From an Uneven Life, a Theory of Roughness
Question: As you write your memoirs, which memories are the most fun and the most difficult to look back on?
Benoit Mandelbrot: Well, my life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept. I was born in Poland and moved to France as a child shortly before World War II. During World War II, I was lucky to live in the French equivalent of Appalachia, a region which is sort of not very high mountains, but very, very poor, and Appalachia we are poorer even, so poorer than Appalachia of the United States. And for me, I was in high school where things were very easy. It was a small high school way up in the hills and had mostly a private intellectual life. I read many books; there were many books, a very good library. I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening. It was a very dangerous period. But since I had nothing to lose, I was dreaming of what I could do.
Then the war ended. I had very, very little training in taking an exam to determine a scientist’s life in France. There were two schools, both very small. One tiny, and one small, which in a certain sense was the place that I was sure I wanted to go. I had only a few months of finding out how the exam proceeded, but I took the exam and perhaps because of inherited gifts, I did very well. In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems. The physics I could not guess, other things I could not guess. But then I had a big choice, should I go into mathematics in a small and **** school. Or should I go to a bigger school in which, in a certain sense would give me time to decide what I wanted to do?
First I entered the small school where I was, as a matter of fact, number one of the students who entered then. But immediately, I left because that school, again, was going to teach me something which I did not fully believe, namely mathematics separate from everything else. It was excellent mathematics, French mathematics was very high level, but in everything else it was not even present. And I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different. Not less, not more but different. Namely, combine pure mathematics at which I was very good, with the real world of which I was very, very curious.
And so, I did not go to École Polytechnique. It was a very rough decision, and the year when I took this decision remembers my memory very, very strongly. Then for several years, I just was lost a bit. I was looking for a good place. I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in. Fortunately, IBM was building a research center, I went there for a summer thing, for a summer only. I knew this summer, decided to stay. It was a very big gamble. I lost my job in France, I received a job in which was extremely uncertain, how long would IBM be interested in research, but the gamble was taken and very shortly afterwards, I had this extraordinary fortune of stopping at Harvard to do a lecture and learning about the price variation in just the right way. At a time when nobody was looking, was realizing that either one needed, or one could make a theory of price variation other than the theory of 1900 at which Bachelier had proposed, which was very, very far from being representative of the actual thing.
So, I went to IBM and I was fortunate in being allowed – to be successful as to go from field to field, which in a way was what I had been hoping for. I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world. And IBM let me do so. I touched on far more topics than anybody would have found reasonable. I was often told, “Settle down, stay in one field, don’t go all the time to another field.” But I was just compelled to move from one thing to another.
And fractal geometry was not an idea which I had early on, for something was developed progressively. I didn’t choose to go into the topic because of any compelling reason, but because the problems there seemed to be somehow similar to the ones I knew how to handle. I had experienced this kind of problem and gradually realized that I was truly putting together a new theory. A theory of roughness. What is roughness? Everybody knows what is roughness. When was roughness discovered? Well, prehistory. Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated. And physics had laid them aside because they were too complicated. One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
So, one of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.
Recorded on February 17, 2010
Interviewed by Austin \r\nAllen
As the celebrated mathematician writes his memoirs, he reflects on the combination of good luck, hard luck, and constant dreaming that made his life a success.
Dominique Crenn, the only female chef in America with three Michelin stars, joins Big Think Live this Thursday at 1pm ET.
Astronomers spot an object heading into Earth orbit.
