Prodigy

The week flew by for Harry, who spent his time preparing quite the presentation. He laid out everything he wanted to go over, and removed some of the things he felt were unimportant, while adding more when he was done about future plans. He didn't get much time to think about the Voldemort problem, but he hadn't forgotten it. The presentation took priority, though, and he made sure it was going to be one of the best. He hardly ventured out of his room at all; he only left to visit Hedwig in the owlery a couple times to make sure she was ok.

Saturday was upon him quickly, almost too quickly as he was up late Friday night putting the final touches on what he was going to say and doing a `dry run' of the entire thing. Sirius kept him fed through the week, but they didn't talk much. The truth of the matter was that Harry was completely mystifying him, and he had absolutely no idea what to do. His godson was far from what he had expected. That was ok, though. They could work through that with time.

Dumbledore came by Harry's room Saturday morning to bring him to the faculty meeting room. Harry was waiting patiently; his M-Machine and projector (along with some other items he was going to show them) packed neatly in his trunk which was sitting nicely in his pocket.

“I think you'll find the presentation very interesting.” Harry recognized the voice of Professor Snape as he and the headmaster neared the room. When they entered the room, Harry looked around at the professors. A couple of them looked bored, and one even seemed to be a ghost of some sort.

Harry pulled out his truck, enlarged it, and began unpacking his equipment. His actions caught the attention of everyone, and some were sitting on the edge of their seats.

“Before we start, it might be a good time for introductions,” Dumbledore said. Harry nodded as completed his setup.

“First we have Professor McGonagall, Transfigurations, then Professor Flitwick, Charms, Professor Binns, History, Professor Snape, Potions, Professor Hooch, flying, Professor Hagrid, Care of Magical Creatures, Madam Pomfrey, School Nurse, Professor Sprout, Herbology, Professor Sinistra, Astronomy, Professor Trelawney, Divination, Professor Vector, Arithmancy, Professor Black, Defense Against the Dark Arts, and finally, we have two others here that are not a member of the Hogwarts staff. Nicholas Flammel and Remus Lupin are here for purely academic purposes,” Dumbledore finished. Harry had followed the introductions around the room, trying to memorize every name and what they taught. The last two had surprised and excited him. He had no idea Nicholas Flammel was still alive. Harry decided he would definitely need to have a long talk with the man sometime.

“And I'm Harry Potter. I would like to begin by thanking you all for allowing me the time to give this presentation. I have quite a bit to go over, so I'll go ahead and get started.”

There was a collective gasp as the projector came on and the image of several different items appeared above it. Harry smiled. He had expected that none of them would have seen such a thing before. Harry stood behind a table with his M-Machine and Projector setting on top of it. The professors were seated around another, longer table in front of him with rapt attention. Harry pressed a button on the Machine, and the holographic-like image above it changed to a list of topics.

“For this presentation, I'm going to begin with the more theoretical portions of my study and then move towards more practical applications. Finally, I'll end with my plans for the future and what I hope to accomplish.”

Dumbledore stiffened slightly. Harry wasn't planning on revealing the prophecy, was he? That definitely needed to stay a secret for as long as possible.

“I'll begin with a fundamental question `What is Magic?' In my studies, I did not start asking this question until about a year or so into my study. I'm sure many of you here have asked yourself the same question. While it may seem to be a personal, subjective question, I believe that there is a scientific answer to be found as well.”

“I started out by learning everything I could about Arithmancy. Unfortunately, or fortunately, what I learned left me looking for more. It might amaze some of you that I discovered the answer in the muggle world. A few hundred years ago, a man by the name of Isaac Newton revolutionized mathematics through the creation of the mathematical art `Calculus.' Calculus is best defined as the manipulation of functions through differentiation and integration to find their limits. To put it more simply, it's a refined method of making more accurate calculation.”

“Before I go further into the math behind magic, I need to back up a little and take a look at potions, and what I discovered through their study. I'm pleased to have Mr. Flammel here today, as it is through one of his books that I was able to make progress.”

A picture of Harry's first failed potions experiment was projected with him looking quite stunned with a blackened face from the explosion. The picture received a few chuckles throughout the group.

“As you can see, my first venture into Potions was not that successful, and I let that area of magic alone for quite some time. However, soon I came to possess a most interesting book the once again got me interested in the subject of potions. I began to map out the different properties of the ingredients I had available using the information from Mr. Flammel's book. Soon I began to notice a pattern between the similarities and differences of the ingredients themselves. I began to wonder if it wasn't necessarily the ingredient as a whole that was needed for potions, but a set of substances that were more basic.”

