## 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 (Jonah & Courtney)**

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

Formula:

a^n +b^n=c^n

a,b,c = positive integers

n = integer greater than 2

According to britannica.com, Pierre de Fermat, (born August 17, 1601, France—died January 12, 1665, Castres), was a “French mathematician who is often called the founder of the modern theory of numbers.”

He also co-founded the theory of probability with Blaise Pascal.

Math professor Andrew Wiles won a prize for solving Fermat's Last Theorem. He is now a professor at Oxford University, but was at Princeton University when he worked out a proof for the theorem that had famously bedeviled mathematicians for centuries.

In 1995, Wiles proved a 358 year old mathematical theory called Fermat's Last Theorem, which until then was listed in the Guinness Book of World Records as the "most difficult math problem" in the world. According to Browse Biography, his IQ is 170.

Video, did Homer Simpson solve Fermat's last theorem?: https://youtu.be/ReOQ300AcSU

**Iterated Algorithms & Fractals (Hailey & Dakota)**

Algorithms are systemic instructions carried out for the purpose of discovering a solution. This sequence is composed of specific steps; similar to a code constructed to result in a desired output. According to BBC’s website, “There are three basic building blocks (constructs) to use when designing algorithms: sequencing, selection, iteration.” This formula is a style of programming that is utilized within the fields of mathematics and science. The particular category of algorithms, termed iterated algorithms, entails the process of repetition. “Iteration” causes the systematic actions of an algorithm to continue in a loop, unless disrupted by a misstep in the order of instructions. One’s daily routine can be considered an iterated algorithm, as it repeats the same objectives, typically according to numbers on a clock. For many teens, their personal algorithm may appear similar to the following: wake up, make breakfast, go to school, attend extracurricular activities, go home, eat dinner, go to bed, repeat. The individual’s process of iteration comes to an end once that routine is broken. Perhaps the person’s alarm does not go off in the morning, resulting in no time to cook breakfast and a late appearance to their first class at school. In mathematics and science, algorithms are purposeful in setting certain requirements or expectations in which something is done nearly, thus preventing unnecessary events that would hinder the efficiency of an objective. However, when designing and perfecting an algorithm, some steps may need to be slightly altered or continued until the desired efficiency is met; “Sometimes an algorithm needs to repeat certain steps until told to stop or until a particular condition is met”(BBC). The iteration of an algorithm can also be utilized to prove a process to be true or false, based upon the process’s alignment with the instructions of the algorithm.

Fractals are similar to algorithms in the sense that they are never-ending patterns that can be computer generated. The technological forms of fractals can be digitally designed to continue for infinite amounts of time, “[…] created by repeating a simple process over and over in an ongoing feedback loop”(FractalFoundation). The prevalence of fractals in mathematics can be seen through the existence of pi (3.141592654 etc.) Fractals, while able to be created digitally, can also be found in various aspects of nature: trees, mountains, and rock formations. These forms of, “fractal patterns are extremely familiar, since nature is full of fractals”(FractalFoundation). Pictures and graphs can also resemble this idea in some situations, where a pattern is repeated multiple times. Finally, fractals can be metaphorically represented with the coming and going of trends and societal norms.

Fractals are similar to algorithms in the sense that they are never-ending patterns that can be computer generated. The technological forms of fractals can be digitally designed to continue for infinite amounts of time, “[…] created by repeating a simple process over and over in an ongoing feedback loop”(FractalFoundation). The prevalence of fractals in mathematics can be seen through the existence of pi (3.141592654 etc.) Fractals, while able to be created digitally, can also be found in various aspects of nature: trees, mountains, and rock formations. These forms of, “fractal patterns are extremely familiar, since nature is full of fractals”(FractalFoundation). Pictures and graphs can also resemble this idea in some situations, where a pattern is repeated multiple times. Finally, fractals can be metaphorically represented with the coming and going of trends and societal norms.

**Sources:**“Conditions and Counters - Iteration - KS3 Computer Science Revision - BBC Bitesize.”

*BBC News*, BBC, https://www.bbc.co.uk/bitesize/guides/zg46tfr/revision/3. Accessed 9 November 2021.

“What Are Fractals?”

*Fractal Foundation*, https://fractalfoundation.org/resources/what-are-fractals/. Accessed 9 November 2021.

**Chaos Theory & Entropy (Boaz & Kendra)**

Chaos Theory is the study of the unpredictable nature of complex yet deterministic systems. For example, a function evolves in a very particular way if given a certain set of values. Every time the same values were given, the function produces the same result. However, if a seemingly insignificant amount is varied from those starting values, the result, depending on the complexity of the function, can be drastically different very quickly. This was first discovered when looking at a machine that predicted the weather based on variables such as temperature, wind, humidity, among others. The machine would use the starting values to produce a prediction of these same variables, which would be used as an input in the same function. This would go on until stopped. But when run side by side by the same machine that had the same value but with three more decimal places of accuracy, the predictions significantly varied.