Minimoons<p>Scientists have confirmed just two prior minimoons. One was <a href="https://en.wikipedia.org/wiki/2006_RH120" target="_blank">2006 RH120</a>, which orbited us from September 2006 to June 2007. The other was <a href="https://en.wikipedia.org/wiki/2020_CD3" target="_blank">2020 CD3</a>, which got stuck in the 2015–2016 timeframe, and is believed to gotten away in May 2020.</p><p>2020 SO, the new kid on the block, is expected to arrive in October 2020 and pop out of orbit in May 2021.</p><div id="37962" class="rm-shortcode" data-rm-shortcode-id="f4c0fc8a2cba6536ea4cd960ebed3e6e"><blockquote class="twitter-tweet twitter-custom-tweet" data-twitter-tweet-id="1307729521869611008" data-partner="rebelmouse"><div style="margin:1em 0">Asteroid 2020 SO may get captured by Earth from Oct 2020 - May 2021. Current nominal trajectory shows shows capture… https://t.co/F5utxRvN6Z</div> — Tony Dunn (@Tony Dunn)<a href="https://twitter.com/tony873004/statuses/1307729521869611008">1600621989.0</a></blockquote></div>
Identifying 2020 SO<p>The first clue 2020 SO isn't your ordinary asteroid is its exceptionally low velocity. It's traveling much more slowly that a typical asteroid — their <a href="https://www.lpi.usra.edu/exploration/training/illustrations/craterMechanics/" target="_blank">average rate of travel</a> <a href="https://www.lpi.usra.edu/exploration/training/illustrations/craterMechanics/" target="_blank" rel="noopener noreferrer"></a>is 18 kilometers (58,000 feet) per second. Even <a href="https://en.wikipedia.org/wiki/Moon_rock" target="_blank">moon rocks</a> sent careening into Earth orbit by impacts on the lunar surface outpace pokey 2020 SO.</p><p>For another thing, 2020 SO has an orbital path very similar to Earth's, lasting about one Earth year. It's also just slightly less circular than our own orbit, from which it's barely tilted off-axis.</p><p>So, what is it? <a href="https://cneos.jpl.nasa.gov/ca/" target="_blank">NASA estimates</a> that the object has dimensions very reminiscent of a discarded Centaur rocket stage from the <a href="https://en.wikipedia.org/wiki/Surveyor_2" target="_blank" rel="noopener noreferrer">Surveyor 2 mission</a> that landed an unmanned craft on the moon. Back in the day, rocket stages were jettisoned as craft were aimed toward their desired position. This stuff, if released high enough, remains in space. It appears that this Centaur rocket, launched in September 1966, is now making its way back homeward, at least for a little bit.</p><p>When 2020 SO arrives at its closest point in December, the rocket is expected to be about 50,000 kilometers from Earth. Its next closest approach is much further: 220,000 kilometers, in February 2010.</p><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQzMDk3NC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyODg1MTQ1MX0.HGknDwqp0GmeuczKY_AS7vrPG7KMFUc_XO95tNoI2xo/img.jpg?width=980" id="e5cda" class="rm-shortcode" data-rm-shortcode-id="85eb1f790d8c3ee5b261f7ba13eaa5e1" data-rm-shortcode-name="rebelmouse-image" alt="Centaur rocket stage" />
Centaur rocket stage
What we may be able to learn<p>Earthly space programs being as young as they are, scientists would love to know what's happened to our rocket during a half century in space.</p><p>While 2020 SO won't get close enough to drop into our atmosphere, its slow progress has scientists hopeful that they'll still get some kind of a decent look at it.</p><p>Spectroscopy may be able to reveal what the rocket's surface is like now — has any of its paint survived, for example? Of course, being out in space, it's likely to have been hit by lots of dust and micrometeorites, so the current state of its surfaces is also of interest. Experts are curious to know how reflective the rocket is at this point, valuable information that can help planners of future long-term missions anticipate how well a craft out in space for extended periods will remain able to reflect sunlight.</p>
From cryonics to time travel, here are some of the (highly speculative) methods that might someday be used to bring people back to life.
- Alexey Turchin and Maxim Chernyakov, researchers belonging to the transhumanism movement, wrote a paper outlining the main ways technology might someday make resurrection possible.
- The methods are highly speculative, ranging from cryonics to digital reconstruction of individual personalities.
- Surveys suggest most people would not choose to live forever if given the option.
