## Enlightenment Vs. Romanticism;

or,

The Head Vs. The Heart

We are all familiar with the proverbial battle between and the heart, logic and emotion, science and art. Well, this struggle also epitomized the differences between the Enlightenment (or Neoclassical) Era and the Romantic Period. Now, I don't mean romantic period like the summer fling you might have had last year when you stayed out until ten o'clock ('those summer nights...") but rather capital "R" Romantic, designating the philosophy and time period, instead of an adjective you hope will apply to whomever you are crushing on.

Some of the differences between the schools are fairly obvious and can be related to variances in viewpoints today, as well. Following on the heels of the Renaissance, the rebirth of Western civilization after the Dark Ages, the Enlightenment valued science, logic, and reason as a means of conquering nature and progressing toward the more industrialized world we know today. Even the arts were concerned with intellectual, metaphysical subjects, rather than an outpouring of emotion. Architecture, engineering, and landscape design were heavily focused on symmetry, sharp angles, and neat patterns. In short, the Enlightenment wanted to overlay a grid on nature.

The Romantic movement, on the other hand, emerged as a sort of counter-culture to the ideals of the Enlightenment. In many ways, the Romantics were similar to the Beat generation of the 1950s and the hippies of the 1960s. Some the main concerns of the Romantics were the increasing pace of life, pollution, working conditions, and disconnect from nature resulting from the Industrial Revolution. And they expressed their discontent with the Enlightenment ideology primarily through poetry (although the pinnacle of Romantic literature is, arguably, a novel: Mary Shelley's

Source:

Here are a few videos delineating some of these differences in a little more detail:

Some of the differences between the schools are fairly obvious and can be related to variances in viewpoints today, as well. Following on the heels of the Renaissance, the rebirth of Western civilization after the Dark Ages, the Enlightenment valued science, logic, and reason as a means of conquering nature and progressing toward the more industrialized world we know today. Even the arts were concerned with intellectual, metaphysical subjects, rather than an outpouring of emotion. Architecture, engineering, and landscape design were heavily focused on symmetry, sharp angles, and neat patterns. In short, the Enlightenment wanted to overlay a grid on nature.

The Romantic movement, on the other hand, emerged as a sort of counter-culture to the ideals of the Enlightenment. In many ways, the Romantics were similar to the Beat generation of the 1950s and the hippies of the 1960s. Some the main concerns of the Romantics were the increasing pace of life, pollution, working conditions, and disconnect from nature resulting from the Industrial Revolution. And they expressed their discontent with the Enlightenment ideology primarily through poetry (although the pinnacle of Romantic literature is, arguably, a novel: Mary Shelley's

*Frankenstein*). The Romantics were also big on the individual experience, as opposed to the collective, experiencing awe in nature, and (not surprisingly) emotion. Rather than a neat and tidy English garden, they preferred ruins and less-manicured "wild" nature in their back yards, reflecting their resistance to the notion of "taming" or controlling the natural world.Source:

*The Language of Literature: British Literature.*McDougal Littell, 2008.Here are a few videos delineating some of these differences in a little more detail:

**Fermat's Last Theorem (Caden)**

Pierre de Fermat originally proposed this theorem in the margin of his own copy of Arithmetica, which is an Ancient Greek text on mathematics. It was only a theorem since until after his death it had still not been proven. In Fermat’s own words, “I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.” Fermat’s Last Theorem has the same format as the Pythagorean Theorem, which states that in right triangles, a² + b² = c², or the sum of the triangle’s sides lengths squared is equal to the the hypotenuse’s length squared. Fermat’s Last Theorem was essentially the situation when one pushed this equation further with larger exponents. Fermat’s Last Theorem states that

aⁿ + bⁿ ≠ cⁿ when (n > 2). This concluded that the equation will never be true if the exponent is greater than 2.

Weisstein, Eric. “Fermat's Last Theorem.” Wolfram Math World, 19 Nov. 2020,

mathworld.wolfram.com/FermatsLastTheorem.html. Accessed 2 December 2020.

aⁿ + bⁿ ≠ cⁿ when (n > 2). This concluded that the equation will never be true if the exponent is greater than 2.

Weisstein, Eric. “Fermat's Last Theorem.” Wolfram Math World, 19 Nov. 2020,

mathworld.wolfram.com/FermatsLastTheorem.html. Accessed 2 December 2020.

