Category: Graphs & Graphics

For those who require a graphical representation of concepts.

Zero One Infinity

Duncan 1 Comment

In life there is great uncertainty. Humans are constantly seeking explanations and crafting theories, struggling to decipher what is meaningless and categorize what is random. This urge to eradicate uncertainty gives rise to superstitions, rituals and maxims. We crave a fixed framework which correlates our behavior with our experience. More often than not, no such correlation exists, but that doesn’t stop us from trying.

In primitive cultures, the harvest of creatures and crops is a matter of survival. Because of the paramount importance and unpredictable nature of these harvests, members go to great length to ensure a bountiful yield. Sacrifice, worship, and ritual are common practices aimed at inducing a favorable outcome. Despite their lack of empirical support, these rituals are often based on inductive reasoning. Imagine, for example, a hunter, before setting out in search of prey, kneels down and rubs dirt on his hands. After having a successful hunt, a correlation is made between the behavior and the result and a ritual is born.

Though we have shed our primal roots, we still operate with an expectation that certain behavior will produce certain results. Slogans such as, “you reap what you sow,” and, “the early bird catches the worm” represent the common association of hard work and fiscal gain. Although these slogans may define a general pattern, as guiding principles they are as reliable as a rain dance or animal sacrifice. There are many notorious quotes by renowned thinkers which describe these  patterns, yet they all fall distinctly short of absolute credibility. Sometimes the diligent are punished while the lazy are rewarded. Sometimes the deceitful are praised while the honest are ostracized.

One avenue to certainty is statistical probability. Instead of attempting to mold rigid models to predict results, we can rely on the malleable and empirical nature of probability. Although this method has great value in certain areas, it does not satisfy our craving. Knowing that honesty is the best policy 57% of the time does not inspire honesty.

Though correlation and reasoning may not produce stable hypotheses, there are other tools which can be used to provide certainty. Mathematics is a field in which certainty is abundant; every equation has one result, one solution. In math, there is no interpretation, no ambiguity and no subjectivity. Unfortunately, mathematics does not correspond to our experience, but his cousin, physics, can be more helpful.

Everywhere we look, we can find patterns and trends in the universe. Truth can be found in the gravity of a black hole and the structure of an atom. The concept that no two things are identical is an example of extracting truth by observing our physical world. This idea reminds us that we should never treat two people or situations the same way. There is another principle which we can pry from the laws of the universe, one which can teach us a great deal about life, death and morality. This concept is known as the Zero One Infinity Theory.

The theory describes how objects and events of significance only manifest in one of three ways:

  1. The object or event has never existed and will never exist in the future.
  2. The object or event will only exist once, or under one condition, for a finite length of time.
  3. The object or event has always existed and will exist for all of time.

From this theory we can learn many things, let’s look at two examples. First, that cosmic and spiritual objects and events must exist in one of the three forms. For example, there is either no such thing as reincarnation, one reincarnation (or under one condition), or eternal reincarnation. The same rule applies to the number of inhabited planets, best men, deities and universes. One need not know a great deal about physics to realize that it does not make sense to only two universes in existence.

The second thing we can learn is that moral behavior in our lives should exist in one of the three forms. For example, we should either never tell the truth, tell the truth under only one condition, or always tell the truth. This also applies to things like theft, divorce, drug use, abortion and eating animals. All significant human behavior should be forbidden, permitted or required under one condition, or always permitted or required. Applying this pattern to our moral code will chisel the surface of the slope of judgement into the rigid and defined steps of judgment.

Some argue that a fourth option should be instated, that two is a legitimate number of occurrences. Though their thoughts are pure, these poor people are mistaken. Any amount of occurrences or exceptions beyond the first is arbitrary and shall be relinquished to the hands of infinity. Humans attach significance to many numbers for many reasons. We might value two because most external body parts appear in pairs, or because relationships require two people, we value three because three points are required to draw an enclosed shape and we value ten because of the decimal system. Regardless of the reasoning, these supposedly sacred numbers are generated by humans, who cannot be trusted in such matters. Principles of this magnitude must exist beyond humanity, uncorrupted by our interpretation. Though the number two may its own significance, you cannot have two universes or two gods. As Isaac Asimov stated, “Two is an impossible number, and can’t exist.”

The Uncanny Canyon: Part II

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In part I we learned about the relationship between humans and artificial beings, such as androids and toasters. We also learned about the plight of such beings which are too human to be treated like a robot, but too robotic to be human. Unfortunately, robots are not the only creatures trapped at the depths of the uncanny.

