Risu nodded. "This is true. Mars, for example, almost certainly had an atmosphere similar to the Earth's once."

Risu nodded and tapped the blackboard. "Number of hospitable planets that develop any kind of life," he read out. "This is, obviously enough, one of the more important milestones that we need to pass in our equation."

"Very good point, and that is indeed something we need to take into account. Any kind of life needs to develop to the point that it can send out detectable signals such as radio waves." He glanced at the blackboard. "I will add this momentarily, let's her what your classmates have to say first. Yes." He pointed at he next student.

"I definitely agree, Miss, er, Carlisle, correct?" He glanced at the girl questioningly. "The origin of life is, of course, a speculative subject, and one I'm not exceedingly familiar with, but we can suspect that after that initial point, the development of life proceeds in evolutionary terms all over the Universe as it does here on Earth. Of course, the results might well look very different. There is no reason to think that an extraterrestrial looks like a human but with, say, large eyes and green skin. We might very well have to discuss this later, though, as there are one or two important details to this argument."

"Stars in and of themselves cannot, as far as anyone knows," Risu said, "but they are, of course, very important to planets as a source of heat and energy. And there are many types of stars that do not lend themselves to support life on planets surrounding them. For example..." He paused and considered. "For example. A lot of stars in our galaxy are bound with a partner star. These are called binary systems. Two stars orbiting each other. Such a system would not be very good for the development of life on any surrounding planets because orbits tend to be very unstable. Planets will get too close or too far, they might be ejected out of the system into deep space, they might fall into the stars... Generally a single star of a certain type, such as our Sun, is thought to be a requirement for life to develop, especially to the point of a civilisation, not just bacteria."

He picked up his wand and tapped the blackboard once more. "To recap briefly, the most important thing to add is that once life has begun on a planet, this life needs to develop to a point where it is advanced enough to be noticeable to other life. And allow me to reorder this list quickly." The words changed position on the blackboard.

Calculating the number of extraterrestrial civilisations we can communicate with

• Rate of star formation
• Number of stars with planets
• Number of hospitable planets
• Number of hospitable planets that develop any kind of life
• Number of planets with life where the life becomes advanced enough to send out signals

He turned around. "Looking at our little list, it seems like we have a pretty good grasp on what our own Drake equation would have to include already. There is one last factor to add, and I will just do this for you: We need the length of time that any civilisation sends those signals into space. Any advanced civilisation that only sent out signals for, say, a few seconds would most likely not be noticed."

Calculating the number of extraterrestrial civilisations we can communicate with

• Rate of star formation
• Number of stars with planets
• Number of hospitable planets
• Number of hospitable planets that develop any kind of life
• Number of planets with life where the life becomes advanced enough to send out signals
• Length of time the advanced life spends on sending signals

"And here we have our very own equation. Now, are there any questions?" He looked around.

OOC: MissFeenella, I'll include your post in the next one. This one is super huge already. ^^
Same with you, Chris.

Kimalia from her seat merely smiled seeing the cloud of dust apprear, "Good day, Professor."

Kimalia raised her hand for this one, "I can't speak for outside our own solar system, but surely the closest that's ever been theorized for life is on the planet Mars." After her contribution she kept quiet taking notes until the next question. No way would she blurt out an answer without being absolutely sure.

So stars couldn't support life, but they helped... somehow. Alright. Helena got that. Thank yooouuu, professor.

And... questions? Yes, Helena had one. "Are we going to calculate this? Now?" She asked with her hand in the air, then let it fall back on her lap.

She REALLY wasn't looking forward to that, even though she liked the lesson.

Questions? Zara had one. 'HOW ON EARTH DID YOU KNOW MY NAME?' She kept repeating in her head. But decided not to say it out loud. It's not related to the topic anyway. She kept quiet for the moment and sat still.

