This post assumes familiarity with “Two’s Complement”, “One’s Complement” and an understanding of “Positional Numeral Systems”.
Why is the Two’s Complement called the Two’s Complement?
Ever wondered why the two’s complement and the one’s complement are named as such? We were told that to calculate the two’s complement of a number, you add 1 to its one’s complement. But why? When calculating the one’s complement, we simply subtract every digit from 1, so why don’t we subtract every digit from 2 in two’s complement? And maybe, you tried to reason with yourself about how there’s no “2” in the binary system and so that mehtod would not work anyway. There is however a much better way to understand and explain it. To understand this, you need to understand the difference between the radix complement and the diminished radix complement.
According to wiktionary:
- The radix complement is the number which, when added to an n-digit number in radix-r, results in r^n. An alternative way of looking at it is that it is the smallest possible (n-1)-digit number in radix-r. The radix complement for radix-r is called r’s complement. We get it by adding 1 to the diminished radix complement.
- The diminished radix complement is the number which, when added to an n-digit number in radix-r results in r^n -1. An alternative way of looking at is is that it is the largest possible n-digit number in radix-r. The diminished radix complement for radix-r is called (r-1)’s complement. We get it by subtracting every digit from (r-1)
Sybill Trelawney, the Divination teacher at Hogwarts, was poorly received by her fellow staff, her students and the fans of her universe for reasons that all translate to “She was a fraud. She wasn’t a true seer and therefore not an eligible candidate for the job.” I however have always had a very different opinion about her. I believe that not only was she not a fraud but also a perfect candidate for the job, not to mention the fact that she did actually possess a gift.
We know that she was the great-granddaughter of some celebrated seer named “Cassandra Trelawney” and that Dumbledore went to meet her at the “Hog’s Head” and that no sooner than he met her, he realized that she didn’t possess her great-grandmother’s gift. Then she went into a trance and made the prophecy about Harry defeating The Dark Lord, and Dumbledore decided to hire her because he could tell that she was gonna make more of these prophecies and wanted her to be close to himself when that happened.
Now I want you to think. You are the headmaster of a school, and you want to hire a teacher for a karate class. You have to choose between a guy who is incredibly strong and can pick up and throw around the room just about anyone who picks a quarrel with him regardless of how good their karate is and a guy who spent years learning and mastering the sport and is a great fighter. Who will you choose? True that the first guy has the gift of strength and therefore has a good chance of winning most fights but he may not know anything about the sport, whereas the second guy has nothing except for a thorough knowledge of exactly what you want him to teach to your students. I don’t know about you, but if I was you I would probably hire the second guy, unless of course the first one demonstrated better karate skills than the second one.
Let’s try a different situation. You are the headmaster of Hogwarts and you want to hire a divination teacher. You have to choose between a woman who is well-versed in all the practices and techniques of divination (e.g. reading tea-leaves and making predictions from a pack of cards or dreams) or a centaur who, like all centaurs, was born with inexplicable knowledge of the cosmos and unfathomable divination skills that only require for him to look up at the sky. The woman doesn’t possess any magical powers that allow her to tap into the spirit world but she knows all that is known to man about the art of divination whereas the centaur who doesn’t have any need for those human methods probably doesn’t even know them. In fact, in the potterverse, the centaurs mainly, if not only, use the skies to predict the future and that too with seemingly minimal calculation or effort. It may be safe to assume that they aren’t even aware of the other methods used by humans. So, if it was for me to decide, I’d hire the woman, because she knows her stuff and so should be able to teach it whereas the centaur may not even know shit about the subject and is just naturally gifted at predicting the future by looking at skies.
We saw enough proof in the book of the fact that Sybill actually did know a lot about divination. She was accustomed to using all the techniques that she taught in class, and a whole lot of her predictions came true. She predicted the death of Dumbledore a few hours before it happened, predicted the order of death of certain groups of people. There are better posts about her predictions coming true so I’m not gonna list all of them here. So we know that Sybill certainly did have the knowledge, and that makes her a good candidate for the job. And we are also aware of the fact that she actually did possess a gift. That makes her a perfect candidate for the job.
One thing to note is that she herself was totally unaware of her gift. Clearly she had no control over it but given time and practice, it could be possible for her to get a handle on it. If Dumbledore wasn’t such a jerk, he’d have told her and tried to help her but he chose to not only keep her in the dark but to also make sure that she was one of the least respected members of the staff. Dumbledore and the Teachers routinely spoke ill of her and didn’t shy away from telling their students that she was a fraud and that her predictions weren’t to be taken seriously.
Let’s address the “fraud” question now. She did, at times, make predictions that sound way too ridiculous and didn’t even come true. Why? The answer is very simple. Entertainment. When you have a job like hers and everyone expects you to make cool predictions every once in a while, you have to have a mysterious air around you and you have to make predictions and you have to say stuff to make sure you have the required amount of attention. Come to think of it, she once predicted that Harry will have 12 children. Everyone knows that sounds made up including herself and so the whole point of saying it was to entertain students with some mildly humorous predictions which was a good change from the darker predictions she used to make, two of which she made in her first class and went on to become popular gossip topics.
Sybill Trelawney is underrated an underappreciated and she deserves better than to be called a fraud and better than to be insulted by her staff members.
I’ve been reading books, more than I’ve been reading lately, lately. Very often, I read them onscreen. A while back, I was starting with H.G. Wells’ “The Time Machine” and the PDF I found had about somewhere slightly above a hundred pages in it and it made me wonder if that was actually the whole book and not a truncated version and so I googled for the last sentence of the book to see if it matched the one in the PDF.
I ended up finding this tumblr blog called “The Final Sentence” that exists solely to serve as an archive of the final sentences of all books. I think it’s pretty cool actually and every once in a while, it makes me feel better about a crappy PDF.
I once wrote an answer on Quora about the improbability of a programming language to completely die out once it has gained popularity. The idea, not so original, was that there are two factors preventing a language from dying:
- A significant amount of code is written in it and a significant amount of people or other code depend strongly on it. An example is Linux. Now Linux has always been C and always will be. As long as Linux exists, it would be impossible for C to die out.
- Everyone knows about it. The problem with a programming language being popular enough for it’s existence to be common knowledge is that there will always be people who’ll be fond of it and would want it to never die out. The best example would be Richard Eng, the smalltalk evangelist who has grown more popular than the language itself and likes to call himself Mr. Smalltalk.
- The language Linux is written in.
- The language most programmers start with. (Often this is because universities prefer to teach it in the earlier semesters.)
- More or less the only mature language that has the least amount of abstraction that one could ask for except for C++, which is a mess and an offspring of C itself and therefore not worth talking about in this post.