Math on a Clock: Exploration in Mathematics

I want to give you a sense of what it’s like doing math “in the wild”. Doing mathematics is not just about learning what other people have already done: it’s about exploring and playing around with a system to figure out what’s going on. Let’s give it a go!

We are all familiar with the 12 hour system for counting time on a clock. The numbers count each digit from 1 to 12 and then circle back to 1. Since 12 is the number just before 1, we can think of 12 just like 0. We will ignore AM/PM for all of this.

One of IU's red clocks, surrounded by red flowers. The picture was taken on campus.
One of IU’s red clocks.

We don’t usually talk about it this way, but we could say that adding 2 and 3 o’clock gives 5, in that 5 o’clock is 2 hours after 3, or 3 hours after 2.

We can ask what 7 + 7 would be. The answer is 14, but this is the same as 2, since 12 is a whole circle around the clock. That is, since 12 is the same as 0.

The next few examples are a little more complicated. Math is a much more interesting subject if you interact with it. It’s rare to find a mathematician reading without something to write on. Find a pencil and paper if you don’t have them around already.

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Catching Brainwaves

Graduate students prepare an eeg cap resembling a shower cap exuding wires.
Graduate student Nancy Lundin sets up on EEG cap on fellow graduate student John Purcell.

If your family is anything like mine, you have that one crazy uncle with his tin foil hat, purportedly to prevent the aliens from electromagnetically manipulating his brain or to prevent his precious brain waves from being read by the government. While few take such fears seriously, significant confusion persists regarding ‘brain waves.’ What are they and where do they come from? Can they be picked up and decoded like radio signals, perhaps even useful for telepathy (or alien-monitoring of your thoughts)?

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Proactively combating the continuing threat of pesticide resistance

A researcher sits at a workbench surrounded by many dozens of small weigh boats.
Research associate Dylan Siniard carefully setting up but one batch of dozens of experimental units in his pesticide resistance assays.

Consider briefly the process of evolution and you might imagine a lumbering process, splitting lineages and bringing new species forth from old, or the gradual formation of morphological novelties like wings. While it’s true that evolutionary processes such as  the formation of new species are generally slow by our standards, other effects of evolution that cannot be seen with the naked eye (but are no less important) can often develop over the course of a human lifetime.

In only a few decades, we have seen the proliferation of pesticide-resistant strains of a number of important crop pests through the differential reproduction of individuals bearing molecular traits that allow them to avoid succumbing to pesticides. Organisms, in this case crop pests, have some variable number of offspring each generation that can survive and reproduce themselves. If a lineage of crop pests has a greater number of viable offspring because it is better able to withstand the pesticides that killed other insects, its descendants will come to represent a larger portion of the population. The population of pests will then have, in aggregate, more of the attributes of the successful lineages, including those that lent increased reproductive success–in this case, pesticide resistance. This is the essence of evolution by natural selection.

It is easy to see why this is a subject of ongoing research. Agricultural pests are responsible for billions of dollars a year in crop damages, totaling 13% of the world’s crop production, and disease-carrying insects, such as mosquitoes, present ongoing challenges to human health. While developing alternative pest-control strategies is an active area for research, our primary means of controlling insect pests is still through the proper use of chemical pesticides. So then, what do we do when evolution is making our main methods for controlling insect populations less effective by the year, and what constitutes proper pesticide application?

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Measuring the mass of Goldilocks molecules: not too big, but not too small

Line graph showing peaks at ~3.8 and 5 megadaltons for the mass of the virus capsid
Figure 1. Mass spectrum obtained using Charge Detection Mass Spectrometry showing the relative amounts of empty, filled, and partially filled viruses from a gene therapy sample. Here the bottom axis shows the mass of the virus in megadaltons, which are very small units (for scale, one megadalton is equivalent to the mass of one million hydrogen atoms). Interestingly, CDMS discovered partially filled capsids in the 3.5-4.0 MDa range that are not readily detectable by other techniques. [1]
Finding out how much you weigh is simple–just step on a scale and see the answer within seconds. Weighing ourselves is easy, but how do we weigh the microscopic things in our world that are too small to see? By using mass spectrometry.

Mass spectrometry has been around since the early 20th century, and researchers have gotten very good at measuring the small atoms and molecules that make up our world. Mass spectrometers work by adding a charge to a molecule or atom of interest and then using sophisticated electric fields to accelerate that charged molecule. Because the moving particle’s energy depends on its mass, measurements of the energy allow researchers to deduce that mass. Mass spectrometry works well for atoms and small molecules, but what about biological complexes–like viruses–which are still small, but have masses millions of times larger than a single hydrogen atom? (more…)

Perks of the Job

What does summer vacation look like for a scientist? For some, summer break is much-needed time to catch up on research projects and writing, but for many of us, summer centers around one thing: field work. Quite often, much of the data that scientists rely upon can only be collected in natural settings outside the lab, so we must take part in extended field projects all over the globe. For a few geologists and paleoanthropologists at IU, this means traveling thousands of miles to Olduvai Gorge, Tanzania and spending several weeks camping out at one of the most famous locations for evidence of human evolution.

