2. Arithmetic
2.1 You don't know Arithmetic?!
“What's that? You've never taken a test that you haven't studied for? Gya ha ha! Well, there's a first time for everything! You'll get it eventually, may as well be now! Clear out your desk! We'll start now!” The teacher happily wrote some questions on the board. A full exam on the first day of class is practically unheard of.“Not even a roll call?” a student asked.
“What for? Your name will be on the paper. I'll learn your names then. If not, you'll get zero. No problem with me.” The teacher then started writing some questions on the board, while the students trembled with fear for the worst. Nevertheless, they began putting away their books and pull up a piece of blank paper for the test.
“Teacher, may we use a scratch paper?”
“Scratch paper? What for?”
“For the math.”
“Huh?” the teacher blinked. Then he looked at the board and see these questions:
3465+2345=
2425-2344=
23*65=
94*23=
121/11=
His expression changed from confusion to rage. “ARE YOU KIDDING ME?! YOU DON'T KNOW ARITHMETIC?!!!!”
“Yikes!” All the students coiled in terror.
“You guys are in HIGH SCHOOL!!! You should know this by now! Are you telling me that you don't know how to add two numbers?!” He just rages on and on. “You! Add these two numbers!” The chosen student paled, and he stared at the board for a long time. No answer was fortcoming. “Well?” the teacher grew impatient. Finally, the student went to the board, and did the sum mechanically, carrying the sum as needed. Finally, he arrived at the answer. He looked at the teacher for approval.
“Too slow! Are you kidding me? You're in HIGH SCHOOL! Are you telling me you still add numbers like you're in grade school? Here, let me show you. Write a random 20 digit number.”
The student meekly wrote this number on the board:
26349355826528364367
“Good. Another one below it. Line it up.”
26349355826528364367
64924473537234235343
And as the student wrote his second numbers, the teacher just wrote the answer immediately, slowing only when he had to add the sequence 3643 with 2353.
26349355826528364367
64924473537234235343
91273829363762599710
“There you go. Nothing to it. Why would you need a scratch paper for?” He sneered.
“But we're not that smart!” protested the students.
“What do you mean? It's just adding two numbers. It doesn't matter how many digits there are, you should be able to do it no problem. It can be a hundred digits, for all I care.”
“What! 100 digits numbers can be added immediately?” The students can't believe it.
“Of course! By the way, I expect each and every single one of you to be able to multiply two 12 digits numbers in your head.”
The students trembled with fear. Impossible!
2.2 Mental Arithmetic
“Come on, guys, get real. All this arithmetic does is just counting. Surely, you know how to count?” asked the teacher.“Yes, we know how to count, but how can you expect us to add two large numbers immediately?”
“Using the same technique that allows you to add two numbers before the second number is completely written, of course. How else?” Such a simple answer. Of course, the students did not know that such technique exists. In fact, had they not witness it for themselves, they would not have believed that it was possible.
After a long uncomfortable silence, finally somebody asked, “How do you do it?”
The teacher smiled. “Ha. Took you long enough to ask that question!” He erased the board and wrote a groups of two digit numbers very, very quickly. After that, he asked, “Alright. Now tell me, assuming you have to add each digit of the numbers, how many of them totals 10 or more?”
32 56 43 72 57 22 76 34 67 23 43 45 23 76 26 85
The students slowly and painfully added the pair of digits. The teacher slam his fist to the table, scaring them all. “Wrong! That's not how you do it!” He glowered. “Do it by counting. First number: Count to 3, then 2 more giving 5. Less than 10!
“Second number: Count to 5, then 6 more giving 11. More than 10! Third: Count to 4. 3 more, giving 7. Less than 10!
“Got it?” He glowered menacingly. “Now do it again! By counting this time!” The student trembled with fear as they slowly count the digits. Finally, they're done. They look at the teacher wondering what they have to do next.
“Good. Now, for those of you who knows the answer to my next question, you'll get 10 points, which is the quiz score. You need to shout your answers because if you are late even by one second, you get zero, get it?” The students gulped and nodded. Finally, everybody nodded.
“Get ready. Here comes the question. Remember, you only have one second to shout it out. Ready. Okay. How many of the pairs totals 10 or more?”
The students were surprised. They were expecting just one pair of numbers, not all the numbers on the board. Those with quick reaction time started counting rapidly.
