When mathematicians get hungry…

Today*, obviously right after I had finished my home-cooked lunch, my labmates and I discovered some free leftover pizza in the kitchen area. While it’s a given that most people love pizza, it is even truer that academics love pizza. And mathematicians, a special breed of academics, are no exception. Their love for pizza is so pronounced that they named a mathematical theorem after it: the pizza theorem.

The pizza theorem states that if you cut a disk in a number of pieces that is divisible by for and greater than or equal to 8, you get two areas of equal size by alternating the slices of the disk. In other words: the sum of the areas of the odd-numbered sectors equals the sum of the areas of the even-numbered sectors.

If you cut a pizza like this, I will get very mad.

What it means is this: if you slice a pizza into a certain number of slices, and that number is 8, 12, 16 or 20 (other multiples of 4 are also possible, but let’s be honest, that gets pretty difficult to cut a pizza into more than 20 pieces), two people will end up eating exactly the same amount of pizza by eating alternating slices. The slicing does not have to go exactly through the center of the pizza (that’s kind of hard to do precisely), as long as all cuts go through the same point.

Here it is in shouty colors. Colors always make everything so much clearer.

The pizza-inspired math does not end there. Apparently, you can prove that if a pizza is divided unevenly, the diner who gets the most pizza actually gets the least crust – a 6-year-old’s dream!

Here’s another: a pizza sliced according to the pizza theorem can be shared equally among n/4 people (with n the number of slices). So 8 pieces can be shared equally among 2 people. 12 slices can be shared between either 2 or 3 people. 16 slices between 4 people, and 20 between 5. Good to remember for those pizza parties!


Okay, I’ll leave you with some pizza facts:

  • An approximate total area of 100 acres of pizza is eaten in the US every year. That’s about 120 football fields (the standard method of size measurements). That means that if the whole of the US was covered in pizza, it would take 2.43 million years to eat it all, considering the eating rate remained constant.
  • Depending on how you define a “pizza”, the origin of pizza might not be Italian! Ancient Greeks and Egyptians were flatbreads topped with olive oil and spices. So kind of like pizza? (Nah, not really.)
  • Another math-pizza-merger is called the lazy caterer’s sequence, a sequence that counts the maximum pieces of pizza you can obtain by a given number of straight slices.
  • In 2001, which was mostly a Pizza Hut publication stunt, the first pizza was delivered to outer space. Cosmonaut Yuri Usachov was the lucky recipient.
  • The first computer-ordered pizza was delivered in 1974. Not through the internet though; the Artifical Language Laboratory at Michigan State was testing out its “speaking computer”.
  • If you thought the fancy pizza dough spinning and throwing was just a tourist attraction, you’re not entirely right. It’s actually the best way to create a uniform disk of  dough.

Obviously, I had a slice of free pizza. You might have heard of a dessert stomach, but I also have a pizza stomach. (There was also free cake later in the day, to satisfy that dessert stomach).


* “Today” as in when I wrote the first draft.

Pizza facts from:

http://mentalfloss.com/article/69737/46-mouthwatering-facts-about-pizza and https://denirospizza.com/blog-post/facts-you-didnt-know-about-pizza/



You might have noticed how I’m a low-key (*ahem*) LEGO fan, but only if you’ve really been paying attention, and it has been quite a while since I went on a Lego-nerd rant (hm, not really).

Anyway, this 86-year-old company, named for the Danish words for “play well” (“leg” and “godt”), is not only known for its iconic building block but also for its iconic minifigure:

Decomposed LEGO figure. Image from (1)

Unlike the building block, which has remained the same for decades (in fact, a current block will still click with a 60-year-old one), the minifigure has gone through some major changes. Between 1975 and 2010, there have been at least 3655 different minifigures, and in 2000 there was an estimated total of over four billion mini Lego people! Actually, according to some predictions, the total number of minifigures will surpass that of humans next week!

