When a mathematician tries to explain Ramsey theory in a sentence, the result is something like this: "There is always order in a disorderly system that is big enough." As a layman who has spent years living in and exploring such systems I’d say there is some truth in the above but it is not "the truth, the whole truth and nothing but the truth." Let us take for example the so called Happy Ending Problem:
Within any 5 points in the plane that are in general position (i.e. points such that there are no 2 of them coinciding and no 3 of them on a straight line) one can always find 4 that are vertices of a convex quadrilateral.
Within any 5 points in the plane that are in general position (i.e. points such that there are no 2 of them coinciding and no 3 of them on a straight line) one can always find 4 that are vertices of a convex quadrilateral.
Within a set of 5 points in general position we can easily find a convex quadrilateral. What is harder to find is the following:
1. After our mind’s eye adjusts to the existence of the convex quadrilateral it stops seeing the points but only sees the quadrilateral. In other words, we accept the order as a given, not as what it really is – a result of special interrelations of many special points. In the same manner we see our economy as a child of the Law (a top-down approach) but not as a child of the efforts of millions of free individuals (a bottom-up approach). However, the truth about the Law is that it only works where it was spontaneously created by the free little points and does not work where it was consciously forced on the points by the big quadrilaterals.
2. Neither the points (the creators of order), nor the quadrilaterals (the symbols of order), nor the order-admirers from higher dimensions, can easily see that the same points may build other convex quadrilaterals. In other words, the same points may build another order that is as logical and legal as the one already established.
1. After our mind’s eye adjusts to the existence of the convex quadrilateral it stops seeing the points but only sees the quadrilateral. In other words, we accept the order as a given, not as what it really is – a result of special interrelations of many special points. In the same manner we see our economy as a child of the Law (a top-down approach) but not as a child of the efforts of millions of free individuals (a bottom-up approach). However, the truth about the Law is that it only works where it was spontaneously created by the free little points and does not work where it was consciously forced on the points by the big quadrilaterals.
2. Neither the points (the creators of order), nor the quadrilaterals (the symbols of order), nor the order-admirers from higher dimensions, can easily see that the same points may build other convex quadrilaterals. In other words, the same points may build another order that is as logical and legal as the one already established.
Whereas in the first red order everybody is behind the wall (or guarding it), in the other versions of order (blue and green) there are free points outside the wall. In a nutshell,
We think of the order not as being a result of our activities, nor as one of the many possible orders, but as IT wants us to think about it, i.e. as the ONLY alternative to the disorder.
We think of the order not as being a result of our activities, nor as one of the many possible orders, but as IT wants us to think about it, i.e. as the ONLY alternative to the disorder.
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