Don't believe what the press is telling you!

Consider this news story (and accompanying video) from the BBC about radioactivity in the sea within 300 m of the Fukushima nuclear plant:

Levels of radioactive iodine in the sea near the tsunami-stricken Fukushima nuclear plant are 1,250 times higher than the safety limit, officials say.

The readings were taken about 300m (984ft) offshore. It is feared the radiation could be seeping into groundwater from one of the reactors.

But the radiation will no longer be a risk after eight days, officials say. [Emphasis added]

There is no explicit by-line on this article, but the video contains an interview with BBC reporter Chris Hogg in Tokyo that repeats that a half life of 8 days means "that after 8 days the risk will have dissipated".

The reporter is WRONG. Twice, because that is also not what the officials said. His ignorance of basic physics, in this case a topic I always teach in a college general education class, led him to misinterpret what was actually said by a government spokesman and hence mislead the public.

The risk will not dissipate after 8 days.

First, what did the official say? The article reports that

"Generally speaking," spokesman Hidehiko Nishiyama told a news conference, "radioactive material released into the sea will spread due to tides, so you need much more for seaweed and sea life to absorb it." He continued: "And, since [the iodine] has a half-life of eight days, by the time people eat the sea products its amount is likely to have diminished significantly."

This (emphasis added) is correct.

The most significant effect is dilution. Levels will be very high near the source, but get reduced significantly as the source gets mixed into a larger volume of water. (Like smoke when you are a long way from a fire.) It also matters what the ratio is of radioactive iodine to the iodine that is naturally in the water, since the seaweed can't tell the difference.

It is also correct because in 8 days the radiation level in the seawater will be half what it is today. Half. Not "dissipated", half. The radiation level of the iodine in that bay will only fall to 625 times the safe level, not zero, in those 8 days. The risk is reduced, but not gone.

But there are other factors. For example, I have no idea how long it takes from the time seaweed is harvested and when it shows up on shelves all nicely dried and packaged, but it is unlikely to be a few days. Only fresh items like milk and vegetables appear "just in time" in supermarkets. Radiation drops every day it sits in a warehouse. It falls to half after 8 days, one quarter after 16 days, one eighth after 24 days, and one sixteenth after about a month.

The obvious fact (pull out your calculator) is that what remains after a month is still 1250/16 = 78 times the safety limit if all of the iodine stayed in the ocean near the plant. This shows why dilution is so important.

Side comment 1:

The other contaminant in seafood, mercury, does not go away with time and is not as easy to detect and monitor as radiation from I-131. I-131 emits a gamma ray which can be detected through the usual plastic packaging used for seaweed, right on the shelf. Mercury requires a careful (and destructive) chemical test.

Side comment 2:

The reporter quite correctly puts attention on cesium, which has a 30 year half life. Isotopes with very short half lives are "hotter" but go away quickly, so you just have to keep your distance for a month or two. Gram for gram, cesium isn't as hot but you have to avoid it for a longer time. That can be hard to do.

However, this ignores the other significant factor, which is biological activity. Our body needs a regular supply of iodine, so it will go looking for it in anything you eat. (Naturally iodine deficient diets in the Ukraine contributed to the uptake of I-131 after Chernobyl.) Further, it gets concentrated in one place, the thyroid.

Cesium (Cs) is in the same chemical family as sodium (Na), in table salt, and potassium (K), in sports drinks and bananas, which are both essential to the operation of our body. However, since it is much heavier, I doubt if it can substitute for the many ionic processes the body uses Na and K for. Any biologist or chemist know if Cs is concentrated by the body?

By the way, one reason I knew this was a major incident was that Cs-137 could be detected above background in California. You see, it takes a significant release to see it above the Cs-137 that still remains from atmospheric nuclear testing. As big as Chernobyl was, its Cs-137 was barely detectable over the stuff left from weapons tests done decades earlier once it got diluted by one trip around the globe.

Side comment 3:

There has been no new I-131 made since fission was stopped on March 11, fifteen days ago. That means only one quarter of the original I-131 remains in the fuel rods inside the three reactors that had been operating at the time of the quake.

The most important thing in this article might be that the levels in sea water had increased by a factor of 8 in the past week. That means I-131 from inside fuel rods inside the reactor vessel is not only finding its way into the water, but a larger fraction of it has been released from the fuel rods. (There is less I-131 available to leak out, but more of what remains is getting out. Did I say that clearly enough?) This is further indication that the fuel rods have been damaged significantly, which we already knew, but might just result from the iodine -- already vented from the reactor vessel -- being washed out of the containment building as they can now pour more water onto and into the containment building.

Side comment 4:

That observation in the quotation at the top of this article, that radiation "might" be seeping into ground water, struck me as strange. There is I-131 in Tokyo drinking water. This is because Tokyo's water supply comes from surface water (mostly behind dams based on a city water department document I found), which will be contaminated by radioactive rain carrying I-131. But everyone should know that rain also soaks into the ground. Apart from geochemical processes that would capture iodine, it will go into the ground water.

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Measuring "pi"

Rhett Allain had an interesting post for "Pi Day" concerning the use of a simple harmonic oscillator consisting of a mass on a spring to measure pi. Clever!

However, he neglected the effect of the spring mass. The correct formula for this problem requires the addition of 1/3 of the mass of the spring to the mass hanging on the spring, which appears inside the square root used to calculate the value that goes on the x axis of his fit. Although it is really hard to tell what his fit looked like or what the mass of the spring might be, including this necessary effect should increase the slope and make his result worse.

Nice idea, however. I'll have to give this a try when we have the lab setup.

That said, I have special praise for his OUTSTANDING blog about how to build you own energy balance thing. I did the human demo in one class before spring break, and might have saved some students some money if the showmen are out on the beaches this week. The plastic version looks like it might make a good demo all on its own ... even without the cute crown with its cell phone re-receiver energy recycling thingy.