And I trust Randall Munroe’s math… Image from (2)

The first minifigure (1975) didn’t even have any moving parts. It wasn’t until three years later, when the familiar yellow smiley-faced figure came out (your friendly neighborhood cop), that the arms and legs could be moved:

1978 guy (right) says: “Hands up!”
1975 guy (left) says nothing, for he has no face. Image from (3)

This was also when the Lego minifigure hand shape was developed. It is very useful for holding Lego-things. However, is very inefficient when your trying to be sarcastic…

Image result for quotation hands lego gif

Throughout the years, the figures have gotten increasingly more complex. It started with the hair (early male minifigures wore hats until the hairpiece was designed in 1979), then the accessories arrived. Hats, bags, hand-held weapons, … the whole shebang. In the meantime, the outfits got more detailed. When licensed playsets started taking off near the turn of the millennium (the first Star Wars series hit the shelves in 1999), a whole franchise originated which would include books, video games, and animation films. More series soon followed, including Harry Potter, Batman, LOTR, … the list is endless. And while the outfits and accessories became more elaborate, the faces became more – well – emotional?

Initially, there was only the blank smile. Now, Lego minifigure faces encompass all the emotions. According to a 2013 paper, there are six main types of facial expressions: disdain, confidence, concern, fear, happiness, and anger.

Scorny, Gutsy, Worry, Scardy, Happy, and Grumpy. Dopey has gone missing. Image from (1)

Happy and angry faces are the most common, with the relative proportion of happy faces decreasing over time. In short, with an increasing emotional range, Lego minifigures seem to be getting more “human.” Soon, they’ll have Myers–Briggs personality types!

Over But for now, we’ll have to do with two-faced police officers…

Over time, Hollywood movies have gotten increasingly less black and white (I do not mean the colors), with multi-dimensional characters, heroes with a dark side or villains that seem relatable, and it seems that the Lego minifigures are following suit.

In any case, Lego might be over 80 years old, and the minifigures over 40, but no matter how old you are, you are never too old to play, build or tinker with Lego!

Adult Valerie admiring the Lego store window. (Photo by Lale)



(1) Bartneck, C., Obaid, M., & Zawieska, K. (2013). Agents with faces – What can we learn from LEGO Minfigures. Proceedings of the 1st International Conference on Human-Agent Interaction, Sapporo pp. III-2-1.

(2) xkcd

(3) http://b1creative.com/blog/the-history-of-the-lego-minifigure/

Je parle très bien français quand je suis bourée (1)

An article popped up on my radar recently that caught my attention about some researchers in the UK that had performed a study looking at the foreign language skills of people after a drink or two. This interested me for a number of reasons. First of all, it’s a scientific publication about alcohol and I have to admit that always spikes my interest (but not my drink). Second of all, after spending almost a year in France (2) on an exchange program, I have experienced firsthand how my (self-perceived) language skills improve after increasing my blood alcohol percentage. However, these experiences were not only anecdotal, but also purely subjective, so I was naturally buzzed when I read that there could be a scientific basis to my observations.

And now we start the selection of general stock pictures of beer.

What’s this scientific basis you’re talking about?

In the study, the researchers measured the self-rated and observer-rated verbal skills of native German speakers who had recently started learning Dutch (3) after drinking a little bit of alcohol (or none for the control group). Basically, they recorded a number of conversations between the Dutch-speaking Germans and a blinded experimenter before and after having a drink: vodka-lemonade for the test subjects and water for the control. These recordings were then rated by native Dutch speakers. The participants were also asked to rate their own verbal skills.

Participants who had had a glass of Russian Water were rated significantly higher by the Dutch native speakers, specifically with regards to their pronunciation. Surprisingly, and against the whole principle of Dutch courage – strength or confidence gained from drinking alcohol, – there was no effect on the self-rating.

This means that the improved pronunciation cannot really be an effect of improved self-confidence, as the self-rating would change in that case. I should remember this next time I have a science stand-up comedy thing. Usually, I adhere to the rule of “no drinking before a gig” because I’ve been told that drinks make you think you’re funnier, while in reality, you are probably less funny. But perhaps my fear of becoming overconfident is completely unsubstantiated? (4)

Anyway, a possible explanation for the results is decreased language anxiety, which is the feeling of nervousness felt by someone using a second or foreign language (also known by the name xenoglossophobia, a word that already just makes me anxious as it is). Basically, when speaking a foreign language, a lot of people are scared of making mistakes or sounding stupid, making them overthink everything they want to say and eventually resulting in a strained conversation. With a bit of alcohol, there is less overthinking et voilà, better pronunciation and more fluid speaking.

