Aphorisms

Starting today, I am going to create my own aphorisms, my own understanding of things that I see. Perhaps one (to two or even longer towards the end of the post) liners that convey my understanding of life.

• People with black and white thinking are touchy. This is because of their inability to see any grey - they can see only limited options to explain others' behavior. And one of those options sees someone else's behavior as personal and meant against themselves. And touchiness is a property or attribute of J (as in MBTI), not of P. It's sad that i know of few touchy P's. I can't explain those rare P's.
• When a person (say P) pushes the boundary of another person (say J) and trespasses, the latter thinks of his own behavior as having been graceful and generous. The former knows he has negotiated a good deal and that he doesn't owe the latter. When the latter realizes that the action he agreed to was a result of negotiation he is cut to the quick. This is one example of the larger rule in human behavior - when our good actions consistently go unacknowledged we stop performing those good actions. 
• Peter Keating says to Catherine Halsey about his boss Guy Francon in Fountainhead "and i have no respect for him at all. And I'm delighted to be working for him" - What a beautiful way to characterize Peter. His heart is delighted because the job provides what he desires (maybe, prestige) and his head has no respect for the man. This is example of Cognitive Dissonance.
• The man in whom the weight of others' feedback weighs heavily is a man that is not worth looking up to. It doesn't mean that all men who do not consider others' feedback are good men. We fear tigers and lions. But we don't fear, as much, the same animals that have been trained to behave as per some trainer's expectation. The first step towards destroying a person's individuality is to get him to seek constant feedback. 
• Some people tend to ostracize those they can't stand. Others tend to destroy people they can't stand. Whether we end up ostracizing or destroying people depends on how strong their Mars (energy level) is. Actually it's a question of fight (destroy) or flight (ostracize or avoid). 
• Some people pride themselves on seeing and depicting reality as it is. Some pride themselves on their ability to change reality - they take pride in amplifying or minimizing what reality is. Remember the senator from Montana in the movie Shooter so says "Truth is what I say it is", meaning he could interpret "truth" any which way. 
• What you hold on to at the end of the day indicates what your capacity and strength are. There is a saying in Tamil "It's when the river runs dry that you get to see the muck."
• If you put off something in your life then that thing was never important to you.
• Some people think of a pointed question that they are unable to answer or one that caught them in a lie as an insulting question.
• Strong Venus (as in Vedic Astrology = F as in MBTI) gives poor introspection ability. Introspection comes from Saturn. I wonder whether Cognitive Dissonance and strong Venus are positively correlated. F also have difficulty in understanding cause and effect (due perhaps to their difficulty in sequencing events which is essential for cause and effect analysis). Intelligent F's do sequencing with ease but usually limit the act to when it's useful for themselves.
• Often we are told to suppress our anger and not vent out and yell. When we do suppress it, it results in disgust being stored inside. This article seems to echo the same thought: http://www.scientificamerican.com/article/study-shows-that-for-wome/. Read: https://en.wikipedia.org/wiki/Expressive_Suppression.
• FP (as in MBTI) needs pleasantness and provides the same. It's the essence of their character. Their ability to say yes to your request without meaning it is phenomenal. TJ can rarely provide the pleasantness sought by an FP. As a result the FP will move away. And TJ will hence also part. A TJ can desire the pleasantness despite not being able to provide it. 
• We say Inshallah (or As God wills it) when we are not driven to ensure something - maybe the thing was not important enough. But when we do go ahead and do something instead of inshallahing (just expressing hope) then the goal was important enough for us. 
• When an Enneagram-8 (or with only a strong Mars without even a strong Mars) really feels someone is good what he means is that the someone is or can be of use to him - a good raw material for the 8. See this: https://www.linkedin.com/pulse/leadership-isnt-being-greatits-enabling-others-great-david-mcqueen. Enneagram 8 are usually leaders and they usually have a very strong Mars and atleast a reasonably strong Venus.
• The thing you crave that you have in plenty is your value. What you crave which you lack is just greed.
• We tend to judge people quite rigorously on those things that we have in plenty. We tend to be very kind on attributes in people which we ourselves lack. If we are a strong T with high intelligence, we tend to judge people harshly on their (lack of) intelligence. While if we were a strong F, we tend not to attack people on their lack of intelligence, we tend to go very soft. Essentially we tend to be bullies - some of us on physical strength, some on attractiveness and so on. We choose that attribute which we think or feel we are strong in and kinda bully others who kinda lack that attribute. The strength of bullying is proportional to the Mars or energy in us. When our energy is low, people may not be aware of our bullying propensity.
• Added on Mar 10, 2017: Paytm planned to levy 2% charge on users who added money to Paytm through credit card. The rationale being that users misused Paytm - they charged their credit card to add money to Paytm, then moved the money from Paytm to their bank and they had a couple of weeks to pay their credit card. Paytm didn't levy any charge for these transactions earlier. Now here is the interesting thing.. People figured out a way to use this loophole in Paytm. Users got free bonus points from their credit card issuer for using the card. Not only that, users got back money in their banks which they had to pay only after a couple of weeks. Beautiful. This is akin to snails homing in on plants or cobras on rats or ants on sugar.. I always wonder. How the hell do they know there is food? The instinct to survive is something God has given everyone including animals. The Paytm users used this instinct. So did the guys who laundered their demonetized notes between Nov and Dec 2016. This instinct comes from keeping all their senses (sense organs) open with a high desire to live well. And so was the caller from RBI ATM. Why did he resort to this con job? My guess is: he might not have found any other routine cleaner jobs to his liking or he didn't get or couldn't keep such jobs. Humans aren't that different from animals. We tend to camouflage our needs better. What we call maturity is our tendency to camouflage or postpone our need for instant gratification 
• Often we see what we want to see. Is it the whole picture? Would our reaction to what we saw change if we knew the whole picture? We often hear of Sri Lankan Navy shooting at or imprisoning poor Indian fishermen off the coast of Rameswaram. I have often felt irritated with Sri Lanka. And I felt the same way about Pakistan about what Pak does off Karachi waters or near LOC. But then read this: http://www.thehindu.com/opinion/op-ed/the-right-to-fish/article17436605.ece
• Our memory may not be as good as we think it is as per http://www.americanscientist.org/bookshelf/pub/disillusionment (relate to the sinking or the whipping)
• When a wife tells her sick husband and child that she will cook bad food as long as they continue to be sick - is she emotionally blackmailing them or is she showing them the way to get better soon? 
• When we are being non egoistic, we are concerned more with our need for people than our own feeling of being wronged or belittled and our need to destroy whoever caused the wron. We sell non egoistic behavior as divine (as against egoistic behavior). No doubt that non egoistic behavior is nicer.. But...
• Some of us defend external attack on our egos and in the process perhaps let go of our material assets. And there are others who better control their egos while capably defending attacks on their material assets or even going on the offensive to conquer someone else's assets. And since generosity involves letting go of assets, does it mean generosity coexists with ego? Does non egoistic and high EQ (emotional quotient) behavior hence rarely coexist with generosity? 
• Quote on intelligence from http://academic.brooklyn.cuny.edu/biology/jbasil/documents/CrowApeCognition.pdf: "One important aspect underlying all flexible behavior is the ability to generalize learned rules in order to apply them to novel stimuli or situations. This ability to solve transfer problems by abstracting general rules is what distinguishes rule learners from rote learners. When presented with a series of different discriminations to learn, corvids (blue jays, rooks, jackdaws, and Eurasian jays), like monkeys and apes, extract the general rule, such as win-stay, lose-shift rather than having to learn each new discrimination afresh. By contrast, pigeons appeared to be rote learners, solving the task eventually by learning each discrimination individually...There are many aspects of corvid and ape cognition that appear to use the same cognitive tool kit: causal reasoning, flexibility, imagination, and prospection"
• We are predisposed or programmed to fear snakes as per https://thehumanevolutionblog.com/2014/10/08/are-humans-predisposed-to-fear-snakes/
