The Mental Benefits of Learning to Play Music at a Young Age

This is a research paper that I wrote for an online writing course. It was my first experience with strictly following writing guidelines(Including margins and spacing, although I could not preserve those settings here) and making citations. In this paper, I used the MLA guidelines. I like how the subject of the paper combines two topics that I am interested in.

Wytse Gensemer

Mrs. McKinley

Writing: Research Papers and Essays

5 October, 2018

The Mental Benefits of Learning to Play Music at a Young Age

There has been music in human culture for longer than you might think. Musical instruments are among the oldest manmade objects ever found. Music was developed long before agriculture, and it might even have preceded language, as it could have been one of the factors that helped to create language. A love for music has not been naturally selected against, meaning that it might be, or might have been, good for survival or breeding in the human population. Thus, it has been very important for early humans and much used in our culture (Levitin 250). As it is such an essential thing in our culture and our minds, music can have life-changing effects. Young people who play music can get the largest benefits from these effects, even if they only play music for one or two years. All children should start learning a musical instrument by the time they are eight years old, because playing music can help brain development in ways that can benefit their thinking, mood and social life.

Why eight years old? The reason why it is best to start learning music at a young age is related to neuroplasticity. Neuroplasticity is the brain’s amazing ability to change, in both structural and functional ways, to suit the environment, making the different parts of the brain similar to muscles in that they grow and become more effective when they are used often. Neuroplasticity for different skills peaks at certain times, known as critical periods. During a critical period for a skill, experiences related to that skill have larger effects on brain development. After a critical period, those experiences have little or no effect on brain development. The critical period for many things, such as learning languages, happens at about six or seven years of age (Mundkur 855-56). Someone can still become a good musician if they started learning after this age, but they would not have some added benefits that they would otherwise have, such as the increased amount of connections across different parts of the brain.

One of the findings about brain changes in musicians is that parts of the corpus callosum are larger when the subject has been playing music for a long time (Jancke). The corpus callosum is a bundle of nerve fibers that link the right and left hemispheres of the brain with each other. Another finding is that musicians have a stronger link in between their auditory and motor brain regions than nonmusicians. These are both adaptations for playing music, but the strengthened linkage in the brain might also be useful in other tasks (Jancke). An increased amount of connectivity is helpful, but there are other changes that music makes to the brain, some of which can be more widely applied.

Besides making the brain more connected, playing music can help develop academical skills. Recent studies have shown that musicians have better working memory than nonmusicians. Working memory lets people remember things temporarily while they are thinking about something else, so improved working memory makes people better at tasks involving reading and math (Benefits of Music Education 3). Amazingly, another study compared IQ scores of two study groups: children who were taught music, and children who were taught drama, and discovered that, after one year, the group that was taught music had a slightly higher average IQ score than the drama group, suggesting that children who play music can do better academically (Schellenberg 513). There are many ways that music is good for thinking and intelligence, but these things also depend on mood and general wellbeing, which music can also affect.

There are many ways that playing music is beneficial with feelings. One benefit is relieving stress or decreasing depression. A study by Jaakko Erkkila and colleagues used 79 adults with unipolar depression. One group was given normal treatment for the depression, and the other group was given music therapy as well as normal treatment. The music therapy consisted of tasks related to making music, including playing simple melodies, singing and improvisation. Over six months, the music therapy group showed a much larger improvement than the control group. The difference between these results is considered to be clinically relevant (132-36). It can be very good for someone’s overall mental health that music works well against depression, but this is not the only time when it can strongly affect feelings.

Music is shown to create positive feelings as well as suppress negative ones. Part of the way that it does this is that it gives musicians a sense of achievement, which can be caused by learning to play a song, getting into an ensemble or performing. Something that a musician will tend to do, especially if they play in an ensemble, is listen to music more often. Music listening has many known benefits. This has been demonstrated by a Swedish study, carried out by Professor Juslin and his team. Several students carried small computers which made beeping sounds at random times of the day. When each student heard the sound, they answered questions about whether they heard music at that time or not, and how they were feeling. The results were that, in any situation, music made them feel happier or more relaxed than at the times when they were not listening to music (Powell 37). Happiness can be elevated by music for all of the reasons described above, but happiness sometimes depends on social contact, and surprisingly, music can benefit a musician’s life in this way too.

