Two opposite parts of one whole.

A dichotomy is an idea or classification split in two. When you point out a dichotomy, you draw a clear distinction between two things.

A dichotomy is also a contrast between two things. When there are two ideas, especially two opposed ideas — like war and peace, or love and hate — you have a dichotomy. You often hear about a "false dichotomy," which occurs when a situation is unfairly represented as an "either/or" scenario. For example, the statement "All cars are either small and efficient or large and polluting" creates a false dichotomy because there are some cars that don't fit into either category.

DEFINITIONS AND USAGE EXAMPLES

Pronunciation: \ dahy-kot-uh-mee\

Being twofold; a classification into two opposed parts or subclasses.

Two opposite parts of one whole. o The film critic discussed the fundamental dichotomy in the movie. o The dichotomy between eastern and western culture o Synonyms: duality

(logic) The division of a class into two disjoint subclasses that are together comprehensive, as the division of man into white and not white.

(biology, taxonomy) The division of a genus into two species; a division into two subordinate parts.

(astronomy) A phase of the moon when it appears half lit and half dark, as at the quadrature.

(biology) Successive division and subdivision; successive bifurcation, as of a stem of a plant or a vein of the body into two parts as it proceeds from its origin.

(biology) A fork (bifurcation) in a stem or vein.

Directions: Discuss the meaning of the word with your students, with special emphasis on any variations or nuances of the word specific to your discipline. Consider taking it a step further by using one or all of the following ideas as you involve students with the new vocabulary. Remember to preview all content you intend to share with students. Not all items on the lists provided below are

appropriate for all classes or age levels.

(Math)

Zeno's Paradoxes

A set of four paradoxes dealing with counterintuitive aspects of continuous space and time.

1. Dichotomy paradox: Before an object can travel a given distance , it must travel a distance . In order to travel , it must

travel , etc. Since this sequence goes on forever, it therefore appears that the distance cannot be traveled. The resolution of the

paradox awaited calculus and the proof that infinite geometric series such as can converge, so that the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances.

2. Achilles and the tortoise paradox: A fleet-of-foot Achilles is unable to catch a plodding tortoise which has been given a head start, since during the time it takes Achilles to catch up to a given position, the tortoise has moved forward some distance. But this is obviously fallacious since Achilles will clearly pass the tortoise! The resolution is similar to that of the dichotomy paradox.

3. Arrow paradox: An arrow in flight has an instantaneous position at a given instant of time. At that instant, however, it is indistinguishable from a motionless arrow in the same position, so how is the motion of the arrow perceived?

4. Stade paradox: A paradox arising from the assumption that space and time can be divided only by a definite amount.

The dichotomy paradox leads to the following mathematical jokes:

For you, not your students: A mathematician, a physicist and an engineer were asked to answer the following question. A

group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are

distance apart at time 0, they are at , at , at , and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.

For your students:

(Science/Astronomy)

“Giant Asteroid Collision May Have Radically Transformed Mars” Scientific American – 25 Feb. 2015

An ancient, global-scale impact could explain the Red Planet’s mysterious “two-faced” appearance.

1--When the team simulated a collision with an asteroid about 4,000 kilometers across (slightly larger than Earth’s moon) they found that it caused the crust of the “virtual” Mars to reform into two distinct zones.

Click on picture to link

to the article.

The planet Mars has been associated with its namesake god of war for millennia, but its own past

may have been more violent than was previously imagined. A new study suggests that Mars was

once hit by an asteroid so large that it melted nearly half of the planet’s surface.

Researchers came to this conclusion while studying a strange feature known as the Martian

hemispheric dichotomy—a dramatic drop in surface elevation and crustal thickness that occurs near

Mars’ equator. In the northern hemisphere the land’s elevation is on average about 5.5 kilometers

lower and the crust is around 26 kilometers thinner.

The dichotomy was discovered in the early 1970s when NASA’s Mariner 9 probe made the first

detailed map of the Martian surface. The feature has perplexed astronomers ever since. Previous

studies hinted that the dichotomy was formed by a glancing asteroid strike near the Martian north

pole. But the new work, published in Geophysical Research Letters in December, suggests that a far

more violent impact, at the opposite end of the planet, may have been the actual cause.

“New Venus NASA Missions Could Lift Planet's Hellish Veil”

Forbes—15 July 2014

If Mars is mysterious, Venus is truly scary. Long called Earth’s twin, it’s only four months away via

unmanned probe and lies more than 70 percent of Earth’s distance from the Sun.

But with surface pressures and temperatures high enough to melt lead and crush steel, why is Venus

so hauntingly different from Earth? And when did it go bad?

“Venus and Earth are virtually identical twins; they’re almost the same size,” said Robert Herrick, a

planetary geophysicist at the University of Alaska in Fairbanks. “But Venus is completely

uninhabitable; we really don’t understand how that dichotomy came about.”

The European Space Agency’s (ESA) Venus Express orbiter has spent the last eight years trying to

dissect its hellish atmosphere and surface. But now with dwindling fuel, by year’s end the spacecraft

is expected to make its final plunge into Venus’ toxic atmosphere.

Scale representations of Venus and the Earth shown next to each other. Venus is only slightly

smaller. (Photo credit: Wikipedia)

Click on the picture to link to the article.

