Big Think Interview With Benoit Mandelbrot
Question: What is fractal geometry?\r\n\r\n
Benoit Mandelbrot: Well, regular geometry, the geometry of\r\nEuclid, is concerned with shapes which are smooth, except perhaps for corners\r\nand lines, special lines which are singularities, but some shapes in nature are\r\nso complicated that they are equally complicated at the big scale and come\r\ncloser and closer and they don’t become any less complicated. Closer and closer, or you go farther or\r\nfarther, they remain equally complicated. \r\nThere is never a plane, never a straight line, never anything smooth and\r\nordinary. The idea is very, very\r\nvague, is expressed – it’s an expression of reality.\r\n\r\n
Fractal geometry is a new subject and each definition I try\r\nto give for it has turned out to be inappropriate. So I’m now being cagey and saying there are very complex\r\nshapes which would be the same from close by and far away.\r\n\r\n
Question: What does it mean to say that fractal shapes are\r\nself-similar?\r\n\r\n
Benoit Mandelbrot: Well, if you look at a shape like a\r\nstraight line, what’s remarkable is that if you look at a straight line from\r\nclose by, from far away, it is the same; it is a straight line. That is, the straight line has a\r\nproperty of self-similarity. Each\r\npiece of the straight line is the same as the whole line when used to a big or\r\nsmall extent. The plane again has\r\nthe same property. For a long\r\ntime, it was widely believed that the only shapes having these extraordinary\r\nproperties are the straight line, the whole plane, the whole space. Now in a certain sense, self-similarity\r\nis a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar\r\nagain, the same seen from close by and far away, and which are far from being\r\nstraight or plane or solid. And\r\nthose shapes, which I studied and collected and put together and applied in\r\nmany, many domains, I called fractals.\r\n\r\n
Question: How can complex natural shapes be represented\r\nmathematically?\r\n\r\n
Benoit Mandelbrot: Well, historically, a mountain could not\r\nbe represented, except for a few mountains which are almost like cones. Mountains are very complicated. If\r\nyou look closer and closer, you find greater and greater details. If you look away until you find that\r\nbigger details become visible, and in a certain sense this same structure\r\nappears at those scales. If you\r\nlook at coastlines, if you look at that them from far away, from an airplane,\r\nwell, you don’t see details, you see a certain complication. When you come closer, the complication\r\nbecomes more local, but again continues. \r\nAnd come closer and closer and closer, the coastline becomes longer and\r\nlonger and longer because it has more detail entering in. However, these details amazingly enough\r\nenters this certain this certain regular fashion. Therefore, one can study a coastline **** object because the\r\ngeometry for that existed for a long time, and then I put it together and applied\r\nit to many domains.\r\n\r\n
Question: What was the discovery process behind the\r\nMandelbrot set?\r\n\r\n
Benoit Mandelbrot: The Mandelbrot set in a certain sense is\r\na **** of a dream I had and an uncle of mine had since I was about 20. I was a student of mathematics, but not\r\nhappy with mathematics that I was taught in France. Therefore, looking for other topics, an uncle of mine, who\r\nwas a very well-known pure mathematician, wanted me to study a certain theory\r\nwhich was then many years old, 30 years old or something, but had in a way\r\nstopped developing. When he was\r\nyoung he had tried to get this theory out of a rut and he didn’t succeed,\r\nnobody succeeded. So, there was a\r\ncase of two men, Julia, a teacher of mine, and Fatu, who had died, had a very\r\ngood year in 1910 and then nothing was happening. My uncle was telling me, if you look at that, if you find\r\nsomething new, it would be a wonderful thing because I couldn’t – nobody\r\ncould.\r\n\r\n
I looked at it and found it too difficult. I just could see nothing I could\r\ndo. Then over the years, I put\r\nthat a bit in the back of my mind until one day I read an obituary. It is an interesting story that I was\r\nmotivated by an obituary, an obituary of a great man named Poincaré, and in that obituary this\r\nquestion was raised again. At that\r\ntime, I had a computer and I had become quite an expert in the use of the\r\ncomputer for mathematics, for physics, and for many sciences. So, I decided, perhaps the time has\r\ncome to please my uncle; 35 years later, or something. To please my uncle and do what my uncle\r\nhad been pushing me to do so strongly.\r\n\r\n
But I approached this topic in a very different fashion than\r\nmy uncle. My uncle was trying to\r\nthink of something, a new idea, a new problem, a new way of developing the\r\ntheory of Fatu and Julia. I did\r\nsomething else. I went to the\r\ncomputer and tried to experiment. \r\nI introduced a very high level of experiment in very pure\r\nmathematics. I was at IBM, I had\r\nthe run of computers which then were called very big and powerful, but in fact\r\nwere less powerful than a handheld machine today. But I had them and I could make the experiments. The conditions were very, very\r\ndifficult, but I knew how to look at pictures. In fact, the reason I did not go into pure mathematics\r\nearlier was that I was dominated by visual. I tried to combine the visual beauty and the\r\nmathematics.\r\n\r\n
So, I looked at the picture for a long time in a very\r\nunsystematic fashion just to become acquainted in a kind of physical fashion\r\nwith those extraordinary difficult and complicated shapes. Two were extraordinarily\r\ndifficult. Computer graphics did\r\nnot exist back then, but to have a machine which was – made it seem\r\ndoable. And I started finding\r\nextraordinary complications, extraordinary structure, extraordinary beauty of\r\nboth a theoretical kind, mathematical, and a visual kind. And collected observations of my trip\r\nin this new territory. When I\r\npresented that work to my colleagues, it was an explosion of interest. Everybody in mathematics had given up\r\nfor 100 years or 200 years the idea that you could from pictures, from looking\r\nat pictures, find new ideas. That\r\nwas the case long ago in the Middle Ages, in the Renaissance, in later periods,\r\nbut then mathematicians had become very abstract. Pictures were completely eliminated from mathematics; in\r\nparticular when I was young this happened in a very strong fashion.\r\n\r\n