Social life can heavily affect feelings, which in turn leads to changes in mental health, and there are ways that music can help people have a better social life through changes in the brain. One of these changes is a better auditory cortex which leads to empathy. In one study, young children who played music for six months showed more improvement in discriminating tones in speech than children who did not (Moreno et al. 712). Because subtle tones in speech sometimes indicate how a person is feeling, this helps children who play music have more empathy. This has been shown in toddlers who played music together (Benefits of Music Education 6). The increase in empathy means that people who play music can do better socially, even though this is mainly with the people they already know.

There are ways that music can make a person more successful socially by meeting new people and bonding with them. A very common thing for musicians is to play together in a small group, band, ensemble or orchestra. This not only gives them more social contact, but it also makes people socially bond with each other (Tarr, Launay and Dunbar). This bonding can let people make new friends more easily, leading to a better social life.

Seeing what kind of changes music causes to the brain, both temporary and permanent, the conclusion is that music benefits a musician’s life in many aspects, including that they are able to do better academically, emotionally and socially. All of these benefits are related to important factors for the success of a person’s life and their wellbeing. Most of the benefits are caused by changes in the brain, so if someone learns music at a young age when they have more neuroplasticity, they keep the benefits for their whole lives. Efforts should be made to teach music to young children more in schools and at homes, and to make learning music more affordable, so that yet more people can enjoy the benefits it brings.

 

Works Cited

The Benefits of Music Education: An Overview of Current Neuroscience Research. Toronto, Canada: The Royal Conservatory of Music, 2012. Web. 1 Oct. 2018.

Erkkila, Jaakko et al. "Individual Music Therapy for Depression: Randomised Controlled Trial." The British Journal of Psychiatry 199.2 (2011): 132-39. Web. 1 Oct. 2018.

Jancke, Lutz. "Music Drives Brain Plasticity." F1000 Biology Reports 1.78 (2009): n.pag. Web. 1 Oct. 2018.

Levitin, Daniel J. This is Your Brain on Music: The Science of a Human Obsession. New York: Penguin, 2006. Print.

Moreno, Sylvian et al. "Musical Training Influences Linguistic Abilities in 8-Year-Old Children: More Evidence for Brain Plasticity." Cerebral Cortex 19.3 (2009): 712-23. Web. 1 Oct. 2018.

Mundkur, Nandini. "Neuroplasticity in Children." The Indian Journal of Pediatrics. 72.10 (2005): 855-57. Web. 1 Oct. 2018.

Powell, John. Why We Love Music: From Mozart to Metallica - The Emotional Power of Beautiful Sounds. Great Britan: John Murray, 2016. Print.

Schellenberg, E. Glenn. "Music Lessons Enhance IQ." Psychological Science 15.8 (2004): 511-14. Web. 1 Oct. 2018.

Tarr, Bronwyn, Jacques Launday and Robin I. M. Dunbar. "Music and Social Bonding: "Self-other" Merging and Neurohormonal Mechanisms." Frontiers in Psychology 5.1096 (2014): n. pag. Web. 2 Oct. 2018.

Woodwinds

I was going to write about musical instruments, but because I have been playing the clarinet in various wind orchestras for a while, the group of musical instruments that I know the most about is woodwind.

Piccolo playing

Since the pitch of woodwind instruments depends on how long the tube is that the air goes along, the musician makes different notes by opening or closing holes in the side. This also means that bigger woodwind instruments make a lower sound. The biggest woodwind instrument that is used in orchestras is the bassoon, which stands more than half as tall as a person. Its lowest notes are much lower than the normal singing range. The smallest is the piccolo, a very small version of the flute. Its highest notes are even higher than those of a piano, and it is so high-pitched that music written for the piccolo has to be written one octave lower than it actually sounds, because otherwise many of the notes would be far too high above the stave. In my experience, woodwind instruments with a more average range have a better sound and are better solo instruments, but the more extreme instruments can help an orchestra a lot.

