STAR LECTURE 2020 The hidden power of mathS Presented by Matt Parker Organised by: Featuring the Christmas Lectures from The Royal Institution, Great Britain (x+y) n n Message from Σ( n )x = k=0 Chief executive k n-k Science centre Board n-k y Assoc Prof Lim Tit Meng Chief Executive Science Centre Board This will mark the ninth year that the Science Centre Singapore and the Agency for Science, Technology and Research (A*STAR) have come together to bring to Singapore the world-renowned Royal Institution (Ri) Christmas Lectures from the United Kingdom, drawn from a proud English tradition of Science learning since 1825. Singapore students, youths and even adults can explore and take learning beyond the classroom through the STAR Lecture presenter. With positive reviews and feedback gathered from past attendees, we hope that the legacy will continue through this year’s lecture which will adopt a slightly n different format due to the travel restrictions in place in view of COVID-19. This year’s lecture would be recorded both in UK and Singapore before the presentations are combined. Cr Our presenter Matt Parker warns us that Written by our unwavering faith in numbers can lead to disaster when we get the sums wrong. I am sure that Matt will get more people Octave Goh He will decode and celebrate what makes excited about mathematics as he is not only our human minds so unique during this a recreational mathematician but also a Science Educator lecture and help probe the limits of Maths YouTube personality and communicator. Physical Sciences Group and its role in our world. So, be ready for a lecture which will take you on an inspirational, fun and mesmerising journey to reveal the Hidden Power of Maths! 2 STAR LECTURE 2020 STAR LECTURE 2020 3 About the y = mx + c Presenter Message from Matt Parker EXECUTIVE DIRECTOR Presenter for STAR Lecture 2020 A*STAR Graduate Academy Prof LisA Ng Executive Director, A*STAR Graduate Academy Matt Parker is a mathematician and Agency for Science, Technology and Research (A*STAR) entertainer who uses humor to communicate mathematical topics to a worldwide audience through YouTube videos, TV and radio appearances, books and newspaper articles Welcome back to another year of STAR as well as stand-up comedy. Matt originally Lecture! This is the ninth successful year of trained as a high school Mathematics this wonderful partnership between the teacher in Perth, Australia, before moving Agency for Science, Technology and to the United Kingdom. He now gives maths Research (A*STAR) and the Science Centre and physics talks for secondary schools Singapore; with the Royal Institution of students and adult audiences all across the Great Britain. Since it debuted in 2012, this UK and internationally. unique series has been immensely popular with our young audiences over the years. Ultimately, he aims to ‘get more people With this year’s show, we look forward to excited about maths’. He is popular online, unravelling the hidden power of mathematics with his YouTube channel, StandUpMaths, through an exciting variety of science having over 500,000 subscribers, and both another mathematics communicator, Matt experiments and demonstrations. Get an of his videos on the Royal Institution won the 2018 Communications Award of insider’s look at the secret algorithms, rules channel gaining well over 1 million views the Joint Policy Board for Mathematics and patterns controlling all aspects of our each. Together with Victoria (Vi) Hart, (USA). As well as BBC Radio, he is regularly world! found talking about maths on BBC News, Sky News, Channel 4, CBBC and occasionally Our speaker Matt Parker will take you on an writes for The Guardian. Matt Parker has exhilarating journey of discovery to learn also written two bestselling popular science how elements like probability determine books, ‘Things to Make and Do in the Fourth the likelihood of everyday happenings such Dimension’ and ‘Humble Pi’. as volcano eruptions. I encourage you to empower yourselves with the knowledge of mathematics and discover how it affects our future in unimaginable ways. Enjoy the show! 4 STAR LECTURE 2020 σ STAR LECTURE 2020 5 The hidden Probability power of Maths Impossible Unlikely Even Chance Likely Certain 0 1 1-in-6 Chance 4-in-5 Chance Visual Representation of Probability Probability is the branch of mathematics using numerical values to describe how likely an event or proposition is true. The numerical value varies between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. We think our lives unfold thanks to a mix of luck and our own personal choices. However, we tend to overlook the Examples of probability include: layer of mathematics that governs every aspect of our world. • When a fair coin is flipped, the probability of either “heads” or “tails” The “chance” that we often speak of is often related to is 1/2. probability. The “choices” that we make are influenced by computer algorithms. • When rolling a die, the probability of getting a 3 is 1/6. Understanding these aspects helps us make better choices and sort fact from fiction. However, putting too • When drawing a card from a shuffled much trust and getting the sums wrong can lead to deck, the probability of drawing the 1/6 disaster. Aces of Spades is 1/52. 