Immortality and identity<p>The paper defines life as a "continued stream of subjective experiences" and death as the permanent end of that stream. Immortality, to them, is a "life stream without end," and resurrection is the "continuation of that same stream of experiences after an arbitrarily long gap."</p><p>Another key clarification is the identity problem: How would you know that a downloaded copy of yourself really was going to be <em>you? </em>Couldn't it just be a convincing yet incomplete and fundamentally distinct representation of your brain?</p><p>If you believe that your copy is not <em>you</em>, that implies you believe there's something more to your identity than the (currently) quantifiable information contained within your brain and body, according to the researchers. In other words, your "informational identity" does not constitute your true identity.</p><p>In this scenario, there must exist what the researchers call a "non-informational identity carrier" (NIIC). This could be something like a "soul." It could be "qualia," which are the unmeasurable "subjective experiences which could be unique to every person." Or maybe it doesn't exist at all.</p><p>It's no matter: The researchers say resurrection, in some form, should be possible in either scenario.</p><p style="margin-left: 20px;">"If no 'soul' exist[s], resurrection is possible via information preservation; if soul[s] exist, resurrection is possible via returning of the "soul" into the new body. But some forms of NIIC are also very fragile and mortal, like continuity," the researchers noted.</p><p style="margin-left: 20px;">"The problem of the nature of human identity could be solved by future superintelligent AI, but for now it cannot be definitively solved. This means that we should try to preserve as much identity as possible and not refuse any approaches to life extension and resurrection even if they contradict our intuitions about identity, as our notions of identity could change later."</p>
Potential resurrection methods<p>Turchin and Chernyakov outline seven broad categories of potential resurrection methods, ranked from the most plausible to most speculative.<br></p><p>The first category includes methods practiced while the person is alive, like cryonics, plastination, and preserving brain tissue through processes like chemical fixation. The researchers noted that there have been "suggestions that the claustrum, hypothalamus, or even a single neuron is the neural correlate of consciousness," so it may be possible to preserve just that part of a person, and later implant it into another organism.</p><p>Other methods get far stranger. For example, one method includes super-intelligent AI that uses a <a href="https://en.wikipedia.org/wiki/Dyson_sphere#:~:text=A%20Dyson%20sphere%20is%20a,percentage%20of%20its%20power%20output." target="_blank">Dyson sphere</a> to harness the power of the sun to "power enormous calculation engines" that would "reconstruct" people who collected a sufficient amount of data on their identities.</p>
Turchin<p style="margin-left: 20px;">"The main idea of a resurrection-simulation is that if one takes the DNA of a past person and subjects it to the same developmental condition, as well as correcting the development based on some known outcomes, it is possible to create a model of a past person which is very close to the original," the researchers wrote.</p><p style="margin-left: 20px;">"DNA samples of most people who lived in past 1 to 2 centuries could be extracted via global archeology. After the moment of death, the simulated person is moved into some form of the afterlife, perhaps similar to his religious expectations, where he meets his relatives."</p><p>Delving further into sci-fi territory, another resurrection method would use time-travel technology.</p><p style="margin-left: 20px;">"If there will at some point be technology that allows travel to the past, then our future descendants will be able to directly save people dying in the past by collecting their brains at the moment of death and replacing them with replicas," the paper states.</p><p>How? Sending tiny robots back in time.</p><p style="margin-left: 20px;">"A nanorobot could be sent several billion years before now, where it could secretly replicate and sow nanotech within all living being[s] without affecting the course of history. At the moment of death, such nanorobots could be activated to collect data about the brain and preserve it somewhere until its future resurrection; thus, there would be no need for forward time travel."</p>
