A question once confused Confucius

Question

A well known story "Two Children arguing about the sun" (From Lie Zi, ca. 500BC):

On the way traveling to the east, Confucius saw two children were arguing. One child thought that the sun is nearer to us at daybreak and far away from us at noon, because in the morning it is as big as the canopy of a carriage, but at noon only the size of a plate or a bowl. The other contended that the sun was far away at dawn and nearby at midday, because when the sun comes out, it is very cool, but at midday it is as hot as putting your hand in boiling water. Confucius was unable to settle the matter for them. The children laughed at him, saying, "Who decided that you were a wise man?"

I think the second kid should be correct. the question is: what is wrong with the first kid's argument or why the Sun in the morning looks bigger?

Answer 1

The first child's observation is the same as the Moon illusion. There are several explanations for it, but the bottom line is that if you actually measure the angular size of the Sun in the sky, it doesn't vary significantly from daybreak to noon (except perhaps for some refraction effects when it's very close to the horizon).

In fact the distance from a ground-based observer to the Sun varies over the course of a day by only a few thousand kilometers (the diameter of the Earth), which is not enough to be detected. (On top of that, the distance between the Earth and the Sun varies by a few million kilometers over a year, since the Earth's orbit is not perfectly circular.)

As for the second child's observation, it's largely a matter of the angle at which sunlight hits the ground. Consider a section of sunlight that's one square meter in cross sectional area. At noon in the tropics, when the Sun is directly overhead, that sunlight hits one square meter of ground. When the Sun is lower in the sky, that same amount of sunlight is spread over a larger area, so there's less of a heating effect. The same phenomenon, spread over a year rather than a day, explains the seasons. Another effect is that incoming heat from morning sunlight is retained, so the hottest part of the day is typically some time after noon (though local weather variations are also quite significant).

The distance between the Earth and the Sun is a factor in determining how much heat we receive, but it's not a big one. The closest approach (perihelion) is in January, which is during the northern winter.

Answer 2

As insightful as Confucius was, even he was susceptible to optical illusions. There is no physical reason for the sun to appear larger over the horizon than overhead.

http://curious.astro.cornell.edu/question.php?number=230

Answer 3

Both children are wrong for they made two mistakes that are common for people that are bad at logic, i.e. almost all people (including myself): They confused causality with correlation and performed an unfeasible transition.

Neither the size nor heat has a causal link to the distance. For example you could blow air into a balloon, which makes it bigger but its center point doesn't need to get closer to an observer.

Percepting a change in size and heat correlates to a change of distance for close objects. Since the sun is anything but close, a transition of the childrens' experience is unfeasible. The sun is so far away, that its rays come in almost in parallel. Therefore you won't be able to tell a difference in size or heat as long as the distance does not change by a relevant part of the overall distance.