Some mathematicians didn’t even perceive of the possibility\r\nof a picture being helpful. To the\r\ncontrary, I went into an orgy of looking at pictures by the hundreds; the\r\nmachines became a little bit better. \r\nWe had friends who improved them, who wrote better software to help me,\r\nwhich was wonderful. That was the good\r\nthing about being at IBM. And I\r\nhad this collection of observations, which I gave to my friends in mathematics\r\nfor their pleasure and for simulation. \r\nThe extraordinary fact is that the first idea I had which motivated me,\r\nthat worked, is conjecture, a mathematical idea which may or may not be\r\ntrue. And that idea is still\r\nunproven. It is the foundation,\r\nwhat started me and what everybody failed to **** prove has so far defeated the\r\ngreatest efforts by experts to be proven. \r\nIn a certain sense it’s a very, very strange because the object itself\r\nis understandable, even for a child. \r\nIf the object can be drawn by a child with new computers, with new\r\ngraphic devices, and still the basic idea has not been proven.\r\n\r\n
But the development of it has been extraordinary, then it\r\nwas slowed down a bit, and now again it is going up. New people are coming in and they prove extraordinary\r\nresults which nobody was hoping to prove, and I am astonished and of course,\r\nvery pleased by this development.\r\n\r\n
Question: What is the unproven conjecture that drove you?\r\n\r\n
Benoit Mandelbrot: The conjecture itself consists in two\r\ndifferent issues in Mandelbrot set – two alternative definitions which are too\r\ntechnical to describe without a blackboard, but which are both very simple and\r\nwhich I assumed naively to be equivalent. \r\nWhy did I assume so? \r\nBecause on the pictures I could not see any difference. Obtaining pictures in one way or\r\nanother way, I couldn’t tell them apart. \r\nTherefore, I assumed they were identical and I went on studying this\r\npiece. I found that, again, many\r\ninteresting observations of which most were very preferred by many other very,\r\nvery skilled mathematicians. But\r\nthe idea that these two conditions, definitions, are identical is still\r\nopen. So there are two definitions\r\nin Mandelbrot set, the usual one and another one, and they may theoretically be\r\ndifferent. People are getting\r\ncloser, but have not proven it completely.\r\n\r\n
Question: Why do people find fractals beautiful?\r\n\r\n
Benoit Mandelbrot: Well, first of all, one explanation of\r\nthat is that the feeling for fractality is not new. It is one very surprising and extraordinary discovery I made\r\ngradually, very slowly by looking again at the paintings of the past. Many painters had a clear idea of what\r\nfractals are. Take a French\r\nclassic painter named Poussin. \r\nNow, he painted beautiful landscapes, completely artificial ones,\r\nimaginary landscapes. And how did\r\nhe choose them? Well, he had the\r\nbalance of trees, of lawns, of houses in the distance. He had a balance of small objects, big\r\nobjects, big trees in front and his balance of objects at every scale is what\r\ngives to Poussin a special feeling.\r\n\r\n
Take Hokusai, a famous Chinese painter of 1800. He did not have any mathematical\r\ntraining; he left no followers because his way of painting or drawing was too\r\nspecial to him. But it was quite\r\nclear by looking at how Hokusai, the eye, which had been trained from the\r\nfractals, that Hokusai understood fractal structure. And again, had this balance of big, small, and intermediate\r\ndetails, and you come close to these marvelous drawings, you find that he\r\nunderstood perfectly fractality. \r\nBut he never expressed it. \r\nNobody ever expressed it, and then the next stage of Japanese image\r\nexperts did some other things.\r\n\r\n
So humanity has known for a long time what fractals\r\nare. It is a very strange\r\nsituation in which an idea which each time I look at all documents have deeper\r\nand deeper roots, never (how to say it), jelled. Never got together until I started playing with the computer\r\nand playing with topics which nobody was touching because they were just\r\ndesperate and hopeless.\r\n\r\n
Question: How has computer technology impacted your work?\r\n\r\n
Benoit Mandelbrot: Well, the computer had been sort of spoken about since the\r\nearly 19th century, even before. \r\nBut until the electronic computers came, which was in reality during\r\nWorld War II, or shortly afterwards. \r\nThey could not be used for any purpose in science. They were just too slow, too limited in\r\ntheir capacity. My chance was that\r\nI was myself a very visual person. \r\nAgain, a mathematician who had started a very unconventional career\r\nbecause my interest was both mathematics and in the eye. And with IBM very primitive\r\npicture-making machines became available and we had to program everything. It was heroic. And my friends at IBM who helped me\r\ndeserve a great thank you. With\r\nthese two, I could begin to do things which before had been impossible. I could begin to implement an idea of\r\nhow a mountain looked like. To\r\nreduce a mountain, which is something most complicated to a very simple idea –\r\nhow do you do it? Well you make a\r\nconjecture, have positives about shapes of mountains, and you don’t think about\r\nthe mathematics of it, you must make a picture of it.\r\n\r\n
If the picture is – everybody to be a mountain, then there’s\r\nsomething true about it. Or a\r\ncloud. It was astonishing when at\r\none point, I got the idea of how to make artifical clouds with a collaborator,\r\nwe had pictures made which were theoretically completely artificial pictures\r\nbased upon that one very simple idea. \r\nAnd this picture everybody views as being clouds. People don’t believe that they aren’t\r\nphotographs. So, we have certainly\r\nfound something true about nature. \r\n\r\n\r\n
\r\n\r\n And on the other side, the completely artificial shapes, the\r\nshapes that don’t exist in nature, which, for example, the Mandelbrot set,\r\nwhich was completely came out of the blue out of a very simple formula which is\r\nabout one inch long and which gives us an endless, endless stream of questions\r\nand results. There what happened is\r\nthat to everybody’s surprise there’s a very strong inner resemblance between\r\nthose shapes and the shapes of nature, which I have been studying. And again, I spent half my life,\r\nroughly speaking, doing the study of nature in many aspects and half of my life\r\nstudying completely artificial shapes. \r\nAnd the two are extraordinarily close; in one way both are fractal.
And on the other side, the completely artificial shapes, the\r\nshapes that don’t exist in nature, which, for example, the Mandelbrot set,\r\nwhich was completely came out of the blue out of a very simple formula which is\r\nabout one inch long and which gives us an endless, endless stream of questions\r\nand results. There what happened is\r\nthat to everybody’s surprise there’s a very strong inner resemblance between\r\nthose shapes and the shapes of nature, which I have been studying. And again, I spent half my life,\r\nroughly speaking, doing the study of nature in many aspects and half of my life\r\nstudying completely artificial shapes. \r\nAnd the two are extraordinarily close; in one way both are fractal.
