Wednesday, June 16, 2010

Frankenfoods, and the villagers with pitcforks!

I love facebook. It is such a nice platform for people to espouse their views, and to call others to arms for their cause.

Take for instance the following wall post:

Call your Rep and Senators and ask them to support the ban on GMO alfalfa.

What? "Why would I do this?" I ask myself, and I reply as such.

Right away comes the reply:

"Click the link and read why.
...and in general GMOs are not what they're cracked up to be. They do more harm than good."
Ok, that is an opinion, but I see no supporting evidence of the claim that GMO do more harm than good, much less a reason why I should support a ban on GMO alfalfa. Therefore I click the link and came to the following conclusion, which I posted to the wall post thread:

Sounds like the multi-billion $ organic food industry does not want cross contamination of their GMO foods (selective breeding over 10000 years of agriculture is in fact a form of GMO) with direct DNA manipulated crops.

The organic industry could lose billions because they could not claim the label "organic" for the contaminated crops, or the milk from cows fed the crops.

This would be bad for the organic industry, the people they employ, the farmers they support, and the stock holders.... See More
Jobs could be lost, farms could go under (or adapt), and vendors could lose money.

However, there is no credible evidence, empirical or scientific that shows such a modern GMO crop would have detrimental effects on the health of humans. There is little evidence that they "do more harm than good", especially when "harm" and "good" have not been defined in this context.

For instance, I would say it is "good" to be able to more economically feed a larger number of humans.
However, too many humans is an issue we face, which can damage the environment. The mere fact of being able to feed more with less is a good and bad thing, depending on what one views as good or bad, and they are not mutually exclusive.

I would urge people to consider the issue carefully before they sign a petition... any petition. The decision needs to be based on careful consideration of all facts available, and all issues, be they political, economic or scientific (not counting moral) rather than on fear based PR.
I am loath to continue the discussion on facebook, because in the past I have lost the battle with people with these sort of viewpoint. In the past I was vilified and thought to be a "hater of nature" or some such crap.
The other side made no attempt at learning, or critical thinking, and would simply dig in and entrench in their worldview, with friends coming to aid and vilified me further. Do I want a repeat?
Oh well... I tried.

Monday, May 31, 2010

What has Google cost us? (FPOTD-Solved)

Today I was reading a MacRumors post about the Google Pacman Doodle.

Some joker posted on the thread the following:
"Oh man, I've been playing all morning. I'm glad the gov't doesn't block Google! I feel bad for wasting your tax dollars. Okay, I won't play any more. Back to work.

Okay, just kidding. I only played one game."

--- A. Joker

Of course, there is always some wanktard on just about any discussion board that wants to whine about how much they hate the government:

"I'm not gonna start on how much I loathe government employees in all areas for reasons like this, so I won't go into the "Nobody Does Their Job" speech. No, the Gov doesn't block that on their computers, but that doesn't mean you should be playing games while you SHOULD be working, and working off of taxpayer dollars I may add. The Gov is the joke it is today thanks to things like this.

I did come to this thread, however, to say how they should leave it like this permanently, but I think I retract that now. People that should be working aren't, because Google turned a standard search function into a game. I know in my mind too, that no one I know is going to pass by it without playing... Sad. "

--- A. Wanktard. 

Somebody later posted the thought that in the grand scheme of things, a government employee playing 10 min of Google Pacman was in-consequential.

But the question to be asked, and the Fermi problem to be considered, is how much did Google cost us?

I posted the following to the discussion, then went back to doing some federally funded physics.

----- Start Fermi ----


About 3 million government employees, not counting shadow hires.
Average annual salary lets assume around $40k, or about $20/hr or $.33/min.

10 min of play costs, just in direct pay, $3.33. Lets not forget the massive overhead costs, assume about 3 times direct pay and those 10 min cost about $10.

If every employee played for 10 min, that is $30 million spent.

Remember that most full time salaried workers in most states are allowed by law two 15 min paid breaks, and we can see this is not a big deal. Just install Pacman in every bathroom stall and save on costs!

Now, of course not every employee is going to spend 10 min, and in fact most of them will not play at all for whatever reason. Lets assume 1% of all government employees played for 10 min, and that comes out to a paltry $30k of time spent.

There are about 300 million people in the USA, lets say 1/2 are of tax paying age.
This means that those employees playing Pacman for 10 min cost each of us $0.0002.

I think I would rather pay for that than for many other things the US government uses my tax money for.

