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We often say the universe obeys laws. It is a useful phrase, but it may also be misleading. To say the universe obeys laws is to imagine reality as if it were governed from the
Continue readingThe Universe Does Not Obey Laws. It Preserves Symmetries.
How Much Time Is Concealed Inside This Outcome? is written for philosophy students who are learning to think mathematically—not as technicians, but as interpreters of structure. This book begins with a simple distinction: counting is
Continue readingHow Much Time Is Concealed Inside This Outcome? – The Book
Why Actualization Is Not Creation The advanced student must be careful with the phrase “making history.” It is a beautiful phrase. It is also dangerous. In ordinary language, when we say a person is making
What if mathematics were not merely a subject to pass, but a beauty to love? In e — The Engine of Lawful Becoming, John Rector invites first-year college students into one of the most elegant
Once the numerator has been disciplined and the denominator has been properly constructed as complex, the next mistake becomes almost inevitable. The student forms the quotient—and then immediately tries to collapse it into a single
Once the student understands that bias has direction, a deeper structural question appears. What exactly is the thing toward which a host is biased? If every idea were treated as a single isolated arrow, the
After the student understands tip-to-tail summation, a new temptation appears almost immediately. The student begins to speak as though bias were merely a matter of amount. One person is “very biased.” Another is “slightly biased.”
The ideational side of the denominator is where most students become imprecise again, even after accepting that Expectation is complex. They accept that there is an imaginary component, but they treat it casually. They say
Continue readingTip to Tail: How to Determine Your Own Prejudges
Once the denominator has been established as complex, the next task is to discipline its real component without letting it collapse into ordinary psychology. That collapse happens quickly if the student hears the word expectation
Once the numerator has been hardened, the next temptation is predictable. The student says: fine, Actual is severe, settled, scalar, and positive. So perhaps the denominator should be treated with the same kind of simplicity.