[S]cientific thought is . . . essentially power-thought--the sort of thought, that is to say, whose purpose, conscious or unconscious, is to give power to its possessor. Now power is a causal concept, and to obtain power over any given material one need only understand the causal laws to which it is subject. This is an essentially abstract matter, and the more irrelevant details we can omit from our purview, the more powerful our thoughts will become. The Scientific Outlook (W.W. Norton & Co., 1931), p. 86.
The left hemisphere is the task hemisphere.
It is given a task or devises a task to be done, and it does it. It seeks a way to do it most efficiently and, therefore, effectively. Hence, science (and industrialization and technology).
The left hemisphere doesn't want to deal with irrelevant details. They slow down the process, so it needs to abstract . . . relentlessly.
Russell's passage later draws a parallel to the economic sphere, pointing out that the cultivator knows every corner of his farm . . . .and makes very little money. Whereas the commodities trader, who knows nothing of the details, makes a lot of money.
More abstraction = more money = more power.
Money is power's master key, Simone Weil observed. Science is power knowledge.
It's a Spiritual Problem, Too
It is "good and right that we want to understand the meaning of everything in our lives. . . The thirst to know the truth in order to welcome it and conform our lives to it is completely in order. But there is also a desire to understand that is a desire for power: taking over, grasping, mastering the situation." Jacques Philippe, Interior Freedom, p. 52.
I found the Russell passage in Understanding Poetry by Cleanth Brooks and Robert Penn Warren (3d ed), p. 22.