“To test this theory, I began breaking down the different ingredients I had into smaller substances through a variety of methods. I had to experiment quite a bit, but soon I began to make progress. Soon, I was able to begin cataloging more basic ingredients. Since I didn't really have a way to keep track of them, I gave them simple names like `B42,' which actually did receive a name later: Liquid Lightning. But I'm getting ahead of myself again.”

“Soon I had so much data that it was getting hard for me to keep track of it all. I built a machine that would automatically break down the ingredients I fed into it and record the basic substances it was able to find, and while that helped getting the data, processing it and tracking it was extremely difficult. So I created a new machine.”

Harry picked up his M-Machine for all to see.

“This is the M-Machine mark II. The original I sold to the goblins and Gringotts. I built it using parts I transfigured from other objects to get what I needed. At the core of the machine is a set of crystals that store data. I new I needed a way to interface commands and data to and from the crystals, so I went about finding a magical way to do that. Unfortunately, I was unable to find one, although today, I'm sure I could do it. Instead, I ended up hooking in electrical connections.”

“I do not know what knowledge you have of muggle electricity, so I'll briefly explain it to you. Basically, it is the movement of something called subatomic particles along paths to create power. This creates the ability to have something move through the magnetic fields created by the movement of these subatomic particles, called electrons. I didn't know this at the time, however, I found that out later. I needed a way to interface the muggle electricity with a magical core, and I turned back to my potions research for my answer.”

“As it turns out, sub-potion substance B42 was able to take the movement of electrons and translate it into magic. Using this substance, I soon had a way to communicate with the crystals. After I got everything connected together, I had a simple way to load, store, and view data. I soon discovered, however, that I needed more. I needed a way to process and manipulate the data. Using transfiguration, charms, and enchantment, I was able to build a small device that would be able to load a set of instructions from the crystals and then follow those instructions. All I had to do was create the instructions.”

“It took me a while, but the M-Machine was finally completed. I hooked up various other instruments I built for data collection and soon had all the data in the machine. I then went about scanning the complete library in as well. Once all of this was done, I had a central repository for all my information. I turned my attention back to Arithmancy.”

“One day while I was working on Arithmancy, my papers became scattered, and while I was picking them up, I accidentally stumbled upon a connection between the numbers I was working on and the Potion data I had collected. There was a definite pattern in the Potion data, and I just needed to abstract it out to create a usable equation.”

The projector changed again to put up what looked to the audience to be a strange set of numbers and symbols. The slide read:

f_m=pw

“This simple formula is the basics of my advanced magical theory. I later found out that this is not complete by any means, but it was a definite starting point. “fm” stands for the frequency of the magic, and it is equal to `power' times `will.' This presented me with several problems. First, how could I create mathematically a way to measure either power and will? Secondly, how were potions ingredients formed in nature without the interference of power and will? Lastly, did this mean that the substances could be created artificially with the correct application of power and will?”

“Some of you may have heard of the famous muggle equation e=mc2. This was famous because it completely changed the may muggles looked at mass and matter - the physical things around us. The equation is basically saying this: energy and mass are related, and it's possible to convert one to the other. This connection between energy and mass got me to thinking about how magic might actually interact with the world around us. There had to me some sort of connection between magical energy and its physical effects.”

“It was this line of thought that led me to hypothesize about the possibility of a new dimension where magic energy resided. Muggles have identified the first four dimensions: length, width, height, and time. With the theoretical addition of a fifth dimension where magic resides, I was able to create an elegant mathematical system.”

Harry stopped briefly with a smile to look around the room. He was just getting to his favorite part. The adults in the room were looking at him in many different ways. Some of them were still on the edge of their seat, others were quite obviously lost. Harry didn't care. The presentation was helping him as much as it was helping them.

“So here is the first example of my new fifth dimensional mathematics. At this time, the theory is incomplete, but I'm hoping to come up with an elegant solution that I'll be able to use. It is important to stress this fact. Right now, this is only a theory, and an incomplete one at that. I need to complete the theory, and run some experiments to confirm it, but I'm optimistic.”

“The basic of the theory is this: The fifth dimension is where magic takes place. When there is action in the fifth dimension, it affects the first four dimensions through a connection as yet unknown. It is possible that substance B42, liquid lightning, may hold the key to this as it is able to translate magic into electrical power and visa versa.”

