The Golden Ratio, Qubits, and Emotional States

Hey there! In this write-up, I wish to introduce a new way of writing poems by using math concepts as poetic devices to embellish my work. ​I find scientific concepts relatable when I read about them, and it's exciting for me to express my thoughts using those concepts. So, this time I attempt to introduce a mathematical poetic device that will help me define a mathematical structure in the form of Fibonacci numbers and Lucas numbers.

In mathematics, Fibonacci and Lucas numbers are sequences, such that each number is the sum of two preceding ones.

Fibonacci Numbers:

$F_0=0$

$F_1=1$

$F_2=1$

$F_n=F_{n-1}+F_{n-2}$

So, the beginning of the Fibonacci sequence is thus:

$0, 1, 1, 2, 3, 5, 8, 13$....

Lucas Numbers:

$L_0=0$

$L_1=2$

$L_2=1$

$L_n=L_{n-1}+L_{n-2}$

and the beginning of the Lucas sequence is thus:

$0, 2, 1, 3, 4, 7, 11, 18$....

This provides a recursive definition for the Fibonacci and Lucas numbers. So, moving further, I will use this to define a structure for two poems connected via mathematical relations such as the Golden ratio and much more.

The first poem, called $|1 \rangle$, will have a theme based on Fibonacci numbers, and the second one, called $|0 \rangle$, will have a theme based on Lucas numbers. The number of words in the $n^{th}$ line in a poem is given by the $n^{th}$ term of the respective sequence. For example, the $5^{th}$ line of $|1 \rangle$ will have five words. Each line will be a continuation or progression of its previous lines, respecting the recursive formula of these sequences.

$|1 \rangle$ will be about positive emotions, and $|0 \rangle$ will be about negative emotions. These poems express what I feel when I am trying to write something creative for myself. So, both of the poems will explain two opposite emotional states of my mind when I try writing something. The poems are named $|1 \rangle$ and $|0 \rangle$ because these emotional states(portrayed in the poems) are the orthonormal basis states(orthonormal basis vectors are unit vectors that are perpendicular to each other) of my emotional state. Together, they are called the computational basis and are said to span the two-dimensional Hilbert space of a qubit. A qubit or a quantum bit is the quantum version of the classical binary bit, and it's the basic unit of quantum information.

A pure qubit state is a coherent superposition of the basis states. A single qubit state can be written as a linear combination of $|1 \rangle$ and $|0 \rangle$:

$|\psi\rangle$$=$$\alpha\cdot$$|1\rangle$$+$$\beta\cdot$$|0\rangle$   $\alpha$,$\beta$$\in$$\mathbb{C}$

So, what I mean is that the poems representing my two opposite emotional states form the orthonormal basis states, and any emotional state of my mind can be written as a linear combination of these two states. My mind seemingly acts like a quantum computer storing all the emotional states(at any instant of time) in the form of qubits and performing necessary complex computations to help me interpret what I feel, and adapt accordingly. 

Keep this in mind while reading the poems:

The first poem talks about the flow of purely positive emotions inside me when I try to write something creative. Similarly, the second poem talks about the flow of purely negative emotions encountered in the process. Note that each line is a continuation of its previous lines, in a sense that my past feelings give rise to my present feelings analogous to the recursive mathematical formula for the $n^{th}$ term of Fibonacci or Lucas numbers ($F_n=F_{n-1}+F_{n-2}$ or $L_n=L_{n-1}+L_{n-2}$). This is shown by using the words expressing emotions from previous lines as themes in the present line (Example, sadness in $L_3$ and $L_4$).

Poems:

spabproject · BoFi

Qubit state $|1 \rangle$:

$F_1$: Curious?

$F_2$: Interested?

$F_3$: Interests isomeric,

$F_4$: interests inspiring passion,

$F_5$: peaceful passion provoking adiabatic ardour,

$F_6$: acting ardent adding elastic elations elevating decent diligence,

$F_7$: diligent displacement drilling hea(r)tful hope heating catalytic confidence contrived via validated viscous visions.

