Category: Graphs & Graphics

For those who require a graphical representation of concepts.

Low Flying Aircraft

Duncan

Most advertisements are irritating, fraudulent and meaningless. This includes sales promotions, public advisories and road signs. Behold the most useless notification ever presented:

Signs like this are often posted on the side of the road near airports in order to notify drivers that planes may be landing nearby. But what, exactly, is the purpose of doing this? What are drivers expected to do? Stop and wait for planes to land? Some say that the purpose of the sign is simply to inform drivers so that they are not startled when they see an aircraft approaching, but there are a few problems with this interpretation.

The first issue is the fact that these signs are usually posted near airports, and airports are far more visible than the signs themselves. Second, some versions of the sign include “CAUTION”, “WARNING” or “DANGER” or even an image of an airplane bouncing off the roof of a car, which implies that the purpose of the sign is to inform drivers of a threat. The final problem is that it is not common practice to use signs to notify drivers of things they can do nothing about. Drivers are constantly distracted by the beauty of nature, the peculiarity of pedestrians and the hideousness of modern exterior home design, but we don’t put up signs with “CAUTION BEAUTIFUL FOREST”, “DANGER WEIRD PEOPLE” or “WARNING UGLY HOUSE” on them.

We don’t need to know what’s above us when we’re driving, especially when we can’t do anything about it.

Two-legged Friends

Duncan

Dogs are often called our four-legged friends, but this label is inaccurate in more ways than one. First of all, many dogs are not friendly. Each year, nearly 4.5 million Americans are bitten by dogs, and half of those are children. That means a child is bitten by a dog every 16 seconds in the United States alone. The other inaccuracy in this title has to do with the physical anatomy of canis lupus familiaris (the domestic dog).

According to the dictionary, a leg is defined as a limb used for support or mobility. Naturally this would imply that humans have two legs and dogs have four. But our understanding of what constitutes a leg varies depending on the species. Gorillas, for example, walk using all four limbs, yet most would agree that they have only two legs. Most contend that the front two limbs of a gorilla should be considered arms because they are used in much the same way that we use them: to forage for food, to use tools and to scratch ourselves. However, dogs use their front limbs for digging, climbing and adorably covering their faces, yet these appendages are somehow not awarded the title of arms. But if a dog’s front limbs aren’t arms, what are they and why?

A common understanding of the distinction between arms and legs is the idea that arms have hands. Proponents of this view would argue that a gorilla’s front limbs should be considered arms because they have hands with opposable thumbs, but there are many other creatures with hands that have thumbs, including the giant panda, the chameleon, the opossum and some species of reptiles, rats and frogs. So not only does the hand-arm theory imply that rats and frogs have arms, it also would mean that a gorilla has no legs at all because its feet have opposable toes as well. In addition to these complications, this understanding fails to address the fact that many animals, including the dog, have significant anatomical differences between the front and rear appendages.

There are yet others who subscribe to the if-it’s-not-a-leg-it’s-an-arm movement (IINALIAA), which implies just that: any limb not used for mobility is an arm. While this idea perfectly explains the anatomy of bipeds such has humans and kangaroos, it also implies that gorillas don’t have arms and that birds might actually have arms. Since this argument specifically tackles the issue of identifying arms among legs, it doesn’t effectively address limbs such as wings, which, while they aren’t legs, are used for mobility. In addition, it’s obvious to everyone that a gorilla’s front limbs are much more armish than a bird’s wings.

Each of these explanations falls short of satisfying our understanding of the difference between arms and legs, and so we have a problem. Both gorillas and dogs use all four limbs for mobility, have different front and rear appendages and use the front two for special functions, and yet we deny dogs arms. What’s not in dispute here is the nature and function of a leg – any child can tell that legs are used for walking. What is in dispute is what makes some legs arms.

To take a brief break from animals with controversial limbs, let’s take a look at a creature with an anatomy that we can all agree upon: the centipede. Centipedes are totally disgusting and possess anywhere between 20 and 300 identical limbs, each used solely for mobility and freaking people out. There’s no debate about whether any of these legs are actually arms because the only purpose of each limb is movement and all of them are the same – and that’s where the difference lies. When we inspect the anatomy of humans, gorillas and dogs, the one feature that they all share is an obvious design difference between the front and rear limbs. And not only is the form and function of each limb set unique, the structure of the joints that connects the limbs to the body is also different.