Then a question hit her. OOHH. Her hand shot up and asked, "I have, Professor," she grinned, "When was this equation made, exactly?" Yeah, she hasn't read about it the books. *tries to remember what she's seen in those books she read*

Nope, it ain't there. Guess she needed to read more.

"Carlisle, yes, you were right," she said, nodding.

Sophia copied exactly what Professor Antares had written on the board, along with the equation.

"Uh, Professor?" she said, raising her hand. "What do all of the letters in the equation stand for?"

CONFUSION.

Ryden was itching. She had writing equipment in her bag, of course, just in case she needed to write an emergency letter to someone... But for lessons, she's never used it. She'd never felt the need to write anything down; mostly because she kind of knew it all already, and then because she didn't WANT to participate and all that.

Now, however, she really wanted to write this down. This class was almost like science and she LOVED science. Rolling her eyes at her own patheticness, the brunette quickly got out her things and began jotting down the things on the board, ignoring the nagging little voice that said, in a sing song voice, "Father's going to be EVER so proud of his little, swotty Ryden." Grrr.

The students ended up having a few questions after all. "To your first question... Yes, there are a lot of boxes that need to be ticked before a planet qualifies as hospitable, you are correct. In this case, though, all those details are included in the phrase 'hospitable planet'. As far as the equation goes, a planet needs to be in the right place, have the right size, have an atmosphere, and so forth," he waved a hand, "to be considered hospitable."

He tapped a slender finger against the relevant line on the blackboard. "If it's, say, too far away from the parent star, it's not considered hospitable and doesn't appear in this factor of the equation. As for your second question... It is generally assumed that it does, yes. Life begins simple and then, in the correct circumstances, evolves more complexity. Actually," he added, "bacteria can be fairly complex already, they're not the first forms of life on which everything else is built, but for shorthand, we'll refer to them. If you're alright with that?" He gave her a questioning look, smiling slightly.

"Very good question," he said, nodding. "And my answer is that yes, you probably would. Perhaps we should add another factor, number of hospitable moons or something along those lines. As you can see already, this equation is no foolproof method of figuring out the question of alien life, and we can certainly poke more holes in it."

Risu laughed. "No, we aren't," he said, shaking his head. "The main reason for this being, most of the actual values in this equation aren't very well known at all. We could plug some random numbers in, of course, but the result wouldn't help us much."

"I do believe this equation was first announced in the 1970s... So more than a century ago. I actually... Hold on a moment." He rummaged around in the stack of books on his desk, eventually flipping open an old encyclopaedia. "Drake, Drake," he murmured, running a finger down the entries. "Oh! Looks like I was off by a decade. The first mention of this equation was in 1961, at a scientific meeting about the search for alien life. There you have it." He flipped the book shut with a thud.

"Well! Miss Carlisle, I will get into that if there are no other questions. Anyone?" He looked around.

No. More. Questions.

She wanted to know about those letters. She stared and stared and stared.

Maybe they would magically appear in her brain? Yeah, right. Magic didn't work like that. She leaned on one arm and listened to the answers. While fascinating (not), she had another question.

"If we're not calculating it," she said. "What does the equation do?"

Riley sat up straighter in his chair and placed his hands on his desk like the good little student he seemed to be. He had guessed something right! In a lesson like this that was quite an accomplishment for him.

He literally sighed with releif after a girl asked if they would be doing this equation today and the Professor said no. That was the answer he was hoping to hear but the shock made the Gryffindor very happy.

The it was to the book!!! The seventh year smirked smally as the Professor flipped through a big tome to find something as small as a fact as was asked and was kind of impressed when he found it so quickly. But pffft...muggles and their Science, he wondered how magic would fit into the world of science but that would be a better question for outside of class.

Helena was so glad to hear those words.

Well, if they'll start calculating, they probably wouldn't finish until the end of the term. Because... Helena couldn't even imagine how many stars were out there, in this HUGE universe. World. Whatever. Aaaand yes, using random numbers wouldn't help at all. Just a waste of time, most probably. But as she thought more about it, it would've been awesome to be able to use the real numbers for the equation.

