Fred, George, and Lily got to transfiguration on time and were there along with some other students. Professor McGonagall sat at her desk, waiting patiently for the rest of the first year students to arrive. She looked up as she heard the rest of her students begin to fill in the classroom. "Welcome students." she beamed a smile and stood up from her seat. She waited patiently until all of her students had taken their seats before starting her lesson as she leaned against her desk for a short bit. "I am Professor McGonagall and I will be your transfiguration professor for your time here at Hogwarts. I'm very excited and pleased to be teaching you. Now, I want you all to know that you can always approach me with any questions that you may have, to please feel free to also talk to me whenever I am least busy. Now, transfiguration is a difficult branch of magic, but I have confidence that each and every one of you can and will succeed. In terms of the assignments, most weeks you will have a short ten question quiz and the occasional extra credit essay. These essays are optional and will not affect your house points, however, they are an opportunity to get better acquainted with the course material or in this case, the spells, and earn some extra points for your house. Additionally, copying or cheating answers by spells or an outside source will be met with losing points and the inability to retake your assignment. I know what most of you are thinking, 'what is transfiguration?' Well, transfiguration is a very precise and delicate branch of magic. It is the alteration of objects in our physical world. This is not just an alteration of appearance, however, but of the molecular structure of the item as well. Transfiguration is a very dangerous form of magic, as it is very easy to mess up. Should transfiguration spells of any kind go wrong, they can lead to catastrophic situations. When you are working with the molecules of an object, you are changing its' basic principles. If this energy or change gets displaced or unfocused, serious harm could befall you and those around you. Now, molecules are defined as a group of atoms that are bonded together to create chemical compounds. These chemical compounds are what create everything in our universe, living and unliving. Individual things have different molecular structures which define what they are. Transfiguration is one of the more scientific branches of magic, meaning there is a strict systematic approach in relation to the incantations and wand movements. This is why many people do not find transfiguration as rewarding as some other forms of magic. Most people have a hard time appreciating how scientific it is, and prefer things that aren't quite as strict in principle. There are four branches of transfiguration: transformation, vanishment, conjuration, and un-transfiguration. We will be studying each of these in your years with me, though most of it will be in the more advanced years. For the first few semesters, we will be focusing on the many forms of transformation, such as inanimate to inanimate, animate to inanimate, inanimate to animate, and eventually animate to animate. The four branches of transfiguration will be discussed in greater detail in the next lesson. As for the transformation formula, this is an integral and essential part of the science of transfiguration according to some, though I must disagree." Professor McGonagall noticed that some of the students were getting nervous, stopped breathing for a moment, or were not really understanding her explanations. Professor McGonagall smiled at them softly before continuing, "Now, stop for a moment, breathe, and I shall explain, so don't start panicking yet my dear students. First, let's begin by saying that this is a theoretical formula. While some claim to use this formula to get an idea of the difficulty of a spell, it is not an actual mathematical formula meant to be solved for a hard value. The reason for this lies mainly in the nature of its variables, but I'll explain that in a moment. For now, let's break down the formula and see if you can figure out what I mean from what the variables represents." Professor McGonagall walked up to her blackboard, used a levitation spell that not only made the chalk float but also write on the board and on it was, 't = intend transfiguration difficulty, w = wand power, c = concentration, v = viciousness, a = mass of beginning object, and z = unknown variable'. Professor McGonagall then turned back to the students and resumed her lesson. "Now, before we go any further, I am going to be completely honest with you. The transformation formula, as I explain the variables, it is a theoretical formula. This goes beyond just the variable z, which researchers have been thus far, unable to identify, though we are coming back to that in a moment. Of the four known variables, only one of them is actually measurable. This is would be the mass of the object, which is defined by how much 'stuff' there is in the object. Though directly related to an object's weight, mass is a slightly different measurement. For you see, mass is an inherent property while weight depends upon the force due to gravity acting on the object. The three variables that cannot be measured are wand power, concentration, and viciousness because they do not have numerical values. Wand power is the strength of your wand and is influenced not only by the wood, core, length, and flexibility, but also by your relationship with it. Now, I