Saturday, May 1, 2010

Double me Down!

Recently I have been reading about the "horrors" of Kentucky Fried Chickens new Double Down Sandwich.
A product that is " meaty, there's no room for a bun!"

According to the advertisements:

"The new KFC Double Down sandwich is real! This one-of-a-kind sandwich features two thick and juicy boneless white meat chicken filets (Original Recipe® or Grilled), two pieces of bacon, two melted slices of Monterey Jack and pepper jack cheese and Colonel's Sauce" 

Actually, the dammed thing sounds and looks pretty dammed tasty to me!

But you should hear (read) the monkey-screaming-while-flinging-feces reaction on the blogsphere.

"Just look at this atrocity."
"...heart attack on a plate."
"How dare KFC attempt to market such an abomination!"
"Makes me sick to think this is available for my kids to eat!" 
"Potentially lethal!"
"Angina on a plate!"

The list goes on.
A spark people article (yes, I use Spark People... I can't help but to spin the login wheel!) goes on to rant about the vileness of the sandwich.
The interesting thing are all the comments, a majority of them agreeing about how the sandwich is vile, a heart attack on a paper wrapper, and how KFC should be boycotted. And what about this "nutritional nightmare"?

Lets take a look at the nutritional content of the Double Down:

Fried Double Down:
540 calories, 32 grams of total fat, 10 of them saturated and 0.5 trans fats, 1380 milligrams of sodium.

OMG run for the hills!

How dare KFC market such an abomination! Lets see, a 540 kcal Double Down is 1/5th my total daily allotment of calories, and 66% of my sodium intake limit according to the RDA. I should sue!
I should go to Wendy's instead!

Umm, wait a min... that Wendy's Triple Baconator sure looks good! I cannot eat the bun because I am sensitive to Gluten, and it makes my hair fall out. I will be "good" and skip the fries and a drink.

Lets see how many calories are in this hamburger:

Holy Crap! 1180 kcal? That is more than twice as much as the Double Down!

"Just look at this atrocity."
"...heart attack on a plate."
"How dare Wendy's attempt to market such an abomination!"
"Makes me sick to think this is available for my kids to eat!" 
"Potentially lethal!"
"Angina on a plate!"

Ok, so one can find an abomination on the menu of nearly every fast food chain.

There is bad shit out there in the world people. Avoid stepping in it. Don't let your kids eat what you think is bad for them, but quit bitching about what is bad for me.

I can do totally fine with eating a Double Down. I can go grilled so that I don't get the breading if it makes me sick. I can do without the excess sodium, but hey, its my body.

A person losing weight has to abide by the laws of physics... to lose weight you must consume fewer calories than you burn. Simple. I can choose those calories to be crap, and feel sick and under nourished, or I can choose my calories to be good for me, with veggies, fruit, meat etc. and feel less sick, or even healthy. I am an experimental physicist, and can read the data. I do not need my research in how my body reacts to food be be hindered a-priori via legislation to ban certain foods. =)

So, I have about 2600 kcal to play with today. I am going to eat a Double Down, with a side of potato wedges, and an iced tea. My total calories will be around 800 kcal. (Still almost 400 kcal less than the bunless hunk of meat Wendy's calls the baconator.)
This is very reasonable calorie count for a meal. 

Hell, I may later on eat a pint of Ben and Jerry's pistachio pistachio ice cream. (Hey, check out their marketing.) This will come out to about 1000 kcal. What do you know, I will still have 800 kcal to play with. Think of how many fruits and veggies I can eat to make up 800 kcal! 
Or... I could eat another Double Down with potato wedges! YUM!

If you never see any more blog posts from me, you will know without a doubt that the Double Down killed me off, and you can say "Ha Ha!"


Friday, April 30, 2010

Let Your Fingers Do The Walking. (FPOTW)

Recently I have returned to my swingers life. 

By this I mean Lindy Hop of course! =)
This means less time for this blog, but not to fear, as I will continue to post despite dancing and Oompaloompas.

On a swinging note, lets talk about Django Reinhardt, perhaps the greatest of the Jazz and Gypsy Swing guitarists.

 As a youth, Django was injured in a house fire, leaving him with reduced leg mobility, and paralyzed the ring and pinkey fingers of his left hand.
Such and injury would be devastating to a guitarist, but despite the handicap, Django retrained himself to excel in guitar despite his injures. His guitar work served as an inspiration to following generations.

