Mathematicians From England

"The cause of undertaking a work of this kind was a good will in this scribling age not to do nothing, and a disproportion in the powers of my mind, nothing of mine owne invention being able to passe the censure of mine owne judgement, much less, I presumed, the judgement of others.... If thy stomacke be so tender as thou canst not disgest Tacitus in his owne stile, thou art beholding to one who gives thee the same food, but with a pleasant and easie taste."

"We don’t just want women in tech – we want women leading tech."

"STEM is about changing lives and making a difference, and that’s what we want young women to see."

"There are many people who don’t believe that people like me exist."

"is much more common than classical . It is estimated to affect about one in every three or four hundred of the general population. More than half a million people in the United Kingdom have some kind of disorder on the autistic spectrum, with over 200,000 of them having Asperger's syndrome. Disorders of the autistic spectrum are found much more often in men than in women, although this may be because women are better at compensating for some of their more noticeable features, being better at social relationships and less likely to exhibit narrow interest patterns."

"Despite poor eyesight, Kepler was one of the pioneers of research into optics. He found a good approximation to the . Descartes, the discoverer of the precise law, said that Kepler was his true teacher in optics, who knew more about this subject than did any of those who preceded him. This research was published in his of 1611, which also contained an account of a new . Towards the end of his life he wrote a small work on the gauging of wine casks, which is regarded as one of the significant works in the ."

"Although the main field of Laplace's research was , he also made important contributions to the and . In his (Analytical theory of probability) of 1812 he summarized, in a masterly introduction, all that was then known in the area of probability and its applications. This work introduces the technique known later as the Laplace transform, a simple and elegant method of solving s."

"Although the theory of s (s where the underlying space is a and the group operations are ) goes back to around 1870 the theory of topological groups in a more general sense seem not to have been considered until 1925 when and , independently, made the basic definitions, rather in the spirit of , and since then this too has developed into a major branch of . It was Weil (1937) who wrote the first definitive study of s and applied the theory to both s and topological groups. However the basic idea was already emerging early in the century, indeed the concepts of and were well understood by Weierstrass and by Cauchy before him."

"Communication is not a one-way process. It's not just telling people things. ...[T]he first rule of communication is to shut-up and... just listen... and good doctors will do that. ...Good doctors will listen and explore the person's values and concerns, and... explore to what extent... that person want[s] to be guided... to be told what to do... and that's... appropriate to want... guidance from a trusted source. ...And ...make sure ...before ...that stage, you have ...genuinely laid out the options in a way that gives it balance. You haven't tried to manipulate them... into a particular direction. ...Very difficult ...but ...a worthy objective, and... having done that, it's perfectly reasonable to... then, give advice."

"Probability was only invented a few hundred years ago. It's not a natural way to think at all. It's extremely difficult and complex. Anything that can help people do it, is of benefit."

"[W]e tend to think... of something that's going to happen... soon, or is well understood as risk, but if we're talking about what will happen in the world in ten years time. Who's going to start putting chances on this. You'd be... deluded... There's much... deeper uncertainty or... radical uncertainty..."

"There is a way... which comes from economics and social science. It was developed by... Frank Knight, and Keynes used this... The distinction between risk and uncertainty... [R]isk is about things... we... understand... known unknowns, to use Donald Rumsfeld's... great phrase... [something] we can put numbers on, things within... circumscribed situations... A lot of medicine is like this... repetition, a lot of data. ...[I]nsurance is like this ...We know roughly what the chances are, and we can talk about the numbers. Uncertainty is when... we don't know the numbers, or... deeper... we don't even know... the problem... the options... the possible outcomes..."

"We know from studying and going... back to Geoffrey Rose's idea that the biggest impact on public health... is not by picking out the real high-risk people and maybe stopping them drinking. It's by reducing the exposure of the vast mass of people at intermediate risk. So... the biggest impact on public health would be if everybody drank a little bit less... But the problem... is the Rose paradox... the very people you want to change the behavior [of] are the ones who don't see why they should change their behavior, because the impact is minimal. They won't notice the benefits. You're asking them to give up something they enjoy for the benefit... they will... never notice... [I]t's only noticeable when... multiplied... ten million times./* Understanding Risk (Mar 24, 2020) */Ref: "a large number of people at a small risk may give rise to more cases of disease than the small number who are at"

"[I]n medicine... ... not manipulation or coercion, is when... as a doctor or... authority, you genuinely believe that this action is in the person's best interests, but they don't... want to do it. ...How do you make that an ethical persuasion? It's based on... two things, first... respecting the autonomy of the individuals, that they can refuse... no matter what, respect their ability to choose... the other thing is your authenticity, your integrity, that... you are doing this on behalf of that individual, for their best interest; not... to keep your clinic numbers up or to stop this person being a nuisance...[etc.]"