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From ridiculous to sublime

Time to weigh in, quickly, on the nuclear crisis in Japan.

As I commented on a link dump at Uncertain Principles that points to a half decent article that has since been moved and corrected to some degree, the news reporting about the reactor problems was truly awful for the first day or two. What an abomination.

It has, however, improved a LOT. Tonight I was stunned at how well MSNBC covered the subject. And not just with the experts, who no longer need scare quotes around their titles, but also in a lengthy intro by Rachel Maddow on her show. Yeah, she was still a bit confused by the fact that rust is oxidation (of iron) but the oxidation of zircalloy is not rust, but the presentation was not wrong and well pitched to a (scientifically illiterate) audience.

It is worth watching on Hulu or wherever they archive it.

The real key, however, is that they have real experts. I missed the name of the guy from Sandia who was on an earlier show, but they had Frank von Hippel from Princeton on the Maddow show along with some others of similar quality but whose work is not personally known to me. Clearly a whole bunch of people were as horrified as I was by the junk that was being broadcast and had the pull to get the attention of the networks and change what is out there. It probably also helped the DOE Sec Chu can teach as well as do physics, and did a good teaching job in front of Congress.

The changes are dramatic.

The comparisons to Chernobyl are now rational, rather than nonsensical.

No idiot is out there saying that a scrammed boiling water reactor will go prompt critical if it melts down. The "expert" that didn't seem to know that the heat in the shut down plant comes from internal radioactive decay of fission products is long gone, replaced by one that knows spent fuel rods are also hot -- and "hot" with radioactive elements that live just long enough to be very dangerous if they were to be released.

OK, one Congressman (who as a physicist should know better) was out confusing a civilian nuclear power program that only uses fuel under IAEA supervision with a rogue state operating a clandestine enrichment program probably designed with help from North Korea and Pakistan, but let's ignore that one.

Actual facts, like the location of the spent fuel storage pools 40 feet in the air !! ????? !! above the containment structure in an earthquake zone, are now clearly featured in the stories. Ditto for giving radiation levels in Sv rather than in "chest x-rays" (which deliver much less radiation than they used to). Even Livermore managed to get out the fact that they have a nuclear weather forecasting program for this, and other purposes.

And I am particularly impressed that we are sending some of our specialized monitoring equipment (I'd guess it is the stuff developed to look for weapons or the result of a "dirty bomb" or an event just like this one) to Japan. I hope it works as well as advertised.

That is about all that I have time for tonight, but I will try to blog about some specific details when I get a chance.

I'll close with the most important point that hasn't been emphasized in the reporting so far, and might have confused people about the extent of the radioactive plume. Radiation detection is EXTREMELY sensitive. I heard of a case where the detectors outside of a nuclear plant were set off by the alpha radiation from the Thorium and Uranium in the smoke from a coal plant that had been pushed down to the ground by an inversion layer. A nuclear carrier would have similarly sensitive monitors on the ship, so we would need to be told the level that was detected -- not just the fact that radiation was detected -- to get a sense of what our carrier picked up off the coast of Japan. Further, it can be far more discriminating that a simple Geiger counter. You can tell what radioactive isotope is out there as well as how much, and the specific isotopes tell you where they came from. That is how people know fuel elements have been damaged without being able to see inside the plant.

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Teaching Majors

Dr. Crazy is back from sabbatical with shorter hair and fully energized to teach the class that introduces students to the real subject matter of the discipline they are going to major in. Now English is not exactly Physics or Engineering, but I've found plenty of common ground with her in the past and this topic is no exception.

I'll start with the comment I posted on her blog:

I never really thought of my Physics for Engineers class as an intro to the major until reading how you described your course, but maybe I should. It has many of the characteristics of yours (mini-PhD curriculum, viewed as a service course, foundation for everything that follows).

Technically, there is another course that physics majors take that is actually the start of the major program, but students won't take it if they don't like the view of physics they get in the class I teach! Once physics departments figured out that they were losing future majors to engineering (where you can also make a living), they put more emphasis on having their best teachers in the intro class and trying to make it more engaging and hands-on ... within the limits of a 200 student lecture hall.

Continuing here, so as to avoid thread hogging "man splaining" behavior ...

And within the limits that the room is not big because there are 200 physics majors in the university. No, most of those students are wannabe engineers and that fact is why calc-based physics devolved into a service course that often discouraged potential physics majors along with potential engineering majors.

Now my classes are not that big. Not even close. Furthermore, I rarely saw a self-identified physics major until recently so I view most of my students as engineering majors and teach the class with that in mind. The result is that I might actually be teaching an into to engineering course! I need to think about that this weekend to get ready for next week.

[Side remark: Some, but not all, engineering majors at nearby Wannabe Flagship have an actual "intro to the major" course with that name, but many have a course that inculcates a particular way of doing things into their majors and require that they take it during their first semester by making it a pre-req for just about everything else. Others appear to trust that someone will teach that new way of looking at the world in a core course for the major.]

And maybe that is why my better students often turn into stars after transfer. Even people who get the concept of prerequisites don't always pick up key basic skills the first time. Learning is hard. But if you fight the battle in my class at least once, your chances of picking it up for good in the actual "Intro to Whatever" class probably gets close enough to 100% to make me happy. Or at least Not Unhappy.

So what do I do? In addition to using the "This week in lab" method of making connections between lecture and lab, I use the "Next year in ..." method of making connections to the next level of application of skills that might blend both physics and, say, third semester (vector) calculus. I use the latter to put an explicit emphasis on skills I know their profs will want them to employ in their major, whether it is physics or engineering. (The computer science majors get hung out to dry here, although the term "algorithm" has been known to cross my lips.) Dare I say the "O" word - Outcomes - in this context?

I shall. (I'll worry about the "A" word - Assessment - to a lesser extent for the time being.) For a course like this it is really all about aligning Outcomes with the most basic needs of the classes that will come along later. And that isn't easy.

