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Andrew S.
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Question:

The threat of rain didn’t … her stroll through the grounds. Even the first drops were no …, and she continued her walk. A. hinder … incentive B. thwart … refuge C. impede … deterrent D. permit … provocation E. prevent … enticement

Andrew S.
Answer:

C. Impede -- (v.) to delay or prevent (someone or something) by obstructing them synonyms: hinder, obstruct, hamper, hold back/up, delay, interfere with, disrupt, retard, slow (down), hobble, cripple Deterrent -- (n.) a thing that discourages or is intended to discourage someone from doing something. synonyms: disincentive, discouragement, damper, curb, check, restraint (can also be used as an adjective in a similar vein, for example, "the deterrent effect of heavy prison sentences", but the context of the sentence in question indicates a noun is needed)

Writing
TutorMe
Question:

Tell me a weird story

Andrew S.
Answer:

I have this idea that before people are born their souls are taken to a mean-o-meter. This device reads the person’s fate, his or her lot in life, and uploads an appropriate set of axiom-intuitions into that persons soul. Generally, the more suffering is ahead of a person, the more “meaning-full” the axiom-intuitions they get. Those with the worst struggles to come get the existence of a personal God as an axiom, constantly watching over them. Those with a slightly easier lot in life get Deism, or a belief in some kind of higher power, allowing a kind of all-purpose spirituality. Next, comes agnosticism. This might be combined with Kantianism or some other notion of intrinsic human dignity and agency. Then, the utilitarians, the existentialists, the hard determinists and finally the true nihilists. It is unclear whether any human fate could actually merit receiving the axioms of true nihilism from the mean-o-meter, although those that come closest to this apportionment are those will encounter little resistance on their path through existence. Or maybe there are some unfortunate souls who received nihilistic axioms by accident when the mean-o-meter malfunctioned. There was a long and bitter debate about whether or not the mean-o-meters should be used, but those meter administrators with conservative principles eventually lost out to sheer convenience. Yes, there were some worries about the moral tribalism that different mean-o-meter outputs might cause, but those arguing for the meter pointed out that the differences in people’s fates would cause social tribalism anyway. And there was no denying that the mean-o-meters avoided many troublesome situations... Then there was another even longer debate, not about the use of mean-o-meters, but about their interpretation, particularly concerning how the meter’s outputs related to the truth. Was one of the meter’s outputs more truthful than the others? It seemed that the meters did not use any kind of universal truth as an input, merely the fate of the individuals to which it assigned axiomatic beliefs. Some meter administrators claimed there was no truth other than the output of the machine. Others claimed that there was a truth beyond the meters, but that we had no hope of accessing it, and so might as well define “truth” as the meter’s outputs. By this time, the meters had been in use for so long that even most of the administrators and operators had been “metered” themselves, and this seemed problematically circular. Still, others claimed that there was a truth beyond the meters and it was in principle accessible, via pure rational reflection, but the detractors claimed that this was only their (optimistic) meters talking. A kind of cult developed around the few administrators who were old enough to not have been metered themselves. These admins formed a “council of elders,” that the rest hoped would settle the issue. Unfortunately, the elder admins debated the issue just as viciously as everyone else, and there seemed to be no immediate hope of resolution. Eventually, this debate too grew stale, and the admins continued their work. It's Christmas Eve, and these are the kind of strange thoughts in my mind. I’m feeling particularly vulnerable to these thoughts, and others as if I am teetering on an edge, stomach queasy with nervous anticipation. One thought that’s too dark and I’ll tumble down to the abyss. Here’s one: It’s as if the whole holiday ritual is this great Sisyphean effort, that only underlines the futility when the rock finally rolls on December 26th. It's still winter, the days are still cold and short. Camus wanted his metaphor to make me feel like Sisyphus, struggling but somehow dignified (?), but I feel much more like the rock about to fall, when the elves of Christmas spirit lose their grip. I’m in the shower, weeping a little and thinking about God, fitting for the holiday I suppose. I have the thought that so many have thought before me, the thought that has become a cliche for those wavering between faith and doubt: “please, just show me that you’re here.” I hate myself instantly for thinking it, and latch onto that little slice of self-hatred as a defense against the thought, as a temporary plug for the God-shaped hole in me. As I’m going through this semi-familiar routine, I look up and my eyes fix upon the shower head opposite me (the shower I’m in has two heads for partners to shower together; this other one is not running). It’s suddenly so obviously an angel, from this perspective: the disk affixing it to the wall is the halo, the pipe is the head, and the showerhead itself is the body. I realize that there must be one just like it behind me too, showing me with water. This is comforting and draws out of me a moment of peace, in which the thought “please, show me you're here” recedes and I don't think about much at all besides the warm droplets hitting