"The worst... medical care would be just say, "Oh well, it's completely up to you. I'm not going to give you any advice." Well... you're the guy who knows... [the] supposed... expert. ...I want your advice. ...[T]his is an invaluable process which I hope all medical students have been taught. How to engage... It's not . ...Paternalism is ...immediately saying, "...I think you should do this," without really allowing that person a full autonomy to choose."

"These s that epidemiologists report, as Michael has so ably shown, tend to get... badly reported in the newspapers. So this... in the '... "Less Meat, More Veg is the Secret for Longer Life" which... probably could well be the case, but the way they report it... They said that if we cut down the amount of red meat... 10% of all deaths would be avoided. ...So 10% of us will live forever eating nuts. This is not true. ...[T]hey're talking about relative risk, but they don't understand."

"If you go to the English Parachuting Association web site... you find this lovely Excel spreadsheet which has got all the deaths... [F]or the last 20 years, 4.6 million jumps, 48 deaths... or 10 in a million. On average, with going up in a plane... I thought there's around 7 or 10 in a million chances of me dying. There's 50 million people in England and Wales... Every day 50 of them have accidental or violent deaths... not to do with their health. So a couple are murdered a day, a few are run over, some people fall off ladders, etc... So that's 1 in a million... Our daily dose of acute risk is a [a 1 in a million chance of dying]. So jumping out of a plane is only about a week's worth. ...[I]n terms of overall mortality... at my age, 59, it's 7,000 micromorts a year in terms of my chances of dying. So an extra 7 or 10 on top of that... [I]t's worthwhile doing... it once....So I did it [parachuted], and I survived."

"So far, these vaccines have shown themselves to be extraordinarily safe."

"Currently, there are few books that can help at school level with communication issues in statistics and DS. One exception is Spiegelhalter, a masterpiece in how to communicate easy, not-so-easy, hard, and very difficult topics in statistics. It uses real-world problem solving as a starting point for introducing statistical ideas. One reviewer of the book suggested “it should be compulsory reading for teachers and students of statistics (indeed all subjects that use or produce data), in schools, colleges and universities.” Although the Spiegelhalter book is a great example of communication, the paucity of material in this area shows that there is an urgent need to develop a pedagogy and a corresponding range of resources in writing and communicating statistics and DS."

"Randomised trials have proved the effectiveness of some Covid treatments and saved vast numbers of lives... also showing... overblown claims about treatments... as hydroxychloroquine and , were incorrect."

"So it's a different sort of risk. These are chronic risks. ...[T]hings that... if you carry on with them, are likely to shorten your life. So how can we express these... [T]hese are the ones that newspapers tend to get terribly wrong."

"When epidemiologists... do studies, when they follow lots of people for years, they measure the effects of various habits, in terms of s. This is what it does to your hazard every year. So if you have a daily sausage or a bacon sandwich, this goes up by about 10%, a fixed amount... as your... annual risk. 10% increase in your annual risk of death, of not making it to your next birthday."

"Life-expectancy reduced by 1 year = about 30 minutes off your life expectancy for each day with the habit = 1"

"[W]e can compare hang gliding... taking heroin... health treatments, with standing next to Hiroshima. We're deliberately... using these numbers to tell uncomfortable stories."

"Psychologists got hold of this lovely idea of why we're trying to do it. I don't care what people do, so I'm not trying to change what they do, particularly. ...It would be nice if they could remember it... get the gist of something... learn something, but I don't even care too much about that. Psychologists have got this great scheme of what, perhaps, we're really trying to do, which is trying to breed some immunity to misleading anecdote, which is... the fact that we're so influenced by idiotic stories we hear on the web, or from our friends and neighbors."

"Misleading anecdote is someone smokes 20 a day and lives to 110, [or] who buys some tablets off the web and their cancer goes away... These are not representative... stories... [T]his is an active area of research, and it's been shown that if you present information in the way that Michael was presenting, as icon arrays, show both the good and the bad, show the totality, [it's been] shown empirically that you can make people less influenced by misleading anecdotes."

"This current COVID-19 virus... is a classic situation... of... an uncertainty problem, rather than a risk problem because we... don't know the parameters. We don't know... how it might spread in Great Britain. We don't know the effectiveness of the interventions that are going to be made. So... when you're making projections... over the next 6 months, there's a massive range of possibilities, up to 1/2 million deaths... from about 5... the most optimistic... [A]ny quantification, giving any probabilities would be... very ambitious..."