Pixabay<p>The paper <a href="https://www.academia.edu/36998733/Classification_of_the_approaches_to_the_technological_resurrection" target="_blank">goes on to outline some more resurrection methods</a>, including ones that involve parallel worlds, aliens, and clones, along with a good, old-fashioned possibility: God exists and one day he resurrects us. </p><p>In short, it's all extremely speculative.</p><p>But the aim of the paper was to catalogue known potential ways humans might be able to cheat death. For Turchin, that's not some far-off project: In addition to studying global risks and transhumanism, the Russian researcher heads the <a href="http://immortality-roadmap.com/" target="_blank">Immortality Roadmap</a>, which, similar to the 2018 paper, outlines various ways in which we might someday achieve immortality.</p><p>Although it may take centuries before humans come close to "digital immortality," Turchin believes that life-extension technology could allow some modern people to survive long enough to see it happen. </p><p>Want a shot at being among them? Beyond the obvious, like staying healthy, the Immortality Roadmap suggests you start collecting extensive data on yourself: diaries, video recordings, DNA information, EEGs, complex creative objects — all of which could someday be used to digitally "reconstruct" your identity.</p>But odds are you're not interested. Although Turchin and other scientists are bent on finding ways to avoid death and extend life indefinitely, <a href="https://www.theguardian.com/uk/2011/may/16/dying-still-taboo-subject-poll" target="_blank" rel="noopener noreferrer">surveys</a> <a href="https://quillette.com/2018/03/02/would-you-opt-for-immortality/" target="_blank" rel="noopener noreferrer">repeatedly</a> <a href="https://www.cbsnews.com/news/60-minutesvanity-fair-poll-the-afterlife/" target="_blank" rel="noopener noreferrer">show</a> that most people would not opt to live forever if given the choice.
Welcome to the world's newest motorsport: manned multicopter races that exceed speeds of 100 mph.
- Airspeeder is a company that aims to put on high-speed races featuring electric flying vehicles.
- The so-called Speeders are able to fly at speeds of up to 120 mph.
- The motorsport aims to help advance the electric vertical take-off and landing (eVTOL) sector, which could usher in the age of air taxis.
Credit: Airspeeder<p>To prevent crashes, Airspeeder is working with the companies Acronis and Teknov8 to develop "high-speed collision avoidance" systems for its Speeders.</p><p style="margin-left: 20px;">"As they compete, Speeders will utilise cutting-edge LiDAR and Machine Vision technology to ensure close but safe racing, with defined and digitally governed no-fly areas surrounding spectators and officials," Airspeeder wrote in a <a href="https://airspeeder.com/news/2020/9/7/airspeeder-worlds-first-flying-electric-car-racing-series-partners-with-cyber-protection-leader-acronis-34g4k" target="_blank">blog post</a>.</p>
Credit: Airspeeder<p>Beyond motorsports, Airspeeder hopes to help advance the electric vertical take-off and landing (eVTOL) sector. This sector is where companies like <a href="https://www.ainonline.com/aviation-news/business-aviation/2020-01-07/hyundai-and-uber-announce-evtol-air-taxi-partnership" target="_blank">Uber, Hyundai</a>, and Airbus are working to develop air taxis, which could someday take the ridesharing industry into the skies. By 2040, the autonomous urban aircraft industry could be worth $1.5 trillion, according to a <a href="https://www.morganstanley.com/ideas/autonomous-aircraft" target="_blank">2019 report</a> from Morgan Stanley.</p><p>Still, many technical and regulatory hurdles remain. Matt Pearson, Airspeeder's founder and CEO, thinks the futuristic motorsport will help to not only speed up that process, but also pave the way for self-driving cars.</p>
Archaeology clues us in on the dangers of letting viruses hang around.
- A University of Otago researcher investigates the spread of disease in ancient Vietnam.
- The infectious disease, yaws, has been with us for thousands of years with no known cure.
- Using archaeology to investigate disease offers clues into modern-day pandemics.