Question: What does the word “chaos” mean to mathematicians?\r\n\r\n
Benoit Mandelbrot: The theory of chaos and theory of\r\nfractals are separate, but have very strong intersections. That is one part of chaos theory is\r\ngeometrically expressed by fractal shapes. Another part of chaos theory is not expressed by fractal\r\nshapes. And other part of fractals\r\ndoes not belong to chaos theory so that two theories which overlap very\r\nstrongly and do not coincide. One\r\nof them, chaos theory, is based on behavior of systems defined by\r\nequations. Equations of motion,\r\nfor example, and classical mathematics, and around 1900, Poincaré and ****, two great\r\nmathematicians at the time, have realized that sometimes the solution of very\r\nsimple looking equations can be extremely complicated. But in 1900, it was too early to\r\ndevelop that idea. It was very\r\nwell expressed and very much discussed, but did not – could not grow.\r\n\r\n
Much later, of course, with computers this idea came to life\r\nagain and became the very important part of science. So both chaos theory and fractal have had contacts in the\r\npast when they are both impossible to develop and in a certain sense not ready\r\nto be developed. And again, they\r\nintersect very strongly but they are very distinct.\r\n\r\n
Question: Do mathematical descriptions of chaos define some\r\norder within chaos?\r\n\r\n
Benoit Mandelbrot: Well a very strong distinction was made\r\nbetween chaos and fractals. For\r\nexample, the rules which generate most of natural fractals, models of\r\nmountains, of clouds, and many other phenomena involve change. And therefore they are not at all\r\nchaotic in the ordinary sense of the word, in an ordinary, current, modern\r\nsense of the word. Not chaotic in\r\nthe old sense of the word, which doesn’t have any specific meaning. But I don’t\r\nlike to discuss the question of terms. \r\nThe term chaos came, but you know something which was very confused, it\r\nhelped it jell, but the use of a biblical name in a certain sense forces us to\r\nfind the implications which were not important in mathematics. That’s why when the time came to give a\r\nname to my work, I chose the word fractal which was new. Before that, there was no need of a\r\nword at all because again there were only a few undeveloped ideas in the very\r\nmany great minds. But when a word\r\nbecame necessary, I preferred not to use an old word, but to create a new one.\r\n\r\n
Question: How did you come up with the word “fractal”?\r\n\r\n
Benoit Mandelbrot: \r\nWell, it was a very, very interesting story. At one point, a friend of mine, an older person, told me\r\nthat he saw a paper of mine on a new topic. And he said, “Look Benoit, I tell you, you must stop writing\r\nall of these papers in that field, that field, that field, that field. Nobody knows where you are, what you\r\nare doing. You just sit down and\r\nwrite a book. A short book, a\r\nclear book, a book of things which you have done.” So, I sat down and wrote the book. Now, the book had to title, why? Because the topics I had been studying had not been the\r\nobject of any theory whatsoever. \r\nAnd there are many words which mean nothing, but many fields which have\r\nno name because they don’t exist. \r\nSo, the publisher didn’t like this very ponderous title, said, “Look.” And a friend of mine, another friend,\r\ntold me, “Look, you create a new field, you are entitled to give it a\r\nname.” So, I had Latin in high\r\nschool and it turned out that one of my son’s was taking Latin in the United\r\nStates, and so there was a Latin dictionary in our house, which was an\r\nexception.\r\n\r\n
I went in there and tried to look for a word which fitted\r\nwhat I had been working on. And\r\nwhen I was playing with the word fraction, and looked in the dictionary for a\r\nword where fraction came from. It\r\ncame from a Latin word which meant, how to say disconnect – rough and\r\ndisconnected, it was a very general – the idea of roughness originally in Latin. So, I started playing with fractus, which I named it that and coined\r\nthe word fractal. First of all, I\r\nput it in this book, Objets Fractals,\r\nin French as it turned out, and then the English translation of the book, and\r\nthen the word took off. First of\r\nall, people applied it in ways in which I didn’t find sensible, but there was\r\nnothing I could say about it. So,\r\nthen the dictionary started defining it, each a little bit differently. And in a certain sense the word became\r\nalive and independent of me. I\r\ncould scream and say, I don’t like it, but it made no difference.\r\n\r\n
I had once a curiosity of looking on the Web in different\r\ncountries having different languages, what is a fractal, and found that in one\r\ncountry, I will not mention, it’s a word that has become applied to some\r\nnightclubs. A fractal nightclub is\r\na kind of nightclub. I don’t know\r\nwhich, because I haven’t been there, but, and I don’t know the language, but I\r\nguess, from what I could guess, what it was. It’s a word which has its own life. I gave it a definition, but that\r\ndefinition became too narrow because some objects I want to go fractal did not\r\nfit the old definition.\r\n\r\n
So some people asked me would I still believe the definition\r\nof whatever – 40 years ago. I\r\ndon’t. But I have no control. It’s something which works by\r\nitself. The fact that very many\r\nadults I know never heard of it, but the children have, is what gives me\r\nparticular pleasure because high school students, even the bright ones, are\r\nvery resistant to, how to say, imposed terms. And the combination of pictures and of deep theory, you can\r\nlook at the picture and find something, some idea about this picture is\r\nsensible, and then be told that very great scientists either can’t prove it, or\r\nhas taken 40 years to prove it, or had to be several of them together to prove\r\nit because it was so difficult. \r\nAnd it can be seen by a child, understood by a child. That aspect is one which very many\r\npeople find particularly attractive in the field.\r\n\r\n
In mathematics and science definition are simple, but\r\nbare-bones. Until you get to a problem which you understand it takes hundreds\r\nand hundreds of pages and years and years of learning. In this case, you have this formula,\r\nyou track in a computer and from a simple formula, in a very short time\r\namazingly beautiful things come out, which sometimes people can prove instantly\r\nand sometimes great scientists take forever to prove. Or don’t even succeed in proving it.\r\n\r\n
Question: How can we understand financial market\r\nfluctuations in fractal terms?\r\n\r\n
Benoit Mandelbrot: Well, what I discovered quite a while ago\r\nin fact, that was my first major piece of work is that a model of price\r\nvariation which everybody was adopting was very far from being applicable. It’s a very curious story.\r\n\r\n
In 1900, a Frenchman named Bachelier, who was a student of\r\nmathematics, wrote a thesis on the theory of speculation. It was not at all an acceptable topic\r\nin pure mathematics and he had a very miserable life. But his thesis was extraordinary. Extraordinary in a very strange way. It applied very well to Brownian\r\nmotion, which is in physics. So,\r\nBachelier was a pioneer of a very marvelous essential theory in physics. But to economics, it didn’t apply at\r\nall, it was very ingenious, but Bachelier had no data, in fact no data was\r\navailable at that time in 1900, so he imagined an artificial market in which\r\ncertain rules may apply. \r\nUnfortunately, the theory which was developed by economists when\r\ncomputers came up was Bachelier’s theory. \r\nIt does not account for any of the major effects in economics. For example, it assumes prices are\r\ncontinuous when everybody knows the prices are not continuous. Some people say, well, all right, there\r\nare discontinuities but they are a different kind of economics that we are\r\ndoing, not because certain discontinuities become too complicated and only will\r\nthe **** look more or less continuous. \r\nBut it turns out that discontinuities are as important, or more\r\nimportant than the rest.\r\n\r\n