• Quote from https://thehumanevolutionblog.com/2016/10/17/dominance-status-affects-the-transmission-of-fear/: "rats, like humans, experience their world through the lens of social contact. Those of high social rank are more influential on others, while being less likely to be influenced by others. Those of lower social rank, on the other hand, have their own advantage: by paying attention to both superiors and other subordinates, they are able to learn from all of members of the group equally."
• Empathy is the ability to see things from another's point of view. J (as in MBTI) hence are least empathetic.. They are so bound by rules and formula and are most fair.. Empathy and fairness rarely coexist. P are usually good at empathy while J show generosity. I wonder whether the existence of empathy and generosity is proof enough of a person's P or J type.
• I love the movie Drishyam (Hindi version). There were two feminine themes. One is how Tabu figures out how Ajay fooled the police. (Incidentally in the Wiki photo, Tabu looks so much like Saira Banu... Beautiful). 
• The other is how cleanly Ajay fools everyone with aptly placed words.. Of course he made some mistakes.. One of which was looking directly at the camera inside the ATM.. People usually don't look at the camera in an ATM.. That act, to prove that he was in the ATM on the said day, aroused suspicion. When his wife tells him at the end that she felt bad that they, as a family, had gotten away free despite having murdered the boy.. And how sad she was for the IG of police. After all the IG was a mother too. Ajay's reply is all about animal behavior with little richness of human behavior. Had the situation been reversed, he tells his wife, the IG would not have been so kind as Shreya is trying to be. Every man to his own. At the deepest level Ajay was concerned about survival than about morals. Are humans very different from animals? 
• Now coming to Tabu...There seemed to be no evidence to support Gaitonde's view that Ajay was the person who drove the yellow car and also probably killed Sam. Tabu and her husband had been hearing all witnesses supporting the explanation given by Ajay...Until she hears one of them blurt out that he didn't remember all the details that happened on Oct 2 and 3. That he had met Ajay 3 - 4 days back and that Ajay mentioned or rather reminded him of the details then... Then Tabu starts figuring out that.. Ajay and his family had gone to Panjim and had eaten Pav Bhaji and stayed at the lodge and watched the movie.. BUT NOT ON the dates Oct 2 , 3 but subsequently. This is the most beautiful part of the movie... This is Ne (as in MBTI) at work.
• Isn't it strange that the people that we expect and do get empathy from are the same ones that we can't let our guard down with... Do we really respect the person with whom we let our guard down? When we let our guard down, we tend to not listen carefully when they are taking, we multitask, we look elsewhere (may be a quick look at the messenger screen in our phone), avoid eye contact.. Would we have done such things when we didn't know the person well? We usually think of letting our guard down as a symptom of getting close.. Is it also a symptom of more distance indicating a lack of respect?
• How often do we say (or heard others say) "Be truthful AND be sensitive to the feelings of others" in the same breath? It is usually not possible to do both, right? 
• Very little of communication is apparently verbal. Much of it is non verbal which includes voice modulation, gestures, facial expression etc.. People with good communication skills use these non verbal techniques while communicating. They convey whatever is necessary. Without any words being uttered leaving no proof. That's diplomacy. Diplomacy is the high end of communication. 
• I had earlier written about line and staff functions and entrepreneurs. It is surprising that people that are not line function (I mean those that are incapable of handling line function. I don't refer to those that are not handling line function) are generally not capable of handling relationships either.. The tendency to specialize too much, which is typified in staff function roles, also extends its impact on family life. Staff function people can not handle deep relationships as well. They can be good counselors, can be a good father, mother, daughter figure etc but usually not a good father, mother or daughter etc.
• When our desire to not get embroiled in a conflict or controversy very high, we convince ourselves that we didn't do anything controversial - even if an impartial observer might opine that we did. Extending this to other behavior, the best of us might lie when it comes to risking public knowledge of our having violated our own strongest personal values. We cannot let it be known that we violated our own values. It is so sacred that we would even lie. 
• Of late I have started reading on evolution, genetics and in the process i came across "natural selection" - how nature ensures that only those attributes are rewarded with survival and procreation that are useful to live.. 
• Charles Darwin: "As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form." See also http://science.howstuffworks.com/life/evolution/evolution1.htm
• And INT (as in MBTI) are lowest in numbers. Could it be that INT's are low because they are UNFIT for survival? Neither having an Extroverted nature or Feelings to relate to others nor the S to be in tune with the world. J adds the last nail on the coffin by eliminating all the built in instincts to survive (which incidentally P's have). Could it be that INTJ'S may have thrived long time back in a different environment? Or are INT's the result of a harmful mutation? I wonder. See below:
• A friend of mine sent me this quote on 14th Feb 2017: "I must learn to love the fool in me -- the one who feels too much, talks too much, takes too many chances, wins sometimes and loses often, lacks self-control, loves and hates, hurts and gets hurt, promises and breaks promises, laughs and cries. It alone protects me against that utterly self-controlled, masterful tyrant whom I also harbor and who would rob me of human aliveness, humility, and dignity but for my fool." .......Theodore Rubin [The masterful tyrant is the J behavior while the so called fun loving fool is the P. And the author seems to have some of both]
• Humans are more restrained than animals in terms of what they are and aren't supposed to do. We have evolved rules of behavior. J's (the ones that are rule based) are most human like. And P's are most animal like. It's rather surprising that the more evolved J behavior (with its umpteen rules ) is less likely to survive. Did our ancestors go wrong somewhere while defining rules? Or are the J's themselves too stupid to understand that that J behavior doesn't help them to survive?
• Some people are very honest and forthright (usually the TJ as in MBTI).. Those people can and will say anything if they know that to be true. These people come across as shockingly clean to others. Most people aren't like that. They, the latter, cannot afford to be so open because they have other agenda and they choose their battles wisely. Being so open or honest will cause an unnecessary battle for the latter. F and or P causes one to be careful about what one says. The cleanliness, of some of the TJ's, is like distilled water. Very pure but quite inedible and tasteless. 
• There is an old saying - "Don't treat someone as though (s)he is a priority when you are only an iron for them. Let me start from that thought. You may have come across people who say they love you. I have often wondered. What exactly do they mean? Mothers love their children and would do anything for them and protect them (children) with their love. Women also love chocolates. They will insert it in their mouth and bite a big chunk of it and swallow and destroy the chocolate. The word love is used in both instances but the two emotions are completely different. One (towards children) is a giving kind of love. The other is one that destroys the chocolate. When someone says they love you, do they mean you are like chocolate or like their child? Rather unfortunate that the English language uses the same word to describe very different things. 
• It is important to differentiate between the what and the why and when to focus on the what and when to drill down to the why.. I have often had an issue with people who tend to get into the why instead of stopping with the what.. As a result they tend to get lost and unable to see clearly what i see.. To know that something happened you don't need to know why.. When we are empathetic we tend to justify the what and hence we inextricably bind the why to the what.. The whole purpose of the why, in such cases, is to negate or deny the what.. The why is usually more ambiguous than the what. By linking the why to the what, we are able to make the what also gray. Isn't that the raison d'etre of P's? To not categorize anything and to leave a lot of room for ambiguity? On the other hand when we want to understand and remove a problem we will go to the why - to understand what causes the problem and hence remove or decrease the problem. It is in such cases, when we do a root cause analysis (RCA), that we need to delve into the why. 
• When we hear of an incident some of us ask WHO (it happened to or was involved). While others ask WHY or HOW (it happened). For example when we hear of an accident do we focus on who got hurt or with how or why the accident happened? Those who focus on the who are into gossip. Those who focus on the who / why are into research. 
• It is interesting that if you allowed me to do something or gave me something which I love then I feel respect for you. But if I took the same liberty, with or without your knowledge , but certainly without your permission I think of you as cuckold.
• The acid test for F (as in MBTI) is the tendency to play Robin Hood - to rob Peter to help Paul. Note I use the word Help rather than the word Pay. This tendency is stronger in FP than in FJ.