So that is my advice to Dr. Crazy. It is GREAT that her department has settled on a common book for the course while developing it collaboratively. As a result, it will be more likely that students will come out with the experiences they expect. Along the way, keep talking about what those expectations actually are.

I've changed my physics class a lot after discovering what engineering faculty were expecting based on their vague recollection of when they first picked up a certain basic skill. We "covered" it, but only in a way that a future PhD in Engineering would be likely to pick it up right away. The Engineering Way is to expose, as much as possible, the inner workings of your analysis of a problem by making certain procedures mandatory. Physicists tend to not do that, using those processes on an as-needed basis, so I have to be even more conscious of each problem solving step when we do problems in class. However, that way and The Physics Way share an emphasis on analysis. Is there also an English Way? Probably, although I'd guess it is more like the let-a-thousand-flowers-bloom physics approach given my past experiences.

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Students helping students

Dot Physics offers an excellent suggestion for communicating good study habits to new students: have this year's students tell next year's students what they need to do. Better yet, he posted what his student's wrote.

I know it is a good idea because I have been doing something similar for several years. It started with an end-of-semester question about prerequisites. (If you follow my blog, you know that I have identified the failure of students to comprehend the meaning of "prerequisite" as a long-standing problem for advanced classes like calculus and physics.) That info got shared with the math faculty who taught those classes, and I think I have seen an impact on what students learned and brought with them to physics (and calculus).

Later, based on discussions with a colleague at another school, I tried something similar to what Rhett Allain is trying: collect advice from current students (mine is entirely anonymous) and distribute it via Blackboard to the incoming class. (That mechanism is still a weakness because our students don't get access to their Blackboard shell until the first day of classes. They really need this kind of info before then.) They seem to appreciate it, but I'm less certain how much it helps.

Measuring changes in the success rate of any class is tricky. There are lots of variables. (To name just one that could be measured, I started getting a significant number of kids with AP calculus experience after the depression of 2008 hit.) The biggest is that they are busy (work or play or both) and sometimes just lazy and unprofessional, still looking for the easiest way to pass. Thus, even though my students, like Rhett's, offer the excellent advice to read the textbook before class and start their homework early, they just won't do it no matter who tells them about it. But they will form study groups, and that sort of collaborative learning has grown significantly in the last few years.

Has anyone else tried this? Any suggestions on how to get them to read?

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Dot Physics gets Power wrong

Rhett Allain has a great blog at Wired.com, but I will not create yet another account just to comment there so my comments will be here instead.

Usually he is on the money, but in this case his bad experiences with ESPN Sport "Science" gets in the way of his analysis of a video about the power of NASCAR cars. For convenience or future reference, I'll embed the video here



and then get to the analysis.

Rhett first objects to the statement that the weightlifter being shown "exerts about 1 hp per rep". Yes, they meant "during", but what is wrong with that? The numbers are right if you take the 275 pound lift as being 2 feet (61 cm) rather than 50 cm (about 20 inches) in 1 second. The weightlifter is producing pulsed power during the lift, which is about half of that 1 second rep, but hardly resting during the other half.

Check out this video of a power lifter doing 26 reps on the NFL 225 pound lift, or this one where the guy does 72 reps at 225 pounds. The first one takes around one second per repetition, locking the arms out each time. The second one is a much shorter, but faster, lift that might make for an interesting video analysis to see what his power output is.

Estimating the average power is trickier, because you really can't use the work done ON the weights as your metric. If you did, the average power would be zero because there is negative work done on the weights as you lower them! !! However, if you shift your focus to the work done by (within) the muscle, it might be more than 1 hp for the entire time the weight is moving. Controlling a weight as it comes down is not quite as hard as lifting it, but it isn't being done for free!

What I like best about this example is that "power lifting" is one of the few cases where a physics term is used correctly in sports. Power lifting, where the emphasis is on multiple reps, is entirely about the rate of doing work in a way that reflects what is done in competitive athletics rather than just lifting the most weight. That is why the NFL tests on the number of reps of 225 pounds. (The NFL record is supposedly 43.) Yes, that is power. And I think it is more obviously power than the similar output required to climb a mountain on a bicycle even though that is probably the most extreme case of continuous power output by humans.

Rhett next complains about a statement that he actually misinterprets. The statement in the video (around 0:50) is that horsepower of a car engine is "calculated by measuring torque". This is 100% correct. Rhett says "First, horsepower is not measured by calculating torque (at least not in physics)." Right but not relevant, because they don't calculate torque. They measure torque and rpm and calculate power by multiplying the two together. Rhett says "I guess the only problem here is using “fast” to describe the relationship between torque and power." except that is not what they are doing. They are using fast to describe the angular velocity, just as you might use "fast" to describe the linear velocity if you said that power was about how fast you can apply a force (Power = force * velocity). This is 100% good physics. Rhett, you messed up this time.

For the record, in physics and engineering and the real world of dynamometers, you determine horsepower by measuring a torque curve (torque in foot-pounds as a function of angular velocity in rpm) with a load cell (which measures force) on the end of a lever that is connected to the load on the engine. Modern ones do the multiplication and plot both power and torque versus rpm, but the actual measurement is torque (or, if you like nits, force that gets autoscaled into torque on the graphical output).

I'll go along with the final nitpick about lifting the space shuttle. Yes, they should have included "in one second" at the end of that last sentence. 850 hp is, indeed, like bench pressing the space shuttle in one second. Time is important. But no one would confuse using a jack (in his video example) with "benching". Everyone knows that you bench press a weight in less than a second unless you are totally whipped, so the same would apply to benching the space shuttle.

My negative nit pick: The video correctly describes the historical origin of horsepower as a marketing term, but the draft horses shown in the video (e.g. at about 0:30) produce more than 1 hp. James Watt used the small horses used in mines as his reference point for selling his steam engines.