The term “chaos theory” is somewhat ironic. The basis of it, after all, is founded on the fact that all things have a natural order and evolve according to a very strict set of rules. The term, though, does acknowledge that even though this is true, no amount of computing power would be able to accurately describe the nature of even one particle to the infinite degree that would be required to predict the future without variance. Thus, the universe can and will only ever be described as chaotic.

The term “chaos theory” is somewhat ironic. The basis of it, after all, is founded on the fact that all things have a natural order and evolve according to a very strict set of rules. The term, though, does acknowledge that even though this is true, no amount of computing power would be able to accurately describe the nature of even one particle to the infinite degree that would be required to predict the future without variance. Thus, the universe can and will only ever be described as chaotic.

Entropy is often defined as a measure of the amount of energy that cannot or will not do work in a shut system and is sometimes just referred to as a measure of confusion or clutter. It basically means that if energy is allowed to move or disperse, it will. Take a popcorn kernel for example. There is a bunch of energy trapped inside of the kernel waiting to be released, so as soon as heat is added, the kernel pops open to let the built up energy out, resulting in a piece of popcorn. If a system or object has high entropy, the disorder levels are high and the energy is low. If a system or object has low entropy, the disorder levels are low and the energy is high. This means that when the energy is trapped in the kernel, the entropy is low and when the energy is released from the kernel it becomes high. Entropy is also a concept not only just seen in physics and chemistry, but is also seen in almost any situation. Whether it be a psychologist diagnosing someone due to the randomness or clutter in their lives, or a business owner trying to get their business and employees to clear up the confusion, it is prevalent.

The Second Law of Thermodynamics (Ele & Lizzie)

The Second Law of Thermodynamics (Ele & Lizzie)

This law states that natural processes go in a direction that maintains or increases the total entropy of the universe. Statements of the probability of events happening, predicts that heat flows spontaneously only from a hot object to a cold object. In this philosophy of physics, it is important for all to understand due to the natural establishment it contains in one's life. This study is an example of how a natural process can occur in a scientific order. Being that through this process the density, pressure, and temperature even out sometime slowly during this process. Before this process occurs, the energy causes matter to move freely from one form to another. This is causing an increase in disorder which is also known as "entropy".

All things over time will become more and more disordered unless some action is taken to keep them ordered.

“The second law of thermodynamics states that heat can flow spontaneously from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object. Carnot engine, heat engine are some examples of the second law of thermodynamics” (Ox Science).

“When we put an ice cube in a cup with water at room temperature. The water releases off heat and the ice cube melts. Hence, the entropy of water decreases” (Vedantu).

Sources:

https://oxscience.com/second-law-of-thermodynamics/

https://www.vedantu.com/question-answer/a-real-life-example-of-the-second-law-of-t-class-11-chemistry-cbse-60d481f673e290701a853938

All things over time will become more and more disordered unless some action is taken to keep them ordered.

“The second law of thermodynamics states that heat can flow spontaneously from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object. Carnot engine, heat engine are some examples of the second law of thermodynamics” (Ox Science).

“When we put an ice cube in a cup with water at room temperature. The water releases off heat and the ice cube melts. Hence, the entropy of water decreases” (Vedantu).

Sources:

https://oxscience.com/second-law-of-thermodynamics/

https://www.vedantu.com/question-answer/a-real-life-example-of-the-second-law-of-t-class-11-chemistry-cbse-60d481f673e290701a853938

Arcadia (Carson & Erik)

Arcadia (Carson & Erik)

Arcadia is a play set in a Derbyshire country estate in both 1809 and 1812, by Tom stoppard. This play compares and examines how order and disorder, past and present, and certainty and uncertainty. This play is a perfect example of romanticism vs. enlightenment, with it being a contrast between aspects of enlightenment such as order and romanticism such as disorder. Arcadia isn’t only a play, it is a geographical place and has a painting referring to it. The geographical area called Arcadia is named after the mythological place Arcadia. Which was a utopia that could be seen as an enlightenment heavy place, but this mythical place also has imperfections such as death which is more on the romantic side. The painting of Arcadia displays well dressed people in a luscious landscape at a tomb, which is a visual example of Arcadia being a utopia with the imperfection of death represented by the tomb. Both the mythical Arcadia and painting of Arcadia are representations of the contrast between romanticism and enlightenment and because of this Arcadia is the perfect name for the play, because the play is also a comparison with romanticism and enlightenment.

“The Arcadian Shepherds.” Artble, 19 July 2017, https://www.artble.com/artists/nicolas_poussin/paintings/the_arcadian_shepherds.

Spielman, Patrick E. Gluing & Clamping: A Woodworker's Handbook. Sterling Pub. Co., 1986.

“The Arcadian Shepherds.” Artble, 19 July 2017, https://www.artble.com/artists/nicolas_poussin/paintings/the_arcadian_shepherds.

Spielman, Patrick E. Gluing & Clamping: A Woodworker's Handbook. Sterling Pub. Co., 1986.