• I saw the movie Mississippi Burning almost 30 years back and i was electrified by it. Watching it on TV again yesterday (15-Apr-2017) I recognized some other dimensions while watching Gene Hackman and Willem Dafoe. Dafoe often goes by the book and says "Bureau procedure, Mr Anderson" to Hackman. Very J. When they interview the deputy (sheriff), Dafoe is with the deputy while Hackman is more unconventional and spends time with the deputy's wife getting useful titbits of information. Towards the end when the county frustrates FBI and Dafoe is in impotant rage because his correct procedure still amounted to nothing... Hackman asks Dafoe whether he [Dafoe] will do it his [Anderson's] way. And was Hackman unconventional!
• I read this article about how $171million was stolen from United Bank Of India (and subsequently recovered within a few days). I wondered about the person who did the heist. Were they any different from the animals we see on Nat Geo Wild? What differentiates us from animals? It's the restraint. We think about rules (more appropriate), we think about how it might affect the other party (more empathetic). When we lack these restraints we are no different from the Chinese, Taiwanese, Vietnamese (and Indians, Pakistanis, Americans etc) who perpetrated the act.
• Negotiation is a trait of the ambitious and of those with high Venus. It is only the assertive people that negotiate. The Aggressive people fight or make war and snatch stuff. Both aggression and assertiveness are symptoms of the "fight" nature as against "flight" nature the symptoms of which are to walk away or show the other cheek. Read this to understand more about the Gandhi / Galt's flight technique. 
• This world makes us change and behave in ways which occasionally makes us feel yucky. So much so that we want to take a small break and live in a pure atmosphere or in the company of a pure person - it's like our own personal Ramzan. The interesting thing is that we can only tolerate so much of the "pure" atmosphere before we start gasping for the normality in our lives and hence disengage from the purity. 
• We come across descriptions like intelligence, சமத்து (non mischievous, dependable, sensible etc), mature, innocent etc. How do these map to MBTI attributes? சமத்து is J, intelligence is N. Innocence is portraying oneself without any embellishmment (WYSIWYG) and is T. Innocence and maturity rarely go together - I would tend to think they are opposites. Maturity is P and not F. Examples of TP are sum, rensrini, and tvran (persons I know).
• I have often wondered why I don't listen to lyrics of songs, though I love listening to songs. I guess it's because of my T. Most F listen to music holistically focusing on the music and voice and lyrics. I am yet to come across a T that listens to lyrics while enjoying a song. Incidentally I read this yesterday. "P. K. Ajith Kumar of The Hindu stated, "Just as [Susheela] does not need to know the language to sing a song perfectly, we need not know Tamil to enjoy her songs like ... Chittukkuruvi... ( Puthiya Paravai )". from https://en.wikipedia.org/wiki/Puthiya_Paravai I doubt whether many people will agree with Ajith Kumar.
• Some people have perfected the art of giving when they can afford to or WHEN they have resources in excess and hence effectively limit demands on their resources at other times (by people who get into trouble and need help). A manufacturing analogy is the practice of doing preventive maintenance (PM), the schedule for which one has control over and thus avoid or minimize breakdown of machinery at times when we can ill afford a breakdown. 
• Some of us walk away from a relationship after judging the behavior of the other person to be unacceptable - they remove the other person from their lives. Others just reduce the amount of involvement with a person and go by the "let's be friends". The latter set show a fine understanding of grey behavior while the former operate on a Boolean scale. Are we describing J and P? 
• Introverts repel each other - unless they share something very great. If an introvert has to reach out to another introvert, he has to network through an extrovert, even if he is not very comfortable with the said extrovert and even if he was good friends with the other introvert.
• We always evaluate people very strictly on those attributes we are good at and we are very lenient while evaluating people on things we ourselves aren't good at.
• FP's (or F's or P's) tend to dream a lot. Not only that they tend to focus a lot on their dreams and trying to interpret it. Unlike TJ's who treat dreams as a waste of time. Like an advertisement.
• Nagging can be triggered by desire P (why didn't you get me this or that) as well as by responsibility J (Why haven't you done this, why is this still not cleaned).
• Sensing, listening to, hearing emotional responses is orgasmic for feelers. Most feelers, even introverted ones and selfish ones, respond positively to emotional expression.
• Negotiation is a legal and cheap way to cheat. Especially true when the other party doesn't know the art of negotiation. Examples Belgians in Congo, England's East India Company with India and also seen in many relationships.
• Venus provides the ability to survive and the desire to live. The stronger the Venus, stronger the tendency to survive at any cost.
• J thinks no problems should arise because of him and hence takes extra steps and plans ahead. A p thinks no problem should be attributable to him and hence takes steps (tasks his way through) at the least minute to ensure that the issue is never blamed on him.
• F thinks that the feelings decide what is best. That the path to Happiness is by following the heart. That the heart understand the dictates of the mind (brain) as well as that of the body and finally gives a composite direction. And that Thought / Rationality is likely to lead one astray. 
• I get the feeling that N can be suffixed by TJ or by FP but not by TP, FJ? Meaning NTP, NFJ are not possible combinations.
• When we are shopping for or choosing something P's (as in MBTI) filter based on what is desired regardless of whether it is correct or not, whether feasible or not. The J's on the other hand tend to filter out based on constraints and feasibility even if it means removing desirable options. 
• How much in mental pain must a person be when they accuse their partner of having a very low libido and also accuse the same person of having committed date / marital rape? 
• It is strange that an F / P (as in MBTI) and a T / J conclude a conversation and each has a different recollection of the minutes of their meeting. 
• Women's equality rights feminist movement is not really about women getting equal rights and having the right to live their life as they wish. It is about having life dictated by their strengths - emotions and aesthetics and curbing any focus on physical strength and hard skills.. What women want is a world that rewards soft skills and EQ. 
• When we are good at something, we can recognize the same in others as well. If we are good at faking, we can catch other fakes easily. 
• Objective of F (as in MBTI) is to lead life primarily through feelings and emotions. They know exactly what to ask, demand, get and know what not to give. And do it with such effortless diplomacy that you wouldn't realize what they have been up to. The ones with high energy are especially cutthroat survivors. They are capable of immense sacrifice for their loved ones as well as exceeding self centered and insensitive nature.
• When you are deeply interested in someone, anything they like, place where they live become important and pleasant to you. When you dislike someone, the opposite happens. You want to desecrate what they like. 
• We do not understand the intensity of pain something creates in someone else if we don't feel the same pain with the same intensity.
• NTJ like to discover a new formula or rule which they hope cannot be broken. This gives them a thrill. NFP like to break a so called unbreakable rule. that's what gives them a thrill.. 
• If mankind had only Thinkers, we would have become extinct. And if we had only feelers, we would still be hanging from the tress and thumping our chests.
• For an introverted feeling J person with low energy (in whom S2 is largely absent), arrival of important guests causes S2 to awaken. 
• We use S2 only when we are very particular about a thing. If its not important for us, we use S1.
• When we are not interested in a subject we do not retrieve stuff related to the subject. Example When we are told not to do something (with reference to something we don't like) we still continue to do it unintentionally.. S1 triggers the act of doing.. The instruction not to do it isn't triggered. Is this an issue of storage in memory or an issue of retrieval? I think its an issue of retrieval. If we are repeated that instruction, we do recollect that we were told earlier.. The issue is hence one of retrieval. Because this instruction is something we don't like, it is perhaps stored in a locker which is not accessible immediately during an emergency.
• Figuring out what answer is appropriate and packaging is a P trait not F trait. Meaning FP/TP will do it but not FJ/TJ. 
• T look for competence. F look for happiness as goal in life.
• "Not everything is black and white..Is this statement made by by a P or a F?
• We think its important to be mature. Until we realize maturity is the opposite of innocence.
• There are two kinds of people: A, those who feel small when they have to stand up and acknowledge that they aren't man enough to do a job and B. Then there are those who confidently say that the job assigned to them is a man's job. And they aren't men. They are women who are only helping out. "Women" is of course a metaphor.
• Experience and maturity can camouflage a complete lack of intelligence.
