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Hiding Behind Abstractions

See also: mind_projection_fallacy

Many people write things that are hard to understand on purpose. This is done, because if no one understands what you write, you don't get criticized. In addition, you appear extremely smart. This was already noted in 1966 by Cornelius Lanczos in his book “The Variational Principles of Mechanics”:

Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman.

In a similar spirit V. I. Arnold noted:

It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: There is a $t_1 <0$ such that the image of $t_1$ under the natural mapping $t_1 \mapsto \text{Petya}(t_1)$ belongs the set of dirty hands, and a $t_{2}, t_{1}<t_{2}\le 0,$, such that the image of $t_2$ under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.

As mathematical formalisms become more and more beautiful, it is increasingly easy to be trapped by the formalism and to become a ‘slave’ to the formalism. We used to be ‘slaves’ to Newton’s laws when we regarded everything as a collection of particles. After the discovery of quantum theory,4 we become ‘slaves’ to quantum field theory. At the moment, we want to use quantum field theory to explain everything and our education does not encourage us to look beyond quantum field theory. However, to make revolutionary advances in physics, we cannot allow our imagination to be trapped by the formalism. We cannot allow the formalism to define the boundary of our imagination. The mathematical formalism is simply a tool or a language that allows us to describe and communicate our imagination. Sometimes, when you have a new idea or a new thought, you might find that you cannot say anything. Whatever you say is wrong because the proper mathematics or the proper language with which to describe the new idea or the new thought have yet to be invented. Indeed, really new physical ideas usually require a new mathematical formalism with which to describe them. This reminds me of a story about a tribe. The tribe only has four words for counting: one, two, three, and many-many. Imagine that a tribe member has an idea about two apples plus two apples and three apples plus three apples. He will have a hard time explaining his theory to other tribe members. This should be your feeling when you have a truly new idea. Although this book is entitled Quantum field theory of many-body systems, I hope that after reading the book the reader will see that quantum field theory is not everything. Nature’s richness is not bounded by quantum field theory

Xiao-Gang Wen

A review for the Americal mathematical Society offered this deep statement in praise of the book: “It is often deeper to know why something is true rather than to have a proof that it is true.” (Indeed, a Fields Medalist once told me that top mathematicians secretly think like physicists and after they work out the broad outline of a proof they then dress it up with epsilons and deltas. I have no idea if this is true only for one, for many, or for all Fields Medalists. I suspect that it is true for many.)

Quantum Field Theory in a Nutshell by A. Zee

Further Reading

causes/hiding_behind_abstraction.1509445683.txt.gz · Last modified: 2017/10/31 11:28 (external edit)