Below is a video of Django playing. Note how he lets his fingers do the walking!

---- Start Fermi Problem ----

Estimate how many miles Django's fingers traveled over the fret board over his lifetime.

How many notes did Django play over his lifetime?

How many calories did he burn playing these notes?

--- End Fermi Problem ---

Tuesday, April 13, 2010


Ommpaloompas are scheduling and hindering my free time, and thus the time I have for this blog.
As soon as I get things ordered and my time managed, I will be back at it!

In the meantime, check out this TED talk by Michael Specter:

The Danger of Science Denial

Friday, March 12, 2010

Space Ring Habitat Fermi (FPOTW)

This is my current desktop theme:

I wish I knew the artist and the name of the piece shown above. For some reason, this particular piece has captured my attention, and my imagination. I have spent some amount of time estimating various physical properties of the space ring habitat represented in the drawing.

The Fermi problem is as follows:

  • Estimate from the picture the diameter of the ring, and the diameter of the tube the habitat is constructed from.
  • What is the angular velocity needed to maintain a 1 gee environment?
  • What is the volume of air in the habitat?
  • Estimate the population.
  • Estimate the mass of the habitat.
  • Estimate the reaction mass needed to "spin up" the station to the angular velocity estimated above.
If anyone knows the piece or artist, please tell me so I can properly attribute the image.

Update: 4/30/2010

As in the comments below, the artist attributions are added! Thank you MJWT.

Monday, March 1, 2010

Tuesday, February 23, 2010

No sense of scale.

I always get a kick out of eavesdropping on conversations at our local coffee shops.

Well, eavesdropping is not really the correct term, as the people pontificating at coffee shops usually do so loudly so that others may bask in their perceived intellectual glory.

The topics range from philosophy:
"All we really know... I mean all we really know, is what we are told."

To the latest in medicine:
"It is the specific type of cheese that works, and the more organic the better! It cures muscle pain."

To current topics in health care and energy policy:
"We don't need nuclear power. If the government wants to solve the current obesity and energy crisis, they need to put the 100 million overweight lard-asses on treadmills hooked to generators, and dangle some bacon in front of them. The energy produced would more than suffice to power the needs of the rest of the US population."

Wait.... what... huh?

First of all, I ask the philosopher what kind of coffee he is drinking and how it tastes. "It's good... it is this special Colombian blend with a hint of vanillia."
"Did someone tell you it tastes good?" I ask, then move on.

"Tell me more about this cheese? Why not simply take aspirin?" I ask the medical student.

"Well. there are these specific enzymes that deaden pain receptors and reduce inflammation! It is all natural and it helped this Olympic skier win a gold medal. If it works for a world class athlete, then there must be something to it!"

"If an Olympic fencer said that trephination would relieve headaches, would you do that?" I ask, then move on.

"Hey, Mr. Bacon, " I interject to the energy/health guru/pundit and his cadre.

"Lets try some critical thinking and some math on your proposed solution to our energy crises."

I take a deep breath.

"100 million overweight people at 40 lb over weight (Using your numbers.) is roughly 4 billion lb. of fat. 3500 kcal of energy per lb of fat. That comes out to roughly 6e16 joules of energy.
America uses about 1.5e19 joules/year of electricity.
So if all the fat energy was magically converted to electricity, we could power the country for .004 years, or about 1 and a half days."

The pundits table falls silent.

Obviously they do not get the point, so I continue:

"Worse yet, the average human puts out 100 Watts of power day and night, and while exercising may get up to a max of 200 Watt for short periods of time. Try the math to figure out how much "treadmill" energy the entire overweight population can provide per day until they lose their excess baggage."


I shrug, bus my coffee cup, and head out into the real world, where the only people caught dead on a treadmill seems to be spandex clad models. (Or cute dogs).

Monday, February 15, 2010

I see dumb people #6 Quantum Zero Point... Zero Pain!

Are you in deep pain? Are your quantum vibrations misaligned with your chakra points?


You are in luck! Linda Miller has the cure for you, Quantum Zero Point Energy!
How does this wonderful treatment work? Lets see what Linda has to say:

"Oh my!  I am BEYOND excited to share with you…
… an Ancient natural therapeutic wisdom of applying Futuristic Technology in the Area of Quantum Physics to support Individuals with Natural Energies to eliminate pain and stress on the body and increase their immunity."

Ancient? Wow! How long has quantum zero point energy been known of? I can only find references at most 100 years old, but perhaps I need to expand my google search to include Linear B?