6 STAR LECTURE 2020 STAR LECTURE 2020 7 NORMAL Normal Distribution Distribution Coin flipping is an independent event. It means that the outcome of the 2nd flip is not influenced by the outcome of the 1st flip. Regardless of the result of the 1st flip, the Graph nd probability of the 2 flip to get a “heads” is still 1/2. As we further increase the number of coin flips, the bar chart will start to take the shape of a normal distribution curve: An equation used to calculate probability of an event (A) occurring is: Number of ways Event A can occur Probability of event A = Total number of Possible Outcomes 0.4 So, what will happen if we flip 2 coins? There is a total of 4 possible outcomes as shown in the table below: 0.3 Outcome 1st Flip 2nd Flip 1 “Heads” “Heads” 0.2 34.1% 34.1% 2 “Heads” “Tails” 0.1 2.1% 2.1% 0.1% 0.1% 3 “Tails” “Heads” 13.6% 13.6% 0.0 4 “Tails” “Tails” -3σ -2σ -1σ 0 1σ 2σ 3σ When we represent this probability in the When we increase the number of coin flips form of a bar chart, we get: to 4, the bar chart will then look like this: The normal distribution is a probability function that Probability of all outcomes for Probability of all outcomes for describe how values of a variable are distributed. It is 2 coin flips 4 coin flips symmetrical where most values lie in the middle region and the probabilities for values further from the average 0.5 0.4 taper off equally in both directions. Extreme values in 0.4 0.3 both tails of the distribution are extremely unlikely (e.g. 2 getting 1000 “Tails” in 1000 coin flips). 0.2 Σ l x - µ l 0.2 0.2 The normal distribution fits many natural phenomena = 0.1 (e.g. heights, IQ score, blood pressure), making it one of σ 0.1 the most important probability distributions in statistics. N 0 0 2 “Heads” 1 “Heads” & 1 “Tails” 2 “Tails” 4 “Heads” 3 “Heads” 2 “Heads” 1 “Heads” 4 “Tails” To see the normal distribution in action, you may want to & 1 “Tails” & 2 “Tails” & 3 “Tails” refer to this video: Probability Probability https://youtu.be/Kq7e6cj2nDw 8 STAR LECTURE 2020 STAR LECTURE 2020 9 Applications of Limitations of STATISTICS AND STATISTICS AND Probability Probability Probability is not knowing what will happen, but what is most likely to happen. Type l and Type ll error Predicting volcanic eruptions Understanding the limitations of probability is You’re pregnant crucial to utilising it effectively. One such limitation is known as “Type I and type II error”. Type I error refers to giving a false positive (e.g. telling a patient he has COVID-19 while in reality, he does not have it) while type II error refers to By looking out for these signs, scientist can giving a false negative (e.g. telling a patient he increase their certainty of whether a does not have COVID-19 while in reality he volcano is near eruption and offer more does). accurate predictions. Type l error Such errors can have huge impact in areas like Mount Fuji, an (false positive) Ball touch event data the medical field. An example is given below: active stratovolcano in Japan You’re not Assuming there is an illness that affects 10 When scientists tell governments or the pregnant people out of every 100. The test for such an general public about the potential of a illness has an accuracy of 80% (20% of the time disaster hitting, they often use probabilities. the test result will be incorrect). For volcanos, there are various signs and symptoms scientists look out for prior to their eruption. Signs and symptoms include, but not limited to: Switzerland • Seismic activities: As magma exerts Type ll error pressure on the rocks beneath, the and Albania playing soccer (false negative) rocks crack and make a small Switzerland and Albania playing soccer, Albinfo, licensed under Creative Commons Attribution- ShareAlike 2.5 Generic earthquake Another application of statistics can be Test showing positive Test showing negative • Gas emissions: As magma nears the found in soccer. Soccer teams in the (with COVID-19) (without COVID-19) surface, the pressure it experiences Premier League employs mathematicians Healthy people = 90 18 72 decreases, allowing gases within the to improve the result of the team on the magma to escape playing field.