Max Born (1882–1970)
Max Born reflecting on the philosophical implications of "Quantum Mechanics and the statistical interpretation of the Wave Function" (His Nobel Prize lecture, 1954):
"I believe that ideas such as absolute certitude, absolute exactness, final truth, etc. are figments of the imagination which should not be admissible in any field of science. On the other hand, any assertion of probability is either right or wrong from the standpoint of the theory on which it is based. This loosening of thinking (Lockerung des Denkens) seems to me to be the greatest blessing which modern science has given to us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world."
Paleoanthropology: Homo erectus and the Limits of a Paleontological Species
Related Posts on this blog:
Fertile Crescent Components Do the Wilson Wakeley Model
Note that in this post "Fertile Crescent Components Do the Wilson . . .", the components are normalized in order to meet the normalization condition of the probability density function. In order to "operate" on population components, the components must be normalized.
In this post, I mention that "To start with, statistically speaking, there will never be a clear horizon for humanness." I add here that humanness could only ever be formulated in terms of the space-time statistics for multiple hominin characteristics.
Mesolithic Western European Hunter Gatherers Partly Descended
from Upper Paleolithic Reindeer Hunters
In this posts, "West Asian", "Northern European" and "South European" components are arranged by major component. Because all ten of the components (entire population) are shown in the plots, the components are inherently normalized. Thus, it is correct to "operate" on the data.
Several "operations" are interesting:
1. Deconvolution of the "West Asian" component from the dataset.
2. Deconvolution of the "South European" component from 1.
In "1", the effect is to shift the populations to the west. In "2", the effect is to shift populations to the north.
Update (February 1, 2014):
This post is a good example of the power of normalization on specific population components in order to focus on specific gene flow processes:
Westward Across the Asian Steppe; Southward Through the Himalayas.
In fact, having now found a good map that shows topology, I would instead name this post something like "North-South Bi-directional Gene Flow by way of Western Afghanistan". Here's the plot:
13: North Kannadi
The analysis focuses on an apparent pattern presented by two components: "East Asian" (lime) and "Northeast Asian" (turquoise), shown at the bottom of the plot, above. These two components are normalized and then arranged in order to show the obviously correlated distributions indicating bi-rectional gene flow between Russia and India. These populations also have quite a lot of "Northern European" ancestry. However, there does not seem to be a correlation of the "Northern European" component distribution with the joint distribution of the other two components. Therefore, it is not included in the normalization. The fact that the "Northern European" component distribution is not correlated would indicate that the arrival of the "North European" component post-dates the normalized north-south bidirectional gene flow process occurring through western Afghanistan.
Update (February 2, 2014): Suggested Reading:
Decoherence and the Transition from Quantum to Classical - RevisitedWojciech H. Zurek