**Iterated Algorithms & Fractals (Johnny)**

Fractals are a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns repeat at progressively smaller scales, and in describing partly random circumstances such as crystal growth, and galaxy formation. In 1975, Benoît Mandelbrot “discovered” fractals. He was the first one to put the occurrence of these geometric shapes, getting smaller and smaller within themselves, into a word. He wasn’t the first one to notice this but his work on “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension”, helped him identify it.

An Iterated Algorithm is when an equation precedes to the next step using the result from the previous step. This pattern can continue indefinitely. This can be seen as plants grow leaves or stems that continually branch out and/or grow, growing from it’s self, resembling the previous growth. Some of these algorithms are very complex, making comples shapes while some are simplier producing patterns such as the Sierpinski Triangle. In the play Arcadia, characters discuss how if there’s mathematics to explain simple geometric shapes, wouldn’t there be mathmatic equations that result in more complex shapes; “why not a rose?”

Work Cited

“Fractal.” Dictionary.com, Dictionary.com, 2012, www.dictionary.com/browse/fractal. Accessed 2 December 2020.

“History of Fractals.” History of Fractals | Sk33lz Is a Geek, sk33lz.com/create/fractals/history-fractals. Accessed 2 December 2020.

“Iterated Algorithms.” p. 5. personal.psu.edu, http://personal.psu.edu/drh20/genetics/lectures/03.pdf. Accessed 2 December 2020.

Yadav, Anjali. “Iterated Algorithms - Arcadia.” Prezi.com, Prezi, 12 Apr. 2013, prezi.com/_srpsm-lygpi/iterated-algorithms-arcadia/. Accessed 2 December 2020.

An Iterated Algorithm is when an equation precedes to the next step using the result from the previous step. This pattern can continue indefinitely. This can be seen as plants grow leaves or stems that continually branch out and/or grow, growing from it’s self, resembling the previous growth. Some of these algorithms are very complex, making comples shapes while some are simplier producing patterns such as the Sierpinski Triangle. In the play Arcadia, characters discuss how if there’s mathematics to explain simple geometric shapes, wouldn’t there be mathmatic equations that result in more complex shapes; “why not a rose?”

Work Cited

“Fractal.” Dictionary.com, Dictionary.com, 2012, www.dictionary.com/browse/fractal. Accessed 2 December 2020.

“History of Fractals.” History of Fractals | Sk33lz Is a Geek, sk33lz.com/create/fractals/history-fractals. Accessed 2 December 2020.

“Iterated Algorithms.” p. 5. personal.psu.edu, http://personal.psu.edu/drh20/genetics/lectures/03.pdf. Accessed 2 December 2020.

Yadav, Anjali. “Iterated Algorithms - Arcadia.” Prezi.com, Prezi, 12 Apr. 2013, prezi.com/_srpsm-lygpi/iterated-algorithms-arcadia/. Accessed 2 December 2020.

**Chaos Theory & Entropy (Samantha)**

**Entropy is the measure of a system's thermal energy per unit temperature found from ordered molecular motion. Although this measurement has not proven to be useful for most work, it provides insight into the reason for molecular randomness in some systems that otherwise would be unexplainable.**

**Similar to entropy in relation to mathematics and mechanics, the chaos theory supports the idea that there can be a paradox between conflicting scientific analyses. Also known as the butterfly effect, it is a conjecture that any mathematical error can alter the future behavior of the system because it is determined by the initial conditions. This enables us to take orderly structures from chaotic natural systems such as a human heart or the trajectory of an asteroid, and find more explainable causes for the phenomenon of these systems and why they work.**

Borwein , Johnathon, and Michael Rose. “Explainer: What Is Chaos Theory?”

*The Conversation*, 15 Apr. 2020, theconversation.

com/explainer-what-is-chaos-theory-10620.

Drake, Gordon W.F. “Entropy.”

*Encyclopædia Britannica*, Encyclopædia Britannica, Inc., 2017, www.britannica.com/science/entropy-physics.

**The Second Law of Thermodynamics (Dillon)**

The Second Law of Thermodynamics

The second law of thermodynamics describes how the total entropy (a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work) of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems will always move to thermal equilibrium.

In simple terms the laws of thermodynamics are the relationships between heat and matter. The second law of thermodynamics has to do with quality of energy. As energy is transformed or changed, it becomes wasted energy over time. Over time it moves toward a more disordered and chaotic state. As the system becomes more disordered entropy increases. In the case of hot and cold bodies the system is in this state of disorder until the hot body has transferred enough energy into the cold body to reach equilibrium.