Oh, I obviously have to point out that this study was conducted with low amounts of alcohol consumption. Don’t try downing half a bottle of vodka before speaking a foreign language because that will most likely result in slurred speech and a headache the day after, at the least.

Oh look another generic beer stock photo.

This almost sounds too good to be true…

As with a lot of scientific research, there are a few caveats in the study, because that’s how science works… For one, it was conducted on native German speakers who learned Dutch as a second language which means that – if we also disregard the sample size issues – the results might only be valid for German speakers who have learned Dutch, and unvalid for any other combination of native-foreign language speakers. The researchers also didn’t look at whether the subjects suddenly became better at speaking their own language after a drink; perhaps a little bit of alcohol just improves verbal skills in any language?

Also, there is some proof that people of alcohol having a placibo effect, for example, people drinking non-alcoholic beer thinking they are getting drunk without actually consuming alcohol (5). This alcohol expectancy effect could have biased the study because the difference between vodka-lemonade and water is pretty obvious, which makes me (and the researchers, who to their credit have pointed out the limitations of their study) wonder what the results would have been if the study participants had been blinded to whether there was alcohol in their drink or not (6).

And yet another foamy beer stock photo.

Final thoughts?

Well, there you go, having a little bit of alcohol might actually make you better at speaking a foreign language. Maybe it actually helps you in the learning process. But for now, I just feel like grabbing a beer. And then maybe speak some French.


(1) This translates to – pardon my French if I may misuse that phrase – “I speak French really well when I’m drunk.” I’ve also just experienced how much a pain it is to type French on a qwerty keyboard and will refrain from doing so from now on.

(2) #HumbleBrag. Well, more like a #NotSoHumbleBrag.

(3) They titled their paper “Dutch courage? Effects of acute alcohol consumption on self-ratings and observer ratings of foreign language skills” which is pretty punny.

(4) I haven’t tested this and don’t plan to. Drink responsibly people. 

(5) I definitely do not just know this from a Freaks and Geeks episode *ahem*

(6) I don’t know how hard this is to do; I for one would like to think that I’d be able to tell if a drink is alcoholic or not but on the other hand, I have had hard cider.

A fluid concept

At the moment, I am working with something called a fluidized bed. 

Which, in first instance, sounds like a water bed. So if I’m imagining what a “fluidized bed reaction” might be, if might be something this:

Though to be honest – and knowing myself – it’d probably be more like this:

But in reality, it has nothing to do with a water bed. Or with any liquid actually. A fuidized bed is when you have the right conditions to make solid particles, such as a powder or sand, behave like a fluid.

Yes, it is possible to make a solid things behave like liquid things, and in the case of a fluidized bed, this is usually achieved by running a gas (which can just be air) through. And it’s pretty fun: on a larger scale, when you “fluidize” a bath of sand, you can make things float and sink in the sand. Things like rubber ducks and toy boats, will actually float on the surface (I know what your thinking: eh, it just sits on the surface, but no!); while heavy things, like a metal ball, will just sink. The most awesome video I’ve seen so far was of people “swimming” in sand*.

The reason this happens is… science! (Yah great – very helpful, Valerie.) You might have ever seen the demo where someone levitates a ping pong ball with a hairdryer (if you haven’t, I have provided a neat lil’ gif for you). The velocity of the air is high enough to counteract gravity and suspend the ping pong ball.**

What happens in a fluidized bed reactor is pretty similar. If the gas flown through the reactor is of high enough velocity, it suspends the particles, making them interact with each other more like particles in a fluid interact with each other: free to move along each other a create a flow.

And this is quite useful for a number of different applications. By having a powder in a liquidized bed, you create a bit more space between the particles, so there is more surface exposed. This increased surface area contact between particles and gas are useful for bulk drying, chemical reactions, powder paint application, and in my case if you want to coat the particles in that powder with something.

Essentially, I get to turn powders into fluids all day. Which is pretty cool. 


 *watch it now:

** There is more going on with the ping-pong-hairdryer thing, but for the purposes of this explanation, let’s just say it’s air velocity counteracting gravity. If you do want to find out what’s going on, you can read about it here.

Murder, she wrote

Don’t worry, I won’t get all creepy on you, I just thought* I’d write a #FunFactoids post about crows…

1. A group of crows is called “a murder”

(Ah, the title makes so much sense now!)

