Cultivating a State of Mind Where New Ideas Are Born

Metadata

• Author: Henrik Karlsson
• Full Title: Cultivating a State of Mind Where New Ideas Are Born
• Category:#articles
• URL: https://www.henrikkarlsson.xyz/p/good-ideas

Highlights

• In practice, however, what they are referring to as solitude is rather something like “a state of mind.” They are putting themselves in a state where the opinions of others do not bother them and where they reach a heightened sensitivity for the larval ideas and vague questions that arise within them. (View Highlight)
• He is concerned by what he sees as a tacit disdain for the more “feminine side” of mathematics (which is related to what I’m calling the solitary creative state) in favor of the “hammer and chisel” of the finished theorem. By elevating the finished theorems, he feels that mathematics has been flattened: people only learn how to do the mechanical work of hammering out proofs, they do not know how to enter the dreamlike states where truly original mathematics arises. To counteract this, Grothendieck in the 1980s has decided to write in a new way, detailing how the “work is carried day after day […] including all the mistakes and mess-ups, the frequent look-backs as well as the sudden leaps forward”, as well as “the early steps […] while still on the lookout for […] initial ideas and intuitions—the latter of which often prove to be elusive and escaping the meshes of language.” (View Highlight)
• being exceptionally talented and trained was, in the long run, not enough to do groundbreaking work because they lacked the capacity to go beyond the context they had been raised in.

  In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone. (View Highlight)

• There is also a lot of confusion and pursuit of dead ends. Newton looking for numerical patterns in the Bible, for instance. This might look wasteful if you think what they are doing is research. But it is not if you realize that they are building up their ability to perceive the evolution of their own thought, their capacity for attention. (View Highlight)
• One thing that sets these intensely creative individuals apart, as far as I can tell, is that when sitting with their thoughts they are uncommonly willing to linger in confusion. To be curious about that which confuses. Not too rapidly seeking the safety of knowing or the safety of a legible question, but waiting for a more powerful and subtle question to arise from loose and open attention. This patience with confusion makes them good at surfacing new questions. It is this capacity to surface questions that set Grothendieck apart, more so than his capacity to answer them. When he writes that his peers were more brilliant than him, he is referring to their ability to answer questions 1 . It was just that their questions were unoriginal. (View Highlight)
• What solitude gives you is an opportunity to study what personal curiosity feels like in its undiluted form, free from the interference of other considerations. (View Highlight)
• In order to create something, Bergman had to go sub-Bergman, to the place in the mind where no name exists, where nothing is as yet nailed down, where one thing can morph into another, where boundlessness prevail (View Highlight)
• There is a difference between knowing what you need to do (be independent and true to the potential in your ideas) and something else entirely to know how to embody that. Orienting in the right way to your thoughts is a skill. Like all skills, it takes practice. You also need to have a rich mental representation of how it is supposed to feel to embody the state so that you can orient toward that. (View Highlight)
• The zone is a place at the margin of society. But strangely enough, this fragile margin is where the ideas that make our society possible come from. Almost everything that makes up our world first appeared in a solitary head—the innovations, the tools, the images, the stories, the prophecies, and religions—it did not come from the center, it came from those who ran from it. (View Highlight)

---

title: “Cultivating a State of Mind Where New Ideas Are Born” author: “Henrik Karlsson” url: ”https://www.henrikkarlsson.xyz/p/good-ideas” date: 2023-12-19 source: reader tags: media/articles

Cultivating a State of Mind Where New Ideas Are Born

Metadata

• Author: Henrik Karlsson
• Full Title: Cultivating a State of Mind Where New Ideas Are Born
• Category:#articles
• URL: https://www.henrikkarlsson.xyz/p/good-ideas

Highlights

• In practice, however, what they are referring to as solitude is rather something like “a state of mind.” They are putting themselves in a state where the opinions of others do not bother them and where they reach a heightened sensitivity for the larval ideas and vague questions that arise within them. (View Highlight)
• He is concerned by what he sees as a tacit disdain for the more “feminine side” of mathematics (which is related to what I’m calling the solitary creative state) in favor of the “hammer and chisel” of the finished theorem. By elevating the finished theorems, he feels that mathematics has been flattened: people only learn how to do the mechanical work of hammering out proofs, they do not know how to enter the dreamlike states where truly original mathematics arises. To counteract this, Grothendieck in the 1980s has decided to write in a new way, detailing how the “work is carried day after day […] including all the mistakes and mess-ups, the frequent look-backs as well as the sudden leaps forward”, as well as “the early steps […] while still on the lookout for […] initial ideas and intuitions—the latter of which often prove to be elusive and escaping the meshes of language.” (View Highlight)
• being exceptionally talented and trained was, in the long run, not enough to do groundbreaking work because they lacked the capacity to go beyond the context they had been raised in.

  In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone. (View Highlight)

• being exceptionally talented and trained was, in the long run, not enough to do groundbreaking work because they lacked the capacity to go beyond the context they had been raised in.

  In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone. (View Highlight)

• There is also a lot of confusion and pursuit of dead ends. Newton looking for numerical patterns in the Bible, for instance. This might look wasteful if you think what they are doing is research. But it is not if you realize that they are building up their ability to perceive the evolution of their own thought, their capacity for attention. (View Highlight)
• One thing that sets these intensely creative individuals apart, as far as I can tell, is that when sitting with their thoughts they are uncommonly willing to linger in confusion. To be curious about that which confuses. Not too rapidly seeking the safety of knowing or the safety of a legible question, but waiting for a more powerful and subtle question to arise from loose and open attention. This patience with confusion makes them good at surfacing new questions. It is this capacity to surface questions that set Grothendieck apart, more so than his capacity to answer them. When he writes that his peers were more brilliant than him, he is referring to their ability to answer questions 1 . It was just that their questions were unoriginal. (View Highlight)
• What solitude gives you is an opportunity to study what personal curiosity feels like in its undiluted form, free from the interference of other considerations. (View Highlight)
• In order to create something, Bergman had to go sub-Bergman, to the place in the mind where no name exists, where nothing is as yet nailed down, where one thing can morph into another, where boundlessness prevail (View Highlight)
• There is a difference between knowing what you need to do (be independent and true to the potential in your ideas) and something else entirely to know how to embody that. Orienting in the right way to your thoughts is a skill. Like all skills, it takes practice. You also need to have a rich mental representation of how it is supposed to feel to embody the state so that you can orient toward that. (View Highlight)
• The zone is a place at the margin of society. But strangely enough, this fragile margin is where the ideas that make our society possible come from. Almost everything that makes up our world first appeared in a solitary head—the innovations, the tools, the images, the stories, the prophecies, and religions—it did not come from the center, it came from those who ran from it. (View Highlight)