Paleolithic bone flute

Woodwind instruments have existed for a very long time. The oldest musical instrument discovered is a mammoth ivory flute found in a cave in Germany, estimated to be over 40,000 years old. Many prehistoric flutes like this have been discovered. Percussion instruments, such as drums, could have been made of decomposable materials, or early peoples could have used rocks and sticks, before this time, but the evidence of these flutes still suggests that humans have invented woodwind instruments very early on.

The first woodwind instruments were made of simple materials, so they would have made sound by the musician blowing air into a hole at the side or end of the instrument, making the air vibrate by the difference in air pressures. Flutes and panpipes make sound this way.

Bassoon reeds

In ancient times, people developed a type of woodwind instrument in which a part of the instrument itself vibrates, instead of the shape of the instrument causing the blown air to vibrate directly. The part of a woodwind instrument that vibrates is usually called the reed. Older reeded instruments had the reed as part of the instrument, but as woodwind instruments developed more, the reed eventually became a separate piece. The reed is so called because, in most woodwind instruments, it is made from the plant Arundo donax, a type of reed plant.

Some instruments have more than one reed. This includes the bassoon and the oboe, which have two reeds. While the reed is normally fixed to the mouthpiece, as in clarinets and saxophones, in double-reeded instruments the two reeds compose the mouthpiece and the musician blows through the gap in between them.

Bass clarinet

Despite the name of the group, not all woodwind instruments are made of wood. About half of them are made of metal. This makes a very distinct difference in the sound, which is why the clarinet, made of wood, makes a different sound than the saxophone, which is related but made of metal. The bass clarinet is a much bigger version of the normal type of clarinet, but some of the sections are curved and made of metal. This includes the bell, so the lower notes sound more metallic than the higher ones. I have played on an alto clarinet, which is halfway in between a bass clarinet and a normal B flat clarinet. It also tends to sound metallic with some notes.

In music composed for wind orchestras, composers often put a solo in the music, when a single instrument is playing and the rest are either playing quietly or not at all. The most common solo woodwind instrument that is chosen is the clarinet(I have had the honor a few times to play a solo in a large ensemble), but oboe solos are also common. Since some notes are very difficult on the oboe, and it is also hard to keep in tune, oboe solos can be very hard to play, but I think the reason that it is chosen so often is that it makes a wonderful sound when played properly. The piccolo is also a common solo instrument because it is very high pitched and stands out from the rest of the orchestra. I have also heard solos on the E flat clarinet and the saxophone in ensemble pieces, but these are rarer.

Woodwind instruments are a very fun group of instruments to play in. They include all sorts of pitch ranges and encompass nearly every style of music. The most popular woodwind instruments are flutes, clarinets and saxophones, and it is good to play them, but a nice bonus with less popular instruments, such as the oboe, the bassoon, the alto clarinet or the baritone saxophone, is that not very many musicians play them, so they are in higher demand and ensembles that do not have them give those musicians a much higher chance to join, sometimes even scholarships. In a wind orchestra together or with brass instruments, woodwinds can be very expressive and make an amazing sound.


Music that features woodwind instruments: This includes music that I have preformed with woodwind and brass ensembles, and music with woodwind solos.

General: 

Air for Band, by Frank Erickson:
A nice, slow melody. Woodwind instruments are highly featured.
Serenade for wind band, by Derek Bourgeois:
Woodwind instruments have the melody for most of the time. If you are interested in the beat pattern, most of the song is in 11/8 time(3+3+2+3), and temporarily changes to 13/8 time(3+3+2+2+3) in the middle.

Clarinet:

Entry March of the Boyars, by Johan Halvorsen:
Clarinet solo at the beginning. Also has some very interesting flute parts.

W. A. Mozart's Clarinet Concerto:
If you listen to this you will see why the clarinet is such a popular solo instrument.

Oboe:

October, by Eric Whitacre:
An amazing, beautiful piece. Starts with an oboe solo.

Piccolo:

Stars and Stripes Forever, by John Philip Sousa:
The national march of the United States of America. It might be an extremely patriotic song, but I had to include it because of the famous, impressive sounding piccolo solo which starts about halfway through the march.