As illustrated above, dogs possess both a set of hips and a set of shoulders, and everyone knows that shoulders connect to arms. Also, if the front and rear limbs of these animals are so different, why should we give them the same name? If gorillas have arms, then arms can be used for mobility. And if kangaroos have arms, then arms don’t need hands with opposable thumbs. So if dogs have shoulders and if arms can be used for mobility and don’t require hands, then we’re left with only one conclusion: dogs must have arms.

The error lies in the false belief that an arm is defined by what it doesn’t do instead of what it does. A leg does not become an arm when it stops being used for mobility; a leg becomes an arm when starts being used for more than mobility. Just think of a panda laying on its back eating bamboo. Is it really using its legs to grab hold of the shoots and bring them up to its mouth? Of course not!

This new understanding of limbs is sure to make some people uncomfortable. After all, what about horses, hamsters, llamas and lemurs, seals, skunks, tigers and turtles? Surely the entire animal kingdom must be reexamined in order for their limbs to be properly classified. But just because a proposition implies a difficult solution, it doesn’t mean it’s incorrect. In fact, it’s likely evidence that the opposite is true.

thINK

Duncan

One of the most popular and accessible forms of art involves the creation of two-dimensional imagery on a surface. This is called drawing. Drawing can be done professionally or casually, for profit or personal satisfaction. It can also involve a number of different mediums, including the more traditional pen and paper or oil and canvas, modern instruments like the computer or Magna Doodle and even human skin.

Tattooing dates back thousands of years and spans many cultures across the globe. Each society’s tattoos are visually distinct, employing unique color, content, size, location and pattern. In addition, these designs can serve many different purposes. For the indigenous Polynesians of New Zealand, tattoos were an indication of higher rank or status and also signified a rite of passage into adulthood. During the Kofun period in Japan, tattoos were placed on criminals as a form of punishment. Many cultures use tattoos for religious or spiritual purposes, to honour the dead, to intimidate enemies, to commemorate marriage or simply to appear more attractive.

In modern Western culture, the design and purpose of tattoos is not standardized, but rather determined by the individual. And as with many of our traditions, including naming our children, we tend to borrow from other cultures in an attempt to find purpose and appear unique and sophisticated. In our quest for meaning, we blend Polynesian tribal patterns with Japanese kanji, dragons with crosses, yin-yangs with Bible verses, skulls with Gothic lettering as well as a myriad of other sacred symbols, producing an amalgamation of ancient art that would likely offend and confuse each culture from which we borrowed. Because our population is multicultural and our society prioritizes the individual, each of us is permitted to create our own reality, religion and tattoo design. But in our apparent quest for meaningful markings, we have forgotten one important fact, the true reason why we actually get tattoos: because we want to.

Whenever we ask someone about the meaning of one of their tattoos, the explanation we get usually seems valid. They’ll explain to us how a rose symbolizes their grandmother, who loved roses, or how the number 27 is lucky because all of their children were all born on the 27th day of the month, or how a bloody reaper-skull wearing a crown of thorns reminds them not to fear death but to live life to the fullest every day. These explanations may all be rooted in truth, but there are many ways to commemorate important people or dates or to remind ourselves of mantras, so why did they choose to draw on themselves? Why not just get a picture framed or a piece of jewelry made?

Many would answer that the nearly inescapable permanence of tattoos adds a dimension of commitment to the expression, and that’s true, but let’s think about what the primary factor is for motivating someone to get a tattoo. If the true cause is the death of a loved one, then the person would think something like, “How can I most effectively express my sorrow? Perhaps I should get a tattoo,” but this is inconsistent with the massive number of people who get multiple tattoos and the growing number of those who identify themselves as tattoo addicts. The truth is that every single person who walks into a tattoo parlor wants a tattoo. They may want to commemorate their dead grandmother or immortalize their mantra, but much like the way we choose names for our children, they ultimately decided on the tattoo medium because they liked it. After all, no one ever reluctantly got a tattoo simply because they figured it was the most effective medium.