• A girl is lucky to marry a man with a lousy mother.. he doesn't have a great feminine role model that the girl has to live up to.
• I wouldn't wish it on my worst enemy - is a classic Feeler's expression.
• The thinker wants to remove noise from anything in order to understand something well. Lyrics (in songs) to them are "noise" meaning non-value add and hence they do not process it. Feelers want to get everything included calling it holistic. 
• The T identifies a goal - for example "one needs to do some specific activity". If no one is there to do it, he does it. The F decides to do the thing if the activity concerned is close to his heart - regardless of whether someone else is already doing it. If not close, the F only expresses sympathy but doesn't do it - No matter if no one else is doing it. For T thus, his head decides. For F his heart does. The two (T, F) do very different analysis.
• The important issue is not whether things are hardwired in people. The question is whether things can be modified as we want.
• Baggage is the dislike of things or of people that over a period of time has moved to S1 in order to not waste time. Hence we respond with a snigger or roll our eyes or scream before we restrain ourselves.
• We are (because we can afford to be) open and honest about things we don't care about.
• Effective way to handle poor chemistry is to switch off communication, neither understand though the heart or the head, turn away when anything is said and if the voice is raised blame the switch off on the raised voice.
• Some people are so superficial that when they plunge headlong into a relationship, not even a single strand of hair gets wet.
• Venus has an ability to compare things across units of measure - i think S1, as per DK, does the same thing.
• Strong Venus, with weak Mars focuses essentially on survival. The same Venus with Mars also strong focuses on winning or conquering. 
• Strange that we judge people based on their S2 (conscious premeditated thought) when so little happens from S2 but mostly through S1 (subconscious).
• The feeler focuses on avoiding conflict. The thinker focuses on avoiding inconsistency.
• Survivors are good for their own families. Non survivors are good for others' families.
• Feelers often think harshness and rudeness are synonyms. Perhaps because both are painful. But the two are very different. Harshness is about saying things without camoflauging, without toning down the message, being blunt and perhaps also being loud. Rudeness on the other hand is about being insulting (Imagine someone saying this prior to Independence. "Only Europeans allowed inside this club. Dogs and Indians not allowed"). And insults can be delivered with a smile, softly in a low voice. Harshness is a masculine trait. Rudeness is a feminine trait.
• The struggle to survive replaces Innocence with maturity. Innocence and honesty go together, as in children. Maturity and dishonesty go together as in feminine people.
• Extreme consequences can restrain the exercise of your preferences.
• S is about a sequence or chronology of events. Specific to one circumstance. N is about a formula more universal.
• In a non-physical conflict between two people, the one that's a lesser (or less sophisticated) feeler is toast.
• The secret of life and survival is to use appropriate peaceful means to exclude rationality from discussion or consideration.
• Insensitivity is driven sometimes by a combination of Innocence and strict discipline. While other times it is driven by self-centered nature.
• The size of a conflict between A and B is directly proportional to the difference in A's forcefulness about an opinion and B's forcefulness that differs from it. The forcefulness of VERBAL EXPRESSION of either opinion is not relevant to the conflict. Feminine people do not express forcefully verbally. They have huge conflicts nevertheless. If what A espouses is strongly disliked by B then A and B are likely to have a strong conflict.
• Feelers introspection is focused on the result (you didn't handle right). Thinkers introspection is focused on the process (why did it happen, who made a mistake).
• I believe that false emotions (showing joy when you don't feel it or hiding your sorrow) are displayed when you are soft meaning while using s2. Other emotions including anger, accusing someone falsely of rape etc are true (sing S1), even if the data may be factually incorrect.
• Feminine people strongly like and appreciate Emotional intelligence. Feminine people judge others on how street smart they are. Feminine people use S2 while applying emotional intelligence.Fairness comes from S2 and is stressful. Emotions come from S1 and cost nothing.
• Context sensitive behavior is an indication of being alive. Autistic people, J's display poor context sensitivity.Don't take seriously the opinion of someone who hasn't introspected ever.
• When I rob Peter to pay many Paul's, all Paul's will come in my support when I am accused of robbing Peter.
• When we are debilitated, for example don't old age, our control on our S2 is limited. We run on S1 more often and hence our true nature is likely to be seen then. 
• Ultimately the game in life is about how much you get by giving the least i.e., maximizing our returns.
• The difference between TJ and FJ (actually between Tx and Fy) is that an F can look at A = B (Equation 1), B = C (Eq 2) and comfortably conclude that A<>C, where A, B, C are real life situations. For example, you tell a feeler: Good husbands take care of their wives (1), Tom never took care of his wife (2). An F will be very comfortable saying Tom is still a good husband. When questioned about point 2, a feeler will say Tom had extenuating circumstances. This is the S1 talking. 
• A feeler judges others (and themselves) on how well they present what is untrue.
• When you do a favor to some people, they return it by asking for some more.
• S2 and thinkers are not synonymous. We use S2 about things we are passionate about. Both Thinkers and feelers use S2 on things they are passionate about. 
• When you understand (or define) something, you should also know what that thing isn't, explain the difference between that thing and closely related things.
• When someone tells you he is entitled to an explanation, it doesn't ALWAYS mean that you are obligated to explain to him.
• Slander is when you say something nasty about someone that is untrue. When what you is true, it's not slander. When you say something nasty, people may say "what a nasty thing for you to say" giving the impression that you have slandered. No, it's slander only when the nasty thing you said is untrue.
• Dream is S1 at work.
• When you are contemplating an issue (whether to go ahead or not) and if there are major issues and if a major issue is removed and you still don't want to go ahead. THEN the major issue removed was never a major issue.
• It's during invigilation time that our base nature raises it's ugly head. We would rather be home sick and do corrections and let someone else substitute for us in invigilation.
• But death, on the other hand, is really tragic. It forces us to do things which we hate.. lend a helping hand to the suffering party - much against our wishes.
• Don't TEST what people say for correctness, fairness etc. They don't mean what they say. They say it because temporarily it seems like a good idea to say it. If you remember this always in your S2, you can deal with people better. Of course, you may become cynical (thinking, oh she doesn't mean what she says).
• Most of what people say - except things that are assignment statements (do this, don't do that), just like in BASIC you can mentally prefix a REM and ignore it.
• Honesty and fairness is nice but not effective if your judgement is poor. It means either 1. Judge blindly and fairly as a judge is supposed to or 2. Judge knowing what is appropriate in the current circumstances. Many a times in order to live and let live, you have to forego fairness.
• If God were ever to grant some people a gift, that they will henceforth only say what is in their mind and what is true... They would die a hundred deaths.
• Feminism is about the world looking at things the way we women do. https://victimfocus.wordpress.com/2018/08/04/why-i-dont-want-to-become-equal-to-men/
• For some people, original thoughts are critical. For some others, expressing commonly held thoughts is important.
• It's nice not to dwell on the subject of character especially if you don't have any. Introspection, then, won't throw up any ugly truths.
• Some people think of duty as responsibility towards the external world, what a person needs to do for someone else. For some other people, duty is fulfillment of their own needs.
• "She is very practical" basically means she is not stubborn and knows how to be flexible and is willing to negotiate and create win-win situation. This is a P. The other kind is a J.
• Our job in life is to manage until death. We can be sorrowful or we can be happy. Life is a little more fun if we laugh.
• We are generous with what we have plentiful of. Some are generous with emotions. Some others are generous with their money. Are thinkers generous with their emotions? About as much as poor people are generous with their money.
• "She is very practical" basically means she is not stubborn and knows how to be flexible and is willing to negotiate and create win-win situation. This is a P. The other kind is a J.
• Our job in life is to manage until death. We can be sorrowful or we can be happy. Life is a little more fun if we laugh.
• We are generous with what we have plentiful of. Some are generous with emotions. Some others are generous with their money. Are thinkers generous with their emotions? About as much as poor people are generous with their money.
• If you deeply respect a person A, you will also deeply respect other persons who are very similar to A.
• Statements in support of inaction:

