The Controversy of -1/12 and Smooth Regulators

🧮By using smooth regulators, it is possible to regulate infinite sums without throwing away infinity.

🔄Different choices of regulators lead to different values for the sum of the infinite series.

💡The choice of regulator determines the value of the sum, and there are infinitely many regulators that produce a sum of -1/12.

🔎The controversy surrounding the value of -1/12 arises from the use of a sharp regulator, which leads to the appearance of infinity.

📈Using smooth regulators allows for a better understanding of the behavior of infinite sums and their values.

How is it possible for the sum of natural numbers to be -1/12?

—The value of -1/12 arises when using a specific regulator and infinite series. It is a result of the mathematical properties of the sum and the choice of regulator.

Doesn't the sum of natural numbers go to infinity?

—The sum of natural numbers without any regulator indeed goes to infinity. However, by using smooth regulators, it is possible to obtain different values for the sum.

Why is there controversy surrounding the value of -1/12?

—The controversy arises from the use of a sharp regulator, which leads to the appearance of infinity in the sum. However, using smooth regulators allows for a better understanding of the true value of the sum.

Are there other regulators that can produce a sum of -1/12?

—Yes, there are infinitely many regulators that can produce a sum of -1/12. The choice of regulator determines the value of the sum.

What is the significance of the -1/12 sum in mathematics?

—The sum of -1/12 has applications in various areas of mathematics and physics, such as string theory and quantum mechanics. It is a result of the mathematical properties of infinite series and regulators.

00:00Introduction to the controversy surrounding the value of -1/12 in the sum of natural numbers.

02:58Explanation of regulating infinite sums using different smooth regulators.

06:30Demonstration of different regulators and their effects on the sum.

10:03Clarification of the behavior of the sum when using a smooth regulator.

12:04Exploration of the implications and applications of the controversy surrounding -1/12.