Math Games

Willa's Math Game

It’s going to be 2 in a row with regards to the kid-science connection, and for that I am totally not sorry.


My daughters are now 6 and 3, and both of them are really into math. There are a ton of free-ish web based math games out there, but they tend to include limits on the number of problems, pop-up ads, or simply aren’t very flexible.  Instead of dealing with all of that, I decided to write my own customizable javascript game for my older daughter, Willa:

It’s pretty simple.  Kids can chose from Addition, Subtraction, Multiplication, Division, Fractions, or Series, and there’s a slider to set the difficulty level.  The code then randomly generates a problem at the appropriate difficulty level.  Kids get two chances, and if they’re correct, they get a star, and if they’re wrong they get a sad face.  After more than 10 correct answers, there’s a random chance of generating a “prize” (in Willa’s case, these include fairy coloring pages, mazes, and the like.)

I’ve found that her cousins, friends, and even her little sister are totally into the game, and can absolutely stay engaged enough to win a prize or two. It’s excellent practice, and surprisingly engaging for what are, essentially, flash cards.

The background is generated by some of Willa’s own artwork, which may not be all that exciting for your kids, which is why I developed a “gamemaker” page:


You can put in your kid’s name, a URL for his/her artwork or something they like for the background, and a few “prize” pages, and poof! we generate a shortened URL for their personalized math page.

Please do try it out, and be sure to share it with friends.  If you have any suggestions, please feel free to leave them in the comments below.

– Dave 


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Kid Science

As you may know, I’m a theorist, which means that my lab generally consists of some grad students and me sitting at computers or a white board. But as I’ve got kids to think about (my oldest, Willa, is now 6), I’ve started stocking up on optics kits, and home telescopes and the like.

My most recent toy was a very reasonable digital microscope, and I decided to inaugurate it by having Willa do a little scientific inquiry.  What would look cool (or gross) magnified up to 250x?  Willa’s selections are below, including 1 or 2 which might also serve as indictments of my parenting.

Her mama’s engagement ring:



The back of her hand:



An extreme closeup of a drawing of a flower:



An actual flower petal:



Her almost completely unused napkin:



Kosher salt:



Her shamefully disgusting fingernail:



It’s just a friendly reminder to try to see the natural world through the eyes of a kid.


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A Physicist Plays Politics: Part III

election_widgetHey gang!  It’s been a while, so let’s just jump in, shall we?

Every now and again (every four years, apparently) the obsessive statistical monster in me lashes out, and I start thinking obsessively about polls.  Full disclosure: while I’m a bleeding heart liberal through and through, I’m mostly motivated by how well polls and other forecasting approaches are able to predict the future; there’s nothing partisan about my approach (though perhaps something partisan in how I react viscerally to it). I should also warn you ahead of time, that there’s a fair amount of weeds-adjacent wonkiness, so if you simply want to click on the picture above and play with the sliders, I wouldn’t blame you. That is the nature of the “technical” tag.

The Widget

I’ve created an awesome new election widget at:

You can see a snapshot of it at the top of the page.  It’s dynamically connected to a database which I keep synced with polling averages from the Huffington Post Pollster, a weighted estimate of statewide and national polling. I like Pollster because it weights by sampling size and has a smooth window for inclusion.

The widget allows you to make whatever assumptions you like about the systematic biases in polling in general, or about the amount of polling error, and the probabilities for each state adjust automatically.  States with more than a 10% probability for either candidate are considered “tossups” (admittedly, that part is a bit arbitrary). A scrollover on the map will give you some useful information like electoral votes, the 2012 outcome, and what the current statewide polling says.

Knowing nothing else, I assume that 2016 will bear at least some resemblance to 2012. I therefore use as my starting point that state margins will be the same as in 2012, but corrected for whatever the national trend is. That is, if Clinton leads Trump by 7% in national polls, but Obama only led Romney at this point in time by 3%, then each state gets a 4% bump in the Democratic direction. Only a few states have polling at this time. For the moment I’m using the Real Clear Politics averages, but will move to Pollster once they start posting aggregates after the conventions. I’m only putting 50% confidence in state polls (also admittedly arbitrary), even if it exists, and am averaging with the national trends. Many polls are still small sample sizes, and vary wildly later in the cycle.

Some might argue that this entire project is a little premature as neither party is actually done selecting their candidate. I would disagree strongly on the Democratic side (where Sanders has run a great campaign, but would be required to win many states with large margins that he currently trails by double digits in the polls). Though the Republican side is a little less settled, Trump is currently the strong favorite, and the one whose candidacy is keeping me up nights. If I turn out to be wrong in either case, it’s easy enough to swap in two new candidates. Three, on the other hand, would be pretty unpredictable.