The graph we looked at in Part I was merely a two dimensional interpretation of a larger concept: the Uncanny Canyon.

Each line, or valley, is a representation of only one variety of the condemned. The canyon depicts the rejection, by humans, of the uncanny – that which closely resembles the familiar, but is not familiar. When we encounter something that is ordinary, yet strange, we can experience cognitive dissonance, resulting in the abjection of that uncanny thing. Basically, we reject that which imitates, or resembles, what we know and love. Anything which rings the bells of familiarity, yet is foreign to us, is a counterfeit and is treated with suspicion, including other people.

Whether we live in a multicultural or agricultural society, we find ways to separate ourselves from others and define our identity. Our clothes, speech, diet, musical taste and preferred sport – we use them all to distinguish ourselves as individuals. However, there is more to identity than individuality, for humans also have a desire to belong. We find others who share our behavior and preference, uniting with them to define our social identity.

Many wars which may appear to have been fought over money, power or religion, were actually fought over identity. In order to have a war, or any conflict, we must have an us and a them, and this distinction is most often made over small differences. If there was no identity, there would be no conflict in the world, but, whether by primal instinct or social convention, identity has become essential. This is why we are suspicious of others who resemble ourselves; they are a threat to our identity. Let’s look at some situations, both historical and ongoing, in which sharing similar behavior, origin and preference has led to rejection and conflict.

  • Schoolyard rivalries
  • Horde vs. Alliance
  • The Rwandan Genocide
  • Nintento vs. Sega
  • Protestants vs. Catholics
  • Mac vs. PC

In all of these examples the two sides share far more in common with each other than they share with any other group. PC users and Mac users may seem drastically dissimilar, sharing no more in common than John Hodgman does with Justin Long, but they actually only disagree on minor differences in user interface. Because the two sides share so much in common, they take intentional measures to segregate themselves from each other by creating unique vocabulary and launching ad campaigns.

High school is a breeding ground for us vs. them behavior. Even though the students may all be of similar age, live in the same area, have the same teachers and attend same classes, they are compulsed to separate themselves from each other, banding into rivalrous factions.

Without similarity, there is no conflict, for those who are vastly different from us cause only curiosity, not contempt. The reason for this conflict is because these groups have enough in common to make them suspicious of each other, but not enough to unite them, for unity is a part of human nature, but unity only with those who have crossed the Uncanny Canyon.

The Uncanny Canyon: Part I

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In the world of robotics there is a peculiar and well-known phenomenon known as the Uncanny Valley. In case you haven’t heard of it, we will briefly define the concept. If you would like to know more, please take a moment to e-search the subject before we continue.

The term Uncanny Valley was first used by a 1,970 year old Japanese robot named Masahiro Mori to describe how people react to humanoid robots, or androids. Some machines are not humanoid at all, such as the toaster, and we do not feel anything for them, apart from a mild appreciation for making our lives more delicious. We treat anthropomorphic contraptions like ASIMO as, in my opinion, a domesticated animal, such as a raccoon or bunny rabbit. The idea is that as robots become more human-like, we treat them with more respect and affection, but only until they reach the edge of the Uncanny Valley.

When encountering an artificial being, whether it’s an android or a computer generated character, we empathize with that being to a level appropriate with its appearance and personality. For example, R2-D2 does not have a humanoid body, but she does have a simple vocabulary of bleeps and whistles which allows us to empathize with the droid. C-3PO, on the other hand, has human form and is fluent in over six million forms of communication, though they must be spoken with a dainty English accent; his appearance and character elicit a response similar to what we would give an annoying child. One would think that as synthetic beings surpassed this stage, they would be welcomed as equals into society. Instead, they tumble down into the depths of rejection.

When a robot such as Wall-E or Johnny 5 embarks on an adventure, we are drawn in by their emotional journey, fragile whimpers and large eyes, but when we saw Actroid unveiled in 2003, something was clearly wrong. There’s no doubt that Actroid is more human in voice and appearance than any of the other androids we’ve mentioned, but there is something unsettling about a machine which so closely resembles ourselves. Theories range from a fear of robot dissent to the existential threat to our individualism – knowing that we could be copied or replaced. For now, let’s agree that there is just something creepy about these machines.

There is hope for aspiring androids; they can ascend out of the Uncanny Valley. Some say that by adding comical features we may restore emotional attachment to these rejected robots, but this merely pulls them backward, toward less convincing models. In order for these machines to achieve equality with humans, they must break through the barrier of believability and earn our love by an impeccable imitation, leaving not a hint of suspicion.

