Evidence: * In math: proof (nothing else accepted) * In Science, medicine, etc.: replicability, randomized control trial, meta-analysis, systematic review * Elsewhere: chaos; what is acceptable evidence varies based on politics, culture, beliefs, etc. 1
Evidence based on coincidence: antibiotics treat ear infections in children New ear infection rule in many cases: give no antibiotics, just wait! (Note: we did not say no antibiotics at all) optional http://www.parents.com/health/ear-infection/the-new-ear-infection-rules/ So, to provide good evidence we must: show that intervention (antibiotic) indeed has an effect (ear infection gone) AND show that when there is no intervention (no antibiotic given), there is no effect (ear infection persists) this is hard, so 2
So, to provide good evidence we must: show that intervention (antibiotic) indeed has an effect (ear infection gone) AND show that when there is no intervention (no antibiotic given), there is no effect (ear infection persists) IN MOST CASES standard: no effect in 19 out of 20 cases (we will connect this with the so-called p-value) Questions we must ask: Is there evidence? What is acceptable as evidence? What exactly does the evidence show? optional reading: http://www.cbc.ca/news/health/8-glasses-of-water-a-day-an-urban-myth-1.1196386 3
[http://www.nzherald.co.nz/lifestyle/news/ article.cfm?c_id=6&objectid=11749101] 4
Evidence based on personal bias Example on the next page from https://www.theguardian.com/society/datablog/2016/dec/13/europeansmassively-overestimate-muslim-population-poll-shows So, when we poll people on all kinds of things, are we collecting good, accurate evidence? 5
Because it sounds good is not evidence optional reading: http://news.bbc.co.uk/2/hi/health/8132857.stm Evidence based on authority, celebrity, popular culture http://www.macleans.ca/society/dont-blame-gwyneth-paltrow/ 6
and in many cases no evidence at all Major example fake news! If a fact in math depends on previously established facts, where does it all start? axioms axioms we must accept, as there is no way to prove them so, we have to believe! all sciences are based on beliefs 7
Other math statements/objects: algorithms examples: solving an equation ( move terms from one side to another ) finding extreme values (or peaks, tipping points) of a function (or some phenomenon) also Algorithms are mathematical routines that are used, for instance, to extract patterns from large data sets optional reading: http://www.forbes.com/sites/kashmirhill/2012/02/16/howtarget-figured-out-a-teen-girl-was-pregnant-before-her-father-did/ #6091340b34c6 8
Pole = Andrew Pole, Target Statistician Father s reply: The words algebra and algorithm come from the same person Abu Abd Allah Muhammad Ibn Musa al- Khwarizmi (ca 780-850 CE) Persian mathematician, astronomer, astrologer, geographer and author, worked in Baghdad 9
Al-Khwarizmi wrote Book of Completion and Balancing defines algebra (al-jabr subtracting a quantity from one side of the equation and adding it to another) the word algorithm is derived from the latinization of Al-Khwarizmi name, Algoritmi 10
Hidden algorithms algorithms embedded in numbers 11
Your symbol is what s special about credit card numbers? 4128 0033 2019 8008 look at digits in odd positions: 4128 0033 2019 8008 multiply them by 2 8 4 0 6 4 2 16 0 and add digits 31 add digits in even positions 1+8+0+3+0+9+0+8=29 add up the two 31+29 = 60 the sum is always divisible by 10!!! 12
change any one digit 4128 0033 2015 8008 look at digits in odd positions: 4128 0033 2015 8008 multiply them by 2 8 4 0 6 4 2 16 0 and add digits 31 add digits in even positions 1+8+0+3+0+5+0+8=25 add up the two 31+25 = 56 interchange two neighbouring digits 4128 0032 3019 8008 look at digits in odd positions: 4128 0032 3019 8008 multiply them by 2 8 4 0 6 6 2 16 0 and add digits 33 add digits in even positions 1+8+0+2+0+9+0+8=28 add up the two 33+28 = 61 called Luhn algorithm 13
Luhn algorithm is an example of an error detecting code upc code QR code isbn credit card number... challenge create a valid visa credit card number!!! 4500 0301 (Aeroplan Infinite Visa Card) 14
