The Relationship between Music and Mathematics with respect to Brain Function

Ever wonder how music is related to mathematics, in the way that our brain interprets the two?  Or, how learning to play a musical instrument can actually raise brain function/development to influence mathematical talent?  If so, then you are not alone in considering such questions.

Ever since the 16th century, many mathematicians, musicians, physicians, and even philosophers  have studied thoroughly the relationship between music and mathematics, and proposed theories of how these two completely different subjects interrelate.  According to Rings (2008), mathematics is the subject that consists of formulae, deep analytical thinking, and concrete materials that provide support for science, whereas music is a subject of poetry and emotion, and a centric part of the arts.  Music, as a mathematical description, is the manifestation of numbers and complex functions within the Pythagorean universe and algebraic systems, where each note of a piano produces a specific sound that contributes to different graphical representations (Padula, 2005).

Mathematics and Music
Source:  Getting Smart

Although music can be described mathematically, learning music and mathematics (separately) develops a unique part of the brain (Brothers et al., 1993).  The cerebral cortex, is the structure responsible for pattern recognition and memory development; both music and mathematics are simply branches of pattern – such patterns are developed within the cerebral cortex (Mountcastle, 1978).  Furthermore, Boettcher et al. (1994) found that both mathematics and music are branches of pattern that are developed in the brain.  With respect to music, within a columnar network of trions, they found that the patterns always formed a “creative” pattern that consisted of “broken” symmetry.  With respect to mathematics however, the patterns always formed an “analytic” pattern with a high degree of symmetry; musical patterns changed with different levels of harmony, melody, and rhythm while mathematical patterns remained consistent.  Such patterns, according to Boettcher et al., trigger the development of a unique portion of the brain.

Patterns developed in (A) a "analytical" brain, and (B) a "creative" brain.

Patterns developed in (A) a “analytical” brain, and (B) a “creative” brain.
Source: Boettcher et. al (1994)

Moreover, other studies show that playing a musical instrument can enhance mathematical ability.  According to Hyde et al. (2009), musical training in young children causes significant brain development than children without any musical training.  Such brain developments, they describe, are due to behavioural changes that are created during long-term musical training rather than simple developments due to age.  In other words, Hyde et al. describe that brain development is due to nurture rather than nature.

Child listening to music.
Source: Funderstanding

Mathematical skill is increased in higher age groups due to practicing music just as it is increased in children.  For example, Vaughn (2000) found that individuals (in college and universities, specifically) who voluntarily choose to study music show a significantly higher mathematical achievement than those individuals who do not take any musical courses.  According to Vaughn, many students who choose to take a course in music score much higher in the mathematics portion of the SAT and university- or college-level math courses compared to other students without a music course.  Furthermore, individuals exposed to a music curriculum in school also show higher mathematical achievement as a consequence of this music instruction.

A comic identifying the mathematics in music.
Source: Odd Quartet

Below is a video of James Stewart, the famous author of university-level calculus textbook, commenting on how mathematics and music relate.

YouTube Preview Image

In conclusion, learning how to play music by any form of instrument can play a key role in improving one’s mathematical skills.

Pedram Laghaei

A Smile Does Not Always Cut It for a Good First Impression

Have you ever felt that you aren’t being trusted by someone who knows nothing about your character and who only briefly looked at you? If so, do not be too offended.  According to a new study done by Charles University in Prague, people with brown eyes appear more trustworthy compared to people with blue eyes.  However, it is not eye colour alone that causes people to develop an unwarranted assumption, face shape is also a key factor.

Photo from Flickr user nelu_bodean.

40 male and 40 female students with either blue or brown eyes were photographed and judged by 238 participants that rated their trustworthiness.  After the initial round, a second group consisting of 106 people was asked to judge the same 80 photos; however, the eyes of the blue students were recoloured to brown and the brown eyed students had their eyes recoloured to blue.  The point of this was to determine whether or not other facial characteristics were influencing the participants’ choices or if it was strictly eye colour.

It was determined that people with brown eyes have a more trustworthy appearance due to the facial qualities linked with having brown eyes.  Interestingly, this phenomenon is more significant in males rather than females.  According to the study, males with blue eyes more commonly have smaller eyes, eyebrows that are further apart and narrow mouths.  On the other hand, brown eyed men generally have the complete opposite with larger eyes, eyebrows that are closer together and wider mouths.  This less dominating and more childish appearance is associated with being more trustworthy.

Photo from Flickr user CarbonNYC.

