On the maximum number of folds of a piece of paper

We argue that a piece of paper, of thickness T and width W, can be folded a maximum number N?=?0.962 ln(f W/T) times, where f is a factor of order unity, determined by mechanical constraints. N typically takes a value of around six.     

The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.     

The requirements of truth and of justification of premisses

Summary The article attempts to give an answer to the question: why for the acceptance of a statementz ₂ implied by another,z ₁, it is required not only thatz ₁ be true but also justified? The application in a given case of the rule allowing to accept a statement implied by another true one is not possible without establishing in an appropriate manner that the statement is true. Practically, therefore, we have to rely in the conditions for the acceptance of a statementz ₂ implied by anotherz ₁ on the manner of acceptance ofz ₁. If we require that this manner of acceptance should guarantee the truth ofz ₁, no special requirement of the truth ofz ₁ is necessary. If the acceptance ofz ₂ implied byz ₁ depends onz ₁ being accepted in a manner which does not ensure the truth ofz ₁ (e. g. by induction), then we have to give up the requirement of the truth ofz ₁. At most, we may prohibit the acceptance ofz ₂ implied byz ₁, inductively justified, if the evidence for the negation ofz ₁ is better than the inductive one forz ₁.     

The occurrence of an increase in correlation by restriction of range

Given three variables,x, y, z, univariate selection onx, usually reduces the correlationr _{y z} . However, in some cases, whenr _{x y} orr _{x z} assumes extreme values,r _{y z} may increase. This reversal is explained by comparison to the effects of suppressor variables and predictors of predictability.     

Making the Quantum of Relevance

Summary  The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → − q) & (q→ − p) or defineable as [(p →− q) & (q →− p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and thus a matter of fact. The two types are therefore diametrically opposed.In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility.To circumvent this undesirable result, I reinterpret E = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν . It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) Δ E Δ t = Δ p Δ q ≥ h’s.     

One Aspect of Hartmann's Review of Human Nature and Enduring Peace

Summary

Eighty Negro boys and girls, ages 3 to 5, were assigned to one of eight conditions. Race of model (Negro vs. white), type of consequence to model (reward vs. punishment), and percent of rewarded or punished responses (20 vs. 80 percent) were varied. The Ss viewed a television tape of a model (M) performing a simple two-choice discrimination task with either verbal reward or verbal punishment administered. After watching M make his choice, the S then made his own choice. When S's choice was the same as M's, imitative behavior was said to have occurred. There were significant effects of both race of M and type of consequence to M. Negro S imitated the white M more than the Negro M and imitated the rewarded M more than the punished M. The punished white M was imitated at approximately the same level as the rewarded Negro M. No significant effects of percent of reinforcement were found. Possible explanations of the experimental results were discussed.     

Immigrant skill utilization in the Canadian labour market: Implications of human capital research

The quantitative significance of the underutilization of immigrant skills may be assessed, albeit imprecisely, in human-capital earnings analysis. Earnings deficits of immigrants may arise from: (a) lower immigrant skill quality, (b) underutilization of immigrant skills, and (c) pay inequities for immigrants doing the same work as native-born Canadians. Consistent with numerous studies, data from the 1996 census micro-data show that underutilization of immigrant skills is significant, though less so than unequal pay within occupations. In 1996 dollars, the total annual immigrant earnings deficit from all three sources was 15.0 billion, of which15.0 billion, of which 2.4 billion was related to skill underutilization, and 12.6 billion was related to pay inequity. Discussion considers adjustments to these estimates, taking account of difficulties measuring the skill levels of occupations and immigrant skill quality. < /div > < div class=Äbstract» < a name=Äbs2» < /a > La signification quantitative de la sous-utilisation des qualifications immigrées peut être évaluée, quoique sans précision, dans l￠analyse humain-capitale de revenus. Les déficits de revenus des immigrés peuvent surgir de: (a) la qualité immigrée inférieure de compétence, (b) sous-utilisation des qualifications immigrées, et (c) injustices de salaire pour des immigrés faisant la même chose fonctionnent les Canadiens indigènesoutenus. Conformé aux nombreuses études, données des micro-données 1996 de recensement prouvent que la sous-utilisation des qualifications immigrées est significative, cependant moins ainsi que le salaire 


 112.6 billion was related to pay inequity. Discussion considers adjustments to these estimates, taking account of difficulties measuring the skill levels of occupations and immigrant skill quality.     

The logic of ability,freedom and responsibility

The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A.     

The relation of multiserial eta to other measures of correlation

Ordinary product-moment correlation and regression methods are frequently not immediately applicable to qualitative data, whereas multiserialr, point-multiserialr, and multiserial eta can be easily applied. The multiserialr is rejected for prediction since it tells us only what the correlationmight be if certain assumptionswere true and if wecould measure what isnot now measured. The point-multiserialr and multiserial eta are identical when the number of categories is two but differ when it is three or greater. The multiserial eta is identical with the product-momentr when categories are assigned scale values equal to their means on the continuous variable. With three or more categories, the point-multiserialr, whichassumes linearity withequal step intervals, is always lower than the multiserial eta, whichforces linearity by adoption ofunequal step intervals based upon difference in criterion attainment. While the multiserial eta expends one degree of freedom with the weighting of each category, this is known and correctable, whereas the vague partial loss of degrees of freedom due to the ordering of categories in the point-multiserial is not correctable.Personnel Research Section, A.G.O.     

