Null Value In Quotes

Ideas about a person's place in society, his role, lifestyle, and ego qualities will lose their hold as the cohesive forces in society disintegrate. Subculture values will proliferate to such a bewildering extent that a whole new class of professionals will arise to control them. Such a Transmutation Technology will deal in fashions, in ways of being. Lifestyle consultants will become the new priests of our civilizations. They will be the new magicians.

And waiting means hurrying on ahead, it means regarding time and the present moment not as a boon, but an obstruction; it means making their actual content null and void, by mentally overleaping them. Waiting, we say, is long. We might just as well—or more accurately—say it is short, since it consumes whole spaces of time without our living them or making any use of them as such. We may compare him who lives on expectation to a greedy man, whose digestive apparatus works through quantities of food without converting it into anything of value or nourishment to his system. We might almost go so far as to say that, as undigested food makes man no stronger, so time spent in waiting makes him no older. But in practice, of course, there is hardly such a thing as pure and unadulterated waiting.

The simple truth is that there is an optimum rate of replacement, a best time for replacement. It would be an advantage for a manufacturer to have his factory and equipment destroyed by bombs only if the time had arrived when, through deterioration and obsolescence, his plant and equipment had already acquired a null or a negative value and the bombs fell just when he should have called in a wrecking crew or ordered new equipment anyway.

When the CERN teams reported a 'five-sigma' result for the Higgs boson, corresponding to a P-value of around 1 in 3.5 million, the BBC reported the conclusion correctly, saying this meant 'about a one-on-3.5 million chance that the signal they see would appear if there were no Higgs particle.' But nearly every other outlet got the meaning of this P-value wrong. For example, Forbes Magazine reported, 'The chances are less than 1 in a million that it is not the Higgs boson,' a clear example of the prosecutor's fallacy. The Independent was typical in claiming that 'there is less than a one in a million chance that their results are a statistical fluke.' This may not be blatantly mistaken as Forbes, but it is still assigning the small probability to 'their results are a statistical fluke', which is logically the same as saying this is the probability of the null hypothesis being tested.

Between concentric pavement ripples glide errant echoes originating from beyond the Puddled Metropolis. Windowless blocks and pickle-shaped monuments demarcate the boundaries of patternistic cycles from those wilds kissed neither by starlight nor moonlight. Lethal underbrush of razor-like excrescence pierces at the skins of night, crawls with hyperactive sprouts and verminous vines that howl with contempt for the wicked fortunes of Marshland Organizers armed with scythes and hoes and flaming torches who have only succeeded in crafting their own folly where once stood something of glorious and generous integrity. There are familiar whispers under leaves perched upon by flapping moths. They implore the spirit again to heed the warnings of the vines and to not be swayed by the hubris of these organizing opportunists. One is to stop moving at frantic zigzags through gridlocked streets, stop climbing ladders altogether, stop relying on drainage pipes where floods should prevail, stop tapping one’s feet in waiting rooms expecting to be seen and examined and acknowledged. Rather, one is to eschew unseemly fabrications and conceal oneself beneath the surface of leaves—perhaps even inside the droplets of dew—one is, after all, to feel shameful of the form, of all forms, and seek instead to merge with whispers which do not shun or excoriate, for they are otherwise occupied in the act of designating meaning. Yet, what meaning stands beyond the rectitude of angles and symmetry, but rather in wilds among agitated insects and resplendent bogs and malicious spiders and rippling mosses pronouncing doom upon their surroundings? One is said to find only the same degree of opportunism, and nothing greatly edifying that could serve to extend beyond the banalities of self-preservation. But no, surely there is something more than this—there absolutely must be something more, and it is to be found! Forget what is said about ‘opportunism’—this is just a word and, thusly, a distraction. The key issue is that there are many such campaigns of contrivance mounted by the taxonomic self-interest of categories and frameworks ‘who’ only seek primacy and authority over their consumers. The ascription of ‘this’ may thusly be ascribed also with that of ‘this other’ and so it cannot be ‘that precisely’ because ‘this’ contradicts another ‘that other’ with which ‘this other’ surely claims affiliation. Certainly, in view of such limiting factors, there is a frustration that one is bound to feel that the answers available are constrained and formulaic and insufficient and that one is simply to accept the way of things as though they are defined by the highest of mathematics and do not beget anything higher. One is, thusly, to cease in one’s quest for unexplored possibility. The lines have been drawn, the contradictions defined and so one cannot expect to go very far with these mathematical rules and boundaries in place. There are ways out: one might assume the value of an imaginary unit and bounce out of any restrictive quadrant as with the errant echoes against the rippling pavement of this Puddled Metropolis. One will then experience something akin to a bounding and rebounding leap—iterative, but with all subleaps constituting a more sweeping trajectory—outward to other landscapes and null landscapes, inward through corridors and toward the centroid of circumcentric chamber clusters, into crevices and trenches between paradigms and over those mountain peaks of abstruse calculation.

