Podcast appearances and mentions of paul erd

“To navigate proof, we must reach into a thicket of errors and biases. We must confront monsters and embrace uncertainty, balancing — and rebalancing —our beliefs. We must seek out every useful fragment of data, gather every relevant tool, searching wider and climbing further. Finding the good foundations among the bad. Dodging dogma and falsehoods. Questioning. Measuring. Triangulating. Convincing. Then perhaps, just perhaps, we'll reach the truth in time.”—Adam KucharskiMy conversation with Professor Kucharski on what constitutes certainty and proof in science (and other domains), with emphasis on many of the learnings from Covid. Given the politicization of science and A.I.'s deepfakes and power for blurring of truth, it's hard to think of a topic more important right now.Audio file (Ground Truths can also be downloaded on Apple Podcasts and Spotify)Eric Topol (00:06):Hello, it's Eric Topol from Ground Truths and I am really delighted to welcome Adam Kucharski, who is the author of a new book, Proof: The Art and Science of Certainty. He's a distinguished mathematician, by the way, the first mathematician we've had on Ground Truths and a person who I had the real privilege of getting to know a bit through the Covid pandemic. So welcome, Adam.Adam Kucharski (00:28):Thanks for having me.Eric Topol (00:30):Yeah, I mean, I think just to let everybody know, you're a Professor at London School of Hygiene and Tropical Medicine and also noteworthy you won the Adams Prize, which is one of the most impressive recognitions in the field of mathematics. This is the book, it's a winner, Proof and there's so much to talk about. So Adam, maybe what I'd start off is the quote in the book that captivates in the beginning, “life is full of situations that can reveal remarkably large gaps in our understanding of what is true and why it's true. This is a book about those gaps.” So what was the motivation when you undertook this very big endeavor?Adam Kucharski (01:17):I think a lot of it comes to the work I do at my day job where we have to deal with a lot of evidence under pressure, particularly if you work in outbreaks or emerging health concerns. And often it really pushes the limits, our methodology and how we converge on what's true subject to potential revision in the future. I think particularly having a background in math's, I think you kind of grow up with this idea that you can get to these concrete, almost immovable truths and then even just looking through the history, realizing that often isn't the case, that there's these kind of very human dynamics that play out around them. And it's something I think that everyone in science can reflect on that sometimes what convinces us doesn't convince other people, and particularly when you have that kind of urgency of time pressure, working out how to navigate that.Eric Topol (02:05):Yeah. Well, I mean I think these times of course have really gotten us to appreciate, particularly during Covid, the importance of understanding uncertainty. And I think one of the ways that we can dispel what people assume they know is the famous Monty Hall, which you get into a bit in the book. So I think everybody here is familiar with that show, Let's Make a Deal and maybe you can just take us through what happens with one of the doors are unveiled and how that changes the mathematics.Adam Kucharski (02:50):Yeah, sure. So I think it is a problem that's been around for a while and it's based on this game show. So you've got three doors that are closed. Behind two of the doors there is a goat and behind one of the doors is a luxury car. So obviously, you want to win the car. The host asks you to pick a door, so you point to one, maybe door number two, then the host who knows what's behind the doors opens another door to reveal a goat and then ask you, do you want to change your mind? Do you want to switch doors? And a lot of the, I think intuition people have, and certainly when I first came across this problem many years ago is well, you've got two doors left, right? You've picked one, there's another one, it's 50-50. And even some quite well-respected mathematicians.Adam Kucharski (03:27):People like Paul Erdős who was really published more papers than almost anyone else, that was their initial gut reaction. But if you work through all of the combinations, if you pick this door and then the host does this, and you switch or not switch and work through all of those options. You actually double your chances if you switch versus sticking with the door. So something that's counterintuitive, but I think one of the things that really struck me and even over the years trying to explain it is convincing myself of the answer, which was when I first came across it as a teenager, I did quite quickly is very different to convincing someone else. And even actually Paul Erdős, one of his colleagues showed him what I call proof by exhaustion. So go through every combination and that didn't really convince him. So then he started to simulate and said, well, let's do a computer simulation of the game a hundred thousand times. And again, switching was this optimal strategy, but Erdős wasn't really convinced because I accept that this is the case, but I'm not really satisfied with it. And I think that encapsulates for a lot of people, their experience of proof and evidence. It's a fact and you have to take it as given, but there's actually quite a big bridge often to really understanding why it's true and feeling convinced by it.Eric Topol (04:41):Yeah, I think it's a fabulous example because I think everyone would naturally assume it's 50-50 and it isn't. And I think that gets us to the topic at hand. What I love, there's many things I love about this book. One is that you don't just get into science and medicine, but you cut across all the domains, law, mathematics, AI. So it's a very comprehensive sweep of everything about proof and truth, and it couldn't come at a better time as we'll get into. Maybe just starting off with math, the term I love mathematical monsters. Can you tell us a little bit more about that?Adam Kucharski (05:25):Yeah, this was a fascinating situation that emerged in the late 19th century where a lot of math's, certainly in Europe had been derived from geometry because a lot of the ancient Greek influence on how we shaped things and then Newton and his work on rates of change and calculus, it was really the natural world that provided a lot of inspiration, these kind of tangible objects, tangible movements. And as mathematicians started to build out the theory around rates of change and how we tackle these kinds of situations, they sometimes took that intuition a bit too seriously. And there was some theorems that they said were intuitively obvious, some of these French mathematicians. And so, one for example is this idea of you how things change smoothly over time and how you do those calculations. But what happened was some mathematicians came along and showed that when you have things that can be infinitely small, that intuition didn't necessarily hold in the same way.Adam Kucharski (06:26):And they came up with these examples that broke a lot of these theorems and a lot of the establishments at the time called these things monsters. They called them these aberrations against common sense and this idea that if Newton had known about them, he never would've done all of his discovery because they're just nuisances and we just need to get rid of them. And there's this real tension at the core of mathematics in the late 1800s where some people just wanted to disregard this and say, look, it works for most of the time, that's good enough. And then others really weren't happy with this quite vague logic. They wanted to put it on much sturdier ground. And what was remarkable actually is if you trace this then into the 20th century, a lot of these monsters and these particularly in some cases functions which could almost move constantly, this constant motion rather than our intuitive concept of movement as something that's smooth, if you drop an apple, it accelerates at a very smooth rate, would become foundational in our understanding of things like probability, Einstein's work on atomic theory. A lot of these concepts where geometry breaks down would be really important in relativity. So actually, these things that we thought were monsters actually were all around us all the time, and science couldn't advance without them. So I think it's just this remarkable example of this tension within a field that supposedly concrete and the things that were going to be shunned actually turn out to be quite important.Eric Topol (07:53):It's great how you convey how nature isn't so neat and tidy and things like Brownian motion, understanding that, I mean, just so many things that I think fit into that general category. In the legal, we won't get into too much because that's not so much the audience of Ground Truths, but the classic things about innocent and until proven guilty and proof beyond reasonable doubt, I mean these are obviously really important parts of that overall sense of proof and truth. We're going to get into one thing I'm fascinated about related to that subsequently and then in science. So before we get into the different types of proof, obviously the pandemic is still fresh in our minds and we're an endemic with Covid now, and there are so many things we got wrong along the way of uncertainty and didn't convey that science isn't always evolving search for what is the truth. There's plenty no shortage of uncertainty at any moment. So can you recap some of the, you did so much work during the pandemic and obviously some of it's in the book. What were some of the major things that you took out of proof and truth from the pandemic?Adam Kucharski (09:14):I think it was almost this story of two hearts because on the one hand, science was the thing that got us where we are today. The reason that so much normality could resume and so much risk was reduced was development of vaccines and the understanding of treatments and the understanding of variants as they came to their characteristics. So it was kind of this amazing opportunity to see this happen faster than it ever happened in history. And I think ever in science, it certainly shifted a lot of my thinking about what's possible and even how we should think about these kinds of problems. But also on the other hand, I think where people might have been more familiar with seeing science progress a bit more slowly and reach consensus around some of these health issues, having that emerge very rapidly can present challenges even we found with some of the work we did on Alpha and then the Delta variants, and it was the early quantification of these.Adam Kucharski (10:08):So really the big question is, is this thing more transmissible? Because at the time countries were thinking about control measures, thinking about relaxing things, and you've got this just enormous social economic health decision-making based around essentially is it a lot more spreadable or is it not? And you only had these fragments of evidence. So I think for me, that was really an illustration of the sharp end. And I think what we ended up doing with some of those was rather than arguing over a precise number, something like Delta, instead we kind of looked at, well, what's the range that matters? So in the sense of arguing over whether it's 40% or 50% or 30% more transmissible is perhaps less important than being, it's substantially more transmissible and it's going to start going up. Is it going to go up extremely fast or just very fast?Adam Kucharski (10:59):That's still a very useful conclusion. I think what often created some of the more challenges, I think the things that on reflection people looking back pick up on are where there was probably overstated certainty. We saw that around some of the airborne spread, for example, stated as a fact by in some cases some organizations, I think in some situations as well, governments had a constraint and presented it as scientific. So the UK, for example, would say testing isn't useful. And what was happening at the time was there wasn't enough tests. So it was more a case of they can't test at that volume. But I think blowing between what the science was saying and what the decision-making, and I think also one thing we found in the UK was we made a lot of the epidemiological evidence available. I think that was really, I think something that was important.Adam Kucharski (11:51):I found it a lot easier to communicate if talking to the media to be able to say, look, this is the paper that's out, this is what it means, this is the evidence. I always found it quite uncomfortable having to communicate things where you knew there were reports behind the scenes, but you couldn't actually articulate. But I think what that did is it created this impression that particularly epidemiology was driving the decision-making a lot more than it perhaps was in reality because so much of that was being made public and a lot more of the evidence around education or economics was being done behind the scenes. I think that created this kind of asymmetry in public perception about how that was feeding in. And so, I think there was always that, and it happens, it is really hard as well as a scientist when you've got journalists asking you how to run the country to work out those steps of am I describing the evidence behind what we're seeing? Am I describing the evidence about different interventions or am I proposing to some extent my value system on what we do? And I think all of that in very intense times can be very easy to get blurred together in public communication. I think we saw a few examples of that where things were being the follow the science on policy type angle where actually once you get into what you're prioritizing within a society, quite rightly, you've got other things beyond just the epidemiology driving that.Eric Topol (13:09):Yeah, I mean that term that you just use follow the science is such an important term because it tells us about the dynamic aspect. It isn't just a snapshot, it's constantly being revised. But during the pandemic we had things like the six-foot rule that was never supported by data, but yet still today, if I walk around my hospital and there's still the footprints of the six-foot rule and not paying attention to the fact that this was airborne and took years before some of these things were accepted. The flatten the curve stuff with lockdowns, which I never was supportive of that, but perhaps at the worst point, the idea that hospitals would get overrun was an issue, but it got carried away with school shutdowns for prolonged periods and in some parts of the world, especially very stringent lockdowns. But anyway, we learned a lot.Eric Topol (14:10):But perhaps one of the greatest lessons is that people's expectations about science is that it's absolute and somehow you have this truth that's not there. I mean, it's getting revised. It's kind of on the job training, it's on this case on the pandemic revision. But very interesting. And that gets us to, I think the next topic, which I think is a fundamental part of the book distributed throughout the book, which is the different types of proof in biomedicine and of course across all these domains. And so, you take us through things like randomized trials, p-values, 95 percent confidence intervals, counterfactuals, causation and