Image source: Wikimedia Commons

All in good taste

This article is about our sense of taste, and mostly about some of the weird molecules that can make tastes beyond the usual four; bitter, salty, sweet and sour. To start with, here is a description how we taste things.

Whenever food goes into your mouth, it gets dissolved by the water in your mouth and goes into your taste buds. Each type of taste bud is tuned to a certain common molecule. When the right molecule goes into those taste buds, it binds to and opens ion channels, which are proteins on the membranes of body cells that they use to make an electric charge which travels to the brain. Sweet taste bud cells, for example, are mainly activated by sugars. A salty taste is mainly activated by positive sodium ions(Na+). Sour is activated by protons(H+), which show the presence of acid. There are many known compounds which make a strong bitter taste.

There are other chemicals that make more unusual and harder to identify tastes. This article is not only about the classical four tastes, but I will also describe some of the other, stranger, tastes, the ones that make food the widely varied and complicated thing it is.

Soy sauce has a lot of umami taste.

The first of these unusual tastes that I am going to explain is umami. Umami, or 'savoriness' should be considered one of the five basic tastes, but since it was not discovered by western scientists until recently, it is usually not counted. Food with a lot of umami taste includes tomatoes, soy sauce, meat stock(broth), some seafood and many fermented foods. One chemical that makes the umami taste is monosodium glutamate(MSG), which is often added to food in Chinese resuraunts to make the food taste better. There is a common belief that MSG is dangerous and causes symptoms like headaches and other kinds of discomfort, but scientific tests have found no evidence to support this. MSG is, in fact, a perfectly normal and healthy substance for flavouring, made out of molecules that are very common in food. It is no more harmful than salt.

The ghost pepper, one of the hottest chillies.

The next taste can be considered more of a sensation. It is spiciness, which is in many foods and usually comes from chili pepper. The spiciest substance in the world is capsaicin, because it is the cause of spiciness. This taste is unlike the normal five tastes in that the normal tastes were evolved by humans, but spiciness was evolved by chili peppers, probably to stop certain mammals from eating their seeds. The active ingredient, capsaicin, can also deter fungi, so it might have evolved for both purposes. The way capsaicin works is that it binds to and opens a certain type of ion channel, which is in the mouth and skin of mammals. This ion channel is otherwise only activated with heat, acid or other kinds of damage to the skin, and it sends a signal to the brain saying that the skin is being burned or heated. This is why spicy food makes a burning sensation when you eat it or touch it for too long. One interesting thing about spiciness is that it only works in mammals. This might be because wild chili peppers are dependent on birds spreading their seeds.

There is another taste which works exactly the same way as spiciness, except that the receptors that sense heat or burning are not activated, and a different receptor, which is normally triggered in cold conditions, is activated instead. This makes a cooling sensation, even if the food itself is not cold. This taste is referred to as coolness. Peppermint and spearmint are some of the things that have this taste.

Another neat taste-related thing is the influence of miracle berries, a type of berry native to Africa. Miracle berries are a kind of fruit which, if you chew on the berry and spit the seed out, changes the taste receptors in your mouth. In the juice of the miracle berry, there is a protein called miraculin, which has two sides; one that binds to the sweet taste receptor cells, and one that triggers the sweet receptor if it is in an acid. Since acid usually triggers only the sour taste receptors, miraculin can make anything sour, like lemons, taste sweet instead. The effect of miracle berries lasts for about 30 minutes. I have tried some miracle berries from a tree in a community garden I used to live close to, and the effect feels very odd. Miraculin is sometimes regarded as a sweetener, but it is not one. It only changes one taste into another.

The last taste effect is the strange effect caused by paracress, also called the 'toothache plant', a widely cultivated plant that is grown for ornamental and medicinal purposes. When its flower buds are chewed up, or rubbed onto the gums, it makes a bitter grassy taste, and soon after it makes a very strong sour, tingling and numbing sensation in the mouth, which lasts for about ten minutes. I have tried one of these before, at a herb farm, and because of this I can understand why they are sometimes called 'buzz buttons' or 'electric daisy'. The effect is very apparent. It is caused by a local anesthetic called spilanthol which is in the juice of the flowers and can be absorbed through the lining of the mouth. Like one of its common names suggests, the 'toothache plant' can be used to stop the pain caused by toothache because of this anesthetic. It is often grown for this purpose.

