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From	Message
clashofpawns 10-Feb-18, 00:43	Some arithmetic So let's say we have a set of Symbols: {0, 1, 2} And a couple operators. Successor, S(), and addition, '+'. Successor will merely map one symbol to another: S(0) = 1 and S(1) = 2 Addition will be defined as follows: a + 0 = a and a + S(b) = S(a + b) Now let's work out 1 + 1 1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2 Let's add a couple more symbols, define successor for some of them, introduce another operator, multiplication, '*', and specify that the new operator has higher precedence than the addition operator. Symbols += {3, 4} (note the liberal usage of '+=') S(2) = 3, S(3) = 4 a * 1 = a and a * S(b) = a * b + a Now let's work out 2 * 2 2 * 2 = 2 * S(1) = 2 * 1 + 2 = 2 + 2 = 2 + S(1) = S(2 + 1) = S(2 + S(0)) = S(S(2 + 0)) = S(S(2)) = S(3) = 4
stalhandske 10-Feb-18, 01:28	So what?
clashofpawns 10-Feb-18, 01:35	You remind me of the kids in school who would argue with math teachers, saying "when will we ever need to know this?" I hated those kids.
stalhandske 10-Feb-18, 01:38	When will we ever need to know this?
clashofpawns 10-Feb-18, 01:41	Don't worry. *You* won't.
stalhandske 10-Feb-18, 01:43	Then there were those teachers at school who were such arrogant, cocksure, and self-secure bullies that they never bothered to explain anything in response to the students' questions. I hated those teachers.
clashofpawns 10-Feb-18, 01:44	Oh. The teachers answered. But to the detriment of real learners. People who could appreciate the beauty of the material for its own sake. You're a step beneath those students asking that question though   You do it out of spite. They do it out of hopelessness.
stalhandske 10-Feb-18, 01:48	No, I simply asked "so what", which was neither not appreciating the beauty of the system, nor out of spite. It was your reply about what my question reminded you of which was out of spite. I simply wanted a little more flesh on the bones - not perhaps so much for me personally, but for the sake of all the other members of this Club of which I am founder. You may not have noticed, but I have taken it as my task or responsibility to try to keep exchanges as understandable for all as possible.
clashofpawns 10-Feb-18, 01:53	No. I've noticed that you take the lazy route of asking leading questions, rarely contributing any substance. And I have identified this aspect of your personality and have adopted a strict policy of shutting down in response. If you want something here, contribute something. Ask leading questions? Get brushed past. I put some effort into the post. I was bored and it seemed like a fun exercise to go through. "So what?" is a slap in the face of a response. And no way in hell going to elicit further discussion of the original topic. In other words, take your own advice. When people post arguments that go against your political views, you insist they provide sources. (and yes. face facts. you only do this when it goes against your view. you don't base it on, for example, the baselessness or unsubstantiated nature of the point.) In short this is you saying "put some effort into your argument" well I put the same to you. Start putting some effort into your contributions to discussions. These conspiracy theorist trolls / trump lover trolls in this club offer more substance than you do when you play this "leading questions" game. Leading questions are even lazier than ad hominem attacks.
stalhandske 10-Feb-18, 02:15	It would have been good to see at least one example of this lazy behaviour of mine. Personally, I think (with a fairly clean conscience) that I have contributed significantly to this Club. Otherwise, it seems odd that you call for "further discussion" of your post, when there was no discussion in the fírst place. As I already said, all I wanted was some explanation of why you brought it up, what it is an example of, and the meaning (hence "so what?"). That was not a "leading question" in any respect - it was a sincere request of a better explanation of the first post. For the benefit of the Club.
clashofpawns 10-Feb-18, 02:16	There's no answer other than "it's cool" and if it prompts something from someone else, I'd love to hear it.
stalhandske 10-Feb-18, 02:19	I am sure that's true - but I suspect that it is true only for relatively few Members of this chess Club. It is for that purpose that I called for some more meat on the bones - perhaps a little story about why it is cool.
clashofpawns 10-Feb-18, 02:41	Gonna have to leave that as an exercise to the reader. It's one of those things where you talk about something beautiful. And if someone else is beautiful, they will love it. And if they aren't, then they won't
mo-oneandmore 10-Feb-18, 04:14	stalh "When will we ever need to know this?" Only if you one day need to the understand the complexities of calculating 1+1. 1+0 or a+1, etc.
apatzer 10-Feb-18, 05:46	It is the teachers Job to create "real learners" and a teacher is not measured by his students , But by how many if her or his students become teachers.
ptitroque 10-Feb-18, 07:51	@clashofpawn ??? Is it about pedagogy ? Is it about maths (as the tittle of the thread suggests it) ? In both cases, what is your statement ?