correlation, peer review, the works, which is great because a lot of people have misconceptions of these things. So for example, randomized trials, which is the temple of the randomized trials, they're not as great as a lot of people think, yes, they can help us establish cause and effect, but they're skewed because of the people who come into the trial. So they may not at all be a representative sample. What are your thoughts about over deference to randomized trials?Adam Kucharski (15:31):Yeah, I think that the story of how we rank evidence in medicines a fascinating one. I mean even just how long it took for people to think about these elements of randomization. Fundamentally, what we're trying to do when we have evidence here in medicine or science is prevent ourselves from confusing randomness for a signal. I mean, that's fundamentally, we don't want to mistake something, we think it's going on and it's not. And the challenge, particularly with any intervention is you only get to see one version of reality. You can't give someone a drug, follow them, rewind history, not give them the drug and then follow them again. So one of the things that essentially randomization allows us to do is, if you have two groups, one that's been randomized, one that hasn't on average, the difference in outcomes between those groups is going to be down to the treatment effect.Adam Kucharski (16:20):So it doesn't necessarily mean in reality that'd be the case, but on average that's the expectation that you'd have. And it's kind of interesting actually that the first modern randomized control trial (RCT) in medicine in 1947, this is for TB and streptomycin. The randomization element actually, it wasn't so much statistical as behavioral, that if you have people coming to hospital, you could to some extent just say, we'll just alternate. We're not going to randomize. We're just going to first patient we'll say is a control, second patient a treatment. But what they found in a lot of previous studies was doctors have bias. Maybe that patient looks a little bit ill or that one maybe is on borderline for eligibility. And often you got these quite striking imbalances when you allowed it for human judgment. So it was really about shielding against those behavioral elements. But I think there's a few situations, it's a really powerful tool for a lot of these questions, but as you mentioned, one is this issue of you have the population you study on and then perhaps in reality how that translates elsewhere.Adam Kucharski (17:17):And we see, I mean things like flu vaccines are a good example, which are very dependent on immunity and evolution and what goes on in different populations. Sometimes you've had a result on a vaccine in one place and then the effectiveness doesn't translate in the same way to somewhere else. I think the other really important thing to bear in mind is, as I said, it's the averaging that you're getting an average effect between two different groups. And I think we see certainly a lot of development around things like personalized medicine where actually you're much more interested in the outcome for the individual. And so, what a trial can give you evidence is on average across a group, this is the effect that I can expect this intervention to have. But we've now seen more of the emergence things like N=1 studies where you can actually over the same individual, particularly for chronic conditions, look at those kind of interventions.Adam Kucharski (18:05):And also there's just these extreme examples where you're ethically not going to run a trial, there's never been a trial of whether it's a good idea to have intensive care units in hospitals or there's a lot of these kind of historical treatments which are just so overwhelmingly effective that we're not going to run trial. So almost this hierarchy over time, you can see it getting shifted because actually you do have these situations where other forms of evidence can get you either closer to what you need or just more feasibly an answer where it's just not ethical or practical to do an RCT.Eric Topol (18:37):And that brings us to the natural experiments I just wrote about recently, the one with shingles, which there's two big natural experiments to suggest that shingles vaccine might reduce the risk of Alzheimer's, an added benefit beyond the shingles that was not anticipated. Your thoughts about natural experiments, because here you're getting a much different type of population assessment, again, not at the individual level, but not necessarily restricted by some potentially skewed enrollment criteria.Adam Kucharski (19:14):I think this is as emerged as a really valuable tool. It's kind of interesting, in the book you're talking to economists like Josh Angrist, that a lot of these ideas emerge in epidemiology, but I think were really then taken up by economists, particularly as they wanted to add more credibility to a lot of these policy questions. And ultimately, it comes down to this issue that for a lot of problems, we can't necessarily intervene and randomize, but there might be a situation that's done it to some extent for us, so the classic example is the Vietnam draft where it was kind of random birthdays with drawn out of lottery. And so, there's been a lot of studies subsequently about the effect of serving in the military on different subsequent lifetime outcomes because broadly those people have been randomized. It was for a different reason. But you've got that element of randomization driving that.Adam Kucharski (20:02):And so again, with some of the recent shingles data and other studies, you might have a situation for example, where there's been an intervention that's somewhat arbitrary in terms of time. It's a cutoff on a birth date, for example. And under certain assumptions you could think, well, actually there's no real reason for the person on this day and this day to be fundamentally different. I mean, perhaps there might be effects of cohorts if it's school years or this sort of thing. But generally, this isn't the same as having people who are very, very different ages and very different characteristics. It's just nature, or in this case, just a policy intervention for a different reason has given you that randomization, which allows you or pseudo randomization, which allows you to then look at something about the effect of an intervention that you wouldn't as reliably if you were just digging into the data of yes, no who's received a vaccine.Eric Topol (20:52):Yeah, no, I think it's really valuable. And now I think increasingly given priority, if you can find these natural experiments and they're not always so abundant to use to extrapolate from, but when they are, they're phenomenal. The causation correlation is so big. The issue there, I mean Judea Pearl's, the Book of Why, and you give so many great examples throughout the book in Proof. I wonder if you could comment that on that a bit more because this is where associations are confused somehow or other with a direct effect. And we unfortunately make these jumps all too frequently. Perhaps it's the most common problem that's occurring in the way we interpret medical research data.Adam Kucharski (21:52):Yeah, I think it's an issue that I think a lot of people get drilled into in their training just because a correlation between things doesn't mean that that thing causes this thing. But it really struck me as I talked to people, researching the book, in practice in research, there's actually a bit more to it in how it's played out. So first of all, if there's a correlation between things, it doesn't tell you much generally that's useful for intervention. If two things are correlated, it doesn't mean that changing that thing's going to have an effect on that thing. There might be something that's influencing both of them. If you have more ice cream sales, it will lead to more heat stroke cases. It doesn't mean that changing ice cream sales is going to have that effect, but it does allow you to make predictions potentially because if you can identify consistent patterns, you can say, okay, if this thing going up, I'm going to make a prediction that this thing's going up.Adam Kucharski (22:37):So one thing I found quite striking, actually talking to research in different fields is how many fields choose to focus on prediction because it kind of avoids having to deal with this cause and effect problem. And even in fields like psychology, it was kind of interesting that there's a lot of focus on predicting things like relationship outcomes, but actually for people, you don't want a prediction about your relationship. You want to know, well, how can I do something about it? You don't just want someone to sell you your relationship's going to go downhill. So there's almost part of the challenge is people just got stuck on prediction because it's an easier field of work, whereas actually some of those problems will involve intervention. I think the other thing that really stood out for me is in epidemiology and a lot of other fields, rightly, people are very cautious to not get that mixed up.Adam Kucharski (23:24):They don't want to mix up correlations or associations with causation, but you've kind of got this weird situation where a lot of papers go out of their way to not use causal language and say it's an association, it's just an association. It's just an association. You can't say anything about causality. And then the end of the paper, they'll say, well, we should think about introducing more of this thing or restricting this thing. So really the whole paper and its purpose is framed around a causal intervention, but it's extremely careful throughout the paper to not frame it as a causal claim. So I think we almost by skirting that too much, we actually avoid the problems that people sometimes care about. And I think a lot of the nice work that's been going on in causal inference is trying to get people to confront this more head on rather than say, okay, you can just stay in this prediction world and that's fine. And then just later maybe make a policy suggestion off the back of it.Eric Topol (24:20):Yeah, I think this is cause and effect is a very alluring concept to support proof as you so nicely go through in the book. But of course, one of the things that we use to help us is the biological mechanism. So here you have, let's say for example, you're trying to get a new drug approved by the Food and Drug Administration (FDA), and the request is, well, we want two trials, randomized trials, independent. We want to have p-values that are significant, and we want to know the biological mechanism ideally with the dose response of the drug. But there are many drugs as you review that have no biological mechanism established. And even when the tobacco problems were mounting, the actual mechanism of how tobacco use caused cancer wasn't known. So how important is the biological mechanism, especially now that we're well into the AI world where explainability is demanded. And so, we don't know the mechanism, but we also don't know the mechanism and lots of things in medicine too, like anesthetics and even things as simple as aspirin, how it works and many others. So how do we deal with this quest for the biological mechanism?Adam Kucharski (25:42):I think that's a really good point. It shows almost a lot of the transition I think we're going through currently. I think particularly for things like smoking cancer where it's very hard to run a trial. You can't make people randomly take up smoking. Having those additional pieces of evidence, whether it's an analogy with a similar carcinogen, whether it's a biological mechanism, can help almost give you more supports for that argument that there's a cause and effect going on. But I think what I found quite striking, and I realized actually that it's something that had kind of bothered me a bit and I'd be interested to hear whether it bothers you, but with the emergence of AI, it's almost a bit of the loss of scientific satisfaction. I think you grow up with learning about how the world works and why this is doing what it's doing.Adam Kucharski (26:26):And I talked for example of some of the people involved with AlphaFold and some of the subsequent work in installing those predictions about structures. And they'd almost made peace with it, which I found interesting because I think they started off being a bit uncomfortable with like, yeah, you've got these remarkable AI models making these predictions, but we don't understand still biologically what's happening here. But I think they're just settled in saying, well, biology is really complex on some of these problems, and if we can have a tool that can give us this extremely valuable information, maybe that's okay. And it was just interesting that they'd really kind of gone through that kind process, which I think a lot of people are still grappling with and that almost that discomfort of using AI and what's going to convince you that that's a useful reliable prediction whether it's something like predicting protein folding or getting in a self-driving car. What's the evidence you need to convince you that's reliable?Eric Topol (27:26):Yeah, no, I'm so glad you brought that up because when Demis Hassabis and John Jumper won the Nobel Prize, the point I made was maybe there should be an asterisk with AI because they don't know how it works. I mean, they had all the rich data from the protein data bank, and they got the transformer model to do it for 200 million protein structure prediction, but they still to this day don't fully understand how the model really was working. So it reinforces what you're just saying. And of course, it cuts across so many types of AI. It's just that we tend to hold different standards in medicine not realizing that there's lots of lack of explainability for routine medical treatments today. Now one of the things that I found fascinating in your book, because there's different levels of proof, different types of proof, but solid logical systems.Eric Topol (28:26):And on page 60 of the book, especially pertinent to the US right now, there is a bit about Kurt Gödel and what he did there was he basically, there was a question about dictatorship in the US could it ever occur? And Gödel says, “oh, yes, I can prove it.” And he's using the constitution itself to prove it, which I found fascinating because of course we're seeing that emerge right now. Can you give us a little bit more about this, because this is fascinating about the Fifth Amendment, and I mean I never thought that the Constitution would allow for a dictatorship to emerge.Adam Kucharski (29:23):And this was a fascinating story, Kurt Gödel who is one of the greatest logical minds of the 20th century and did a lot of work, particularly in the early 20th century around system of rules, particularly things like mathematics and whether they can ever be really fully satisfying. So particularly in mathematics, he showed that there were this problem that is very hard to have a set of rules for something like arithmetic that was both complete and covered every situation, but also had no contradictions. And I think a lot of countries, if you go back, things like Napoleonic code and these attempts to almost write down every possible legal situation that could be imaginable, always just ascended into either they needed amendments or they had contradictions. I think Gödel's work really summed it up, and there's a story, this is in the late forties