That is my list of 'unusual tastes'. There are many more of these that I left off this list, because they would make it too long. It makes sense that there are so many tastes like this, because how would seafood, paprika or even peppermint be able to have such an unusual effect on the mouth with only sourness, saltiness, sweetness and bitterness?

Holidays in the Grampians

This article is about what my family and I did over the holidays at the end of the first term. The holidays were only two weeks long. During the first week, I mostly stayed at home, but during the second week of holidays we went to the Grampians, a range of mountains and national park in Victoria. I took some photos there, so all of the pictures in this post were taken by me.

While we were still in South Australia, we crossed a part of the Murray river which is downriver from the part that makes most of the New South Wales/Victoria border. Afterward, if we were going farther southward, our route would have taken us along the Coorong, a narrow 160 km long body of water that extends along the coast, but hardly reaches the sea the whole way.

Our main stop while driving through Victoria on the way to the Grampians was Mount Arapiles, a large mountain in the middle of a flat expanse of farming fields. On one side, Mount Arapiles is shaped like a plateau, with a level top and steep, tall cliffs at the side. It is extremely popular and well known for its rock climbs. We stopped and camped for the night so that we could have time to explore the rock formations there.

The Organ Pipes at Mount Arapiles

After we set up our tents at a campground near the climbs, me and one of my brothers went to explore the cliffs. The main features there include the Organ Pipes, which is a row of rock columns in the main cliff face, and a very large rocky bluff that appears to loom over the trees at the campsite and is easily visible from many directions. At the side of the bluff, there is a huge unbroken cliff which stretches along the entire length of the bluff and is so tall that climbers need to use four or five pitches to get to the top. During the walk, we passed a very large number of rock climbs, and a lot of climbers as well. I also got to see a lot of native wildlife, including kangaroos and wallabies.

The bluff at Arapiles

In the morning on the next day, my brothers and my dad went to try some of the climbs. The place we climbed was on a relatively small rock outcrop at the base of the enormous bluff. A plaque for the original discoverer of Mount Arapiles is set halfway up the cliff there, and we climbed near the plaque. After finishing a climb, I saw a fox walking along the bottom of the cliff(Foxes are common in Australia, but they are non-native and very bad for the native wildlife).

In the early afternoon, we walked up a side valley to the summit of the bluff. The view there was amazing, and the flat horizon was unbroken except for the hazy outline of the Grampians.

The shape of the mountains

Most of the mountains in the Grampians have a peculiar shape, due to their formation. On our first day there, we went to a lookout where we could clearly see the shape of the mountains. They were most likely formed by layers of hard sandstone, which were tilted at an angle and then got eroded. The tilt of the original rock layers gives a lot of the mountains a long, gradual slope on one side, and a steep slope with cliffs on the other. They are all pointed roughly the same direction. This makes the Grampians an excellent place for bushwalking, because people can walk up one slope of a mountain and see a good view from the cliffs at the other side. We did many walks like this.

One of the first few walks we did in our six-day stay in the Grampians was a six hour walk that went from Halls Gap, a small town in between the mountains, to the Pinnacles, a place at the top of a mountain that has wide views of an entire valley from the top of an overhanging cliff.

The rock features that we saw along the way include the Venus Baths, which is a group of perfectly round rock pools at the base of the mountain, a small gorge known as the Grand Canyon, and a very long, narrow cleft called Silent Street. The walls of these gorges looked very unusual, as if they were made of round rocks stacked on top of each other in layers, and I thought it was strange how the gorges seemed to muffle all of the sound from outside. Silent Street seems like it was appropriately named, because if you stand in the gorge and not make any sound, it can get perfectly quiet.

Another place that we went to in the Grampians, and a place that I highly recommend if you go there and are adventurous, is Hollow Mountain. Hollow Mountain is surrounded by stony plains and is close to Mount Zero. It is near the edge of the mountain range. After we did a long rock scramble to get to it, we arrived at what looked like a boring rectangular bluff. It is much more interesting than it looks, however, because if you go into one of the openings at the side, it leads into a spectacular sandstone cave system. At one place, the mountain is filled with these caves, making it hollow. Once you scramble up the rocks in the largest cave, you can get to a famous rock window on the other side, which is very high up and has a view of the plains and many of the other mountains, including Mount Zero.