So... no more questions. Helena was just curious to know more. Or whatever professor Antares wanted to tell them next.

Evan listened contently to the discussion. It was an interesting topic, surprisingly for Astronomy, and even though he didn't believe in 'life on other planets' at all, he still wanted to ask something, perhaps to show his scepticism and point something out that bugged him greatly about this alien issue.

"You answered to Fee that if the star is too far, life cannot develop," he said, hand in the air. "But, what if that form of life dies with heat? I mean, we only know out civilisation and as far as we're concerned they may be living on different conditions..."

Listening to the answers to the other questions, Zara was beginning to learn more from this equation. Awesome. Then it came to her question.

Zara smiled and nodded to the answer. Around 1961. Wow, that was a long time ago.

Okay, no more questions. Zara wanted to know the answer to that Carlisle girl's question.

"Are you asking me historically or mathematically? Mathematically, the equation does do what I described. That is, if you enter correct values for all those factors, it will give you the number of alien civilisations in our galaxy we might possibly be able to communicate with. Of course, you have to assume that the factors will give you a result that is correct in the actual, real Universe, and you have to know the values, and so on..." He waved his hand expansively.

"But that aside, that's what the equation does. If you're asking me about the equation's history, then its original purpose was to show that the search for extraterrestrial life was, in fact, a scientific endeavour, and that the chances of finding life could be expressed in easily expressed numbers. Does that, er, help at all?"

"What if, indeed," Risu said, nodding. "Very good point, and this is, in fact, one of the criticisms of the Drake equation." He paused. "Of the search for other life in general, actually. We assume that such life, while most likely not looking similar to what we can find on Earth, will be close enough essentially to say that it needs... water, air, an atmosphere, a balance of heat and cold, and all those things we have here on our planet. It is very possible that other forms of life work completely differently."

He rested against the blackboard. "Of course, there are good reasons for looking for life that is similar to us. We know what sort of planets to look for, we can expect certain signature radio waves, and so on. But as you said, there is no, say, universal principle that decrees that life has to be even remotely similar to what we have here."

Ohhhhhhhhhhhhhhhh.

Okay.

"Yeah, that does help," she said. "We COULD find that out, but first we'd need the numbers, and know all of the other factors, and yeah. We don't."

She nodded her head.

"So is this where we learn what the letters represent?"

Aurora stared at the blackboard. She had been confused since the minutes Professor Antares had started with the Drake equation. She sat behind her desk with a frown on her pale face. She scribbled down the notes from the blackboard onto her parchment and looked at them, thoroughly confused.

They were moving in to deeper questions. AHH, her head was exploding. Zara felt all the hyper-ness slowly fading away. But hey, it was aliens.

Lalalala~ She began to think absently. Then something struck her head. Raising her hand, "I have one last last question, she smiled awkwardly, hoping Professor Antares didn't mind her asking too much questions. "How are we sure that the Drake equation gives accurate results? Aren't there some stuff that contradicts what it says? Like factors that make the equation seem questionable or something?" She wasn't sure how to put it into words, but hopefully professor got the point.

Okay, after this, no more questions. Really. Hopefully. Maybe. Heh.

"That's essentially it, yes," Risu said with a nod. "I'll get to the letters in a moment. I see we have one more question."

Risu shrugged. "Straight answer? We don't. As your classmate just pointed out, we aren't even close to having accurate values for any of the factors involved in the equation. We can sort of make an educated guess at some of them, the star formation rate, for example, but some of the other values we have no clue about, the ones about the development of life in particular. No clue whatsoever. And since this is an equation with multipliers, not plus or minus signs, any uncertainty becomes greater with each multiplication. Any results from the equation at this point would be wildly inaccurate.

"But!" He straightened up. "We will now tackle the equation itself. Here it is." He tapped the blackboard once more.

