tales from my teachers of the beer parties where someone would produce a beat up and well played VHS or Beta of a Feynman Lecture.

Now days, it is rather easy to "bittorrent" a copy of almost all of Feynman's works, be it written or in Audio or Video.
The ease of getting these gems on the net in no way detracts from their power. Feynman had a powerful way of presenting ideas, and in presenting physics. Perhaps only Carl Sagan rivaled Feynman in clarity and insight. But Feynman was first, and as much as I like Sagan, in my opinion was the better at "explaining things."

Bill Gates recently announced his Project Tuva. He rhapsodizes on his goal of bringing science and physics to the masses by making Feynman's Messenger Lectures freely available to the masses.

These lectures have long been available through sharing sites, or torrents, but it is nice to be able to view a legit copy, with captions!

I highly recommend everyone to watch these lectures. They explain the place of science and physics in the world. Feynman goes into detail on what science cannot explain, and what it excels at explaining. And how scientists think about problems.
They are a template for critical thinking. They are scientific literacy embodied.


Some Google Fu will tell you why the website is named Project Tuva. For a more interesting explanation, read Surely you're joking Mr. Feynman.

Sunday, November 1, 2009

I see dumb people # 1. The physics of Homeopathy

Sometimes I come across (or someone sends me) an example of stupidity so mind-shattering,  I am left speechless.

For your enjoyment I present to you the Physics of Homeopathy.

Saturday, October 31, 2009

Microwaved Nuts (FPOTW)

Critical thinking skills.
Sadly, such skills are not taught in class or in school.
There was a time when the ability to think critically would help ensure survival. Now, medical advances keep dumbasses alive long enough to procreate.
Critical thinking has gone out the window.

Cell phone radiation! I know several people who will absolutely not carry their cell phone in their pockets for fear of irradiating their nuts.
"I want to have children some day!" they cry.
Some people are dumb enough to drop a small fortune on an air acoustic headset for their cell phone, so that the microwaves do not travel up the headset wire and irradiate their brains.
Humm... balls or brains... quite the tossup on what to nuke.

A few simple numbers for consideration:

Average maximal cell phone power is about a Watt.

Cell phones transmit at a frequency of about 800-900 MHz. Call it an even GHz.

To cause a chemical reaction, a couple of eV are needed. To ionize a molecule, a few eV are needed.

The average human body produces about 100W of power.

---- Fermi Problem ----

Estimate how much you will raise the temperature of your left nut (if you don't have one, substitute your right ovary) if you were to dump a Watt of energy into it over a period of an hour.

Calculate the energy of the incident microwaves in terms of electron volts.

Estimate how many people think that microwaves are only good for cooking their food.

---- End Fermi Problem ----

Of course, high tension power lines are another matter... I mean just look at the grass under them! The grass is taller under the wires than away from the wires. If you don't believe me, just ask the row of birds sitting on the wires.

Tuesday, October 27, 2009

Critical Think Link #1

Below are some links I came across that are good practice for critical thinking skills.
Some of them hit emotional buttons.

Does Economics violate the laws of physics? (Is this the new global warming?)

Dark Energy rips cosmos and agencies. (Anti-Science types love to pick on dark matter)

Iraq Veterans wife faces deportation. (Sometimes immigration laws are total bullshit.)

French court convicts Church of Scientology of Fraud. (Score one for the side of critical thinking!)

Gang rape (What the fuck is wrong with people? I am with Penn & Tell on most topics, but this story scores a point for capital punishment.)

Sunday, October 25, 2009

Games with Wolfram Alpha

Last week Wolfram Research, the makers of Mathematica and more recently Wolfram Alpha, had their first annual Wolfram Alpha Homework Day.
Having nothing better to do that day but suffer from the effects of the H1N1 flu, I tuned in and watched the festivities.
The whole point of the day was to encourage students to send in their homework problems online, and the wizards at Wolfram would show you how to use Wolfram Alpha (W|A) to find the answer.
Actually, the whole point of the day was to advertise W|A out the wazoo, but I digress on the obvious. =)

The event lasted 14 hours, and had a live video feed of interviews with people like Brian Greene and Lawrence Krauss discussing the roll of computable knowledge in education, pitching W|A and the like, and a painful interview with Richard Dreyfuss.