"[S]easonal flu—average year—kills 6,000 people in this country. Mainly old... vulnerable... frail...[etc.] So we are hit by this, year after year... epidemics... we've got to put this into perspective... [T]o an extent it is a trade-off between massive disruption... [I]f you say everyone has to stay in their home for 4 weeks... that's not just economic loss. It has a massive... health... [detriment] in terms of... mentality and fitness. Norsemen of harm will be done... so it's not just a matter of... "Minimize the number of deaths.""

"When it comes to vaccines and infectious diseases, nobody is an individual... [With] [i]nfectious diseases... measles when it comes to vaccine decisions, or COVID-19 when it comes to taking precautions, we're not individuals. We are members of society, and there's no... "optimize your individual situation." You have... an absolute responsibility... to protect the people around you, particularly the vulnerable... [T]hat's why... people who avoid vaccinating their kids is outrageous and irresponsible... they are endangering weaker kids who might not be able to have the vaccines because their immune system is compromised or for some [other] reason... [S]imilarly, if young... healthy people... not... harmed by the virus, go around being irresponsible, they are endangering the lives of older people surrounding them, in particular, their own family."

"When it comes to trying to prevent you endangering other people, I don't see anything wrong with persuasion. ...[Y]ou shouldn't be... [endangering people] and you should be trying to be persuaded, if not forced... I get quite Stalinist on these things because... it's so irresponsible for some people to endanger the health of others. If they wanted to make their own decision that only affects them, it's very different, and I wouldn't want to persuade anyone..."

"In the trials that led to the vaccines... adverse events were reported by 38% of those receiving the real vaccine... 28% of those who received the control [dummy, or fake vaccine, of which some were meningitis vaccine] also reported a side-effect. ...[F]ewer than 1% reported a serious adverse event, and of these... slightly more had received the dummy than the active vaccine. ...So there was no evidence of increased risk ..."

"We need to think slow instead of fast, and resist drawing causal links between events where none may exist."

"It’s a common human tendency to attribute a causal effect between different events, even when there isn’t one present..."

"In the UK, adverse reactions are reported using the “yellow card”... Up to 28 February, around 54,000 yellow cards have been reported... from... 10 million vaccinations... three to six reports per 1,000 jabs [0.3-0.6%]. That means a far greater number of side-effects are reported in the trials..."

"s are disastrous. ...Relative risks are deeply misleading. They're a manipulative form of communication. To ever say, "Oh, this doubles your risk, or increases your risk 50%," absolute No-no! They are hopeless. In some situations they can be very valuable... but in general, medical things what... should be always given... s... with and without something... Like my s... I was getting... 15%, 10 year risk: 15 out 100 people like me might expect to have a heart attack or stroke. So I... roughly halved it... only in terms of relative risk... from 15% to 7-8%. ...Being told it halved it does sound good, but if wasn't a very big number in the first place, halving it is of no interest... especially if the thing's going to give me some side-effects... if it did, it would be completely pointless... [Y]ou cannot know... whether you should do something... [Y]ou cannot trade off the benefits... [and] the harms from a medical treatment without knowing the absolute risk. You cannot do it in any rational way whatsoever. ...A lot of the communication now is using absolute risk, which is a huge improvement."

"Framing is absolutely vital. ...All the work in communications is driven by the work of psychologists like Kahneman, Tversky...[etc.] The simplest one... is not always to talk about s, but to talk about s, and preferably... to give both. Our predict systems are almost always... positively framed, all in terms of survival. So we draw survival curves, not mortality curves... How long can you be without this condition. ...In a way you should give both, but ...it makes a big difference ...whether you talk about 2% mortality or 98% survival. ...2% mortality sounds rather terrifying while 98% survival sounds rather good, and we don't want to unnecessarily upset people... [W]e are all going to die ...It's 100% mortality in the end, but you want to show a decline in survival ...because it's just fairer and more likely to get people engaged rather than frighten them off immediately. ...[W]hen we ...provide an icon array that shows everybody, it shows the deaths ...patients like it. ...They like seeing out of 100 people ...in 10 years time, how many people are going to be alive ...because they have the chemotherapy now, or dead because of breast cancer...[etc.]"

"[W]hen... there have been 30 "thromboembolic events" after around 5m vaccinations, the crucial question... is: how many would be expected anyway, in the normal run..?"

"(DVTs) [normally] happen to around one person per 1,000 each year... out of 5 million people getting vaccinated, we would expect... 5,000 DVTs a year, or... 100 every week. So it is not at all surprising that there have been 30 reports."