"This will not be for everyone because everyone will not choose to believe it… and that’s ok.  This is for those who do choose to believe."

Wait, what... huh?
If all I need is belief, then why use something like Quantum Zero Point Energy? Why not use bananas? They may help align my root chakra with my splenic chakra!

"The products, backed by over 25 years of R & D, supports Self Care and these tools empower people to allow their bodies to heal naturally."

25 years? GREAT! With all those years in researching the quantum mechanics needed to understand what exactly is meant by zero point energy, also known as the vacuum energy, perhaps you can answer this question:

Consider a p-orbital electron characterized by |n,l=1,m=+-1,0> (You can ignore the spin angular momentum in this state vector)

Subject this electron to a potential:

V = lambda(x^2 - y^2)  where lambda is a constant.

Obtain the "correct" zeroth order energy eigenstates that diagonalize the perturbation. Don't worry about evaluating the energy shifts in detail, but show us the three-fold degeneracy that are now completely removed.
What happens to the energy eigenstates under time reversal?

If you can answer this, I might switch from the banana brand pain killer!

Friday, February 12, 2010

Darwin Day Fermi Problem (Darwin Award)

Happy Darwin Day!

200 years ago today Charles Darwin was born.
You may also have heard of the Darwin Awards, an award given (usually) posthumously to commemorate those who improve our gene pool... by accidentally removing themselves from it.

 Here is a nice Fermi problem to determine candidacy for a Darwin Award. This is based on a discussion I had at work.

------- Start Fermi Problem -------

A manager brings a problem to a physicist to design a system to put a pure nitrogen blanket into a small enclosed (but vented) box. However, there is some concern on assuring that the percentage of nitrogen in the box is as close to 100% as possible, and how to measure this.

A first design is to pump pure nitrogen from a gas cylinder into the box, and (relatively) quickly empty the bottle so that there is no diffusion of O2 back into the box through the vent holes. This should purge most of the O2 from the box.

The manager has read about people dying from Nitrogen asphyxiation, and is concerned that he could suffocate if he used too much nitrogen.

The physicist, after glancing at the room where the box is to be located, and the size of the pressurized nitrogen bottle, confidently proclaims that there is no real danger.

Is the physicist a Darwin award candidate?

Note that the dimensions of the room are 15 ft x 30 ft x 8 feet.

As an aside, assuming a standard airgas bottle of compressed nitrogen (250) what is the smallest size room you could safely vent such a bottle in?

You may have to look up (or estimate) what O2% is dangerous to such a candidate. =)

And finally, as a back of the envelope problem:
Say the box is 3 feet by 4 feet by 3 feet.
Design the flow rate of N2 and vent holes such as to assure a 99.99% purity of N2 after 1 hour. ;)

---- End Fermi problem ---

Note, because nitrogen does not trigger a suffocation reflex in the human body, breathing pure nitrogen gas is very dangerous. Just two or three breaths reduces the amount of O2 in the lungs where the O2 diffuses back into the lungs from the blood stream. For this reason, even if you determine the physicist is not a Darwin award candidate, please take precautions in dealing with nitrogen gas, and maintain adequate ventilation of the room. 

A quick rule of thumb to file away for future Fermi problems:

Liquid to gas expansion ratios: Liquid:gas (approximate)

N2.    1:700
O2.    1:860
He2.  1:760
H2.    1:850
Ne.    1:1400

Taking the average expansion of the first 4 gases, a rule of thumb is that if you deal with many liquid cryogens, the expansion ratio is about 1:800.

Monday, February 8, 2010

To err is human, and part of skepticism


The article is a very interesting read, and impels me to re post a list of what I believe skepticism is and is not.

  • 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 denial-ism.

Friday, February 5, 2010

The Printed Word (FPOTW)

Newspapers have been the mass media for a few hundred years. In this day and age of instant CNN coverage, web pages and blogs, people have predicted the end of the newspaper.
However, the printed word still has great power. Power to change things for the better, or to act as fuel for destruction and death.
Lets examine the Fermi of the newspaper.

---- Start Fermi Problem ----

How many newspapers are printed each day in the United States?

Estimate how many trees are used to make the paper, per day.

Estimate how much ink is used in printing these papers each day.

Make the same estimates for the world each day, each year.

A few years back, 12 (I believe) caricatures of Mohammad were printed in various newspapers around the world.