This isn’t meant to discredit or insult those who have tattoos, since those who choose other mediums also do so because they prefer them. But it’s important to be honest with ourselves and to understand our true intentions, especially when we’re doing something that cannot be easily undone. There’s always a chance that our tattoo will come out wrong because of mistranslation or poor quality artwork, that the tattoo will degrade over time, that the shape of our body will change, that we’ll change our opinion of the subject or that our taste in art will simply evolve.

The idea of sewing a pair of pants to our legs is ridiculous, but even if it was safe to do so, it would seem absurd to imagine that we would always enjoy wearing the same pair of pants. And yet we somehow convince ourselves that we will always love our tattoos, that we won’t be ashamed of them and that the issues that our future selves will face are somehow detached from the choices we make now. Deep down we all know that permanently marking our bodies for aesthetic purposes is foolish. But those who want tattoos are still going to get them, so in light of what we’ve learned, let’s set a few rules in order to minimize the risk of regret and avoid a design that offends another culture or doesn’t make any sense.

  1. Don’t choose someone’s name or face. You might end up feeling differently about them.
  2. Don’t choose another language. There’s always a chance of mistranslation.
  3. Don’t choose a slogan or mantra that may become unpopular.
  4. Do a spell check.
  5. Choose an area of the body that ages well.
  6. Choose an area of the body that can be easily hidden by clothing.
  7. Get a temporary tattoo and see if you like it.
  8. Finish the tattoo.

In other words, don’t get this:

No one who didn’t want a tattoo ever got one.

Griddle

Duncan

What if grids began to speak,

Would this be called gridtalk?

And what if grids could tell the time,

Would they all use gridclocks?

What if grids could blaspheme things,

Would their god be gridmocked?

And what if grids had little shoes,

Would they also wear gridsocks?

What if grids could play music,

Would we call this gridrock?

And what if grids could move around,

Would we say they gridwalked?

‘Cause after all, when a grid get’s stuck,

We all know it’s gridlock.

Sine

Duncan

Yesterday you woke up from your bed and dressed yourself for the day. In addition to accomplishing the day’s necessary tasks, you ate some food and enjoyed leisure time, possibly with friends or family.

When you woke this morning, you dressed yourself in different clothes, and after accomplishing your daily tasks, ate different food and spent your leisure time in a different way, likely with different people. Why the change? Why didn’t you wear the same clothes, eat the same food and relax the same way as yesterday? Your clothes are still in style, the food tastes the same and your friends and activities are just as interesting. The answer is actually woven into the very nature of the universe: the inevitability of change.

At some point in the distant future, gravity will condense all matter in existence into a singularity. This is likely the end of the universe, after which there will be no more change. But until entropy finally conquers the universe, collapsing all matter and dissipating all energy, everything must always be changing. Particles collide and energy transfers as stars and planets dance and scatter light through space.

Inside the fabric of reality, beneath our subconscious and between the helices of our DNA is the necessity for change. We battle against entropy, attempting to minimize the chaotic nature of universe, but we can’t truly escape it. It’s impossible for anything to remain truly constant, but the closest thing to constant is undulation, and that is what we experience: the sine wave of life.

X can be anything from happiness to hunger, sleepiness to sexual desire, even wealth, fashion, friendship or conflict. The undulation describes each individual, family, city or nation, and it’s accurate on a variety of time scales. It describes our days, weeks, years, lifetime or even our entire history. Here are some common places in which the wave’s undulations can be witnessed:

  • A person observed daily: sleep, bathe, get dressed, work, eat, relax, sleep.
  • A student observed during a semester: enroll, learn, study, write exams, vacation, enroll.
  • A lineage observed during a lifetime: birth, adolescence, adulthood, old age, death, birth.
  • A constituency observed through a term of office: elect, celebrate, complain, yearn for change, elect.

Obviously the highs and lows are not always equal, and the undulations are not uniform in length. Sometimes we will experience terrible tragedy or great joy, creating an unusually intense wave. There are also periods of dullness or inactivity, both large and small, in which the waves are so tiny and so fast they could hardly be said to have occurred at all. But this steady undulation is generally accurate and does provide a unique view of our existence.

Now it’s true that all things come to an end, so the undulation cannot continue indefinitely. Some argue that after the end of the universe, another big bang will occur and create a new universe, but this idea is based almost entirely on wishful thinking and a poor understanding of the origin of the universe. Regardless, the undulation must eventually end, and we already know how this will end: the same way it began.