Bachelier assumed that each price changes in compared of the\r\npreceding price change. It’s a\r\nvery beautiful assumption, but it’s completely incorrect because we know very\r\nwell, especially today that for a long time prices may vary moderately and then\r\nsuddenly they begin to vary a great deal. \r\nSo, even we’re saying that the theory changes or you say the theory\r\nwhich exists is not appropriate. \r\nWhat I found that Bachelier’s theory was defective on both grounds. That was in 1961, 1962, I forgot the\r\nexact dates and when the development of Bachelier became very, very rapid. Since nobody wanted to listen to me, I\r\ndid other things. Many other\r\nthings, but I was waiting because it was quite clear that my time would have to\r\ncome. And unfortunately, it has\r\ncome, that is, the fluctuation of the economy, the stock market, and commodity\r\nmarkets today are about as they were in historical times. There was no change which made the\r\nstock market different today than it was long ago. And the lessons which are drawn from **** peers do represent\r\ntoday’s events very accurately. \r\nBut the situation is much more complicated than Bachelier had\r\nassumed. Bachelier, again, was a\r\ngenius, Bachelier had an excellent idea which happened to be very useful in\r\nphysics, but economics, he just lacked data. He did not have awareness of discontinuity which is\r\nessential in this context. Not\r\nhaving an awareness of dependence, which is also essential in this context. So, his theory is very, very different\r\nfrom what you observe in reality.\r\n\r\n
Question: As you write your memoirs, which memories are the\r\nmost fun and the most difficult to look back on?\r\n\r\n
Benoit Mandelbrot: Well, my life has been extremely\r\ncomplicated. Not by choice at the\r\nbeginning at all, but later on, I had become used to complication and went on\r\naccepting things that other people would have found too difficult to\r\naccept. I was born in Poland and\r\nmoved to France as a child shortly before World War II. During World War II, I was lucky to\r\nlive in the French equivalent of Appalachia, a region which is sort of not very\r\nhigh mountains, but very, very poor, and Appalachia we are poorer even, so\r\npoorer 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\r\nhills and had mostly a private intellectual life. I read many books; there were many books, a very good\r\nlibrary. I had many books and I\r\nhad dreams of all kinds. Dreams in\r\nwhich were in a certain sense, how to say, easy to make because the near future\r\nwas always extremely threatening. \r\nIt was a very dangerous period. \r\nBut since I had nothing to lose, I was dreaming of what I could do.\r\n\r\n
Then the war ended. \r\nI had very, very little training in taking an exam to determine a\r\nscientist’s life in France. There\r\nwere two schools, both very small. \r\nOne tiny, and one small, which in a certain sense was the place that I\r\nwas sure I wanted to go. I had\r\nonly a few months of finding out how the exam proceeded, but I took the exam\r\nand perhaps because of inherited gifts, I did very well. In fact, I barely\r\nmissed being number one in France in both schools. In particular I did very well in mathematical problems. The physics I could not guess, other\r\nthings I could not guess. But then\r\nI had a big choice, should I go into mathematics in a small and ****\r\nschool. Or should I go to a bigger\r\nschool in which, in a certain sense would give me time to decide what I wanted\r\nto do?\r\n\r\n
First I entered the small school where I was, as a matter of\r\nfact, number one of the students who entered then. But immediately, I left because that school, again, was\r\ngoing to teach me something which I did not fully believe, namely mathematics\r\nseparate from everything else. It\r\nwas excellent mathematics, French mathematics was very high level, but in\r\neverything else it was not even present. \r\nAnd I didn’t want to become a pure mathematician, as a matter of fact,\r\nmy uncle was one, so I knew what the pure mathematician was and I did not want\r\nto 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,\r\nwith the real world of which I was very, very curious.\r\n\r\n
And so, I did not go to École Polytechnique. It was a very rough decision, and the\r\nyear when I took this decision remembers my memory very, very strongly. Then for several years, I just was lost\r\na bit. I was looking for a good\r\nplace. I spent my time very nicely\r\nin many ways, but not fully satisfactory. \r\nThen I became Professor in France, but realized that I was not – for the\r\njob that I should spend my life in. \r\nFortunately, IBM was building a research center, I went there for a\r\nsummer thing, for a summer only. I\r\nknew this summer, decided to stay. \r\nIt was a very big gamble. I\r\nlost my job in France, I received a job in which was extremely uncertain, how\r\nlong would IBM be interested in research, but the gamble was taken and very\r\nshortly afterwards, I had this extraordinary fortune of stopping at Harvard to\r\ndo a lecture and learning about the price variation in just the right way. At a time when nobody was looking, was realizing\r\nthat either one needed, or one could make a theory of price variation other\r\nthan the theory of 1900 at which Bachelier had proposed, which was very, very\r\nfar from being representative of the actual thing.\r\n\r\n
So, I went to IBM and I was fortunate in being allowed – to\r\nbe successful as to go from field to field, which in a way was what I had been\r\nhoping for. I didn’t feel\r\ncomfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of\r\neverything and explore the world. \r\nAnd IBM let me do so. I\r\ntouched on far more topics than anybody would have found reasonable. I was often told, “Settle down, stay in\r\none field, don’t go all the time to another field.” But I was just compelled to move from one thing to\r\nanother.\r\n\r\n
And fractal geometry was not an idea which I had early on,\r\nfor something was developed progressively. I didn’t choose to go into the topic because of any\r\ncompelling reason, but because the problems there seemed to be somehow similar\r\nto the ones I knew how to handle. \r\nI had experienced this kind of problem and gradually realized that I was\r\ntruly putting together a new theory. \r\nA theory of roughness. What\r\nis roughness? Everybody knows what\r\nis roughness. When was roughness\r\ndiscovered? Well, prehistory. Everything is roughness, except for the\r\ncircles. How many circles are\r\nthere in nature? Very, very\r\nfew. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside\r\nbecause they were too complicated. \r\nAnd physics had laid them aside because they were too complicated. One couldn’t even measure roughness. So, by luck, and by reward for\r\npersistence, I did found the theory of roughness, which certainly I didn’t expect\r\nand expecting to found one would have been pure madness.\r\n\r\n