**Newton (Nate & Ady)**

Issac Newton was born in Woolsthorpe, England in 1643. He received an education at Cambridge University allowing him to develop his theories on calculus, celestial mechanics, and light. His research led him to publish a work called “Principia” which established the universal laws of motion and gravity. He also later published a book called “Optics”, which discussed the properties of light and his experimentation on the topic. Sir Issac Newton is probably known most for his three laws of motion.

Newtons laws of motion

Sources:

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/

https://www.history.com/topics/inventions/isaac-newton

Newtons laws of motion

- Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia
- His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of object times its velocity V.
- His third law states that for every action (force) in nature there is an equal and opposite reaction. If object A exerts a force on object B, object B also exerts an equal and opposite force on object A. In other words, forces result from interactions.

Sources:

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/

https://www.history.com/topics/inventions/isaac-newton

**Euclid - The Father of Geometry (Micah & Janessa)**

- Wrote series of mathematical arguments (treatise) called
*The Elements*focused on geometry that “influenced the development of Western Mathematics for more than 2000 years.” (mathhistory) - 13 total books/chapters
- Born about 300 BCE
- Very little is known about his life except that he was a teacher at Alexandria in Egypt
Basic chapter focuses: 1-4 plane geometry 1- definitions and 10 initial assumptions; triangles; parallelograms; Pythagorean Theorem 2- geometric algebra 3- properties of circles 4- construction of regular polygons (pentagon in particular) 5- ratios and proportions, solution to problem of irrational numbers, formed foundation of the geometric theory of numbers 6- applies ratios to plane geometry and the “application of areas” to solve quadratic problems geometrically 7-9 number theory 7- Euclidean Algorithm 8- geometric sequences 9- proves infinite number of primes 10- comprises ¼ of The Elements 11-13 three dimensional figures 11- intersections of planes and lines 12- method of exhaustion 13- construction of the 5 regular Platonic solids |

Taisbak, Christian. “Euclid - Renditions of the Elements.” Britannica, https://www.britannica.com/biography/Euclid-Greek-mathematician. Accessed 8 November 2021.

O’Connor and Robertson. “Euclid of Alexandria.” MacTutor, January 1999, https://mathshistory.st-andrews.ac.uk/Biographies/Euclid/. Accessed 8 November 2021.

Image: (https://www.maa.org/press/periodicals/convergence/mathematical-treasure-euclids-elements-in-both-greek-and-latin)

O’Connor and Robertson. “Euclid of Alexandria.” MacTutor, January 1999, https://mathshistory.st-andrews.ac.uk/Biographies/Euclid/. Accessed 8 November 2021.

Image: (https://www.maa.org/press/periodicals/convergence/mathematical-treasure-euclids-elements-in-both-greek-and-latin)

Youtube: 0:00 - 2:24

**Lord Byron (Beth & Robyn)**

On January 22 of 1788, George Gordon Noel Byron was born to the single mother, Catherine Gordon. Byron was raised in an unstable home, constantly questioning his emotional mother’s every move. Byron’s birth defect of a clubbed foot, often made this relationship more tense and strained. “From his Presbyterian nurse Byron developed a lifelong love for the Bible and an abiding fascination with the Calvinist doctrines of innate evil and predestined salvation.” (Source 1). In 1798, Byron gained the title “Lord” through the passing of his great-uncle. Shorty after this, Byron began his schooling; attending the Harrow School from 1801-1805 and Trinity College, Cambridge from 1805 to 1808. Byron’s love for writing and oral display of poetry became very obvious and his first book, Fugitive Pieces, was printed and distributed in 1906. A new version was published in 1907 titled Poems on Various Occasions. Byron’s poetry was a reflection of the societal happenings all around him. His poetry reflected the newfound romanticism, and Byron was a mirror of this himself. Byron was openly bisexual, fashionable, expressive, and the very image of a romanticist. His lifestyle was often questioned by those around him, including suspicion of an incest relationship with his half sister, Augusta resulting in a child. By the time he died in 1824, it is guessed that Lord Byron published about 275 poems.

1. “History - Lord Byron.” BBC, BBC, https://www.bbc.co.uk/history/historic_figures/byron_lord.shtml.

Date Accessed: 09 November 2021

2. “Lord Byron (George Gordon).” Poetry Foundation, Poetry Foundation, https://www.poetryfoundation.org/poets/lord-byron.

Date Accessed: 09 November 2021

3. McLean, Amy. “Complete List of Lord Byron's Poetry, 1807-1824.” Amy McLean, 1 Jan. 1970, https://mcleanamy.blogspot.com/2011/09/complete-list-of-lord-byrons-poetry.html.

Date Accessed: 09 November 202

Date Accessed: 09 November 2021

2. “Lord Byron (George Gordon).” Poetry Foundation, Poetry Foundation, https://www.poetryfoundation.org/poets/lord-byron.

Date Accessed: 09 November 2021

3. McLean, Amy. “Complete List of Lord Byron's Poetry, 1807-1824.” Amy McLean, 1 Jan. 1970, https://mcleanamy.blogspot.com/2011/09/complete-list-of-lord-byrons-poetry.html.

Date Accessed: 09 November 202