my back. The Thought, in addressing “you,” already assumes that the “you” exists and is there to listen. I could have thought: “if you exist, show me you’re here,” but I didn’t, and wouldn’t. If I'm at a point to think such a thing as the Thought, any added conditional would not have my heart and soul behind it, so to speak. But I even as I am assuming God, I snatch the assumption back. The showerhead angel was not enough, just a figment of an agitated mind, seeing what it wanted to see. I had decided to be an atheist, and I would be damned if I would have that rationally weighed decision taken away from me by my emotions. I had encountered images of God before, in the love of my life and in that pink pill I take every morning. I would study that chemical formula like the Bible. I would pray to her soul like it was God’s own. Together they were and are my divine salvation, and how different they are. How different all the minor salvations, the angels are. Like these stupid and wonderful showerhead angels. I suppose this is what they mean by “mysterious ways.” Whenever I teeter on that all too familiar edge a wave of meaning rises to support me. I just wish I wouldn't have lost my balance so often… There is a movement among certain atheists called anti-theism. It consists both in the claim that there is no God, and the perhaps counterintuitive claim that it is better this way. Most of the arguments allude to the totalitarian nature of a theistic God. I think this movement is utterly misguided. We all, by nature of our very humanity, have a God-shaped hole inside us, however much we try to plug it. So I am not the kind of atheist that denies God’s literal truth, but claims it has value as a projection of the best parts of ourselves (for why are these virtues the best parts, and not just those that can spread the religion meme? This appraisal of religion seems circular.) The purpose of religion is just to address this God-shaped void, to soften the endless current that rages into this black hole. Notice, I say “address” and not “fill,” “soften” and not “still.” This Godvoid is the same as the Selfvoid (this convergence is represented by the religious figure of the prophet, both God and Human, as William Blake said, “that which is above, is within”) and this void cannot be filled or sealed. I think religion is more than a palliative drain-plug to soften the fear of nothing (the opium of the masses). It does have a positive subject matter: not the Godvoid itself (this is unspeakable in the Wittgensteinian sense of the mystical) but the current it necessarily creates this distinctively human current. I believe this current is the defining aspect of our humanity. Over the course of our lives, we take in pieces of driftwood which are sometimes swallowed up and sometimes catch on the bottom. These pieces of wood and stone might be too deep to be seen but they affect the current in subtle ways, changing its direction speed and patterning. My current has sent me past the joy of scientific discovery (which so many describe as knowing the mind of God), the joy of seeing the unseen, and transcending our ordinary experience and common sense. At the heart of poetry too is the desire to blow up an experience until it is bigger than itself (or bigger than yourself). Metaphor and simile are the means of blowing up experience and it starts with the first sound that leaves one’s mouth. The cry of a newborn is what it's like to be her (I wonder what emotion is behind that first cry, pain, wonder, or something else entirely?) “Blowing up” an experience is, of course, itself a metaphor. There is the physical referent of the metaphor: an explosion. The violence that this invokes is characteristic of poetry, science, philosophy, religion. What do all these divergent disciplines have in common (and here I ask you to be wary but not close-minded, that attentive, meditative state that one should always adopt when approaching a broad synthesis proposed by another)? Their subversive ability to tear us out of a given common understanding-- is a religion not the very palliative common understanding that the others subvert? I do not think so. Religious violence (that pervades religious dogma) is not a mere conjunction of religion and violence, it is a peculiar synthesis with a subversive character. It is the same impulse that inspires certain brands of emancipatory politics. In an administered deterministic world, freedom can only appear as violence, in the first instance against the laws of nature, and in the second instance against the laws of man, (although the laws of man come to appear as laws of nature, just as we metaphorically describe social obstacles as physical: a boulder too heavy to be moved off of one’s arm (have to cut it off), an insurmountable wall, or just a grain of sand in the cogs, etc.) The flotsam we acquire are individually distinctive, but what is common to all is the uprooting power of the current. And this uprooting takes the form of a perpetual yet discontinuous series of explosions, with the power to overturn earth and sediment. “Blowing up” has a metaphorical referent in logic, too: the phenomenon referred to as logical explosion by which anything can be proven from a premised contradiction. I felt a certain awe at this absurdity when I first encountered it. All that one needed to break (explode) the logical system was a contradiction, because the universality of such a system did not allow for the contradiction to remain localized, but would rather initiate an infinite chain of detonation. Truths remain in such inspiringly close logical solidarity with each other. It's wonderful. I cling to this thought and allow it to carry me from the shower to bed, and from my bed to my dream world, full of personified sugarplums with beards that make strange indecipherable philosophical arguments to me and argue with each other.