Also featured were various educators singing the praises of Wolfram Alpha and Mathematica in their classes.

Throughout this whole presentation I was constantly feeling like many the teachers and students intervewied were pushing for a rather shallow understanding of the subjects they were teaching, or learning.
For instance, rather than letting a student come up with further questions after W|A gave them their answers, W|A would do that sort of chain of thought thinking for the student.
And example would be after a student calculates a volume of an object, W|A then goes on to compare that volume to a bunch of other objects. I myself would like the student to be thinking to herself: "Humm... how does this compare to say, a baseball?" and then go looking for or calculating the answer themselves.

I think that tools like W|A, if misused, can atrophy the already poor critical thinking skills of many students, and put them in a mindset that answers should be given to them rather than sought out or figured out on their own.

However, when used correctly W|A is an exceedingly powerful tool, and fun as heck to use! Just like I am apt get caught up in a wiki hunt, where each link takes me to something new and fun to learn, I can get caught up in the same sort of thing with W|A.

To this end, I would like to explore last Friday's Fermi Problem of the Week: The Great Flood
I will introduce a neat little trick to add to your toolbox, go over three of the questions using basic back of the envelope calculations and also show how W|A can be used to rapidly come up with and explore answers to back of the envelope calculations.

----- Start Playing! -------

I will not give away the answer to the first part of the question, which is asking how much the oceans will rise if the polar ice caps melt.
Instead, we will go over another question:

Estimate how much water is needed to cover the Earth such that the highest mountain was under water.

To calculate this answer as a back of the envelope, you need to know the following:

Radius of Earth

Height of the tallest mountain.

The radius of the Earth can be found with some Google-Fu. As you may realize, the Earth is not a sphere, but because of its spin angular momentum is an oblate spheroid with a polar radius of approximately 6356.8 km, an equatorial radius of 6378.1 km, and a mean radius of 6371.0 km.

Since this is a Fermi problem, we will assume the Earth is a sphere of mean radius r = 6371 km.

The tallest mountain is Mt. Everest and is h 8848 m tall (above sea level, which we take as Earth mean radius)

What we would like to do is compute the volume of a spherical shell of inner radius r, and outer radius (r + h), which will give us the volume of water (not including the oceans) that will cover the Earth to a depth of the highest mountain. 
Of course, this volume will be different than the actual volume, due to other mountain ranges and the like, but we are estimating to order of magnitude.

One may calculate this volume by subtracting the volume of the Earth from the volume of the water covered Earth as:

And then we would be done, and by plugging in the numbers we would obtain a volume of water of:

Vss = 4.52034*10^9 km^3

However, at this point I would like to introduce you to a common trick that physicists like to use when dealing with small changes, such as in the term (r + h)^3.
This trick involves simplifying the Vss equation to a more tractable form for computation.
One may wonder why we would care to do so, when in this day and age of Mathematica we can simply plug and chug? The answer in terms of a Fermi problem solution is that making calculations of this type as simple as possible is a great thing to do, as it saves writing, and the chance of making errors.

In a general sense, a physicist is always interested in how the model behaves at extreme values, such as the very small, the very large, very slow and very fast. Being able to know what terms affect the solution in various regimes is an important skill do develop. Knowing how to deal with infinitesimal changes is one of those skills.

Cute Trick Digression, AKA the binomial series

First we note that h << r. In some cases, if we were to simply approximate the volume of the sphere of radius (r + h) we could neglect the h term, and be done. But in this case doing so would yield a spherical shell volume of zero.
To solve this problem we manipulate the sphere radius equation as follows:

Here we notice that h/r << 1. Again we could neglect the h/r term, but we will use the binomial series, which states:

where n is an integer.