Lucas, Jim. “What Is the Second Law of Thermodynamics?” LiveScience, 22 May 2015,

https://www.livescience.com/50941-second-law-thermodynamics.html. Accessed 2 December 2020.

The second law of thermodynamics describes how the total entropy (a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work) of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems will always move to thermal equilibrium.

In simple terms the laws of thermodynamics are the relationships between heat and matter. The second law of thermodynamics has to do with quality of energy. As energy is transformed or changed, it becomes wasted energy over time. Over time it moves toward a more disordered and chaotic state. As the system becomes more disordered entropy increases. In the case of hot and cold bodies the system is in this state of disorder until the hot body has transferred enough energy into the cold body to reach equilibrium.

Lucas, Jim. “What Is the Second Law of Thermodynamics?” LiveScience, 22 May 2015,

https://www.livescience.com/50941-second-law-thermodynamics.html. Accessed 2 December 2020.

**Arcadia (Will)**

The 20th century era of drama and theater was brought to life by the unforgettable play, Arcadia, by which is written from the mind of Tom Stoppard and has been ruled not only as the best play by Stoppard himself, but also as one of the most significant playwrights of the century. This comical, scientific, and cerebral piece of work evaluates the concerning relationship between past and present, structure and chaos, forgone conclusions and impossibility. Yet this Romanticised play is most commonly recognized for is unique ability to span the idealism of physics, art, poetry, and the inevitable attraction towards sex.
CITE: “Arcadia (Play).” Wikipedia, Wikimedia Foundation, 5 Nov. 2020, en.wikipedia.org/wiki/Arcadia_(play). Accessed 2 December 2020. “Arcadia Plot Summary.” Course Hero, www.coursehero.com/lit/Arcadia/plot-summary/.Accessed 2 December 2020. |

**Newton (Blazen)**

Sir Isaac Newton was an english mathematician, physicist, astronomer, theologian, and author. He is known for being the most persuasive scientist of all time. He created the laws of motion and founded the universal gravitational theory. Newton invented the telescope which eventually led to his theory of the sophisticated theory of color. Newton also also in his later years wrote religious tracts dealing with the literal and symbolic interpretation of the Bible. This is just a small amount of the many achievements and discoveries Newton was able to find in his lifetime.

Newton is important to Arcadia because of his Chaos Theory. The Chaos Theory States that cause and effect are relatively easy to determine and predict, given enough information. However, complex systems such as the weather or population growth have proven to be infinitely complicated to accurately predict, despite their ability to be modeled with equations. This is applied in Arcadia when deciphering between the classical and romantic thought process. Classical people are easier to understand and predict. Romantic people are more chaotic and impulsive, making them harder to predict.

“Isaac Newton.” Biography.com, A&E Networks Television, 5 Nov. 2020, www.biography.com/scientist/isaac-newton.

“ARCADIA Explored: Chaos Theory.” Explore the Art, 23 Mar. 2016, www.writerstheatre.org/blog/arcadia-explored-chaos-theory/.

Euclid - The Father of Geometry (Eli)Lived in Alexandria, that is why he is often called Euclid of Alexandria. Being in a Egyptian who was pardoned by the Ptolemies he was not well recognized but by writing two text books on the basis of Geometry earned him a credible mentioning. The two textbooks that he wrote, with the help of Pythagoras, Hippocrates, Theudius, Theaetetus and Eudoxus; the “Stoicheion” and “Elements” is work on the book “Elements” in it is he explains 465 theorems and proofs. Euclid explained many different ideas in his book like elementary theorems about plane geometry, geometric algebra, properties of circles, and a lot more but Euclid is most famous for his work on his five general axioms. The five ideas are things which are equal to the same thing are equal to each other, if equals are added to equals the wholes (sums) are equal, if equals are subtracted from equals the remainders (differences) are equal, things that coincide with one another are equal to one another, and the whole is greater than the part. The second thing he is most famous for is five geometrical postulates were it is possible: to draw a straight line from any point to any point, to extend a finite straight line continuously in a straight line, it is possible to create a circle with any center and distance, all right angles are equal to one another, and if a straight line crossing two straight lines makes the interior angle (unless parallel). Work Cited “EUCLID OF ALEXANDRIA - The Father of Geometry.” The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day, 20 Feb. 2020, www.storyofmathematics.com/hellenistic_euclid.html. “Home.” Famous Scientists, 24 June 2020, www.famousscientists.org/euclid/. |