My other negative nit pick is that engine size is not nearly as important as the rate of fuel consumption. After all, a top fuel dragster only needs about 550 cu.in. (compared to 358 cu.in in NASCAR) to make over 8000 hp (rather than 850 hp). It is all about the fuel and the rate you can burn it -- and how long the engine lasts! You have to put power in to get power out. Like the co-host commented during his 259 mph test drive of the Bugatti Veyron Super Sport on "Top Gear", before the pro took it to 267, you can actually see the gas gauge moving when you are burning 1.7 gallons per minute pushing out about 1200 hp. Wide Open Throttle is like that. (I'll have to save for another day the effort to figure out the Reynolds number comparison between air and treacle they used. I like it, but I'm not buying it.)

But I also have a positive nit pick. I loved their description of the added power from opening up the exhaust, although they oversimplified it a lot. Part of it is to "tune" the exhaust so it resonates at a frequency that matches the rate at which you want to pull exhaust out of the cylinder. Back pressure from the exhaust makes the engine less efficient. Getting a rarefaction as the exhaust valve opens is ideal.

However, the distinctive engine sound they played comes more from the Doppler effect than the resonating pipes. You need to stand next to one to appreciate that.

PS - The best thing about the Top Gear Bugatti video is you can actually see the exponential approach to terminal velocity as the spinning of the digital speedo slows down.

PPS - This was started ages ago, but only finished up and posted at the end of December. I'll try to monitor comments to be sure they don't sit too long in the moderation queue.

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It's a miracle!

The VERY long-awaited assessment of research doctoral programs by the National Research Council is, so they say, going to be released on September 28.

I think that makes this update of the 1982 and 1995 reports about two years late.

Why? Could the fact that they will release a revised version of the Methodology guide, updating the 2009 update of the 2003 report that proposed a methodology for this new set of rankings have anything to do with it?

It sure sounds like they kept tweaking the methodology until they got what they wanted. Will there be a hue and cry? We will see. The biggest problem is that the data it uses are so old that they will probably have to start the next study before ink is dry on this one.

However ...

I can't wait to see if that means "traditional" top schools remain above one physics program that I thought should have been marked with a bullet (record rating lingo) based on some of the raw data from 1995. Those data suggested that one program in particular had higher cites and other objective measures of research quality than the schools between it and #1.

For the record, that program was #10 UC Santa Barbara. Their Pubs per faculty number was second only to #1 Harvard, and their cites per faculty (178) exceeded Harvard (170) as well as #2 Princeton (110) and #3 MIT (121). Notice that gap? I sure did.

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Thesis Repulsion Potential

Jorge Cham is brilliant.

Follow the link above to his latest cartoon at PHD Comics. Click to the previous comic to see the setup.

For those of you who don't know this, which might be everyone reading this blog, the potential shown in that cartoon is typical of the attractive force that holds protons and neutrons in the atomic nucleus. The nuclear force is short range and weakly attractive, but there is a very large repulsion at short distances that arises, essentially, from the Pauli exclusion principle acting between the quarks that make up the proton and neutron.

That repulsion sets the size of neutron stars.

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Mathematics (and Physics) and Calculators

This is the third of three articles concerning calculators and mathematics triggered by a blogspot and IHE blog article by Dean Dad, a community college dean who appears to be writing from another part of the country yet has the same problems we have at our CC. The original article concerned calculator use in Developmental math classes that typically cover fractions and 7th grade algebra, but the comments spanned a range from that topic through mathematics and its applications beyond calculus. My first article merely laid out a common set of definitions, but does include a few assertions about various types of calculators and levels of mathematics that might deserve comment. The second article tried to focus on Developmental math but also included some comments about Algebra. In between these, I posted a shorter article that included a more polemical set of comments about the "modern" Z80-based Graphing calculators. Comments on the second article made me realize I also owe the community a long-deferred article about the math preparation of elementary ed teachers.

My second article limited itself to classes that are remedial in the sense that their goal is to get students to finally learn skills that were supposed to be taught in elementary and middle school as well as the first year or so of high school. College Algebra occupies a fuzzy territory because it is sometimes learned in high school (where it would be Algebra II) but is considered a college-level math class that is sometimes a general education requirement. I included it in my previous article because it is not the only gen-ed math option at our CC and serves many masters. In this article, I will take up the issue of most interest to me: whether students are prepared to use calculators and algebra to do physics, calculus, and (perhaps) engineering problems.

My expectations

As noted earlier, I allow my students to use a Scientific calculator and I expect them to have a decent one and be fairly fluent in its use. I do not allow them to use a Graphing calculator or one that is capable of doing computer algebra. The former is excluded because I do not have time to police all of them for cheat sheets, the latter is excluded because I want a level playing field. They can use MathCAD or Maple or Mathematica when they get into upper division classes where everyone will be using equivalent tools on any given assignment. I expect them to do algebra with pencil and paper in a freshman physics class.

The calculus teachers here have a similar expectation. Many (but not all) give exams where no calculators are allowed on part of the test, but a Graphing calculator (mainly for the numerical integration feature that is on some Scientific calculators as well) is allowed on others. Sometimes they even use a computer algebra program on an exam, but that is rare.

One thing I mentioned in a comment on Dean Dad's blog was the importance of defining outcomes. I forgot to mention that outcomes are best defined so the match the desired inputs for a subsequent class. It is for that reason that our calculus faculty require that students actually know certain derivatives cold, like times tables, and why they were stunned into disbelief when a student transferred here from a school where they used an Algebraic calculator that can do all of the basic derivatives and integrals symbolically. That outcome (being able to take a derivative with a calculator) is mismatched to the requirements of physics and engineering. (True, an engineer taking the "fundamentals" exam has a reference book handy that contains the basic derivatives, but the few minutes you are given to answer each question does not give you enough time to look up every basic result.)

