A Brief History of Time

A Brief History of Time

Imaginary numbers/time Term Analysis

If real numbers run on a left to right axis, imaginary numbers run up and down. They allow for negative answers to multiplication, for example -2 times -2 equals 4, but i2 times i2 equals -4. Scientists use these numbers to deal with difficult mathematics where real numbers won’t do the job, for example calculating the sum over histories of a particle.
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Imaginary numbers/time Term Timeline in A Brief History of Time

The timeline below shows where the term Imaginary numbers/time appears in A Brief History of Time. The colored dots and icons indicate which themes are associated with that appearance.
Chapter 8
The Search for a Unifying Theory of the Universe Theme Icon
Human Curiosity and Ingenuity Theme Icon
...possible path. Scientists know how to measure this, but actually doing the math requires using imaginary numbers . This is a normal mathematical tool, by which numbers can be multiplied against themselves... (full context)
Human Curiosity and Ingenuity Theme Icon
To calculate sum over histories, one must use imaginary time , that is, imaginary numbers to represent time, which clears away any difference between space... (full context)
Human Curiosity and Ingenuity Theme Icon
...on toward the South Pole. The poles are not singularities in this model, which uses imaginary time as the axis from pole to pole, though they may seem like them in real... (full context)
Human Curiosity and Ingenuity Theme Icon
The Danger of Stubbornness  Theme Icon
It seems, there might be no singularities in imaginary time , undoing Hawking’s earlier work. But, singularity theories showed gravity to be so powerful at... (full context)
Chapter 9
The Search for a Unifying Theory of the Universe Theme Icon
Human Curiosity and Ingenuity Theme Icon
To unify gravity with quantum mechanics, one must apply imaginary time . Imaginary time is no different from the dimensions of space. You can go back... (full context)