The applications of non-euclidean distance | Metric Spaces

The video explores the concept of distance beyond Euclidean space, discussing various metrics like taxicab and maximum metrics. It highlights real-world applications in digital communications, crime solving, and chess. The video also explains the requirements for a valid metric and introduces non-metric distance functions. Advanced concepts like the Hamming distance and its applications in information theory are covered, emphasizing the importance of metrics in space-time and relativity.

How would light behave differently if we lived in a hyperbolic space?

• It would travel in straight lines.

• It would curve more than in Euclidean space.

• It would not be affected at all.

• It would travel faster than in Euclidean space.

In chess, what is the minimum number of moves a king needs to travel between two squares?

• The number of turns needed.

• The number of pieces in between.

• The number of diagonal moves required.

• The number of squares between them.

What is a key requirement for a function to be considered a distance function?

• It must satisfy the triangle inequality.

• It must be zero for different points.

• It must always be negative.

• It must be asymmetric.

What is a metric in the context of distance?

• A function that measures time.

• A function that measures area.

• A function that defines distance between two points.

• A function that calculates speed.

Which metric is used to estimate travel distance in a city with a grid layout?

• Euclidean metric

• Taxicab metric

• Maximum metric

• Discrete metric

What is the maximum metric used for in chess?

• Determining the number of moves for a king.

• Calculating the shortest path for a knight.

• Finding the distance for a bishop.

• Measuring the area of the board.

Which metric is used to calculate the number of moves a king needs to reach a square in chess?

• Taxicab metric

• Euclidean metric

• Maximum metric

• Discrete metric

What does the discrete metric define the distance between two points as?

• The sum of their coordinates.

• Always 1 unless they are the same point.

• The product of their coordinates.

• The difference in their coordinates.

What is the Hamming distance used for?

• Measuring the area of a triangle.

• Calculating the number of errors in binary strings.

• Measuring the distance between two cities.

• Determining the shortest path in a maze.

How is the distance between two binary strings determined using the Hamming distance?

• By counting the number of differing bits.

• By measuring the length of the strings.

• By calculating the sum of the bits.

• By counting the number of matching bits.