will explain concentration to you in more detail in the coming weeks, but in general, it is how your mind focuses and directs your magic. For the sake of transfiguration, viciousness is the liveliness of the target object. Though it may sound counter-intuitive, viciousness cannot be zero, even for inanimate objects. The reason for this is that at the atomic level, there is always movement in an object. The only possible way to have a thing with absolutely no viciousness, is if that thing is at absolute zero, where all atomic motion is stopped. There are multiple theories as to what would happen if one tried casting a transformation on an object at absolute zero, however none can be proven as it is impossible to cool something to that temperature, even with magic. How many of you have ever heard of quantum physics? Anyone?" Professor McGonagall paused for a moment to see if any of her students would raise their hands. Lily raised her and she was the only one with her hand risen. Professor McGonagall nodded to Lily before continuing. "For you all who don't know, quantum physics is a theoretical type of physics. The theories are hard to wrap your mind around and seen at first glance to hold little practical application. The transformation formula is much more or less the same. It is a basis upon which people attempt to understand the science of transfiguration, quantifying what we can. No one truly understands exactly how transfiguration works, but they formulize the parts that they know affect it. Due to the lack of exact knowledge of how transfiguration works and the difficulty in connecting the theoretical to the practical, the variable 'z' is placed in the formula. It is the one piece of transformation that no one can truly quantify, though there are many theories. Some believe it refers to the complexity of life within an object, while others believe it is the molecular makeup of the object, and still others believe it is an individual's aptitude for the spell or a combination of several factors. The 'z' variable is one of those concepts that both exists and does not exist simultaneously, as no one can pinpoint exactly what it is. It is one of the big mysteries of transfiguration. Once you have all of the variables straightened out, you can get an idea for the difficulty of a spell using what you know and trying to balance the formula. A larger 'value' for the difficulty, 't', means an easier spell, while a smaller value means a more difficult spell. With this in mind, you can figure that if a target object has a large mass, adding more concentration will make it easier. Conversely, if you know your wand isn't the greatest with transformation spells, a less vicious target will be easier to transform. Even without the numbers, we can get an idea for the relative difficulty of the transformation. As you progress through transfiguration, you will get a more intuitive feel for how to cast, what aspects need to be strengthened when, and what objects are more or less easy to transform to the point that you will not need to reference the formula at all. It is merely a construct through which we try to understand the many mysteries of magic. Now we will discuss the dangers of transfiguration as I've already told you, transfiguration can be dangerous, but now I feel it is appropriate that we get into exactly why this is. This type of magic has many opportunities for things to go wrong, and disastrously so. This is a possibility for even the most practiced of transfigurists. This is why it is important that you do not try spells above your year. Attempting to cast transfiguration spells you have not yet learned is something that you will be severely docked for in house points as this is an extremely dangerous practice that will not be encouraged or condoned in my class. When spells backfire or aren't completed correctly, it can prevent items from completing their transfigurations. While this may not seem like a big deal when working with simple transfigurations, such as an apple to an orange, think about what this could mean when you get into deeper things, like human transformation for example. Can you imagine what would happen if you went to do a transformation to give yourself gills and it only worked halfway? Or if you were to try to vanish something and only managed to vanish half of it? Surely you can see the dangers here. That concludes our first lesson for today students. I hope you all enjoyed the lesson. A quick note, please do not stress about the transformation formula. It is not important that you fully understand it, as it will not be a focus in this course at all. I look forward to seeing you at the next lesson tomorrow." Professor McGonagall smiled at her students and then returned to her desk. Fred, George, and Lily finally spotted Percy. "PERCY!" Lily shouted with such joy, she ran up to him and embraced him. "Mmm. I missed you so much big brother, where have you been and been up to? We hadn't seen you almost all morning." Lily said in full curiosity. "I had different courses, but now it's the beginning of the afternoon and soon to be lunch time. "Oh, shall we enjoy ourselves out in the courtyard?" suggested Lily. "I think that is a wonderful idea." Percy and the twins all said in unison which made Lily couldn't help but giggle. "Alright then, let's go to enjoy this gorgeous day since we haven't really had an opportunity to relax in between our three classes." The three boys nodded their heads and made their way to the courtyard.