Numbers and Nature

May 11th, 2011


banana2.jpgDid you know that bananas have five sides?  Not sure?  Pick up a banana and count the sides.  Bet you there are five.

How many one- or two-petalled flowers have you ever seen?  Probably not many.  They are relatively rare in nature.  Flowers with three petals are more common, those with five petals more common still.  But flowers with four or six petals are few and far between.

What’s the deal?  The answer lies with Fibonacci.

Leonardo Fibonacci was born in Pisa, Italy, around 1170 and spent several years in Algeria with his father, a wealthy merchant.  Roman culture had spread widely in Europe by the Middle Ages and the Roman numeral system was commonly used for arithmetic.  While addition and subtraction are relatively easy with the system, anything more advanced — even multiplication or division — is difficult; the lack of zero poses a particular problem.  In Algeria, Fibonacci learned of the Hindu-Arabic numeral system and recognized the simplicity and efficiency of mathematics in this system compared to the Roman system.  He traveled throughout the Mediterranean, studying under many leading Arab mathematicians, and returned to Pisa around 1200.  The publication of his book Liber Abaci (Book of Calculation) two years later helped to popularize the Hindu-Arabic numeral system in Europe, becoming the numeral system we still use today.

In Liber Abaci, Fibonacci introduced a number sequence that solved a problem relating to the growth of a population of rabbits generation by generation assuming some idealized constraints.  This number sequence had been known to Indian mathematicians since the 6th century, but after publication of his book, it became known as the “Fibonacci sequence.”

In the Fibonacci sequence, each number is the sum of the two preceding numbers, starting with 0 and 1:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

(In mathematical terms, we can write this as Fn = Fn-1 + Fn-2, with F0 = 0 and F1 = 1.)

The amazing thing about the Fibonacci sequence (aside from rabbit populations, of course) is that numbers in the sequence occur regularly in nature.  Look at your banana again.  Five sides – a Fibonacci number.  The most common flowers have 3, 5, 13, 21 petals – again, Fibonacci numbers.

In other cases, pairs of consecutive Fibonacci numbers determine the pattern of seeds in a sunflower, fruitlets on a pineapple, or scales on a pinecone.  Let’s look at the chamomile flower as an example.


To get the most compact arrangement, the florets are arranged in a spiral pattern, and — surprise! — the number of spirals corresponds to Fibonacci numbers!  Highlighted in turquoise in the picture are the florets spiraling counterclockwise.  Count the spirals, and you get 13.  Now count the number of spirals circling in the opposite direction.  Another Fibonacci number!

The next time you have a pinecone or pineapple in hand, look for the Fibonacci numbers.  (Hint: the pineapple has three.)  Where else do you find the Fibonacci numbers in nature?  We’d love to hear from you!

Merging Art and Science

May 7th, 2011

Do you paint, write, dance, sing or sculpt?  Are you an artist who is inspired by science?  CERN may be the place for you.

The science that goes on at the laboratory has long been an inspiration for artists.  One current artist you may have heard of is Kate McAlpine, otherwise known as the rap artist Alpinekat.  She rose to fame with her hit Large Hadron Rap, which describes the Large Hadron Collider and its related science at CERN.  Check out that video and others here.

CERN, the French acronym for the European Organization for Nuclear Research, is a high-energy physics laboratory located mostly in Switzerland.  It is here that the largest accelerator in the world, the Large Hadron Collider, is located.  It spans the Swiss-French border about 330 ft (100 m) underground.  This instrument is essentially a ring, 17 mi (27 km) in circumference, consisting of a series of superconducting magnets.  The magnets serve to accelerate subatomic particles that are then smashed together in one of several detectors, each the size of a house.  The result is a spectacular computer display of brightly colored lines that look something like this:


It’s easy to see why science here can inspire artists.

Just look at the movie Angels & Demons.  Dan Brown was inspired by science at the lab when he wrote his book.  In it, the bad guys steal a canister of antimatter from a secret underground lab at CERN, and portions of the movie were filmed at the ATLAS experiment at the lab (check out the multimedia tab on the website).

Now, with ever increasing interest in merging art and science, a new experiment is taking place at CERN.  Called Great Arts for Great Science, the goal is to bring artists to the lab where they can connect with scientists and, through their art, bring science into a broader cultural setting.  And broad it is.  The gallery on the website shows examples of sculpture, music, photography, and dance.  The organization behind the project is due to Ariane Koek, a cultural specialist dedicated to arts development at CERN.  As part of the initiative, a residency program for artists at the lab is expected to launch this year, which is predicted to ease the flow of information between artists and scientists.  Artists will have the opportunity to visit the lab and talk with scientists, and support their artistic work with scientific knowledge.