Einstein != Mohammad of course, and I do not risk a Fatwa for posting a caricature of Einstein that is for sure.

Estimate how much ink was used to print these caricatures.

How many people died as a result of the protest riots? (Time to practice your google-fu)

Compare the volume of blood of the dead to the volume of ink used to print the caricatures.

---- End Fermi Problem ----

I guess the power of caricature is greater than that of the printed word.

Wednesday, February 3, 2010

Fun back of the envelope!

Sometimes I run across a blog that just makes me smile!

Rhett Allain over at Science Blogs posted on his blog, Dot Physics, a back of the envelope solution on the power source of a light-saber.

I love this type of back of the envelope problem, as readers of my blog know well.

More... MORE! =)

Tuesday, February 2, 2010

Earning a grade?

I am constantly astounded by the contortions some students will go through in an attempt to improve their grades. These contortions are usually more strenuous and less likely to work than simply studying harder.


For instance, and most recently, a friend of mine who is a Teaching Assistant was lamenting the fact that a student was constantly emailing him about a grade given him last semester.

"Man, this guy keeps emailing me about grades. And this is from a class that he took last semester!" My friend states one day over coffee.

"Really? What did he get?" I reply.
"A C+. He really did not deserve even that, and I gave him and the class a bit of slack."

"And he is still bitching? What does he want?"

"He says he would like to meet me and discuss his grade, and that he needs at least a B+ to keep his GPA up."

"Oh..." I smirk, "let me guess... he is either a Bio-Chem major, or pre-med?"

"I am not sure, let me check... yes! How did you know?"

I just laugh. It seems that the worst offenders of the "I deserve to get a good grade in your class even though I did not study" type students are the pre-med or bio-chem (read pre-med here as well) majors.
All of these students are required to take undergraduate physics, and many feel it is a waste of their time.

Many of the complainers are shameless in their whining for higher grades. They do not even bother with claiming the death of their grandmothers... no... they come right out with statements like: "I need an A- in your class or I will not get into medical school. What can you do to get me a higher grade?"
They nit pick on missing one point in a 15 point quiz, when the net effect of that one point is negligible on their grade.

They do not seem to respond well to replies such as: "I cannot do anything for you except give you a list of good books to study, and the name of a good tutor."

The usual response to this is more whining and threats, such as how they pay my salary and that they have better things to do than waste time with a stupid subject such as physics.
They seem to think that insulting a subject I love, and a vocation I have chosen will make me more sympathetic?
They threaten to go over my head to the instructor. This is funny because the instructors, after years of dealing with students likes this, are even less sympathetic than the TA's.

I once told one very persistent and whiny student I could help her with her grade if she promised to give me 30% of her future gross earnings after (if) she graduated medical school.

"That's unethical!" she complains.
"And asking me to give you a grade you do not deserve is ethical?" I reply.

She goes storming off to the instructor to tattle on me. The instructors prompt reply? "The going rate from professors is 45%, so you should have taken him up on the offer."

I defend my acerbic remarks on whining students by asking a simple question.
Do you, as a possible future patient of one of these students, really want a dishonest cheating person treating you for an illness? If they do not work hard enough, or are not smart enough to get the grades they need for medical school, is it in the public best interest to graduate them in the first place?

Well, as for contortions, perhaps they should be careful, for this is the "end" result.

Saturday, January 30, 2010

Compactified Dementia - The hierarchy problem of cranks

Over the last couple of days I have come across several blogs (and tweet's) relating to cranks (crackpots) and how they choose to interact with scientists, the general public, and themselves.
I have had a special place in my heart for crackpots (cranks, kooks, nutters) for the last 15 years since running into them abruptly on Usenet (now google groups). I have framed my very first snail mail crackpot letter I received shortly after publishing a paper in Nature. The rest I have consigned to a cardboard box.

There are many useful web sites and resources out there regarding cranks, and I very highly recommend reading Underwood Dudley's fantastic books on cranks.


