I find that for me, and I get the vibe that for many others as well, there’s often a slight sense of moral superiority happening when conceptual rounding happens. Like “aha, I’m better than you for knowing more and realizing that your supposedly novel idea has already been done”.
If I notice myself having that slight smug feeling, it’s a tip-off that I’m probably rounding off because some part of me wants to feel superior, not because the rounding is necessarily correct.
I may feel smug if the “novel idea” is basically a worse version of an existing one, but there are more interesting possibilities to probe for.
The novel idea is a meaningful extension/generalization of an existing concept. E.g., Riemann --> Lebesgue integration
The novel idea is equivalent to an existing concept but formulated differently. E.g., Newton and Leibniz versions of calculus.
The novel idea is a more detailed explanation of an existing concept. E.g., chemical bonding --> molecular orbital theory.
Less likely to be rounded away:
The novel idea overlaps with existing concepts but is neither a subset nor an extension. E.g., General Relativity and Quantum Mechanics.
The novel idea applies existing concepts to a new domain. E.g., applying information theory to DNA.
The novel idea synthesizes multiple existing concepts into a greater whole. E.g., Darwinian evolution as a combination of Malthusian population dynamics and natural variation.
The novel idea provides a unifying framework for previously disconnected concepts. E.g., Maxwell’s equations unifying electricity, magnetism, and optics.
Nearly all conceptual rounding errors will not be anything as grand as the extreme examples I gave, but often there is still something worth examining.
I find that for me, and I get the vibe that for many others as well, there’s often a slight sense of moral superiority happening when conceptual rounding happens. Like “aha, I’m better than you for knowing more and realizing that your supposedly novel idea has already been done”.
If I notice myself having that slight smug feeling, it’s a tip-off that I’m probably rounding off because some part of me wants to feel superior, not because the rounding is necessarily correct.
I may feel smug if the “novel idea” is basically a worse version of an existing one, but there are more interesting possibilities to probe for.
The novel idea is a meaningful extension/generalization of an existing concept. E.g., Riemann --> Lebesgue integration
The novel idea is equivalent to an existing concept but formulated differently. E.g., Newton and Leibniz versions of calculus.
The novel idea is a more detailed explanation of an existing concept. E.g., chemical bonding --> molecular orbital theory.
Less likely to be rounded away:
The novel idea overlaps with existing concepts but is neither a subset nor an extension. E.g., General Relativity and Quantum Mechanics.
The novel idea applies existing concepts to a new domain. E.g., applying information theory to DNA.
The novel idea synthesizes multiple existing concepts into a greater whole. E.g., Darwinian evolution as a combination of Malthusian population dynamics and natural variation.
The novel idea provides a unifying framework for previously disconnected concepts. E.g., Maxwell’s equations unifying electricity, magnetism, and optics.
Nearly all conceptual rounding errors will not be anything as grand as the extreme examples I gave, but often there is still something worth examining.