Random Errors and Outliers

How good are the polls?

Short answer: Collectively, they’re pretty damn good.

While my widget allows for setting random measurement errors or a systematic bias, it’s not self-evident how those numbers should be set or even if polling predictions are normally distributed.  If polls followed a normal or Gaussian distribution, we’d expect that about 68% of the time, the true state outcome would be within 1 \sigma (the standard distribution) of the polled value, and 95% of the time, within 2 \sigma.

To investigate, I looked at the results of the 2008 and 2012 presidential elections (data here).  I didn’t compare every state.  In 2012, Romney won Utah by 48 points, and Obama won Washington DC by 83! There would have been little use in extensively polling either, since the outcomes were never in dispute.  Instead, I’m focusing on the states which most closely mirror the national outcome.  That is, Obama won the national vote by 3.90% in 2012.  He won Virginia by 3.87%, making it the closest bellwether of the states as a whole.  I sorted by deviation from the national average and then took the top 23 states (after which the polling got sparse) and compared them to the Pollster averages leading up to the election:

2012_scatterBy visual inspection, the average of polls did a pretty good job.  To quantify this somewhat, I made a histogram of the true versus the polled result:

2012_histogramEven the worst polled states only missed by a few percent. To give you a sense of the distribution:

  • 2008
    • 0.7% bias for McCain (That is, Obama did slightly better than expected)
    • 2.5% random error by state
  • 2012
    • 1.9% bias for Romney
    • 2.3% random error by state

The average of polls, especially in competitive states was a very good estimate of the final outcome. I wouldn’t read overly into the very slight Republican bias in the polling, but note the relatively small scale.

Finally, there’s the question of outliers. For 40 or so state results (over 2 elections), we’d expect approximately two “2-\sigma” results assuming a Gaussian distribution. Instead, there was only 1 (New Mexico in 2008). The statistical distribution of errors seems to be more or less Gaussian.

Yes, the polling could be very off in this cycle because of how unusual the election is, but given the Obama candidacy in 2008 and the hitherto unknown effect that race might have the on the race, it seems strange that the pollsters could have gotten it so right back then, but not this time.

The World of Prediction

These days, there’s a whole cottage industry around trying predict exactly what will happen on election day in every state.  And with due respect to Nate Silver at 538, Sam Wang at the Princeton Election Consortium or even my dear friends Rich Gott and Wes Colley there’s a degree to which trying to predict each state with certainty smacks of trying to retroactively get the 2000 election right.

There’s an important question here. If an algorithm suggests that there’s a 55/45 chance of a state going to, say, Clinton over Trump, does it really make sense to make a prediction.  To be fair to Silver and Wang, they do give confidence estimates, but the reality is that people tend to focus only on the bottom line predicted winner.

Rather, I think the most important question is: who will be the next president and (to a much lesser degree) will she/he win by a large enough margin to have real coattails and or claim a mandate?


Time Variation

There’s something almost pathological about posting the odds this far out.  One thing that I haven’t really included is the variability between now and the election as the pictures of the candidates crystallize in the minds of the electorate (though the bias slider allows you to explore that manually).  I will say that both Clinton and Trump have been national figures with enormous media attention for a very long time, so perhaps people’s views are already settled.  On the other hand, based especially on the Republican primary and initial signs from the general, this promises to be a particularly nasty election.  Opinions may swing dramatically.

In either case, I’ll close with a little more historical data.  At this point in 2012, Obama led Romney nationally by 3.3% in the Pollster average.  That gap was 1.5% by the end, with Romney never leading past this point, and with a maximum gap of only 4.2%.  Obama, as I’ve noted, won the national vote by 3.9%.  In other words, in 2012, the March snapshot told you almost everything you needed to know about the final state of the race.

On the other hand, at this point in 2008, Obama and McCain were statistically tied, but Obama led consistently after that, with the exception of a few days in August after the initial excitement about Palin’s nomination as VP.

There are some comparisons to be made with the 2008 race with this one.  By March of 2008, Clinton and Obama were still in a tight race, with Obama up by about 100 delegates.  Clinton didn’t concede the nomination until June 7 of that year.  Clinton has a much larger lead over Sanders (about 300 delegates) than Obama did at a similar point in the 2008 nominating contest, so an argument could be made that the candidates are more settled at this point than in 2008 at the same point. Regardless, Obama held a typical lead of about 5%, with a final polling advantage of 7.6%.  Obama won the actual popular vote by 7.3%.