Physics

In general terms, my views on calculators are similar to what Chad Orzel wrote in response to Dean Dad's blog. Real math (meaning math major math classes) have no need at all for calculators unless the topic is numerical analysis, and then you are better off with a programmable computer. Ditto for upper division physics majors classes, although they can have a computational component as well (that is, arithmetic rather than the symbolic mathematics of algebra or calculus). My impression from former students is that engineering expects correct computation as well as algebra, so exams require computation as well as the proper setup of the problem.

I should add that the exam security issues inherent in larger classes, where students are unavoidably sitting within copying range, also requires numerical variations between problems. (Exam fairness has, so far, kept me from putting totally different problems on versions used in the same class.) Most on-line homework systems also do this, although some have symbolic variations as well as numerical ones. This leads to an emphasis on problems with numerical values.

Further, because my students tell me what they do in their first engineering classes, I know computation is only part of it. Setting up the problem algebraically and simplifying before computing is ALSO part of it. For this reason, I require them to state the problem symbolically before plugging in the numbers. However, primarily because of their comfort level, I do not take off if they do the algebra with numbers present rather than keep the symbols until the end. (Having numbers and unknowns makes it easier for most of them to keep track of what is unknown and needs to be isolated or eliminated.) I'll let someone else break them of that habit later on, but I will encourage them to work on it in my class. That said, I do sometimes give exam problems where a symbol like L has to be in the final answer. See below.

Computing

What has surprised me is the degree to which students either cannot compute efficiently or use their calculators inappropriately when solving a problem.

The first problem has only become evident to me recently. I don't think it is a new development; I just happened to see a particularly egregious case last year where the student would evaluate something like A*B*C/D by doing A*B, write down the answer, enter the answer*C, write down that answer, then enter that answer/D. Painful. And slow. And prone to error. I should have suspected this sort of problem because the other version, entering ((A*B)*C)/(D), is a bit of craziness not uncommon in Algebra classes. They don't know order of operations and, even if they do, some have used bad calculators that violate those rules and been burned.

This is, however, a real handicap. They need to use one calculator type and use it enough to understand what it does under different circumstances, but might never have been taught that it is OK (and even necessary) to hit lots of buttons and see what they do under different circumstances. I'm going to mention that this year, going beyond such simple things as whether your calculator does -3^2 correctly or whether it knows automatically that the arcsin of 2 (or the ln of -1) is imaginary.

The second problem is doing algebra with long messy numbers in the equations. This came up in an earlier blog post about algebra, with some nice observations in the comments. This summer I've been thinking about where this comes from, and I am convinced it is because they never use realistic numbers in Algebra classes. Their equations all have numerical coefficients that are small whole numbers, not the 10 digit value for the y component of the velocity, v*sin(theta). There is no penalty for using 3 as a coefficient. There is a penalty for using 34.5619288 as a coefficient. They also seem to have not been exposed much to subscripts, so they are initially quite uncomfortable using Vx as a symbolic replacement for that nasty number.

My preferred solution would be to have pre-calc and trig classes use symbols with subscripts so they get comfortable with that math skill, just as I would like them to work with functions like g(y) or x(t) or even x(y). As we talk more about outcomes at my college, I have to see where those skills fit into the goals of our math curriculum. It might be that these are one-and-done skills (like some skills in physics) because instructors at one level don't know how important it is when you do kinematics in physics or power series in calculus and how much students struggle with those concepts. However, I also know that this is overly optimistic. Instead, I am thinking about ways to work those in from the beginning in my class, perhaps by starting with y(t) motion rather than x(t) motion and using v_y and a_y even when they aren't really required at that point.

Finally, there is the way I model doing problems in class. Comment number 4 on Chad's article mentioned math exams where you could only use a calculator on part two, something some of our math teachers do, but then came up with a nice insight:

it also could be used to introduce the concept of only taking out your calculator when you reach the stage where you've gotten the problem to its simplest state, and need only put in the numbers.

I've seen students do exactly that while taking an exam, just as I do, but I've never thought about really making a SHOW of pulling out the calculator at that point of the problem. I need to model that step as clearly and explicitly as I model algebraic steps when solving a problem. I also need to find or invent more problems where a symbol is in the final answer, like it would be if you were writing a program where a few values are fed in by the user but others are fixed by material properties or whatever.

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Calculators - Background Info

This is the first of three articles concerning calculators and mathematics triggered by a blogspot and IHE blog article by Dean Dad, a community college dean who appears to be writing from another part of the country yet has the same problems we have at our CC. The original article concerned calculator use in "developmental" math classes that typically cover fractions and 7th grade algebra. I have already commented on the blogspot version of this blog (more than once) and the two together have generated more than 80 comments. I added some more in my second article of this series.

I won't actually comment on this topic here. My purpose is solely to set the terms of the debate, as it were, because the wide-ranging discussions of this topic by Dean Dad and others are seldom clear about which of the four or more levels of "calculator" available to students are being discussed and/or which of the three or more levels of math classes (plus physics and chemistry) provides the context for the discussion.

The divisions I make are somewhat arbitrary and perhaps idiosyncratic, so I want to spell them out somewhere without cluttering up a discussion of the teaching and learning issues as I see them. That way I can link here for future discussions of this topic and not have to repeat myself.

Although I think three levels of "calculator" suffice for most classroom use, and hence for later discussion, I think I need to list at least five to make the definitions as sharp as possible.

• Basic - Here I have in mind a wide range of very cheap calculators that can do arithmetic, including parentheses and scientific notation, but cannot deal with trig functions.
  
  
• SCIENTIFIC - These calculators can evaluate all of the basic functions (trig, hyperbolic, log, exponential, power) but cannot store text or programs. Some can work with complex numbers and/or hexadecimal numbers. At the high end, some can numerically evaluate definite integrals or derivatives or solve simple equations, but they cannot show any intermediate algebraic steps or work purely with symbols.
  
