Positive Algebraic Quotes

Men are liars. We'll lie about lying if we have to. I'm an algebra liar. I figure two good lies make a positive.

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing. [Statement of the second law of thermodynamics, 1862]

Our problem is that we assume prayer is something to master the way we master algebra or auto mechanics. That puts us in the “on-top” position, where we are competent and in control. But when praying, we come “underneath,” where we calmly and deliberately surrender control and become incompetent.

If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if one could.

Do not grab pawns at the expense of development or position.

Well, three reasons. First, because I've been thinking about our Theorem and I have a question. How does it work if you're gay?" "Huh?" "Well it's all graph-going up means boy dumps girls and graph going-down means girl dumps boy, right? But what if they're both boys?" "It doesn't matter. You just assign a position to each person. Instead of being 'b' and 'g', it could just as easily be 'b1' and 'g', it could just as easily be 'bi' and 'b2.' That's how algebra works.

Descartes was a philosopher, a mathematician, and a man of science. In philosophy and mathematics, his work was of supreme importance; in science, though creditable, it was not so good as that of some of his contemporaries. His great contribution to geometry was the invention of co-ordinate geometry, though not quite in its final form. He used the analytic method, which supposes a problem solved, and examines the consequences of the supposition; and he applied algebra to geometry. In both of these he had had predecessors—as regards the former, even among the ancients. What was original in him was the use of co-ordinates, i.e. the determination of the position of a point in a plane by its distance from two fixed lines. He did not himself discover all the power of this method, but he did enough to make further progress easy.

We also find *physics*, in the widest sense of the word, concerned with the explanation of phenomena in the world; but it lies already in the nature of the explanations themselves that they cannot be sufficient. *Physics* is unable to stand on its own feet, but needs a *metaphysics* on which to support itself, whatever fine airs it may assume towards the latter. For it explains phenomena by something still more unknown than are they, namely by laws of nature resting on forces of nature, one of which is also the vital force. Certainly the whole present condition of all things in the world or in nature must necessarily be capable of explanation from purely physical causes. But such an explanation―supposing one actually succeeded so far as to be able to give it―must always just as necessarily be burdened with two essential imperfections (as it were with two sore points, or like Achilles with the vulnerable heel, or the devil with the cloven foot). On account of these imperfections, everything so explained would still really remain unexplained. The first imperfection is that the *beginning* of the chain of causes and effects that explains everything, in other words, of the connected and continuous changes, can positively *never* be reached, but, just like the limits of the world in space and time, recedes incessantly and *in infinitum*. The second imperfection is that all the efficient causes from which everything is explained always rest on something wholly inexplicable, that is, on the original *qualities* of things and the *natural forces* that make their appearance in them. By virtue of such forces they produce a definite effect, e.g., weight, hardness, impact, elasticity, heat, electricity, chemical forces, and so on, and such forces remain in every given explanation like an unknown quantity, not to be eliminated at all, in an otherwise perfectly solved algebraical equation. Accordingly there is not a fragment of clay, however little its value, that is not entirely composed of inexplicable qualities. Therefore these two inevitable defects in every purely physical, i.e., causal, explanation indicate that such an explanation can be only *relatively* true, and that its whole method and nature cannot be the only, the ultimate and hence sufficient one, in other words, cannot be the method that will ever be able to lead to the satisfactory solution of the difficult riddles of things, and to the true understanding of the world and of existence; but that the *physical* explanation, in general and as such, still requires one that is *metaphysical*, which would furnish the key to all its assumptions, but for that very reason would have to follow quite a different path. The first step to this is that we should bring to distinct consciousness and firmly retain the distinction between the two, that is, the difference between *physics* and *metaphysics*. In general this difference rests on the Kantian distinction between *phenomenon* and *thing-in-itself*. Just because Kant declared the thing-in-itself to be absolutely unknowable, there was, according to him, no *metaphysics* at all, but merely immanent knowledge, in other words mere *physics*, which can always speak only of phenomena, and together with this a critique of reason which aspires to metaphysics." ―from_The World as Will and Representation_. Translated from the German by E. F. J. Payne. In Two Volumes, Volume II, pp. 172-173

The reason that I do not typically use the command word “stay” during training is because it is redundant.  If I instruct you to sit, I should not have to tell you to stay sitting.  What value is a sit without the stay?  Sit implies stay.  Once I have given the sit command, the assumption is that the dog should remain in that position until told otherwise.  That’s the standard.  The sit command can be considered the warning that it’s unacceptable to get up.  However, if you want to offer the additional information, you may say “stay” once the dog is sitting.  Then, that becomes the warning.  Only say it once.  That is the message that tells the dog of your expectations.  A warning should be delivered one time.  If the dog does not heed the warning, then the consequence must be delivered.  Otherwise, you will create a dog that will simply wait for the second or third or fourth warning word before changing his behavior.