I have battle cranks for many years, but some comments on a blog about how cranks never seem to communicate with other cranks reminded me of a Usenet post I made several years ago. At the time I was doing research on short range tests of gravity, which would be able to put constraints on the size of compactified extra dimensions according to some string theory models by Arkani-Hamed et. al. I decided to write the following post. Enjoy. =)

Compactified Dementia - The hierarchy problem of cranks

The hierarchy problem of cranks is an interesting topic. Why are their arguments so weak compared to the average person? One answer might be that they reside in their own dimensions, compactified and placed out of the way somewhere.
Many people think that cranks (crackpots) live in their own universe, a universe that has nothing to do with our own. However, the Yankovich theory states that universes cannot interact directly. Since it is empirically obvious that cranks do in fact interact with our universe, this would mean that cranks in fact reside somewhere in our universe. This would mean that crackpots (cranks) live in their own compactified dementias, with bits of their crankiness "leaking" across to our regular Space-time.
There are some interesting properties associated with those compactified dementias.
1. There are absolute reference frames in Dementia-Space. This allows such things as faster than light travel, and the Ether.
2. Any GPS device entering such a Dementia is rendered useless.
3. Computer Keyboards have broken shift keys.
4. While communication from Dementia-Space is easy, communication into Dementia-Space is very difficult. In fact, one could postulate that there is no information transfer into Dementia-Space. Further tests are needed.
5. Residents of Compactified Dementias are very xenophobic. They think that occupants of regular space-time are in a vast conspiracy to "Hide the truth" and "Steal tax payers money".
6. Mathematics in Dementia-Space do not allow proper multiplication of negative numbers, but seem ideally suited to solve Fermat's last theory.
7. Time does not exist.
8. Clocks are broken.
9. The second law of thermodynamics does not hold in Dementia-Space.
10. Intelligence in Dementia-Space is dictated by the NIT. [1]
11. Diversified population makeup. [2]
This is but a short list. At this time, very few studies have been made into the fundamental physics of Compactified Dementias. At this time, most study has been simply to categorize (and catalog) the crank species that are emitted. For example, the list compiled by OM [3], while interesting, does not in fact explain why the interaction length of a crank is so small. Usually, crank interaction is limited to such an extent that the general population is rarely aware of cranks. Cranks have little effect on the physical world, much less any socio-political clout.
There is a new parameter space to explore when it comes to Compactified Dementias.

[1] M. Crank, Negative Intelligence, sci.physics, March 3, 2003

Friday, January 29, 2010

Meniscus Fermi

As you have probably guessed from a previous post, I find that dimensional analysis is a powerful tool for back of the envelope type problems.

Therefore I present this problem on surface tension as an exercise in dimensional analysis. Of course, most dimensional analysis solutions, as with most solutions to Fermi problems, are order of magnitude. So after having some fun with the following problem, see if you can refine your model a bit.

---------- Start Fermi Problem -----------

Add water to a clean glass, and you will notice that the water likes to "climb" up the wall to a certain height. This is called a Meniscus, and is caused by a physical property called surface tension.

You can put some water in an ice tray, and freeze it, and you will be able to see the frozen meniscus as a raised lip on the top surface of the ice cube.

Estimate how high the meniscus is for water.

Here is a hint for you: 
The surface tension for water is about 0.07 N/m

------------ End Fermi Problem --------------

At the end of the day, you can do an experiment to help refine your model. Freeze some ice, and measure the height of the meniscus.

Monday, January 25, 2010

Liquid Crystals and the Buckingham Pi Method

Physicists have at their disposal many mathematical tools to help them solve problems. However, some of the most powerful are dimensional analysis methods.

Dimensional analysis not only helps you check if a formula you derived (or copied down to your test sheet if you are a student) is correct at least dimensionally, but it can help you estimate the answer to many physical systems.

For example, say you are a physicist who is trying to understand how their watch liquid crystal display works.
They have done some reading in the popular press and have found that a watch LCD is probably made of a twisted nematic liquid crystal cell, which can be switched with a magnetic field. (Or electric field).
The physicist reads up on Wikipedia about liquid crystals, how energy efficient they can be, how they are switched on and off, how polarizes are used and that nematic is derived from the Greek nema, which means thread. After some more reading our physicist starts wondering how strong of a magnetic field is needed to switch the LC cell.

Of course one can simply look up the answer online, but our intrepid physicist decides to use dimensional analysis, and more specifically the Buckingham Pi method to determine the general form of the strength of the magnetic field.

Lets start with an aside on the Buckingham Pi method.

Suppose you are attempting to describing a physical system with a physically meaningful equation of n measurable variables.

f\left( {{x_1},{x_2}, \ldots ,{x_n}} \right) = 0

where each {x_n} is expressed in terms of k independent physical units.

The above equation can be restated in terms of p = k - n dimensionless parameters constructed from {x_n} of the form

\pi  = x_1^{{m_1}}x_2^{{m_2}} \ldots x_n^{{m_n}}

where each {m_n} are rational numbers.