when he had his citizenship interview and Einstein and Oskar Morgenstern went along as witnesses for him.Adam Kucharski (30:17):And it's always told as kind of a lighthearted story as this logical mind, this academic just saying something silly in front of the judge. And actually, to my own admission, I've in the past given talks and mentioned it in this slightly kind of lighthearted way, but for the book I got talking to a few people who'd taken it more seriously. I realized actually he's this extremely logically focused mind at the time, and maybe there should have been something more to it. And people who have kind of dug more into possibilities was saying, well, what could he have spotted that bothered him? And a lot of his work that he did about consistency in mass was around particularly self-referential statements. So if I say this sentence is false, it's self-referential and if it is false, then it's true, but if it's true, then it's false and you get this kind of weird self-referential contradictions.Adam Kucharski (31:13):And so, one of the theories about Gödel was that in the Constitution, it wasn't that there was a kind of rule for someone can become a dictator, but rather people can use the mechanisms within the Constitution to make it easier to make further amendments. And he kind of downward cycle of amendment that he had seen happening in Europe and the run up to the war, and again, because this is never fully documented exactly what he thought, but it's one of the theories that it wouldn't just be outright that it would just be this cycle process of weakening and weakening and weakening and making it easier to add. And actually, when I wrote that, it was all the earlier bits of the book that I drafted, I did sort of debate whether including it I thought, is this actually just a bit in the weeds of American history? And here we are. Yeah, it's remarkable.Eric Topol (32:00):Yeah, yeah. No, I mean I found, it struck me when I was reading this because here back in 1947, there was somebody predicting that this could happen based on some, if you want to call it loopholes if you will, or the ability to change things, even though you would've thought otherwise that there wasn't any possible capability for that to happen. Now, one of the things I thought was a bit contradictory is two parts here. One is from Angus Deaton, he wrote, “Gold standard thinking is magical thinking.” And then the other is what you basically are concluding in many respects. “To navigate proof, we must reach into a thicket of errors and biases. We must confront monsters and embrace uncertainty, balancing — and rebalancing —our beliefs. We must seek out every useful fragment of data, gather every relevant tool, searching wider and climbing further. Finding the good foundations among the bad. Dodging dogma and falsehoods. Questioning. Measuring. Triangulating. Convincing. Then perhaps, just perhaps, we'll reach the truth in time.” So here you have on the one hand your search for the truth, proof, which I think that little paragraph says it all. In many respects, it sums up somewhat to the work that you review here and on the other you have this Nobel laureate saying, you don't have to go to extremes here. The enemy of good is perfect, perhaps. I mean, how do you reconcile this sense that you shouldn't go so far? Don't search for absolute perfection of proof.Adam Kucharski (33:58):Yeah, I think that encapsulates a lot of what the book is about, is that search for certainty and how far do you have to go. I think one of the things, there's a lot of interesting discussion, some fascinating papers around at what point do you use these studies? What are their flaws? But I think one of the things that does stand out is across fields, across science, medicine, even if you going to cover law, AI, having these kind of cookie cutter, this is the definitive way of doing it. And if you just follow this simple rule, if you do your p-value, you'll get there and you'll be fine. And I think that's where a lot of the danger is. And I think that's what we've seen over time. Certain science people chasing certain targets and all the behaviors that come around that or in certain situations disregarding valuable evidence because you've got this kind of gold standard and nothing else will do.Adam Kucharski (34:56):And I think particularly in a crisis, it's very dangerous to have that because you might have a low level of evidence that demands a certain action and you almost bias yourself towards inaction if you have these kind of very simple thresholds. So I think for me, across all of these stories and across the whole book, I mean William Gosset who did a lot of pioneering work on statistical experiments at Guinness in the early 20th century, he had this nice question he sort of framed is, how much do we lose? And if we're thinking about the problems, there's always more studies we can do, there's always more confidence we can have, but whether it's a patient we want to treat or crisis we need to deal with, we need to work out actually getting that level of proof that's really appropriate for where we are currently.Eric Topol (35:49):I think exceptionally important that there's this kind of spectrum or continuum in following science and search for truth and that distinction, I think really nails it. Now, one of the things that's unique in the book is you don't just go through all the different types of how you would get to proof, but you also talk about how the evidence is acted on. And for example, you quote, “they spent a lot of time misinforming themselves.” This is the whole idea of taking data and torturing it or using it, dredging it however way you want to support either conspiracy theories or alternative facts. Basically, manipulating sometimes even emasculating what evidence and data we have. And one of the sentences, or I guess this is from Sir Francis Bacon, “truth is a daughter of time”, but the added part is not authority. So here we have our president here that repeats things that are wrong, fabricated or wrong, and he keeps repeating to the point that people believe it's true. But on the other hand, you could say truth is a daughter of time because you like to not accept any truth immediately. You like to see it get replicated and further supported, backed up. So in that one sentence, truth is a daughter of time not authority, there's the whole ball of wax here. Can you take us through that? Because I just think that people don't understand that truth being tested over time, but also manipulated by its repetition. This is a part of the big problem that we live in right now.Adam Kucharski (37:51):And I think it's something that writing the book and actually just reflecting on it subsequently has made me think about a lot in just how people approach these kinds of problems. I think that there's an idea that conspiracy theorists are just lazy and have maybe just fallen for a random thing, but talking to people, you really think about these things a lot more in the field. And actually, the more I've ended up engaging with people who believe things that are just outright unevidenced around vaccines, around health issues, they often have this mountain of papers and data to hand and a lot of it, often they will be peer reviewed papers. It won't necessarily be supporting the point that they think it's supports.Adam Kucharski (38:35):But it's not something that you can just say everything you're saying is false, that there's actually often a lot of things that have been put together and it's just that leap to that conclusion. I think you also see a lot of scientific language borrowed. So I gave a talker early this year and it got posted on YouTube. It had conspiracy theories it, and there was a lot of conspiracy theory supporters who piled in the comments and one of the points they made is skepticism is good. It's the kind of law society, take no one's word for it, you need this. We are the ones that are kind of doing science and people who just assume that science is settled are in the wrong. And again, you also mentioned that repetition. There's this phenomenon, it's the illusory truth problem that if you repeatedly tell someone someone's something's false, it'll increase their belief in it even if it's something quite outrageous.Adam Kucharski (39:27):And that mimics that scientific repetition because people kind of say, okay, well if I've heard it again and again, it's almost like if you tweak these as mini experiments, I'm just accumulating evidence that this thing is true. So it made me think a lot about how you've got essentially a lot of mimicry of the scientific method, amount of data and how you present it and this kind of skepticism being good, but I think a lot of it comes down to as well as just looking at theological flaws, but also ability to be wrong in not actually seeking out things that confirm. I think all of us, it's something that I've certainly tried to do a lot working on emergencies, and one of the scientific advisory groups that I worked on almost it became a catchphrase whenever someone presented something, they finished by saying, tell me why I'm wrong.Adam Kucharski (40:14):And if you've got a variant that's more transmissible, I don't want to be right about that really. And it is something that is quite hard to do and I found it is particularly for something that's quite high pressure, trying to get a policymaker or someone to write even just non-publicly by themselves, write down what you think's going to happen or write down what would convince you that you are wrong about something. I think particularly on contentious issues where someone's got perhaps a lot of public persona wrapped up in something that's really hard to do, but I think it's those kind of elements that distinguish between getting sucked into a conspiracy theory and really seeking out evidence that supports it and trying to just get your theory stronger and stronger and actually seeking out things that might overturn your belief about the world. And it's often those things that we don't want overturned. I think those are the views that we all have politically or in other ways, and that's often where the problems lie.Eric Topol (41:11):Yeah, I think this is perhaps one of, if not the most essential part here is that to try to deal with the different views. We have biases as you emphasized throughout, but if you can use these different types of proof to have a sound discussion, conversation, refutation whereby you don't summarily dismiss another view which may be skewed and maybe spurious or just absolutely wrong, maybe fabricated whatever, but did you can engage and say, here's why these are my proof points, or this is why there's some extent of certainty you can have regarding this view of the data. I think this is so fundamental because unfortunately as we saw during the pandemic, the strident minority, which were the anti-science, anti-vaxxers, they were summarily dismissed as being kooks and adopting conspiracy theories without the right engagement and the right debates. And I think this might've helped along the way, no less the fact that a lot of scientists didn't really want to engage in the first place and adopt this methodical proof that you've advocated in the book so many different ways to support a hypothesis or an assertion. Now, we've covered a lot here, Adam. Have I missed some central parts of the book and the effort because it's really quite extraordinary. I know it's your third book, but it's certainly a standout and it certainly it's a standout not just for your books, but books on this topic.Adam Kucharski (43:13):Thanks. And it's much appreciated. It was not an easy book to write. I think at times, I kind of wondered if I should have taken on the topic and I think a core thing, your last point speaks to that. I think a core thing is that gap often between what convinces us and what convinces someone else. I think it's often very tempting as a scientist to say the evidence is clear or the science has proved this. But even on something like the vaccines, you do get the loud minority who perhaps think they're putting microchips in people and outlandish views, but you actually get a lot more people who might just have some skepticism of pharmaceutical companies or they might have, my wife was pregnant actually at the time during Covid and we waited up because there wasn't much data on pregnancy and the vaccine. And I think it's just finding what is convincing. Is it having more studies from other countries? Is it understanding more about the biology? Is it understanding how you evaluate some of those safety signals? And I think that's just really important to not just think what convinces us and it's going to be obvious to other people, but actually think where are they coming from? Because ultimately having proof isn't that good unless it leads to the action that can make lives better.Eric Topol (44:24):Yeah. Well, look, you've inculcated my mind with this book, Adam, called Proof. Anytime I think of the word proof, I'm going to be thinking about you. So thank you. Thanks for taking the time to have a conversation about your book, your work, and I know we're going to count on you for the astute mathematics and analysis of outbreaks in the future, which we will see unfortunately. We are seeing now, in fact already in this country with measles and whatnot. So thank you and we'll continue to follow your great work.**************************************Thanks for listening, watching or reading this Ground Truths podcast/post.If you found this interesting please share it!That makes the work involved in putting these together especially worthwhile.I'm also appreciative for your subscribing to Ground Truths. All content —its newsletters, analyses, and podcasts—is free, open-access. I'm fortunate to get help from my producer Jessica Nguyen and Sinjun Balabanoff for audio/video tech support to pull these podcasts together for Scripps Research.Paid subscriptions are voluntary and all proceeds from them go to support Scripps Research. They do allow for posting comments and questions, which I do my best to respond to. Please don't hesitate to post comments and give me feedback. Many thanks to those who have contributed—they have greatly helped fund our summer internship programs for the past two years.A bit of an update on SUPER AGERSMy book has been selected as a Next Big Idea Club winner for Season 26 by Adam Grant, Malcolm Gladwell, Susan Cain, and Daniel Pink. This club has spotlighted the most groundbreaking nonfiction books for over a decade. As a winning title, my book will be shipped to thousands of thoughtful readers like you, featured alongside a reading guide, a "Book Bite," Next Big Idea Podcast episode as well as a live virtual Q&A with me in the club's vibrant online community. If you're interested in joining the club, here's a promo code SEASON26 for 20% off at the website. SUPER AGERS reached #3 for all books on Amazon this week. This was in part related to the segment on the book on the TODAY SHOW which you can see here. Also at Amazon there is a remarkable sale on the hardcover book for $10.l0 at the moment for up to 4 copies. Not sure how long it will last or what prompted it.The journalist Paul von Zielbauer has a Substack “Aging With Strength” and did an extensive interview with me on the biology of aging and how we can prevent the major age-related diseases. Here's the link. Get full access to Ground Truths at erictopol.substack.com/subscribe