"We spent ages... working... for child heart surgery... such a delicate area, trying to find the wording for... random error or binomial variability... [Y]ou can give a percentage... 95% . Well, am I going to be one of the 5% or one of the 95%? We don't know. It's just chance or luck, fortune. We can't... use those words in... delicate situations... operating on children... Then we came up with a good phrase... which we used and tested on parents... It's "unforeseeable factors," not "unforeseen factors," because that would suggest someone's to blame... [T]he unforeseeable factors could lead some people to... not survive the operation, and some to survive. So... we can put you in a group, but we can't go beyond that... [O]nly what develops over time, in terms of complications, or something like that, could... put... you in one group or another. "Unforeseeable factors," I really like that phrase. I try to use it all the time, I recommend it."

"So we've been trying to think of another metaphor... and the one we caught hold of is... speed of aging. So it's turning these numbers, rather bold numbers quite difficult to understand, into stories, and the story we've got is, "Getting older quicker" or "Aging Slower"..."

"What we use in the book... are ways which we think might... provide gripping narratives, and yet provide a realistic way of communicating small risks..."

"I do math and statistics. That's what I do, so I come at the whole business of turning numbers into stories. ...How can we turn numbers into stories?"

"The point is... that you can make these comparisons quite easy... is... 8 [micromorts], running a marathon is... 7, ... 5, 's going to be 400..."

"So... in the book we make all these comparisons... That's acute timing risk, things that are going to kill you on the spot. ...What about the other sort of risks? ...You can have your spam ...[T]hat is not going to kill you on the spot. Well, it might. ...You might choke on...[it]... but it's... unlikely..."

"This is called a hazard curve. ...This is the chance of dying before your next birthday, on average. ...[I]t's... on a , so 10%... (1 in 10) 83 year olds will not see 84... 1 in 100 people like me [age 59] will not see their next birthday. 1 in 1,000 thirty-two year olds, and 1 in 10,000 7 year olds... and there is a... lump, sadly jumping up at 17, as you can imagine... boys... a risk-taking lump, but if you ignore that lump... it's a... straight line between... 7 and 90."

"This was discovered by Gompertz in 1825. There's something about our bodies, the way that we age, that means that every year our chance of dying increases by the same amount, 9%."

"That change in life expectancy is not that gripping in itself. So what we've done in the book, it does seem a rather a strange thing to say... "Over an adult lifetime, about... 50-60 years... take a year off your life." It's like losing roughly 1/50 of your life. It's actually ' because of... these daily habits... like losing a week every year of your life, the same as losing 1/2 hour off a day. So we could say... that... 2 hours watching television... it's as if it's taking 1/2 hour... off your life. ...You're aging an extra 1/2 hour sitting on your backside watching television ..."

"There'a a nice thing about 1/2 hour because an adult life expectancy is 55 to 60 years... is actually a million 1/2 hours. A million 1/2 hours is 57 years. So you have got, not all of you... some of you have got a million 1/2 hours to fritter away."

"One of the other things we do in the book is talk about radiation... [Y]ou can say exposure to radiation, you can talk in terms of micro-lives or cigarette equivalents. So... a flight to New York, the radiation you get from that is equivalent to smoking a couple of cigarettes, about 1/2 hour of your life... The whole body CT scan... exposing yourself... to possibly an unhealthy dose of radiation... 150 microlives, smoking about 300 cigarettes, about the same as standing about 1 1/2 miles from the Hiroshima explosion. ...[W]hen they advertise these things for a thousand quid, they don't tell you that."

"s are very valuable in... low probability, high impact events. Every time you cross the road there is a low probability and high impact that you're going to get run over. ...You take extra precautions to reduce... very small risk to... even smaller. ...[O]n an absolute risk scale, you [might] say, "Oh, I'm not going to bother... It's not worth doing..." but... by making that low risk even smaller, it's... valid... [P]eople discovered this... doing earthquake predictions... [T]he absolute risk... it's always low. They're very unpredictable... but telling people it's 10 times normal, or 100 times normal, people will act... appropriately. ...They won't panic. They won't rush away. ...[I]n Italy ...they ...sleep outside for a bit. ...So in certain circumstances relative risk can be very valuable... [U]sing both in... situations... with very small risks.., where... consequences are... severe... [and] the cost of the intervention, the action, is... minimal. Taking a bit more precautions, being a bit more careful... not putting a big investment into making a very small risk even smaller.... not walking under ladders... a low-cost change in your behavior to make a small risk even smaller... [A]bsolute risks really don't deal well with that, because you're talking 0.000..."