  
• GRAPHING - Here I have in mind several calculators that are similar in capability to the TI-83Plus. They can do all of the calculations of a top end "Scientific" calculator, but can also make graphs and store programs (including large amounts of text that can serve as a sophisticated crib sheet). They can store text, but cannot work with symbols. Functions are limited to y(x) except in the rarely-used parametric or polar modes.
  
  
• ALGEBRAIC - These calculators can solve equations written symbolically and can, in some cases, even show step-by-step the algebra or calculus used in the solution. They are typically somewhat limited in how much calculus they can do symbolically, but they make it unnecessary to learn any of the derivatives typically encountered in calculus.
  
  
• Computer Algebra - Here I have in mind small computers that can run computer algebra programs like Maple, Mathematica, MathCAD, etc. Now you might say "a laptop is not a calculator", but there is actually a rather modest size difference between a notebook-sized laptop and the top end TI "calculator" that comes with a full keyboard and a wide screen. Besides, these are widely used in classes at the Junior level and above so they help frame the discussion.

The three in the middle, in all caps, are the ones I will refer to most often within the context of lower division classes taught at a community college.

For the record, I allow Scientific calculators in my introductory physics classes but do not allow formula sheets or cell phones or Graphing calculators to be used on exams. I encourage students to get one of the high-end Scientific calculators that can be used throughout their engineering career, including on licensing exams, so they become fluent in its use.

The four levels of mathematics classes are defined as follows:

• Developmental - The content here ranges from arithmetic and fractions (what I characterize as 4th and 5th grade math) to basic algebra (the first class where "x" is used, taught in 7th grade when I was in school). These do not carry college credit. A well-calibrated placement test determines where a student starts, and some have an exit exam to verify competency at a certain level.
  
  
• Intermediate - The content here is algebra through what I knew as the 9th grade level (the quadratic formula, for example, but no logarithms). This might earn college credit at a community college, but not at a university. It is not considered to be at the college level. A well-calibrated placement test is used to place students in or through this level of math.
  
  
• College Algebra and Trig - I group all of the pre-calculus "college level" courses here but exclude other "college level" classes that exist mainly to ensure that liberal arts majors can graduate even if they can't do college algebra. (Those other classes usually cover enough about exponential behavior to understand compound interest on credit cards and enough probability so you should know better than to play the lottery, both very valuable life skills!) At our college, College Algebra serves many masters so skills not needed for the pre-business curriculum are put in an "advanced" college algebra class (pre-calc) and a trig class. (I know that some colleges, like my high school and undergrad university, combine these into a single course but I will use our curriculum as my reference point.) A different, also well calibrated, test is used to place students above this level although most students take the class.
  
  
• Calculus - Although my students will usually take everything through differential equations and linear algebra, I'm mainly thinking about first semester calculus because that is where the bulk of students fail.

The distinction between Developmental and Intermediate might seem unnecessary to some readers, because both levels are usually non-credit classes at a university. Indeed, some universities define college algebra as a remedial course. I make the distinction because our math department teaches classes at the Intermediate level and above, while the Developmental classes are taught by a separate department that specializes in teaching those skills. I know that smaller colleges do not make this distinction, but we are not a small college. (We have more t-t faculty in our Developmental math department than a private school like Union College has in its regular Math department.)

If I just say "Algebra", I mean College Algebra. I will say "Basic Algebra" or "Arithmetic" when I am talking about Developmental skills classes.

For the record, our Developmental classes use a Basic calculator for some things but some exams must be taken without any calculator. (The placement test and exit exam do not allow use of a calculator.) I believe they allow the use of any calculator up through a Graphing calculator when they allow a Basic one, but that might depend on the instructor. Our Intermediate classes all use calculators. Our Algebra classes require a specific Graphing calculator that is also required for statistics. Our calculus classes are a bit less picky about which Graphing calculator students can use, but ban Algebraic calculators and computers except in some special situations.

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A big day in history

Today, June 16, is:

• the 65th anniversary of the first test of an "atomic" bomb outside Alamogordo, NM;
  
  
• the 41st anniversary of the launch of Apollo 11, the first mission to land men on an extraterrestrial body, the Moon.

It is also the 37th anniversary of Butterfield's testimony that President Nixon had been taping conversations inside the oval office, tapes that eventually showed he was guilty of obstruction of justice and other major felonies, but I want to talk about technology today.

So, in the context of "if we can put men on the Moon, why can't we stop the leak at the bottom of the Gulf of Mexico", what is the relative difficulty of these three tasks?

Based solely on the time required to complete the project, the Moon mission was by far the most difficult and complex. The project started more than eight years earlier, before we had even put a man in orbit. Although the Saturn I was already on the drawing boards as an orbital launch vehicle, the Saturn V project started in early 1962. After about 4 years of research and development, there were two unmanned test flights (both showing problems that had to be fixed) before the first manned test flights. Even though we rather boldly used the first manned test flight to orbit the Moon, almost two years elapsed between the first unmanned test and the Moon landing mission. Given that this was a very high priority project that went as fast as possible (too fast, at times, resulting in three astronaut deaths) with essentially unlimited resources in the early years, it is almost nonsensical to compare design and construction of the "capping stack" to a Moon mission.

Next would be the development of the plutonium bomb first tested on this date in 1945. Plutonium was first isolated in 1941, so it only took four years to determine that one isotope, Pu-239, could be used as a nuclear explosive (it was already known that U-235 could be used that way) and figure out how to produce kg quantities of it and turn it into a weapon. Like the Moon mission, this was a "money is no object" project on the same scale as radar and a pressurized bomber that could fly at high altitude and carry a payload big enough to drop an atomic bomb. So, on the basis of time alone, this was easily half as difficult as going to the moon even if you include the U-235 weapon and the need for both radar and that bomber if the project was going to succeed.