In our example we will take the binomial series to order 1 and we obtain:

Plugging this into our spherical shell equation and simplifying gives us:

Plugging in the numbers:

Vssa = 4.51407*10^9 km^3

Note that this is much simpler to compute with than the first version, and indeed for our problem the answer differs from the "exact" solution by a bit over 0.1%

At this point we can see how the rest of the problem goes. We can calculate the rain fall over 40 days and 40 nights, we can assume the earth is 75% covered by water to a depth of on average 2 km and calculate the volume of water already in the oceans. Indeed it would be a good exercise to do so, as it will work your problem solving muscles.
However, after all this is done it will be interesting to see how we can solve this problem using W|A.

Wolfram Alpha Solution

Lets answer the question above using W|A.

First, the site to go to, if you have not already found it, is:

The current incarnation of the site as of 10-25-09 looks like the following:

Lets try a simple search term: "Volume of earth"

Lo and behold we get the volume of the Earth with the assumption of a perfect sphere. Note the radius is the same we used.
What is cool to note is that there are many conversions to different units

Lets try: "height of mt everest"

This is pretty cool! We not only get the height of mount Everest, but also some other possibly useful results such as air pressure, temperature etc.

Lets go for the money shot here and calculate the volume of water needed to cover the earth to a depth of the height of Mt. Everest.

Note the answer is in cubic feet, which for some reason W|A decided to use. That is ok because one can click on the answer and open a separate query and convert to other units. The answer given by W|A to our question is the same order of magnitude as our result, because it decided to use different radius for the various calculations. So while W|A allows you to, with a few queries, "solve" this problem, the student may not realize that different radii were used in the calculation.
This can most likely be fixed by a person who is very facile with W|A, but the average student would not get a consistent result.

The upshot of this post in my opinion is that one should go to pen and paper first, then afterwards you can explore using W|A. At some point you will develop to the point where you can go to W|A first, and be able to understand the limitations of the search queries you use.

Friday, October 23, 2009

The Great Flood (FPOTW)

Recall the opening moments of the movie Water World, with Keven Costner?

At the beginning is shown a graphic of the Earth with continents and the poles while some guy whines about mankind unleashing a great flood by melting the poles and flooding the lands. Hold on... wasn't that God's fault? He (She... it... what... existence proof not needed) already did that once already, right?
I digress...
Anyhow, the graphic shows that all the land disappears under water and humanity is forced to live on the world spanning ocean, tattooing maps on kids backs and drinking their own urine rather than filtering the sea water.

Now, in the Bible, God flooded the Earth cause he was pissed or something, and gave warning to Noah to build an ark and save his critters. (I guess God can flood the Earth, but can't be bothered to save the critters herself)
It rained for 40 days and 40 nights and covered the highest mountain to a depth of 2 fathoms. Wow, this sounds a bit like the depth of the supposed water world.

Fermi problem time!

---- Start Fermi Problem ----

Estimate the change in the level of the oceans if the poles were to melt. (Watch out here, there is a standard trick question involved... think of melting ice cubes)

Estimate how much water is needed to cover the Earth such that the highest mountain was under water.

Compare this volume of water to that of the current volume of the seas.

If it rained for 40 days and 40 nights, how much water per square meter per second would have to rain down?

---- End Fermi Problem ----

God, of course, can do anything... including violating common sense.
What is Hollywood's excuse?

Monday, October 19, 2009

Balloon Boy, what have you cost us? (And who should pay?)

Balloon Boy... what have you cost us? Who should pay?

I was going to post this as a Fermi problem, but decided to have fun myself.
The first question is, considering only the Thursday afternoon media frenzy, how much money in lost work did the whole balloon boy fiasco cost?

For nearly 2 hours on Thursday, October 15th 2009, "millions" of viewers across the world sat "transfixed" in front of their televisions and computer screens following the "harrowing" plight of poor little Falcon Heene. At least, according to the news.
However, it turns out that there were a significant number of people watching the TV and surfing the next on the balloon boy story who should have been working. I heard accounts by friends and family of their co-workers watching the news raptly.
So lets start:

Lets assume only the people in the US as our sample. If we assume that only 1 in 3000 Americans watching during work, and an average pay of $10/hr for a period of two hours that comes out to be 2 million dollars in direct wage costs lost to the balloon boy frenzy.
Adding 30% overhead costs in benefits and such for each employee, and that comes out to 2.6 million in direct.
Now add to the cost to other people who may be held up from completing their projects and have to sit twiddling their thumbs or working on other less pressing projects. Lets say equivalent of 10% of the number of people watching, so add another 260 thousand dollars.