There was an image depicting this type of interaction being projected as Harry talked. Nicholas Flammel, Remus Lupin, and Dumbledore were all nodding their heads as if they understood what Harry was trying to say. Harry was encouraged and continued.

“By hypothesizing this interaction, I can abstract out how certain spells interact. For example, I took this reading of a levitation spell.”

A graph appeared depicting a wavy line similar to a sine curve with a low frequency.

“I created another machine to take this reading. Basically, by shooting a spell at it, it will take the magical energy and convert it into electrical signals using the liquid lightening substance I found before. The electric signal is something I can record and do calculations on. Now, let's look at a cleaning spell.”

Another graph appeared, looking very similar, but with a different frequency and amplitude.

“As you can see, the two spells are very similar looking. They only differ in a few specific ways, but those ways are important enough to create a completely different outcome. I'm hoping to be able to create a connection between the observed results - the purpose of the spell - and the properties of its magical cause. Once a connection is found, I will be able to take a desired cause and form the spell through a sort of reverse engineering.”

The professors sitting around the table were now either completely engrossed or wide-eyed and lost. Nicholas Flammel appeared to be very excited and was now taking notes.

“I believe this to be possible because I've already been able to do it with potions.”

“What?” Dumbledore exclaimed. Snape was smiling, something that seemed to Harry to be somewhat rare. Of course, he and the potion master had already discussed it the previous week. Harry grinned and pulled up a new slide. The chart of potions ingredients appeared.

“What I mean, Professor, is that by knowing the sort of potion I want to create, I can look at the basic properties of the different basic ingredients and form a few possible recipes for the potion. Then by testing each of the different recipes, I can further refine my basic data in order to make the process even faster. I understand from talking to Professor Snape that this is completely different from the current method of potion creation and research. I do believe that this will be much faster.”

“There is no doubt about that,” Remus Lupin couldn't help himself from commenting. Lily and James' son was certainly impressing him. The possibilities were endless! Harry smiled knowingly and continued.

“The final theoretical portion of my presentation will be about how wizards are able to interact with this fifth dimension to create a magical effect. During my studies, I recognized a couple things. Nearly all magic is accomplished through a movement of some sort by the witch or wizard, whether it's with a wand or otherwise. For example, a wizard is able to create powerful magic through the creation of different runes, while a muggle cannot. My theory is that it is not the rune itself that holds the power, but the action required to create the rune.”

“The obvious problem with this theory is that if a wizard can create a magical effect through action, and it is the action that causes the effect, why can't a non-magical person, do the same?”

“While I do not yet have an answer to this question, I do hope that I'll be able to solve this problem. Before I move on to the practical portion of my presentation, are there any questions?”

“This is outrageous!” A woman Harry did not recognize flew out of her chair and stormed out of the room. Harry was horrified! What happened? With wide eyes he looked to Professor Dumbledore.

“Please excuse Professor Horntide,” Dumbledore said. “You have challenged many of her basic beliefs about magic, and she is probably rather confused at this moment. I must point out that she is probably not alone. Even I was only able to follow portions of your presentation.”

“I have a question. You mentioned that you broke down potion ingredients into their basic substances. Obviously, these substances have a magic reading of some sort. Have you tried plugging those into you little machine to see what sort of reading you would get?” Nichole Flammel asked politely. Snape raised an eyebrow. It certainly was an interesting question.

“That is a very good point; I'm surprised I've not thought of that. Hmmm…” Harry said obviously deep in thought. A moment later, he pulled out a pen and started to write on the M-Machine. “I'll have to get back to you on that, but you might have stumbled onto something very big!”

“Where can I get one of those?” Sirius asked, pointing to the M-Machine. Harry grinned. His market was already forming!

“Well, for a small fee, I can build one for you. Or, since I've already given you the basic theory behind it, you can try building one for yourself,” Harry said.

“I wouldn't mind having one myself,” Professor Snape said. Harry nodded and began writing again.

“Anyone else? It'll probably take me a month or two to make these, but I believe it'll be worth it,” Harry said while scribbling.

“Are you serious? You would really make one for me?” tiny Professor Flitwick squeaked out. His eyes, though, were as big as saucers as he was thinking about all the things he could do.

“Of course, sir. I understand that some of the greatest minds in the wizarding world are sitting in the room right now. They need to have the best tools available in their hands.”

Soon everyone had admitted to wanting one, even the large man named Hagrid, though he wasn't sure if he would be able to learn how to use it or not. Harry assured the big man that he would help when the time came.