From this we can construct the new equation:

F\left( {{\pi _1},{\pi _2}, \ldots ,{\pi _p}} \right) = 0

Note that this solution is not unique, and is only one of a set of dimensionless parameters you can generate with your measurable variables in terms of physical constants. This method does not choose the best form, or even the most physically meaningful form. But it is very useful none the less.
Note that independent physical units are those such as length, time, mass etc. The fundamental SI units (of which there are seven) represent such a set of independent units.

New, lets see how we can use this method to determine a physically meaningful form for an equation to determine the magnetic field strength needed to switch the LCD cell in question.

Consider that we have a cell full of a nematic liquid crystal. The liquid has an elastic constant K, which is measured in Newtons. The LC is also diamagnetic in that it will anti-align with the magnetic field. How strongly the little "threads" or "nemas" in the LC will interact with an external magnetic field has to do with the diamagnetic susceptibility of the LC, {\Delta \mu } .
The "threads" in the LC are twisted, which means that the "threads" in each layer of the LC is rotated, or "twisted" a bit from the direction the previous layer is facing. Picture a DNA molecule, or a helix spiral staircase. This means that the thickness, l, of the cell that is holding the LC is an important variable, as each layer will require a stronger or weaker magnetic field to anti-align the "threads".

In general terms, the little threads like to align along the direction (actually opposite) with the external magnetic field. But the restoring force of the liquid surrounding the threads want to keep this from happening. Sort of like trying to rotate raisins in a bowl of jello. Unless you hold the raisin in place, they spring back to their old alignment due to the elastic constant of the jello.

These little threads act as a polarizer, and you can rotate this polarizer using an applied magnetic field. Crossing the LC polarizer with another fixed polarizer stops light from being transmitted through the LC cell. This is switching the LCD ON.

So, using dimensional analysis, the general form of a dimensionful equation is:

H \propto {l^\alpha }{K^\beta }\Delta {\mu ^\gamma }

We then construct a set of dimensionless quantities from this equation, and equate the exponents to determine the final form.
Lets examine each variable, and determine its dimensional quantities.

H -> magnetic field -> Amperes/meter -> [A][L^-1]

K -> elastic constant -> Newtons -> [M][L][T^-2]

delta_mu -> diamagnetic susceptibility -> Henry/meter -> [M][L^2][T^-2][A^-2][L^-1]

So, equating the fundamental SI units we get:

Equating exponents we get a set of 3 equations and 3 unknowns.

Solving this set of equations we get:

Therefore the dimensionful equation is:

Now, lets do a sanity check; Does this equation make sense?

First, the units check out. So the equation is dimensionally correct. Check.

As the elastic constant K increases ("jello" force increases), it makes sense that you would need a stronger magnetic field to rotate the "threads" in the LC. Check.

If a larger {\Delta \mu } means a greater interaction with the magnetic field. This means that a weaker magnetic field can couple to the "threads" and overcome the "rubberyness" of the LC, and therefore the magnetic field does not have to be as strong to rotate the "threads". Check.

As the thickness of the cell increases, there are more "threads" that are already nearly aligned to the ON position. The more threads that are aligned, the less light makes it through the cross polarizers, and therefore a weaker field is needed to switch ON the LCD. Check.

So, the equation makes physical sense, and is dimensionally correct.

Our physicist uses their google-fu and determines that indeed this is the correct form, up to a multiplicative constant.

Of course, there may be a reliance on other variables, such as temperature, on how the LC behaves. More than likely these are subsumed into K, but can be put into our model later.

This is a very simplistic treatment of the Buckingham Pi theorem, as well as of twisted nematic liquid crystals. However, I hope the power of dimensional analysis is evident in this example.

Thursday, January 21, 2010

Fermi Gravity (FPOTW)

Here is a Fermi problem with a (perhaps) surprising answer, and several methods of attack.
The question is simply stated thus:

Where is gravitational acceleration greater, on the Earths surface, or 100 km underground?

There is a very easy way to solve this, a Fermi way that will answer the question. There is also a back of the envelope method, which will give a numerical answer.

For a hint I give you the following picture:


Thursday, January 14, 2010

SkyCity Restaurant Diameter (Fermi Problem)

These last couple of weeks since Christmas have been very busy for my wife and I. We are preparing to move to a new apartment in Boulder, we traveled locally to a family get together for Christmas and for New Years, and we have just returned from a trip to Seattle.