Unlike in most programming languages, SQL treats null as a special value, different from zero, false, or an empty string.

The values in any primary key must be unique and non-null so you can use them to reference individual rows, but that’s the only rule—they don’t have to be consecutive numbers to identify rows.

2. "HOW COULD anything originate out of its opposite? For example, truth out of error? or the Will to Truth out of the will to deception? or the generous deed out of selfishness? or the pure sun-bright vision of the wise man out of covetousness? Such genesis is impossible; whoever dreams of it is a fool, nay, worse than a fool; things of the highest value must have a different origin, an origin of THEIR own—in this transitory, seductive, illusory, paltry world, in this turmoil of delusion and cupidity, they cannot have their source. But rather in the lap of Being, in the intransitory, in the concealed God, in the 'Thing-in-itself— THERE must be their source, and nowhere else!"—This mode of reasoning discloses the typical prejudice by which metaphysicians of all times can be recognized, this mode of valuation is at the back of all their logical procedure; through this "belief" of theirs, they exert themselves for their "knowledge," for something that is in the end solemnly christened "the Truth." The fundamental belief of metaphysicians is THE BELIEF IN ANTITHESES OF VALUES. It never occurred even to the wariest of them to doubt here on the very threshold (where doubt, however, was most necessary); though they had made a solemn vow, "DE OMNIBUS DUBITANDUM." For it may be doubted, firstly, whether antitheses exist at all; and secondly, whether the popular valuations and antitheses of value upon which metaphysicians have set their seal, are not perhaps merely superficial estimates, merely provisional perspectives, besides being probably made from some corner, perhaps from below—"frog perspectives," as it were, to borrow an expression current among painters. In spite of all the value which may belong to the true, the positive, and the unselfish, it might be possible that a higher and more fundamental value for life generally should be assigned to pretence, to the will to delusion, to selfishness, and cupidity. It might even be possible that WHAT constitutes the value of those good and respected things, consists precisely in their being insidiously related, knotted, and crocheted to these evil and apparently opposed things—perhaps even in being essentially identical with them. Perhaps! But who wishes to concern himself with such dangerous "Perhapses"! For that investigation one must await the advent of a new order of philosophers, such as will have other tastes and inclinations, the reverse of those hitherto prevalent—philosophers of the dangerous "Perhaps" in every sense of the term. And to speak in all seriousness, I see such new philosophers beginning to appear.

Here are the falsy values: false null undefined The empty string '' The number 0 The number NaN All other values are truthy, including true, the string 'false', and all objects.

CUSTOM_HASH Function create or replace function custom_hash (p_username in varchar2, p_password in varchar2) return varchar2 is l_password varchar2(4000); l_salt varchar2(4000) := 'XV1MH24EC1IHDCQHSS6XQ6QTJSANT3'; begin -- This function should be wrapped, as the hash algorithm is exposed here.  You can change the value of l_salt or the --method of which to call the DBMS_OBFUSCATOIN toolkit, but you must reset all of your passwords if you choose to do --this. l_password := utl_raw.cast_to_raw(dbms_obfuscation_toolkit.md5 (input_string => p_password || substr(l_salt,10,13) || p_username || substr(l_salt, 4,10))); return l_password; end;   CUSTOM_AUTH Function create or replace function custom_auth (p_username in VARCHAR2, p_password in VARCHAR2) return BOOLEAN is l_password varchar2(4000); l_stored_password varchar2(4000); l_expires_on date; l_count number; begin -- First, check to see if the user is in the user table select count(*) into l_count from demo_users where user_name = p_username; if l_count > 0 then -- Fetch the stored hashed password & expire date select password, expires_on into l_stored_password, l_expires_on from demo_users where user_name = p_username; -- Next, check whether the user's account is expired. If it isn’t, execute the next statement, else return FALSE if l_expires_on > sysdate or l_expires_on is null then -- If the account is not expired, apply the custom hash function to the password l_password := custom_hash(p_username, p_password); -- Finally, compare them to see if they are the same and return either TRUE or FALSE if l_password = l_stored_password then return true; else return false; end if; else return false; end if; else -- The username provided is not in the DEMO_USERS table return false; end if; end;