Since you’ve probably heard about a murder of crows, I’ll hit you with some other strange groups-of-animal names. Have you ever encountered a cauldron of bats? Or a tower of giraffes? You better get your business straight when you run into a business of ferrets, and pray you never run into a mob of kangaroos. That conspiracy of lemurs is most definitely going to conspire against you, and I hope your not afraid of storms because there is a thunder of hippopotamuses on its way. Okay, I am getting carried away, you can probably just click here and read through the list yourself so I can get back to this murder…

This crow’s got murder on his mind. And arson.

2. How to recognize a crow: if you see a black bird and it’s larger than a pigeon, it’s a crow. Well, it might be a raven. This is not helpful.

Recognizing birds can be tricky. Not all black, menacing birds are crows, though there are some tricks you can use to recognize one. Crows are black (duh). If the bird you’ve spotted** is smaller than a pigeon, you are probably not looking at a crow but at a blackbird (Turdus merula), though only if you’re in Eurasia.

To tell a crow from a raven, check if they have any murderous friends with them; ravens typically travel in pairs while crows like to be in large groups. Their tail also has a slightly different shape (wedge vs fan respectively). The best clue – probably – is to listen: the raven will often be heard reciting Edgar Allen Poe Poems.

In all seriousness, the names crow and raven are actually arbitrary, not very scientific, and region-specific. In America, the common raven (Corvus corax) refers to a pretty large bird that sounds super croaky, travels with only one other friend, and looks like it’s a familiar to some witch. The smaller black bird, and the topic of this blog, would be the Americal Crow (Corvus brachyrhynchos) and they like other tunes…

Crows are secreatly tune-connaiseurs.

3. Crows are songbirds

Depending on your taste of music – maybe you do enjoy the raw voice of a heavy smoker – it might not seem obvious that birds of the Corvus genus are  part of the Passeri suborder, also known as songbirds. I learned today that the classification “songbird” is not based on the quality of a bird’s tune, but on their anatomy. Songbirds have a syrinx – or song box – which is a specific bony organ in the windpipe of a bird and causes vibrations when air passes through, causing vocalization. Not all songbirds actually sing, let alone sing melodically. In any case, crows are wonderful singers (ahem)

Poor crow. Stand-up comedy is hard you know.

4. Crows are very social animals and have a strong sense of family

Young crows have often been seen helping take care of their younger siblings, by defending the nest from predators or finding food for their lil’ bros and sisters. In addition, crows show some pretty strange behavior when a crow dies, congregating in masses (or as one might say, in murders) around the dead animal but never touching it, seemingly holding some kind of funeral.

They also like grouping together for other reasons, like throwing crow parties (I’ve heard they’re #lit) or just to hang out and laugh about how weird humans are.

Don’t choke on your coffee, crow.

5. Crows are super smart, perhaps smarter than you*** 

Some types of crows have brains that are proportionally bigger than human brains: their brain accounts for ~ 2.7% of a crow’s overall weight, compared to ~1.9% brain-to-body mass in humans. Though (proportional) brain size is not directly an indication of intelligence, there are several examples of how crows are pretty nifty.

For example, crows are known to build tools to help them get to their food, including making prods, poles, scoops, and hooks out of leaves and twigs. Researchers actually think that the crow’s beak has evolved to its shape (sharper and straighter than one would expect for their diet) to better hold and use tools.

Crows have also been seen taking advantage of passing cars to crack open nuts, and they don’t even jaywalk in the process*****. They wait for a red light, place the nut on the road, get out of the way by the time the light turns green and go get the nut during the next red light. 

If that wasn’t impressive enough, crows can remember the faces of people that have annoyed them in the past. They even tell their murder-friends, and all gang up to caw at their enemies. They definitely hold a grudge and pass it on to the next generations. Better give them the respect they deserve, or you’ll never be safe.

You should listen, rabbit, or you’ll be haunted by murderous caws for the rest of you life.

And so, that concludes the oh-so-original-list-format blog on crow factoids. By the way, she (I) wrote “murder” exactly 10 times.


Webcomics shown here are from falseknees.com who does these really quirky comics about various birds.
Factoids loosely based on this article, Wikipedia, and sort of random google searches – lazy referencing 101.


