Cutting down: Postdocs and Investors

As I said before, Harvard lost a lot of money, $8Billions, to be exact. Hiring is frozen everywhere, impacting postdocs whose contracts are year-to-year.  I’m optimistic that the grants we have written will get funded; I like it here, except the horrible weather, and don’t want to leave yet.

Now, Harvard fires the people that managed the endowment.

Harvard University said today that it’s cutting about a quarter of the staff — or about 50 jobs — from the company that manages its endowment after the fund tumbled $8 billion in four months.

The estimated 22 percent decline, by far the largest in higher education, was the sharpest drop in the endowment’s history. The fund was valued June 30 at $36.9 billion before falling to $28.7 billion by October.

The university is projecting the endowment will decline by a total of 30 percent by the end of the fiscal year in June.

Quantum Superposition: An Analogy with a pig, a chicken and no cats

Quantum superposition is one of the most difficult concepts to understand in all physics. It lies at the heart of what makes quantum mechanics so counter intuitive. I find myself always saying things like “It is in both states at the same time, until you look at it, and then it is only one thing.”, which sounds like pure hocus-pocus. It is not. I plan to have a mathematical description of quantum superposition, but decided for now to start with a simple analogy.

A quantum state is a mathematical representation of a physical property. The act of determining the physical property is called a measurement, that is, “looking” at the state to determine what it is. Quantum mechanics allows for a simple mathematical way to describe both the state, and the outcome of the measurement. The price for this mathematical simplicity is a conceptual inconsistency in the physical description of the object.

Thus, the quantum state can have two incompatible physical properties simultaneously, while when the state is actually measured, only one of them physical properties is measured, either one, it is determined by chance. Now, the analogy.

I cannot stress enough how this is an analogy, a mnemonic device if you will. This is not the full story of what quantum superposition is, just something to wet your appetite.

Think of the quantum state as a wireframe cube, that is, a simple drawing of a cube in paper, like the cube on the left side of the image.

The cube on the right is a 2D representation of a 3D object. Our brain can interpret it in different ways, incompatible with each other.
The cube on the left is a 2D representation of a 3D object. Our brain can interpret it in different ways, incompatible with each other, as shown in the right side of the diagram.

The cube on the left side is not really a cube at all! It is just a 2D representation of a 3D object. However, our brain likes to interpret it as a 3D object, a real thing. The drawings on the right serve as suggestions of possible ways our brain could interpret the 2D image. For example, we could imagine it as a box, I decided to put a little pig on top of it. You can see how a box like is perfectly consistent with the 2D image on the left. Likewise, the 2D image could be seen as a corner, like the corner of a room. I used a chicken to help you visualize this interpretation, that is also consistent with the 2D image.

However, altough the diagram with the pig and the one with the chicken are both compatible with the 2D wireframe, they are incompatible with each other! Your brain can visualize the 2D wireframe as a Box, or as a Corner, maybe even switch between both visualizations, but not have them both at the same time.

The analogy is complete now. The 2D image is the quantum states, in a sense it can be said to contain many choices of 3D visualizations within it. A quantum measurement is then analogous to the limitations our brain demand of the image following the laws of perspective. Only one interpretation at a time is allowed by the brain, just like the quantum state can show only one physical property of the two incompatible physical properties at a time.

The analogy breaks in several ways, I’ll point one. Although our brain has some control of the 3D image it decides to see out of the 2D object, there is no such control in quantum superposition. The measured physical property that is seen is chosen at random from the incompatible options. Quantum superposition does not in any way mean that our brain gets to chose what physical reality is, but it does stresses the fundamental probabilistic nature of reality.

Remember, superposition means that two incompatible properties can exist simultaneously, without any inconsistency.


If you try to fail and succeed, which one have you done?

Outreach: Back to La Iupi

I just came back from Puerto Rico, into the Bostonian winter.

Although I had a very brief opportunity to see my people back home, the main purpose of the trip was work. Several young professors from the Chemistry and Chemical Biology department at Harvard have started an effort to outreach, but for real. The main purpose of the program is to visit universities with a big population of under-represented minorities. I proposed to go to Universidad de Puerto Rico, Rio Piedras. I still have many friends there, and it was very good to see again so many professors that gave me many opportunities as an undergrad to grow as a researcher. Without their support, I wouldn’t be a physicist now.

