It is a paradox that reality can be better apprehended by thinking, not about the real world directly, but about simple, pure models that are not real themselves but that capture one dimension of reality better than the messy and confusing real objects.
The Turing machine is not a real computer but a model for real computers. It's a computer in "hyperbolic form". It is not real, yet it is a tool to help us think about some essential aspects of reality. We can understand reality better by starting from that model. The Genesis is not a real account of the start of humanity but a model. It is not real, but it helps us think about some essential aspects of the start of humanity such as all human beings forming a family-like community. Polynomial runtime is not a real execution time but a model. It is not real, but it helps think about the design of efficient computations. Ensoulment at conception is not a real account of the beginning of personhood but a model. The Ising model. The state of nature. Classical mechanics. The free market. Alice and Bob.
All models.
All those models enrich our understanding, but they're also limited. When we use one and are led to exciting insights, it is tempting to give that model a broader scope and view everything through the lens of that particular model, but that's a mistake. We must not lose sight that they are not a catch-all substitute for reality. The risk is that asking the wrong questions about them leads to nonsensical answers or to sterile quests. How is Turing computation affected by the presence of several tapes? How does one make archeological and paleontological finds fit the story of the Creation? Can you reduce runtime from n^{1000} to 2^{100000}n^{999}? What happens to the soul during twinning with late separation or for conjoined twins? Such questions are close to vacuous: by and large, they do not produce new understanding of the real world but only serve to show the limitations of our models. Any question that exploits the aspects of a model that diverge from the real world is of lesser interest at best: it's only about the model, not about the phenomenon that the model is aiming to describe.
To my mind, it is of course of great importance not to get blinded by the beauty of our model, but at the same time it does not rule out quests about the model. These quests can indeed be there to confirm or infirm its validity.
ReplyDeleteIn other words, how could you say that results on the number of tapes in a Turing machine are sterile? That is a blasphemy ;-) !
The usefulness of models is not a paradox. It's a well understood, standard, classical tool both for science and for applications, has been with us for a long time. It's advantages and limitations are well appreciated.
ReplyDeleteSome seconds after finishing reading this post, my mind (after thinking about "Ensoulment at conception" ) took me back to "Brave New World" which we read in the school English class 20 years ago - the book has embryo-splitting - was this the point Huxley was making ? What was it called ? Bok-- something ? ... one Google suggestion later ... Bokanovsky process.
ReplyDeletehttp://en.wikipedia.org/wiki/Bokanovsky%27s_process