The null hypothesis of normality is that the variable is normally distributed: thus, we do not want to reject the null hypothesis. A problem with statistical tests of normality is that they are very sensitive to small samples and minor deviations from normality. The extreme sensitivity of these tests implies the following: whereas failure to reject the null hypo thesis indicates normal distribution of a variable, rejecting the null hypothesis does not indicate that the variable is not normally distributed. It is acceptable to consider variables as being normally distributed when they visually appear to be so, even when the null hypothesis of normality is rejected by normality tests. Of course, variables are preferred that are supported by both visual inspection and normality tests. In Greater Depth … Box 12.1 Why Normality? The reasons for the normality assumption are twofold: First, the features of the normal distribution are well-established and are used in many parametric tests for making inferences and hypothesis testing. Second, probability theory suggests that random samples will often be normally distributed, and that the means of these samples can be used as estimates of population means. The latter reason is informed by the central limit theorem, which states that an infinite number of relatively large samples will be normally distributed, regardless of the distribution of the population. An infinite number of samples is also called a sampling distribution. The central limit theorem is usually illustrated as follows. Assume that we know the population distribution, which has only six data elements with the following values: 1, 2, 3, 4, 5, or 6. Next, we write each of these six numbers on a separate sheet of paper, and draw repeated samples of three numbers each (that is, n = 3). We

safety at the beginning of the program was 4.40 (standard deviation, SD = 1.00), and one year later, 4.80 (SD = 0.94). The mean safety score increased among 10th graders, but is the increase statistically significant? Among other concerns is that the standard deviations are considerable for both samples. As part of the analysis, we conduct a t-test to answer the question of whether the means of these two distributions are significantly different. First, we examine whether test assumptions are met. The samples are independent, and the variables meet the requirement that one is continuous (the index variable) and the other dichotomous. The assumption of equality of variances is answered as part of conducting the t-test, and so the remaining question is whether the variables are normally distributed. The distributions are shown in the histograms in Figure 12.3.12 Are these normal distributions? Visually, they are not the textbook ideal—real-life data seldom are. The Kolmogorov-Smirnov tests for both distributions are insignificant (both p > .05). Hence, we conclude that the two distributions can be considered normal. Having satisfied these t-test assumptions, we next conduct the t-test for two independent samples. Table 12.1 shows the t-test results. The top part of Table 12.1 shows the descriptive statistics, and the bottom part reports the test statistics. Recall that the t-test is a two-step test. We first test whether variances are equal. This is shown as the “Levene’s test for equality of variances.” The null hypothesis of the Levene’s test is that variances are equal; this is rejected when the p-value of this Levene’s test statistic is less than .05. The Levene’s test uses an F-test statistic (discussed in Chapters 13 and 15), which, other than its p-value, need not concern us here. In Table 12.1, the level of significance is .675, which exceeds .05. Hence, we accept the null hypothesis—the variances of the two distributions shown in Figure 12.3 are equal. Figure 12.3 Perception of High School Safety among 10th Graders Table 12.1 Independent-Samples T-Test: Output Note: SD = standard deviation. Now we go to the second step, the main purpose. Are the two means (4.40 and 4.80)