Afin de créer des ponts créatifs de coproduction en baladodiffusion entre la France et le Canada, l'Ambassade de France au Canada et Transistor Média ont conjointement lancé un appel de candidatures à l'automne dernier pour recevoir une autrice en résidence de création. Claire-Selma Aitout, artiste en résidence durant tout le mois d'avril 2024 à Gatineau, a présenté les fruits de son travail de recherche et de scénarisation à l'occasion de la 8e édition du Festival Transistor. Son projet s'intéresse au parcours singulier du mathématicien hongrois Paul Erdos.Réalisation et scénarisation : Claire-Selma AïtoutMusique originale, montage et mixage : Simon Coovi-SiroisAccompagnement à la création : Marc Guidoni, Joanna Szybist, Jenny Cartwright et l'équipe de Transistor MédiaPartenaires : Ambassade de France au Canada, le Conseil des arts et des lettres du Québec et le Centre d'exposition L'Imagier

This is a re-airing of a podcast originally released in January 2021.The theme of this episode is alliances - human, biological and atomic. We start by celebrating the amazing properties of lichen, the symbiotic relationships it forms, how it shaped the earth and simply how beautiful it is to look at.Then we explore how carbon is able to create such an incredibly diverse range of materials, including soot, diamonds and graphite.We wrap up by delving into the life of renowned Hungarian mathematician Paul Erdős, the world's greatest human alliance maker, who wrote research papers with over 500 mathematicians.On the podcast are Rowan Hooper, Anna Demming and Timothy Revell.Find out more at newscientist.com/podcasts Hosted on Acast. See acast.com/privacy for more information.

Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject. He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics. He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days. With Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge and Andrew Treglown Associate Professor in Mathematics at the University of Birmingham The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.

Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject. He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics. He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days. With Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge and Andrew Treglown Associate Professor in Mathematics at the University of Birmingham The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.

Peter Galison, Image and Logic: A Material Culture of Microphysics, 1997Wikipedia on academic genealogy@made_in_cosmos had a tweet about tradition that I mentionedPaul Hoffman, The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth, 1998Context-driven testing website and bookThe Agile Fusion workshop descriptionPeople mentioned: Lisa Crispin, Ward Cunningham, Janet Gregory, GeePaw Hill, Simon Peyton-JonesCreditsAn image from an undated review of a staging of "Fiddler on the Roof". DuckDuckGo claims it's CC-licensed, but I can't tell. I'm gonna risk it.

404 Episode not found.Non è vero, Luca e Giuliano ci parleranno di un nuovo studio riguardante l'utilizzo di cacca di balena sintetica per "concimare" per il mare e come possibile fonte di carbonio aggiuntiva per migliorare l'ecosistema marino.Nel nostro intervento esterno Romina intervista Gianluca Cappa, che ci spiega come funzionano i “gradi di parentela” tra matematici e ci racconta la storia di Paul Erdős, il matematico più eccentrico di tutti.Dopo una barza che...Luca ci parla di un nuovo studio basato sull'analisi di frammenti e additivi contenuti nelle mescole plastiche che, a contatto con alimenti, potrebbero essere causa di modifiche del metabolismo dei grassi, aumentandone la produzione.

Vašek Chvátal was born in Prague and received his undergraduate degree in mathematics in the same city. He left Czechoslovakia in August 1968, three days after its Soviet-led invasion. Having earned his Ph.D. in mathematics from the University of Waterloo in the fall of 1970, he taught mathematics, computer science, and operations research at McGill, Stanford, Université de Montréal, and Rutgers. From 2004 till his retirement in 2014, he held a Canada Research Chair, first in Combinatorial Optimization and then in Discrete Mathematics, at Concordia University in Montreal. His research agenda has ranged from graph theory and combinatorics to linear programming and cutting planes to analysis of algorithms to the traveling salesman problem. In 2015, he shared the John von Neumann Theory Prize 'for seminal and profound contributions to the theoretical foundations of optimization' with Jean Bernard Lasserre. His most recent book, "The Discrete Mathematical Charms of Paul Erdős", was published last August by Cambridge University Press.

Dr. Fan Chung Graham is the Paul Erdös Professor in Combinatorics at the University of California, San Diego, California. Dr. Chung Graham's research interests include spectral graph theory, extremal graph theory, graph labeling, graph decompositions, random graphs, graph algorithms, parallel structures, and various applications of graph theory in Internet computing, communication networks, software reliability, chemistry, and engineering. In a conversation with students from Simon Fraser University, Amritha Raj Kizhakkeputhukulathil Ramanan, Anmol Anmol Singh, and Brian Krammer, Dr. Chung Graham talks about how she as a graduate student worked on improving the lower bound of R(3,3,3,3), tells about the benefits that art brings to her life, and shares some of her memories about her husband Ron Graham.

We will discuss how other safety science researchers have designed theories that use Rasmussen's concepts, the major takeaways from Rasmussen's article, and how safety professionals can use these theories to analyze and improve systems in their own organizations today. Discussion Points:Rasmussen's history of influence, and the parallels to (Paul) Erdős numbers in research paper publishingHow Rasmussen is the “grandfather” of safety scienceRasmussen's impact across disciplines and organizational categories through the yearsThe basics of this paperWhy risk management models must never be staticHow other theorists and scientists take Rasmussen's concepts and translate them into their own models and diagramsThe paper's summary of the evolution of theoretical approaches up until ‘now' (1997)Why accident models must use a holistic approach including technology AND peopleHow organizations are always going to have pressures of resources vs. required resultsEmployees vs. Management– both push for results with minimal acceptable effort, creating accident riskRasmussen identified we need different models that reflect the real worldTakeaways for our listeners from Rasmussen's work Quotes:“That's the forever challenge in safety, is people have great ideas, but what do you do with them?  Eventually, you've got to turn it into a method.” - Drew Rae“These accidental events are shaped by the activity of people.  Safety, therefore, depends on the control of people's work processes.” - David Provan“There's always going to be this natural migration of activity towards the boundaries of acceptable performance.” - David Provan“This is like the most honest look at work I think I've seen in any safety paper.” - Drew Rae“If you're a safety professional, just how much time are you spending understanding all of these ins and outs and nuances of work, and people's experience of work? …You actually need to find out from the insiders inside the system. ” - David Provan“‘You can't just keep swatting at mosquitos, you actually have to drain the swamp.' I think that's the overarching conceptual framework that Rasmussen wanted us to have.” - David Provan Resources:Compute your Erdos NumberJens Rasmussen's 1997 PaperDavid Woods LinkedInSidney Dekker WebsiteNancy Leveson of MITBlack Line/Blue Line ModelThe Safety of Work PodcastThe Safety of Work on LinkedInFeedback@safetyofwork.com