N = R* x fp x ne x fl x fi x fc x L

"First of all, the obvious. N is the end result, the number of alien civilisations with which we might be able to communicate." He tapped at the letter with a finger. "The other letters are more or less those factors we already discussed earlier." His hand slid lower to indicate the list the students and he had put together. "R* is the rate of star formation. And then, one after the other, stars with planets, planets that can support life, planets that actually have life, planets with intelligent life, that's fi, fc is the intelligent life that sends out signals into space, and finally, L is the length of time an alien civilisation actually sending signals."

He paused. This sounded very confusing, but, with the equation on the blackboard, hopefully not impossible to understand. "There is one more subtlety here that I need to talk about. These values are all built upon each other. We sort of neglected this in our discussion, but the original Drake equation did not, which complicates things. See the little f signs? This means we are talking about fractions. For example, if you take the first fractioned value, fp, then this is the fraction of all stars that have planets, not the number of stars with planets itself."

He paused again. "And so, further on, fl isn't just the number of planets with life, it's the fraction of all planets, and fi is not the sum of all intelligent life in the galaxy but the fraction of planets with any kind of life in them. This makes figuring out the values even more difficult since, as I said, they all rely on each other."

o_________O

Alright. This was a little harder than what Sophia had bargained for. But, none the less, she flipped to the paragraph in the book that had it as well. It wasn't as easy to read as what Professor Antares had said out loud. So, as best as she could, she wrote it down, again.

For the second time.

Sophia's Extended Notes
But she was missing one.

"What does the ne stand for, professor?" she asked. Then she thought back to the discussion, and she felt she was missing something. "Wait, does that have to do with the planets themselves? Like, which ones CAN support life... or the stars that have planets?" Or something?

WHOA. Lots of information. Ryden scribble everything down furiously, a tiny almost unnoticeable smile on her lips as she concentrated hard. The brunette bit her lip thoughtfully as the professor continued to explain the various aspects and variables - that's what they were called, right? - of the Drake equation. She only had one thing she needed to clarify, so all in all Ryden felt like she knew what he was talking about.

Then he got to the fractions part and Ryden's eyebrows furrowed. She'd mentioned fractions before but THIS? This she had not meant. "But professor, how could we POSSIBLY ever know those fractions? There are an infinity's amount of stars aren't there? And then an even BIGGER infinity of planets? Or - wait - could you like, say there's x stars out there and use that? But then again, you'd never get an answer... You'd get something with x," she said, slightly annoyed at this equation for being so useless. Or maybe she was missing something? Hmm. She glanced back down to reread her notes.

Oh, and also... "And, professor, the 'L'... I'm not quite sure I understood you right - it means the amount of TIME the signals have been up? As in, how long it's been transmitting stuff?" she asked, understanding through her question what the professor had meant. AND, she'd noticed, the L didn't have an 'f' thing, so it WASN'T dependable on the stupid infinity x thing. AHA. Something substantial. But - HOW would humans ever know how long a civilisation has been transmitting? It seemed so far-fetched to her.

This lesson's AWESOME.

Nodding again, Zara ran all this through her head, trying to get the information straight. 'Right, so first N means the end result, the number of alien civilizations. The rest are factors. R* is the rate of star formation,' she began to think as she quickly wrote this all down. It's good to have some notes since she couldn't get her hands onto those books she had before. Now would be the time to start making her own little 'book.'

She continued to take this all in her mind as she wrote them down. 'fp means stars with planets. ne are planets that can support life. fl are planets that actually have life. fi are planets with intelligent life. fc refers to the intelligent life that send out signals to space. L means the length of time aliens send signals.' Alright, she was done. Looking down, she saw her notes. Perfect. She smiled to herself.

Not numbers, fractions. Then she put a strikethrough through the words "number" and wrote on top of it, "fraction." Not so perfect writing anymore, but the information was. So it was all good. But how did they formulate these fractions?