12.2. The transformed variable has equal variances across the two groups (Levene’s test, p = .119), and the t-test statistic is –1.308 (df = 85, p = .194). Thus, the differences in pollution between watersheds in the East and Midwest are not significant. (The negative sign of the t-test statistic, –1.308, merely reflects the order of the groups for calculating the difference: the testing variable has a larger value in the Midwest than in the East. Reversing the order of the groups results in a positive sign.) Table 12.2 Independent-Samples T-Test: Output For comparison, results for the untransformed variable are shown as well. The untransformed variable has unequal variances across the two groups (Levene’s test, p = .036), and the t-test statistic is –1.801 (df = 80.6, p =.075). Although this result also shows that differences are insignificant, the level of significance is higher; there are instances in which using nonnormal variables could lead to rejecting the null hypothesis. While our finding of insignificant differences is indeed robust, analysts cannot know this in advance. Thus, analysts will need to deal with nonnormality. Variable transformation is one approach to the problem of nonnormality, but transforming variables can be a time-intensive and somewhat artful activity. The search for alternatives has led many analysts to consider nonparametric methods. TWO T-TEST VARIATIONS Paired-Samples T-Test Analysts often use the paired t-test when applying before and after tests to assess student or client progress. Paired t-tests are used when analysts have a dependent rather than an independent sample (see the third t-test assumption, described earlier in this chapter). The paired-samples t-test tests the null hypothesis that the mean difference between the before and after test scores is zero. Consider the following data from Table 12.3. Table 12.3 Paired-Samples Data The mean “before” score is 3.39, and the mean “after” score is 3.87; the mean difference is 0.54. The paired t-test tests the null hypothesis by testing whether the mean of the difference variable (“difference”) is zero. The paired t-test test statistic is calculated as where D is the difference between before and after measurements, and sD is the standard deviation of these differences. Regarding t-test assumptions, the variables are continuous, and the issue of heterogeneity (unequal variances) is moot because this test involves only one variable, D; no Levene’s test statistics are produced. We do test the normality of D and find that it is normally distributed (Shapiro-Wilk = .925, p = .402). Thus, the assumptions are satisfied. We proceed with testing whether the difference between before and after scores is statistically significant. We find that the paired t-test yields a t-test statistic of 2.43, which is significant at the 5 percent level (df = 9, p = .038 < .05).17 Hence, we conclude that the increase between the before and after scores is significant at the 5 percent level.18 One-Sample T-Test Finally, the one-sample t-test tests whether the mean of a single variable is different from a prespecified value (norm). For example, suppose we want to know whether the mean of the before group in Table 12.3 is different from the value of, say, 3.5? Testing against a norm is akin to the purpose of the chi-square goodness-of-fit test described in Chapter 11, but here we are dealing with a continuous variable rather than a categorical one, and we are testing the mean rather than its distribution. The one-sample t-test assumes that the single variable is continuous and normally distributed. As with the paired t-test, the issue of heterogeneity is moot because there is only one variable. The Shapiro-Wilk test shows that the variable “before” is normal (.917, p = .336). The one-sample t-test statistic for testing against the test value of 3.5 is –0.515 (df = 9, p = .619 > .05). Hence, the mean of 3.39 is not significantly

different from 3.5. However, it is different from larger values, such as 4.0 (t = 2.89, df = 9, p = .019). Another example of this is provided in the Box 12.2. Finally, note that the one-sample t-test is identical to the paired-samples t-test for testing whether the mean D = 0. Indeed, the one-sample t-test for D = 0 produces the same results (t = 2.43, df = 9, p = .038). In Greater Depth … Box 12.2 Use of the T-Test in Performance Management: An Example Performance benchmarking is an increasingly popular tool in performance management. Public and nonprofit officials compare the performance of their agencies with performance benchmarks and draw lessons from the comparison. Let us say that a city government requires its fire and medical response unit to maintain an average response time of 360 seconds (6 minutes) to emergency requests. The city manager has suspected that the growth in population and demands for the services have slowed down the responses recently. He draws a sample of 10 response times in the most recent month: 230, 450, 378, 430, 270, 470, 390, 300, 470, and 530 seconds, for a sample mean of 392 seconds. He performs a one-sample t-test to compare the mean of this sample with the performance benchmark of 360 seconds. The null hypothesis of this test is that the sample mean is equal to 360 seconds, and the alternate hypothesis is that they are different. The result (t = 1.030, df = 9, p = .330) shows a failure to reject the null hypothesis at the 5 percent level, which means that we don’t have sufficient evidence to say that the average response time is different from the benchmark 360 seconds. We cannot say that current performance of 392 seconds is significantly different from the 360-second benchmark. Perhaps more data (samples) are needed to reach such a conclusion, or perhaps too much variability exists for such a conclusion to be reached. NONPARAMETRIC ALTERNATIVES TO T-TESTS The tests described in the preceding sections have nonparametric alternatives. The chief advantage of these tests is that they do not require continuous variables to be normally distributed. The chief disadvantage is that they are less likely to reject the null hypothesis. A further, minor disadvantage is that these tests do not provide descriptive information about variable means; separate analysis is required for that. Nonparametric alternatives to the independent-samples test are the Mann-Whitney and Wilcoxon tests. The Mann-Whitney and Wilcoxon tests are equivalent and are thus discussed jointly. Both are simplifications of the more general Kruskal-Wallis’ H test, discussed in Chapter 11.19 The Mann-Whitney and Wilcoxon tests assign ranks to the testing variable in the exact manner shown in Table 12.4. The sum of the ranks of each group is computed, shown in the table. Then a test is performed to determine the statistical significance of the difference between the sums, 22.5 and 32.5. Although the Mann-Whitney U and Wilcoxon W test statistics are calculated differently, they both have the same level of statistical significance: p = .295. Technically, this is not a test of different means but of different distributions; the lack of significance implies that groups 1 and 2 can be regarded as coming from the same population.20 Table 12.4 Rankings of