“Time's up!” the teacher said just as a student jumps up and shouted “Seveeeen!!!” The teacher looked at him, then he smiled.
The teacher waved him down. “That was quick, but the answer is six. Let's count them. 56 57 76 67 76 85. Six. Where'd you get number seven?”
“Ah, I made a mistake. I counted 72 as well.”
“Well, that happens when you in a rush. Next time make sure to do your calculations as soon as possible instead of waiting until the last moment.”
“But that's not fair. You hardly gave us any time!” another student said.
“You have 8 minutes to do it. I asked that question immediately right after I wrote the numbers down, remember?”
The students were speechless. That, indeed, was the original question. They had forgotten it in the heat of the moment. The students hung their head in shame.
“Gya ha ha ha! Total failure! What a bunch of idiots. Even after I gave you guys an extra second per problem, too.”
“Do you really expect us to do it one per second?”
“Not really. I expect you to be able to do it faster than that. Of course, that comes after practice, so practice!”
“Alright. Let's move on. By the way, homework for tonight. Take a stopwatch and set a timer. Hit the lap button randomly, and add the last two numbers on the stopwatch. That means the hundredth and the milisecond digit. Keep doing that until you get used to it.”
“How long will it take?” ask a student.
“That is entirely up to you.” said the teacher.
“Will you be scoring the homework?”
“No. What for? Just extra work for me.”
“Then how would you know if I did the homework?”
“I'll know that you didn't do the homework when you score zero on the quiz tomorrow. Is that not obvious to you? Gya ha ha ha”
The student looked embarrassed. As should be. That was a dumb question, after all. Of course, the sadistic teacher would let it known to everyone.
“Yeah, that was a stupid question. Do you know why it's stupid? Because you know the answer to the question. You don't need anybody to tell you the answer! All you need to do is just think about it, and you'll have the answer. Are you really that stupid that you cannot think about it? Gya ha ha ha!”
The student cannot say anything, but another student raised his hand. “But there is no stupid question!” he protested.
“Wrong! Or rather, incomplete. There is no stupid question IF you don't know the answer. If you know, or can figure out the answer yourself, then it's a stupid question. What's your name?”
“Tommy.”
“Good. Was that a stupid question? When I asked for your name?”
“No, of course, not. There's no stupid question.”
“Alright. By the way, Tommy, what is your name?”
“Um, Tommy.”
“No, Tommy. I asked for your name. So, what's your name, Tommy?”
“My name is Tommy!”
“No, your name is dum-dum. I already know your name, and still asked for it. How many times do I have to ask the same question before you get to admit that was stupid?” Tommy hesitates. The teacher smiled. “More than once is not acceptable. That is why your name is no longer Tommy, Dum-dum! Gya ha ha ha!”
Red faced, Tommy buried his face on his desk. Obviously, a sadistic teacher. Certainly not like the old gentle, understanding teacher.
“Alright, let's move on. Knowing that 2 numbers may add to more than than, that's called a carry. The point is that you don't need to worry whether or not this carry number is more than one. It's either 0 or 1. Of course, if you do it the formal way, that's done right to left. I have just shown you the informal way, that's left to right. So, here's the trick:”
26349355826528364367
64924473537234235343
91273829363762599710
“Look at the sequence 2634 and 6492. Do you see them? So pair them like this:
26 64 39 42
“Now you see that 26 pair is 8, remember that 8, and look to the next pair 64. That's more than 10, so add 1 to 8. That makes 9. Write it down.
“Go to the next pair: 64. That's 10. We remember that 0, and look to the next pair 39. That's more than 10, so add 1 to 0. That makes 1. Write it down.
“Go to the next pair: 39. That's 12. Remember that 2, and look to the next pair 42. That's less than 10, so write down 2.
“Keep repeating until you are done. Simple as that!”
The students were wild-eyed. They've never seen this technique shown before. They then keep working on the numbers until a student raised his hand. “Teacher! I'm having trouble on the last numbers.”
“You mean the sequence 3643 and 2353? You need to be specific in describing the problem! Do you take me as a mind reader?”
“Yes. Those numbers. Sorry.”
“Alright. Do it just like usual, but with a difference. Watch this!
“32 makes 5 and 63 makes 9. You can't write 5 down immediately because 9 maybe turned to 10, and you need to carry it over. So, remember 5 and look over to the next pair 45. It makes 9 so look over to the next pair 33 which makes 6. 6 is less than 10, so no carry over. Write down 599 because that's the answer.