History-Changing Archaeological Finds<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="ed6ad05071e93f257aa0b73f4001c805"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/gydYHHfnLhE?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>While we rightfully look toward infectious disease experts during times such as now, archaeologists also have plenty to offer. A <a href="http://journals.upress.ufl.edu/bioarchaeology/article/view/1173" target="_blank">new research article</a>, published in the journal, Bioarchaeology Journal, turns back the clock to ancient Vietnam. The findings offer important clues about why we need to eradicate COVID-19.</p><p>Lead author Melandri Vlok, a PhD student at the University of Otago in New Zealand (with support from researchers in Australia, Vietnam, Japan, and the UK), investigated a case of yaws that ran through the Neolithic archeological site of Mán Bạc in Northeast Vietnam. </p><p>Yaws remains a common infectious disease in at least 13 tropical countries, with up to a half-million infected each year. Hard skin lesions form on the victim's bodies; they can form painful ulcers. While lesions usually subside within six months, bone and joint pain and fatigue are common. Some cases last many years and result in permanent scars. On occasion, death follows a long battle. </p><p>Subsistence farmers in mainland China have long battled the environment. Finding the right soil and water sources for their crops has been a generational battle. Roughly 4,000 years ago, such farmers made their way into Mainland Southeast China (modern day Vietnam), where, as Vlok writes, "genetic admixture and social transition occurs between foragers and farmers." In 2018, Vlok traveled to Mán Bạc to study the remains of seven skeletons, which included two adults, two adolescents, and two children.</p><p>Her findings help give us perspective on today's proliferation of the coronavirus. As she <a href="https://www.otago.ac.nz/news/news/releases/otago744185.html" target="_blank">says</a>, </p><p style="margin-left: 20px;">"This matters, because knowing more about this disease and its evolution, it changes how we understand the relationship people have with it. It helps us understand why it's so difficult to eradicate. If it's been with us thousands of years it has probably developed to fit very well with humans." </p>
My Son Sanctuary, Quang Nam, Vietnam.
Credit: Mrkela / Shutterstock<p>Yaws is not the only disease considered in the article. Tuberculosis, brucellosis, and cancers were also discussed. The goal of the research was to identify disease spread through cultures and the chronic problems left behind, sometimes for millennia. Vlok notes how temperature fluctuations in the Mán Bạc region affected a variety of diseases. Yaws appeared to have spread easily due to an abundance of water and vegetation, combined with increased population density—children are more likely to spread this disease.</p><p style="margin-left: 20px;">"Pre-industrialized agricultural communities have also been associated with increased incidence of yaws. The coastal region is also slightly warmer and more humid than inland northern Vietnam and therefore more conducive to the spread of yaws."</p><p>The Climate Clock is <a href="https://www.washingtonpost.com/climate-environment/2020/09/21/climate-change-metronome-clock-nyc/" target="_blank">ticking down</a>. We're already experiencing the ravages of this global shift, and it's not going to get any easier if interventions are not immediately legislated. While no single science will help us wrap our heads around the immediate future, Vlok suggests factoring in archaeology. Past precedent matters.</p><p>Gazing back a few hundred generations offers important clues for the future—really, the present—that we must confront. A concerted effort by the World Health Organization in the 1950s couldn't eradicate yaws. Diseases that have an opportunity to hang around will exploit every advantage it can. The blasé attitude too many Americans currently hold about the novel coronavirus's dangers is going to have a reverberating effect through the generations. As Vlok concludes, </p><p style="margin-left: 20px;">"This shows us what happens when we don't take action with these diseases. It's a lesson of what infectious diseases can do to a population if you let them spread widely. It highlights the need to intervene, because sometimes these diseases are so good at adapting to us, at spreading between us."</p><p>--</p><p><em>Stay in touch with Derek on <a href="http://www.twitter.com/derekberes" target="_blank">Twitter</a>, <a href="https://www.facebook.com/DerekBeresdotcom" target="_blank" rel="noopener noreferrer">Facebook</a> and <a href="https://derekberes.substack.com/" target="_blank" rel="noopener noreferrer">Substack</a>. His next book is</em> "<em>Hero's Dose: The Case For Psychedelics in Ritual and Therapy."</em></p>