Similar research conducted by Alexander Todorov and Nikolaas Oosterhof at Princeton University determined that people will make instant assumptions about others based on whether they appear strong or weak and whether they should be avoided or not.  Knowing this, the scientists utilized a computer software program that would display a broad spectrum consisting of 300 faces to participants who would decide how trustworthy, dominating and threatening the faces were.  With this information, more analysis and testing was done to understand what specific facial characteristics are the most important for making judgements about others.  The clip below demonstrates the changing facial features that make one appear more or less trusting.  The video gradually transitions through different faces with the least trustworthy in the middle and the most at the beginning and end.

YouTube Preview Image

Therefore, if you find that you are being avoided for no reason and people are not immediately putting their faith in you don’t take it to heart.  Instead perhaps embrace the challenge and prove to people that their initial judgements are sometimes incredibly inaccurate.

Below Absolute Zero?

When someone talks about negative temperature, what usually comes to your mind first? Probably the cold winters with endless snow causing traffic problems in the city if you read temperature in Celsius, or the frozen wasteland of Antarctica if you read temperature in Fahrenheit. But if you are studying thermodynamics and read temperature in Kelvin, then negative temperatures would be very puzzling to understand.

Comparison between Fahrenheit, Celsius, and Kelvin scales

On the Kelvin scale, the lowest possible point is 0 K, absolute zero, where everything ceases to move because of the lack of energy, and the highest possible point depends on which model or theory you coincide with, but for simplicity sake, we’ll call this point absolute hot. Temperature is measured based on the following formula T = dU/dS, where S is entropy and U is internal energy, and if U is zero, that means temperature must be zero as well. Already, we see that the temperature cannot be negative because a system having negative energy is confusing and we don’t deal with it in our daily lives. Although scientists have been able to create negative temperature in the past, recently, according to Nature, Schneider and his fellow researchers published an article about managing to produce a stable substance at negative temperatures using a quantum gas, lasers and magnetic fields.

Under positive temperature systems, atoms too close to each other would repel one another due to the charges the subatomic particles possess. However, once Schneider and his team switched the magnetic field, it caused the atoms to attract one another and be from their lowest possible energy state to the highest. “It’s like walking through a valley, then instantly finding yourself on the mountain peak,” says Schneider. Under normal circumstances, the atoms’ configuration is unstable, but maintaining this with the help of laser fields has caused the atoms to be just below absolute zero, a few billionths to be exact.

One of the properties of negative temperature molecules: more atoms occupy higher energy states

Having negative temperature is not only a strange concept, but atoms reaching this state elicit some strange properties as well, some of which are from dark energy.  Investigating its properties will help cosmologists out with figuring out the secrets of dark energy and the Universe. Maybe more innovations may arise after further research has been done, such as incorporating superconductivity in our lives.

For more visuals and information, you can watch the following Youtube video:

YouTube Preview Image

 

Derrick Lee

SCIE 300 Course Blog

Welcome to the SCIE 300 course blog!

Here are few things to make note of before you get started with your posts. First of all, you should read the blogging resources page under the Create menu. This will help you out a lot if you are brand new to using WordPress. On this page you will find video tutorials about writing posts on this blog, adding media to your posts, tagging, and categorizing. You will also find a link to the rubric we’ll use to grade your blog posts.

Next, check out the blogging guidelines. Here you will find the answer to the question: “What are we supposed to blog about?” You can also check out one of last term’s blogs for some additional inspiration.

There are a few important things to keep in mind when blogging. Please do not assume that just because something is online, it is OK for you to use it. For example, unless it is explicitly stated, an image on the internet can not just be copied, saved, and used in your own post without permission to do so. We’ve provided you with a lot more detail about properly using online content, but if you have questions, let us know.

This blog also contains a lot of resources for you. For example, still under the Create menu, there is a list of equipment available for you to borrow and a list of suggested software to use for your projects. We’ve also collected some writing and presentation resources.

Under the Explore menu, you will find some sample podcasts and videos, links that may be of interest or assistance, a list of groups and associations related to communicating science as well as a list of local museums and science centres. The Explore menu also contains a library resources page, which you should definitely have a look at. Finally, there is a bookshelf that lists relevant books that are on reserve for you in Woodward Library or available for borrowing from Eric’s office (BioSci 3532).

Let us know if you have any questions about the blog or would like to see any other resources made available. Or, if you find something that you think would be useful to the rest of the class, tell us, and we can add it to the resources. Better yet — write a post about it!

Happy blogging!

Jackie and Reinhard