Stalin formulated the economic aims of socialism as: “The securing of the maximum satisfaction of the constantly rising material and cultural requirements of the whole society.” [Economic Problems of Socialism in U.S.S.R., English edition, p. 45.] Taken positively, this has no more content than any metaphysical slogan; like the slogan “All men are equal,” it expresses its point of view through negations. “Constantly rising” requirements means that there is no foreseeable limit to the possible rise in productivity (for, of course, it is not so much the needs as the means to satisfy them that will continually increase). “Cultural” requirements means that growing wealth is not to be confined to physical goods (though these alone enter into the Marxist definition of output). “The whole society” implies a condemnation of the arbitrary distribution of wealth. There is nothing in this that the orthodox economists can object to. Indeed, it takes the very words out of their mouth. But they were wont to excuse the inequality generated by private property in the means of production because it was necessary to make total income greater. If income grows faster without it, they are in an awkward situation. Perhaps this is why they have crept off to hide in thickets of algebra and left the torch of ideology to be carried by the political argument that capitalist institutions are the bulwark of liberty. [pp. 109-110]

Time Tipping happens when constraints create freedoms that prevent future negative chain(s) of events.

Chris Argyris, professor emeritus at Harvard Business School, wrote a lovely article in 1977,191 in which he looked at the performance of Harvard Business School graduates ten years after graduation. By and large, they got stuck in middle management, when they had all hoped to become CEOs and captains of industry. What happened? Argyris found that when they inevitably hit a roadblock, their ability to learn collapsed: What’s more, those members of the organization that many assume to be the best at learning are, in fact, not very good at it. I am talking about the well-educated, high-powered, high-commitment professionals who occupy key leadership positions in the modern corporation.… Put simply, because many professionals are almost always successful at what they do, they rarely experience failure. And because they have rarely failed, they have never learned how to learn from failure.… [T]hey become defensive, screen out criticism, and put the “blame” on anyone and everyone but themselves. In short, their ability to learn shuts down precisely at the moment they need it the most.192 [italics mine] A year or two after Wave, Jeff Huber was running our Ads engineering team. He had a policy that any notable bug or mistake would be discussed at his team meeting in a “What did we learn?” session. He wanted to make sure that bad news was shared as openly as good news, so that he and his leaders were never blind to what was really happening and to reinforce the importance of learning from mistakes. In one session, a mortified engineer confessed, “Jeff, I screwed up a line of code and it cost us a million dollars in revenue.” After leading the team through the postmortem and fixes, Jeff concluded, “Did we get more than a million dollars in learning out of this?” “Yes.” “Then get back to work.”193 And it works in other settings too. A Bay Area public school, the Bullis Charter School in Los Altos, takes this approach to middle school math. If a child misses a question on a math test, they can try the question again for half credit. As their principal, Wanny Hersey, told me, “These are smart kids, but in life they are going to hit walls once in a while. It’s vital they master geometry, algebra one, and algebra two, but it’s just as important that they respond to failure by trying again instead of giving up.” In the 2012–2013 academic year, Bullis was the third-highest-ranked middle school in California.194

It's only in Algebra that two negatives make a positive

mean proportional, i.e., if b and c are two given positive numbers, then x is the mean proportional of b and c if it satisfies the statement “b is to x as x is to c.” Or, in algebra which

False negatives, false positives, the moral algebra of fat men pushed in front of onrushing trolleys. The strident emotional belief that children made you happy, even when all the data pointed to misery. The high-amplitude fear of sharks and dark-skinned snipers who would never kill you; indifference to all the toxins and pesticides that could. The mind was so rotten with misrepresentation that in some cases it literally had to be damaged before it could make a truly rational decision—and should some brain-lesioned mother abandon her baby in a burning house in order to save two strangers from the same fire, the rest of the world would be more likely to call her a monster than laud the rationality of her lifeboat ethics. Hell, rationality itself—the exalted Human ability to reason—hadn’t evolved in the pursuit of truth but simply to win arguments, to gain control: to bend others, by means logical or sophistic, to your will.

According to Thom “coherent systems of catastrophes” (i.e., chreods) con- stellate into structures that become “abstract algebraic entities independent of any substrate.” He furthermore posits that the transformations of our space-time may be directed or “programed” by another “algebraic structure” that is itself outside our space-time entirely (refer to quotation above).

All Protestants are Crypto-Papists,’ wrote the Russian theologian Alexis Khomiakov to an English friend in the year 1846. ‘ . . . To use the concise language of algebra, all the West knows but one datum a; whether it be preceded by the positive sign +, as with the Romanists, or with the negative − as with the Protestants, the a remains the same. Now a passage to Orthodoxy seems indeed like an apostasy from the past, from its science, creed, and life. It is rushing into a new and unknown world.’ Khomiakov, when he spoke of the datum a, had in mind the fact that western Christians, whether Free Churchmen, Anglicans, or Roman Catholics, have a common background in the past. All alike (although they may not always care to admit it) have been profoundly influenced by the same events: by the Papal centralization and the Scholasticism of the Middle Ages, by the Renaissance, by the Reformation and Counter-Reformation, and by the Enlightenment. But behind members of the Orthodox Church — Greeks, Russians, and the rest — there lies a very different background. They have known no Middle Ages (in the western sense) and have undergone no Reformations or Counter-Reformations; they have only been affected in an oblique way by the cultural and religious upheaval which transformed western Europe in the sixteenth and seventeenth centuries. Christians in the west, both Roman and Reformed, generally start by asking the same questions, although they may disagree about the answers. In Orthodoxy, however, it is not merely the answers that are different — the questions themselves are not the same as in the west. (p.1–2)