ace-of-aces 10-Feb-18, 08:44	It is pure mental masturbation ! youtu.be We have information overload nowadays. I don't think my brain can handle to upload and digest even all the information that is essential for my daily live to earn a living. Clash of pawns is exceptional. She has more room to spare, store and digest the information but stal including me do not have this capability. So, I am not surprised when Stal answered or questioned, " So what? " Some people enjoy this kind of stuff because it is pure mental masturbation and will keep on doing for brain pleasure.
winslowhightower 10-Feb-18, 08:52	I think it's interesting. In school the first thing they make you do is memorize the addition function for base ten, and the multiplication table. You don't learn about generalizing operations until many years later. Of course, you still have to know how to add and multiply in order to use clash's examples above, so I'm not sure if there is a bit of circular reasoning going on. But generalizations are why I like those math puzzles on the "mindYourDecisions" youtube channel. He always presents the solution to his problem, but then he also presents the generalized solution so you can find the answer for all similar cases. for example youtu.be
clashofpawns 10-Feb-18, 16:15	ace-of-aces While a crude term, "mental masturbation" is probably close to correct. It just "feels" good to think about things like this
itchynscratchy 11-Feb-18, 10:19	<<When will we ever need to know this?>> I’ve always considered this to be a fair question. Sure, often the answer really is “you won’t”, but it’s part of the teacher’s role to ensure that the students believe there to be a point in and a use for what they are learning. If you can’t give them a context, then you’ve failed, not them.
clashofpawns 11-Feb-18, 18:29	itchynscratchy I guess it is harder to me to relate to. I have always hated that question. It always set the class back. I just wanted more and more information and to move faster. But I could never speak up. I was already an outlier and had only a few "niche" friends at best. I was 11 when I started university and was trying to keep a positive attitude to mitigate depression. But when a class was on a roll and the teacher was blazing through content and actually ahead of the curriculum and (rarely) in a math class I was actually learning something interesting and new. Or maybe not new to me but still a topic I loved to talk and hear about so I was enjoying myself, and then some jock or MRS-seeking nitwit complains about how the material has no utility in their life, I just wanted to shrivel up and die. Like a shark gracefully breathing through water suddenly grappled by a cephalopod!
brigadecommander 11-Feb-18, 18:53	When will we ever need this...... that's what i thought when my over-bearing Father decided that will learn Chess at all costs.Also Huge History Lessons. Both now are among my favorite interests. The History of Military Warfare compliments my Chess strategies and Tactics.The Logical beauty of Chess helped me through Algebra and Geometry, Trig and Cal. At least a passing grade in those subjects.
clashofpawns 11-Feb-18, 18:54	> Logical beauty That's it
ace-of-aces 11-Feb-18, 19:14	I wish I can grope and cope with the logical beauty but I cannot handle it since I am a dummy and my brain function is poor.
clashofpawns 11-Feb-18, 19:16	ace-of-aces There is a trick which massively augments brain function in a permanent and global way. You need to observe copious amounts of Rick & Morty.
brigadecommander 11-Feb-18, 19:32	Come on Ace you play some strong Chess. And I'm sure there are other things you do equally well. Don't knock yourself.
clashofpawns 11-Feb-18, 19:38	My IQ was tested when I was a child. At the time the score was 85. Not learning disabled but slow and weak enough that it was clear I wasn't going very far, academically. Less than a year later, my future self arrived with VHS recordings of all EIGHT seasons of Rick & Morty and instructions to watch them from start to finish, rinse, repeat, and then go from there. What followed was a period of rapid intellectual growth. Rick's nihilism, evil morty's intricately woven plans. They all augmented different aspects of my neuroplasticity and glial activity until I had actually reached a respectable level of intelligence. Within a year, my IQ had soared to over 300 and I was religiously watching seven episodes simultaneously at 2.5x speed in seven different languages to maintain and slowly incrementally continue to enhance my mental intellectual mindtelligence. I realize that I have some years left before I figure out how to travel back in time and deliver the VHS encodings of R&M. In the meantime I have devoted myself to theoretical physics towards that goal.
winslowhightower 11-Feb-18, 19:43	8 Seasons! Let's hope so.
clashofpawns 11-Feb-18, 19:46	For the sake of all our mortelligence, indeed.
lord_shiva 12-Feb-18, 01:52	TNT Typographical Number Theory. She is starting you out with Peano's postulates, and building up from there. Fundamental building blocks. We do not make things simpler than our axioms, or we end up with infinite regress. Or circular reasoning. What I was always curious about was the generalization of the operators. Multiplication is successive additions. Exponentiation is successive multiplications. What operation represents successive exponentiations, and why would we ever need it?
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