Another of the mountains we climbed was Mount Rosea, in a completely different part of the mountains, which also had good views, but unfortunately the summit was surrounded by mist, so we did not have good views from there. When we were walking up Mount Rosea, we crossed a bridge over the Gate of the East Wind, an extremely deep, narrow chasm through the mountain.

In the Grampians, there are a few places where someone could have a good view that does not require a very difficult walk. We went to some of these. One of the views included the valley that Halls Gap is in, and from that view we could also see the reservoir in that valley and the fields behind the mountains.

We did many things for our last few days in the Grampians. One of those things was that we visited two old, abandoned towns. The first one was planned to be built around a quarry, but was never finished. There was a lot of old, rusty mining equipment lying around near the quarry. The second one was called Mafeking. It was built during a gold rush, but got completely abandoned after 20 years when the gold rush was over. In both towns, most of the old buildings were taken down when the town was abandoned, so in Mafeking there is hardly anything left except for mining pits.

Another of the things we went to in the last few days was Mt William, which has a road going up it. The road is closed for public vehicles for the last stretch, so we had to walk up the road to the summit. Because there are not very many trees on the slopes that we walked up, we had very good views on the way up. From the summit, a lot of the other mountains are visible, however, when we were there, controlled burning was being done in the mountains and in the surrounding fields, so there was a lot of smoke.

The chimney pots

On our last day in the trip to the Grampians, we hiked to the Chimney Pots, a group of enormous smokestack-shaped rock features protruding out of a mountain. They look very strange, and they are clearly made of many layers. They resemble the sides of the Grand Canyon, a feature from another walk we did in the Grampians.

The last walk we did on our trip was a short walk to the top of a dam that we could see from our campsite at Halls Gap. We took the walk so that we could see the sunset from the dam. Behind the dam was a reservoir which spanned the entire valley. Walking along the dam and looking over the trees and the water, I could see the rock features around the valley very clearly. I could also see the general shape of the valley.

We did not do much on the way back, except for stopping for lunch and to look at some murals in a small town near the Coorong in South Australia.

The Grampians is an amazing place. The mountain range is so large that we met some people we met there had been living there and doing walks frequently for over half a year and had not seen very much of it. For adventurous bushwalkers there is a multi-day hike going across the park. It was a good road trip for us, but six days was not nearly enough to explore the massive scale of the Grampians.


Here are a few more photos from the trip:

"At the side of the bluff, there is a huge unbroken cliff which stretches along the entire length of the bluff and is so tall that climbers need to use four or five pitches to get to the top."

Some cliffs near Halls Gap

Another view of the inside of Hollow Mountain

The view out of the rock window at Hollow Mountain

More pictures from the dam:

A guide to the fourth dimension

The idea of this article is to imagine what it would be like to be in four dimensions. Of course, since we live in only three dimensions, it is impossible to visualize a four-dimensional space, but we can show how everything would work in the fourth dimension by using mathematics.

To start with, we need to know what a transition to a higher dimension is like. The start is zero dimensions. In a zero-dimensional world, it is impossible to move, and there would be no space around, and no amounts of anything. There can only be something, or nothing. The shape of a 0-dimensional world is a simple dot.

To go to the first dimension, imagine taking two zero-dimensional worlds(dots), and connecting them. This world is simply a line. In the first dimension, nothing can move past anything else, and any object is basically a line, with varying length. The ends of each line are zero-dimensional points.

To make a two-dimensional world, imagine taking two one-dimensional lines, and connecting them at every point. The result is a flat sheet. An infinite world of two dimensions is called a plane in mathematics. It would be the same as in three dimensions, except that one of the directions is missing, so it would be like moving pieces of paper around on a flat table.