“Suppose instead of 33 pair, we have 73 pair or any other pair that's over 10. Add 1 to 5 and write down 6, followed by zeros. 600 on the spots.
“And that's all there is to it. It doesn't matter how many nines there are since you're just writing down the digit on the first blank spot followed by either 9 or 0 on the remaining spots for as long as the pair totals 9.
“That's adding two numbers. Now try it a few more times, and later use the remainder of the class time to see if you can do something similar to the opposite: Substraction.
“In the meantime, though, let's take a detour and do a little explanation on numbers. You know that there are 10 digits, right?”
“Yes, teacher.”
“So, how does that work?”
The students just looked at one another. They expect the teacher to go on explaining things. They didn't expect a teacher to be asking them questions. Nobody moved for a while. Finally, the teacher pointed to a student. “You. How does that work?”
“Well,” the student got uncomfortable being singled out. “There are 10 digits, 0 through 9.”
“And if it goes higher than 9?”
“Then it goes to 10, 11, and so on.”
“Two questions. First, what happens if you don't have zero? Second, how come there's 10 digits and not other more natural number?”
“Uh,” the student got flustered, “I guess there's no 10 if you don't have zero. And I don't know why any other number would be more natural than 10.”
“Ha!” the teacher went smug. “How old are you know that you do not know these things? How many years has it been since you learn how to count? Still stuck in elementary skills, I see.” The teacher surveyed the class. “Does anybody know what happens if you don't have zero?”
The class went silent for a while. Then Peter raised his hand. “Does Roman numeral have zero?” The class collectively did a face palm. The teacher laughed.
“Yes, that's correct. Roman numeral does not have zero. It has digits denoting 1,5,10,50,100,500,1000. That's why there's a limit on how high a number can be. Interestingly enough, there are smart people back then. There were Aristotles, Archimedes, and so on, but somehow, nobody bothered to invent zero back then.” He smiled, “It's amazing that they managed to do as much as they did without the number zero.”
“Now on to the second question. Why 10? Why not some other natural numbers?”
The student puzzled over this question. Finally somebody ask the question: “What can be more natural than 10?”
“Before I answer that, what makes you think 10 is natural?”
“We have 10 fingers.”
“True, but we also have 2 feet. Which makes 12. Therefore, I propose that 12 is a more natural number!”
“That's just silly!”
“Is it? Then why would God decree that there be 12 months to a year? Or 12 hours to the clock?” The students were speechless. “Or perhaps you can explain why there are 7 seas, 7 continents, 7 colors of the rainbow, 7 wonders of the world?”
“Because there are seven seas?”
“Whadaya mean there are seven seas? It's all one big ocean!” There was no reply.
“Most people can remember 5 or 6 items in their head. That's why it's seven!”
“And the twelve?”
“There's no one single big reason for it, but a year is 365 days, and moon cycle is 30 days. Therefore, 12 fits just fine. After that, it's a simple matter to divide the day buy the same 12. The big question isn't why we divide by 12. The big question is, why do we settle 10 as the base of numbers, instead of 12?”
The students couldn't answer that kind of question. They thought, and they thought, but for the life of them, cannot answer the question. Finally, they look at the teacher for answer.
The teacher shrugged. “Don't look at me. Ask the long dead Arab about it.”
“The long dead Arab? How can we asked him that?”
“You can't. He's dead. But the numbering system that we have is what is called Arabic numbers because that's where it originates. So there you go.” The students were confused. It's not usual practice for a teacher to ask unanswered question.
The teacher laughed. “So, if you have to create a numbering system, what would be the base numbers? Will it be 10 or 12?”
“12 seems to be more natural.”
“Actually, I'd say 2 would be best. Zero and One.” The student thought about this for a moment. “Which means,” the teacher continued, “there would be one, ten, eleven, hundred, hundred one, hundred ten, hundred eleven, and so on.”
The students were unconvinced. Finally somebody said “But only unreasonable people would do that!”
“Ah, that's why we're not using that. We're using something else, which is called hexadecimal. Zero and one is called 'bit', and if you take 3 of them together it's called 'octal', and if you take 4 of them together, it's called 'hexadecimal'.” The teacher smiled. “You'll be using bits or binary number for the foreseeable future. Do you know why?”
