SUMMARY - Humble Pi_ When Math Goes Wrong in the Real World - Matt Parker

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Here are the key points summarized:

  • In 1981, a walkway collapse at the Hyatt Regency in Kansas City killed over 100 people during a crowded event.

  • The original design had long support rods running the length of the walkways. To ease installation, the rods were split in half and attached to both walkways, overloading the connections.

  • Structural calculations were not redone after this design change. So the upper walkway ended up directly supporting both itself and the lower walkway.

  • During the event, the overloaded bolt connections tore through the support beams, causing both walkways to collapse onto the atrium floor below.

  • An investigation found the original design also did not fully meet building codes. But the accident likely would have been avoided if the original, safer design was built instead of the modified version without re-evaluating structural calculations.

  • It highlights the importance of thoroughly checking designs and calculations, especially after any changes, to catch safety risks, as engineering mistakes can have tragic consequences for structures handling large crowds.

    Here is a summary of the key points:

  • Off-by-one errors are a common type of counting mistake that occurs when someone starts counting at 1 instead of 0.

  • Examples include the "fence post problem" where someone underestimates the number of posts needed, and mistakes made counting music intervals, days, or leap years.

  • Counting from 0 breaks the intuitive link between what is being counted and the total number. This can lead to underestimating or overestimating time periods.

  • Even modern systems like phone company contracts have reportedly made this error by starting countdown periods at day 1 instead of day 0.

  • Such mistakes have been made for over 2000 years, showing how ingrained the tendency is for humans to incorrectly start counts at 1 rather than 0.

  • In legal matters, it is important to clearly define when a time period starts and ends to avoid ambiguity from these types of counting errors. The example given was of a customer disputing an off-by-one error in his phone bill.

So in summary, the passage discusses how off-by-one errors are a common and long-standing type of counting mistake caused by starting counts at 1 instead of 0, with examples of consequences in domains like music, fences, and legal time periods.

Here is a summary of the key points:

  • In 2012, Knight Capital, a financial services firm, experienced a major technical glitch that caused its trading algorithms to buy and sell stocks incorrectly for over an hour.

  • This resulted in erratic price movements and a $461 million loss for Knight Capital in a single day due to the accidental activation of untested software during market hours.

  • The incident highlighted the risks of employing complex automated trading systems and algorithms without sufficient testing and controls. Even minor software bugs can have huge financial consequences at the speeds of modern markets.

  • It showed how easily human and technical errors can interact and snowball due to the interconnected nature of markets and reliance on technology. Automated trading demands very high reliability and control.

  • The incident led to increased regulation and calls for reform to ensure financial technology is properly tested before use in live markets, where failures can significantly impact prices, firms and investor confidence. Oversight and risk management are important given technology's growing role.

In summary, a technical glitch at Knight Capital caused unintended trading losses of $461 million, demonstrating how software errors can wildly impact markets and firms due to automated trading speeds, and the need for robust controls over financial technology.

Here is a summary of the key points:

  • Knight Capital had a software bug in its automated trading system that caused it to make unintended trades, losing the firm $460 million in a day. It was bailed out by other firms who took a majority stake.

  • The 2010 Flash Crash saw the Dow plunge 9% in minutes due to high-frequency algorithms trading erratically in response to a large sale by another trader, underscoring the impact of uncontrolled automated systems.

  • Amazon once had the price of an academic book rise to over $23 million due to an unintended feedback loop between algorithms from two sellers adjusting prices based on each other.

  • These incidents highlight issues that can arise from uncontrolled interactions between automated systems without safety limits, as well as the real-world consequences of even small errors in algorithms. Proper controls and testing are important with complex automated systems.

    Here is a summary of the key points:

  • The Ariane 5 rocket disaster in 1996 was caused by a software error during launch.

  • The rocket's computer tried to copy a 64-bit number into a 16-bit space in memory, overflowing the space and causing a fatal error.

  • This number was related to the rocket's horizontal velocity which had a larger value than anticipated. The software was reused from the Ariane 4 launch system without being properly adapted.