Today, androids of this caliber must still reside in the land of fiction. In movies and television their roles are filled by actors wearing cosmetics and costumes. Some motion pictures have attempted to capture the human form using computer generated images, but none have quite convinced audiences of the legitimacy of their characters.

In part II we will explore what the Uncanny Valley can teach us about subjects beyond the mechanical imitation of human beings.

The Good Stone

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Most of us think we are a pretty good person. Although we may not declare the fact with words, our self-righteousness is spoken by our actions. We all do things that we know aren’t right, but we do them anyway because they aren’t really that bad, like spitting our gum on the sidewalk or writing a blog while we’re at work. However, each of us has a list of things we would never do, because those things are really wrong, like stealing a car or cheating on a spouse. This list of inconceivable acts keeps us safely elevated above others, so that we may gaze down with contempt at those who do not hold to our standards.

This system also applies to social laws, ensuring that we don’t fall into that stereotypical group of people we enjoy disliking so much. We may have a nice house, but we don’t waste money like those people. We may not have the best kept yard, but at least we don’t have car parts lying about like them. Even if we were to break one of our rules, we would have a completely logical reason for this exception. All of our deeds are reasonable and fair, neither too hot nor too cold.

Basically, the idea is that, no matter who we are, we can use certain rules and behaviors to distinguish ourselves from others. We create an arbitrarily line in the sand, or a point on a slope, based on what we feel is right and say, “Anything beyond this point is unacceptable.”

As shown above, you rank somewhere slightly above average goodness which those people cannot seem to attain. Wait, why is A Stone on the graph? The reason is that the whole system we have set up to measure our goodness uses only negative indicators. We think we are good because we don’t swear too much, drink too much, drive too fast or watch too much television, but, according to that standard, a rock is superior to us in every facet.

A stone will never hurt, never steal, never lie,

Never will it curse you, or ever leave your side.

But a stone will never love, never smile, never give,

And never will it praise you, for it will never live.

Be better than a stone.

Kilometerage

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The traditional way in which we have measured fuel consumption for automobiles in America has been in miles per gallon (mpg). Since many countries are use the metric system, there has been a shift away from using mpg. Now this sounds like a great move, since the metric system is far superior to its imperial counterpart, but instead of simply converting miles to kilometers and gallons to liters, giving us kilometers per liter (km/l), we are now stuck with liters per hundred kilometers (l/100 km). It may seem like an insignificant difference, but there is a movement aimed at extinguishing mpg from the face of the Earth and replacing it with l/100 km. So if there’s people out there making websites and handing out pamphlets, there must be an obvious advantage to using the l/100 km system, right?

Proponents of the l/100 km system, or 100kers, try to confuse you by asking questions like, “Which saves more gasoline, going from 10 to 20 mpg, or going from 33 to 50 mpg?” Then they tell you that the answer is that the first option saves five times as much gas as the second. Upon hearing the correct answer, you are then shocked and upset, confused by why a 10 mpg change is much greater than a 17 mpg change. Instead of questioning why math is so dumb, let’s answer a better question: what is a consumption per unit system actually measuring?

Let’s face it, most people don’t know their mpg, let alone their km/l or l/100 km. When you ask someone what kind of mileage their car gets, the answer is something like, “I put $40 in there every two weeks,” or, “I can go three weeks before I have to fill up.” These answers are worse than useless, as we are not told the value of any variables in the equation.

Before we continue, let’s get a handle on what we’re measuring by calculating the mpg for an average car at the pump. Imagine that, after starting with a full tank of gas, you drove your Chevrolet Cavalier 300 miles, then decided it was time for a refill. After topping up, the display shows 10 gallons pumped. To find out how many mpg your car gets, you simply divide miles driven by gallons pumped (300m/10g) which gives us 30 mpg. What this number means is that for every gallon of gas you pump into your car you can drive 30 miles. Confused? No.

Similar to the previous example, let’s pretend that you drove your Cavalier 450 kilometers and then pumped 30 liters of gas to fill it up. Now to get your km/l you preform the same calculation as you would to get mpg, except you are dividing kilometers driven by liters pumped, which results in 15 km/l. However, if you’re a 100ker, you will divide liters pumped by kilometers driven, then multiply the answer by 100, resulting in 6.67 l/100 km. The meaning of this number is less obvious to the average driver, unless you are only driving in 100 kilometer increments.