The outreach activity was very successful. The people at the Resource Center for Science and Engineering did an amazing job of coordinating the activity. We were able to talk to many researchers there, and spent a good day with many talented science undergraduate students from all around the island. I’m sure new collaborations will grow from this.

To see information about many undergraduate research programs and how to apply, click here.

To read about graduate school at Harvard, click here.

To see pictures of the event, click here.

DisCover: Quantum rules Photosynthesis (follow up)

The cover of the Discovery issue that discusses the work at my lab.
The cover of the Discover issue that discusses the work at my lab.

This is a follow up to the post about the Discover magazine article that discusses our group’s research studying quantum effects in photosynthesis. The issue (February) is out in stores now. I never liked Discover magazine much, but this time I had to purchase it.

Click here to see the full article.

Quantum mechanics is controlling my thoughts

Kids were very different then.  They didn’t have their
heads filled with all this Cartesian Dualism…
-Monty Python on Nostalgia

Quantum rules Photosynthesis

My main research project was featured in Discover magazine! The cover has some abstract flowery-looking explosion that represents quantum mechanics.

My work in the Aspuru-Guzik group focuses on the quantum aspects of excitonic transfer as applied to photosynthetic complexes and solar harvesting devices. The mistitled article can be found here:

Is quantum mechanics controlling your brain?

Then came the revelation: Instead of haphazardly moving from one connective channel to the next, as might be seen in classical physics, energy traveled in several directions at the same time. The researchers theorized that only when the energy had reached the end of the series of connections could an efficient pathway retroactively be found. At that point, the quantum process collapsed, and the electrons’ energy followed that single, most effective path. […]

Elated by the finding, researchers are looking to mimic nature’s quantum ability to build solar energy collectors that work with near-photosynthetic efficiency. Alán Aspuru-Guzik, an assistant professor of chemistry and chemical biology at Harvard University, heads a team that is researching ways to incorporate the quantum lessons of photosynthesis into organic photovoltaic solar cells. This research is in only the earliest stages, but Aspuru-Guzik believes that Fleming’s work will be applicable in the race to manufacture cheap, efficient solar power cells out of organic molecules.

Unfortunately, the pretty good article about quantum effects in photosynthesis is ruined by its title, title that refers only to the final section of the article containing some wild speculations on quantum mechanics and consciousness. Please, don’t take that last part seriously. Although there is strong experimental evidence supporting the role of quantum effects in photosystems, there isn’t anything that suggests a connection between quantum mechanics and consciousness.

Solar Energy Harvesting

What about solar energy?

What about it?

Life on Earth depends on extracting energy from the solar radiation that reaches the planet, or eating stuff that does it. Professor Sun is the main source of energy required for us to live. Professor Sun generates energy by transforming Hydrogen into Helium by means of nuclear fusion, a process that excretes energy in the form of light that in turn reaches our planet after 8 minutes.

How much of this energy is being used by life on the planet? The question is a complex one, but I decided to do some back of the envelope calculations to the order of magnitude of the light that could be used in principle, is used in practice, and would be needed for Human consumption.

Energy of the Light that Reaches the Atmosphere (1LRA) per year: 10^25 Jules/year ~ 1LRA/y.

This is the total energy that gets to the planet every year, most of it useless to life.

Energy of the light that could be absorbed by photosynthetic organisms: 10^24 J/y ~ 1LRA/month.

This is the total energy that could in principle be used by living organisms. This calculation accounts for light of frequencies that cannot be used by photosynthetic complexes, and also for light falling on areas on the planet where it couldn’t be used anyway. For example, a lot of the energy that hits the surface of the oceans is reflected. The one transmitted gets scattered and some of it is lost.

In order to get a sense of the scale of these processes, we should compare it to the energy consumption of the human race.

Energy consumption of humans: 10^21 J/y ~ 1LRA/minute.

We humans consume about 1minute of the total solar energy that reaches the planet in a year. This includes not only energy spent on machines, but also the actual food we eat. Remember, those plants that we eat, or that our cows eat, harvest energy from the sun. Plants store their unused energy in the form of carbohydrates.
The energy (think: calories) of all the living things that can harvest energy from the sun gives us of an upper bound of much energy could be extracted from processing them.