So, one of the high points of my life was when I suddenly\r\nrealized that this dream I had in my late adolescence of combining pure\r\nmathematics, very pure mathematics with very hard things which had been long a\r\nnuisance to scientists and to engineers, that this combination was possible and\r\nI put together this new geometry of nature, the fractal geometry of nature.\r\n\r\n
Question: Which honor means more to you: your Légion\r\nd'Honneur medal or the “Mandelbrot Set” rock song?\r\n\r\n
Benoit Mandelbrot: Well, I happen to know this song, it was\r\nsent to me and I was very impressed by it and by its popularity. In a certain sense, it is not which\r\none, but the combination. When\r\npeople ask me what’s my field? I say,\r\non one hand, a fractalist. Perhaps\r\nthe only one, the only full-time one. \r\nOn the other hand, I’ve been a professor of mathematics at Harvard and\r\nat Yale. At Yale for a long\r\ntime. But I’m not a mathematician\r\nonly. I’m a professor of physics,\r\nof economics, a long list. Each\r\nelement of this list is normal. \r\nThe combination of these elements is very rare at best. And so in a certain sense, it is not\r\nthe fact that I was a professor of mathematics at these great universities, or\r\nprofessor of physics at other great universities, or that I received, among\r\nother doctorates, one in medicine, believe it or not. And one in civil engineering. It is the coexistence of these various aspects that in one\r\nlifetime it is possible, if one takes the kinds of risks which I took, which\r\nare colossal, but taking risks, I was rewarded by being able to contribute in a\r\nvery substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems. The problems are just so old that in a\r\ncertain sense, they were no longer being pursued. And nobody – I didn’t know anybody who was trying to define roughness\r\nof ****. It was a hopeless subject. \r\nBut I did it and there’s a whole field by which has been created by\r\nthat.\r\n\r\n
In a certain sense the beauty of what I happened by\r\nextraordinary chance to put together is that nobody would have believed that\r\nthis is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step. Lately I realized that all these things\r\nheld together, and very lately I see that in each field very old problems could\r\nbe if not solved, at least advanced or reawakened, and therefore gradually very\r\nmuch improved in your understanding.
Recorded on February 17, 2010
Interviewed by Austin Allen
A conversation with the mathematician and Professor Emeritus at Yale University.
Northwell Health CEO Michael Dowling has an important favor to ask of the American people.
- Michael Dowling is president and CEO of Northwell Health, the largest health care system in New York state. In this PSA, speaking as someone whose company has seen more COVID-19 patients than any other in the country, Dowling implores Americans to wear masks—not only for their own health, but for the health of those around them.
- The CDC reports that there have been close to 7.9 million cases of coronavirus reported in the United States since January. Around 216,000 people have died from the virus so far with hundreds more added to the tally every day. Several labs around the world are working on solutions, but there is currently no vaccine for COVID-19.
- The most basic thing that everyone can do to help slow the spread is to practice social distancing, wash your hands, and to wear a mask. The CDC recommends that everyone ages two and up wear a mask that is two or more layers of material and that covers the nose, mouth, and chin. Gaiters and face shields have been shown to be less effective at blocking droplets. Homemade face coverings are acceptable, but wearers should make sure they are constructed out of the proper materials and that they are washed between uses. Wearing a mask is the most important thing you can do to save lives in your community.
New cancer-scanning technology reveals a previously unknown detail of human anatomy.
- Scientists using new scanning technology and hunting for prostate tumors get a surprise.
- Behind the nasopharynx is a set of salivary glands that no one knew about.
- Finding the glands may allow for more complication-free radiation therapies.
PSMA PET/CT technology<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="676e611b970c9b516cace0870447b325"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/RHAyoQF09X4?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>PSMA PET/CT is a new combination of <a href="https://www.mayoclinic.org/tests-procedures/pet-scan/about/pac-20385078" target="_blank">PET scans</a> and <a href="https://www.mayoclinic.org/tests-procedures/ct-scan/about/pac-20393675" target="_blank">CT scans</a> that is believed to offer a more reliable means of locating prostate cancer metastasis. A <a href="https://www.cancer.gov/news-events/cancer-currents-blog/2020/prostate-cancer-psma-pet-ct-metastasis" target="_blank" rel="noopener noreferrer">study</a> published last spring suggests it may be the most accurate way to diagnose prostate cancer metastasis than any method previously available.</p><p>Prior to PSMA PET/CT, the primary way to look for metastatic prostate cancer was to image the body using x-ray-based CT scans and to perform bone scans, since bone is where prostate cancer often spreads. CT scans, however, often miss small tumors, and bone scans can generate false positives as a result of other damage or abnormalities that have nothing to do with prostate cancer.</p><p>PSMA PET/CT scans track the travels of an intravenously administered radioactive glucose tracer throughout the body. For hunting down prostate cancer, this tracer contains a molecule that binds to the <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1472940/" target="_blank">PSMA</a> protein that's present in large amounts in prostate tumors. The molecule is linked to a radioisotope, <a href="https://netrf.org/2018/11/13/gallium-68-scan-for-neuroendocrine-tumors/" target="_blank" rel="noopener noreferrer">gallium-68</a> (Ga-68).</p><p>In last spring's research, PSAM PET/CT was shown to be 27 percent more accurate than previous methods at finding metastases (92 percent accuracy as opposed to 65 percent). In addition, it was found to be much less likely to produce false positives, and it was particularly good at detecting tumors far removed from the prostate.</p>
A good kind of avoidance behavior<p>"Radiation therapy can damage the salivary glands," says Vogel, "which may lead to complications. Patients may have trouble eating, swallowing, or speaking, which can be a real burden."</p><p>The researchers looked back through the cases of 723 patients who had undergone radiation treatment, interested in seeing if inadvertent radiation of the tubarial glands was associated with the complications experienced by the patients. It turned out that this <em>was</em> the case: In cases where more radiation had been delivered to this area, patients did indeed report more in the way of complications of the type one would expect when salivary glands are radiated.</p><p>Now that we know the tubarial salivary glands exist, therapists can stay out of their way. Vogel says, "For most patients, it should technically be possible to avoid delivering radiation to this newly discovered location of the salivary gland system in the same way we try to spare known glands."</p><p>He's hopeful that that things may be about to get at least a bit better for cancer patients: "Our next step is to find out how we can best spare these new glands and in which patients. If we can do this, patients may experience less side effects which will benefit their overall quality of life after treatment."</p>
A new survey found that 27 percent of millennials are saving more money due to the pandemic, but most can't stay within their budgets.