Even in 2008, a year which saw the first female Republican VP candidate, the first African-American presidential candidate and president, a huge upheaval in the stock market, and much else, the variation in the polling at this point was considerably less than 10 points. I wouldn’t bet the farm, but a Clinton win in November looks very, very likely.  Incidentally, the electronic futures markets agree.  At present, the Iowa Electronic Markets give the Democrats a 70-30 chance of winning the election.

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Podcast Appearances

Just a quicky. I’ve been doing a lot of podcasts lately, and I’d hate for you to miss them, especially since they have run the gamut from mind-bending to absurdist. I’ll post them as they come up, but over the last few weeks, we’ve had:



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I’m thrilled to announce that my most recent book, “The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality” has been shortlisted for the Phi Beta Kappa Science Book Award.

This is extremely competitive and very exciting. Past winners have included Nate Silver’s “The Signal and the Noise,” Neal Subhin’s “Your Inner Fish” (which features Drexel’s own Ken Lacovara), Briane Greene’s “The Elegant Universe,” and Jared Diamond’s “Guns, Germs, and Steel” (which also won the Pulitzer). We’ll find out the winner in early October, and should I win, there’s a gala in Washington in December.

In the meanwhile, please do show the other excellent shortlisted books some love:


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On Raising Daughters

She wants to be just like me!
This morning, over breakfast, I asked my 4 1/2 year old daughter if she wanted to see something cool. I showed her a news story about Maryam Mirzakhani, the Stanford Mathematician who is first woman to win the prestigious Fields Medal. Willa, my daughter, has only a cursory grasp of the world of higher learning, so I explained it to her (and with no disrespect meant to the other 3 laureates) by saying that Mirzakhani is the “best in the world in math,” (immediately followed by a ‘kids say the darnedest things’ moment when Willa replied, “I thought you were.”)

It’s incredibly important to me that Willa and her little sister, Lily, see prominent women in the sciences, but I struggle with trying to achieve a balance between “Of course there are lots of outstanding women scientists (and so it’ll be no problem for you to join their ranks),” and “There are still too few women in science (and I want you to break down some barriers).” I’ve gone with approach #1, because society is going to give them the latter all on its own.

Despite the progressiveness of their parents, Willa and Lily are awash in “traditional” examples of gender roles. Willa’s doctor is a man; the nurses are all women. I work outside of the home, while, for now, my wife, Emily, (an excellent Speech Language Pathologist, by the way) stays at home with Lily. The issue isn’t that we’re setting a bad example with how we’ve set up our home, but rather, that smart kids tend to extrapolate from what they see around them.

Willa doesn’t have to be a scientist, but it’s important that she decide to be a scientist (or a musician, or a shoemaker, or whatever) based on her preferences and abilities, not because she’s internalized the idea that certain roles are for certain genders. While I’m trying not to princess shame her, I’ve looked on with unease as Willa picks Elsa, Ariel, and Sofia the First as her role models. The heart wants what it wants, I suppose. We’ve at very least tried to mitigate things by pointing to bravery and kindness as the defining qualities of princesses, rather than beauty (and in a fair bit of subversion, we give her the option of having princesses marry other princesses in her fairy tales).

To some degree, we end up cherry-picking examples to give Willa a deliberately skewed state of affairs. We focus on Mirzakhani or Emmy Noether, or the occasional female doctor who sees Willa at the doctor’s office. The hope is that in 10 or 20 years, these won’t be the exceptions, but for now, the societal messaging produces awfully lopsided results. The most recent report from the American Institute of Physics, for instance, shows that only 14% of physics and astronomy faculty are women. The numbers are similar for women in undergraduate physics programs. This last year — and only through fairly Herculean efforts — we were thrilled to have an enrollment at Drexel that was slightly less lopsided, about 30% women. We still have a long way to achieve anything like real gender equity in most sciences.*

Right now, I’m operating in a very limited realm. I’m trying to give my daughters a sense of the possibilities in the world around them. This is, in some sense, just a stalling maneuver while I hope for (and try to help) the world to catch up. It’s dismal and disturbing that primitive attitudes prevail among some in my and the older generation. But I’m hoping that every positive example I show to my girls moves us one step closer to the world I’d like them to live in.


* It is a sad thought that both Emily and I were raised on Free to be…You and Me in the 70’s and early 80’s which, of course, preached the same message. Gender equality seemed pretty close at the time, but it’s not obvious that we’ve made that much progress since then.

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The 1st floor table at Barnes and Noble in Rittenhouse, yesterday.

Exciting news! The Universe in the Rearview Mirror is out in paperback as of yesterday! There will be a bunch of new interviews and columns, beginning today with a new “Ask a Physicist” on Emmy Noether.