So, rounding up we can estimate at least 3 million dollars were directly lost because of the balloon boy fiasco! Take ~10% of that in taxes, and the government will sure be pissed!

That is just for those two hours during the whole "harrowing" ordeal.
How can we start on the hours spent online by people reading the news for the latest information of balloon boy, reading and writing blogs over the last 5 days?

Oh my.

Who should pay for this mess?

Here are some candidates:

Richard Heene:
They guy has already paid in getting the short end of the stick genetically. Jail time for him will suffice. And blood from a turnip after all.

The Media:
Hands down this is who should pay. They were the fear mongering exploitative people who made this hoax into a much bigger deal than it needed to be. Hello, and average cable tv show costs 3-5 million an episode to produce. I doubt too many people will miss an episode wife swap. Hey, the producers of wife swap should pay as well.

Of course, that is my opinion! ;)

Saturday, October 17, 2009

Falcon Heene, Balloon Boy

I have got to learn to keep a pen handy with me at all times.

There are many times where I need to do a quick calculation, usually at a restaurant for some reason, and when I ask the server to borrow a pen they give me a wary look and act like I am going to steal their prized pen. Heaven help me if I ask for a piece of paper!

Thursday afternoon I was coming back home after a doctors appointment, and being hungry I decided to stop at one of my favorite restaurants, Pho 78 in Westminster near my home. I walk in,place my usual takeout order of Pho Tai, Chin, Nam, Gan and Sach (special characters omitted) with a yummy mango boba, and sit down to wait.

At this point I notice that everybody in the place is staring raptly at the wide screen TV mounted to the wall, on which an image of a silvery, flying saucer looking Mylar balloon is tumbling and spinning.
Captioned below is the usual "breaking news" and I saw that the event was taking place in Colorado. I assume this is a local news story, and curious, I start paying attention to the voice over:
"The boy may have fallen from the balloon... mumble mumble"

"Huh?" I eloquently think to myself.

I turn and ask an older woman sitting at the next table what is going on, and she responds: "What, you haven't heard?  There is a little boy trapped in that balloon! Poor boy has been in there for hours and hours and must be scared to death!"

First thing I think to myself is "Shit! Poor kid... I hope he does not hit any power lines!"

Over the next 5 min I hear a constant babble about how old the kid is, how long he has been trapped, perhaps that he fell, and other sometimes contradictory statements. All this time I become more and more skeptical. Something was bothering me.

First, the balloon was acting very strange as it was tumbling, it looked like it had way to little inertia to have a 60 lb 6yo kid inside. Second, the balloon looked a bit too flimsy and small to hold the weight of the child.
Finally the news anchor gave the dimensions of the balloon, at which time I turned and asked the person behind the counter if I could borrow a pen.

I was scrutinized closely, and was handed a pen that was 10 inches long, an inch thick, and had a flower glued to the end.

Oh brother.

I grabbed a paper takeout menu and began a quick and dirty estimation of the lifting capacity of a helium filled balloon.

------- Calculation section ---------

Density of air in Colorado ~ 1 kg/m^3

Density of Helium ~ 0.2 kg/m^3

So lifting capacity of Helium in Colorado is about 0.8 kg/m^3

The weight of a 6yo boy I estimated to be about 60 lb, and the weight of the Mylar and frame to be about 10 lb to be conservative. So a total weight of about 70 lb, or 32 kg.

~~~~ Short digression

At this time my pen ran out of ink. When I asked for another one the person behind the counter said: "What you do that pen? No more pen!"
I saw another one behind the counter top and after a while spent asking for it, she capitulated and loaned me the other pen, and I got back to work.

~~~~ End Short digression

Therefore the volume of the balloon needed to lift 32 kg was 40 m^3.