The students shook their heads. It's all new to them.
“The reason is that it's very simple! You don't have to do a lot of things just to do arithmetic. This way, you can understand how numbers supposed to work, as opposed to just memorize the instructions on how to add, substract, multiply numbers and so on. Furthermore, there are other benefits to hexadecimal in terms of space. Very convenient, that's why we use it.
“For now, though,” the teacher surveyed the class, “you need to work on your aritmetic. I have shown you how to PROPERLY add two numbers. For now, you need to learn how to PROPERLY subtract two numbers. Get to it!” The student then worked on the problem.
2.3 Multiplying large number with calculator
The students was working on a quiz. They're working on 2 kinds of problems. The first page was filled with 2 digit numbers. The second sheet was filled with 2 rows of numbers, printed double size. They're supposed to circle the pair whose digit totals more than 10. On the second, they're supposed to first add the pair of numbers together, and the second subtract them. No scratch paper is permitted. They're supposed to do it in their head.5 minutes later, “Time's up! Bring your paper here!” The teacher gleefully looked over the answers as the papers were brought in. “Remember that each mistake costs 10 points, so if you make 10 mistakes, you get zero! Looks like plenty of mistakes there. I see bunch of zeros already! Gya ha ha ha!” The students threw their arms up in frustration.
“Ready for the next step? Multiplication, and no scratch paper for that either! Here's the multiplication table.” He wrote this on the board:
0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 56
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81
“You need to memorize this. The faster the better, but no fear! Even if you're stupid, you will be able to memorize this eventually. It'll just take you longer to get there. Gya ha ha ha!
“Now, who's up to multiplying 10 digit number all at once?” The teacher surveyed the class. “Nobody? There's nobody here who can do 10 digit multiplication in their head?” Nobody moved. “Who among you has memorized the multiplication table?” A few hands went up. “All right, you, you, and you get up here. Write down this number:”
26184453923
“And multiply that by 4. Let's see you do it.” The students dutifully wrote their answers. All of them got it right. “See there? No problem at all, is there? I knew you can do it.”
The students went back to their seat. “For the rest of you, let me break it down to you. We're going to multiply these numbers right to left, because only geniuses multiply these numbers left to right.
“So, that's the trick! Instead of multiplying the numbers left to right like those geniuses do, we simply take a shortcut and multiply the number from right to left. Now, we see a 3 there. Multiply by 4 and we get 12. Write down 2, REMEMBER 1. Use your fingers if you have to.
“Next digit 2. Multiply that by 4, we get 8. Add to the number you remember earlier. We get 9. Write down 9. REMEMBER 0 (because it's less than 10).
“Next digit 9 times 4 is 36. That's the benefit of memorization: you don't have to think about it. Add 6 to 0. Write down 6. REMEMBER 3. Keep going.
“Next digit 3 times 4 is 12. 2 plus 3 is 5. Write it down. REMEMBER 1. And so on.
“Keep going until you're done. Do you notice how each step is very simple and easy? All you have to do is add two numbers in your head. Write one, remember one. And that's why you are all capable of doing it! Unless you're handicapped, you should be able to remember 5 or 6 digits in your head, and you only have to remember 1! Got it?”
After a few times practicing, the students' time are improving. “All right. That's enough for now. Time to keep moving! For homework later tonight, write down a bunch of numbers. Use your stopwatch and multiply it by the last digit on your stopwatch. Keep doing it until you get comfortable with it. Now get out a fresh piece of paper.”
“We're now going to go over the way to multiply 2 digit numbers. Let's say we have this:”
63
14
“You can do it like we did and come up with this:”
63
x 24
-----
252
126
------
1512
“Or you can do it like smart people and do this: 60x20 + 60x4 + 20+3 + 3x4. So, let's try it: 1200 + 240 equals 1440. 1440 + 60 equals 1500. 1500 + 12 equals 1512. And there goes your answer! Got it? That's how smart people do it.
“If you notice, you actually keep the sum in your head from 1200 to 1440 to 1500 to 1512. And you can do it, too, because most people can keep track 5 or 6 digits in their head. Once you memorize the multiplication table by heart, these sort of things are easy to do!
“The problem is if you have to multiply larger numbers than this. Let's say you have 3 digits to be multiplied by another 3 digit number. Unless you're super smart and can keep the number in your mind, the whole thing breaks apart. That's when everybody is reaching for tools to help them do this. You know what tool it is, right?”