Of the two bomb projects going on at the same time, the Pu-239 weapon was by far more complicated technically. The only challenge with U-235 was producing the purified isotope. (That remains the reason it poses the greatest threat for the spread of nuclear weapons, but that is a topic for another day. Our confidence in the U-235 weapon was so high that it was never tested before being used on Hiroshima.) With Pu-239, you had to produce the isotope essentially one atom at a time in a reactor and then separate it chemically from a huge quantity of preposterously radioactive material. Even then, you have to figure out how to assemble it into a weapon that will explode. That was enough of a challenge that it required a test before being used in combat a few weeks later. Again, based on time alone, four years does not compare to a few months of work to develop the capping stack (and the tools to cut off the pipe and install it) as well as the temporary fixes that were used until it was ready.

It is a good thing that fixing the mistakes made by BP was not nearly as complicated as rocket science or weapons. Those took years, this took months.

As I said yesterday, I don't think most people realize how long it takes to design and build something, even something as "simple" as a highway. You don't notice it until construction begins, but the work was going on for years before that.

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Memo to Apple: Humans conduct electricity

Perhaps you saw the news stories reporting many complaints about signal loss on the new Apple iPhone 4? (Here is one from yesterday.)

As I guessed, the problem is not with the antenna itself, but the fact that there are two antennas on the phone, separated by a small distance on the case. (See this news story, among others, on what the user must not do and how to fix it.)

The problem is that humans conduct electricity. No problem if there is only one antenna, since that just makes you part of the antenna if you touch it. The problem arises when the user short circuits the gap between the two antennas by touching both sides at the same time. (That means a quick fix would be a bit of electrical tape around that corner until you get the more expensive, but better looking, plastic or rubber case mentioned in the articles.) And since MSNBC does not have a physicist in the news room ... I'll add that connecting the cell and network antennas certainly could explain the problem.

It changes the tuning of both antennas, which is bad enough, but it also means that one poor antenna is feeding two separate receiver circuits rather than each one getting its own signal. It would also short the transmitted signal from one side into the input for the other side, reducing the energy that goes out of the antenna to the cell tower. I have no clue at all what those circuits look like, but a decent impedance match could kill the outgoing signal needed to keep the "line" to the cell tower open.

I don't have one or I would do the simple experiment of shorting the gap with a potentiometer to watch what happens as the gap resistance varies.

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Lasers and Art

Interesting story about using lasers to clean artwork from the BBC this weekend.

This application (and its cousin, removing tattoos) didn't make it into Chad's laser smackdown, but it is an interesting combination of applied physics and chemistry.

What was interesting to me was that they have had to design lasers with the specific frequency needed so the energy gets deposited in the grime rather than the paint of the frescoes they are using it on, and also research the duration of the pulse so the damage is limited to the undesirable material and not the pigments or surface coating on the wall.

What struck me as really clever was using a laser underwater to do in situ cleaning of a coin in a shipwreck. It must be really useful to identify the value of an archaeological site without having to excavate a found object and bring it back to the lab.

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Laser fusion milestone

What better way to mark the 50th anniversary year of the laser than by producing a 669 kJ laser pulse (reported in Science), and then following that up with a 1 MJ pulse? (See BBC News article.)

Maybe getting it over the 1.2 MJ threshold and observing ignition of controlled thermonuclear fusion? This year?

They claim that it can be done this year, even though they did these initial experiments without the neutron shielding in place that is needed before doing that experiment because of the energetic neutrons that are produced by the d-t fusion reaction.

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Uncertain Christmas Gift

At first, this gift was in a mixed state.


It was clearly a book, and the odds favored it being a particular book, but could we know for sure without opening it?


Ah, now we know for sure ...

It is a GREAT book!

Notes added to correct a major oversight -

Link to the How to teach physics to your dog book web site. (Chad gets an extra cut if orders go through there.)

Here are the two semi-famous blogs that started it all:

• Bunnies Made of Cheese
• Many Worlds, Many Treats

Those stories are the basis for two of the chapters. Each chapter starts with a dialog with Emmy, followed by an elaboration on the science behind that idea.

Chad deserves major kudos in my view for including a final chapter that debunks much of the junk that has been written based on pseudo-quantum non-science.

Other material can be found in Chad's general category of Physics with Emmy, but that is mostly about writing (including the story of how he got the book contract) and promoting the book. So you don't have to dig through all of that for the best bits, here is the link to one that includes the slides from a talk he gave, and two movies that deserve special mention:

• The Bohr-Einstein Debates, with Puppets (*****)
• Quantum Zeno Effect: The Movie (staring Emmy)

The Bohr-Einstein Debate (with puppets) should not be watched while drinking coffee. The choice of character actors is, shall we say, priceless. But it is not just whimsy. As a long-time student of those discussions and owner of a personal library of some of the key books, I think Chad did a very good job selecting what belongs in his little play.

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Torque and Angular Momentum

Rhett Allain has a very nice blog post about angular momentum featuring the precession of a bicycle-wheel gyroscope that he demonstrates here:


I find wearing a long-sleeve shirt with shorts to be an interesting touch.

In addition to my comment on his blog, I'll add the following about how I introduce it in my classes:

Based on experience as a student and an instructor, I think it is usually best to present the prediction before doing the experiment. However, in this case I generally interleave the two.

As with most intro textbooks, mine packages angular momentum along with the cross product definition of torque in its own section so it is easy to omit completely. I integrate tau=rxF into my initial introduction of torque and the various ways of calculating it, but then stick with tau = I*alpha until I get to L.

As soon as I introduce L, I go into the generalized second law as tau = dL/dt (pretty much the way we jump from F = ma to F = dp/dt once momentum is defined). After connecting this to tau = I*alpha, I then ask "So don't you wonder if that cross product in the definition of torque is real? Is torque really perpendicular to the force?".

Then I do the demo, quickly, just enough to see the rotation.

WTF? At this point I do the detailed calculation, exactly as shown in Rhett's blog, and then REPEAT the demo. This time, however, I slip an "L" arrow onto the handle so they can see it precess.