Minor Studies of Aggression: V. Strength of Frustration-Reaction as a Function of Strength of Drive

The purpose of this study was to investigate the relative effectiveness of two methods of presenting visualized instruction to Ss and to determine the effectiveness of different types of visuals in facilitating S achievement of different educational objectives. Five hundred twenty Ss participated in the study; each received a pretest, participated in his respective instructional presentation, and received four criterial tests. Analysis indicated that (a) the method of presenting visualized instruction determines the type of visualization most effective in facilitating S achievement of different educational objectives; (b) for facilitating S achievement of certain objectives, color in visuals is an important instructional variable; and (c) not all visuals are equally effective in facilitating S achievement of different educational objectives.     

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

Split identity: intransitive judgments of the identity of objects

Identity is a transitive relation, according to all standard accounts. Necessarily, if x = y and y = z, then x = z. However, people sometimes say that two objects, x and z, are the same as a third, y, even when x and z have different properties (thus, x = y and y = z, but x ≠ z). In the present experiments, participants read stories about an iceberg that breaks into two icebergs, one to the east and the other to the west. Many participants (32–54%, in baseline conditions across experiments) decided that both successors were the original iceberg, despite the different spatial locations of the successors. Experiment 1 shows that this tendency is not due to participants failing to understand both to mean both are simultaneously the original. Similarly, Experiment 2 demonstrates that the tendency is not solely due to their interpreting the question to be about properties of the icebergs rather than about the icebergs themselves. Experiments 3 and 4 suggest, instead, that participants may understand Which is the original? to mean Which, in its own right, is entitled to be the original? Emphasizing entitlement increases the number of seemingly intransitive responses, whereas emphasizing the formal properties of identity decreases them.     

The Point of Scientificity,the Fall of the Epistemological Dominos,and the End of the Field of Educational Administration

The point of scientificity, or pos,represents a place in history whereeducational administration was founded as ascience. A pos creates a field of memoryand a field of studies. A pos isepistemologically sustained in its claim forscientific status by a line of demarcation orlod. A lod is supported by truthclaims based on various forms ofcorrespondence. As these forms have beeninterrogated and abandoned, correspondence hasgiven way to coherentism and finally to testsof falsification. As falsification has shownto contain serious flaws when compared to theactual history of scientific discoveries, theentire project of a distinct and unitaryfield known as educational administration isseriously cast into doubt. Contemporaryexaminations in educational administrationdiscourse show that even when the lod hasbeen undermined by epistemological shifts, theinitial pos has remained to supportclaims regarding the project of a ``science ofleadership.' The analysis contained in thisarticle show, however, that when claims of thelod are demonstrably unsustainable, theinitial pos must be similarly abandoned. With that collapse the concept of a fieldis likewise effaced. The epistemologicalalternative is to envision fields ofstudy which do not require a lod, excepton a longitudinal basis to ascertain whether aresearch program shaped and sustained by it isprogressive or regressive. In short, there areno aprori meta-criteria to separate sciencefrom non-science in educationaladministration.     

A Five‐dimensional Model of Attributes: Some precursors of executive coach selection

The purpose of this study was to specify a set of attributes, identified as important precursors to coach selection. Executive coaching has grown exponentially, but there have been few studies as to the efficacy of coaching, including the factors that influence a manager's choice of coach. This study sought to identify these factors. The 45‐item, online survey produced 267 useable responses. Results of the principal component analysis suggested a five‐factor solution, with women showing a statistically significant preference over men for coaches who have the Ability to Develop Critical Thinking and Action, the Ability to Forge the Coaching Partnership and Coach Experience and Qualifications. The impact of coachee age was not significant in selecting executive coaches. The findings show a statistically significant relationship between coach attributes and the intention to continue with coaching. The implications of these findings for the selection of coaches, and for the coaching profession are discussed.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

On a shortened method of estimation of mental factors by regression

A shortened method of finding the regression for estimation of the scores on mental factors is presented. If the correlations amongn tests are accounted for byr factors, the regression equation involves the inverse of anr ×r matrix instead of the inverse of ann ×n matrix. Whenr is much less thann, there is considerable saving in computational labor. A numerical example is presented to illustrate the method.     

Estimation of other coefficients of correlation from the phi coefficient

Formulas are developed for estimating a point-biserialr or a tetrachoricr from an obtained phi coefficient. The estimate of a tetrachoricr, which is calledr _φ, is shown to be equivalent to that obtained from first-order use of the tetrachoricr series. A tabulation is made of corrections needed to maker _φ equivalent numerically to the tetrachoricr. In spite of its greater generality than estimates of tetrachoricr by previous methods, there are limitations, which are pointed out.     

Valuation Semantics for First-Order Logics of Evidence and Truth

This paper introduces the logic QLET_F, a quantified extension of the logic of evidence and truth LET_F, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LET_F is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLET_F combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.

     

A Study of the Questions of Young Children Concerning Sex: A Phase of an Experimental Approach to Parent Education

Summary

Ninety-six male and female Ss were exposed to a Spanish E speaking Spanish, a Spanish E speaking English, or an Anglo E speaking English, who requested change for a dime. Sex and clothing (well dressed or sloppy) of E were also varied, creating a 3 × 2 × 2 × 2 design. Both helpfulness and language of S served as dependent measures. Spanish Es speaking Spanish were helped the most, and Anglo Es helped the least. Es were helped more when well dressed than when sloppily dressed. A strong modeling effect for language was found—viz., Ss were likely to respond in the language in which they were addressed; however the altruism and language of Ss were not related.     

Differential Prediction of Resilience Among Individuals With and Without a History of Abuse

The authors evaluated the differential relationship between mutuality, hope, and spirituality for predicting resilience among 253 young adult participants (47 men, 206 women; M = 22, SD = 5.7) with a history of abuse (n = 64) and without (n = 189). Backward stepwise multiple regression analyses revealed statistically significant models in populations with a history of abuse (p < .01, R ² = .43) and those without (p < .01, R ² = .36), with no statistical difference in the variance between models (z = 0.51, p = .30). Implications for counselors are provided.