Okay, one last question. Really. One last. Her hand slowly raised into the air with a sheepish smile on her face. She was asking questions again. Well, you can't blame Zara. She is just a firstie. A very curious one too. "How do we formulate these fractions, professor?" she asked, and clarified it a bit, "I mean, which one's go to the numerator and which one's to the denominator?" Frowning a bit, she wasn't sure if her question was understandable. Maybe he was mentioning a different fraction? Not those she learned in Math before? Oh well, no use taking back the question she asked.

Aurora frowned, she had been scribbling furiously as the professor was talking and trying desperately to make head or tail of what he had said. "Professor, is 'ne' the hospitable planets?" she asked. It made sense, it was the only one left.

An equation!? B-b-but Nika got enough math in arithmancy! Now they have to learn equations here too. AHHH her brain hurt.

Now Nika is confused. This professor likes to talk. A LOT. Nika massaged her forehead as she looked up at the board again. Okay. Equation. Right. EHHHH. Why couldn't astronomy be like it was last term. All they had to do was look through telescopes and find equations and stuff. Nothing complicated like equations. Save that stuff for Arithmancy professor.

OH and now he is starting to talk about the equation? Nika held up her quill and began to scribble things down. Grrr... He's just going way to fast. She was only able to write the first two things that he said before she really fell behind. "Professor, do you mind repeating that again? But Slower and without any of that extra stuff?" EH, so what if she sounded stupid.

Zara was itching to answer the question of the two girls. But maybe professor should answer it. AHH, she might lose points. But she couldn't help herself.

Raising her hand, "Professor, may I answer their question? Please please?" She smiled.

"ne refers to the planets that can support while the next one, fl are planets that actually have life." She looked at the professor. Let it be okay, pleasee? She just wanted to help. Besides, he himself stressed out the words, "actually have."

"Erm..." He glanced at the blackboard. "Let me make sure, I wouldn't want to say something that was off... If I remember correctly, ne is an average. It's the average number of hospitable planets per star system. So, any star without planets is not included, as per fp, and ne is the average number of planets that can support life per star with planets. So yes, ne has to do with the planets themselves."

"To answer the second question first, L is the length of time for which intelligent extraterrestrial life sends signals into space. For example, in our case the answer would be around 140 years. The first television transmissions that reached into space took place in the 30s of the last century. And if our planet exploded tomorrow, that's what L would be. 140 years. Of course, this is just an example. L is the value for all civilisations, so we would have to figure out a way of coming up with an average amount of time that any civilisation would be expected to keep the signals up for."

He leaned against the edge of his desk, almost upsetting a stack of books. "That, of course, ties in with your first question. Realistically, we will most likely never know the exact values for any of the factors, in particular those pertaining to intelligent life. There simply isn't any data from which we can draw conclusions. This is the problem with the Drake equation. But, other questions." There were a few raised hands.

"Usually the equation isn't written out in fractions but in decimal points. For example, if half the stars in the galaxy have planets, then the value for fp would be 0.5. Of course, this is most likely not the actual value, just an example."

"Yes, it is," he said with a nod. "On average. That is, if a star has planets, any star with any planets, then ne is the amount of planets it has. Perhaps each star has, on average, two hospitable planets. Then ne would be 2."

Risu nodded and smiled apologetically. "Of course. I do apologise. We can skip the equation, if you want, and we are nearly done with it in any case. What you should take away from our discussion is the fact that this equation exists, and that it's an attempt to come up with a way of calculating how many alien civilisations exist in our galaxy. The idea is that if one multiplies a number of parameters, such as the number of stars with planets, average number of hospitable planets per star, the planets with life on them, and so on, one will get the total number of alien civilisations. Does that help at all?"

OOC: Oh sorry lol, I just noticed your post, Yssa. As usual, it's noted for the points board.

"Decimal points. Got it." She smiled, thankful the professor wasn't mad at her excessive questions. She sat straight in her chair and began to add some more notes coming from the answers to the questions of the other students.