• Things happen as per destiny.

• Set something free. If it comes back to you, it was always yours. If it doesn't, it was never yours.

• Evolution is a strong argument against racism and religion.
• An SJ's (as in MBTI) ability to consider and store a new piece of information is inversely proportional to how much that information contradicts their view of the world.
• The non rational person's prayer: "Let not my opinion be hindered by silly little facts."
• Conviction + Influence = Forcefulness. 
• At a young age some of us have conviction (ki yeh sahi hai aur wo galat hai). When we use that conviction to influence someone else it becomes Forcefulness. When we were younger hence we may not have been seen as forceful even if we had conviction.
• Be pleasant, nice and sweet. The tangible returns will exceed that of Bajaj Finance.
• When generosity comes out by itself it's beautiful. It's ugly when you are manipulated to be generous.
• A lack of energy and extreme focus on comfort and peace (for self first and then for others) - signified by weak Mars and non weak Venus - makes one wait for the opportune time to do something for others while generally being needy. Opportune as in most convenient to oneself than looking at the urgency of someone's need.
• Multitasking by feelers is never done with the aim of getting more things done. It's done primarily when each of the tasks is boring. Even while making love, a feeler would think of other unrelated things when they just want to get it over with. But if they are really into it, they would hate to multitask, say answer a phone.
• The rational NT takes pride in the fact that he uses the K(nowledge) of an event and analyzes it with the Rational Why to create something like an airbag. The feminine mind (SF) uses the same K(nowledge) to determine the Emotional Why. 
• Insensitivity is our desire triumphing our aversion to cause trouble to others. 
• Extreme J nature makes you think of "What should be" instead of "What is" while answering a question or pondering a problem. And hence J's responses are likely wrong or "false" for certain kind of questions.
• Claiming frequent sickness or poverty or other distress or claiming to be frequently busy are both survival strategies. In either case, people generally won't easily come to you for help since you are already in distress or busy. You are given a waiver. And if you do help, you are appreciated much more for having taken time out. This is a win strategy for self most of thee time. The busy option is chosen by positive people, the distress option by negative people.
• We will not take stress for on a routine basis for anything that's unimportant to us.We will not take stress for on a routine basis for anything that's unimportant to us.
• That we are suffering doing something is no proof that we are doing a great job of it.
• Sometimes we don't mean what we say when we are nasty. Other times we don't mean what we say when we are sweet. Lying is preferable to being nasty.
• Caring for someone is not about how much you think of them. It's how much you will do to ensure they don't come to any harm.
• Always express your good feelings and intentions. Then you can get away even with murder, We are being brainwashed into judging people by their intentions and not by their actions.
• Nice quotes are like oxygen for the unthinking mind.
• A string and wind can make a KITE soar high majestically. Another string can cut its leg off in a second. If our position comes primarily through (efforts of) other things, our position is shaky.
• An N (as in MBTI) understands metaphors. S doesn't. S interprets literally.

Estimating The Fraction of Numbers That Are Primes

In an earlier post, I had found the list of prime numbers up to about 50000 and thus determined the fraction of all positive integers that were primes.

Now let's try to evaluate the percentage of numbers that are prime theoretically. In the earlier post I had referred to a wiki link above regarding the same: that the number of prime numbers up to x is 1/ln(x) for large values of x. I couldn't understand the proof. I thought I will try to find my own way to determine the same. So here goes.

I continued from what I had done in the previous post listing prime numbers.

My method estimates the fraction of numbers that are prime by checking the fraction of numbers that have divisors or factors and then subtracting that fraction from 1. 

If we can find the fraction of numbers that have some factor, then 1 minus that fraction will be the fraction of primes. The method below uses this rule to estimate the fraction of primes. I also check only for factors that are themselves primes, since there is no point checking with composite numbers as divisors.

First I found all the numbers that are not divisible by 2. This is half of all numbers. Put another way, the number of numbers that are not divisible by 2 is 0.5 of all numbers.

Then I found the number of numbers not divisible by 3. Number of numbers divisible by 3 (3, 6, 9 etc) are 1/3 of all numbers, of which 1/3*1/2 =1/6 are numbers are divisible by 2 also and are already included in the 0.5 mentioned above. 

1/3-1/6= 1/6 is the fraction of numbers which are divisible by 3 but not by 2.

Hence the unique fraction of numbers which are divisible by 2 or by 3 is equal to the sum of the fraction of numbers that are divisible by 2 (=0.5) and the fraction of numbers that are divisible by 3 but not by 2 (=1/6=0.17) = 0.67. Hence the fraction of numbers that are neither divisible by 2 nor by 3 = 1-0.67 = 0.33.

Now let's extend this to find the fraction of numbers that are not divisible by 2 or by 3 or by 5.

The fraction of numbers divisible by 5 = 1/5. Of this, the fraction of numbers neither divisible by 2 nor by 3 = 1/5 * 0.33 = 1/15 = 0.07.

The total fraction of all numbers that are divisible by 2 or by 3 or by 5 = 0.67+0.07=0.73. Remember that when you add the fractions, the fractions should represent entities that are mutually exclusive.

To recap, 0.67 is fraction of all numbers divisible by 2 or by 3. 0.07 is the fraction of numbers that are divisible by 5 but not by 2 nor 3. Hence 0.67 and 0.07 are mutually exclusive.

Hence the fraction of numbers that are neither divisible by 2 nor by 3 nor 5 = 1-0.73 = 0.27.

Considering all numbers from 1 to 30, the numbers that are not divisible by 2, 3, 5 are 1, 7, 11, 13, 17, 19, 23, 29: total 8 in number. 8 out of 30 = 8/30 = 0.27. Same as the value we got theoretically from the previous step.

Continuing this way we come to the values in the table below:

   

   A                   B                              C                                  D

Prime       Fraction of all        Fraction of all numbers         Fraction of all 

Number    numbers              divisible by this prime           numbers that are not

               divisible by the      number or by any other       divisible by this prime

               prime number       smaller prime number          nor by smaller primes

               but not divisible     from Column A                    in column A

               by earlier 

               prime numbers

-----------------------------------------------------------------------------------------

2                   0.5                              0.5                         1-0.5=0.5

3          1/3*0.5=0.17                0.5+0.17=0.67                  1-0.67=0.33

          (0.5 from col D above)     (0.17 from Col B

                                                and 0.5 from Col C)                 

5          1/5*0.33=0.07               0.67+0.07=0.73               1-0.74=0.27

7          1/7*0.27=0.04               0.73+0.04=0.77               1-0.77=0.23

11        1/11*0.23=0.02              0.77+0.02=0.79               1-0.79=0.21

and so on... repeating the steps for each prime number beyond 11.

4253                    0.00                              0.93                          0.07

          (to 2 decimal places)

4253 is the 607th prime number (in the series 1, 2, 3, 5, 7...). I just happened to calculate till the 607th prime number. 607 is just an arbitrary number with no significance in this method.

As we go beyond 4253 we will find that the fraction of numbers that are not divisible by any prime number keep decreasing from 0.07 towards (but never becoming) zero. And this is the value that will probably be equal to 1/ln(x) mentioned in the wiki article mentioned earlier.

The calculation is shown in the sheet"Reaction that are not primes" inhttps://docs.google.com/spreadsheets/d/1B2vJgPILb2Cm29Xvc8pa3TASfzoKa35fiiFzrdWqsm8/edit?usp=drivesdk

Using notations:

Column A:

Prime number 

n (2, 3, 5, 7, 11, 13...). I did not consider the number 1.

