Isidore Nabi on the Tendencies of Motion
In 1672 the First International Conference on the Trajectories of Bodies was convened in order to organize a concerted systems approach to the problem of motion. This was made necessary on the one hand by the widespread observation that objects move, and on the other by the currency of extravagant claims being made on the basis of an abstracted extrapolation of the motion of a single apple. Practical applications related to our peacekeeping mission were also a consideration.
The organizing committee realized that a unified interdisciplinary approach was required in which the collection of data must be looked at over as wide a geographic transect as possible, ancillary information must be taken without prejudice on all the measurable properties of the objects, multiple regression and principal factor analysis applied to the results, and the nature of motion then assigned to its diverse causes, as observation and analysis dictated.
It was further agreed that where alternative models fit the same data, both were to be included in the equation by the delta method of conciliatory approximation: let M be the motion of a body as function F(X1, X2, ...) of the variables Xi (parametric variables of state, such as the location, velocity, mass, color, texture, DNA content, esterase polymorphism, temperature, or smell of M), and let M1 = F1(X1, X2, X3, ...) be an alternative model that fits the data more or less equally well. Then (M1, M2) = d F1(X1, X2, X3, ...) + (1-d) F2(X1, X2, X3, ...) is the conciliated systems model. The value of d is arbitrary and is usually assigned in the same ratio as the academic rank or prestige of its proponents. Similarly, when dichotomous decisions arose, such as whether to include only moving objects or to also allow those at rest in the regression, both of the alternative modes were followed and then combined by delta conciliation.
A total of 100,023 objects were examined, measured, and used in the statistical analysis. From these we calculated 100 main effects, 49,500 pairwise interaction terms, 50,000 three-way, and 410 four-way interaction coefficients, leaving 13 degrees of freedom for error variance. The data and coefficients have been deposited in the British Museum and may be published someday. Sample data are shown in Tables 1-1984.
Some of the objects were Imperial Military Artifacts (IMAs), such as cannonballs. Since their tendencies of motion were similar to those of non-IMAs and were independent of the nature of the target (the variance caused by schools, hospitals, and villages all had insignificant F values), this circumstance need not concern us further. The IMAs were relevant only in that their extensive use in noncooperative regions (NCRs) provided data points that otherwise would have required Hazardous Information Retrieval (HIR), and that their inclusion in the study prevented Un-Financed Operations (UFOs).
The motion of objects is extremely complex, subject to large numbers of influences. Therefore further study and renewal of the grant are necessary. But several results can be reported already, with the usual qualifications.
1. More than 90 percent of the objects examined were are rest during the period of observation. The proportion increased with size and, in the larger size classes, decreased with temperature above ambient at a rate that increased with latitude.
2. Of the moving objects, the proportion moving down varied with size, temperature, wind velocity, slope of substrate if the object was on a substrate, time of day, and latitude. These accounted for 58 percent of the variance. In addition, submodels were validated for special circumstances and incorporated by the delta method in the universal equation:
- Drowning men moved upward 3/7 of the time, and downward 4/7.
- Apples did indeed drop. A stochastic model showed that the probability of apple drop increases through the summer and increases with the concentration of glucose.
- Plants tend to move upward very slowly by growth most of the time, and downward rapidly occasionally. The net result is a mean tendency downward of about .001 percent +/- 4 percent.
- London is sinking.
- A stochastic model for the motion of objects at Wyndam Wood (mostly birds, at the .01 level) shows that these are in fact in a steady state except in late autumn, with upward motion exactly balancing downward motion in probability except on a set of measure zero. However, there was extreme local heterogeneity with upward motion predominating more the closer the observer approached, with a significant distance x observer interaction term.
3. Bodies at rest remain at rest with a probability of 0.96 per hour, and objects in motion tend to continue in motion with a probability of 0.06.
4. For celestial bodies, the direction of movement is influenced by proximity to other bodies, the strength of the interaction varying as the distance to the -1.5+/-.8 power.
5. A plot of velocity against time for moving objects shows a decidedly non-linear relation with very great variation. A slope of 32ft/sec/sec is passed through briefly, usually 1-18seconds after initiation of movement, but there is a marked deceleration prior to stopping, especially in birds.
6. For 95 percent +/- .06 percent of all actions, there is a corresponding reaction at an angle of 175 +/- 6 degrees from the first, and usually within 3 percent of the same magnitude.
7. On the whole, there is a slight tendency for objects to move down.
8. A general regression of motion was computed. Space considerations preclude its publication.
9. In order to check the validity of our model, a computer simulation program was developed as follows: the vector for velocity of motion V was set equal to the multiple regression expression for all combinations of maximum and minimum estimates of the regression coefficients. Since we had a total of 100,010 such parameters, there were 2 to the power of 100,010 combinations to be tested, or about 1030,000. For each of these, the error terms were generated from a normal random variable generator subroutine (NRVGS). Finally, a statistical analysis of the simulated motions was tested for consistency with the model. Computations are being performed by the brothers of the monastic orders of Heteroscedastics and Cartesians, each working an abacus and linked in the appropriate parallel and serial circuits by their abbots. We have already scanned 105 combinations, and these are consistent with the model.
Acknowledgement. This work was supported by the East India Company.
From The Dialectical Biologist (Levins and Lewontin)