How computers get it wrong: 2+2 = 5 - Tony Mann

TL;DR

Computers have progressed from making errors in calculations to now having the ability to recognize speech and faces, leading to new kinds of errors.

Transcript

good evening and welcome to Gresham College and a very special world and to anybody who's come here for the first time computers are wonderful machines they perform complex calculations from credibly quickly and these often directly improve the quality of our lives for example in heart pacemakers which maintain the health of about 3 million people ... Read More

Key Insights

• 😯 Computers have evolved from being human calculators to complex machines capable of speech recognition, face detection, and other intelligent tasks.
• 🦺 Error checking and redundancy have been important techniques to ensure accuracy in calculations and safety-critical systems throughout history.
• 🥺 Computers have finite storage capacity, leading to rounding errors and overflow in arithmetic calculations.
• 😯 As computers become more advanced in tasks like speech recognition and face detection, new kinds of errors can arise that are different from traditional mathematical errors.

Questions & Answers

Q: How did astronomer royal Nevil Maskelyne ensure accuracy in the calculations performed by human computers in the 18th century?

Nevil Maskelyne arranged for calculations to be performed by two different computers and compared the results. If they agreed, the calculation was accepted. If they disagreed, a mistake was identified, and the calculation was reviewed.

Q: How do computers handle arithmetic calculations with limited storage capacity?

Computers represent numbers using a finite number of digits, which means they can only represent a limited range of numbers. This can lead to rounding errors and overflow, where the intended result exceeds the computer's capacity to represent the number accurately.

Q: Can you explain the concept of two's complement arithmetic in computer systems?

Two's complement arithmetic is a way to represent negative numbers in binary form. The first digit of a binary number represents the sign, with 0 indicating a positive number and 1 indicating a negative number. By using this representation, computers can perform arithmetic operations on integers, including multiplication and addition.

Q: How do errors in computer arithmetic affect safety-critical systems?

Errors in computer arithmetic can have serious consequences in safety-critical systems like aircraft control or medical devices. To mitigate the impact of errors, multiple redundant computers may be used, and a voting system can be implemented to ensure that the majority calculation prevails.

Summary & Key Takeaways

• Computers have greatly improved our lives through their ability to perform complex calculations quickly and accurately.

• In the 18th century, computers were human beings who performed calculations for tasks like determining longitude at sea, and they would always double-check each other's work to ensure accuracy.

• Today, computers can still make errors in arithmetic due to finite storage capacity, rounding errors, and the representation of whole and fractional numbers.