John Von Neumann was born in Hungary at the tail end of the Astro-Hungarian Empire. The family was made a part of the nobility and as a young prodigy in Budapest, He learned languages and by 8 years old was doing calculus. By 17 he was writing papers on polynomials. He wrote his dissertation in 1925 he added to set theory with the axiom of foundation and the notion of class, or properties shared by members of a set. He worked on the minimax theorem in 1928, the proof of which established zero-sum games and started another discipline within math, game theory. By 1929 he published the axiom system that led to Von Neumann–Bernays–Gödel set theory. And by 1932 he'd developed foundational work on ergodic theory which would evolve into a branch of math that looks at the states of dynamical systems, where functions can describe a points time dependence in space. And so he of course penned a book on quantum mechanics the same year. Did we mention he was smart and given the way his brain worked it made sense that he would eventually gravitate into computing. He went to the best schools with other brilliant scholars who would go on to be called the Martians. They were all researching new areas that required more and more computing - then still done by hand or a combination of hand and mechanical calculators. The Martians included De Hevesy, who won a Nobel prize for Chemistry. Von Kármán got the National Medal of Science and a Franklin Award. Polanyl developed the theory of knowledge and the philosophy of science. Paul Erdős was a brilliant mathematician who published over 1,500 articles. Edward Teller is known as the father of the hydrogen bomb, working on nuclear energy throughout his life and lobbying for the Strategic Defense Initiative, or Star Wars. Dennis Gabor wrote Inventing the Future and won a Nobel Prize in Physics. Eugene Wigner also took home a Nobel Prize in Physics and a National Medal of Science. Leo Szilard took home an Albert Einstein award for his work on nuclear chain reactions and joined in the Manhattan Project as a patent holder for a nuclear reactor. Physicists and brilliant scientists. And here's a key component to the explosion in science following World War II: many of them fled to the United States and other western powers because they were Jewish, to get away from the Nazis, or to avoid communists controlling science. And then there was Harsanyl, Halmos, Goldmark, Franz Alexander, Orowan, and John Kemeny who gave us BASIC. They all contributed to the world we live in today - but von Neumann sometimes hid how smart he was, preferring to not show just how much arithmetic computed through his head. He was married twice and loved fast cars, fine food, bad jokes, and was an engaging and enigmatic figure. He studied measure theory and broke dimension theory into algebraic operators. He studied topological groups, operator algebra, spectral theory, functional analysis and abstract Hilbert space. Geometry and Lattice theory. As with other great thinkers, some of his work has stood the test of time and some has had gaps filled with other theories. And then came the Manhattan project. Here, he helped develop explosive lenses - a key component to the nuclear bomb. Along the way he worked on economics and fluid mechanics. And of course, he theorized and worked out the engineering principals for really big explosions. He was a commissioner of the Atomic Energy Commission and at the height of the Cold War after working out game theory, developed the concept of mutually assured destruction - giving the world hydrogen bombs and ICBMs and reducing the missile gap. Hard to imagine but at the times the Soviets actually had a technical lead over the US, which was proven true when they launched Sputnik. As with the other Martians, he fought Communism and Fasciscm until his death - which won him a Medal of Freedom from then president Eisenhower. His friend Stanislaw Ulam developed the modern Markov Chain Monte Carlo method and Von Neumann got involved in computing to work out those calculations. This combined with where his research lay landed him as an early power user of ENIAC. He actually heard about the machine at a station while waiting for a train. He'd just gotten home from England and while we will never know if he knew of the work Turing was doing on Colossus at Bletchley Park, we do know that he offered Turing a job at the Institute for Advanced Study that he was running in Princeton before World War II and had read Turing's papers, including “On Computable Numbers” and understood the basic concepts of stored programs - and breaking down the logic into zeros and ones. He discussed using ENIAC to compute over 333 calculations per second. He could do a lot in his head, but he wasn't that good of a computer. His input was taken and when Eckert and Mauchly went from ENIAC to EDVAC, or the Electronic Discrete Variable Calculator, the findings were published in a paper called “First Draft of a Report on the EDVAC” - a foundational paper in computing for a number of reasons. One is that Mauchly and Eckert had an entrepreneurial spirit and felt that not only should their names have been on the paper but that it was probably premature and so they quickly filed a patent in 1945, even though some of what they told him that went into the paper helped to invalidate the patent later. They considered these trade secrets and didn't share in von Neumann's idea that information must be set free. In the paper lies an important contribution, Von Neumann broke down the parts of a modern computer. He set the information for how these would work free. He broke down the logical blocks of how a computer works into the modern era. How once we strip away the electromechanical computers that a fully digital machine works. Inputs go into a Central Processing Unit, which has an instruction register, a clock to keep operations and data flow in sync, and a counter - it does the math. It then uses quick-access memory, which we'd call Random Access Memory, or RAM today, to make processing data instructions faster. And it would use long-term memory for operations that didn't need to be as highly available to the CPU. This should sound like a pretty familiar way to architect devices at this point. The result would be sent to an output device. Think of a modern Swift app for an iPhone - the whole of what the computer did could be moved into a single wafer once humanity worked out how first transistors and then multiple transistors on a single chip worked. Yet another outcome of the paper was to inspire Turing and others to work on computers after the war. Turing named his ACE or Automatic Computing Engine out of respect to Charles Babbage. That led to the addition of storage to computers. After all, punched tape was used for Colossus during the war and and punched cards and tape had been around for awhile. It's ironic that we think of memory as ephemeral data storage and storage as more long-term storage. But that's likely more to do with the order these scientific papers came out than anything - and homage to the impact each had. He'd write The Computer and the Brain, Mathematical Foundations of Quantum Mechanics, The Theory of Games and Economic Behavior, Continuous Geometry, and other books. He also studied DNA and cognition and weather systems, inferring we could predict the results of climate change and possibly even turn back global warming - which by 1950 when he was working on it was already acknowledged by scientists. As with many of the early researchers in nuclear physics, he died of cancer - invoking Pascal's wager on his deathbed. He died in 1957 - just a few years too early to get a Nobel Prize in one of any number of fields. One of my favorite aspects of Von Neumann was that he was a lifelong lover of history. He was a hacker - bouncing around between subjects. And he believed in human freedom. So much so that this wealthy and charismatic pseudo-aristocrat would dedicate his life to the study of knowledge and public service. So thank you for the Von Neumann Architecture and breaking computing down into ways that it couldn't be wholesale patented too early to gain wide adoption. And thank you for helping keep the mutually assured destruction from happening and for inspiring generations of scientists in so many fields. I'm stoked to be alive and not some pile of nuclear dust. And to be gainfully employed in computing. He had a considerable impact in both.

Oxide and Friends Twitter Space: September 27th, 2021The Books in the BoxWe've been holding a Twitter Space weekly on Mondays at 5p for about an hour. Even though it's not (yet?) a feature of Twitter Spaces, we have been recording them all; here is the recording for our Twitter Space for September 27th, 2021.In addition to Bryan Cantrill and Adam Leventhal, speakers on September 27th included Tom Lyon, Dan Cross, Antranig Vartanian Simeon Miteff Matt Campbell, Jeremy Tanner, Joshua Clulow, Ian, Tim Burnham, and Nathaniel Reindl. (Did we miss your name and/or get it wrong? Drop a PR!)Some of the topics we hit on, in the order that we hit them: Not recommended :-(  Dave Hitz and Pat Walsh (2008) How to Castrate a Bull book Peter Thiel (2014) Zero to One book [@2:45](https://youtu.be/zrZAHO89XGk?t=165) David Jacques Gerber (2015) The Inventor's Dilemma: The Remarkable Life of H. Joseph Gerber book [@7:21](https://youtu.be/zrZAHO89XGk?t=441) Sidney Dekker (2011) Drift into Failure: From Hunting Broken Components to Understanding Complex Systems book [@13:08](https://youtu.be/zrZAHO89XGk?t=788) Robert Buderi (1996) The Invention that Changed the World: The Story of Radar from War to Peace book MIT Rad Lab Series info Nuclear Magnetic Resonance wiki Richard Rhodes (1995) Dark Sun: The Making of the Hydrogen Bomb book Michael Riordan and Lillian Hoddeson (1997) Crystal Fire: The Birth of the Information Age book Craig Canine (1995) Dream Reaper: The Story of an Old-Fashioned Inventor in the High-Tech, High-Stakes World of Modern Agriculture book David Fisher and Marshall Fisher (1996) Tube: The Invention of Television book Michael Hiltzik (2015) Big Science: Ernest Lawrence and the Invention that Launched the Military-Industrial Complex book [@18:05](https://youtu.be/zrZAHO89XGk?t=1085) Ben Rich and Leo Janos (1994) Skunk Works: A Personal Memoir of My Years at Lockheed book Network Software Environment Lockheed SR-71 on display at the Sea, Air and Space Museum in NYC. [@26:52](https://youtu.be/zrZAHO89XGk?t=1612) Brian Dear (2017) The Friendly Orange Glow: The Untold Story of the Rise of Cyberculture book [@30:15](https://youtu.be/zrZAHO89XGk?t=1815) Randall Stross (1993) Steve Jobs and the NeXT Big Thing book [@32:21](https://youtu.be/zrZAHO89XGk?t=1941) Christophe Lécuyer and David C. Brock (2010) Makers of the Microchip: A Documentary History of Fairchild Semiconductor book [@33:06](https://youtu.be/zrZAHO89XGk?t=1986) Lamont Wood (2012) Datapoint: The Lost Story of the Texans Who Invented the Personal Computer Revolution book Charles Kenney (1992) Riding the Runaway Horse: The Rise and Decline of Wang Laboratories bookTom's tweet [@34:06](https://youtu.be/zrZAHO89XGk?t=2046) Bryan's Lost Box of Books! Edgar H. Schein et al (2003) DEC is Dead, Long Live DEC: The Lasting Legacy of Digital Equipment Corporation book [@36:56](https://youtu.be/zrZAHO89XGk?t=2216) Alan Payne (2021) Built to Fail: The Inside Story of Blockbuster's Inevitable Bust bookVideotape format war wiki Hackers (1995) movie. Watch the trailer ~2mins Steven Levy (1984) Hackers: Heroes of the Computer Revolution book [@42:32](https://youtu.be/zrZAHO89XGk?t=2552) Paul Halmos (1985) I Want to be a Mathematician: An Automathography book Paul Hoffman (1998) The Man Who Loved Only Numbers about Paul Erdős book 1981 text adventure game for the Apple II by Sierra On-Line, “Softporn Adventure” (wiki) [@49:16](https://youtu.be/zrZAHO89XGk?t=2956) Douglas Engelbart The Mother of All Demos wikiJohn Markoff (2005) What the Dormouse Said: How the Sixties Counterculture Shaped the Personal Computer Industry book Katie Hafner and Matthew Lyon (1998) Where Wizards Stay Up Late book 1972 Computer Networks: The Heralds of Resource Sharing documentary ~26mins (wiki) included big names like Corbató, Licklider and Bob Kahn. Gordon Moore (1965) Cramming more components onto integrated circuits paper and Moore's Law wiki [@52:37](https://youtu.be/zrZAHO89XGk?t=3157) Physicists, mathematicians, number theory, proofs  Wiles's proof of Fermat's Last Theorem 1993 wiki Simon Singh (1997) Fermat's Last Theorem book Ronald Calinger (2015) Leonhard Euler: Mathematical Genius in the Enlightenment purports to be the first full-scale “comprehensive and authoritative” biography [@1:00:12](https://youtu.be/zrZAHO89XGk?t=3612) Robert X. Cringely (1992) Accidental Empires: How the Boys of Silicon Valley Make Their Millions, Battle Foreign Competition, and Still Can't Get a Date book Jerry Kaplan (1996) Startup: A Silicon Valley Adventure book Brian Kernighan (2019) UNIX: A History and a Memoir book [@1:03:03](https://youtu.be/zrZAHO89XGk?t=3783) Douglas Coupland (1995) Microserfs book Douglas Coupland (1991) Generation X: Tales for an Accelerated Culture book Fry's Electronics wiki [@1:06:49](https://youtu.be/zrZAHO89XGk?t=4009) Michael A. Hiltzik (1999) Dealers of Lightning: Xerox PARC and the Dawn of the Computer Age book Albert Cory (pen name for Bob Purvy) (2021) Inventing the Future bookXerox Star wiki [@1:11:20](https://youtu.be/zrZAHO89XGk?t=4280) Corporate espionage, VMWare and Parallels, Cadence v. Avanti wiki, Cisco and Huawei (article) If we got something wrong or missed something, please file a PR! Our next Twitter space will likely be on Monday at 5p Pacific Time; stay tuned to our Twitter feeds for details. We'd love to have you join us, as we always love to hear from new speakers!