Philosophy
TutorMe
Question:

describe and evaluate three theories of chess decision making?

Andrew S.
Answer:

Your opponent has just made a move, and hits the clock. It’s your turn. You instantly start assessing the new position and attempting to formulate your move. But what is actually going on in your mind when you play chess? Is it procedurally different than what goes on in a Grandmaster’s mind? Is there a ‘correct’ form of a chess thought process, one that is most efficient? All of these questions have been answered multiple times by chess players and non-chess players alike, and this essay will survey some of those theories. Alexander Kotov’s model of chess thought is by far the most well known in the chess community. Kotov’s model is called the candidate moves system, and was originally developed in his book Think Like a Grandmaster (1971). The idea is that, when you’re presented with the new position after your opponent makes a move, you instantly disqualify a large percentage of the available moves based on your previous chess experience. Indeed, this previous chess experience has developed your pattern recognition and chess intuition to the point that a few specific moves might seem most appealing, and demand further calculation. You might have some positional justification for these moves that seem to jump out at you, but the justification is not what is important. Look one layer further back, asking what prompted that recognition and we hit the rock bottom of intuition, which is really just a result of pattern recognition from previously played games. This might start to give you a sense that chess was very concrete and move-by-move for Kotov; not a lot of emphasis was placed on positional factors. Now back to the system that Kotov proposed. These moves that jump out at you in a given position are what Kotov called candidate moves. After mentally making one of the candidate moves in your mind, you are presented with another potential position, in which it is your opponent to move. Again, intuition and pattern recognition might cause a couple moves to stand out to you as potential candidates for your opponent’s best reply. You then mentally make one of these moves and it is back to your turn. You repeat the candidate moves process, and the back and forth aspect of calculation continues until either it is evident that a line tactically fails, or you stop when the position is tactically stable and your powers of calculation are close to their limit. You then repeat this process for the other candidate moves you originally selected. The result is a number of variation trees equal to the number of candidate moves. The number of moves being considered at each step of calculation should decrease with increasing depth (for instance, there should be more original candidate moves than considered opponent responses for your later moves) so as the to keep the trees from getting overgrown and to make some reasonable depth possible. If we were computers we would not need this restriction, but as humans we have to weigh the cost of any calculation we make. Our finite mental capacities result in objectively speaking quite weak ability to penetrate deeply into a position. Since the marginal benefit of considering another line decreases with increasing depth of calculation, we have to make these sorts of trade-offs. It is for these same reasons that forcing moves are valuable in calculation: (A) there is a low calculation cost for forcing moves since there is only one or maybe two reasonable opponent responses that need to be considered, and (B) there is a higher potential tactical payoff, since tactics by their nature usually operated based on forcing moves. Once the trees are formed, the ‘trimming’ process begins. One the end of a branch/line is reached, and you judge the resulting position to be tactically stable, we can then evaluate that position. The evaluation is not calculation in any way (this is why the position must be relatively tactically stable), but rather takes into account positional factors such as material balance, positional dominance/control, structural factors (statics), piece activity (dynamics), king safety, etc. These positional factors may not be taken into account explicitly under Kotov’s model, again being placed under the umbrella of intuition. If the evaluation of the end of a branch is significantly worse than other evaluative ends, then it can be ‘trimmed’ and removed from consideration. This trimming continues until you have the line you consider to have the best result for yourself given the best play by your opponent. This may sound fairly common-sensical, and indeed it is. What Kotov is proposing is a highly concrete model of chess thought, centered around three steps: 1. Formation of candidate moves (intuition) 2. Calculation 3. Evaluation (positional factors and intuition) We notice that steps 1 and 3 both involve the exercise of intuition (by which we mean pattern-recognition), but indeed so does calculation which, of course, also has an evaluative component. Therefore, we can express the candidate moves model as just an iterated two step process, both steps of which require that very abstract capacity of intuition: 1. Formation of candidate moves 2. Evaluation of resulting position This is essentially how computers play chess, the main difference being that, instead of forming candidate moves, computers exhaust all legal options in a given position (there may be some pruning methods for cutting lines, but this is for the most part accurate). This is how computers make up for the intuition required in the first step, and