The lifespan of any system, entity, event or organization tends to start with a dramatic rise, experience an apex near the center, then decline sharply toward the end. So if we were to zoom out from the sine wave and observe the subject from beginning to end, we would see that the wave is actually part of a much larger parabolic arch.

An example of this parabolic effect would be the sharp rise and eventual decay of satisfaction while eating a meal, or the initial excitement and appreciation for a new vocation, which eventually fades into boredom, apathy and finally termination.

If we zoom in on any sine wave, we can see that there are even smaller undulations that occur during the larger ones, for each experience or undulation is comprised of an infinite number of smaller events, right down to the subatomic level.

These waves reflect the less significant fluctuations that occur throughout an experience. Here are some examples:

  • A mouth observed during a meal: bite, chew, swallow, drink, wipe, bite.
  • A student observed during a study session: focus, read, get distracted, take a break, focus.
  • A mother observed during childbirth: push, wonder when it’s over, breathe, push.
  • A politician observed during a campaign: do an interview, give a speech, shake hands, kiss a baby, travel, do an interview.

As individuals, much of our time and energy is dedicated to the satisfaction of temporary urges – urges that return again and again. Most of us derive a great deal of satisfaction from appeasing these requirements, and some even extract meaning and identity through this process. After all, without constant cravings for food, sleep, sex, fun and friends, how would we spend our time?

Lack of appetite for food, sex and social interaction is often a sign of illness, for no healthy person would choose to avoid these things. But if there was a procedure that eliminated these urges without compromising health, such as a pill that eliminated the need for sleep, it’s likely that few would be frantic to sign up.

There are those who would describe this view of existence as nihilistic or depressing and argue that there are more noble aims, such as helping those in need. But is helping others not simply assisting them in satisfying their own temporary cravings? By devoting ourselves to feeding the hungry, clothing the naked, befriending the lonely or eliminating disease, we are affirming the paramount importance of food, clothing, friends or health. And while we may improve quality of life, the formerly in need are not exempt from the undulations of life and its inevitable parabolic end.

Those who preach salvation would likely contend that the true purpose of life is not found in the satisfaction of needs (or even the needs of others), but in the glorification of a deity and eventual perfection of existence in the afterlife. But glorifying a deity is merely providing satisfaction to a being that craves glory, and most religions promise an afterlife that fulfills our needs and desires with feasts, kingdoms, virgins and gold. And if heaven is merely dedicated to the eternal gratification of a deity and of our own Earthly appetite, does this not mean that we, like our deities, are destined to be eternal consumers?

Time Math: Part II

Duncan

French philosopher Marquis de Condorcet declared that the metric system would be, “for all people for all time,” but time, ironically, is the one subject that has not been transformed by the metric system. In part I we discussed how math is made much more difficult when working with units of measure that don’t have a base of 10. Now we’ll talk about why metric time is such a uniquely complex concept.

In order to implement the metric system, we must simply choose a base unit for measurement and apply the metric prefixes. To measure length, for example, we simply choose an arbitrary distance, like a meter, and then scale out from it in multiples of ten. The base unit could be any size, but it’s helpful to select a measurement that we can relate to easily. It could be argued that inches and pounds are better base units than meters and grams, since we can more easily and accurately convey their size.

Choosing a base unit for mass, volume and distance is easy because we can just make up their duration. However, time has the unique and complicated quality of being derived from observable constants. We cannot choose the length of a day, for a day is based on the rotation of the Earth. If we were forced to use the day as our base unit for metric time, it wouldn’t be a serious problem, but time is actually based on more than one constant. Let’s take a look at each of the standard units of time and see which ones are arbitrary and which are fixed.

  • Year: fixed, one revolution of the Earth around the Sun.
  • Season: arbitrary, 1/4 of a year.
  • Month: arbitrary, approximately 30 days or 1/12 of a year.
  • Lunar month: fixed, approximately 27 days.
  • Week: arbitrary, 7 days or approximately 1/4 of a month.
  • Day: fixed, one rotation of the Earth on its axis.
  • Hour: arbitrary, 1/24 of a day.
  • Minute: arbitrary, 1/60 of an hour.
  • Second: arbitrary, 1/60 of a minute.