second variable, we find that Z = 2.103, p = .035. This value is larger than that obtained by the parametric test, p = .019.21 SUMMARY When analysts need to determine whether two groups have different means of a continuous variable, the t-test is the tool of choice. This situation arises, for example, when analysts compare measurements at two points in time or the responses of two different groups. There are three common t-tests, involving independent samples, dependent (paired) samples, and the one-sample t-test. T-tests are parametric tests, which means that variables in these tests must meet certain assumptions, notably that they are normally distributed. The requirement of normally distributed variables follows from how parametric tests make inferences. Specifically, t-tests have four assumptions: One variable is continuous, and the other variable is dichotomous. The two distributions have equal variances. The observations are independent. The two distributions are normally distributed. The assumption of homogeneous variances does not apply to dependent-samples and one-sample t-tests because both are based on only a single variable for testing significance. When assumptions of normality are not met, variable transformation may be used. The search for alternative ways for dealing with normality problems may lead analysts to consider nonparametric alternatives. The chief advantage of nonparametric tests is that they do not require continuous variables to be normally distributed. The chief disadvantage is that they yield higher levels of statistical significance, making it less likely that the null hypothesis may be rejected. A nonparametric alternative for the independent-samples t-test is the Mann-Whitney test, and the nonparametric alternative for the dependent-samples t-test is the Wilcoxon

The test statistics of a t-test can be positive or negative, although this depends merely on which group has the larger mean; the sign of the test statistic has no substantive interpretation. Critical values (see Chapter 10) of the t-test are shown in Appendix C as (Student’s) t-distribution.4 For this test, the degrees of freedom are defined as n – 1, where n is the total number of observations for both groups. The table is easy to use. As mentioned below, most tests are two-tailed tests, and analysts find critical values in the columns for the .05 (5 percent) and .01 (1 percent) levels of significance. For example, the critical value at the 1 percent level of significance for a test based on 25 observations (df = 25 – 1 = 24) is 2.797 (and 1.11 at the 5 percent level of significance). Though the table also shows critical values at other levels of significance, these are seldom if ever used. The table shows that the critical value decreases as the number of observations increases, making it easier to reject the null hypothesis. The t-distribution shows one- and two-tailed tests. Two-tailed t-tests should be used when analysts do not have prior knowledge about which group has a larger mean; one-tailed t-tests are used when analysts do have such prior knowledge. This choice is dictated by the research situation, not by any statistical criterion. In practice, two-tailed tests are used most often, unless compelling a priori knowledge exists or it is known that one group cannot have a larger mean than the other. Two-tailed testing is more conservative than one-tailed testing because the critical values of two-tailed tests are larger, thus requiring larger t-test test statistics in order to reject the null hypothesis.5 Many statistical software packages provide only two-tailed testing. The above null hypothesis (men and women do not have different mean incomes in the population) requires a two-tailed test because we do not know, a priori, which gender has the larger income.6 Finally, note that the t-test distribution approximates the normal distribution for large samples: the critical values of 1.96 (5 percent significance) and 2.58 (1 percent significance), for large degrees of freedom (∞), are identical to those of the normal distribution. Getting Started Find examples of t-tests in the research literature. T-Test Assumptions Like other tests, the t-test has test assumptions that must be met to ensure test validity. Statistical testing always begins by determining whether test assumptions are met before examining the main research hypotheses. Although t-test assumptions are a bit involved, the popularity of the t-test rests partly on the robustness of t-test conclusions in the face of modest violations. This section provides an in-depth treatment of t-test assumptions, methods for testing the assumptions, and ways to address assumption violations. Of course, t-test statistics are calculated by the computer; thus, we focus on interpreting concepts (rather than their calculation). Key Point The t-test is fairly robust against assumption violations. Four t-test test assumptions must be met to ensure test validity: One variable is continuous, and the other variable is dichotomous. The two distributions have equal variances. The observations are independent. The two distributions are normally distributed. The first assumption, that one variable is continuous and the other dichotomous,