Stepping up to three dimensions can be done by taking two parallel planes and connecting them at each point. This results in a three dimensional space. This is the dimension that we are the most familiar with. Many more things are possible in three dimensions than in two. The second dimension to us would be so thin that it could not influence the third dimension. There are still two-dimensional things in our world, though, like shadows, surfaces and images.

The best way to imagine the fourth dimension would be to recognize that the third dimension is to the fourth dimension as the second is to the third. A four dimensional space would be the space in between two volumes that are separated from each other in only the fourth dimension, which is at right angles to each of our three dimensions. Of course, we know of no evidence that a four dimensional world exists, but it is possible in mathematics.

The simplest way to imagine these transitions through the dimensions is to imagine a hypercube. A hypercube is an object in any dimension, where its lengths in each dimension are the same, and it takes up the maximum amount of space for a given side length. For example, a 1-dimensional hypercube is a line. Stepping up to two dimensions makes it into a square, and in the third dimension it becomes a cube. The 1-dimensional hypercube has two 0-dimensional endpoints. The 2-dimensional hypercube has four 1-dimensional sides and four 0-dimensional corners. The 3-dimensional hypercube is a bit more complicated, with six 2-dimensional faces, twelve 1-dimensional edges and eight 0-dimensional corners. As the hypercube goes up through each dimension, it gains a different property. The next step is where it starts to get weird.

An animation of a hypercube

A 4-dimensional hypercube is called a tesseract or 8-cell. The tesseract is to the cube as the cube is to the square. Because a square has four sides and a cube has six, a tesseract has eight sides. These 'sides' are all three-dimensional cubes and are called cells. The two additional sides are extended in the fourth dimension as follows: if you go straight ahead all of the way around a cube or a square, you will go around three other sides before you get back to the starting side, and this is the same with a tesseract. Following the normal pattern of hypercubes, each cell of a tesseract has six square sides. Going through any one of those sides takes you onto another side. At each of the 32 edges, three cells meet, and four cells meet at each of the 16 corners. In normal three-dimensional space, four cubes can meet at an edge, and eight can meet at a corner, so at those areas the tesseract would be especially warped from three dimensions.

The Dali cross

One way to make this all simpler is by unfolding the tesseract, just like how you can unfold a cube into two-dimensional space. In a cube, the resulting shape looks like a cross made of six square panels. In a tesseract, the shape would look like a four-sided cross made of eight cubes, four cubes tall with four additional cubes sticking out in all four directions. This is called a 'net' of a tesseract, which is known as the Dali cross.

The common way to display a tesseract(see below) is to have a cube with a smaller one inside it, linked to the bigger one by twelve walls, one for each edge of the inside cube. The inner cube is the cell that is facing away from us in the fourth dimension, and the space in between the inner and outer cubes is divided by the walls into six semi-trapezoidal shapes. These shapes are six of the other cells. The last one, which is facing toward us in the fourth dimension, is the bigger cube and has all of the other cells shown inside it.

This is the classical projection of a tesseract onto three dimensions. It is three-dimensional, but it has all of the same edges, corners and faces of the actual tesseract. The only thing that is changed is the shape. It is what the shadow of a tesseract would look like if it was rotated in the right way.

There are many other shapes in the fourth dimension besides a tesseract, which include 6 shapes that are closely related to the five three-dimensional platonic solids. There is also a shape related to the circle or sphere, which is called the 3-sphere or glome. It consists of all of the points at a certain distance x(in four dimensions) to a certain point. The cross-section of a 3-sphere is a sphere, just like how the cross-section of a tesseract can be a cube.

The shadow of a rotating 8-cell

Visualizing the fourth dimension is impossible, because we live in only three dimensions, however, there are three different ways we can make a small understanding of the fourth dimension. The first is by using three dimensional graphs that capture some of the elements of the fourth dimension. These can be like shadows or cross-sections of four-dimensional objects. They give some of the information about these objects, but never all of it. The second is by keeping in mind that four dimensions is to three as three is to two, so we can imagine how three dimensional objects would relate to a two-dimensional world.

The third is by using our own fourth dimension: time. Even though we can influence the future and it is impossible to look into it, and we can only see three dimensions, time can still be compared to a fourth. We can represent a four dimensional object by using time as one of the axes. Maybe we do live a four dimensional world.