“I believe that it is going to take some time to digest everything you've talked about here, Mr. Potter,” Dumbledore said after a few moments of silence. “I'm sure we will all have plenty of questions for you later, but for now, why don't you continue with the practical portion of your presentation?”

Harry nodded, and finished putting the projector back in his trunk.

“Well, you have already seen the M-Machine and what it can do, so I will skip over that part. The next thing is somewhat embarrassing to me, but I believe is important for you all to know. It seems that for the last four years I've been doing wandless magic without realizing it.”

There were gasps from all around the gathered adults. Surely, Harry wasn't being serious? As a silent demonstration, Harry motioned towards the M-Machine and levitated it. The professor's eyes grew once again as they realized Harry was telling the truth.

“I only found this out last week as I spoke to the Headmaster. It seems that the wand I was using was not a proper wand, but just an ordinary stick. I had no way of telling the difference at the time, however, so I worked for four years with my stick in hand.”

Sirius was laughing outright and just got louder when Harry pulled the wand he had been using out of one of his pockets. Others were joining in. A wave of Harry's hand silenced him, however as he found he was no longer making any noise. Harry looked at him innocently while grinning.

“Yes, I can do silencing spells as well,” Harry chuckled, getting another laugh from the group.

Harry spent the next hour and a half demonstrating an extensive knowledge of different spells, runes, rituals, and potions. The staff present grew more and more excited by each demonstration, knowing that they were experiencing a once in a lifetime thing. Heck, there probably hadn't been someone like Harry since the time of Merlin.

“Well, I think that's everything,” Harry said after completing his last demonstration of a potion. It had turned Sirius Black's hair green.

“I think you might have left something out,” Dumbledore said with a twinkle in his eye.

“What was that?” Harry asked curiously as he thought hard about what he might have missed.

“How about turning my hair back,” Sirius said while trying to hide his laughter. He had been released from the silencing spell just to have his hair changed.

“Besides that,” Dumbledore said immediately. “How about how you arrived in my office last week?”

“Oh that!” Harry said, remembering. “I didn't think it was that important.”

“I do believe that it is important, Mr. Potter,” Dumbledore answered brightly.

“Well, if you say so,” Harry said. He concentrated for a moment before disappearing and reappearing behind them all.

“Where did he go?” Sirius asked the question on everyone except the Headmaster's mind.

“Back here, guys,” Harry said with a smile. The professor's whipped around to see him.

“How in the world did you do that?” Professor Snape asked.

“I think the term is apparate, but I'm not sure. I can just do it,” Harry said.

“But you can't apparate inside Hogwarts!” An unidentified voice pointed out.

“I don't think our usual rules apply to Mr. Potter,” Dumbledore said brightly. Harry concentrated for moment before returning to his place behind the front table.

“Ok, now I'm done. Are there any questions?” Harry said.

There was silence all around. The professors didn't really know how to react.

“I think that's everything we needed, Mr. Potter. If you could please let us talk about your education now, I believe it might be helpful for you to begin to know some of the students?”

“Sure thing,” Harry said, but inside he began to get nervous. He put the machine away, tucked his `wand' back in his pocket and disappeared back to his room.

“Hey! What about my hair?” Sirius exclaimed.

End Chapter

A/N: Hey, sorry it took so long for me to get this out. I won't give you an excuse, because they just get old after a while. Some people have expressed concern about Harry being too smart. That is simply not the case, and that will become apparent as the story progresses. He has a lot to learn, and his theories are far from complete. In fact, he is completely wrong about some very big things.

One of the things that I struggled with was what to do about third year, since Sirius is already free and clear. I've now come up with a great solution, and let me just say this: Third year is going to be a ride! Well, ok, maybe that's the wrong word. There's not going to be a lot of action third year, but there is going to be an extremely large problem that Harry is going to undertake. I really don't want to write the fourth year tri-wizard tournament, but it's currently in the outline, so I've not decided what to do about that, yet. Fifth year is going to be totally different, and going to end with a bang.

Lastly, those of you who would like to be spoiled, let me know, and I will post my outline on my website. I would be nice to get some feedback on that, but I know that a lot of you want to be surprised as well. If there is a lot of people who want to see the outline, I'll do it. Otherwise, things will stay as they are - safely tucked away on my computer.

One more thing. I did not put any more equations in as I realized that the mathematical symbols were taken out.

Until next time, so long, do well, win awards, and thanks for all the fish. See you in the funny papers.