What does it mean to assign the value null to a variable? How about “We intend to assign an object to this variable at some point, but we haven’t yet.” Now, if you’re scratching your head and saying “Hmm, why didn’t they just use undefined for that?” then you’re in good company. The answer comes from the very beginnings of JavaScript. The idea was to have one value for variables that haven’t been initialized to anything yet, and another that means the lack of an object. It isn’t pretty, and it’s a little redundant, but it is what it is at this point. Just

There are five falsey values in JavaScript: undefined is falsey. null is falsey. 0 is falsey. The empty string is falsey. NaN is falsey.

So, if it’s not actually probable that the true value of a parameter is contained within a given confidence interval, why report it? If it’s not actually highly probable that the null hypothesis is false, why reject it?

The p-value is the probability of obtaining a result equal to or more extreme than what was observed, assuming that the Null hypothesis is true. The conditioning on the Null hypothesis is critical.

duality between p-values and confidence intervals. For the Null hypothesis of no-difference commonly used in controlled experiments, a 95% confidence interval of the Treatment effect that does not cross zero implies that the p-value is < 0.05.

Correlations have a hypothesis test. As with any hypothesis test, this test takes sample data and evaluates two mutually exclusive statements about the population from which the sample was drawn. For Pearson correlations, the two hypotheses are the following: Null hypothesis: There is no linear relationship between the two variables. ρ = 0. Alternative hypothesis: There is a linear relationship between the two variables. ρ ≠ 0. A correlation of zero indicates that no linear relationship exists. If your p-value is less than your significance level, the sample contains sufficient evidence to reject the null hypothesis and conclude that the correlation does not equal zero. In other words, the sample data support the notion that the relationship exists in the population.

The p-value for each independent variable tests the null hypothesis that the variable has no relationship with the dependent variable.

P-values indicate the strength of the sample evidence against the null hypothesis. If it is less than the significance level, your results are statistically significant.

P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is correct.

p-values tell you how strongly your sample data contradict the null.

If the p-value is less than or equal to the significance level, you reject the null hypothesis and your results are statistically significant.

When the p-value is low, the null must go. If the p-value is high, the null will fly.

The effect is the difference between the population value and the null hypothesis value. The effect is also known as population effect or the difference.

A p-value describes the probability of getting data at least as extreme as those observed, if the null hypothesis were true.