Column B

Fraction of all numbers divisible by the prime number but not divisible by earlier prime numbers:

B(n) = 1/n * D(n-1)                                                     : Equation (1)

B(n-1) = 1/(n-1) * D(n-2) 

and so on

B(n) = 1/n * [1 - C(n-1)] from equation (3)
= 1/n * [1- Sigma (B(n), n running from n-1 to 2)] from equation (5)
                                     Let's call this  Equation (4)

Note: n-1 is not an algebraic expression, instead it refers to the previous prime number; example, when n=11, n-1=7.

Column C

Fraction of all numbers divisible by this prime number or by any other smaller prime number from Column A:

C(n) = B(n) + C(n-1)                                                    : Equation (2)

C(n-1) = B(n-1) + C(n-2)

and so on

C(n) = C(2) + Sigma (B(n), n running from n to 3) 

= Sigma (B(n), n running from n to 2), since B(2) = C(2): Equation (5)

This makes sense. The fraction of all numbers that are not primes is equal to the sum of B(n) where each B(1), B(2) etc are mutually exclusive. 

The percentage of non-primes = the fraction of numbers divisible only by 2 + the fraction of numbers divisible only by 3 + the fraction of numbers  divisible only by 5 + ...

Column D

Fraction of all numbers that are not divisible by this prime nor by smaller primes in column A:

D(n) 

= 1 - C(n)                                                                : Equation (3)

= 1 - B(n) - C(n-1) 

= 1 - 1/n * D(n-1) - (B(n-1) + C(n-2) )

= 1 - 1/n * D(n-1) - 1/(n-1) * D(n-2) - C(n-2) 

= 1 - 1/n * D(n-1) - 1/(n-1) * D(n-2) - 1/(n-2) * D(n-3) - C(n-3)

and so on until n=2. This is another form of writing Equation (2) above.

And remember that B(2) = C(2) = D(2) = 0.5. Also when n increases, B and D decrease while C increases towards 1.

Let's now focus on Equations (2) and (4).
Equation 2: C(n) = B(n) + C(n-1)
Equation 4: B(n) = 1/n * [1 - C(n-1)]
Now if you visualize C running a race to reach the value of 1.0, and each time C is incremented by the latest value of B [=B(n)], the divisor n in Equation (4) prevents C from reaching 1. If n was less than or equal to 1, C(n) would reach 1. But n is a prime number which keeps increasing from 2 to 3 to 5 to 7 to 11 and so on. Never will C(n) reach 1. No matter how high the value of n, C(n) will still be less than 1. 

Just like the series 1/2 + (1/2)^2 + (1/2)^3... is converging because each number in the series is a fraction, between 0 and 1, of the number to make the sum reach 1.

B(2) + B(3) + B(4) + ... + B(n)

This is shown in the 'Fractions That are Primes' sheet in https://docs.google.com/spreadsheets/d/1B2vJgPILb2Cm29Xvc8pa3TASfzoKa35fiiFzrdWqsm8/edit?usp=drivesdk

Additional reading:

• http://vbala99.blogspot.com/2016/04/goldbachs-conjecture-gc.html
• http://vbala99.blogspot.com/2016/03/an-interesting-thing-about-primes.html
• http://vbala99.blogspot.com/2010/12/maths-puzzle-5.html

Gurukul

Interesting: https://www.facebook.com/chitra.jha/posts/10152379417964513

A friend said about Gurukul: "That Gurukul idea us very good.  It explains the reason why life is a bigger teacher than schools.. we mix with all ages and learn more than in the ways school teaches"

My belief: It's useful for learning without being taught. And for slow learners or for those who aren't fascinated by the subject. it may not be useful for those who love the subject and who want to be on a fast track to learn it. Imagine 30 years back Sachin Tendulkar and me and 20 others were in the same cricketing Gurukul. (I hardly know how to play the game). After completing the Gurukul, I think I would have become a better cricketer while Sachin would perhaps have been trying hard to even get into the Bombay team.

Friend's response: "I think.. Gurukul should be a place of freedom of choice. All preschools could be like that..and specialized schools take over when talent was recognized and needed to be pursued."

I agree with this. A Gurukul should be a place where heterogeneity (rather outliers) is a non goal. If the SD (standard deviation) varies too much what I said earlier is likely to happen. We will produce a lot of mediocrity and few outliers. Outliers being people like Sachin (extremely good) and me (very poor).
A Gurukul is a place which is a homogenizing pot. The poor (in skills) want homogeneity. The rich would not. Gurukul is another form of socialism or communism.

Estimate The Quotient And Remainder For A New Divisor

Assume there is a number a. Assume a is divided by b - the quotient is q and the reminder is r.

All numbers are positive integers (non zero).

Now you are given a new positive integer c (less than a).

Estimate the quotient and remainder when a is divided by c.

Solution:

The quotient will be b/c * q and the remainder same as before =r. But this is correct only if b/c is an integer.

In case where c is not a factor of b:
New quotient = Rounddown(b/c  * q, 0)
Now because we took only the integer part of the quotient, the decimal part still remains and that will affect the old remainder.

Truncate the value of b/c  * q and take only the decimal part: 

In Microsoft Excel, this will be (b/c  * q) - Rounddown(b/c  * q, 0)

Take the above value and multiple by the new divisor c. Add the product with the old remainder r. That will be the new remainder.

Meaning new remainder nr = [(b/c  * q) - Rounddown(b/c  * q, 0)] *c + r

Note:
If the new remainder is bigger than c, then  divide nr by c. Add the quotient from this division to nq. This sum will be the final quotient. The remainder from this division (nr / c) will be the final remainder.

Goldbach's Conjecture (GC) - Prime Numbers

I had earlier written about prime numbers. Continuing from that post, I got interested in Goldbach's Conjecture.

The strong conjecture (SGC) holds that every even number can be expressed as a sum of two primes. The weak conjecture (WGC) holds that every odd number can be expressed as a sum of three primes - the primes need not be all different. As per the wiki link above, the WGC has been proved in the last few years while the SGC remains unproven even today.

If a and r are even positive numbers and p, q, s are prime numbers then any number a can be expressed as some p+q. (SGC)

And any odd number y can be expressed as the sum of three primes (=p+q+s). (WGC).

If SGC were true then to prove WGC:

We know that any odd number can be expressed as a sum of another smaller prime number and some even number. The latter even number can be expressed as the sum of two prime number (as per SGC). 

So any odd number can be expressed as a sum of three prime numbers.

Coming to the proof of SGC: These are my thoughts. (No proof yet.)
a = p + q : 

Note that p, q are prime numbers. We do not know whether p is bigger than or smaller than or equal to q.

Assume above equation is true for any even number a. Take the next higher even number a+2. We have to prove that there exists some even number r such that,

a+2 = p + q + 2 = (p + r + 2) + (q - r) where (p + r + 2) and (q - r) themselves are both positive and prime numbers. Note that the even number r can be positive or negative. But p+r+2 and q-r should both be positive. The minimum absolute value of r is the lower of (p+1) or (q-1).

Meaning from the values of p and q, there are two prime numbers which are r+2 higher than one number and r less than the other number. This predicts the proximity of a prime number from another prime.

How did we get p+1? The minimum value of p+r+2=1, so r = -p-1. Minimum absolute value of r = p+1. 
This will be continued later.


Searching for prime numbers
I was thinking of the list of prime numbers. When you (a) go 2 to the left of or 4 to the right of any odd number in the number line you will likely get a prime number. If you find composite numbers instead, (b) go 4 to the left of and 2 to the right of the odd number. You will likely find prime numbers.