I’m always looking for new questions, so by all means give me your best. As a reminder, topical is good, but not necessary. They should be broadly interesting, ideally quirky, and if they have a sci-fi tie-in, so much the better.

I also got word from my publisher yesterday that we’ve sold the Polish rights to Prozynski. They’re the same publishers who brought you this beauty:

Finally, a personal note. I have just been appointed associate dean for science research and graduate education for my college for the next few years. Just in case you were concerned that I wasn’t an actual scientist, but rather some raving lunatic in his garage.


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Ask a Physicist is back, baby!

After an unacceptably long hiatus, I’m back with new “Ask a Physicist” columns over at io9. Today, I have a piece up about PeV neutrinos, and tomorrow I’ll be doing one on Emmy Noether. Thereafter, I’ll be posting a bit more regularly, and I’m need of some good questions.

So send me some.

Send me some now.

Oh, and in case you were one of the three people who missed it, Annalee Newitz (io9’s editor in chief) broke the internet the other day when she interviewed various scientists about misused ideas in science. I contributed “Theory” and “Quantum Weirdness.” Check out the other entries as well.


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Arbitrary Rankings Corner: The Best of Sci-Fi

I got a fun email a few days ago from Time Out magazine. They’re asking contacting a bunch of writers, artists, and scientists including such luminaries as George R R Martin and, er, myself, and asking us for our top 10 science fiction films of all time. From this, they’ll compile a top 100. They left it to us to determine our own definition of sci fi. Here’s the one I went with.

For me, science fiction includes any film that uses either extragalactic life or as yet unknown technology to forward the plot, whether or not either element is at the heart the film. To be truly great sci-fi, I feel as though the internal rules of the world need to be well-established and most importantly, self-consistent. So, for example, “Back to the Future,” while a great movie, is a mess in terms of self-consistency of the time travel rules.

My list is, I think, diverse enough where it would be tough to rank them, so I’ve simply listed them chronologically. I will note that for my money, Terminator is the most outstandingly self-consistent time travel narrative out there (if you’re looking to have a “best of breed” for different types of sci-fi).

  • Planet of the Apes (1968)
  • Fantastic Planet (1973)
  • Empire Strikes Back (1980)
  • ET (1982)
  • Bladerunner (1982)
  • Terminator (1984)
  • 12 Monkeys (1995)
  • Wall-E (2008)
  • Inception (2010)
  • Her (2013)

In writing this, I was reminded of some of the goofier stuff that Jeff and I included in A User’s Guide to the Universe. In particular, our recap of the failings of sci-fi television:

and our “two-sentence time-travel summaries”:

which, continuing onto the next page reads, “Timecop (1994) (no stars). In 2004, time travel is illegal. Jean-Claude Van Damme is (predictably) a time cop who saves his (supposedly) dead wife’s life without changing the timeline.”

Feel free to comment on how I’ve entirely missed the point of science fiction.


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What should a physics major know?

It’s summer. In academia, it’s a time to get some real research done, take a little R&R with ones family, perhaps wait in breathless anticipation of the paperback release of ones book, and most relevant to today’s discussion, to think about the successes and failures of the previous year.

In addition to my regular duties as a professor, I am also the director of Drexel’s undergraduate Physics program. Each year I have the opportunity to meet with prospective students and parents, guide admissions and curricular policies, and keep an eye on our students to see how they’re doing and where they’re going. And for the most part, our students do great things and go on to great places. For many of them, going on to do great things doesn’t necessarily mean that they go on to be physicists.

Oftentimes, when asked to talk about the value of a physics degree, I focus on how a physicist can do just about anything: finance, engineering, computing, medical school. But these outcomes suggest that the degree that many students actually go to school for — Physics — serves as nothing more than a testament to the fact that they can survive a challenging environment. We could, I suppose, simply take the view that it doesn’t matter whether they go into physics. Research skills, programming, electronic design, data analysis, mathematical rigor and so forth are useful skills for everybody. Certainly, there is a national push for so-called STEM education, and a very real recognition that these skills make a graduate employable.

I think that physics should go beyond an elite STEM accreditation field. The degree matters, even for those students (most of them, actually) who don’t go on to become physicists. They should learn what the state of the science is; they should be prepared to interpret for the world at large, to bring science and subject-specific literacy into their and others’ lives. And what else?

I have a few thoughts on that.

  1. Physics education should not be “engineering light.”

    Let’s start with the introductory sequences. Pick up just about any high school or calculus-based college textbook and you’ll see physics presented in almost the exact order it was discovered. (As a sidenote, you’ll also see virtually identical tables of contents, making it particularly easy for lazy instructors who don’t want to alter their lecture notes one whit to change textbooks without doing any additional work.)