Breakdown of $|1 \rangle$:

A writing idea always starts with curiosity. This curiosity starts developing my interest in that idea, and these interests are isomeric. Isomerism is the phenomenon in which more than one compound has the same molecular formula but different chemical structures or orientations. So, my interests are isomeric, meaning they originate from the same person, but they have different structures and properties since I have a changing mindset for multiple interests. These interests gradually inspire my passion, and I start feeling passionate about my Work. It's peaceful when I feel passionate, and I slowly start feeling enthusiastic(ardour) about my Work. Ardour is adiabatic. Adiabatic systems are systems whose conditions are altered without gaining heat from or losing heat to the surroundings. To get the essence of this reference, wait for the breakdown of the last line("heatful hope"). I start acting enthusiastic about my Work, which adds happiness(elations) which is elastic to my emotions. It's elastic because it's flexible and adaptable to the change of my enthusiasm. Basically, my happiness changes depending on how excited and enthusiastic I am. My happiness elevates my sincerity and hard work (diligence), which is fulfilling(decent) to me. Diligent displacement is a wordplay. My diligence showcases my hard "work" and work($W$) is the product of force($\vec{F}$) and displacement($\vec{s}$).

$W=\vec{F}\cdot \vec{s}$

My thoughts are displaced in the sense that they move forward and grow, and they are moving or manifesting into something substantial because I am doing some work in the form of my sincerity. This diligence drills my hope because I think of my hope as some precious material mined by my hard work which makes it close to my heart. This hope is ‘heatful’. In the sense that coming back to the "adiabatic ardour" reference, my enthusiasm prevents the heat flow from my system, meaning it contains my hope and shields me from any negative influences on my work. This hope heats catalytic confidence which emerges from the validation of my viscous(deep and thick) visions from my peers. Given the right amount of hope(heat), this confidence acts as a catalyst for my reaction(writing and creating content) hence providing better results. But, having too much hope and expectations(overheating) doesn’t help, as the catalyst(confidence) cannot function at this temperature. 

spabproject · Calus

Qubit state $|0 \rangle$:

$L_1$: Boredom brimming? 

$L_2$: Tired?

$L_3$: Tiredness teasing sadness, 

$L_4$: symbiotic sadness seeking pessimism,

$L_5$: pessimistic pathogens plaguing poisoned passion antagonizing ardour, 

$L_6$: anxious antagonist aiding hopeless heathens harnessing intensive insanity irradiates polarized pain.

Breakdown of $|0 \rangle$:

This poem is how I feel when I can't think of anything intelligent or significant to write, and it starts bothering me, resulting in a flow of negative emotions. It starts with boredom and tiredness. I am exhausted from overthinking and brainstorming ideas. I start feeling sad that I am incapable of creating content which I yearn to make. Sadness and pessimism have a symbiotic relationship in my head. So, my sadness seeks my pessimistic thoughts, and both rely on each other for their survival. This negativity inside me acts like a pathogen(a virus) and plagues my poisoned passion(all these negative emotions poison my passion). I start antagonizing my ardour, which then slowly turns into anxiety because I feel insecure and stressed. The stress aids my hopelessness. I start turning into a hopeless heathen (a person regarded as lacking culture or moral principles) capable of harnessing insanity, which is vigorous in its nature. The phrase "intensive insanity irradiates polarized pain" is a reference to Malus' Law. The negativity starts driving me insane, irradiating it in the form of a light . This light in the form of insanity passes through a polarizer, which is my ability to resist pessimistic thoughts (In spite of being a heathen I have some morality left which offers some resistance to insanity), which decreases the transmitted intensity(diminished insanity) causing me mental pain. 

Note: The last lines are not the ending of the poems since the sequences continue to grow and diverge to infinity, symbolizing how I will mature to become a slightly better person each time as time progresses.

How are the poems related mathematically?

1)Mathematically, Fibonacci and Lucas numbers are related via the Golden ratio. The Golden ratio is defined as:

$\lim_{n\to\infty} \phi=\frac{F_{n+1}}{F_n}=\frac{L_{n+1}}{L_n}$

The Golden ratio gives a rough estimate of how Fibonacci and Lucas numbers increase/grow. So, the Golden ratio represents the rate at which my emotions grow and this is in turn determined by my choices to act in different situations.

2)The poems are also related to each other via a relation defined by the expression:

$L_n=F_{n-1}+F_{n+1}$

It is said that a negative emotion exists so that we can feel good about positive emotions. So, negative emotions are a counter as well as the crux to our positive emotions. This interdependence of positive and negative emotions fascinates me, and I wanted to showcase this relation in my poems. For example, take the lines: $L_6$, $F_5$ and $F_7$ where I antagonized ardour which was a protagonist("acting ardent") in $|1 \rangle$. Also, I was hopeful in $F_7$ and hopeless in $L_6$. There are many such cases in the poems and are left for the readers to be discovered and relished. 

I hope through this article I could convey my emotional states at different instances as well as provide a tool for you to discover your own emotions. Thank You for reading! 

Credits:

Written By: Manav Shah

Editors: Amey Danole and Rahul Krishnakumar

Music By: Aaryan Shah