reality reality 15
Serious problems with algorithms and AI (= artificial intelligence): machines learn from humans! optional reading: http://www.cbc.ca/news/technology/algorithms-hiring-bias-ramona-pringle-1.4241031 More examples of algorithms * all of artificial intelligence * encryption/decryption of information sent over internet * driving directions; autopilot * social networks (news, advertising, linking) * search engines * trading (financial markets) 16
Formulas use data to obtain results, hopefully meaningful Wind chill based on air temperature and wind speed (describes feeling of being cold) Humidex based on air temperature and humidity BMI = body mass index UV index intensity of our Sun s radiation which reaches us How to think about a fraction: A B A B if A increases (B fixed), than the fraction increases if A decreases (B fixed), than the fraction decreases but A B if B increases (A fixed), than the fraction decreases A B if B decreases (A fixed), than the fraction increases 17
Example: body mass index BMI = mass [kg] ( height [m]) 2 Of two people with the same mass, the taller one has smaller BMI Of two people of the same height, the heavier one has a larger BMI When numbers make no sense 9-year old girl Ana Optional video: http://www.cnn.com/video/data/2.0/video/us/2014/05/26/mxp-wabc-bmi-school-program-girl-overweight.hln.html 18
According to her school administrators, Ana is overweight NORMAL GROWTH PATTERN FOR KIDS height (m) weight (kg) 1.24 28 1.25 30 1.27 31 1.30 31 1.33 32 BMI 19
Ana: height = 4 ft 1 in = 1.25 m weight = 66 lb = 29.94 kg = 30kg height (m) weight (kg) 1.24 28 1.25 30 1.27 31 1.30 31 1.33 32 BMI BMI = weight in kg divided by height in m squared mass [kg] i.e., BMI = ( height [m]) 2 height (m) weight (kg) 1.24 28 BMI 1.25 30 19.2 1.27 31 1.30 31 1.33 32 20
BMI = weight in kg divided by height in m squared mass [kg] i.e., BMI = ( height [m]) 2 height (m) weight (kg) BMI 1.24 28 18.2 1.25 30 19.2 1.27 31 19.2 1.30 31 18.3 1.33 32 18.1 height (m) weight (kg) BMI 1.24 28 18.2 normal 1.25 30 19.2 overweight 1.27 31 19.2 overweight 1.30 31 18.3 normal 1.33 32 18.1 normal 21
It is well known that patterns of child growth vary significantly there is no simple relation (such as the one expressed in BMI) between height and weight Reasoning based on BMI does not apply to children Evidence: [optional reading: Cogan, Smith, Maine (2008). The risks of a quick fix: a case against mandatory body mass index reporting laws. Eat Disord. 2008 Jan-Feb;16(1):2-13. doi: 10.1080/10640260701771664.] This article describes the state level activity on mandatory BMI reporting, offers numerous arguments against this practice, and suggests an alternative approach to promoting health in youth. Mandatory BMI reporting laws place a new and inappropriate responsibility on the schools. Proponents of such laws imply that BMI reporting will have positive outcomes, yet there is virtually no independent research to support this assumption. The authors argue that these laws could do significant harm, including an increased risk for children to develop eating disorder symptoms. 22
According to her school administrators, Ana is overweight total nonsense, stupid, dangerous! However, New York City Education Department defended their fitness program, saying that it is effective and helps students get healthy on the next slide we will write it as a math formula optional reading: https://ca.style.yahoo.com/many-calories-burn-while-walking-231202871.html 23
Calories per minute = 0.035 B + 0.029 B V 2 B= body mass in kilograms V = velocity in metres per second H = height in metres H Calories per minute = 0.035 B + 0.029 B V 2 B= body mass in kilograms V = velocity in metres per second H = height in metres H the taller you are, less energy it takes how is it reflected in the formula? 24
Good to remember Kcal means kilocalories; so 1 Kcal = 1000 calories BUT NOT when food is concerned: in that case, 1 Kcal = 1 (food) calorie When you travel, keep in mind: EU food labels sometimes use Kcal 25