What if I hold it by the opposite handle? What is tau now? Aha, it goes the other way!

What if L = 0? Ah, so "falling" is actually rotation in this case.

... and finally ...

What force keeps the center of mass from falling with L is not zero?

The string! Now if I could only measure the force on the string during the demo with L not zero and compare it to the force when L is zero ....

But to summarize: In this case I think they need to see a taste of the phenomenon to understand why I would bother with such a detailed calculation. It also means that I end up doing the demo itself several times, and I use the wheel with the L arrow on it when doing the drawings, since they are not yet experienced at getting a 3-D image out of two projective views. Few have had a drafting class or Calc III.

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Historic papers available on line

The Royal Society has put 60 historic papers on line for free public access. It is available here.

Franklin's paper about his experiments with lightning and Newton's with color components in white light appear to be well worth a visit.

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Must read!

Check out the new PHD Comics offering: Buzzwords!

This clearly shows the evolving importance of various research topics. By the way, a big part of the "Carbon" peak would be due to the "nano" peak: Carbon Nanotubes.

Also, anyone from my generation has to be amused to see "blog" passing "postmodern" in the post-postmodern era.

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Racing Helmets

The problem is not that of a standard inelastic collision, yet that is the essence of the problem: how to dissipate energy while conserving momentum, and how to reduce the acceleration of the head inside the helmet when the impulse being applied is not under your control. Complicating this is the need to keep the weight of the helmet down so that the helmet itself does not cause injury by increasing the forces on the neck in a crash (the problem that the HANS device helps solve as part of a coordinated systems approach to safety). More on the physics at the bottom of this article.

There is an excellent story on the Formula 1 website about the evolution of racing helmets, driven by the amazing survival of Felipe Massa after being hit in the helmet by a 1 kg spring that came off of Barrichello's car (at a closing speed of about 160 mph), although it doesn't give much credit where it is really due over the history of motorsport. The helmet they show Fangio wearing, which originated for use when playing polo, was similar to the one worn in a key death in the US that started the move toward today's safer helmets.

It was the Sports Car Club of America that was the first to require seat belts in automobile competition (1954), and it was an SCCA member who started the Snell Memorial Foundation in 1957 to provide testing for helmets used for automobile racing after the death of Pete Snell in a racing incident. Their page about the history of the organization and its current activities shows the crash that killed Pete Snell, discusses the physics of a crash, and shows the sort of testing that goes into certifying a helmet. The photo at the very bottom of this page shows a sample drop test of a helmet that tests for the sort of thing that happened to Massa.

The Massa incident was as close as it gets. Getting hit in the head by 1 kg spring at a relative velocity of about 160 mph would be fatal without a helmet even when the spring was deflected by the nose of the car and the bolster on the side of the cockpit. Even the helmet was put to the ultimate test, because the impact point was at the edge of the opening. You can see the effect in the AP photo that accompanies this news article. Higher resolution images of just his helmet and eye injury are available if you search "massa crash" on google images, but I don't recommend doing so.

The Physics

Some things about the collision of an object with a helmet are outside your control. The momentum of the incoming object is a given. The amount of momentum transferred to your head and helmet is somewhat under your control, but mostly depends on things like the angle of impact that you really can't do much about. Bouncing off (elastic collision) makes the momentum transfer worse for your head, so design can help a bit, but physics puts a lower limit on what engineering can do about this part of the problem.

The amount of momentum transferred to the helmet is what is called "impulse". You can reduce injury if the helmet or its lining is soft enough to increase the duration of the collision, thereby reducing the force applied to the head. This is also the job of seat belts and other safety systems, but only a helmet can protect you against the impact of an object or the road itself.

BTW, there isn't much that a helmet can do if something large (like a wheel) hits you at high speed. There are things that will kill you in motorsport. Based on one of Hemingway's rules, that is what makes car racing a sport. (If there is no chance that the animal you are hunting can kill you, he did not consider it a sport.)

The helmet has to provide an artificial skull, to protect your skull. (That means it has to be hard and strong, so it is the job of the lining to dissipate energy.) Even though the impact was right at the edge of the "eye socket", the helmet Massa was wearing did an amazing job. It appears that fragments from the helmet or visor injured his eye, although the damage could also result from a fracture as the helmet hit his head. That is the other thing the helmet has to do: absorb energy and redistribute the forces over the entire head. Massa's helmet just barely managed perform that task. He still had a fractured skull as well as a concussion from the forces that were applied to his head by the helmet.

Apparently he also had a fracture at the base of the skull (what killed Dale Earnhardt), which is supposed to be less likely with a HANS device. His roughly 120 mph impact with the tire barrier should not have produced this, as I understand the designs, so that might also have resulted from an unanticipated motion of the helmet from the spring impact. It also makes me worry about how the emergency people were moving him in the news photo I link to above!

And just to be clear:
Physics is not the entire story. Physics tells you the constraints of the problem. It tells you what physical principles apply and what forces MUST result from those principles under specified conditions. Engineering is the task of choosing materials that will handle those forces and dissipate energy without adding too much weight, so the forces that get to the head are within limits known from the analysis of deaths and injuries from past crashes. More will be learned from this one.

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New Element Named Cp

It is semi-official:

Now that the existence of element 112 has been certified, the discoverers have given their recommendation that it be named "copernicium", Cp, in honor of Nicolaus Copernicus.

Interesting choice.

This breaks a long string of names for trans-plutonium elements that reflect either the location of the discovery (Am, Bk, Cf, Db, Hs, Ds) or key people in the early history of nuclear physics and nuclear chemistry (Cm, Es, Fm, Lr, Rf, Sg, Bh, Mt, Rg). Until now, the exceptions were Md (101) and No (102).

I am stuck on the pronunciation. Will it be

1. koh-per-NEE-cee-em (similar to other names)

or

2. koh-PER-ni-CEE-em (to preserve some similarity to the name)

???

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