The Rosetta Stone of Women’s Behavior By Old, Fat, and Bald BRIFFAULT’S LAW: The female, not the male, determines all the conditions of the animal family. Where the female can derive no benefit from association with the male, no such association takes place. There are a few corollaries I would add: Past benefit provided by the male does not provide for continued or future association. Any agreement where the male provides a current benefit in return for a promise of future association is null and void as soon as the male has provided the benefit (see corollary 1) A promise of future benefit has limited influence on current/future association, with the influence inversely proportionate to the length of time until the benefit will be given and directly proportionate to the degree to which the female trusts the male (which is not bloody likely). Deriving mutual benefits from a relationship is not a bad thing. Where Brokenman and the rest of us men lose the plot is when we expect past benefit provided to the woman to continue generating current or future association (see corollary 1). Loyalty, honor, gratitude, and duty are male values that we men project on women, but which very few, to no, women actually possess. We aren’t born with these values; they are drummed into us from the cradle on by society/culture, our families, and most definitely by the women in our lives (sorry, but that includes you too, Mom). Women get different indoctrination, so they have different values; mostly, for a woman, whatever is good for her and her (biological) children is what is best, full stop. So, do not expect that the woman in your life will be grateful, and sacrifice for you, when you can no longer provide for her and hers. And make no mistake, you have never been, and never will be, part of what is hers. What are hers will be first herself, then her (biological) children, then her parents, then her siblings, and then the rest of her blood relatives. The biological imperative has always been to extend her blood line. It stops there, and it always will.

It’s not comfortable in here. But it’s not not comfortable, either. It’s neutral, it’s the null point on the comfort–discomfort axis, the exact fulcrum, the precise coordinate located between the half infinity of positive comfort values to the right and the half infinity of negative values on the left. To live in here is to live at the origin, at zero, neither present nor absent, a denial of self- and creature-hood to an arbitrarily small epsilon–delta limit.

regression results. Standardized Coefficients The question arises as to which independent variable has the greatest impact on explaining the dependent variable. The slope of the coefficients (b) does not answer this question because each slope is measured in different units (recall from Chapter 14 that b = ∆y/∆x). Comparing different slope coefficients is tantamount to comparing apples and oranges. However, based on the regression coefficient (or slope), it is possible to calculate the standardized coefficient, β (beta). Beta is defined as the change produced in the dependent variable by a unit of change in the independent variable when both variables are measured in terms of standard deviation units. Beta is unit-less and thus allows for comparison of the impact of different independent variables on explaining the dependent variable. Analysts compare the relative values of beta coefficients; beta has no inherent meaning. It is appropriate to compare betas across independent variables in the same regression, not across different regressions. Based on Table 15.1, we conclude that the impact of having adequate authority on explaining productivity is [(0.288 – 0.202)/0.202 =] 42.6 percent greater than teamwork, and about equal to that of knowledge. The impact of having adequate authority is two-and-a-half times greater than that of perceptions of fair rewards and recognition.4 F-Test Table 15.1 also features an analysis of variance (ANOVA) table. The global F-test examines the overall effect of all independent variables jointly on the dependent variable. The null hypothesis is that the overall effect of all independent variables jointly on the dependent variables is statistically insignificant. The alternate hypothesis is that this overall effect is statistically significant. The null hypothesis implies that none of the regression coefficients is statistically significant; the alternate hypothesis implies that at least one of the regression coefficients is statistically significant. The

NAN – ‘not a number’, only applying to numeric vectors. NULL – ‘empty’ value or set. Often returned by expressions where the value is undefined. Inf – value for ‘infinity’ and

It is clear that Bhu Mandala, as described in the Bhagvatam, can be interpreted as a geocentric map of the solar system out ot Saturn. But an obvious and important question is: Did some real knowledge of planetary distances enter into the construction of the Bhu Mandala system, or are the correlations between Bhu Mandala features and planetary orbits simply coincidental? Being a mathematician interested in probability theory, Thompson is better equipped than most to answer this question and does so through computer modelling of a proposed 'null hypothesis' -- i.e., 'that the author of the Bhagvatam had no access to correct planetary distances and therefore all apparent correlations between Bhu Mandala features and planetary distances are simply coincidental.' However, the Bhu Mandala/solar system correlations proved resilient enough to survive the null hypothesis. 'Analysis shows that the observed correlations are in fact highly improbable.' Thompson concludes: 'If the dimensions given in the Bhagvatam do, in fact, represent realistic planetary distances based on human observation, then we must postulate that Bhagvata astronomy preserves material from an earlier and presently unknown period of scientific development ... [and that] some people in the past must have had accurate values for the dimensions of the planetary orbits. In modern history, this information has only become available since the development of high-quality telescopes in the last 200 years. Accurate values of planetary distances were not known by Hellenistic astronomers such as Claudius Ptolemy, nor are they found in the medieval Jyotisa Sutras of India. If this information was known it must have been acquired by some unknown civilization that flourished in the distant past.