So since we now have a grasp on how to calculate each of these measurements of mileage, let’s see if they are really that different. mpg measures miles driven per gallons used. km/l measures kilometers driven per liters used. l/100 km measures liters used per 100 kilometers driven. The third option is slightly different than first two because it is actually just the reciprocal of the second option multiplied by 100. The reason they use 100 kilometers is that dividing liters used by kilometers driven gives you a very small number between 0 and 1, as all modern consumer vehicles drive more than one kilometer for every liter of fuel they use. So if the third option is just the second one flipped upside-down, why all the debate? Let’s do some graphing. For the sake of comparison we are going to leave out mpg and use only kilometers and liters.

The graph above shows the mileage, or, more accurately, the kilometage of two vehicles. All vehicles plotted on this graph will show a straight line, unless they have inconsistent fuel consumption, which they don’t. The first line shows a vehicle which gets 4.5 km/l, likely a sport utility vehicle or large truck, while the second line represents a small sedan, showing an impressive 15 km/l. We can see that after driving 100 kilometers, the first vehicle consumes around 22.2 liters of fuel, while the second consumed only 6.67.

The confusion begins when 100kers compare the two lines on the graph and wonder why the difference in (km/l) is not the same as the difference in liters used. Basically, the amount of fuel used should not vary as you move along the graph. What they want is a graph which compares km/l  to liters used, but you can’t make that graph because there’s no way to know how many liters you are using unless you define how many kilometers you are driving. So we will plug in 100 km and graph how many liters are used every 100 kilometers as the km/l changes.

Now we have a nice graph which we can use to see how many liters we are saving as we adjust the km/l, just what the 100kers want. But why should everyone in the world use a system that is more difficult to calculate and less obvious in terms of daily use? At its core, the issue is that these people think fuel economy should always be used to determine how much fuel you can save when driving a set distance. What if you wanted to know how many kilometers you could drive with a set amount of fuel, or how many liters you will burn when driving any distance other than 100 kilometers? Apparently these questions aren’t worth asking.

The l/100 km method is also inconsistent with our fuel consumption language, since as fuel economy increases, l/100 km decreases. A vehicle that gets 2 l/100 km is twice as fuel efficient as one which gets 4 l/100 km. In addition, as fuel economy improves in the future, the number may drop below 1, which means that we could see hybrid sedans advertised with a fuel consumption of 0.33 l/100 km. Eventually we will switch to l/1000 km, all because of those selfish short-sighted 100kers.

So if you think that every motorist should do more calculations and use an ambiguous fuel consumption system which approaches zero as fuel economy increases, just so those who analyze fuel economy don’t have to do extra math, then go on, go the wrong way. We never wanted you with us anyway.

Engine House

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Despite the vast entertainment and luxury that can be found in urban environments, many of us long to escape, to get away, to a more peaceful and natural setting. There is something in us that can be satisfied only by a raw experience with the strength and tranquility of nature. Exploration and adventure are inescapable aspects of human imagination. Indeed, we long to travel the world, see new sights and overcome challenges, but we are restricted by our affection for comfort. This is why camping exists.

Camping is a diluted simulation of primal existence. Depending on the age and taste of the participants, the comfort level of a camping experience can range greatly.

To some, camping is a way to escape the grasp of technology and tedium. Hoping to renew their spirit, these hardy folk tend to employ tents and sleeping bags rather than more inviting facilities. The grass is their floor, the trees are their walls and a nearby bush is their lavatory. A flint-lit flame guides them by night, enchanting and entrancing with gaze lost deep in the flicker.

For young people, camping is as much an escape from society as it is from sobriety. Often unable to recall the origin of various bruises and swellings, the young camper is usually too intoxicated to be concerned with sleeping arrangements or niceties.

After years of hard work and stress, camping can be an attractive lifestyle choice for the aged. They are often observed piloting enormous bus-like vessels, known as recreational vehicles, down the highway. RVs vary in size and complexity; they can be as large as a log cabin and are extravagantly furnished. Satellite television and leather upholstery ensure that these campers must never endure a moment of silence or discomfort. An RV attempts to combine the transportation capabilities of an automobile with the habitability of a house. Unfortunately, when combining these two, the RV’s inventors decided that the exterior must be painted with a design that does not resemble an automobile or a house. It usually has strange arcs and waves splashed across a beige background. Whatever your opinion of this design, if somebody asked you to paint their house or their car, you wouldn’t choose something like this:

Now it’s obvious that sleeping in a king size bed while watching television could hardly be considered camping. At some point camping loses its essence, ceases to be camping and becomes something else. Thick-skinned pioneers may say that it ends when you bring shelter or matches, some say electricity or plumbing ruins all of the fun, while others contend that sleeping in anything bigger than a tent is the stake in the ground. Whatever the case, it’s clear that there is a camping chasm between survivalists and seniors.