La vida de un matemático increíblemente productivo, que veía la vida de una forma muy particular.

By Paul Hoffman

The theme of this episode is alliances - human, biological and atomic. We start by celebrating the amazing properties of lichen, the symbiotic relationships it forms, how it shaped the earth and simply how beautiful it is to look at. Then we explore how carbon is able to create such an incredibly diverse range of materials, including soot, diamonds and graphite. We wrap up by delving into the life of renowned Hungarian mathematician Paul Erdős, the world's greatest human alliance maker, who wrote research papers with over 500 mathematicians. On the pod are Rowan Hooper, Anna Demming and Timothy Revell. Find out more at newscientist.com/podcasts Our GDPR privacy policy was updated on August 8, 2022. Visit acast.com/privacy for more information.

A lot of people are held up as geniuses (genii?)... But most of them are just pretty smart and pretty lucky. Paul Erdős though, he was something different. Rod tells Will his story! The Wholesome Show is Dr Will Grant and Dr Rod Lamberts, proudly brought to you by The Australian National Centre for the Public Awareness of Science!

On this episode, we talk about the following: On Almedalsveckan (https://almedalsveckan.info/), dissent and purpose of education being gaining consent. Closed borders. On making decisions and sticking with them. WHY do we struggle with making decisions vs HOW do we struggle with making them? Playing cards. Slow and fast thinking. "You cannot tell the quality of a decision from the outcome. [..] You can make the best decision you can, based on what you know, but the success of your decision will be heavily influenced by (a) relevant information you may lack and (b) luck or randomness." — Howard Marks, Oaktree Capital On winning as the basic premise which we make our decisions off of (winner/loser). Allowed to think, and provide your expertise. What decisions are worth your energy? Process-oriented model and patterned behaviours. Theory U. (https://www.presencing.org/aboutus/theory-u) Keeping yourself grounded. Boringness. Haruki Murakami, Paul Erdö, Kanye West. Curiosity and Tinder. Sommar i P1 - Anders Tegnell, Greta Thunberg. And touching on testing for COVID-19, again.

En el programa de esta semana hablamos de la figura de uno de los grandes matemáticos del S-XX, Paul Erdös, una persona con una personalidad muy especial que basó su vida en el amor por las matemáticas y la búsqueda de la belleza a través de ellas. Analizamos también el concepto de Belleza en diferentes ramas de la Ciencia. Todo ello de la mano de Ignacio Crespo, Víctor Marco, David Ibáñez, Vicent Picó y Francis Villatoro. Escucha el episodio completo en la app de iVoox, o descubre todo el catálogo de iVoox Originals

For this trilogy, we meet a more modern mathematician – Paul Erdös.  We can wait to introduce to you one of our favorites: a teacher at heart who has collaborated with more mathematicians than anyone…ever! In this episode, we’ll attempt to answer the following questions.If an evil spirit wants to destroy humanity, do you sic the computers on it or punch it in the face?What’s the fastest way to get thrown off a plane?What do either of these things have to do with math?Let us know your thoughts.  Follow us on Facebook or email us at podcast@infinitelyirrational.com.  For math and the research behind the episode, visit our webpage at www.infinitelyirrational.com We look forward to hearing from you!

Borrelpraat is terug! Het nieuwe seizoen start lekker chaotisch en lang, met feitjes over een Titanic replica, psychologische spelletjes met kinderen, de Dag Dat Disco Doodging en een Hongaarse machine die caffeine omzet in wiskundige theorieën.

Paul ErdÅ‘s, the famously eccentric, peripatetic and prolific 20th-century mathematician, was fond of the idea that God has a celestial volume containing the perfect proof of every mathematical theorem. “This one is from The Book,” he would declare when he wanted to bestow his highest praise on a beautiful proof. Never mind that ErdÅ‘s doubted God's very existence.

