where G is a constant of proportionality that is an inherent part of the nature of the universe. The theory holds that there is such a value and that, marvelously, using local data that are practical to gather, we can estimate it to whatever accuracy our measurements allow. We may never get it perfectly, but the wonderful fact that Newton pointed out in his transformative Principia (Newton, 1687) is that what we study locally applies universally, thus providing a means of prediction in settings not studied before. The theory doesn’t explain why G has that particular value, if there even is a reason, or why it’s universal, but it’s comforting that we can at least know such underlying parameters of our cosmos (see NOTES). However, even if the cosmos has these sorts of law-like properties, reality is often too complex for us to understand or predict things analytically; that is, by solving equations. For example, when the number of objects such as planets, stars, or galaxies is more than a few, their gravitational motion relative to each other is too complex to solve the way we did in algebra or calculus class. In such situations, one now routinely turns to a computer simulation to find at least a close approximation to the truth (we’ve discussed this here; see The 100-Billion-Body Problem, among other places). For example, at each instant in time, the position and motion of each object is taken and Newton’s law used to predict their positions one timeinterval later. When a precise force like gravity determines a phenomenon, the results will approach that truth asymptotically; that is, the more we increase the complexity of the simulation and the more computer power applied, the closer the result is to that truth. But if the simulated motion doesn’t match what is actually observed, it indicates that something missing or wrong with the theory being simulated. In the case of cosmology, one such hypothesized factor is known as “dark matter.” If the explanation is true, the effect of dark matter on gravitational attraction can be estimated and built into improved models of galactic motion. In this way, simulation can reveal things not previously known and approximate solutions to formal equations that are assumed to be true but can’t be directly solved. Each simulation is a single run through the underlying causal processes; that is, the values of the theoretical parameters controlling the situation. In many situations, even if that process is thought to be deterministic, a random probabilistic “noise” factor may need to be added to represent measurement error. Because of this, each simulation run will be slightly “off,” but after running the same simulation many times the effect of the noise evens out and the average results ever more closely represent what we are trying to model. This is, for example, the way that many weather forecasts are produced, the reason being that the atmosphere is too large and complex to be measured perfectly at any, much less all, times and places.
[1]
Weighted pedigree-based statistics for testing the association of rare variants
,
2012,
BMC Genomics.
[2]
John Novembre,et al.
forqs: forward-in-time simulation of recombination, quantitative traits and selection
,
2013,
Bioinform..
[3]
S. Fullerton,et al.
Phenogenetic drift and the evolution of genotype-phenotype relationships.
,
2000,
Theoretical population biology.
[4]
Brian W. Lambert,et al.
Does history matter?
,
2010
.
[5]
I. Newton.
Philosophiæ naturalis principia mathematica
,
1973
.
[6]
Kenneth M. Weiss,et al.
ForSim: a tool for exploring the genetic architecture of complex traits with controlled truth
,
2008,
Bioinform..
[7]
I. Newton,et al.
The Principia : Mathematical Principles of Natural Philosophy
,
2018
.
[8]
Brian W. Lambert,et al.
What type of person are you? Old-fashioned thinking even in modern science.
,
2014,
Cold Spring Harbor perspectives in biology.
[9]
M. Daly,et al.
An excess of risk-increasing low-frequency variants can be a signal of polygenic inheritance in complex diseases.
,
2014,
American journal of human genetics.
[10]
A. Wagner.
Causal Drift, Robust Signaling, and Complex Disease
,
2015,
PloS one.