By now you’re probably thinking that there should be a word to describe this comfort-coated camping, and you’re right.

Plotting Prudence

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A $200 computer can do almost everything that a $2,000 computer can do, yet it is one tenth of the price. A Toyota can do almost everything that a Ferrari can, but you can own seven fully loaded Camrys for the price of a 458 Italia. It’s true that a Ferrari outperforms a Camry in almost every area, but is that extra performance worth so much?

This phenomenon is present in every category, from studying for a test to cooking a meal. In anything which we invest time, energy or money to get a result, we will find that we get 90% of the value for the first 10% of the cost.

Of course, the value on this graph is in relation to functionality, not luxury or aesthetics. A painting which has received countless hours of detail is much more beautiful and meaningful than a doodle on a napkin, though they may depict the same scene. Likewise, a meal, when cooked with care for a loved one, conveys the appreciation and love not found in microwaving a frozen burrito. However, if you are going to make an investment or purchase for the sake of necessity or functionality, the efficient choice lies somewhere around the 10% mark.

Eco-Track

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One of the worst inventions in recent years has to be the Segway, a personal transportation device which uses gyrostabilizers and an electric motor to whisk pedestrians up and down the town. Besides the fact that the Segway accomplishes nothing that a bicycle or scooter cannot, no one in their right mind would spend upward of $5,000 for such gimmicky apparatus. In an age saturated with laziness and brimming with obeisity, people do not need another means to avoid physical activity. That is why many companies are now turning to HP (human-powered) technology in favor of electric devices. One of these devices is especially interesting, as it combines the health benefits of a treadmill workout with the modern sophistication of a Segway.

Now the future is one step closer, introducing the Eco-Track:

Take all the joy and satisfaction of physical exertion and put it together with hip, new-age technology and you get the Eco-Track. Who wouldn’t want to be seen moving down the street by the power of their own legs on this snazzy gadget?

The Eco-Track uses an electric motor, powered by a battery which stores the energy generated from the track; so simple, it’s brilliant. The speed of the Eco-Track ranges from a comfortable walk to a brisk jog, depending on what the rider prefers. If you want to increase the speed, simply walk faster and if you want to stop, just stand still.

Obviously, this invention is a forgery intended to point out the inherent stupidity of having a machine walk for you. Instead of inventing contraptions which separate physical activity from transportation, we should be seeking to unite them. We can start by taking things away from people and forcing them to use their bodies. No more Segways, no more forklifts, no more Zero-Point Energy Field Manipulators and no more crutches.

Faux Jock

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A faux jock is a male human who, by his physique and aggression, seems athletic, but only imbibes these traits for social purposes. The faux jock is identified by a few key characteristics:

  1. A disproportionately overdeveloped upper body.
  2. Readiness to engage in fisticuffs over trivial matters.
  3. A unique grip of cellular phones.

We will be focusing on the third identifier since the other two are fairly straightforward. The following step-by-step instructions will take you from ring to faux jock grip.

To begin, simply wait until your phone rings. While you are waiting you may take your phone from your pocket and send an insulting text message to a friend. Once the ringing begins you may answer or, if the caller is a girl, notify your peers that the call is, in fact, from a female. It also helps if you have the latest club song as your ringtone (the volume at maximum, of course).

Once the call is accepted, elevate the elbow connected to your grip hand as to make yourself appear larger. This is a common behavior exhibited by certain species of birds and reptiles to attract mates and intimidate competition. It also gives people a better view of your biceps. Ideally, the elbow should be raised high enough to give you a level surface on the outside of your forearm.

With the phone resting in a nearly open palm, use your index finger to firmly plant the upper part of the phone to your ear. You do not want to be seen as merely supporting the phone with your hand, but controlling it. You are the boss of the phone, not the other way around.

Once you’ve engaged in conversation do not yell but be sure that everyone nearby can hear everything you’re saying. This is another common demonstration in the animal kingdom – emitting loud noises to alert others of your presence. You may now roam the area, making sure to keep your torso upright and muscles flexed.

After the conversation is finished put your phone away and return to your group. It is now customary to downplay your enthusiasm, referring to the conversation or caller as a nuisance.

Now that you can recognize the faux jock grip be sure to conceal your laughter; the faux jock will charge at even the slightest threat to his pride.