Points and lines inside human brains.

Area of Science:

• Neuroscience
• Philosophy of Science
• Geometry

Background:

• The study challenges the validity of Euclidean geometry in describing the physical world.
• It highlights the psychological and neuroscientific basis for human perception of abstract concepts like points and lines.
• Existing scientific models often encounter problems with infinite values, hindering the description of extreme events.

Purpose of the Study:

• To biologically demonstrate the limitations of human knowledge acquisition regarding the external world.
• To propose a novel, biologically tenable geometry that replaces Euclidean concepts.
• To offer a region-based topological account for power laws in neural activity.

Main Methods:

• Analysis of human imagination's tenets (points, lines, infinity).
• Neuroscientific and psychological elucidation of perception.
• Development of a point-free geometrical framework.

Main Results:

• Euclidean points and lines are conceptual devices, not physical realities.
• Scientific descriptions of shapes and trajectories require revision.
• A new geometry based on bounded surface regions is proposed, eliminating infinities.

Conclusions:

• Points, lines, volumes, and infinity are human constructs, not descriptors of reality.
• The proposed region-based geometry offers a more accurate portrayal of the physical world.
• This framework resolves the issue of infinities in scientific equations and enhances understanding of neural activity.