Example: start from 15. (a) 2 the left of 15 is 13. 4 to the right of 15 is 19. Both 13 and 19 are prime numbers. Using procedure (b) 2 to the right and 4 to the left of 15 are 17 and 11, which are also prime numbers

Start with 67. Procedure (a) 2 to the left of and 4 to the right of 67 are 65, 71, of which 71 is a prime but 65 is not. Procedure (b) 2 to the right and 4 to the left of 67 are 69 and 63 both of which are non primes.

Starting with the primes 5 and 7. Add  6 and multiples of 6 to each of these numbers and leave out the numbers that end in 5. The resultant numbers are likely to be primes (except the occasional multiples of 7, 11, 13 etc). 

Thus 5+6x, 7+6y (where x, y are positive integers) provide better source of prime numbers. Of course, not all of these numbers will be prime as explained above. But, all prime number will definitely be part of one of these two series. When I say better I mean, the probability of a number in that series being prime is higher. The percentage of numbers that are primes in the two series above is about 38% as against about 10% when all positive numbers were considered. The series above are rich in prime numbers. Incidentally while browsing, I realized that 5+6x and 7+6y can be written in a simpler way as 6n+1 and 6n-1. 

I generated the series above as a set of potential prime number candidates. I determined whether each candidate has any divisors. I used the same prime candidates from the series above as divisors. Remember that composite numbers obviously can never be divisors for prime numbers. I do not mean prime numbers will have other prime numbers as divisors. When you have a number a prime number as a potential candidate - where we do not know yet if the number is a prime, we need to only see if the candidate has any primes as divisors.

I found an interesting thing.

Prime numbers were about 23% of all numbers till the first 100 (my first prime number was 5, I left out 2 and 3). The ratio decreased rapidly first and slowly subsequently till it reached 10.3% for numbers up to 50000. 

There is a theorem that states that the prime number % upto the number x = 1/ln(x) as x becomes very large. 

Ln denotes log to the base e where e = 2.71828 approximately. The exact definition formula for e is (1+1/n)^n as n tends to infinity.

Incidentally 1/(log 50000 to the base e)= 9.2%, which kinda matches with the figure of 10.3% that I found.

Estimation of prime numbers through factors is continued in this post: http://vbala99.blogspot.com/2016/05/estimating-fraction-of-numbers-that-are.html

Difference Between Knowledge And Understanding

https://www.bigquestionsonline.com/2014/05/19/what-difference-between-knowledge-understanding/

I guess understanding comes from relating knowledge to what human being normally do - emoting, relating things to their personal life...

What Watson (IBM Computer) did was to relate different sets of data knowledge.. Somewhat like what Google does when you search. It takes the search parameters and searches web pages using the search parameters and then finally ranks the result in an appropriate sequence, with the most relevant on top. Is Google better at searching than most human beings? Probably yes. Does Google understand my emotions when I am searching? Maybe not. 

And that's why think of the term artificial intelligence while thinking of Google or Watson.

The idea of Google or Watson is to be exceptionally good and better than most people in providing answers to questions (or questions to answers in case of Jeopardy). 

Let's take the metaphor to a human level. What kind of a person is like a Google or Watson? It is a person who has exceptionally intelligence but is spending his time on a subject(s) that he is not passionate about. If one were passionate about a subject, it is inconceivable that he would not have understanding.

This is an interesting thesis on education and teachers: http://education.msu.edu/ncrtl/pdfs/ncrtl/issuepapers/ip894.pdf

Quotes from the link (without permission):

A conceptual mastery of subject matter and the capacity to be critical of knowledge itself can empower students to be effective actors in their environment.  

When teachers possess inaccurate information or conceive of knowledge in narrow ways, they may pass on these ideas to their students. They may fail to challenge students' misconceptions; they may use texts uncritically or may alter them inappropriately. Subtly, teachers' conceptions of knowledge shape their practice--the kinds of questions they ask, the ideas they reinforce, the sorts of tasks they assign.  

"Teachers must not only be capable of defining for students the accepted truths in a domain. They must also be able to explain why a particular proposition is deemed warranted, why it is worth knowing, and how it relates to other propositions."

My wish [was] to present mathematics as a subject in which legitimate conclusions are based on reasoning, rather than on acquiescing to teacherly authority.

Teachers' intellectual resources and dispositions largely determine their capacity to engage students' minds and hearts in learning. For instance, Lampert's deep interest in numbers and their patterns is contagious. And her understanding of mathematics as an active domain of human interest and inquiry leads her to orchestrate opportunities for learning that differ from those found in many mathematics classes.

This teacher's engagement with history as a way of making sense of our past is part of what he communicates to his students.

Because of a student's question, a particular textbook activity, or an intense class discussion, teachers often report that, for the first time, they came to really understand an idea, a theme, or a problem that heretofore they had just known as information. 

Only about half the 17-year-olds were successful with problems such as calculating the area of a 6 x 4 cm rectangle or solving a simple algebraic equation. Most high school seniors (94%) were unable to solve multistep problems: "Suppose you have 10 coins and have at least one each of a quarter, a dime, a nickel, and a penny. What is the least amount of money you could have?" 

I asked a friend to ask her daughter who has just graduated to class 1 from Nursery. "My sister has 2 hands, my brother has 2 hands, i have two hands. How many more brothers should i have so that together we have 12 hands?" She was able to solve the first step (that 6 more hands are needed) but she couldn't go to the 2nd step (that 3 more brothers are needed).  But then the daughter is only 6 years old. She will learn the second step in a year or two.

Dossey at al. (1987) argue that many students "are unlikely to be able to match mathematical tools to the demands of various problem situations that permeate life and work". 

This is also true, in India, of disciplines other than Maths. Are engineering majors "able to match their engineering tools to the demands of engineering situations that permeate life and work?" What went wrong with teaching?

As the researchers observed classes, they saw a predominance of so-called discussions that consisted of teachers asking convergent questions that demanded only one-word answers. 

A liberal education, after all, is education not for any specific end but for its own sake. Still, since teachers' work is centrally involved with knowledge and the life of the mind, their own intellectual qualities are critical. Teachers must care about knowing and about inquiry. 

Can the care to know and inquiry be taught?

Write an equation using the variables S and P to represent the following statement:

"There are six times as many students as professors at this university." Use S for the number of students and P for the number of professors. (Maestre and Lochhead, 1983, p. 24)Typically, students who offer an incorrect equation reverse the variables: 6S = P.

Clement and his colleagues (1981) report that over one-third of the engineering students they tested and nearly 6 out of 10 nonscience majors could not offer an appropriate representation. It appears that many students, even when they have mastered the mechanics of the subject, fail to develop an understanding of the underlying meanings.  

In both physics and mathematics, evidence is mounting that all students, not just those intending to be teachers, can meet the expectations for satisfactory work without developing a conceptual understanding of the subject matter--the lack of which, we have argued, seriously inhibits teachers' capacities to help school pupils learn in ways that are meaningful. 

In mathematics, textbooks often foster an algorithmic approach to the subject--e.g., "To divide by a fraction, just multiply by the reciprocal".
Stodolsky's (1988) analysis of elementary math textbooks suggests that concepts and procedures are often inadequately developed, with just one or two examples given, and an emphasis on "hints and reminders" to students about what to do. 

Teachers' subject matter knowledge may also be affected by the attitudes and expectations that their students bring to the classroom. As was discussed above, if teachers face learners who rebel against uncertain or complex intellectual tasks, they may feel pulled to simplify content, to emphasize algorithms and facts over concepts and alternatives.

Wonder how such rebel learners ought to be taught..

While teachers' knowledge about learners, the curriculum, pedagogy, and the context seems to increase from their practice, that they will learn enough about their subject matter from their teaching to shore up inadequate knowledge and understanding is unclear.  

Family and community influences on children's learning are more powerful than the schools' influences.

http://www.columbia.edu/cu/tat/pdfs/psych_learning.pdf: Quotes: 

"Deep learning entails examining facts and ideas critically, relating new and older knowledge, linking ideas together, and constructing novel conceptual structures. It involves the ability to place isolated, unlinked facts into larger conceptual structures. 