Taking control of bad luck<p>According to <a href="https://themanifest.com/accounting/budgeting-money-tips-for-millennials" target="_blank">a recent survey by The Manifest</a>, a business news website, millennials agree with Cramer. The study found that, of millennials surveyed, their largest expenses were housing (66 percent), educational expenses (9 percent), and health insurance (6 percent). In light of the COVID-19 pandemic, millennials are using the remaining 19 percent of their paychecks to budget and increase their savings.</p><p>About a third of millennials said they are saving more money in response to the pandemic and creating new budgets for themselves. In fact, of all generations surveyed, millennials felt the most comfortable creating personal budgets. They were also willing to think critically and adjust budgets to match financial changes, both signs that this highly-educated generation is willing to learn and adapt.</p><p>Millennials still have a rough road ahead, though. According to the survey, about half of millennials make less than $50,000 a year. That puts them into the upper-lower or lower-middle <a href="https://www.pewresearch.org/fact-tank/2020/07/23/are-you-in-the-american-middle-class/#:~:text=In%202018%2C%20the%20national%20middle,(incomes%20in%202018%20dollars)." target="_blank">income class</a>, depending on where in the country they live. That matches <a href="https://www.bls.gov/opub/mlr/2019/article/time-use-of-millennials-and-nonmillennials.htm#:~:text=Among%20full%2Dtime%20wage%20and,with%2031%20percent%20of%20nonmillennials." target="_blank" rel="noopener noreferrer">BLS data</a>, which shows millennials earning less than older non-millennials. <a href="https://www.bls.gov/opub/mlr/2019/beyond-bls/the-kids-are-alright-millennials-and-the-economy.htm" target="_blank" rel="noopener noreferrer">The BLS also notes</a> that while millennials have less debt than GenXers, most of that is student loan debt rather than mortgages.</p><p>And despite their budgetary plans, only 11 percent of millennials surveyed were able to stay within budget, while uncertainty still looms in the future job market.<em></em></p><p>With all this said, there are caveats to The Manifest survey. It hosted a relatively small sample size, only surveying 502 Americans. Of those, millennials made up 22 percent of respondents. They weren't even the largest cohort in the study. That was the baby boomers at 32 percent. </p><p>This makes the survey more suggestive than indicative. But the suggestion is that millennials, to borrow a phrase from writer Vicki Robin, are ready to reinterpret their relationship with finances.</p>
A push for financial freedom<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="a463513bfbe5a2b7d5bcc59f8be265a7"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/J-B-b393epk?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 budgeting and financial savvy have always been important, the millennial generation will need to be far more critical of their relationship with the economy. What <a href="https://www.youtube.com/watch?v=T_tDthUWsVM" target="_blank" rel="noopener noreferrer">Robin calls the old roadmap</a>—the idea that "growth is good, more is better, game over"—is unlikely to support millennials as it did past generations. They'll need a new roadmap, charting both a new macro (the relationship between our economic and ecological footprints, for example) and micro (our individual relationships with money).</p><p>Because the macro is a whole other article, we'll stick with the micro here:</p><p><strong>1) Track and cut your spending</strong></p><p>The first step to financial freedom is to track your spending and cut unnecessary purchases. For Robin, these are often the things, services, and subscriptions that we buy out of habit, but we no longer consider whether they add value to our lives.</p><p>A pernicious modern example is the subscription economy. We subscribe to services for food, clothes, television, exercise, self-help, video games, bric-a-brac, computer programs, and on and on. These services quickly fade into the financial background as just another bill we pay. </p><p>But if we watch Netflix nine times out of ten, why pay for Hulu and Disney+ and HBO Max and CBS All access? Instead, every month or so, we should scrutinize our subscriptions to ask whether they still add value to our lives. If they don't, unsubscribe.</p><p><strong>2) Kill your debt</strong></p><p>Debt doesn't just take away money we could save elsewhere; it's also a self-replicating devourer of wealth. Your debt interest rates are almost certainly higher than your investment returns, especially on credit cards. Because of this, no matter your saving rituals, you're likely bleeding wealth the longer you remain in debt.</p><p>Instead, focus on removing debt from your life. Again, credit card debt especially. The good news is that most companies have hardship programs to help debtors. You can call them to see if they can lower your interest rates or provide other helpful services.</p><p>"Financial accommodations are generally readily available right now," Amy Thomann, the head of consumer credit education at TransUnion, <a href="https://www.nytimes.com/2020/08/29/at-home/manage-finances-save-money-millennials-coronavirus.html" target="_blank" rel="noopener noreferrer">told the New York Times</a><u>.</u> "Lenders, just like consumers, understand the hardships that are going on in the economy."</p><p><strong>3) Have an emergency fund</strong></p><p>Of course, you'll need some savings when the unexpected happens. Say—I don't know—a worldwide pandemic? Experts like Robin and Thomann recommend people have three to six months' worth of expenses on reserve. These should be in liquid assets so you can access them easily and quickly.</p><p>Of course, that's not always feasible, but you should save what you can. </p><p><strong>4) Find social outlets that don't cost</strong></p><p>The economic shutdown has offered one financial boon: It has revealed ways we can enjoy each other's company with overspending. We can host movies remotely with our friends. Play video games online. Enjoy physical-distance strolls through the park. And a host of other creative connections. After the pandemic, the occasional bar hop or Friday dinner out can still be a guilty pleasure. But unlike sitcom characters, we shouldn't be spending our social lives on the set of our favorite coffee shops or local watering holes.</p><p><strong>5) Reconsider your relationship with money</strong></p><p>Robin pushes her readers to be financially free. That is, to understand that there's an economy, people have a relationship with it, but it shouldn't become an obsession that runs their lives. As <a href="https://www.youtube.com/watch?v=xDaBjc4QyWU" target="_blank" rel="noopener noreferrer">she told <em>Big Think</em></a>: "It's like there are so many presumptions that drive us into wage [slavery], and it doesn't matter whether you are at the low end or the high end. If you are engaged in that sort of anxious process of 'more, more, more,' you are not free."</p><p>The millennial generation has certainly been dealt a bum hand, but it's perhaps defeatist, and more than a little premature, to label them the unluckiest generation. Perhaps after being led astray by the old roadmap, they will be the generation to reconsider their relationship with money—not as an end itself but a means to a healthier and more beneficial life. </p>
Two massive clouds of dust in orbit around the Earth have been discussed for years and finally proven to exist.
- Hungarian astronomers have proven the existence of two "pseudo-satellites" in orbit around the earth.
- These dust clouds were first discovered in the sixties, but are so difficult to spot that scientists have debated their existence since then.
- The findings may be used to decide where to put satellites in the future and will have to be considered when interplanetary space missions are undertaken.