    Generally, there’s a first term in 17th century physics (Newton’s laws), and a second term on 19th century physics (electromagnetism), while a truly excellent teacher might spend a week or two at the end on the more esoteric chapters from the early 20th century (relativity up to E=mc^2 or quantum mechanics up to a vague description of the double-slit experiment). Anything more sophisticated than the bank of a racetrack or the trajectory of a basketball is generally ignored. Speeds above a few hundred mph are generally considered “fast.” This, while we have accelerators capable of accelerating protons to within a few parts in a billion of the speed of light.

    These texts are written with the assumption that everyone reading them is going to be an engineer. The fact that future politicians might also be dozing in the audience is generally of only passing concern (a concern typically dealt with by putting a volcano or a bullet train on the cover ostensibly to jazz things up). This means that the T and the E in STEM get virtually all of the attention, and assumes that the S will simply take care of itself. There seems to be a societal shift away from interest in “basic science,” with the assumption that anything that’s not immediately applicable to technology is simple navel-gazing.

    Introductory physics, at least for majors, but ideally for everybody else, should ideally talk about what’s going on today, with an absolutely minimal focus on pulleys and blocks on planes. Drexel’s intro sequence, we use the (imperfect, but innovative) Matter and Interaction, by Chabay and Sherwood, which focuses on 20th and 21st century physics from the outset.

  2. Most majors aren’t going to be Physicists.

    This is okay. It doesn’t represent a failure on the part of physics educators (though perhaps I’m being too forgiving to myself), but a reality of both people’s interests as well as the job market.

    We’ve always known that students are likely to go into other fields, and we’ve treated that as an excuse to make to sure that they have lots of other skills. While I’m not arguing that we should forgo general education requirements (the etymology of University stems from Unversis meaning “whole” or “entire,” from a desire to have a universal education — a sentiment with which I wholly agree), it’s worth considering that for most physics majors, this is the end of the road, all of the physics that they’re going to see.

    Degree programs that focus only on solving electric fields for configurations of charges or deriving Hamilton’s equations give students the tools of physics, but not the basis. This term I taught a “Standard Model” course for the first time. This was an advanced class officially listed for grad students, but open to undergrads which explored the basis for E&M, the weak and strong forces, open questions with regards to neutrinos, and so on, without requiring Quantum Field Theory. It was literally the most fun I’ve ever had teaching a course, and the students seemed to have a ball as well.

    The more I think about it, the more I think that this is exactly the sort of course that should be required at the advanced undergraduate level. If the BS really is the terminal degree for most of our majors, then by the time they finish, they need to really see how everything fits together. And yet, courses like this seem to be the anomaly. I was only able to cobble together the course from various Classical Field, QFT, and Particle Physics textbooks, even though we were, in essence, justifying the study of just about everything else they’d seen.

    In order to make a coherent (or semi-coherent) whole, I put together a set of ever-evolving course notes with the long-term goal to turn them into a textbook. If you’d like, please check them out, and be sure to send me any corrections and comments you might have. (Please be kind.)

  3. “Physicist” doesn’t just mean one thing.

    It never did, of course. There is an enormous push for “interdisciplinary” research and academic programs at the university level, and you’ll find few people as skeptical as me. Oftentimes, the push is made at the institutional level so that individual researchers will be eligible for federal grants that they might not be otherwise, occasionally at the cost of focus on disciplinary areas of research.

    That said, the boundaries between basic research in condensed matter and applied research in materials engineering is a narrow one, as are the boundaries between biophysics and biomedical engineering, biochemistry (and several other fields). A graduate of physics can be a physicist without following the same career trajectory as even a generation ago. One approach that we take (which, admittedly, is a bit ad hoc) is to allow a much more a la carte approach to completing the degree outside of the essentials (which I’ve taken a stab at above). Physics is far too large to imagine a degree focused around course subfields or core methodologies (theorist? computational “experimentalist”? instrumentalist? You’re all physicist here.)

    That said, I’d like to issue an unresolved word of caution. It’s very easy to suppose that there are no boundaries between disciplines and that a student with a particular career trajectory should simply pick and choose. Beyond the question of whether an 18 or 20 year-old is prepared to map out their future in that way, it’s worth remembering that undergraduate degrees are not a professional degree. Also, that even within those permeable membranes, there’s a lot about physics that is physics, and nothing else. And while I’d like to be able to offer a rigorous definition of what defines a physicist for the next generation, I’m afraid I’m left with Justice Stewart’s definition: “I know it when I see it.”

    Hopefully, some of you can do better.


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