Let them ask you questions and then and only then will you realize how little you know. This has been my life. It's very depressing realizing how little I know. as I have said before in the rush to stuff kids with information we have taught them to avoid the most important element of survival-the power to think. At least this is my case.
But my daughter is different, and thankfully so. So is my son.
Ballet girl asked me: 'How did life begin'. As intriguing as evolutionary biology, it tells you of a journey but not of the origin of the journey, much like physics tells you of the evolution of the entire universe but says nothing about the onset of this evolution. As an applied mathematician, a person who knows a thing or two about dynamics and chaos, I am reluctant to believe that the universe, as complex as it is, has such a simple dynamics that we can track it in time. Similarly, I am skeptical of the linearity exhibited by nature according to the theory of evolution. My main question there is: of all possible solutions to the survival process, why did only a particular subset become realized? What probabilistic law governs that selection?
I later asked myself: Why are he gaseous planets gaseous?
I am also very curious to understand more classifications. Classifications in science to a great extent have been the result of luck and intuition but not necessarily 'science'. Look at Mendeleev. Classification of our senses, for instance, is very misleading because it is incomplete. Classification of plants is equally so, which is the reason I did not biology in elementary school. So, what I would like to do is collect information with Sophia on plants, and see if we can use an algorithm to classify them, and maybe recognize groups that are not 'standard' in some way i.e. see a pattern that has not been listed in the elementary texts.