Next I assumed the balloon could be modeled as a disk of volume  V=\pi r^{2} h
Of course this assumption is not perfectly valid, as the balloon was not a perfect disk, and there was considerable uncertainty to the exact dimensions. Also, I did not consider leakage rate, or air resistance, or temperature rate with altitude etc. Assuming a disk is the best case scenario, and would over-estimate the volume, and was good enough for a quick and dirty

According to the news, the balloon was 20 feet in diameter, and 5 feet high. Turning the crank:

V ~ 3*(5 ft)*(10 ft)^2 = 1500 ft^3 ~ 42 m^3

--------- End Calculation ---------

At this point I was done. This was a best case model of the balloon, being conservative on the weight of the child, the balloon frame and materials, and the volume as I knew it at the time. I was pretty darned convinced that the kid never was in the balloon as it could not have take off, and either the whole thing was a hoax, or the kid was scared and hiding for letting his daddy's balloon fly away.

I said as much to the older lady at the next table, and her reply?

"That is not what the news people say!"

Oh well.

At this time my order was ready, and I returned my pen (much to the relief of the owner I am sure) and went home to gorge on pho!

I say people should think over things critically, and they should. But I also can see why this is easier said than done.
People are protective of their young, and are concerned on the safety of other young people.
The media knows this, and knows they can sell papers, or draw viewers to advertisements if they concentrate on taking advantage of this tendency.

You see, even after I had left and gone home, I had been thinking this was a local news story. I do not watch broadcast TV, but instead I watch my shows online. I was tired, and coming down with the flu and went to bed after the pho, and it was not until the next morning on the drive to work that I found out that this had been an international story!

Thus is the power of media, and a prime example of why one should try and think critically of such news stories.
I cringe to think of the hours of productive work that were wasted by people watching this program. (Hey! I feel a Fermi problem coming on!)

Yes, remained concerned, but try not to get caught up in the hysteria pushed by the news. What the "news people say" has a high probability of not being correct.

Friday, October 16, 2009

A Snowballs Chance (FPOTW)

I love snow! There is so much physics involved with snow. You can study thermodynamics, kinetics, optics, fluid dynamics, crystallography, solid state physics and statistical mechanics and still not know enough about snow. Quantum mechanics, chemistry…

There are some quick Fermi problem associated with snow:

--- Start Fermi Problem ---

  • Estimate how much snow falls over the Earth each year.

  • About how many snow flakes is this?

  • How many protons are in this amount of snow?

  • Estimate how much energy it would take to melt all that snow.

  • Estimate how much energy it would take to vaporize all that snow.

  • How many snow men could be made with all that snow?

  • If all that snow was turned into snowballs, and a great world war with snowballs were launched involving the entire planets human population, about how much energy would the people throwing the snowballs expend (neglect throwing each snowball more than once).
  • How long would the war last (assuming the snow does not melt first) ?

--- End Fermi Problem ---

War is hell, so what are the snowball’s chances?

Tuesday, October 13, 2009

Cool as Hell! (Or hot?)

Back in May I came across a wonderful picture of the transit of the Shuttle Atlantis and the HST across the sun, as captured by astrophotographer Thierry Legault.

The little dot you see in quadrant III is the space shuttle and the HST.

I wanted to post a quick little Fermi problem, even though it is not Friday yet:

Determine from the image the rough dimensions of the space shuttle.

Like any good Fermi problem, there seems to be too little information.
And perhaps there is.
So, you are allowed to use your Google-fu to determine how far away the sun is (about 8 light min) or the diameter of the sun. You can also use distance of the moon and recall that its angular diameter in the sky is about that of the sun (that is why we get such nice eclipses).
Perhaps you can look up some basic trig formulas?

There is not "right" way to do a Fermi problem, just way's that make sense.

Saturday, October 10, 2009

Penny Lane (FPOTW)

Copyright © 1955 - 2009 Roger J. Wendell. All Rights Reserved. 

Here in the peoples republic of Boulder, Colorado, there used to be a coffee house called Penny Lane. All the flakes and nuts hung out there to write bad poetry, sing lousy music, play chess and perhaps buy some coffee.
It was a great place!

Note: If you want to practice critical thinking skills, spend some time in a college town coffee shop. ;)

Ahh... Penny Lane the Beatles song, released in 1967. Great song. A nice history of it can be found here:

And, for all the Rolling Stones people who will complain about what band is better... FOAD.