*This thought has nothing to do with recently having watched The Vile Village, an episode of A Series of Unfortunate Events, which takes place in VFD – Village of Fowl Devotees. Basically, a village of weirdos that have a weird devotion to crows. No, the inspiration for this post should be credited to A., who is giving me a ton of ideas of stuff to blog about, almost annoyingly so.

** Out of context this sentence fragment sounds like a 1950s guide for approaching a lady.

*** I in no way am implying that you, my dear reader, or not smart! Also, thank you for being super awesome and reading my blog and please keep reading and I’m sorry if I have offended you in any way and you personally are definitely a lot smarter than a dumb little crow!****

**** No offence meant to crows. In case any of them are reading. (Footnote-within-a-footnote, how Prachett of me).  

***** Eeeey, check out that bird joke. It’s especially good because jays are part of the Corvus/crow family!

I apologize for the out of hand footnotes. 

How to write better in 280 characters or less

I wrote a post for the Marie Curie Alumni Association blog about effectively communicating in 280-characters-or-less (you can find it here) and may I just point out how I managed to write my biography in 280-characters-or-less and how this makes me secretly very proud?

Yes, I may, and have done just that.

Note but mostly a reminder to myself: this does not count as your weekly blog post, you lazy bum!

In the spotlight: Juana Inés de la Cruz

Since I first gained the use of reason my inclination toward learning has been so violent and strong that neither the scoldings of other people … nor my own reflections … have been able to stop me from following this natural impulse that God gave me. He alone must know why; and He knows too that I have begged him to take away the light of my understanding, leaving only enough for me to keep His law, for anything else is excessive in a woman, according to some people. And others say it is even harmful. 

I read this quote in Contact by Carl Sagan. It was written by Juana Inés de la Cruz in her Reply to the Bishop of Puebla in 1691. The Bishop had attacked her scholarly work as being inappropriate for a woman; while he claimed to agree with her views, he didn’t think them appropriate for her sex. Rather than writing, she should devote her life to prayer, an endeavor much more suitable for a woman.

Aargh. 17th century clergymen are just the worst.

We’d better talk about this amazing woman then:

Juana Inés de la Cruz lived in (what was then New Spain but what is now) Mexico in the 17th century and was a self-taught polyglot (my favorite type of inspirational people). She studied scientific thought and philosophy, she was a composer and a poet, all in an age long before women were allowed to do anything involving using their brain. 

If we may believe the stories, Juana started teaching herself at a young age by hiding to read her grandfather’s books. She supposedly learned how to read and write Latin at the age of three. At the age of 16 she had asked her mother’s permission to disguise herself as a man so she could study in some avant la lettre version of She’s the Man; but her mom wouldn’t let her so she had to continue to study in secret. But by then, she already knew Latin, Greek, Nahuatl, and accounting – the most important language of them all *ahem*.

In 1669, she became a Hieronymite nun so she could study in freedom – other monasteries were a lot more strict and wouldn’t allow her to pursue her passion for knowledge, philosophy, and writing. As a nun, she would write on the topics of religion, feminism, and love; often criticizing the hypocrisy of men and defending women’s right to education. In Reply to Sister Philotea, she wrote:

Oh, how much harm would be avoided in our country [if women were able to teach women in order to avoid the danger of male teachers in intimate setting with young female students.]

[Such hazards] would be eliminated if there were older women of learning, as Saint Paul desires, and instructions were passed down from one group to another, as in the case with needlework and other traditional activities.

Okay, now I’m imagining needlework maps of our universe. That’d be cool.

Unfortunately, this story has an unhappy ending. According to some sources, rather than being censored by the church, Sister Juana decided to stop writing and sell all her books, musical instruments, and scientific tools. Other sources claim that her belongings were confiscated by the bishop due to her defiance towards the church. Nevertheless, a lot of her writings have gone lost and soon later, in 1695, after caring for other nuns with the plague. 

There’s a lot of humdrum about inspirational women, in science or not, nowadays. With a lot of books with inspiring stories, such as Rachel Ignotofsky’s Woman in Science, finding empowering role models has never been easier. And I love it. Showing an as diverse possible range of inspirational historical figures provides everyone with role models than can identify with and aspire to. However, I have noticed that my knowledge of inspirational women is primarily European-based. So this is me trying to change that.  

“One can perfectly well philosophize while cooking supper.” – Multitasking 101


Soucre: ye old trustworthy