After all this running around frantically (and having little time for blogging btw) I decided it would be nice to blog about a nice dinner I had with my wife at the SkyCity restaurant atop the SpaceNeedle!

We were within a short walking distance of the SpaceNeedle, and so 47 min before our reservation we headed out.
This being Seattle in January, the weather was drizzly and cool, with fog. Surprisingly, even though it was 47F, the air felt warmer than an equivalent temperature would in Colorado. Any rain that came down did not feel like the soaking-freezing kind that is common in Colorado, but just seemed like an ever present misting. My wife and I rather enjoy such weather, so we were happy on our walk.

On our ride up the elevator we are regaled by the busboy about how tall the SpaceNeedle is, how fast the elevators go and what sort of earthquakes and winds the tower can withstand.

As we looked out the window of the elevator, we were a little disappointed that the view would be obscured by the rain and fog. The busboy commented: "The view from the SpaceNeedle, on a clear day is unrivaled, with views of the sound and Mt. Rainer. The SkyCity reasteruant rotates once in exactly 47 min, and is powered by a 1.5 HP motor. So you should be able to go around at least once or twice during your meal!"

We were shown to our table and our server (who earned her tip!) gave us our menu and took our order. (I wont go into detail, but it was not cheap!).
As my wife and I sipped our martinis, we gazed out of the window at the view, which despite the fog and snizzle was still really nice!

As we awaited our food, I wondered out loud about the diameter of the restaurant. When our server returned, with our food, I asked her about the diameter.
"Wow, no one has asked that one before! They always ask how high the SpaceNeedle is or some other question. I am not sure! I will ask the others and see if I can find out." And off she goes to ask around on the diameter of the SkyCity restaurant.

"Well heck..." I say to my wife; "I have enough information right now to estimate the diameter.

"Why not look it up online on your iPhone?" My wife asks as I look around for a piece of paper to scribble on.

"What is the fun in that?" I reply; "I will do that later for verification."

So, on to one method of estimating the diameter of the SkyCity restaurant!

------------------ Start Problem --------------------

So, the restaurant rotates once every 47 min. The dining seats and table are on a rail while the windows and the rest of the super structure remain stationary.
This can be seen in the cutaway drawing below.

As you can see in the picture, the windows slope outward on the rise. This means that there is an average diameter, as the max diameter is near the ceiling, and the min are at the floor. I decided to say the diameter of would be at my eye level as I was seated. Since this was a back of the envelope type problem, I did not really expect to estimate much better than a few percent anyhow.

So, first lets draw a rough sketch:

By simple trigonometry, the distance S is given by:
Where theta is in radians.

For a quick and dirty estimate, I would assume that the width of the window we were sitting in front of represented a short enough chord to use a small angle approximation for the radius.

The small angle approximation states that when the angle as measured in radians is much less than 1, or "small", then Sin[angle] ~ angle. Using this approximation and rearranging terms, I get an estimate for the radius R.

Then by adding up all these little chords I can approximate (and slightly underestimate) the radius of SkyCity.

Now lets consider some numbers:

The window pane I  estimated to be about 6 feet in length. There is some error as I did not have a measuring tape, and my wife insisted I not get up to measure with my arms.
Taking out my handy dandy iPhone I timed the transit of the window to be approximately 57.5 seconds.
This allows me to set up the following ratio that is equivalent to adding up the chords:

On solving for R I estimated the radius to be:

R = 93.7 feet.


------------------------ End Problem ----------------------

A few minutes later our server returns:
"You know, no one knows the answer. Sorry about that."

"That's ok. It is about 94 feet in diameter, give or take." I reply.

"Really? Where did you find that out?"

"I estimated it." I reply.

My wife and I return to gazing out the windows and at each other while enjoying our meal. For desert we ordered the Lunar Orbiter, which was wonderful and foggy! As we finished off the last of the ice-cream, I decided to look up the diameter on my handy dandy iPhone using some google fu.
According to the SpaceNeedle  web site the diameter is 94.5 feet. This is surprisingly close to my estimate.

In fact, my estimate is within 0.9%, or around 1.25 feet of the real answer. That is simply too fortuitous. Perhaps a future blog will deal with error propagation and error sources in such an estimate.

Well, all in all it was a wonderful evening! I was with my wonderful wife, at a nice restaurant, and I got to play with a Fermi problem.

Images from: