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<<nobr>><div class="container-fluid"> <div class="row"> <div class="col-md-9"> <img src="img/maps/office_50.jpg" usemap="#image-map"> <map name="image-map"> <area data-passage="2" target="" alt="" title="Approach the Manager" href="" coords="202,246,176,259,163,273,153,291,141,300,146,311,156,322,152,334,143,345,151,359,167,371,151,386,145,403,155,415,167,425,183,439,207,446,231,445,250,431,258,412,263,391,251,376,255,363,260,343,253,329,255,317,263,300,244,279,226,259" shape="poly"> </map> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="narration"> Mo enters the main PMS office with his manager, and Manager looks angry and irritated as ever. Maybe you should check in with him...? </div> </div> </div> </div><</nobr>>

<<script>> // Read this starting with the last code chunk first :) // The last chunk activates maphilight with default styling. // The first chunk allows you to style multiple maps differently // The second chunk allows you to style multiple areas differently // If you have multiple maps in your story and you want to apply // different styling to each: // 1: Put a class on each map (or maps) that needs different styling // 2: Use the below code, but replace "show-all-map" with the // class name // Note: you can use any of the styling options here. Any that you // don't specify are set by the default styling. $("img.show-all-map").data("maphilight", { fillColor: '00ffff', stroke: false, alwaysOn: true }); // If you want to have multiple areas with different styling: // 1: Put a class on the area (or areas) that needs different styling // 2: Use the below code, but replace "green-area" with the // class name // Note: you can use any of the styling options here. Any that you // don't specify are set by the default styling. $("area.green-area").data("maphilight", { fillColor: '13dd38', fillOpacity: 0.25, strokeColor: '9aefaa', strokeOpacity: 0.5 }); // Apply maphilight to all images that have a usemap attribute, e.g. // all the maps that are in this twine. This sets the default styling // for all the maps. These are all the possible styling options. // Note: for picking colors, check out http://hslpicker.com/. You can // copy the HEX value as long as you leave off the "#". $("img[usemap]").maphilight({ fill: true, // Fill the area? fillColor: 'f50000', // HEX format without the starting "#" fillOpacity: 0.5, // Opacity of the filled area stroke: true, // Outline the area? strokeColor: 'a80000', strokeOpacity: 1, strokeWidth: 5, // Outline width fade: true, // Animate when hovered with a fade? alwaysOn: false, // Always show the areas? neverOn: false, groupBy: false, wrapClass: true, shadow: false, shadowX: 0, shadowY: 0, shadowRadius: 6, shadowColor: '000000', shadowOpacity: 0.8, shadowPosition: 'outside', shadowFrom: false }); <</script>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="4" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span class="narration">(He interrupts you.)</span> <p>You joined the company during a crisis. Good for you. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<widget "mos_notes">> <<button "How to Play">> <<popover>> <big>__''Resizing Your Screen''__</big> If you hate scrolling, you can resize your screen by using the default commands. Some common ones are listed below. ''Mac:'' Command + Scroll ''PC:'' Ctrl + Scroll <big>__''How to Play''__</big> The ► icons will guide you as to what options you have to influence the story. Sometimes, there won't be any and this means there's something in the environment which you have to find to continue. You will be rewarded for exploring difficult pathways. Consider this throughout your journey. <big>__''Interacting with the Environment''__</big> Mouse over the environment until something glows! This means you can interact with it. <big>__''Puzzles''__</big> There will be moments when you have to solve puzzles to move forward with the story. In these puzzles, you will drag and drop the correct tiles into their designated boxes. The boxes will change color when you've enetered a correct answer. Look for the "You have finished! Click here to continue!" message to proceed. <</popover>> <</button>> <<button "Mo's Notes">> <<popover>> __''Model of Particle on a Mobius Strip''__ <img src="img/gifs/mobius_strip_model.gif" style="width:50%;"> __''Symbol Definitions''__ <<if $TakenPsiTest is true>> 𝛹 denotes the wavefunction. <</if>> <<if $TakenPhiTest is true>> φ is the angular position variable. <</if>> <<if $BeenToParticleOnARing is true>> //i// is the imaginary number equal to √(-1). <</if>> <<if $BeenTo69 is true>> //m~~l~~// is the quantum number in the Particle on a Ring system. //m~~s~~// is the quantum number in the Particle on a Mobius strip system. <</if>> __''Equations''__ <<if $BeenToParticleOnARing is true>> ''General rotational wavefunction'' //𝛹(φ) = e^^ i m φ^^// <</if>> <<if $BeenToEulersIdentity is true>> ''Euler’s Identity'' // e^^ i 𝜋^^ = -1// <</if>> <<if $BeenTo101 is true>> ''Wavefunction for Particle on a Ring'' //𝛹(φ) = e ^^i m~~l~~ φ^^ * (-1)^^2 m~~l~~^^// <</if>> <<if $BeenTo104 is true>> ''Wavefunction for Particle on a Mobius Strip'' //𝛹(φ) = e ^^i m~~s~~ φ^^ * (-1)^^4 m~~s~~^^// <</if>> __''Pamphlets You've Read''__ <<if $BeenToQSP is true>> <<button "Quantum States">> <<popover>> __''Quantum States Pamphlet''__ Hello valued T. H. E. I. S. employee! This pamphlet series aims to inform the up-and-coming new space clouds in the vast knowledge of Universe 42. Today on the menu: Quantum States. A quantum state corresponds to a specific wave packet or wavefunction, and can be characterized by a set of quantum numbers, each arrangement of numbers corresponding to a specific quantum state. Each observable quantity of a particle in a quantum state, like the energy or momentum, is associated with an operator, which is just a function that acts on a wavefunction or vector. The eigenvalues, or output of the operator, are representations of the quantity that is being observed by the operator. So for example, if the energy operator is applied to a wavefunction, then the output from the application of the operator is the wavefunction and the actual value for the energy. This means the wavefunction is a quantum state with a definite value for the energy with no quantum uncertainty. If the energy of the particle was measured, it is guaranteed by the value the operator dictates. Among quantum states, there is not a state which is simultaneously an eigenstate for all different observables. This means that if we have a state where we know the position exactly, then we will not be able to know momentum, it will have a range of values and not an exact value. This, in Universe 42 terms, is called the “Heisenberg Uncertainty Principle”. The following graphic depicts the probability density, or probability that a particle exists at any given point in space, for an electron in a Hydrogen atom in different quantum states: <img src="img/pamphlet/hydrogen_density_plots.jpg" style="width: 50%;"> <</popover>> <</button>> <</if>> <<if $BeenToPQNP is true>> <<button "Particles & Quantum Numbers">> <<popover>> __''Particles: A guide to Universe 42’s Smallest Constituents''__ Hello dear reader, and welcome to an introductory look at particles! Particles make up everything in Universe 42 and are quite important. The most important class of particles are the fermions, which have half-integer spins. The three most important fermions are called the proton, neutron, and electron, because they are what makes up every atom, and atoms are what make up EVERYTHING in universe 42. Protons and neutrons are a class of particles called a hadron, and are made up of something called a quark, which is an even smaller type of elementary particle. There are 6 types of these quarks, called up, down, strange, charm, top, and bottom, but protons and neutrons are just composed of up and down quarks. These protons and neutrons are joined by electrons, which are the smallest ‘negative-one’ elementary charge. These particles are special. <img src="img/pamphlet/particles.jpg" style="width:50%;"> Not only are they ‘particles’ in the literal sense, but when you get down to the quantum scale, particles take on wave character and can also be classified as waves. This phenomenon, known as ‘Wave-Particle Duality’, is used to explain where the particle could be; it’s a wave of probability, and dictates where the particle COULD be. The particle, in this case considered to be an electron, exists as this wave of probability until it is observed. Then, it cannot exist as a wave of probability, since it has been located in one position, and assumes a particle-like nature. Once the electron is out of observation however, it goes back to being located somewhere in the wave of probability, until it becomes observed once again. This wave of probability is dictated by the wave function, which you can learn all about in the third installment of the T.H.E.I.S New Employee guide Part 3: The Wavefunction of Universe 42. <img src="img/pamphlet/wpd.jpg" style="width:50%;"> __''Quantum Numbers: What are they even good for?''__ Quantum numbers are very important, as they describe completely the movement and trajectory of each electron that makes up an atom. Each electron in an atom has a unique set of quantum numbers, because according to Universe 42 fundamental rule 1940, also known as the ‘Pauli exclusion principle’ no two electrons can have the same 4 quantum numbers. But what are these quantum numbers, and what do they describe? The first one, n, also known as the principal quantum number, describes the principal electron shell. This means it describes the probable distance of the electrons from the nucleus. N can only be represented by a whole number positive integers. The next quantum number, l, also known as the angular momentum quantum number, describes the shape of the orbital. Each value of l indicated a different subshell (s,p,d,f). The number of angular nodes in the orbital is equal to the value of l, and it’s value can be anywhere from 0 to (n-1). The third quantum number, the magnetic quantum number, ml, determines the number of orbitals and their orientation. Its value can span from -l to l. Finally, the last quantum number, ms, describes the spin of the electron in an orbital. It can have values of +1/2, positive spin represents spin up and negative spin represents spin down. Each orbital can have one spin up and one spin down electron in it, which obeys the Pauli exclusion principle! <img src="img/pamphlet/qn.jpg" style="width:75%;"> <</popover>> <</button>> <</if>> <<if $BeenToWP is true>> <<button "Wavefunctions">> <<popover>> __''T.H.E.I.S New Employee Guide Part 3: The Wavefunction of Universe 42''__ Welcome, reader, to the 3rd installment of the T.H.E.I.S New Employee guide! This part focuses on wavefunctions. You know them, you love them, and you know how to apply them to the code that makes up Universe 42. But what exactly are they and what do they represent? This pamphlet runs down the basics on wavefunctions needed to continue maintaining Universe 42. The wavefunction Ψ is a mathematical expression, which provides crucial information regarding the electron it represents. Electrons behave as both particles and as waves, a behavior called the “Wave-Particle Duality!” This is why we can represent the motion of electrons as a wave using wavefunctions, and each electron has its own wavefunction! <img src="img/pamphlet/i_hate_it.jpg" style="width:50%;"> From the wavefunction, we can obtain the electron's energy, angular momentum, and orbital orientation, because in the wavefunction we have the quantum numbers n, l, and ml. These quantum numbers are discussed in the informative //“Quantum numbers: what are they even good for?”// pamphlet which can be provided to you via your supervisor! The sign of the wavefunctions help determine how electrons interact with each other. Wavefunctions interacting with similar signs (in phase waves) will constructively interfere and form a bond. Wavefunctions with opposite signs (out of phase waves) will destructively interfere. More applicable however, the wavefunction gives information about the location of the electron. The square of the wavefunction, |Ψ|^^2^^, is also known as the probability density of the wavefunction. If a wavefunction of an electron has the value Ψ at any point //x//, then the probability of finding said electron between //x// and //x+dx// is proportional to //|Ψ|^^2^^//, which we previously stated to be the probability density. Even if the wavefunctions are negative or portions of the wavefunctions are negative, the probability density never can be. You can’t have a negative probability of finding an electron somewhere (the lowest you can have is 0%). <img src="img/pamphlet/wfxn_probably.jpg" style="width:50%;"> These wavefunctions need to undergo a process called normalization, which is used to ensure that the probability of finding the particle somewhere in the space of interest is equal to 1. This is useful, since //|Ψ|^^2^^ dx// is only proportional to the probability of finding the particle in dx space, we want to normalize it to give the probability according to a percent. Lastly, wavefunctions need to obey certain conditions: they need to be continuous, single-valued, and square-integrable. This means basically that the wavefunctions cannot abruptly change probability which in a physical sense makes sense. Congratulations, after one simple pamphlet, you are now a master of Universe 42’s wavefunction! Now go out there and make some good universes better! <</popover>> <</button>> <</if>> <<if $BeenToMSEP is true>> <<button "Mobius Strip">> <<popover>> __''What Even Is a Mobius Strip?''__ Ever get tired of having a piece of paper with two sides? Want to get rid of that pesky ‘other side’? Try the Mobius strip! This amazing discovery is a way to create a loop with only one side! All you need to seemingly defy reality is simply connect a strip to itself with one extra step. Adding an odd number of twists before connecting the two sides will create this topological wonder! <img src="img/pamphlet/mobius_paper_demo.png" style="width: 50%;"> Here’s what it looks like. See how easy it is! This example is shown with one twist. But wait there’s more! In addition to a single half-twist making this geometrical marvel, it can be done with any number of odd numbered half-twists. Here is what this looks like with three! <img src="img/pamphlet/mobius_3_loop.png" style="width: 50%;"> Notice that in addition to having a single side, the mobius strip also has one edge! <img src="img/gifs/mobius_animation.gif" style="width: 50%;"> Now this creates all sorts of interesting models. For instance, if we were to place a vector perpendicular to the plane of the strip and transform it around the strip, this is what it would look like. Notice that it takes two rotations to recover the original vector! All these amazing creations are available to you using just a strip of paper and a piece of tape! <</popover>> <</button>> <</if>> <<if $BeenToEulersIdentity is true>> <<button "Euler's Identity">> <<popover>> ''Euler's Identity'' Have you ever wanted to add an infinite number of items together, but just don’t have the time to figure out the answer? Introducing Taylor series! These simplifying mathematical quantities take those pesky infinite sums and simplify them into a single usable form. Many of your favorite expressions have their own taylor series, like Sine and Cosine! See?! <img src="img/equations/eulers_sin.jpg" style="width: 30%;"> <img src="img/equations/eulers_sin_sum.jpg" style="width: 30%;"> <img src="img/equations/eulers_cos.jpg" style="width: 30%;"> <img src="img/equations/eulers_cos_sum.jpg" style="width: 30%;"> But wait there’s more! We can use these to show the origin of one of the most famous identities of all time, Euler’s identity! <img src="img/equations/eulers_identity.jpg" style="width: 25%;"> First let’s see the Taylor expansion of ex: <img src="img/equations/eulers_e_sum.jpg" style="width: 50%;"> Comparing these to the Sine and Cosine series, notice the terms look incredibly similar! <img src="img/equations/eulers_e_series.jpg" style="width: 50%;"> However, our exidentity doesn’t have any negative terms. So in order to have negative terms, we need a factor that won’t change the value, just the sign. While the simplest guess would be -1, that won’t work. Our pattern needs to be two positives followed by two negatives, like this! <img src="img/equations/eulers_cos_sin_series.jpg" style="width: 50%;"> This is where our imaginary friend //i// comes in! By inserting this into our exponential function to make eix, we create the alternating pattern we’re looking for! Unfortunately, it’s not a perfect match but that’s not gonna stop us!! Let’s see what the series looks like now. <img src="img/equations/eulers_ei_series.jpg" style="width: 50%;"> Let’s try grouping all the terms with i together, then factoring it out! <img src="img/equations/eulers_ei_series_split.jpg" style="width: 50%;"> This simple rearrangement now really shows us the first term can be written as //cos(x)// and the second as //i × sin(x)//. Putting this all together, we get... <img src="img/equations/eulers_e_cos_sin.jpg" style="width: 50%;"> For our final step, lets set //x = π//, then evaluate sin and cos! <img src="img/equations/eulers_ei_cos_sin.jpg" style="width: 50%;"> This very fundamental equation allows us to navigate both imaginary and real dimensions. Trippy, right? Just see if you can wrap your mind around this one! We plot the imaginary dimension on the y-axis and the real dimension on the horizontal axis. <img src="img/pamphlet/euler_circle.jpg" style="width: 50%;"> So just by looking at this picture, we can see that... //e^^ 2π i^^ = 1// //e^^ π i / 2^^ = i// //e^^ 3 π i / 2^^ = - i// and last but not least... //e^^ i π^^ = -1// See for yourself! (The y-axis is in terms of //i,// as in //... -1*i, -0.5*i, 0*i, 0.5*i, 1*i,// etc...) //As the i*sin(ϕ) and cos(ϕ) functions generate the circle...// <img src="img/gifs/circle-two-sine-waves.gif"> //... the Euler's identity simplifies the output as it falls on the axes.// <img src="img/gifs/desmos_euler_circle.gif"> In summary, the Euler's Identity simplifies an //e^^ i π^^// term to -1, or... //e^^ i π^^ = -1// Ta-Da!! <</popover>> <</button>> <</if>> <</popover>> <</button>> <</widget>> <<widget "UnlockedEqn">> <<popover>> <span style="color:white;">You've unlocked something! Your notes have been updated.</span> <</popover>> <</widget>> <<widget "incorrect">> <<popover>> <span style="color:white;">That is incorrect. Try again!</span> <</popover>> <</widget>> <<widget "correct">> <<set $exp =+10>> <</widget>>

<<cacheaudio "bg_soundtrack" "audio/temple.mp3">> <<set $OpenedNotes to false>> <<set $exp == 0 >> <<set $ParticleOnARing to false>>

<div class="center container-fluid opening_text">You are a member of an omega-class civilization, working for a company called the "Theoretical Heuristic Energy Implementation Squad (T.H.E.I.S.)" that specializes in building multi-verses. <<linkreplace "► Continue" t8n>>\ You are an alien called Mo that works for the "Particle on a Mobius Strip (PMS)" division of the company as a coder. <<linkreplace "► Continue" t8n>>\ You’re not really sure what your work is about, but your friend put in a strong recommendation for you, you got the job, and you weren’t going to turn down an offer. <<linkreplace "► Continue" t8n>>\ As you’re coding your little heart out, you notice there’s a set of numbers constantly repeating itself… <<linkreplace "► Continue" t8n>>\ ½… ½... ½… <<linkreplace "► Continue" t8n>>\ Seems redundant. <<linkreplace "► Continue" t8n>>\ So you delete it. <<linkreplace "► Continue" t8n>>\ Little did you know that you had deleted something called an "essential quantum number, m~~s~~". <<linkreplace "► Continue" t8n>>\ The fermions in universe #42 spin out of control, ruining all physics as we know it. <<linkreplace "► Continue" t8n>>\ The parallel universes begin to unravel. Alarms go off. <<linkreplace "► Continue" t8n>>\ You have royally messed up. <<linkreplace "► Continue" t8n>>\ All departments gather for an emergency meeting as all of their civilization’s hard work begins to destroy itself. [[► Continue... |0.5]] <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ </div>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="7" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ok. "Building a Universe 101." We start small. And when I say small, I mean REALLY SMALL. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="8" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>That means we're workin' in the quantum realm, kid. You're familiar with that, yeah? ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>><div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>You know about quantum states and all of that?</p> <p class="mo"> [[► Quantum-what?|9A]]</p> <p class="mo"> [[► Yeah, duh. How else do you think I got this job?|9B]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="quantum_states_explanation" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span class="narration">(Manager sighs, pulls out an iridescent piece of paper from his desk and hands it to you.)</span> <p> Just read this pamphlet, kid. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<set $BeenToQSP to true>>''Quantum States Pamphlet'' Hello valued T. H. E. I. S. employee! This pamphlet series aims to inform the up-and-coming new space clouds in the vast knowledge of Universe 42. Today on the menu: Quantum States. A quantum state corresponds to a specific wave packet or wavefunction, and can be characterized by a set of quantum numbers, each arrangement of numbers corresponding to a specific quantum state. Each observable quantity of a particle in a quantum state, like the energy or momentum, is associated with an operator, which is just a function that acts on a wavefunction or vector. The eigenvalues, or output of the operator, are representations of the quantity that is being observed by the operator. So for example, if the energy operator is applied to a wavefunction, then the output from the application of the operator is the wavefunction and the actual value for the energy. This means the wavefunction is a quantum state with a definite value for the energy with no quantum uncertainty. If the energy of the particle was measured, it is guaranteed by the value the operator dictates. Among quantum states, there is not a state which is simultaneously an eigenstate for all different observables. This means that if we have a state where we know the position exactly, then we will not be able to know momentum, it will have a range of values and not an exact value. This, in Universe 42 terms, is called the “Heisenberg Uncertainty Principle”. The following graphic depicts the probability density, or probability that a particle exists at any given point in space, for an electron in a Hydrogen atom in different quantum states: <img src="img/pamphlet/hydrogen_density_plots.jpg" style="width: 50%;"> [[► Let's keep talking to Manager!|10]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="particle_explanation" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span class="narration">(Manager rolls his eyes as he pulls out another pamphlet from his desk and hands it to you.)</span> <p> You're killin' me, kid. Read this one. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<set $BeenToPQNP to true>>You open the two sided pamphlet, one side titled “T.H.E.I.S New Employee guide Part 2: Particles: a guide to Universe 42’s smallest constituents” and the other titled “T.H.E.I.S New Employee guide Part 2.5: Quantum numbers: what are they even good for?” [[► Read “Particles: A guide to Universe 42’s Smallest Constituents”|particles_smallest_constituents]] [[► Read “Quantum Numbers: What are they even good for?”|particles_good_for]]

<span class="narration">You decide to start on the left side with “Particles: a guide to Universe 42’s smallest constituents”</span> Hello dear reader, and welcome to an introductory look at particles! Particles make up everything in Universe 42 and are quite important. The most important class of particles are the fermions, which have half-integer spins. The three most important fermions are called the proton, neutron, and electron, because they are what makes up every atom, and atoms are what make up EVERYTHING in universe 42. Protons and neutrons are a class of particles called a hadron, and are made up of something called a quark, which is an even smaller type of elementary particle. There are 6 types of these quarks, called up, down, strange, charm, top, and bottom, but protons and neutrons are just composed of up and down quarks. These protons and neutrons are joined by electrons, which are the smallest ‘negative-one’ elementary charge. These particles are special. <img src="img/pamphlet/particles.jpg" style="width:50%;"> Not only are they ‘particles’ in the literal sense, but when you get down to the quantum scale, particles take on wave character and can also be classified as waves. This phenomenon, known as ‘Wave-Particle Duality’, is used to explain where the particle could be; it’s a wave of probability, and dictates where the particle COULD be. The particle, in this case considered to be an electron, exists as this wave of probability until it is observed. Then, it cannot exist as a wave of probability, since it has been located in one position, and assumes a particle-like nature. Once the electron is out of observation however, it goes back to being located somewhere in the wave of probability, until it becomes observed once again. This wave of probability is dictated by the wave function, which you can learn all about in the third installment of the T.H.E.I.S New Employee guide Part 3: The Wavefunction of Universe 42. <img src="img/pamphlet/wpd.jpg" style="width:50%;"> [[► Read Other Side of Pamphlet|particles_good_for]] [[► That's enough reading for now...|12]]

<span class="narration">You look over to the right, at “Quantum Numbers: What are they even good for?”</span> Quantum numbers are very important, as they describe completely the movement and trajectory of each electron that makes up an atom. Each electron in an atom has a unique set of quantum numbers, because according to Universe 42 fundamental rule 1940, also known as the ‘Pauli exclusion principle’ no two electrons can have the same 4 quantum numbers. But what are these quantum numbers, and what do they describe? The first one, n, also known as the principal quantum number, describes the principal electron shell. This means it describes the probable distance of the electrons from the nucleus. N can only be represented by a whole number positive integers. The next quantum number, l, also known as the angular momentum quantum number, describes the shape of the orbital. Each value of l indicated a different subshell (s,p,d,f). The number of angular nodes in the orbital is equal to the value of l, and it’s value can be anywhere from 0 to (n-1). The third quantum number, the magnetic quantum number, ml, determines the number of orbitals and their orientation. Its value can span from -l to l. Finally, the last quantum number, ms, describes the spin of the electron in an orbital. It can have values of +1/2, positive spin represents spin up and negative spin represents spin down. Each orbital can have one spin up and one spin down electron in it, which obeys the Pauli exclusion principle! <img src="img/pamphlet/qn.jpg" style="width:75%;"> [[► Read Other Side of Pamphlet|particles_smallest_constituents]] [[► That was informative!|12]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="13" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Now we got that out of the way, I'm gonna start this training video on wavefunctions up on the screen. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<audio bg_soundtrack fadeout unloop>> Are your naughty particles going out of control?! Then you need something that’s going to tell these particles how to behave - a wavefunction! Just watch this video sponsored by the T. H. E. I. S. corporation to understand what a wavefunction does! <iframe width="560" height="315" src="https://www.youtube.com/embed/_riIY-v2Ym8" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> <a class="traininglink"><<link "► That was interesting...">><<correct>><<goto "14">><</link>></a>

<<nobr>><<audio bg_soundtrack volume 0.25 play loop>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Got it, kid?</p> <p class="mo"> [[► Got it.|15B]]</p> <p class="mo"> [[► Not really...|15A]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="wavefunction_explanation" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span class="narration">(Manager stares at you blankly as a pamphlet slowly prints behind him. Without breaking eye contact, he snatches the pamphlet from the printer and hands it to you without saying anything.) ►</span> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<set $BeenToWP to true>>''T.H.E.I.S New Employee guide Part 3: The Wavefunction of Universe 42'' Welcome, reader, to the 3rd installment of the T.H.E.I.S New Employee guide! This part focuses on wavefunctions. You know them, you love them, and you know how to apply them to the code that makes up Universe 42. But what exactly are they and what do they represent? This pamphlet runs down the basics on wavefunctions needed to continue maintaining Universe 42. The wavefunction Ψ is a mathematical expression, which provides crucial information regarding the electron it represents. Electrons behave as both particles and as waves, a behavior called the “Wave-Particle Duality!” This is why we can represent the motion of electrons as a wave using wavefunctions, and each electron has its own wavefunction! <img src="img/pamphlet/i_hate_it.jpg" style="width:50%;"> From the wavefunction, we can obtain the electron's energy, angular momentum, and orbital orientation, because in the wavefunction we have the quantum numbers n, l, and ml. These quantum numbers are discussed in the informative //“Quantum numbers: what are they even good for?”// pamphlet which can be provided to you via your supervisor! The sign of the wavefunctions help determine how electrons interact with each other. Wavefunctions interacting with similar signs (in phase waves) will constructively interfere and form a bond. Wavefunctions with opposite signs (out of phase waves) will destructively interfere. More applicable however, the wavefunction gives information about the location of the electron. The square of the wavefunction, |Ψ|^^2^^, is also known as the probability density of the wavefunction. If a wavefunction of an electron has the value Ψ at any point //x//, then the probability of finding said electron between //x// and //x+dx// is proportional to //|Ψ|^^2^^//, which we previously stated to be the probability density. Even if the wavefunctions are negative or portions of the wavefunctions are negative, the probability density never can be. You can’t have a negative probability of finding an electron somewhere (the lowest you can have is 0%). <img src="img/pamphlet/wfxn_probably.jpg" style="width:50%;"> These wavefunctions need to undergo a process called normalization, which is used to ensure that the probability of finding the particle somewhere in the space of interest is equal to 1. This is useful, since //|Ψ|^^2^^ dx// is only proportional to the probability of finding the particle in dx space, we want to normalize it to give the probability according to a percent. Lastly, wavefunctions need to obey certain conditions: they need to be continuous, single-valued, and square-integrable. This means basically that the wavefunctions cannot abruptly change probability which in a physical sense makes sense. Congratulations, after one simple pamphlet, you are now a master of Universe 42’s wavefunction! Now go out there and make some good universes better! [[► Ok, I'm done.|16]]

<<nobr>><div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Let's give you a little test, then. What symbol denotes a wavefunction?</p> <p class="mo"><<link "► //φ//">><<incorrect>><</link>></p> <p class="mo"><<link "► //ψ//">><<correct>><<goto "19">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="20" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Alright, kid. You might not be the brightest conscious space cloud here, but you're doin' alright. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>> <<set $TakenPsiTest to true>><<UnlockedEqn>>

<img src="img/gifs/mobius_strip_model.gif" style="width:50%;"> [[► Alright, I've stared at it long enough.|22]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="24" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>This right here is the key to figurin’ out what the wavefunction is. We gotta tell the wavefunction to treat all particles on mobius strips to act like this particle here. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="25" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>So first, we gotta decide what variable of the particle the wavefunction is actually controllin’. Try lookin’ at this list of variables we collected from the uncorrupted database of Universe #42. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<div class="container-fluid"> "This right here is the key to figurin’ out what the wavefunction is. We gotta tell the wavefunction to treat all particles on mobius strips to act like this particle here. First we gotta decide what variable of the particle the wavefunction is actually controllin’. Try lookin’ at this list of variables we collected from the uncorrupted database of Universe #42." "Compare it to the model. Ask yourself - what is changing in the picture? Then pick the variable that changes as a function of time." <br> <img src="img/gifs/mobius_strip_model.gif" style="width:50%;"> <br> <div class="listvariables"> <span class="narration"><strong>List of Variables</strong></span> <<link "► Mass of Particle (m)">><<incorrect>><</link>> <<link "► Number of Lattice Points in the Eiffel Tower (N)">><<incorrect>><</link>> <<link "► Length of Mobius Strip (L)">><<incorrect>><</link>> <<link "► Most Common Type of Pumpkin Species used for Halloween (C)">><<incorrect>><</link>> <<link "► Angular Position of Particle (φ)">><<correct>><<goto "26">><</link>> <<link "► Number of Beans in a Heinz Can of Beans (beans)">><<incorrect>><</link>> </div> </div>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="23" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>You can always look at this model in the "Mo's Notes" panel in the upper right corner. Try it now. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="27" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Yeah, that's right. The angular position is what's changing. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>> <<set $TakenPhiTest to true>><<UnlockedEqn>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="29" tabindex="0"> </a> <div class="narration"> As you enter the server room, you can hear the gentle hum of the servers generating their universes. The manager motions you toward the desk. ► </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="30" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Okay, remember what we talked about. Let's review real quick. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="31" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>The wavefunction, ψ, depends upon the variable, φ. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="31.5" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>You got this, kid. Go ahead and give it a shot. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<big>Universe #42 Command Console</big> <small>//What variable shall the wavefunction command?//</small> <span id="result"></span> <div class="row"> <div id="droppable-1" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br> </div> <div id="equal" class="col-md-1"> = </div> </div> <div class="row"> <div id="draggable-3" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> (-1) </div> <div id="draggable-4" class="draggable ui-widget-content" style="width: 100px; height: 100px; padding: 0.5em;"> 7 </div> <div id="draggable-1" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(ϕ) </div> <div id="draggable-5" class="draggable ui-widget-content" style="width: 100px; height: 100px; padding: 0.5em;"> x^2 </div> <div id="draggable-6" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(x) </div> <div id="draggable-2" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ϕ(ψ) </div> </div> <<mos_notes>> <<script>> $(document).one(":passagedisplay", function(event) { setup.DragDrop("33", { "#droppable-1": "#draggable-1" }) }); <</script>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="34" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Good job, kid! We just told the wavefunction that it’s controllin’ the angular position of our particle. It’s a start. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="35" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>They're callin' an emergency meeting in the auditorium. Let's head up there. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<div class="center container-fluid"> <<timed 2s transition>><big>Chapter 2</big> <<next>><small>Another piece of the puzzle is revealed...</small> <<next>>[[► Continue...|36]]<</timed>> </div>

<div class="center container-fluid"> <<timed 2s transition>><big>Chapter 1</big> <<next>><small>Building A Universe 101</small> <<next>>[[► Continue...|0]]<</timed>> </div>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="38" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p>When we forced the Mobius Server to shut down, we lost all of our code related to the wavefunction that controlled the spin of fermions in Universe #42... even all the back-ups were lost… ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="39" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p>This has been utterly devastating for not only universe #42, but for the subsequent universes that lie parallel to it as well… </p> <p class="narration">(She motions to the screen.) ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="40" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p>We must rebuild the wavefunction as soon as possible... or all is lost. </p> <p class="narration">(Murmuring breaks out across the auditorium and then quickly quiets as she begins to speak again.) ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="41" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p> I’ve called this meeting because I think our data collection team has discovered something quite paramount to our efforts. While we don’t have the wavefunction any longer, we are very lucky to have uncovered this written theorem that inspired it. It will guide our next steps in re-deriving the code for the spin of our fermions. Here is the theorem.... ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="42" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10" style="text-align: center;"> <p> //"For a particle rotating around an axis twice, it must end up where it originally started."// ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="43" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p> Thanks again goes to our data collection team. This is the theorem that prevented fermions from spinning out of control. If we don’t impose this in the wavefunction, fermions will continue to be any spin they like, continuing to wreak havoc across our universes. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/auditorium_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="44" tabindex="0"> </a> <div class="row"> <div class="dialogue headofdmv col-md-10"> <p> Return to your teams and get back to work. Go to the main conference room if your team has anything to share. Complete the wavefunction! ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="46" tabindex="0"> </a> <div class="narration"> You follow Manager down the hallway to the conference room. You're deep in thought about how much you've messed everything up. You look nervously up at Manager, who is looking directly ahead, his stellar brows furrowed together in his usual surly expression. ► </div> </div> </div> </div> </div><</nobr>>

<<nobr>><div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_talking.jpg"> </div> <div class="dialogue mo col-md-8"> <p>[[► So... where do we go from here? We told the wavefunction what variable to manipulate. Now we just have to tell it what to do with the variable, right?|47]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>//"For a particle rotating around an axis twice, it must end up where it originally started..."//</p> <p class="mo">[[► What’s with the “twice” thing anyway? That doesn’t really make sense… if something is rotating about an axis, won’t it reach the same spot after just going once around?|49]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="48" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>I think it’s best to sit over the pieces of information we have. We know we have to use the mobius strip as a model. Now we have this theorem… ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>That’s obviously talkin’ about the mobius strip. I just hadn’t thought about it that way before.</p> <p class="mo">[[► How does that theorem relate to the mobius strip model?|50]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ah, sheesh kid. You know what a mobius strip is, right?</p> <p class="mo">[[► Yeah, I’ve seen it.|51]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>I know you’ve seen it, but do ya KNOW what it is?</p> <p class="mo">[[► ...uhh...|52]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Fer cryin out loud, kid… you know your internship is with the Department of Mobius Validation, right? You didn’t think to at least look up what we specialize in?</p> <p class="mo">[[► ...yeah, that might've been a good idea, now that I think about it...|53]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span class="narration">(Manager reaches in his pocket and pulls out a crumpled pamphlet.)</span> <p>Yeesh... just read this pamphlet.</p> <p class="mo">[[► ... don’t you think the pamphlets are a little excessive at this point?|54]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p class="narration">(Manager turns to look at you. His brow is even more furrowed somehow.)</p> <p>I ain't explainin' this one to ya, kid! We don't got the time!</p> <p class="mo">[[► Alright, alright...|mobius_strip_pamphlet]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<set $BeenToMSEP to true>>''What Even Is a Mobius Strip??'' Ever get tired of having a piece of paper with two sides? Want to get rid of that pesky ‘other side’? Try the Mobius strip! This amazing discovery is a way to create a loop with only one side! All you need to seemingly defy reality is simply connect a strip to itself with one extra step. Adding an odd number of twists before connecting the two sides will create this topological wonder! <img src="img/pamphlet/mobius_paper_demo.png" style="width: 50%;"> Here’s what it looks like. See how easy it is! This example is shown with one twist. But wait there’s more! In addition to a single half-twist making this geometrical marvel, it can be done with any number of odd numbered half-twists. Here is what this looks like with three! <img src="img/pamphlet/mobius_3_loop.png" style="width: 50%;"> Notice that in addition to having a single side, the mobius strip also has one edge! <img src="img/gifs/mobius_animation.gif" style="width: 50%;"> Now this creates all sorts of interesting models. For instance, if we were to place a vector perpendicular to the plane of the strip and transform it around the strip, this is what it would look like. Notice that it takes two rotations to recover the original vector! All these amazing creations are available to you using just a strip of paper and a piece of tape! [[► Hopefully, that's the last pamphlet...|55]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <span style="narration">Manager hears you make the rude comment about his pamphlets and scoffs.</span> <p>You got it now, kid?</p> <p class="mo">[[► Yeah!|56]]</p> <p class="mo">[[► Actually, I need to read it again...|mobius_strip_pamphlet]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/hallway_walking.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="57" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Great. Let's get to the conference room and see where things stand. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue secretary col-md-8"> <p> We have a message from DPR!</p> <p class="mo">[[► (Whisper to Manager) What's DPR?|60]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/secretary_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p><span class="narration">(He whispers back.)</span>The Department of Particle on a Ring. They’re practically like PMS’ sister.</p> <p class="mo">[[► (Whisper back.) I see.|61]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="59" tabindex="0"> </a> <div class="narration"> You and Manager enter the conference room. The head of the DMV and her secretary are among the gathering crowd. Just when you two get settled, the secretary begins to make an announcement. ► </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="62" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue secretary col-md-8"> <span class="narration">You both zone back in to what the secretary is saying.</span> <p> Apparently, the wavefunction for the particle on a ring is still intact! ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/secretary_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="63" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue headofdmv col-md-8"> <p> Let's see it. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p> Hmm… Let’s see if we can break this down a little. So if 𝛹 is the wavefunction, then our variable must be φ. Since it’s describing a particle confined to a ring, that value must be the angular position. As far as the rest of the equation, //e// and //i// are both mathematical constants. So it looks like we need to define //m// before this will be functional again.</p> <p class="mo">[[► How do we do that?|66]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p> Well, we know that the ring fermions travel on resembles a circle, so it has to have a circumference of 2π. If the particle starts at some angular position φ, then after one rotation what would be the new value of φ?</p> <p class="mo"><<link "► //φ + 1//">><<incorrect>><</link>></p> <p class="mo"><<link "► //φ + 2𝜋//">><<correct>><<goto "67">><</link>></p> <p class="mo"><<link "► //φ + 𝜋//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Yeah that makes sense, it’s now the original value plus one rotation, which is 2𝜋. Here’s where it gets fun though, since we need to remember that DPR deals with just a ring and we here in the PMS division deal with mobius strips. Do you remember how many rotations it takes for a particle on a mobius strip to return to its original state?</p> <p class="mo"><<link "► It will never return to its previous state.">><<incorrect>><</link>></p> <p class="mo"><<link "► One rotation.">><<incorrect>><</link>></p> <p class="mo"><<link "► Two rotations.">><<correct>><<goto "68">><</link>></p> <p class="mo"><<link "► Three rotations.">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Right. So if a particle on a mobius strip starts at some angular position φ, then when it finally returns to its original position, what would be the new value of φ?</p> <p class="mo"><<link "► //φ + 𝜋^^2^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► //φ + 2𝜋//">><<incorrect>><</link>></p> <p class="mo"><<link "► //φ + 3𝜋//">><<incorrect>><</link>></p> <p class="mo"><<link "► //φ + 4𝜋//">><<correct>><<goto "69">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ok, I think we’re starting to get the hang of this! But if we’re going to have these two different systems, one for a normal ring and another on a mobius strip, we should have two separate versions of our wavefunction. Since we are characterizing the //m// term in the wavefunction, let’s use two different versions. For the system on a ring, we’ll use m~~l~~. Then we'll have m~~s~~ for the mobius strip system. Just remember the subscript //s// is talking about the strip. Hopefully that’ll keep ya straight! </p> <p class="mo">[[► So ml is used for a particle on a ring, while ms is for a particle on a mobius strip. Got it!|70]] </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/conference_room_eqn.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="71" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p> Our two related systems mean that any characterization or restriction we set for one system must have an equivalent restriction in the other. Let’s head back to the office and finish up this work. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>> <<set $BeenTo69 to true>><<UnlockedEqn>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Okay, kid, back to characterizing those pesky m terms, let’s start with ml. For a particle that has come full circle, that must mean that it’s in the exact same position from where it started, with a value of //φ + 2𝜋//. Since the wavefunction just describes where we are likely to find the particle, what can we say about the wavefunction at the start and after the particle travels around the ring once?</p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ + 2𝜋)//">><<correct>><<goto "74">><</link>></p> <p class="mo"><<link "► //𝛹 (φ) > 𝛹 (φ + 2𝜋)//">><<incorrect>><</link>></p> <p class="mo"><<link "► //𝛹 (φ) < 𝛹 (φ + 2𝜋)//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Good, you got it. So, generally, what does the wavefunction look like if we plug in the values from before and after one rotation? Remember that, here, we need to use ml because we’re talking about our particle on a ring system.</p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ > e ^^i m~~l~~ (φ + 2𝝅)^^ //">><<incorrect>><</link>></p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ < e ^^i m~~l~~ (φ + 2𝝅)^^ //">><<incorrect>><</link>></p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ (φ + 2𝝅)^^ //">><<correct>><<goto "75">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p> That’s right kid, but it sure looks weird. Maybe we can simplify it a little using the exponent rules? What’s another way to write //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ (φ + 2𝝅)^^ //?</p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ φ^^ + e^^i m~~l~~ (2𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ φ^^ * e^^i m~~l~~ (2𝝅)^^//">><<correct>><<goto "75.5">><</link>></p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ φ^^ - e^^i m~~l~~ (2𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► //e ^^i m~~l~~ φ^^ = e ^^i m~~l~~ φ^^ ÷ e^^i m~~l~~ (2𝝅)^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>I think we’re getting somewhere, finally. This isn’t quite what we’re looking for, though, since this all applies to the particle on a ring, and we need to deal with the particle on a mobius Strip. We’ve got our restrictions for a particle on a ring, so let’s try to do the same process for a mobius strip. Do you remember how the angular position value changes after you return to the original state? ''Hint: One rotation is 2𝜋.''</p> <p class="mo"><<link "► //φ + 4𝜋//">><<correct>><<goto "77">><</link>></p> <p class="mo"><<link "► //φ + 2𝜋//">><<incorrect>><</link>></p> <p class="mo"><<link "► //φ + ∞𝜋//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ok, so after returning to its original state, the particle has a position of φ + 4𝜋. If it’s back where it started, what does this mean about the wavefunction before and after this change? </p> <p class="mo"><<link "► The particle is in a different place, so //𝛹(φ) ≠ 𝛹(φ + 4𝜋)//">><<incorrect>><</link>></p> <p class="mo"><<link "► The particle is in the same place, so //𝛹(φ) = 𝛹(φ + 4𝜋)//">><<correct>><<goto "78">><</link>></p> <p class="mo"><<link "► What even is a particle?">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>//𝛹(φ) = 𝛹(φ + 4𝜋)// looks right, so plug those values into the wavefunction, and see what it looks like. Remember, now we are working with our mobius strip, so we need to use m~~s~~. </p> <p class="mo"><<link "► //e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ + 4𝝅)^^//">><<correct>><<goto "79">><</link>></p> <p class="mo"><<link "► //e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ + 2𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► //e ^^i m~~s~~ φ^^ < e ^^i m~~s~~ (φ + 4𝝅)^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Now we’re cooking with (space) gas! Ok kid, put those algebra skills to work again! How can we rewrite //e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ + 4𝝅)^^// ?</p> <p class="mo"><<link "► //e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ)^^ + e^^i m~~s~~ (4𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "►//e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ)^^ * e^^i m~~s~~ (4𝝅)^^//">><<correct>><<goto "79.5">><</link>></p> <p class="mo"><<link "► // e ^^i m~~s~~ φ^^ = e ^^i m~~s~~ (φ)^^ ÷ e^^i m~~s~~ (4𝝅)^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="83.5" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>You know the math, kid! Go ahead and put it all together! ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<big>Universe #42 Command Console</big> <small>//Enter the wavefunction for a particle on a mobius strip.//</small> <span id="result"></span> <div class="row"> <div id="droppable-1" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br> </div> <div id="equal" class="col-md-1"> = </div> <div id="droppable-2" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br><br> </div> <div id="droppable-3" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br> </div> </div> <div class="row"> <div id="draggable-3" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e^^i m~~s~~ (4𝝅)^^// </div> <div id="draggable-2" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(ϕ) </div> <div id="draggable-5" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e^^i m~~s~~ (2𝝅)^^// </div> <div id="draggable-1" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(ϕ) </div> <div id="draggable-6" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e ^^i m~~l~~ φ^^// </div> <div id="draggable-4" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e^^i m~~s~~ (4𝝅)^^// </div> </div> <<mos_notes>> <<script>> $(document).one(":passagedisplay", function(event) { setup.DragDrop("85", { "#droppable-1": "#draggable-1, #draggable-2", "#droppable-2": "#draggable-2, #draggable-1", "#droppable-3": "#draggable-3, #draggable-4" }) }); <</script>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="86" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Yes!! Start the server back up! ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="89" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/manager_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>ERROR 19304781289360219630123615301351275: WAVEFUNCTION TOO COMPLICATED ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="90" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg"> </div> <div class="dialogue manager col-md-8"> <p style="text-align: left;">Wh… what?! Try it again! ►</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="91" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/manager_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>ERROR 19304781289360219630123615301351275: WAVEFUNCTION TOO COMPLICATED ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="92" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/manager_profile.jpg"> </div> <div class="dialogue headofdmv col-md-8"> <p>The wavefunction must not be complete… it needs to be simplified somehow for the computer. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>GAH!!!</p> <p class="mo">[[► Too complicated for an omega-civilization-aged computer capable of generating entire multi-verses???|93]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue secretary col-md-8"> <p>What? You thought all that must mean we’re just gods and our technology is flawless?</p> <p class="mo">[[► I guess not...|94]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/secretary_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>MO, GIT BACK WITH ME TO THE OFFICE NOW!!!</p> <p class="mo">[[► Away we go!|95]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<div class="center container-fluid"> <<timed 2s transition>><big>Chapter 3</big> <<next>><small>Back to the Drawing Board...</small> <<next>>[[► Continue...|95.5]]<</timed>> </div>

This paper looks like a recipe for a very delicious baked bean meal. Not helpful, but you'll keep a mental note of this for dinner later [[Back to the stack. ► |97A]]

This seems like a form to submit for something in Universe 42 called a drivers license? What's driving, and why //wouldn't// everyone just float? This one is useless, you think to yourself. [[Back to the stack. ► |97A]]

This is a paper listing all the pumpkin species. Every one. Even as omega civilization space clouds, you still have an appreciation for pumpkins! This doesn't help the quest for the wavefunction, however. [[Back to the stack. ► |97A]]

This is Manager's ID papers. It says his real name is Ronald. You'll probably still just call him Manager, seems more professional. Anyways, onto the next paper! [[Back to the stack. ► |97A]]

See if you can find anything that might help simplify the wavefunction... [[► A Ferret’s Identity|e]] [[► Euler’s Identity|Euler's Identity]] [[► Your Identity - A Journey into your soul|g]] [[► The Eiffel Tower’s Identity|h]] [[► Return to the original pile...|97A]]

This paper has a picture of a ferret named Jessica on it. Not a useful document. [[Back to the stack. ► |97B]]

<<set $BeenToEulersIdentity to true>><<UnlockedEqn>>Have you ever wanted to add an infinite number of items together, but just don’t have the time to figure out the answer? Introducing Taylor series! These simplifying mathematical quantities take those pesky infinite sums and simplify them into a single usable form. Many of your favorite expressions have their own taylor series, like Sine and Cosine! See?! <img src="img/equations/eulers_sin.jpg" style="width: 30%;"> <img src="img/equations/eulers_sin_sum.jpg" style="width: 30%;"> <img src="img/equations/eulers_cos.jpg" style="width: 30%;"> <img src="img/equations/eulers_cos_sum.jpg" style="width: 30%;"> But wait there’s more! We can use these to show the origin of one of the most famous identities of all time, Euler’s identity! <img src="img/equations/eulers_identity.jpg" style="width: 25%;"> First let’s see the Taylor expansion of e^^x^^: <img src="img/equations/eulers_e_sum.jpg" style="width: 50%;"> Comparing these to the Sine and Cosine series, notice the terms look incredibly similar! <img src="img/equations/eulers_e_series.jpg" style="width: 50%;"> However, our e^^x^^ identity doesn’t have any negative terms. So in order to have negative terms, we need a factor that won’t change the value, just the sign. While the simplest guess would be -1, that won’t work. Our pattern needs to be two positives followed by two negatives, like this! <img src="img/equations/eulers_cos_sin_series.jpg" style="width: 50%;"> This is where our imaginary friend //i// comes in! By inserting this into our exponential function to make eix, we create the alternating pattern we’re looking for! Unfortunately, it’s not a perfect match but that’s not gonna stop us!! Let’s see what the series looks like now. <img src="img/equations/eulers_ei_series.jpg" style="width: 50%;"> Let’s try grouping all the terms with i together, then factoring it out! <img src="img/equations/eulers_ei_series_split.jpg" style="width: 50%;"> This simple rearrangement now really shows us the first term can be written as //cos(x)// and the second as //i × sin(x)//. Putting this all together, we get... <img src="img/equations/eulers_e_cos_sin.jpg" style="width: 50%;"> For our final step, lets set //x = π//, then evaluate sin and cos! <img src="img/equations/eulers_ei_cos_sin.jpg" style="width: 50%;"> This very fundamental equation allows us to navigate both imaginary and real dimensions. Trippy, right? Just see if you can wrap your mind around this one! We plot the imaginary dimension on the y-axis and the real dimension on the horizontal axis. <img src="img/pamphlet/euler_circle.jpg" style="width: 50%;"> So just by looking at this picture, we can see that... //e^^ 2π i^^ = 1// //e^^ π i / 2^^ = i// //e^^ 3 π i / 2^^ = - i// and last but not least... //e^^ i π^^ = -1// See for yourself! (The y-axis is in terms of //i,// as in //... -1*i, -0.5*i, 0*i, 0.5*i, 1*i,// etc...) //As the i*sin(ϕ) and cos(ϕ) functions generate the circle...// <img src="img/gifs/circle-two-sine-waves.gif"> //... the Euler's identity simplifies the output as it falls on the axes.// <img src="img/gifs/desmos_euler_circle.gif"> In summary, the Euler's Identity simplifies an //e^^ i π^^// term to -1, or... //e^^ i π^^ = -1// Ta-Da!! [[Let Manager know you found something useful. ► |98]] [[Keep snooping through the stack and let him know later. ► |97B]]

This is a 400 page dossier on you, everything you've ever done, and everything you stand for. After an insightful read, you feel more connected to yourself than ever, and remember what it's like to truly be 'you'. Doesn't help with the wavefunction though. [[Back to the stack. ► |97B]]

This paper describes some Universe 42 marvel called the Eiffel Tower. Big buildings are cool! Helpful for space trivia night, but not the mission at hand. [[Back to the stack. ► |97B]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Huh… this might just be it! I don’t want to get my hopes up again, though… good thing I only "almost" bet my career on it… </p> <p class="mo">[[► Let's try it!|99]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>If we’re gonna use Euler’s identity to refine our wavefunction formula, first we need to rewrite our equation again. Any ideas to isolate //e^^ i 𝝅^^// from our previous equation //𝛹 (φ) = 𝛹 (φ) * e^^ i m~~l~~ (2𝝅) ^^//? </p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * (e^^i 𝝅^^)^^2 m~~l~~^^//">><<correct>><<goto "100">><</link>></p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * 2 m~~l~~ (e^^ i 𝝅^^)//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="201.5" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Go ahead, kid... you know all you need to know. ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<big>Universe #42 Command Console</big> <small>//Enter the wavefunction for a particle on a mobius strip.//</small> <span id="result"></span> <div class="row"> <div id="droppable-1" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br> </div> <div id="equal" class="col-md-1"> = </div> <div id="droppable-2" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br><br> </div> <div id="droppable-3" class="droppable ui-widget-header col-md-3"> <br><br><br><br><br> </div> <div id="droppable-4" class="droppable ui-widget-header col-md-2"> <br><br><br><br><br> </div> </div> <div class="row"> <div id="draggable-6" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> (1) </div> <div id="draggable-3" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> (-1) </div> <div id="draggable-2" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(ϕ) </div> <div id="draggable-5" class="draggable ui-widget-content" style="width: 100px; height: 100px; padding: 0.5em;"> 4 m~~l~~ </div> </div> <div class="row"> <div id="draggable-1" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> ψ(ϕ) </div> <div id="draggable-7" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e ^^i 0.99¢ φ^^// </div> <div id="draggable-8" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e ^^i x φ^^// </div> <div id="draggable-4" class="draggable ui-widget-content" style="width: 100px; height: 100px; padding: 0.5em;"> 4 m~~s~~ </div> <div id="draggable-9" class="draggable ui-widget-content" style="width: 150px; height: 150px; padding: 0.5em;"> //e ^^i π^^// </div> </div> <<mos_notes>> <<script>> $(document).one(":passagedisplay", function(event) { setup.DragDrop("203", { "#droppable-1": "#draggable-1, #draggable-2", "#droppable-2": "#draggable-2, #draggable-1", "#droppable-3": "#draggable-3", "#droppable-4": "#draggable-4" }) }); <</script>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="204" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>INITIATING SERVER START UP… ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="205" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>DOWNLOADING NEW START UP FILES… ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="206" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>GENERATING UNIVERSE #42… ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="207" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue computer col-md-8"> <p>FERMION SPIN… ½… ½… ½... ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/computer_profile.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ya did it kid!!! </p> <p class="mo">[[► Yeah!! You're a straight-up G, boss!|209]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="210" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue secretary col-md-8"> <p>Incredible!! ► </p> </div> <div class="profilePic col-md-2"> <img src="img/characters/secretary_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue headofdmv col-md-8"> <p>What is your name, young one? </p> <p class="mo">[[► Mo...|213]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue headofdmv col-md-8"> <p>Mo. Thank you.</p> <p class="mo">[[► Yeah, no problem...|214]]</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/mobius_server_room_1.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="215" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue headofdmv col-md-8"> <p>Everyone! T. H. E. I. S. and its multiverses are saved! ►</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/headofdmv_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<big>Good job, you multiverse-saving-hero you!</big> <big>You have been rewarded with a picture of FLUFFY B O I S in a stroller.</big> <img src="img/theboys.jpg" style="width: 50%;"> Thanks for playing! :) [[► Restart|Main Menu]] ''Credits'' Art & Programmer Extraordinaire | //Angela Shipman// | <a href="https://www.linkedin.com/in/angela-m-shipman/" target="_blank">LinkedIn</a> //Special Thanks to brwarner and Josh Grams for your help with the puzzles. ♥// Quick Math Proofing Guy | //Chris Nelson// | <a href="https://www.linkedin.com/in/canestrangeiro/" target="_blank">LinkedIn</a> Pamphlet Lord & Writer Guy | //Harrison Worster// | <a href="https://www.linkedin.com/in/harrison-worster-446ba2164/" target="_blank">LinkedIn</a> //Game Project Created for Dr. Thomas Theis' Advanced Physical Chemistry Class, Fall 2020, North Carolina State University//

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>That’ll do nicely. Applying Euler’s identity to</p> <p>//𝛹 (φ) = 𝛹 (φ) * (e^^ i 𝝅^^)^^2 m~~l~~^^//</p> <p>gives us what? </p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * ( -1)^^2 m~~l~~^^//">><<correct>><<goto "101">><</link>></p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * ( 1)^^2 m~~l~~ ^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Wow, kid, that’s looking mighty fine! Now in order to make </p><p>//𝛹 (φ) = 𝛹 (φ) * ( -1)^^2 m~~l~~^^//</p><p> true, what restrictions does ml have?</p> <p class="mo"><<link "► //m~~l~~// can be any number.">><<incorrect>><</link>></p> <p class="mo"><<link "► //m~~l~~// can be any positive value.">><<incorrect>><</link>></p> <p class="mo"><<link "► //m~~l~~//= 0, ±1, ±2, etc.">><<correct>><<goto "102">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>> <<set $BeenTo101 to true>><<UnlockedEqn>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Well, that makes it mighty simple, huh? You know what’s next, how would this work with the mobius strip version? Remember, //𝛹 (φ) = 𝛹 (φ) * e^^ i m~~s~~ (4𝝅)^^// . Can we write that in a way where we can use Euler’s identity?</p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * 4 m~~s~~ (e^^ i 𝝅^^)//">><<incorrect>><</link>></p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * (e^^i 𝝅^^)^^4 m~~s~~^^//">><<correct>><<goto "103">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>We’re getting close I can feel it! Keep going kid, what’s next with </p><p>//𝛹 (φ) = 𝛹 (φ) * (e^^ i 𝝅^^)^^4 m~~s~~^^// ?</p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * (-1)^^4 m~~s~~^^//">><<correct>><<goto "104">><</link>></p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * (1)^^4 m~~s~~^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► //𝛹 (φ) = 𝛹 (φ) * (0)^^4 m~~s~~^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="mydiv"> <a class="link link-internal" data-passage="106" tabindex="0"> </a> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>I think we got it! To the server room! Let’s hope this works because I wanna get home in time for dinner. Speaking of which, I wonder what I’m gonna make... ►</p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_mo_approaches.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>So if //𝛹 (φ) = 𝛹 (φ) * ( -1)^^4 m~~s~~^^//, //m~~s~~// is restricted to what values?</p> <p class="mo"><<link "► //m~~s~~// can be any half integer: 0, ±1/2, ±1, ±3/2, ±2, etc">><<correct>><<goto "105">><</link>></p> <p class="mo"><<link "► //m~~s~~// can be any whole number: 0, ±1, ±2, etc">><<incorrect>><</link>></p> <p class="mo"><<link "► //m~~s~~// can be $0.99.">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>> <<set $BeenTo104 to true>><<UnlockedEqn>>

<<audio bg_soundtrack volume 0.25 play loop>> <div class="center container-fluid"> P A R T I C L E O N A M O B I U S S T R I P [[Start Game ► |0.1]] [[Tutorial ► |tutorial]] </div>

<big>__''Resizing Your Screen''__</big> If you hate scrolling, you can resize your screen by using the default commands. Some common ones are listed below. ''Mac:'' Command + Scroll ''PC:'' Ctrl + Scroll <big>__''How to Play''__</big> The ► icons will guide you as to what options you have to influence the story. Sometimes, there won't be any and this means there's something in the environment which you have to find to continue. You will be rewarded for exploring difficult pathways. Consider this throughout your journey. <big>__''Interacting with the Environment''__</big> Mouse over the environment until something glows! This means you can interact with it. <big>__''Puzzles''__</big> There will be moments when you have to solve puzzles to move forward with the story. In these puzzles, you will drag and drop the correct tiles into their designated boxes. The boxes will change color when you've enetered a correct answer. Look for the "You have finished! Click here to continue!" message to proceed. [[► Return to Main Menu|Main Menu]]

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p> Now we can put our original wavefunction symbol, 𝛹 (φ), back in. If we do that to //e ^^ i m~~l~~ φ^^ = e ^^ i m~~l~~ φ^^ * e^^ i m~~l~~ (2𝝅)^^//, what will it look like? ''(Hint: Check your notes for the general wavefunction equation.)''</p> <p class="mo"><<link "► // 𝛹 (x) = 𝛹 (x) * e^^ i m~~l~~ (2𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► // 𝛹 (φ) = 𝛹 (φ) * e^^ i m~~l~~ (2𝝅)^^//">><<correct>><<goto "76">><</link>></p> <p class="mo"><<link "► // 𝛹 (φ) = 𝛹 (φ) + e^^ i m~~l~~ (2𝝅)^^//">><<incorrect>><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="map_dialogue col-md-9"> <img src="img/maps/office_facing.jpg"> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="profilePic col-md-2"> <img src="img/characters/mo_profile.jpg"> </div> <div class="dialogue manager col-md-8"> <p>Ok let’s pretty it up again and put the original wavefunction symbol back in where appropriate.</p> <p class="mo"><<link "► // 𝛹 (x) = 𝛹 (x) * e^^i m~~s~~ (4𝝅)^^//">><<incorrect>><</link>></p> <p class="mo"><<link "► // 𝛹 (φ) = e^^i m~~s~~ φ^^ + 𝛹 (φ) //">><<incorrect>><</link>></p> <p class="mo"><<link "► // 𝛹 (φ) = 𝛹 (φ) * e^^i m~~s~~ (4𝝅)^^//">><<correct>><<goto "80">><</link>></p> </div> <div class="profilePic col-md-2"> <img src="img/characters/manager_talking.jpg" style="transform: scaleX(-1);"> </div> </div> </div> </div> </div><</nobr>>

<div class="center container-fluid" opening_text>The department heads begin to grill their employees, desperately digging for where the error went wrong... <<linkreplace "► Continue" t8n>>\They deduce that the source of the error came from within the PMS division. <<linkreplace "► Continue" t8n>>\Sure enough, you go down to the galaxy computers that store all of the physical laws for universe #42 and find that something called the "wavefunction for the particle on a mobius strip" was completely corrupted! <<linkreplace "► Continue" t8n>>\To stop the spread of the corruption, the executives make the decision to delete it. <<linkreplace "► Continue" t8n>>\The galactic computer reads blank… <img src="img/empty_wvfxn.jpg" style="width: 50%;"> [[► Continue... |0.75]] <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ <</linkreplace>>\ </div>

<div class="center container-fluid opening_text"> It doesn't take long for them to realize it was you... <<linkreplace "► Continue" t8n>>\ As punishment, you're to be at the front of the team to fix the problem you've created. <<linkreplace "► Continue" t8n>>\You must work with your PMS team to rebuild the conditions for the wavefunction from scratch… the only hint left behind is the mobius strip model in the office… <img src="img/gifs/mobius_strip_model.gif" style="width: 50%;"> [[Continue... ►|1]] <</linkreplace>>\ <</linkreplace>>\ </div>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="col-md-9"> <img src="img/maps/mobius_server_room_50.jpg" usemap="#image-map"> <map name="image-map"> <area data-passage="32" target="" alt="" title="Input Wavefunction to Computer" href="" coords="666,117,652,323,765,339,759,352,745,355,732,356,701,354,694,374,710,380,726,390,757,397,784,405,812,403,825,396,835,385,831,372,839,348,939,354,946,91" shape="poly"> </map> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="dialogue narration col-md-8"> <p>Go to the computer and tell the wavefunction what variable to define! </p> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="col-md-9"> <img src="img/maps/mobius_server_room_50.jpg" usemap="#image-map"> <map name="image-map"> <area data-passage="84" target="" alt="" title="Input Wavefunction to Computer" href="" coords="666,117,652,323,765,339,759,352,745,355,732,356,701,354,694,374,710,380,726,390,757,397,784,405,812,403,825,396,835,385,831,372,839,348,939,354,946,91" shape="poly"> </map> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="dialogue narration col-md-8"> <p>Go to the computer and submit the wavefunction for the motion of a particle on a mobius strip! </p> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="col-md-9"> <img src="img/maps/mobius_server_room_50.jpg" usemap="#image-map"> <map name="image-map"> <area data-passage="202" target="" alt="" title="Input Wavefunction to Computer" href="" coords="666,117,652,323,765,339,759,352,745,355,732,356,701,354,694,374,710,380,726,390,757,397,784,405,812,403,825,396,835,385,831,372,839,348,939,354,946,91" shape="poly"> </map> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="dialogue narration col-md-8"> <p>Go to the computer and submit the wavefunction for the motion of a particle on a mobius strip (again!) </p> </div> </div> </div> </div> </div><</nobr>>

<<nobr>> <div class="container-fluid"> <div class="row"> <div class="col-md-9"> <img src="img/maps/office_papers.jpg" usemap="#image-map"> <map name="image-map"> <area data-passage="97A" target="" alt="" title="Go through pile of papers." href="" coords="839,347,903,349,910,363,932,365,944,387,943,412,887,416,867,401,847,403,839,388" shape="poly"> </map> </div> <div class="menu_bar col-md-3"> <<mos_notes>> </div> </div> <div class="row"> <div class="textBubble col-md-12"> <div class="row"> <div class="dialogue narration col-md-8"> <p>Better get going through those papers!</p> </div> </div> </div> </div> </div><</nobr>>