The students nodded. “A calculator.” Such obvious answer.
“That's right. A calculator. But what if you don't have it with you? What other ways can you do it?”
The students got confused. “Isn't the calculator answer good enough?” somebody asked.
“Gya ha ha ha! Of course not! You think coming up with a right answer is good enough? What kind of stupid are you?”
“But, what else can we use if not a calculator?”
“Let me run this off of you. You can use scratch paper, slide, ruler, abacus, your classmates, playing cards, coins, rope, rocks, and so on.”
The students were dumbfounded. The first few answers makes sense, since that is what people use to calculate, but classmates? How does that work?
Finally a student raised her hand. “But teacher! We can't use our classmates to calculate numbers!”
“Gya ha ha ha! Are you sure about that? Next you're going to tell me that you can't use coins to calculate.”
“But you can't use coin to calculate! It's impossible!”
The teacher frown. “You're not supposed to say that. What you mean to say is that it is impossible FOR YOU. Because it certainly is not impossible for me!”
“But how can you do that? Coins don't calculate, do they?”
“Listen, do you know abacus?”
“Yes.” The student nodded her head.
“Good, now grab a bunch of coins and line them up like those abacus beads. What do you have?”
After a long time to think, she finally said, “It looks like an abacus.”
“And there you go. It doesn't matter that it's made of pebble, or rock, or coins, as long as the function is the same, then it will work just fine.
“You guys are too dependent upon others to do your work for you! Remember, you're computer programmers now. That means you write programs. That means you make stuff. That means you're a Maker. If you don't have an abacus, then you make one yourself! Simple as that! Got it?”
The students were having trouble processing the flood of information coming rapidly all at once. But the teacher doesn't say anything else until most of the students managed to digest the information.
“And I suggest you write it down, lest you forget, because I will be reminding it to you over and over again. If you don't have it, you need to make it. Crying or complaining about something because you don't have it is strictly not allowed!”
“We won't forget.” The students promised.
“Gya ha ha ha! Of course you will forget! Do you take me as an idiot? It's not whether or not you will forget, it's how often you forget it.” There's a cruel glistening look on the teacher's face. “And when you do, there'll be hell to pay!” He winked. “Notice I said 'when', not 'if'. Gya ha ha ha!
“So now how you're going to use your classmates to calculate?”
“That's easy. You just line them up 5 to a line like in abacus, and ...”
WHAM! The teacher slammed both palms on the student's desk, scaring her into silence. “Are you kidding me? That's not how you do it! Anybody else?” Nobody else said a word. They have not a clue.
“Listen, a person can do more than being a stone. Here, let me show you. Multiply 127 by 364.” He wrote the numbers on the board. “Now you multiply 127 by 300. That's 38100. You will remember 38100.
“Next multiply 127 by 60. That's 7620. You, “ the teacher picked another student, “will remember 7620.”
“Finally, we multiply 127 by 4. That's 508. You, “the teacher picked yet another student, will remember 508.
“Now, back to you, “ he motioned to the first student. “What's your number?”
“38100”
“And you?” He motioned to the second student.
“7620”
“Add them together and they total 45720. What's your number?” he asked the third student, as he wrote the number 4 on the board.
“508”
“Add 5720 and 508, and you get 6228.” He wrote down 6228 next to the 4. Therefore, 127 timex 364 equals 46228. Got it?”
A student pulled out his calculator and verified that it is true.
“So, there you go. That's how you use your classmates for multiplying two numbers. You certainly do not line them up like abacus stones. That's just stupid.” The student's face was red with embarassment.
“If you want to use them line them up like an abacus, then have them store the digits, one on each hand, two numbers per hand. Although, that's not the most efficient use of your classmates, it's simple and is acceptable.”
“How can you keep a number on just one hand? It's only got 5 fingers!”
“With five fingers, you actually can keep up to 32. But here's one way how you can keep your digit with one hand. Make a fist. That's zero. For 1-5, extend your thumb, forefinger, middle finger, ring finger, and pinky. With all your finger extended that's 5. Got it?” The students nodded. “Now fold your thumb. That's 6 (not four). For 6 to 0 fold your thumb(6), forefinger(7), middle finger(8), ring finger(9), and pinky(0). And there you go. That's how you keep a digit on one hand.”