Student learning can be enhanced or hindered by the classroom environment. A safe, inclusive, and stimulating environment encourages students to actively participate. Fostering such an environment requires an instructor to be acutely sensitive to individual differences and make sure that students understand the instructor’s expectations and goals, as well as the steps the student must take to meet these objectives. In addition to promoting sensitivity, an inclusive classroom encourages dialogue, a process that might include collaborative inquiry, peer criticism, and intellectual give-and-take. 

Best Practices and New Practices

R-Courses: These are research oriented courses that emphasize “bounded inquiry.” The purpose is to encourage students to think like an anthropologist, biologist, chemist, literary critic, political scientist, sociologist, or statistician. Components typically include reviewing and critiquing journal articles, providing students with data sets, and having students make hypotheses and test them.

Encouraging Student Reflection: Specially-designed assignments encourage various forms of student reflection, leading students to assess their knowledge and reflect critically upon their assumptions and perspectives. These include reflection upon content and concepts, personal reflection (description of reactions, thoughts, and feelings), and metacognitive reflection (monitoring of one’s own thought processes).  

A friend sent me this link: http://infed.org/mobi/what-is-education-a-definition-and-discussion/ 

A friend sent me this excerpt and couple of links (of the three, the Telegraph article seems to make sense:

Richard Leblanc, Ph.D.
York University

Editor’s note: In 1998, professor Leblanc was awarded the Seymous Schulich Award for Teaching Excellence. His top ten requirements for good teaching was originally published in The Teaching Professor, Vol. 12, # 6, 1998.

GOOD TEACHING is as much about passion as it is about reason. It’s about not only motivating students to learn, but teaching them how to learn, and doing so in a manner that is relevant, meaningful, and memorable. It’s about caring for your craft, having a passion for it, and conveying that passion to everyone, most importantly to your students.GOOD TEACHING is about substance and training students as consumers of knowledge. It’s about doing your best to keep on top of your field, reading sources, inside and outside of your areas of expertise, and being at the leading edge as often as possible. But knowledge is not confined to scholarly journals. Good teaching is also about bridging the gap between theory and practice. It’s about leaving the ivory tower and immersing oneself in the field, talking to, consulting with, and assisting practitioners, and liaising with their communities.GOOD TEACHING is about listening, questioning, being responsive, and remembering that each student and class is different. It’s about eliciting responses and developing the oral communication skills of the quiet students. It’s about pushing students to excel; at the same time, it’s about being human, respecting others, and being professional at all times.GOOD TEACHING is about not always having a fixed agenda and being rigid, but being flexible, fluid, experimenting, and having the confidence to react and adjust to changing circumstances. It’s about getting only 10 percent of what you wanted to do in a class done and still feeling good. It’s about deviating from the course syllabus or lecture schedule easily when there is more and better learning elsewhere. Good teaching is about the creative balance between being an authoritarian dictator on the one hand and a pushover on the other. Good teachers migrate between these poles at all times, depending on the circumstances. They know where they need to be and when.GOOD TEACHING is also about style. Should good teaching be entertaining? You bet! Does this mean that it lacks in substance? Not a chance! Effective teaching is not about being locked with both hands glued to a podium or having your eyes fixated on a slide projector while you drone on. Good teachers work the room and every student in it. They realize that they are conductors and the class is their orchestra. All students play different instruments and at varying proficiencies. A teacher’s job is to develop skills and make these instruments come to life as a coherent whole to make music.GOOD TEACHING is about humor. This is very important. It’s about being self-deprecating and not taking yourself too seriously. It’s often about making innocuous jokes, mostly at your own expense, so that the ice breaks and students learn in a more relaxed atmosphere where you, like them, are human with your own share of faults and shortcomings.GOOD TEACHING is about caring, nurturing, and developing minds and talents. It’s about devoting time, often invisible, to every student. It’s also about the thankless hours of grading, designing or redesigning courses, and preparing materials to further enhance instruction.GOOD TEACHING is supported by strong and visionary leadership, and very tangible instructional support resources, personnel, and funds. Good teaching is continually reinforced by an overarching vision that transcends the entire organization from full professors to part-time instructors and is reflected in what is said, but more importantly by what is done.GOOD TEACHING is about mentoring between senior and junior faculty, teamwork, and being recognized and promoted by one’s peers. Effective teaching should also be rewarded, and poor teaching needs to be remediated through training and development programs.AT THE END OF THE DAY, good teaching is about having fun, experiencing pleasure and intrinsic rewards…like locking eyes with a student in the back row and seeing the synapses and neurons connecting, thoughts being formed, the person becoming better, and a smile cracking across a face as learning all of a sudden happens. It’s about the former student who says your course changed her life. It’s about another telling you that your course was the best one he’s ever taken. Good teachers practice their craft not for the money or because they have to, but because they truly enjoy it and because they want to. Good teachers couldn’t imagine doing anything else.

THE CORE
Association for Experiential Education
Schools & Colleges Professional Group Newsletter
Spring 1999, Vol. 2, # 1

Are you truly a bad teacher? https://www.washingtonpost.com/news/answer-sheet/wp/2014/12/19/are-you-a-truly-bad-teacher-heres-how-to-tell/

What makes a good teacher: http://www.telegraph.co.uk/education/educationopinion/11347131/You-dont-need-a-qualification-to-be-a-good-teacher.html 

Microsoft Excel - What Happens To Cell References When You Sort

http://stackoverflow.com/questions/7979923/how-do-i-sort-a-table-in-excel-if-it-has-cell-references-in-it

The link has some nice suggestions. 

A problem occurs when you have some data in a sheet that are referred in, say, another sheet 9say, sheet2) and when you sort the data in sheet 1 of a sheet. The cell references do not change when you sort data and hence the data in the other sheet now point to different cells.

I have given a sample example. Click the google spreadsheet. Column A in Sheet2 is set to the values in column A of sheet 1 through formula. Columns A and B in each sheet are pasted again in columns D and E for visual reference only.

N sort the data in cols A and B by selecting these two columns, sort on column A. Go to sheet 2 and see where the values for the fruits were same as before.. Compare with columns D and E in sheet 2.. See?

But if cells or rows or columns were cut and pasted somewhere else (in sheet1), the referring cells (shee2 in this case) retain their integrity. If you sort the values, they don't. 

This isn't intuitive but that's the way it works.

Similarly, let's say we use vlookup (or hlookup) on a set of columns (or rows). Now if we insert a new column (or row) within that set, the formula is likely to go wrong depending on where you inserted the new row (or column). Again not intuitive.

Generosity And Avarice

No amount of generosity is enough to appease the avaricious. Chamberlain tried that with Hitler.

A bunch of little boys were picking mangoes which were strewn around a mango tree that belonged to an elderly lady. The lady asked the boys to go away. The boys took a bunch of mangoes and ran away. A few minutes later they were back trying to pick more mangoes.

Do they do it for fun? Or is it a harbinger of things to come? Are they doing with mangoes today and will graduate to something bigger in the years to come?

It's not just little boys who do it.. I have seen women also pick the mangoes which is obviously not theirs.

Did Human Sacrifice Create Social Stratification Or The Other Way Around

http://www.csmonitor.com/Science/2016/0404/Did-human-sacrifice-create-social-stratification: An amazing article that explains why we love sacrificing (others).

I wonder whether any T would believe in stratification. All the people that I know who believe in stratification are F's. I do know a F who doesn't believe in it. Weird, isn't it...

As it was pointed out in the article itself, I wish the study focused on the number of sacrifices instead of only on whether there were sacrifices.

Apparently the people who liked stratification were also the ones who inherited wealth and unlikely to have their status change much in one lifetime. 

Perhaps people who are born into such families (those who believe in stratification especially women) are likely to be insensitive towards the smaller people - the drivers, waiters, maids et al..

And people who are basically soft-natured inside are the ones who do not believe in stratification.