  • The error occurred because of lack of input validation and exception handling in the code. Small changes in requirements were not properly accounted for.

  • The accident highlighted the importance of robust type checking and exception handling when reusing code for new hardware/software configurations. Rigorous testing is needed for any changes.

  • It showed that even small, subtle software errors can have catastrophic consequences in safety-critical systems like rockets. Careful software design and verification are essential for such applications.

    Here are summaries of the phrases in bold:

  • Daylight saving - Refers to adjusting clocks forward or backward by one hour in spring and fall.

  • Deliberately vague - Purposefully unclear or ambiguous, providing a range rather than a specific value.

  • Dice-O-Matic - Coordinates pointing to somewhere in England.

  • Diehard package - Coordinates pointing to somewhere in California.

  • Dow Jones - Coordinates pointing to New York City.

  • Drug trial - Coordinates pointing to somewhere in England or Wales related to drug trials.

  • Electron beam - Coordinates pointing to somewhere in England related to electron beams.

  • Expensive book - Coordinates pointing to somewhere in England related to an expensive book.

  • Explain why - Multiple coordinates pointing to locations in England and US coupled with a phrase about explanations.

  • False positives - Multiple coordinates pointing to locations in England and US related to false positives.

  • Fat-fingers error - Coordinates pointing to locations in England related to typing errors.

  • Feedback loop - Multiple coordinates pointing to locations in England related to feedback loops.

  • Fence post problem - Coordinates pointing to locations in England related to a fence post counting problem.

  • Fenchurch Street - Coordinates pointing to London, related to Fenchurch Street station.

  • Feynman, Richard - Coordinates pointing to locations in England related to physicist Richard Feynman.

  • Fiber-optic cable - Coordinates pointing to locations in England related to fiber optic technology.

  • Flash crash - Coordinates pointing to locations in England related to a stock market crash.

  • Foot doughnut - Coordinates pointing to somewhere in England.

  • Frigorific mixture - Coordinates pointing to somewhere in England.

  • Fuel gauge - Coordinates pointing to somewhere in England related to fuel gauges.

  • Full-body workout - Coordinates pointing to locations in England related to full-body workouts.

  • Functional sausage - Coordinates pointing to somewhere in England related to functional foods.

  • Gene names - Coordinates pointing to somewhere in England related to gene nomenclature.

  • Gates, Bill - Coordinates related to Bill Gates.

  • Gimli Glider - Coordinates in Canada related to a famous glider landing.

  • Good luck - Multiple coordinates in England and US coupled with a phrase about luck.

  • Gregorian calendar - Coordinates in England related to Gregorian calendar reforms.

  • Grime dice - Coordinates in England related to a type of dice.

  • Harrier jet - Coordinates in England related to Harrier military aircraft.

  • Heart attacks - Coordinates in England related to heart health.

  • High-frequency trading - Coordinates in England related to high-frequency financial trading.

    Here is a summary of the details provided:

  • The coordinates usually point to locations in England and are related to topics in various fields like science, technology, history, mathematics, entertainment, sports, transportation, infrastructure, business, finances, government and more.

  • Many entries provide coordinates coupled with a phrase that provides additional context about the topic, like "should open" or "went wrong" or "most important".

  • Some topics are about real world things, people and events while others refer to fictional concepts, people or placeholders like "Null, Steve" or "something else".

  • The locations referenced through coordinates include cities, places and geographical features in England, the United States, Canada, Japan, Washington state and the Pacific ocean.

  • Fields/industries referenced include neuroscience, calendar systems, construction, toys, banking, hotels, aerospace, computing, statistics, games, coin production, mining, transportation, securities/stock trading, mapmaking, residential/retail areas and more.

  • Engineering concepts mentioned are related to structures, materials, algorithms, randomization, failures, accuracy, errors, oscillations and dynamics.

So in summary, the coordinates provided refer to a wide variety of topics from different domains paired with brief descriptive contexts. Most point to locations in England but some refer to places worldwide.

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