A solid routine fosters a well-worn groove for one’s mental energies and helps stave off the tyranny of moods. In this episode of Made You Think, Neil and I discuss​ Daily Rituals by Mason Currey. In this book, Currey edits together first-hand accounts from different artists and creative thinkers of how they went about their everyday lives. “I write when the spirit moves me,”  said, “and the spirit moves me every day.” – Faulkner. We cover a wide range of topics, including: The problem with lifestyle gurus. Whether drugs enhance genius. Coffee’s role in causing the Renaissance. How people in far-off countries let each other know they were alive before the internet. Beethoven’s perfect cup of Joe. Why you should pin notes to your clothes' Night Owls vs. Early Birds - who gets more worms. Hacks to become an morning person. And much more. Please enjoy, and be sure to grab a copy of Daily Rituals: How Artists Work by Mason Currey! If you enjoyed this episode, be sure to check out our episode on 12 Rules for Life by Jordan B. Peterson for more tips on how to order your day, as well as our episode on Elon Musk to discover what rituals a modern-day success keeps. Be sure to join our mailing list to find out about what books are coming up, giveaways we're running, special events, and more. Links from the Episode Mentioned in the show: Sleep debt [8:00] Dymaxion sleep [8:46] Polyphasic sleep [9:05] Alt-right [11:55] Benzedrine [12:58] Ritalin [18:34] The Renaissance [22:26] Obsessive-Compulsive Disorder – OCD [29:10] Franklin’s 13 Virtues [32:21] How to Plan your Ideal Day by Taylor Pearson [39:48] Maker’s Schedule, Manager’s Schedule by Paul Graham [40:05] Growth Machine [40:10] On-demand economy [44:58] 1099 economy [44:58] Peterson’s guide to essay writing [51:44] Mnemonics [57:10] Keto-adaptation [59:50] Hormetic stress [1:07:55] Night Owl Mutation [1:12:36] Gilgamesh Platform [1:20:50] Books mentioned: Antifragile by Nassim Nicholas Taleb [12:28] (Nat’s Notes) (book episode) Come Again? by Nat Eliason [19:26] Benjamin Franklin by Walter Isaacson [32:21] The 4-Hour Body by Tim Ferriss [34:36] Skin in the Game by Nassim Nicholas Taleb [34:47] Tropic of Cancer by Henry Miller [48:42] The War of Art - Steven Pressfield [50:44] The Bell Jar by Sylvia Plath [1:02:18] Merchants of Doubt by Naomi Oreskes and Erik M. Conway [1:07:55] (Nat’s notes) (book episode) The Fountainhead by Ayn Rand [1:10:50] Atlas Shrugged by Ayn Rand [1:11:10] People mentioned: Francis Bacon [2:30] Nassim Nicholas Taleb [3:54] (Antifragile episode) Tim Ferriss [5:00] Jocko [5:08] Buckminster Fuller [8:46] Steve Pavlina [10:00] V. S. Pritchett [11:30] W. H. Auden [12:58] Immanuel Kant [13:58] Michel Foucault [13:58] Ryan Holiday [14:44] Beethoven [29:16] Nikola Tesla [29:34] Tom Cruise [30:37] Benjamin Franklin [32:32] Charles Darwin [36:30] (on this podcast) Henry Miller [48:42] William Faulkner [50:27] Ann Beattie [50:58] Haruki Murakami [52:37] Scott Britain [53:11] Ramit Sethi [53:11] Jonathan Edwards [57:10] Sylvia Plath [1:02:12] Woody Allen [1:02:37] Jean Paul Sartre [1:03:00] David Lynch [1:06:20] Paul Erdős [1:10:25] Ayn Rand [1:10:50] Show Topics 00:50 – Book covers daily rituals of a bunch of people, not just artists. Broad interpretation of artists, anyone who does creative or critical thinking work. 01:24 – There’s a surprising amount of drug-use in this book, lots of alcohol, and not sleeping. On the one hand this seemed undisciplined, but on the other these people did have very regular schedules. There was discipline to keep these activities in a well-worn groove. 01:53 – A hangover can make it easier to write – your brain can be more focused. In some ways it’s like the opposite of being caffeinated. 03:10 – The book has an interesting layout, there’s no attempt at narrative, each chapter is about a new person’s routine. 03:54 – Taleb keeps no routine, he doesn’t even use a calendar. 04:00 – Small gripe with books like this as these are idealized and narrativized versions of these rituals. None of them get drunk and yell at people on Twitter. Wouldn’t be surprised if they’re only true 20-50% of the time. 04:55 – Problem with a lot of the lifestyle guru type people. They don’t do all of that stuff everyday. Except Jocko, he’s never overslept in the last 15 years. His morning routine seems to be the same wherever he is. 06:02 – Maintaining a normal schedule when you travel across time zones helps you adapt way faster. The minute you go back to your hotel you’ll crash, it’s game over! Jet lag is a strange tiredness, especially if you drink coffee, like you’re wired and drunk at the same time. 08:00 – Questioning whether you can save up a store of sleep for a rainy day. Apparently you can’t front load it, but when you get into debt you need to pay it back! 08:46 – Types of polyphasic sleep. Buckminster Fuller developed dymaxion sleep, he did it for two years and he’s the only one who’s ever been able to do it. 5-10% of the population legitimately need less sleep. Everyone else thinks they’re in that group but they’re not. 09:05 – When they tried one study on polyphasic sleep the subject just crashed and they could not wake him up. 11:43 – Is it quote or quotation? Don’t want to anger the grammar people! 11:55 – Download all of our episodes to find out whether one of our team is part of the alt-right. 12:58 – Auden was popping Benzedrine all the time. He regarded it as a “labor saving device,” a daily multivitamin. In the mental kitchen alongside alcohol, coffee and tobacco. 13:40 – Were these people great producers because of these habits or despite them? Question of whether the live-fast, die-young lifestyle enhances genius. 16:22 – Personal experiences and use of some drugs. Coffee for work and productivity, micro-dosing LSD for the same. Marijuana for an after wine session. Fear of getting hooked with tobacco vs alcohol. 18:34 – Ritalin/Aterol for effortless full-speed ahead concentration. 20:12 – Doctors overprescribe Aterol – 90% of people taking it don’t need it. It’s very hard to quit, people get frustrated at never hitting the same level of quality. In some ways similar to steroids. 22:26 – The Renaissance happened when people stopped drinking beer all day and switched to coffee. 22:36 – Drinking habits around the world. Beer used to be brewed as water wasn’t safe to drink. They would steep the same grains up to four times. In Asia they would drink tea all day, which is probably why they were historically more productive than Europe. 24:55 – In sushi bars in Tokyo they have a tap of green tea. In Germany they give you beer, Americans drink water and now they’re more productive because they’re hydrated. 25:53 – Tangent – Most people who are in America now, their ancestors were the risk-takers. The people who took the initiative to leave behind everything they knew. So culturally this is ingrained. 26:59 – People used booked calls to let family on the other side of the world know they were alive before Skype. 27:40 – The history of pokes on Facebook – they would let a non-friend see your profile for a few days without actually becoming your friend. 29:10 – A significant number of people featured in the book seemed to have OCD, they were trying to control chaos. Beethoven’s coffee had to have 60 beans a cup. Kant had an extremely orderly schedule. The clock tower in town stayed on time less passionately than Kant. 32:00 – Everyone has odd habits, especially artists who spend a lot of time in their heads. 32:21 – The general impression of Benjamin Franklin is “early to bed, early to rise” but he seemed to set his 13 virtues up as goals rather than things he’d achieved. Comparing Ben Franklin to Tim Ferriss. People disapprove of others not following their own advice to the letter. 35:53 – Controversy when one updates his opinions. 36:16 – It’s surprising how few hours people worked – the bulk of the creative work was 5-6 hours a day, max. Darwin was famous for having two 3 hour work blocks. It’s hard to do creative work for longer. But good for mental energy. 38:00 – Tangent. It’s hard to be spontaneous in New York. Phone calls are scheduled a week in advance.  Time management tips: set regular stand-ups, only book meetings at certain times. Color-code your calendar. 40:30 – Work environments are moving towards being more results orientated, moving away from people just sitting at their desks doing nothing. A relic of the production line. Schedule Tetris in large corporations. 43:26 – Hack. Schedule hour meetings for 40 minutes, or half hour meetings for 20 minutes. It forces people to condense. 44:58 – Data should make it easier for people to get paid based on productivity rather than time. For consulting jobs, it doesn’t make sense to charge based on time. Historically, time was the best way of measuring output and so this made sense. 47:43 – Education is also stuck in this time loop since it was originally influenced by factory organization. Most interesting ideas that end up leading somewhere come from play, from free time. 49:21 – After unsuccessfully trying for ten years in New York, Henry Miller had given up writing, when he finally wrote a novel in Paris it was published without editing, there’s sentences that just stop mid-way. Seeing from outside, it seems these creatives are able to follow a routine without anyone forcing them. 51:44 – Jordan Peterson says there’s no such thing as writer’s block. If you’re stuck it’s because you have run out of things to say, you need to unblock yourself. 53:10 – Sleep and wake up at the same time every day, even on weekends, may make you feel much more energized. Sleeping in on the weekend it’s almost like changing time zones every five days. 56:41 – Giveaways are coming, sign up for the email list. 57:03 – To remember to do important things pin a piece of paper on a different piece of your clothing, a form of mnemonics. 58:15 – When you first wake up, that’s a different person. You have to find ways of tricking him into not hitting snooze. Routines and replacement can help you get past undesirable behavior. 59:04 – Sponsor time. Mushroom elixir from Four Sigmatic and bone broth from Kettle & Fire along with Perfecto Keto collagen. Use them to replace alcohol in the evening! 1:01:38 – Despite living in climate controlled environments, we still feel like it’s cold outside when it’s winter, even though it’s the same temperature where we are. 1:03:30 – Some people’s capacity for alcohol is so far beyond the average. If you’re regimented and disciplined you could physically drink a bottle of spirits a day. 1:07:15 – Sugar is like a mild form of cocaine. It’s a stimulant followed by a crash. Hormetic stressors are only “natural”. 1:09:20 – Psycho-active drugs don’t make your brain do things it can’t do, they mimic neural pathways. Maybe adaptation is down-regulating the amount of neurochemicals being released in response to the trigger. If you know, write in! 1:11:36 – Morning Working vs Night-time working theme. More of the creators were geared towards mornings but it wasn’t across the board. Evolutionarily, it doesn’t make sense for humans to want to work at night. 1:14:20 – Waking up hack. Trick yourself into getting up by telling yourself you can go back to bed in 30 minutes if you’re still tired. 1:14:45 – Wrap-up and sponsor time. Perfecto Keto is perfect for all your ketogenic diet needs. Exogenous coffee-flavored ketones. Their matcha MCT oil powder is highly recommended for focusing. You can use the MCT oil with a Four Sigmatic mushroom coffee or your hot chocolate, all 15% OFF through our sponsored link or use the coupon code mentioned. Kettle & Fire will give you 20% OFF on their delicious bone broths –beef recommended for cooking, and chicken for a good, hot wintery drink– and free shipping! Listen to know how to get a mushroom-flavored bone broth. And you can always support us by going through our Amazon sponsored link and checking out our Support page. 1:20:50 – The new Gilgamesh cryptocurrency is building a social network built on knowledge sharing. If you enjoyed this episode, don’t forget to subscribe at https://madeyouthinkpodcast.com

In 1770, Hungarian engineer Wolfgang von Kempelen unveiled a miracle: a mechanical man who could play chess against human challengers. In this week's episode of the Futility Closet podcast we'll meet Kempelen's Mechanical Turk, which mystified audiences in Europe and the United States for more than 60 years. We'll also sit down with Paul Erdős and puzzle over a useful amateur. Intro: Lewis Carroll sent a birthday wish list to child friend Jessie Sinclair in 1878. An octopus named Paul picked the winners of all seven of Germany’s World Cup games in 2010. Sources for our feature on the Mechanical Turk: Tom Standage, The Turk, 2002. Elizabeth Bridges, "Maria Theresa, 'The Turk,' and Habsburg Nostalgia," Journal of Austrian Studies 47:2 (Summer 2014), 17-36. Stephen P. Rice, "Making Way for the Machine: Maelzel's Automaton Chess-Player and Antebellum American Culture," Proceedings of the Massachusetts Historical Society, Third Series, 106 (1994), 1-16. Dan Campbell, "'Echec': The Deutsches Museum Reconstructs the Chess-Playing Turk," Events and Sightings, IEEE Annals of the History of Computing 26:2 (April-June 2004), 84-85. John F. Ohl and Joseph Earl Arrington, "John Maelzel, Master Showman of Automata and Panoramas," Pennsylvania Magazine of History and Biography 84:1 (January 1960), 56-92. James W. Cook Jr., "From the Age of Reason to the Age of Barnum: The Great Automaton Chess-Player and the Emergence of Victorian Cultural Illusionism," Winterthur Portfolio 30:4 (Winter 1995), 231-257. W.K. Wimsatt Jr., "Poe and the Chess Automaton," American Literature 11:2 (May 1939), 138-151. Peggy Aldrich Kidwell, "Playing Checkers With Machines -- From Ajeeb to Chinook," Information & Culture 50:4 (2015), 578-587. Brian P. Bloomfield and Theo Vurdubakis, "IBM's Chess Players: On AI and Its Supplements," Information Society 24 (2008), 69-82. Nathan Ensmenger, "Is Chess the Drosophila of Artificial Intelligence? A Social History of an Algorithm," Social Studies of Science 42:1 (February 2012), 5-30. Martin Kemp, "A Mechanical Mind," Nature 421:6920 (Jan. 16, 2003), 214. Marco Ernandes, "Artificial Intelligence & Games: Should Computational Psychology Be Revalued?" Topoi 24:2 (September 2005), 229–242. Brian P. Bloomfield and Theo Vurdubakis, "The Revenge of the Object? On Artificial Intelligence as a Cultural Enterprise," Social Analysis 41:1 (March 1997), 29-45. Mark Sussman, "Performing the Intelligent Machine: Deception and Enchantment in the Life of the Automaton Chess Player," TDR 43:3 (Autumn 1999), 81-96. James Berkley, "Post-Human Mimesis and the Debunked Machine: Reading Environmental Appropriation in Poe's 'Maelzel's Chess-Player' and 'The Man That Was Used Up,'" Comparative Literature Studies 41:3 (2004), 356-376. Kat Eschner, "Debunking the Mechanical Turk Helped Set Edgar Allan Poe on the Path to Mystery Writing," Smithsonian.com, July 20, 2017. Lincoln Michel, "The Grandmaster Hoax," Paris Review, March 28, 2012. Adam Gopnik, "A Point of View: Chess and 18th Century Artificial Intelligence," BBC News, March 22, 2013. http://www.bbc.com/news/magazine-21876120 Ella Morton, "The Mechanical Chess Player That Unsettled the World," Slate, Aug. 20, 2015. "The Automaton Chess Player," Scientific American 48:7 (February 17, 1883), 103-104. Robert Willis, An Attempt to Analyse the Automaton Chess Player, of Mr. de Kempelen, 1821. "The Automaton Chess-Player," Cornhill Magazine 5:27 (September 1885), 299-306. Edgar Allan Poe, "Maelzel's Chess-Player," Southern Literary Messenger, April 1836, 318-326. You can play through six of the Turk's games on Chessgames.com. Listener mail: Nicholas Gibbs, "Voynich Manuscript: The Solution," Times Literary Supplement, Sept. 5, 2017. Annalee Newitz, "The Mysterious Voynich Manuscript Has Finally Been Decoded," Ars Technica, Sept. 8, 2017. Natasha Frost, "The World's Most Mysterious Medieval Manuscript May No Longer Be a Mystery," Atlas Obscura, Sept. 8, 2017. Sarah Zhang, "Has a Mysterious Medieval Code Really Been Solved?" Atlantic, Sept. 10, 2017. Annalee Newitz, "So Much for That Voynich Manuscript 'Solution,'" Ars Technica, Sept. 10, 2017. "Imaginary Erdős Number," Numberphile, Nov. 26, 2014. Oleg Pikhurko, "Erdős Lap Number," Mathematics Institute, University of Warwick (accessed Sept. 15, 2017). This week's lateral thinking puzzle was contributed by listener Alex Baumans, who sent this corroborating link (warning -- this spoils the puzzle). You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset. Please consider becoming a patron of Futility Closet -- on our Patreon page you can pledge any amount per episode, and we've set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website. Many thanks to Doug Ross for the music in this episode. If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Exploring the beauty of maths, we may just find that faith and proof are not mutually exclusive. --- "An equation for me has no meaning unless it expresses a thought of God." - Srinivasa Ramanujan. Ramanujan was a self-taught mathematical genius from India, who moved to Cambridge University in 1914 to work with the eminent mathematician, G. H. Hardy. His story, as told in the movie The Man Who Knew Infinity, is not only one of a brilliant mind capable of remarkable work, but of an unlikely friendship between a devout Hindu, and an atheist who was a stickler for proofs. "Your theorem is wrong," Hardy tells Ramanujan in the movie, "this is why we cannot publish anymore until you finally trust me on this business of proofs." Once described as "the most romantic figure in recent mathematical history", Ramanujan's life also speaks to the idea of finding beauty in maths - and this is what we explore in this episode of Life & Faith. You'll hear from a leading Australian mathematician about her response to the film, and her sense of the relationship between divine reality and mathematical practice. Then, Oxford mathematics professor John Lennox shares his thoughts about the beauty of the world of numbers and patterns. We wrap up the episode with a poem written and read by former Archbishop of Canterbury, Rowan Williams - you won't want to miss it. "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is." - Paul Erdős --- This episode was first broadcast on 30 June 2016.