(English)

Dichotomy is a Greek word dichotomia that means “dividing in two.” Dichotomy is a literary technique that divides a thing into two equal and contradictory parts or between two opposing groups. In literary works, writers use this technique for creating conflicts in the stories and plays. Its common examples in literature are good and evil, soul and body, real and imaginary, heaven and hell, male and female, and savage and civilized, etc. Often, dichotomy appears in a single character; however, sometimes writers use separate characters for representing opposing ideas.

Examples:

From Star Wars, Luke Skywalker/Darth Vader-- Both representing the dichotomy between the Jedi

and the Dark Side.

Dr. Jekyll/Mr. Hyde--Here the dichotomy is centered in one character, representing good and evil.

The Hunger Games, The setting forms a dichotomy--the corrupt Capitol versus the

honest, hard-working districts.

Doctor Faustus

Good Angel: O Faustus! lay that damned book aside,

And gaze not upon it lest it tempt thy soul.

Evil Angel: “Go forward, Faustus, in that famous art,

Wherein all Nature’s treasure is contain’d…

Good Angel: Sweet Faustus, think of Heaven, and heavenly things.

Evil Angel: No, Faustus, think of honour and of wealth.

(Doctor Faustus by Christopher Marlowe)

This is the most notable example of dichotomy, where good and bad angels represent two parts of

Faustus’s consciousness. Good angel asks him to repent and ensures his path to heaven, while bad

angel asks him to seek power, lust and knowledge that would lead to eternal damnation.

Beowulf

You can find a perfect example of dichotomy in the old English poem, Beowulf, that

dilates upon the theme of good versus evil, where Beowulf is a good character,

while three monsters are evil characters. Beowulf is larger than life personality, who

kills Grendel, his mother as well as the dragon. As a descendent of Cain, Grendel is

an evil, selfish and strives for personal gains, whereas Beowulf is a triumphant

hero, who fights for others, serves them and defends them. This poem also

contains the dichotomy of light versus darkness, such as when Grendel appears to

attack on mead hall at night, which shows evil and dark attacking good and light.

Like Grendel, death represents darkness, whereas treasures Beowulf receives represent light.

Macbeth

Shakespeare uses dichotomy in his complex characters. Macbeth is a good

example of the conflict between good and evil as Macbeth, rewarded for valor

on the battlefield and considered the king's loyal ally, cannot fight his "vaulting"

ambition which, he admits, "o'er leaps itself" and to which he refers in Act I,

scene vii, line 27. Macbeth has the power to discount the witches' prophesies

but, instead, due to his tragic flaw and his over-zealous wife, he transforms

into a killing machine, callously attempting to dispose of anyone in his way.

The Lord of the Flies

Dichotomy is represented in Lord of The Flies by the democracy and order of the

conch contrasted with the savagery of Jack and his hunters. Ralph and Jack

reflect two opposing sides of the leadership struggle, despite the fact that they

both have certain characteristics which could have, under different

circumstances, complemented each other. By the end of the novel, however, the

situation has changed and the dichotomy between good and evil is uncertain as

the reader sees the change in Ralph who cries, "for the end of innocence."

Consider a discussion based on this quote:

(Science)

In biology, dichotomies are often used in keys, tools that are used to help people identify things. For example, a

plant key might help people identify plants with a series of questions like “are the stems green?” Such a key is

known as a “dichotomous key,” and these tools can be quite reliable when well designed, as they neatly rule out

options until the user is left with one solid identification.

(Philosophy)

False Dilemma or Dichotomy

A false dichotomy or false dilemma occurs when an argument presents two options and ignores, either purposefully or out of ignorance, other alternatives.

In general, a false dichotomy gives the impression that the two opposite options are mutually exclusive (that is, only one of them may be the case, never both) and that at least one of them is true, that is, they represent all of the possible options.

False dichotomy examples:

For example, the claim that “you’re either with me, or you’re against me” is an example of a false dichotomy. This form of rhetoric is used to persuade or even threaten, but it ignores the fact that the individual or group addressed may have a neutral opinion towards the speaker. It is logically possible for someone to be neither with nor against an individual.

A more obvious example would be the claim ‘All animals are either mammals or fish.’ We could use that, with the premise ‘my pet parrot is not a mammal’ to conclude that ‘my pet parrot is a fish’. Clearly, something went wrong. The problem here is not a failure of logic in the argument form, but that the first premise is a false dichotomy. That premise is false — there are also birds, for one, as well as other groups of animals.

Falsum in uno, falsum in omnibus

A special version of this fallacy is known as falsum in uno, falsum in omnibus, essentially “false in something, false in everything”. This is a combination of a false dichotomy and an ad hominem attack, because it attempts to disregard everything the person is saying by the claim that they’re either presenting the truth or presenting falsehoods. It ignores the possibility that the individual is wrong about one thing but right about others. The fact that someone has been proven wrong about claims they made is a potential reason to suspect other claims they make, but not a logical reason to disregard them entirely.

(Technology)

Discuss this quote with your students. Do your students agree, and if so, what proof can they provide? (Ben Parr is an American journalist, author, venture capitalist and entrepreneur. He is the author of Captivology: The Science of Capturing People’s Attention, a book on the science and psychology of attention and how to capture the attention of others.)