As we can see, most of the units used to measure time are constructs of our own design, with years, days and lunar months deriving their duration from the movement and rotation of the Earth, Sun and Moon. The problem here not that there is a fixed unit of measure, but that there are multiple fixed units that do not factor into numbers conducive to a metric (base 10) numeric system. Metric systems are founded on the multiplication of a single unit in a decimal pattern, but a day is 1/365 of a year, and both units are necessary. Now we find ourselves in a difficult situation.

With time, we do not have the luxury of choosing a unit to construct a metric system around. Since both days and years are fixed and prove quite necessary for keeping time, we are forced to incorporate two units. This produces an aberration that prevents a pure metric system from being implemented. Although we may not be able to achieve a perfect system, this doesn’t mean that we should accept a terrible one. Let’s see if we can come up with something that at least improves on standard time and allows us to solve some of the problems posed in part I more easily.

First of all, we must choose what unit our system should be based around. Because we must incorporate both the day and the year, we are forced to choose one of these two units. Since the length of a day is more easily communicated, though not as easily as a second, let’s go with that. Before we continue, let’s take a look at how the units in our current time system scale based on a day.

Aside from the massive inconsistencies displayed above, it’s worth noting that the duration of the units range from 10^-5 to 10^3 days. This is because the length of a day is actually quite large in comparison to the volume of a liter, as strange as that sounds. If we were to create an arbitrary unit of time on which to base a time system, we wouldn’t make it a day, for a day takes an entire day to happen. We would probably choose a duration somewhere between a second and a minute, likely ranging from 2 to 6 seconds. Unfortunately we’re stuck with a day, so we’ll have to work from there.

In order to have the system function in multiples of ten, we must change the length all arbitrary units. We also need to add units near the lower end to fill in the gaps in order to keep seconds, minutes and hours relatively similar to their current duration. Some have suggested using the names like chron and tick, so let’s go with that.

But should we really be adding more names for units of time? In order to remain consistent with metric measurement, we should abandon the naming of each individual unit, accept the day as the base unit and the year as an anomaly. Now let’s compare the new day-based metric units to the old standard ones.

So according to metric time, a second is now .86 seconds. This seems like a difficult change to adopt, but it might help to start counting with Missouri instead of Mississippi. Another problem could be that we are used to counting time using many different units. In standard time we use measurements like 15 minutes and half an hour, but it seems odd to say 15 millidays or half a deciday. The way time is written also needs to change. In the past, clocks would read 6:15, which is 6.25 hours or .26 of the day. But 6:15 in metric time is 6.15 hours or .615 of the day. So how to we communicate metric time?

There are many different ways to write the date and time in our current system. Here’s a popular choice:

Monday, December 31, 11:59 and 59 seconds PM

Notice that we often use the specific name of the day and month, but we never indicate the week. The date is also written in reverse order of time, which can be confusing. Here’s another example of a more uniform way to write the same time:

12:31:23:59:59

This format is difficult to understand, for it doesn’t tell us which digits are what units. If we were to speak it out loud it would sound like this:

12 months, 31 days, 23 hours, 59 minutes and 59 seconds

Since the base of the units varies, it may not be obvious that the following time occurs just one second later:

01:01:00:00:00

It’s worth noting that the month and day are both automatically bumped to the first, despite never counting past zero – yet another inconsistency. In metric time, we don’t have to keep track of seconds, minutes, hours, weeks and months, since we’re only measuring time in days and years. Here’s the first example written again in metric time:

365:9:9:99

Said aloud in standard time, it reads:

365 days, 9 hours, 9 minutes and 99 seconds

Remember that there are 100 seconds in a minute when using unit names taken from standard time. If we were to simply use one unit of measure, the day, then metric time would look like this:

365.9999

And then the time one second later:

0

That’s right, one second after midnight on December 31 would be 0 in metric time. Pretty cool, huh? Unfortunately, this doesn’t solve all of our time problems, since we still have daylight savings time, leap years and time zones. We’ll explore how these mechanics work in part III and attempt to resolve them peacefully.

Attacking Art

Duncan

Although it’s completely unnecessary for survival, most consider art to be an essential part of human life. After all, it is one of the five pillars of civilization. Despite the importance we place on it, offering an adequate description of art can be difficult. Most of us have a general understanding of art, pointing to classical paintings and sculptures such as Michelangelo’s Sistine Chapel ceiling and statue of David as examples, but what about more contemporary and peculiar pieces like Jackson Pollock’s No. 5 or Ellsworth Kelly’s Cowboy?