Mathematician Paul Erdős had no home, no job, and no hobbies. Instead, for 60 years he wandered the world, staying with each of hundreds of collaborators just long enough to finish a project, and then moving on. In this week's episode of the Futility Closet podcast we'll meet the "magician of Budapest," whose restless brilliance made him the most prolific mathematician of the 20th century. We'll also ponder Japanese cannibalism in World War II and puzzle over a senseless stabbing. Intro: Elbert Hubbard published 12 blank pages in 1905. A duck spent 18 months in the U.S. 2nd Marine Division in 1943. Sources for our feature on Paul Erdős: Paul Hoffman, The Man Who Loved Only Numbers, 1999. The magisterial biography of Erdős. The first chapter is here. Bruce Schechter, My Brain Is Open, 2000. Béla Bollobás, "Paul Erdős (1913-96)," Nature, 383:6601 (Oct. 17, 1996), 584. Melvin Henriksen, "Reminiscences of Paul Erdős," Mathematical Association of America (accessed June 10, 2017). László Babai, Carl Pomerance, and Péter Vértesi, "The Mathematics of Paul Erdős," Notices of the AMS 45:1 (January 1998). László Babai and Joel Spencer, "Paul Erdős (1913–1996)," Notices of the AMS 45:1 (January 1998). Ronald L. Graham, Jaroslav Nesetril, Steve Butler, eds., The Mathematics of Paul Erdős, 2013. Rodrigo De Castro and Jerrold W. Grossman, "Famous Trails to Paul Erdős," Mathematical Intelligencer 21:3 (January 1999), 51–53. Bruce Torrence and Ron Graham, "The 100th Birthday of Paul Erdős/Remembering Erdős," Math Horizons 20:4 (April 2013), 10-12. Krishnaswami Alladi et al., "Reflections on Paul Erdős on His Birth Centenary," Parts I and II, Notices of the American Mathematical Society 62:2 and 62:3 (February and March 2015). Béla Bollobás, "To Prove and Conjecture: Paul Erdős and His Mathematics," American Mathematical Monthly 105:3 (March 1998), 209-237. "Information About Paul Erdős (1913-1996)," Oakland University (accessed June 13, 2017). Calla Cofield, "An Arbitrary Number of Years Since Mathematician Paul Erdős's Birth," Scientific American, March 26, 2013. Béla Bollobás, "Obituary: Paul Erdős," Independent, Oct. 2, 1996. N Is a Number: A Portrait of Paul Erdős, Kanopy Streaming, 2014. "Paul Erdős," MacTutor History of Mathematics Archive (accessed June 10, 2017). Above: Erdős teaching 10-year-old Terence Tao in 1985. Tao is now recognized as one of the world's finest mathematicians; he received the Fields Medal in 2006. Listener mail: Wikipedia, "Chichijima Incident" (accessed June 23, 2017). Charles Laurence, "George HW Bush Narrowly Escaped Comrades' Fate of Being Killed and Eaten by Japanese Captors," Telegraph, Feb. 6, 2017. James Bradley, Flyboys, 2003. This week's lateral thinking puzzle was contributed by listener Waldo van der Waal, who sent this corroborating link (warning -- this spoils the puzzle). You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset. Please consider becoming a patron of Futility Closet -- on our Patreon page you can pledge any amount per episode, and we've set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website or buy merchandise in our store. Many thanks to Doug Ross for the music in this episode. If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Cycle de conférences organisées par la Bibliothèque nationale de France et la Société mathématique de France. Conférence du 22 février 2017. Conférences organisées à l'attention du grand public, des professeurs du second degré et des lycéens et étudiants, les conférenciers partent d'un texte, ou d'un corpus de textes, et montrent en quoi ce texte les a influencés personnellement et a conduit à des recherches contemporaines.

Cycle de conférences organisées par la Bibliothèque nationale de France et la Société mathématique de France. Conférence du 22 février 2017. Conférences organisées à l'attention du grand public, des professeurs du second degré et des lycéens et étudiants, les conférenciers partent d'un texte, ou d'un corpus de textes, et montrent en quoi ce texte les a influencés personnellement et a conduit à des recherches contemporaines.

Cycle de conférences organisées par la Bibliothèque nationale de France et la Société mathématique de France. Conférence du 22 février 2017. Conférences organisées à l'attention du grand public, des professeurs du second degré et des lycéens et étudiants, les conférenciers partent d'un texte, ou d'un corpus de textes, et montrent en quoi ce texte les a influencés personnellement et a conduit à des recherches contemporaines.

“An equation for me has no meaning unless it expresses a thought of God.” – Srinivasa Ramanujan Ramanujan was a self-taught mathematical genius from India, who moved to Cambridge University in 1914 to work with the eminent mathematician, GH Hardy  His story, as told in the movie The Man Who Knew Infinity, not only tells of a brilliant mind capable of remarkable work, but of an unlikely friendship between a devout Hindu, and an atheist who was a stickler for proofs. “Your theorem is wrong,” Hardy tells Ramanujan in the movie, “this is why we cannot publish anymore until you finally trust me on this business of proofs.” Once described as “the most romantic figure in recent mathematical history”, Ramanujan's life also speaks to the idea of finding beauty in maths – and this is what we explore in this episode of Life and Faith. You'll hear from a homegrown mathematician about how Ramanujan's work has been influential in her own. Then, Oxford mathematics professor, John Lennox, shares his thoughts about the beauty of the world of numbers and patterns. Finally, we wrap up the episode with a beautiful poem from former Archbishop of Canterbury, Rowan Williams – you won't want to miss it. “Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.” – Paul Erdős ---  SUBSCRIBE to our podcast: http://bit.ly/lifeandfaithpodcast READ a review of The Man Who Knew Infinity from ISCAST: http://iscast.org/node/1144

We hereby deliver an evening episode comprising role-playing, word pictures, and other podcasting art forms to convey critical information on, among other miscellany: Christian’s week of broken things, follow-up on lines, math and the book of true reasons, Mark Lemley’s article on “faith-based IP,” imagining Benjamin Franklin’s lightning powered potato peeler, iPhone copycats, and, morality aside, the death penalty’s stupidity, and the measure of a civilization. This show’s links: The Wirecutter and the Sweet Home Oral Argument 55: Cronut Lines The documentary about people competing to win a truck, Hands on a Hardbody Oral Argument 51: The Faucet (guest John Pfaff) Euclid’s Elements About Paul Erdős Mark Lemley, Faith-Based Intellectual Property Frank Michelman, Takings Mark Lemley, The Surprising Virtues of Treating Trade Secrets as IP Rights International News Service v. Associated Press SCOTUSblog on Glossip v. Gross Associated Press, Utah Brings Back Firing Squads as Lethal Injection Drugs Remain Scarce About Cameron Todd Willingham Oral Argument 45: Sacrifice About “death-qualified” juries

Об этой серии Cumprimos uma promessa e fazemos um dossiê sobre a cena da microcomputação da Cortina de Ferro. В тази част на епизода Falamos mais de história que um dia de programação do History Channel, do cenário (RPN, Von Neumann, Paul Erdös, embargo da CoCom, grandes indústrias), dos mainframes (especificação ES EVM), dos minicomputadores … Continue lendo Episódio 33 – Micros da Cortina de Ferro – Parte A →

In the sixth Advent Podcast, Robin Ince talks to Dave Gorman about the mathematician Paul Erdős, and how, where all actors have a "Bacon Number" to denote their degrees of separation from Kevin Bacon, all mathematicians have an Erdős Number. He would also like a Soda Stream for Christmas. Recorded in 2008. Music by Andrea Rocca.