What are they?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDA0NC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzNTM1ODc0Mn0.NH33LuauIo__sUBi4tvhwxDcsvhflDFD-Nhx9FjlSNk/img.jpg?width=1245&coordinates=148%2C0%2C149%2C0&height=700" id="cec96" class="rm-shortcode" data-rm-shortcode-id="acb78abe2ab46a17e419ad30906751d6" data-rm-shortcode-name="rebelmouse-image" />
Artist's impression of the Kordylewski cloud in the night sky (with its brightness greatly enhanced) at the time of the observations.
G. Horváth<p>The<a href="https://en.wikipedia.org/wiki/Kordylewski_cloud" target="_blank"> Kordylewski clouds</a> are two dust clouds first observed by Polish astronomer Kazimierz Kordylewski in 1961. They are situated at two of the <a href="https://www.space.com/30302-lagrange-points.html" target="_blank">Lagrange points</a> in Earth's orbit. These points are locations where the gravity of two objects, such as the Earth and the Moon or a planet and the Sun, equals the centripetal required to orbit the objects while staying in the same relative position. There are five of these spots between the Earth and Moon. The clouds rest at what are called points four and five, forming a triangle with the clouds and the Earth at the three corners.</p><p>The clouds are enormous, taking up the same space in the night sky as twenty lunar discs; covering an area of 45,000 miles. They are roughly 250,000 miles away, about the same distance from us as the Moon. They are entirely comprised of specks of dust which reflect the light of the sun so faintly most astronomers that looked for them were unable to see them at all. </p><p>The clouds themselves are probably ancient, but the model that the scientists created to learn about them suggests that the individual dust particles that comprise them can be blown away by solar wind and replaced by the dust from other cosmic sources like comet tails. This means that the clouds hardly move but are <a href="https://www.nationalgeographic.com/science/2018/11/news-earth-moon-dust-clouds-satellites-planets-space/" target="_blank">eternally changing</a>. </p>
How did they discover this?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDAzNi9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY1Nzc4MjQ4MX0.7uU9OqmQcWw5Ll1UXAav0PCu4nTg-GdJdAWADHanC7c/img.jpg?width=1245&coordinates=0%2C180%2C0%2C181&height=700" id="952fb" class="rm-shortcode" data-rm-shortcode-id="a778280a20f1c54cd2c14c8313224be2" data-rm-shortcode-name="rebelmouse-image" />
"In this picture the central region of the Kordylewski dust cloud is visible (bright red pixels). The straight tilted lines are traces of satellites."
J. Slíz-Balogh<p>In their study published in the <a href="https://academic.oup.com/mnras" target="_blank">Monthly Notices of the Royal Astronomical Society</a>, Hungarian astronomers Judit Slíz-Balogh, András Barta, and Gábor Horváth described how they were able to find the dust clouds using polarized lenses.</p><p>Since the clouds were expected to polarize the light that bounces off of them, by configuring the telescopes to look for this kind of light the clouds were much easier to spot. What the scientists observed, polarized light in patterns that extended outside the view of the telescope lens, was in line with the predictions of their mathematical model and ruled out other possible sources. </p>
Why are we just learning this now?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDAzOS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MjUyNDMyMH0.Zl8GmQ_rJHiL4b7hN0r_YBmgb6_ZqIRvqOVuko2ubpw/img.jpg?width=1245&coordinates=0%2C141%2C0%2C185&height=700" id="87afe" class="rm-shortcode" data-rm-shortcode-id="dd4c0b5088e601d7279cc5eb226f8b7b" data-rm-shortcode-name="rebelmouse-image" />
"Mosaic pattern of the angle of polarization around the L5 point (white dot) of the Earth-Moon system. The five rectangular windows correspond to the imaging telescope with which the patterns of the Kordylewski cloud were measured."
J. Slíz-Balogh<p>The objects, being dust clouds, are very faint and hard to see. While Kordylewski observed them in 1961, other astronomers have looked there and given mixed reports over the following decades. This discouraged many astronomers from joining the search, as study co-author Judit Slíz-Balogh <a href="https://ras.ac.uk/news-and-press/research-highlights/earths-dust-cloud-satellites-confirmed" target="_blank">explained</a>, <em>"The Kordylewski clouds are two of the toughest objects to find, and though they are as close to Earth as the Moon are largely overlooked by researchers in astronomy. It is intriguing to confirm that our planet has dusty pseudo-satellites in orbit alongside our lunar neighbor."</em></p>
Will this have any impact on space travel?<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="c3d797fff5430c64afcb5a49bddc3616"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/Ou8N3v9SFPE?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>Lagrange points have been put forward as excellent locations for a space station or satellites like the <a href="https://jwst.nasa.gov/about.html" target="_blank">James Webb Telescope</a> to be put into orbit, as they would require little fuel to stay in place. Knowing about a massive dust cloud that could damage sensitive equipment already being there could save money and lives in the future. While we only know about the clouds at Lagrange points four and five right now, the study's authors suggest there could be more at the other points.</p><p>While the discovery of a couple of dust clouds might not seem all that impressive, it is the result of a half-century of astronomical and mathematical work and reminds us that wonders are still hidden in our cosmic backyard. While you might never need to worry about these clouds again, there is nothing wrong with looking at the sky with wonder at the strange and fantastic things we can discover. </p>
Your health and the health of the planet are not indistinguishable.
- Transitioning to a plant-based diet could help reduce obesity, cardiovascular disease, and type 2 diabetes.
- Humans are destroying entire ecosystems to perpetuate destructive food habits.
- Understanding how to properly transition to a plant-based diet is important for success.