But do you think this inspiration moves only from scientist to artist?  Surprisingly, the cultural exchange happens in both directions.  Great scientists often use creative thinking in solving a particularly difficult problem.  Just think of Leonardo da Vinci.  During the Renaissance, there were no strong divisions between art and science as there are today.  In spite of his work as an artist, da Vinci used his creativity to design various barricades, bridges and flying machines.  Or consider the names of the moons orbiting around Uranus.  Astronomers were inspired by the names of characters in the works of William Shakespeare and Alexander Pope.  By bringing artists to CERN, scientists will have the opportunity to tap into their artistic side and think more creatively about their projects and science in general.

As the advising scientist for Great Arts for Great Science, Michael Doser says, “Science can provide understanding, while art can provide meaning to the human enterprise.” 

By bridging art and science, we can more easily see the relevance of basic research to society and science can be allowed to engage within the larger cultural context.  There is a tight relationship between art and science in that both are ways of exploring our existence: what it means to be human and where we are in the universe.

I tend to overanalyze things. That’s why I do physics, because -unlike people- she doesn’t mind being dissected

December 13th, 2009

A story about academic debates, Twitter and the deep emotions surrounding the Global Warming debate

July 2nd, 2009


The Pew Center for Global Climate states that “the scientific community has reached a strong consensus regarding the science of global climate change. The world is undoubtedly warming, and the warming is largely the result of emissions of carbon dioxide and other greenhouse gases from human activities. “[1]

While the majority of scientists hold this opinion, some scientists question a number of aspects of the Global Warming debate. The disagreement primarily revolves around two areas: questions of the validity of climate models, and whether the fundamental causes of Global Warming are human-made or, as of yet, unknown.[2]

Regardless of how you view this debate, the prospect of our planet warming up is a huge threat to our environment and should be taken seriously. The costs of not proactively prevent and/or minimizing the warming of our planet would be catastrophic. 

Actions aside, I believe that it is worth our time to continue an open discussion about the underlying science behind this phenomenon, including the academic papers that cast doubt on some of our basic assumptions. Having worked with complex data before and sharing conversations with scientists who study climate, I know there is a reason this science is part of a field called Complex Systems: accurate results are difficult to predict. There are multiple articles questioning various aspects of the Global Warming problem[3] and some scientists such as Richard Lindzen[4] from MIT have expressed the “opposing side” of the Global Warming debate. Some researchers suggest that “Antarctica as a continent is actually getting cooler,”[5]“Glaciers are not melting all over the world; they’re growing in some places,”[6] and the observation that “there are large errors in Global Climate Predictions.”[7]  The sources of these articles are among the most reputable journals in the field of science: NatureProceedings of the National Academy of Science, and Science. If we are truly interested in discerning the underlying causes of Global Warming, it seems prudent to investigate these claims further.  While I am not claiming they are correct, I think maintaining an open mind in the pursuit of truth is the only way to arrive at the root of this complex problem.

This brings me to part two of the story. Recently, I had an interesting experience on Twitter, the acclaimed social networking medium where roughly 6 million users have real-time conversations through posts of less than 140 characters at a time. People who “follow” you can read your tweets, comment on them publically or privately, or re-tweet them to share them with their own followers. I am active on Twitter under the handle @thesciencebabe.

While using Twitter, I recently learned, just how difficult it is to communicate scientific concepts in 140 characters in real time, and, furthermore, how heated and politicized the discussion of global warming can be. Based on this experience I am concerned that we have so deeply enmeshed this topic with politics and emotion that we can no longer calmly discuss the facts. I am not an expert in the field of Global Warming, and I am conscious that views contesting the Intergovernmental Panel on Climate Change (IPCC)’s claims[8] are not ubiquitous. But why not keep the question open to a healthy debate?I believe in harnessing the power of social networks as a learning tool and as a means of fostering education. As Wikipedia demonstrates, knowledge is increasingly becoming a collective process. The Internet and Twitter are tools for enabling open debates that help increase our collective knowledge. This can only be the case, however, if we remain open to and respectful of those expressing new ideas.I find it wonderful that the climate change debate has incited social change by pushing many of us to conserve the beautiful planet we inhabit –a worthwhile endeavour regardless of Global Warming. Additionally, reducing our wasteful consumption of energy and searching for alternative energy sources is a necessary and sensible undertaking. However, I don’t want to see our social mediums become too averse to discussing the scientific facts behind an issue – even when “sensitive topics” are involved. Many times topics such as these are the ones directly in need of the kind of spirited debate social media can foster.  