Panoramic view of the edge of the large gorge, with desert plants all around.
Panoramic view of a small section of Olduvai Gorge, which is over 30 miles long.

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An Event Like No Other–Science Fest 2016

A child, 10-12 years of age, is surrounded by the inner components of a computer, while a volunteer stands by watching.
A young student gets his hands on the inner workings of a computer, while a volunteer stands by.

You’d have to wonder what could bring close to 600 students, faculty, staff, and parent volunteers to the IU campus on a Saturday morning. They could instead be home mowing the lawn, enjoying a nice stack of pancakes at the Runcible Spoon, or sleeping in…..but no. This team of people is  on a mission to guide young children and their families to a better understanding of the natural world using inquiry and hands-on discovery. For this reason, they wake up early and head to IU on a Saturday morning. (more…)

Protein Machines: the Molecules of Your Body in Motion

Proteins move.  Most people are likely familiar with proteins in the context of their own nutrition – you get protein from meat, unless you’re a vegetarian, in which case you might get protein from soy or milk.  But proteins are not just a part of your diet.  The extremely broad category of molecules contained under the word “proteins” varies wildly in terms of size, shape, and composition, and their activity in your cells determines your health and survival.  

Proteins – large molecules that are the workhorses of living cells – facilitate many important functions through their interactions with other proteins, DNA, and small molecules, such as drugs.  It has been fifty years since the first protein structure was determined, and the insight gained from studying these structures should not be understated.  A major theme of biochemistry is the “structure-function paradigm” which says that a protein’s structure will dictate its function.  Textbooks are graced with colorful images of protein structures, making it easy to think of protein molecules as trapped in a single configuration.  But in a living cell, proteins are quite mobile and dynamic molecular machines.

A well-known animated video from a collaboration between XVIVO, a studio which specializes in scientific animations, and Harvard University (watch it here) illustrates the dynamic nature of proteins in a cell.   (more…)

Bio-Inspired Nanomaterials – Viruses aren’t all that bad

Viruses are often associated with disease, but they can also be useful. Viruses infect many organisms other than humans, including plants and bacteria. Aside from being infectious, the actual structure of a virus can be harnessed as a material. For example, a virus cage can be used to deliver drugs to our cells or to protect catalytic cargo. This is possible because of the amazing structural properties that viruses exhibit.

The two basic components of a standard virus are 1) the genetic information that codes for the creation of more viruses (either DNA or RNA) and 2) the protective protein cage that surrounds that genetic information. For materials scientists, it is this protective cage that is a source of bio-inspiration. The cage is composed of various proteins that self-assemble into three-dimensional shapes (usually sphere-like) around the DNA or RNA in the same way carefully designed magnetic puzzle pieces ‘click’ into place when shaken (pictured right).

Three flasks with pieces of a magnetic puzzle. The puzzle is shown diassembled in the first flask, being shaken in the second flask, and assembled into two spheres in the third flask.
Magnetic components can be designed to selectively self-assemble in the same way some viruses self-assemble. Photo credit-Self Assembly Lab (http://www.selfassemblylab.net/)

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Chemistry Nobel: Rise of the (Tiny) Machines

Banner graphic announcing Sauvage, Stoddart, and Feringa as the winners of the 2016 Chemistry Nobel Prize

The turn of the 20th century saw an industrial revolution that saw the rise of machines to handle tasks previously beyond our grasp. Mechanization and automation in our civilization have created a higher quality of life than our physical bodies could ever achieve. Scientists are continually pushing the upper limits of engineering to create gigantic machines–from the International Space Station, orbiting the planet with a size greater than a football field, to massive oil rigs that drill the depths of our oceans. Recently, however, the Chemistry Nobel Committee recognized a group of scientists for their pioneering work to extend the lower bounds of machines. (more…)

The Brain Science of Cognitive Control

A doctor inserts a patient into a large cylindrical MRI scanner.
An MRI scanner. The large cylinder is a giant magnet which produces a powerful magnetic field in the center of the machine, which can be used to detect changes in the brain.

Ever wonder how your brain knows exactly what to do to achieve the goal of acquiring a cup of coffee, even if you’ve just stumbled out of bed? You need to take a number of steps in the correct order, including putting in the filter, adding the water, adding the coffee and turning on the machine. From our conscious perspective, this process appears rather ordinary, maybe even dull. However, the great mystery of brain science is that all of your behavior can be understood as an incredibly complex dance of electro-chemical patterns flowing through a hundred billion neurons (specialized cells which send messages to each other as well as your muscles). We have very little idea how it all works, but a diverse range of research labs at IU are doing their best to figure it out. (more…)