One of the ramifications of a poor definition of art is the frivolous labeling of individuals as artists. Classic forms of art include painting, sculpting and pottery, music, dance, acting and literature, but the term has been increasingly used to include modern vocations and hobbies such as photography, graphic design, 3D modeling, architecture, tattooing and rap. In its advertisements, Subway even claims that its employees are sandwich artists, stretching the concept of art so thin as to bankrupt it of meaning.

While it’s true that there is a degree of creativity and skill involved in nearly all aspects of life, that alone doesn’t make it art. If we include every craft, structure, schematic, machine, weapon, tool, toy, sport, code and clothing in the definition of art, then every person on Earth is an artist (as well as most animals). In that case, we would need to create a new term to describe works done for aesthetic and expressive purposes and another to describe those who devote themselves to their creation. However, creating a new word simply because its definition has been corrupted by misuse is no way to build a language.

Debate over the legitimacy of various artists and expressions can be intense, with parties citing arbitrary qualifications to suite their particular understanding of art. However, without a universally-accepted set of criteria to recognize it, how can one claim that something is or isn’t art? Although placing a restrictive definition on something as diverse and interpretive as art may seem impossible, perhaps it’s possible to establish some general guidelines. By looking to history for examples, we can glean at least four crucial criteria:

  1. Originality
  2. Meaning
  3. Skill
  4. Purpose

In order to qualify as art, a piece must be original. If a painter were to merely reproduce a famous painting, such as Picasso’s Guernica, it would not be heralded as a great work but merely an homage. In addition, a mass-produced item, such as a dime, may be beautiful, but it is not unique and therefore can’t be art. It’s also important to note the difference between an artist and a performer, since a performer is not necessarily generating something new. Although a performance may be meaningful and skillful, displaying another’s creation does not make the performer an artist.

The second criteria of art is meaning. The piece must be an expression of an emotion, event or experience, and it must attempt to draw some kind of reaction from its audience. Merely displaying mundane objects like a cotton swab, rock or hammer does not conjure an emotional response. Some may argue that mundane objects can have exceptional meaning, but this meaning is only created by the perception of the object is art, not from the object itself. If placing everyday objects in an art gallery makes them art, then everything on Earth is art, and we run into the same vocabulary issues again. It is possible for mundane objects to be incorporated into art, but this must be done with an intent to convey a greater meaning than that of the object itself.

Another important feature of art is that it requires skill to create. If a piece of art can be easily and quickly produced by most people, then it can’t be art, no matter how unique and meaningful it is. This is why some feel that advanced tools, such as computers and painting machines, erode the legitimacy of art. Consider Microsoft’s Songsmith software, which automatically generates music to accompany a vocal recording. Using this program, a few simple clicks can produce an elaborate, unique song. However, most would agree that music produced so easily is not art, for the artist did not invest time, energy or emotion into its creation. In order for art to be recognized, it must require some level of devotion from its creator. This is part of the reason why traditional forms of art, like paintings and sculptures, are still popular, and it also explains why artists sometimes use strange, rudimentary materials like toothpicks, broken glass and old, discarded sandwiches. The more simple and demanding the instrument, the more legitimate the art.

Finally, the purpose of the piece must be taken into consideration. It must not perform a function that transforms it into a tool or gadget; it must exist for the precise purpose of expression. A creation made with the intent to be used, worn or eaten is an invention or a product, not art. A car may be beautiful, but its beauty is secondary to its function. Sometimes the line between art and invention is blurred. Exotic furniture, fancy cakes and Rube Goldberg machines all have functions, but they are secondary to their beauty.

It’s debatable whether a work must meet all four of these requirements in order to be considered legitimate art, but it’s clear that these are important factors to consider. One criteria not mentioned here is beauty, which is supremely subjective and difficult to define. There are also many legitimate works of art which few would consider beautiful, like William Blake’s Great Red Dragon paintings. It could be argued that there is beauty in the hideous nature of such works, but if the definition of beauty can be expanded to include the ugly, then it’s not a useful classification.

Establishing clear definitions before engaging in any debate is essential, but it is especially important when arguing about something as trivial as art.