Richard Dawkins: No Civilized Person Accepts Slavery So Why Do We Accept Animal Cruelty? | Big Think<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="c09f23c34faacc8ec55aba054fae9c7c"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/_4SnBCPzBl0?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><h3>Get your hands dirty—in the kitchen</h3><p>Quarantine offered an entire world the opportunity to get into the kitchen and put on a chef's apron. Complaints about "not enough time" are the biggest barriers to preparing home-cooked meals. Of course, pandemic fatigue has resulted in a number of recent chefs ordering out more. That said, this is the perfect time to try your hand at new dishes. With infection rates <a href="https://www.vox.com/coronavirus-covid19/2020/10/11/21511641/covid-19-us-cases-update-testing-deaths-hospitalizations" target="_blank">increasing across the country</a>, stocking up on seasonal vegetables is a great idea. </p><p>Simple seasonal ways to begin your plant-based exploration include <a href="https://nomnompaleo.com/post/11136213353/roasted-kabocha-squash" target="_blank" rel="noopener noreferrer">roasted kabocha squash</a>, <a href="https://www.delicious.com.au/recipes/no-chop-pumpkin-soup/seblnp2r?r=recipes/collections/autumnrecipes&c=f3bf723a-05a7-487d-bd4b-5bc8af042ca9/autumn%20recipes%20you%27ll%20fall%20in%20love%20with" target="_blank" rel="noopener noreferrer">Bombay potatoes</a>, and <a href="https://www.delicious.com.au/recipes/no-chop-pumpkin-soup/seblnp2r?r=recipes/collections/autumnrecipes&c=f3bf723a-05a7-487d-bd4b-5bc8af042ca9/autumn%20recipes%20you%27ll%20fall%20in%20love%20with" target="_blank" rel="noopener noreferrer">no-chop pumpkin soup</a>. If you're feeling a bit more adventurous, <a href="https://www.thecuriouschickpea.com/masoor-dal-tadka/" target="_blank" rel="noopener noreferrer">Masoor Dal Tadka</a> will keep you warm into the winter months. A delicious <a href="https://www.delish.com/cooking/recipe-ideas/a23362341/sweet-potato-salad-recipe/" target="_blank" rel="noopener noreferrer">sweet potato salad</a> will never fail you. This <a href="https://www.buzzfeed.com/hannahloewentheil/easy-meatless-monday-recipes" target="_blank">round-up of 25 vegetarian recipes</a> will keep you busy for a few months (or a month if you're ambitious). </p><h3>Educate yourself on the benefits</h3><p>Education is essential for beginning any endeavor. Weeding through propaganda and bunk science to find credible evidence of any diet is difficult, though many experts agree that for individual and societal health, a plant-based diet is key. </p><p>Even vegetarianism has its pitfalls. For example, <a href="https://michaelpollan.com/books/cooked/" target="_blank">one-fifth of all calories</a> consumed by Americans come from nutritionally-worthless white flour. If you're eating processed bread every day, you're missing out on the benefits of a rich and varied diet. </p><p>Many of the "<a href="https://www.who.int/chp/chronic_disease_report/media/Factsheet4.pdf?ua=1" target="_blank">diseases of affluence</a>," such as cardiovascular and obesity-related ailments, originate with a poor diet (and lack of exercise). Meat has been an essential component of the human diet throughout our evolution. Today, we eat too much of it—and too much of it is produced in factory farms. Transitioning to a plant-based diet could help cut down on carbon emissions and the aforementioned diseases. </p><p>Plants are full of valuable phytochemicals and antioxidants that support a <a href="https://www.mdanderson.org/publications/focused-on-health/5-benefits-of-a-plant-based-diet.h20-1592991.html" target="_blank" rel="noopener noreferrer">strong immune system</a>. A (non-processed) plant-based diet reduces inflammation and offers plenty of fiber. It has been shown to reduce your risk of diabetes, stroke, and heart diseases. Those are all great reasons to transition. </p><h3>Begin your journey with a single step</h3><p>Going cold turkey rarely works for addicts. The same is true of diets. If you're interested in a plant-based diet, try to eat veg every other day for a few weeks. Notice how your body reacts on days you eat this way compared to other days. Gradually phase out meat products. Attempt meat-free weekdays and see if your craving for meat persists on the weekend. Try using meat as a garnish instead of the main course. </p><p>More importantly, have a replacement plan. Dropping all meat products to consume frozen dinners isn't the best course of action. Filling your cart with bags of foods you've never eaten before will overwhelm you. Prepare meals as you taper off of meat; arm yourself with a broad knowledge of healthy plants and vegetables. At some point, you might forget what you've been missing. </p>
Photo: anaumenko / Adobe Stock<h3>Start with foods you already love</h3><p>The good news is that you likely have a number of plant-based side and main dishes that you love. Transitioning into a new diet requires a certain level of enjoyment. Otherwise, you're going to loathe eating, and eating should bring some level of satisfaction. </p><p>Try a one-to-one ratio to begin. On one night, cook a meal you love. Then try something completely new the next night. Follow that up with old faithful. This way, you constantly have new dishes to look forward to yet don't get stuck in thinking you have to be creative every single day. You'll likely find some winners and decide not to repeat other dishes. Regardless, you'll have a broader menu to work from. </p><h3>Avoid ingredients you can't pronounce</h3><p>The produce section of your grocery store provides almost everything you need to survive. You can likely pronounce every ingredient in this section. There's a vast difference between food and foodstuffs. Plenty of plant-based companies offer too much of the latter. Potato chips are technically vegetarian, and some use simple ingredients, yet it's easy to fill your cart with foodstuffs. The health benefits of this are not only negligible but potentially dangerous. </p><p>Qi Sun, an assistant professor of nutrition at the Harvard T.H. Chan School of Public Health, <a href="https://www.webmd.com/diet/obesity/news/20191104/are-there-health-downsides-to-vegetarian-diets" target="_blank">explains</a>. "If you eat a vegan diet, but eat a lot of french fries, refined carbs like white bread, white rice, that's not healthy." He suggests "emphasizing fruits and vegetables. Not fruit juice but whole food. And nuts."</p><h3>Utilize the wisdom of the internet—but don't get indoctrinated</h3><p>There's a lot of terrible advice—and worse, propaganda—on the internet. While you likely don't want to eat eggs every day, they're not "toxic," as one popular documentary claims. Eggs are <a href="https://www.bbcgoodfood.com/howto/guide/ingredient-focus-eggs" target="_blank">one of the best</a> low-cost, high-value foods around. </p><p>Read websites like <a href="https://www.everydayhealth.com/diet-nutrition/scientific-benefits-following-plant-based-diet/" target="_blank">Everyday Health</a>, which uses clear language, like "may improve" and "may decrease," with links to credible studies. This way you follow the going science without becoming fanatical about a particular diet or being disappointed if it turns out the research doesn't hold up. Good science evolves with evidence. And right now, the evidence points to more vegetables in our diets. </p><p>--</p><p><em>Stay in touch with Derek on <a href="http://www.twitter.com/derekberes" target="_blank">Twitter</a> and <a href="https://www.facebook.com/DerekBeresdotcom" target="_blank" rel="noopener noreferrer">Facebook</a>. His new book is</em> "<em><a href="https://www.amazon.com/gp/product/B08KRVMP2M?pf_rd_r=MDJW43337675SZ0X00FH&pf_rd_p=edaba0ee-c2fe-4124-9f5d-b31d6b1bfbee" target="_blank" rel="noopener noreferrer">Hero's Dose: The Case For Psychedelics in Ritual and Therapy</a>."</em></p>