as for the second step, the human touch has not been so easily eliminated, as the computer still requires subjective evaluation criteria (programmed in by humans) at the end of the line. The game theoretical way to think about this is that, for any chess position, there is a massive multi-dimensional matrix with subjective payoffs in each cell. Once this matrix is constructed the move that is made will be the equilibrium of that matrix, the best possible result for you given the ultimate rationality and best possible decisions of your opponent. This connection to game theory along with the analogy to computer chess may make kotov’s model seem somewhat dry, failing to tell us anything meaningful about the very human, not often perfectly rational, weak in calculation, process that occurs when we try to come up with a move over the board. We will now examine two challenges to this sterility: the theory of imbalances, and the odds-giving strategy. The face of the matter is that, despite what Kotov’s model implies, humans do not think like computers. When we calculate, we may undergo some process similar to the one Kotov describes, but psychologically speaking, it is not nearly as formal. One of the things chess players are commonly asked by non-chess players is something like “how many moves ahead can you see?” Of course the answer can vary greatly, largely depending on the amount of forcing moves which increase the potential for deep calculation. However, casting this important dimension aside and focusing on averages, the non-chess player may very well be surprised how shallowly even strong chess players calculate on an average move. Kotov’s model overemphasizes calculation and therefore underemphasizes the less structured, even less rational or conscious, aspects of picking a chess move. Emergent from the bare rules of chess, patterns emerge, and these patterns tend to be indicative of a general sort of action in the chess game. Chess players have formalized this patterns in various ways (e.g. “doubled pawns are a structural weakness”). We must keep in mind that these formalizations and chess “rules” are a map, not the territory (the territory in this analogy being the concrete strings moves on the chess board). Nevertheless, whereas computers may be able to navigate the territory well-enough, our human nature necessitates the use of subjective mapping. A very large portion of chess thought occurs in this subjective arena, which Kotov does not address. To better idea of how this portion of chess thought works, we can turn to an example of one such subjective model, imbalance theory. The theory of imbalances was proposed by International Master Jeremy Silman, and has since been widely adopted as both an effective teaching tool for club players, and as an effective organizational model for stronger players. And imbalance is essentially a asymmetry between your position and that of your opponent. They can be positive (e.g. a lead in development) negative (e.g. a structural weakness) or relatively neutral/to be determined by future changes in the position (e.g. bishop vs. knight). Silman’s imbalances are as follows: 1. Material Imbalance 2. Minor Piece Imbalance (Knight/Bishop) 3. Pawn Structure 4. Spacial Control 5. Development and the Initiative (the dynamic imbalances) For each of Silman’s imbalances, we could analyze how the raw patterns that occur in chess games were modeled into more subjective criteria, but for the sake of brevity we will make do with one example, on first glance the most objective of the imbalances. The relevance of the material imbalance is hardly a revelation. Indeed, it is obvious that having more pieces is monotonically preferable to having fewer pieces, and every chess player learns very early on that certain pieces are worth more than others, and by how much relative to the pawn (pawn=1, knight=3, bishop=3, rook=5, queen=9). What is less obvious, due to their deeply ingrained use, is just how arbitrary these numbers are. The raw pattern underlying the material imbalance is the fact that, when there is a difference between the number/type of pieces that both players have, then the games tend to go better for one side in a certain proportion. How incredibly unlikely that those proportions can all be expressed as varying numbers of whole pawns? Even more unlikely that there are no piece interactions that change their values, no piece combinations that work especially well together. Of course, neither of these is the case. The integer values for the pieces are only rough approximations, and there are indeed some piece combinations that work better than others, thereby enhancing the effective value of both pieces (e.g. the bishop pair, knight and queen). This analysis can get quite complex (see the following article: http://www.chess.com/blog/HelloChessfriend/the-evaluation-of-material-imbalances ) but just because the territory/raw patterns can be accounted for more accurately with a more complex model does not necessarily make it better. The more complex the model, the closer we get to the task that chess computers take on, wading through raw data, since any general principle will distort concrete analysis. Silman places a much larger emphasis on subjective evaluation than did Kotov, and accordingly, his model for chess thought is structured somewhat differently, although it still contains a “candidate moves” step: 1. Figure out the positive and negative imbalances for both sides. 2. Determine where on the board you wish to play (the center or either wing). You can only play when a favorable imbalance or the possibility of creating a favorable imbalance exists. 