Physics in the Kitchen

June 4th, 2009


Chocolate SouffleNot all science is done in labs. In fact, most of us are scientists around our house every day without even realizing it. Step into the kitchen for example. You don’t have to channel Rachael Ray if you want to be Mrs. Wizard — even the most simple culinary tasks are chock-full of science! The academics call this Molecular Gastronomy. But I call it Chemistry in the Kitchen.


Let’s say you want to bake a cake. Even if you use mix out of a box, guess what, youre running a number of science experiments! Step 1: As you add the water, egg and oil to the powdered mix you are creating what is called an emulsion — though you call it batter. Other examples of emulsions in the kitchen are mayonnaise and butter. An emulsion is a stable combination of two liquids that normally do not mix. Oil and water are famously difficult to combine, as you probably already know from the phrase “they’re like oil and water” or from endlessly shaking up your salad dressing. But, while salad dressing separates into two layers unless constantly shaken, the oil and water you add to your cake mix form a batter. Why? Well the secret ingredient — the emulsifier — is the egg.


Egg yolk contains molecules called lecithins. These molecules are rod-shaped and each end has a different property — kind of like a magnet. One end of the magnet is hydrophilic — it attracts water — while the other is hydrophobic — it repels water. The lecithins in the egg yolk pull the batter together: hydrophobic ends grab the oil; hydrophilic sides grab the water. The emulsifying egg coaxes these two stubborn liquids together into a stable batter. And there you have it: oil and water together at last, with the help of one little egg.


Ok, Step 2: time to mix. The directions on the box tell you to beat your batter for 2-3 minutes after the ingredients are combined, much longer than you might thinkWhy? Well, mixing is one form of leavening  — the process that changes your cake from a dense batter to the light and fluffy treat that comes out of the oven. Leavening works by creating gas-filled bubbles in the batter — these small gaps cause the cake to expand, and rise up in the pan. Think of a piece of cake or bread: look closely and you’ll notice that much of what you’re eating is empty space. Creating these spaces is what leavening is all about.


Mixing your cake batter is a form of mechanical leavening; other examples include creaming, beating, stirring and kneading. What you are really doing during those 2-3 minutes is physically adding air molecules to the batter. Think about how you stir a bowl of hot soup to cool it down; the motion of swirling the soup with your spoon adds air to the hot liquid. By beating your batter, you are doing the same thing: adding air molecules that will expand in the oven and create the gaps of fluffiness. If you like your cake lighter, beat it a little bit more; if you like a denser cake, beat it a little bit less. You’re the scientist, after all!


Though you aren’t adding them, your cake mix also contains chemical leaveners. You probably have some chemical leaveners in your kitchen, but you call them baking powder and baking soda. Chemical leaveners are used because they release carbon dioxide when they combine with moisture and heat. So your cake rises due to bubbles of air created mechanically and bubbles of carbon dioxide produced chemically. No wonder it is so fluffy and delicious!


Step 3:  time to bake. The instructions on the box suggest different cooking times for different baking dishes. Why? Well, heat moves through solids when atoms vibrate against each other and exchange electrons, in a process called conduction. Metals are good conductors because the electrons in their atoms are easily transferred — loose, in a way — so heat moves faster through metal than through, say, woodBecause metal conducts so well, putting your cake in a metal pan will allow the heat from the oven to move more quickly through the pan to the batter, so you can cook it for less time than in a glass or ceramic dish.


Because heat moves through conduction, each heated-up molecule transfers heat to the one next to it. So, the outside of your cake will be cooked first while the center is the last to receive the vibrations. That’s why you check the center of the cake to see if it’s doneConductive heat transfer creates texture and heat gradients in the food you cook: think of a seared steak with a juicy pink centerDo you like your cake slightly crispy on the outside and softer in the middle? Experiment with the concept of conductive heat transfer until you find the temperature, material and baking time to create your perfect cake.


Congratulations kitchen chemists — you’ve not only baked a delicious cake but dropped some major science on the way. And now for the best experiment of all: bon appétit!