The students all tried to do it. Some did it better than others. Some students have to press their hand on the desk to separate their ring finger with their pinky.
“All right, move on to the next step. What I just showed you is how to multiply 2 numbers the genius way. Of course, smart people can remember those numbers all by themselves. But you're not smart, are you? Just a bunch of losers. So, we're going to do it the simple way! First make a matrix like this:
1 2 7
3
6
4
“Now as you can see there are nine boxes. Fill them like like you did your multiplication table!”
1 2 7
3 3 6 21
6 6 36 42
4 4 8 28
“If you remember, we multiplied 127x3, then 127x6, then 127x4. That's equivalent to doing it in this order:” The teacher drew another matrix alongside it.
1 2 7
3 1 2 3
6 4 5 6
4 7 8 9
“But what you want to do, is do it in this order. Watch the diagonal lines 1, 2-3, 4-5-6, 7-8, 9.”
1 2 7
3 9 7 4
6 8 5 2
4 6 3 1
“First line 4x7 is 28. Write down 8, remember 2.
“Second line, 6x7 is 42. 42+2 is 44. Remember 44.
“Next, 4x2 is 8. 8+44 is 52. Write down 2. Remember 5.
“Third line, 3x7 is 21. 21+5 is 26. Remember 26.
“Next, 6x2 is 12. 12+26 is 38. Remember 38.
“Next, 4x1 is 4. 4+38 is 42. Write down 2. Remember 4.
“Fourth line 3x6 is 6. 6+4 is 10. Remember 10.
“Next, 6x1 is 6. 6+10 is 16. Write down 6. Remember 1.
“Fifth line 3x1 is 3. 3+1 is 4. Write down 4.
“And you're done. The number you wrote down is 46228! And that's how you multiply 2 numbers in your head!”
2.4 BASIC causes Brain damage
“I hope you don't mind my verifying the process,” Peter said. “I checked it and it works, but I still don't quite understand it.”The teacher looked at him carefully. “I don't mind explaining fuzzy concept. In fact, I'd be glad to. Just make sure it isn't some stupid question you're asking here.”
Peter gulped. The teacher sure doesn't play around. “Well, the way I see it, is that each line stands for a digit.”
“That's correct. It's the power of 10. 10^0, 10^1,10^2, and so on.”
Peter saw that now. “So, then, for each line you write down the last digit.”
“That's correct. That's because there's no possibility of it changing.”
“For each line, I need to keep track of the sum of all the multiplied digits, in addition to the carryover from the last line.”
“That's correct. The nice thing about it is that you're only remembering a number, and adding the number from the multiplication table. Trivial process, once you get used to it.”
“And finally, just keep carrying the process until you're done.”
“Exactly. So, is there any part of it that you don't understand?”
Peter thought about it for a while. “I guess I got it. Just want to make sure. I guess I can use this to multiply just about any two numbers in my head.”
“Well, no, that's not true. Remember that you can remember 5 or 6 digits in your head?” Peter nodded. “Well, the process of adding the carryover value to the multiplication table value requires you to remember 3 digit number and 2 digit number. That's 5 digits. So, that's the limit that you can have.”
Peter mulled about it. “So what's the limit?”
“That's a stupid question because you can figure it out yourself. But I worked it out to 12 by 12.”
“How long will it take for me to multiply such numbers. I guess that's a stupid question because I can just do it and find out.” The teacher smiled. “Sorry, for asking such a stupid question.”
“That's okay. It's good that you have all these questions. It means you don't have brain damage.”
Peter didn't understand. He thought about it, but couldn't find the reasoning behind it. Finaly he asked, “What do you mean by that?”
The teacher sat back in his chair. “Remember when your old teacher claimed that BASIC caused brain damage?”
“Yes.”
“So many people claim that, so I researched it. I actually found the paper by Djikstra. Blah, blah, blah brain damage. Blah blah blah once a student learned something he can't unlearn it. Most people concentrated on the first sentence. I focused on the second. If you cannot unlearn what you learn, you will not succeed. That's brain damage. Basic does not cause brain damage. The damage is already there!”
“How do I unlearn what I already learn? And is that really a good thing?” asked Peter.
“It's very simple, although it's difficult for most people to do. Simply accept that you may be wrong about something. Have the humility to accept that the other person may be right. That's it!”
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