3. Don’t calculate. Instead, dream up various “fantasy positions”, i.e., the position(s) you would most like to achieve. 4. Once you find such an ideal position, you must figure out if you can reach it. If you find that your choice was not possible to implement, you must create another dream position that is easier to achieve. 5. Only now do you look at the moves you wish to calculate (called candidate moves). The candidate moves are all the moves that lead to the dream position. Notice all the evaluative, subjective, imaginative work (steps 1-4) that was put in before any calculation occurred at all. Computers do not imagine dream positions, and if we humans had their powers of calculation, then we wouldn’t have to either. However, all the non-calculational thought lowers the amount of calculation necessary for a certain level of play. This is one reason why a common anti-computer strategy is to enter slower, closed-type positions. In these types of positions the immediate consequences of making one move over another are much smaller, and so the calculation tree widens, making effective raw calculation at a high depth more difficult, and thereby making non-calculational, strategic/positional considerations (the human area of expertise) relatively more valuable. Another way in which humans think about chess differently than computers has to do with the existence of a psychological element. Some players reject any talk of psychology in chess (whereby psychology we mean psychological considerations not having to do directly with the analytical task of finding the best move in a given position), attempting to uphold its status as a pure rational pursuit. Bobby Fischer, for instance, famously said, “I don’t believe in psychology. I believe in good moves.” This statement would later take on some irony as Fischer’s own mental health deteriorated during and after the 1972 world championship match with Boris Spassky, and he then dropped out of the professional chess world. The fact of the matter is that, in human chess, our psychology plays a role. While some psychological tactics do not belong in the world of competitive chess (pre-game emotional attacks, attempts to psych out or distract the opponent during the game, etc.) within the scope of the game itself, practical psychological strategies are perfectly legitimate. For instance, it is legitimate to play cat and mouse, the phrase used to mean taking one’s time in a slightly better endgame, hoping that your opponent with make some small slip that will allow you to squeeze out a win instead of a draw, even if theoretically the endgame should probably be drawn. It is reasonable, of course, to prepare a surprising opening in the attempt to take your opponent out of their comfort zone and preparation. Neither of these strategies would be especially effective against a computer, but under the scope of human chess, they take in account certain practical realities of the game. Another such psychological method is the so-called the odds-giving strategy, elaborated by Garry Kasparov. It is the theory that, paradoxically, as the stronger player in a given match up, one might not want to make only the theoretically best moves. At this point, it might seem like I am describing playing otherwise strange/unproductive moves to lay cheap traps for the opponent. This is indeed an extreme form of the odds-giving strategy, and is generally viewed as not very good (or honorable) chess at higher levels, even potentially insulting. However, a subtler version of this strategy has to do with opening choice. It is a fact of opening theory that there are certain openings (including but not nearly limited to aggressive gambits) in which one can sacrifice a small amount of objective soundness of one’s position, and in turn make the position complex, tactically sharp, double-edged, difficult for the opponent to navigate, etc. Kasparov himself subscribed to this strategy for most of his chess career, and these types of practical decisions are completely reasonable; they are part of the game, as it were. Note that it would be rather foolish to adopt this sort of strategy against the computer (making the position sharper would have the opposite effect of the anti-computer strategy of entering closed positions, explained above), which has no significant fallibility of calculation. A computer would also never adopt this strategy, unless specifically programmed to do so. It would not be a cohesive element of the computer’s “thought process”, but rather an artificial add-on taylor made to combat human psychology. Whereas such a psychological strategy is artificial in the world of computer chess, it comes very naturally in the human arena. Chess players have been incentivized and conditioned to take such considerations into account by the fact that weighing psychological factors has consistently improved results. Even more fundamentally though, chess players will naturally think and strategize about the psychological portion of the game because we instinctively recognize that it is another human agent like us sitting across the chessboard. This is certainly far from irrational. This has been a survey of three theories of chess thought: Kotov’s candidate moves model, subjective principle-based models like Silman’s imbalance theory, and psychological considerations such as the odds-giving strategy. Each of these categories adds something to our understanding of what goes on (and what should go on for the purpose best play) in our minds when our opponent hits the clock.

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