Energy stored in the total photosynthetic biomass: 10^21J

This is about the total energy of all photosynthetic organisms. If you kill each bacteria, algae, plant in the world and magically extracted all of its energy in a perfectly efficient manner, it would barely provide the human race with energy for one year.  And of course, there would no more plants to replant!
Proposals that suggest extracting energy from the stored carbohydrates, such as ethanol-from-corn, are even worse; only a small fraction of the total biomass of the planet is carbohydrates. In other words, we cannot plant enough to ever extract enough energy to fulfill our current energy needs.

Comparing this number to the amount of fossil fuel highlights how small it is. Of course, how much fossil fuel there is in the planet is not known, much less how much of it can we actually reach.  Do not take these numbers too seriously, but think about them to have an idea of the order of magnitude of how much energy there is in photosynthetic organisms represent.

Guesstimated Fossil Fuel Reserves: 10^22J
Guesstimated Total Fossil Fuel in Earth, including the unreachable fuel: 10^23J

The fossil fuel reserves are 10 times more than the total current photosynthetic biomass! This is very suggestive: any source of energy that uses biological systems to directly extract energy from the sun, such as harvesting algae, will not be a major factor in any long term energy solution for the human race.
However, look at that very first number. There is a lot of energy falling into the planet. Harvesting this energy directly, by means of photovoltaic solar panels, is a reasonable strategy.

A Big Hint to the Cube of Resistors

Still working on the puzzle titled A Cube of Resistors?

Imagine welding a cube of resistors, each resistor with the resistance of 1 Ohm. If you measured the resistance between opposite corners, what would it be?

I’ll give you a hint. Well, more of a hint, I’ll suggest some guidelines of how a clever method of how to solve it. Don’t read anymore if you want to figure it out on your own.


Do not read any further if you don’t want any clues on how to solve the A Cube of Resistors puzzle. Be an Electrical Engineer! Don’t cheat!

Alright, here is the hint. The cube has many planes of symmetry. Exploiting them provides a very elegant solution. I decided to redraw the color to illustrate how many resistors are in similar circumstances.

There is a symmetry of the puzzle. The different colored zones have similar properties.
There is a symmetry of the puzzle. The different colored zones have similar properties.

For example, all the resistors corresponding to the blue lines have a common point, the red one, with the same potential. But, the other end of the blue lines must also have the same potential. Why? Just look further down… there is a symmetry to each line. Follow the path from each blue line to the other end, and you will they look the same. Thus, although technically the blue lines are not in parallel, the symmetry of the cube makes them be in the same potential on both ends so they can be treated as if they were in parallel.

A similar argument works for the 6 resistors corresponding to the black lines; they can all be thought as if they were in the same potential difference between their ends. Also, treat the 3 green lines in the same manner, as if they were parallel resistors.

Following this argument, the Cube of Resistors will have the same resistance as the following figure.

This is not a cube. Yet, it has the same resistance and potential changes as the Cube of Resistors.
This is not a cube. Yet, it has the same resistance and potential changes as the Cube of Resistors.

This figure is obtained by collapsing all the points with the same potential in the cube to one. After all, if the have the same potential, you can short circuit them without changing anything, right?

Now, this problem is much easier to solve. Treat the blues as 3 resistors in parallel, followed in series by 6 in parallel, followed in series by 3 in parallel. Come on, you can do it!

If you want to check your final answer, read ahead. Otherwise, don’t as it will spoil the fun.


Do not read any further if you don’t want the answer to A Cube of Resistors puzzle.

Correct answer to the puzzle coming ahead.

Don’t read any further if you don’t want to know the numerical answer.

5/6 of an Ohm

Where does the number come from? Well, the equivalent resistance of the 3 blue lines as if they were in parallel is 1/3 Ohm (three resistance in parallel can carry three times as much current as one of them on its own. By a similar argument, the equivalent resistance of the 6 black lines as if they were in parallel is 1/6 Ohm. The equivalent resistance of the 3 green lines as if they were in parallel is 1/3 Ohm.

Since each color is in series with each other, the resistances add.

1/3 Ohm + 1/6 Ohm + 1/3 Ohm = 5/6 Ohm.

“Let’s play this with balalaikas. Give me the biggest balaika! We were open about stuff, we could do that.”
-The Clash