In any event, while driving home the other night I listened to the radio and heard, you guessed it, Penny Lane! Well, I had a flash back to that morning on the way to school when I was listening to the radio, and guess what... Penny Lane was playing then as well!

Humm... I wonder how many times the Beatles version of Penny Lane has been played. Not just over the radio, but on personal CD, tapes, records, 8-tracks, reel to reel, and MP3's. How about on TV and other visual media? How many times was Penny Lane in our ears and in our eyes?

---- Start Fermi Problem ----

Estimate the total number of times Penny Lane has been played since it came out in Feb 1967.

How many minutes of time does this represent?

(Time for some physics)

How much energy was expended as sound to play Penny Lane?

If you were to raise the temperature of a body of water by 1 C using this "Total Penny Lane energy", what volume would this body of water be?

Post your solution in the comments if you wish. =)

---- End Fermi Problem ----

"Penny Lane is in my ears and in my eyes.
A four of fish and finger pies
In summer, meanwhile back..."

Thursday, October 8, 2009

AutoTuning Carl Sagan

I remember as a child watching Cosmos on PBS. The show, written and hosted by Carl Sagan, was one of the very few television shows my parents would let me watch. Cosmos also had the honor of being one of only three TV shows I could always watch if I asked to, a distinction shared with the Muppet Show and 60 min. (Well, on occasion there was MASH)

But Cosmos did not affect me very deeply at the time.

Ultimately however, Carl Sagan was to have a huge impact on the direction my life was to take.

I remember quite clearly the day I was rummaging through the garbage at a swap meet in Tuscon Arizona, and I came across a book. This day was back in 1986, and I was a young teenager living in a converted school bus with my family.
Long past were the days of my aborted formal education, replaced by lessons of life in making a living selling items at swap meets, scrounging for food in dumpsters, and in some cases learning how to swindle people of their cash for some crappy trinket we were selling.

Any education I received that was not directly related to survival I obtained via the books and magazines discarded by others. This day, my prize was a hardbound copy of Carl Sagan's Contact.
The book was missing its dust cover, but was otherwise in great shape... what a find! Carl Sagan, the guy from TV! Knowing that as soon as my parents saw the book, they would force me to give it up to be sold, I hid the book as best as I could under my grubby shirt and smuggled it past their watchful eyes.

Over the next week I stole off every chance I could to read the book. 15 minutes here, 20 there I would wander off to read, and was pulled deeper into the story of Ellie Arroway's discovery and decoding of an alien signal. Her work as a scientist grabbed my imagination. In one scene I was charmed that she made her own jewelry from synthetic ruby she grew for her detectors, something I resolved to do someday. (Mine turned out to be synthetic opal!)  Her explorations of Pi sparked in me a great interest in mathematics, which later I pursued via more discarded books.

Some have said the writing was pedantic, turgid etc. But for me it set the course of my life. I resolved to become a scientist.

One day my parents found the book while I was out getting water for our dishes. They put the book for sale and immediately a customer bought it for $2.00.  I was walking back to the bus carrying two 5 gallon water jugs full of water, and from a distance of over 100 feet I recognized the book as it exchanged hands! The water jugs went crashing to the earth as I dashed towards my parents and the customer.

I went straight up to the customer and forthrightly pleaded for him to return the book. When he hesitated I offered to give back the money plus the $2.50 I had saved and stashed.
My parents were, in their embarrassment, pulling me by the arm to leave the guy alone, but I would not budge. The kind gentleman relinquished the book, saying that one who wanted a book that badly should keep it, and I gave him the refund from my own money.
My battle was only started as I had to beg and plead that my parents let me keep the book, to at least be able to finish it.

The outcome? Well... I still own that very same book, which has a prominent place in my large science fiction collection!

I never had the chance to meet Carl Sagan. He was younger than my Grandmother, whom to me was a picture of health! I thought there would be time. Alas time ran out for Carl, who passed away in 1996.

I cried.

Yesterday I came across this YouTube video where Carl was Auto-Tuned to original music.
Chills went up my spine, and I remembered.

For your enjoyment: