How do you observe something you can’t see? This is the basic question of somebody who’s interested in finding and studying black holes. Because black holes are objects whose pull of gravity is so intense that nothing can escape it, not even light, so you can’t see it directly.

So, my story today about black holes is about one particular black hole. I’m interested in finding whether or not there is a really massive, what we like to call “supermassive” black hole at the center of our galaxy. And the reason this is interesting is that it gives us an opportunity to prove whether or not these exotic objects really exist. And second, it gives us the opportunity to understand how these supermassive black holes interact with their environment, and to understand how they affect the formation and evolution of the galaxies which they reside in.

So, to begin with, we need to understand what a black hole is so we can understand the proof of a black hole. So, what is a black hole? Well, in many ways a black hole is an incredibly simple object, because there are only three characteristics that you can describe: the mass, the spin, and the charge. And I’m going to only talk about the mass. So, in that sense, it’s a very simple object. But in another sense, it’s an incredibly complicated object that we need relatively exotic physics to describe, and in some sense represents the breakdown of our physical understanding of the universe.

But today, the way I want you to understand a black hole, for the proof of a black hole, is to think of it as an object whose mass is confined to zero volume. So, despite the fact that I’m going to talk to you about an object that’s supermassive, and I’m going to get to what that really means in a moment, it has no finite size. So, this is a little tricky.

But fortunately there is a finite size that you can see, and that’s known as the Schwarzschild radius. And that’s named after the guy who recognized why it was such an important radius. This is a virtual radius, not reality; the black hole has no size. So why is it so important? It’s important because it tells us that any object can become a black hole. That means you, your neighbor, your cellphone, the auditorium can become a black hole if you can figure out how to compress it down to the size of the Schwarzschild radius.

At that point, what’s going to happen? At that point gravity wins. Gravity wins over all other known forces. And the object is forced to continue to collapse to an infinitely small object. And then it’s a black hole. So, if I were to compress the Earth down to the size of a sugar cube, it would become a black hole, because the size of a sugar cube is its Schwarzschild radius.

Now, the key here is to figure out what that Schwarzschild radius is. And it turns out that it’s actually pretty simple to figure out. It depends only on the mass of the object. Bigger objects have bigger Schwarzschild radii. Smaller objects have smaller Schwarzschild radii. So, if I were to take the sun and compress it down to the scale of the University of Oxford, it would become a black hole.

So, now we know what a Schwarzschild radius is. And it’s actually quite a useful concept, because it tells us not only when a black hole will form, but it also gives us the key elements for the proof of a black hole. I only need two things. I need to understand the mass of the object I’m claiming is a black hole, and what its Schwarzschild radius is. And since the mass determines the Schwarzschild radius, there is actually only one thing I really need to know.

So, my job in convincing you that there is a black hole is to show that there is some object that’s confined to within its Schwarzschild radius. And your job today is to be skeptical. Okay, so, I’m going to talk about no ordinary black hole; I’m going to talk about supermassive black holes.

So, I wanted to say a few words about what an ordinary black hole is, as if there could be such a thing as an ordinary black hole. An ordinary black hole is thought to be the end state of a really massive star’s life. So, if a star starts its life off with much more mass than the mass of the Sun, it’s going to end its life by exploding and leaving behind these beautiful supernova remnants that we see here. And inside that supernova remnant is going to be a little black hole that has a mass roughly three times the mass of the Sun. On an astronomical scale that’s a very small black hole.

Now, what I want to talk about are the supermassive black holes. And the supermassive black holes are thought to reside at the center of galaxies. And this beautiful picture taken with the Hubble Space Telescope shows you that galaxies come in all shapes and sizes. There are big ones. There are little ones. Almost every object in that picture there is a galaxy. And there is a very nice spiral up in the upper left. And there are a hundred billion stars in that galaxy, just to give you a sense of scale. And all the light that we see from a typical galaxy, which is the kind of galaxies that we’re seeing here, comes from the light from the stars. So, we see the galaxy because of the star light.

Now, there are a few relatively exotic galaxies. I like to call these the prima donna of the galaxy world, because they are kind of show offs. And we call them active galactic nuclei. And we call them that because their nucleus, or their center, are very active. So, at the center there, that’s actually where most of the starlight comes out from. And yet, what we actually see is light that can’t be explained by the starlight. It’s way more energetic. In fact, in a few examples it’s like the ones that we’re seeing here. There are also jets emanating out from the center. Again, a source of energy that’s very difficult to explain if you just think that galaxies are composed of stars.

So, what people have thought is that perhaps there are supermassive black holes which matter is falling on to. So, you can’t see the black hole itself, but you can convert the gravitational energy of the black hole into the light we see. So, there is the thought that maybe supermassive black holes exist at the center of galaxies. But it’s a kind of indirect argument.

Nonetheless, it’s given rise to the notion that maybe it’s not just these prima donnas that have these supermassive black holes, but rather all galaxies might harbor these supermassive black holes at their centers. And if that’s the case – and this is an example of a normal galaxy; what we see is the star light. And if there is a supermassive black hole, what we need to assume is that it’s a black hole on a diet. Because that is the way to suppress the energetic phenomena that we see in active galactic nuclei.

If we’re going to look for these stealth black holes at the center of galaxies, the best place to look is in our own galaxy, our Milky Way. And this is a wide field picture taken of the center of the Milky Way. And what we see is a line of stars. And that is because we live in a galaxy which has a flattened, disk-like structure. And we live in the middle of it, so when we look towards the center, we see this plane which defines the plane of the galaxy, or line that defines the plane of the galaxy.

Now, the advantage of studying our own galaxy is it’s simply the closest example of the center of a galaxy that we’re ever going to have, because the next closest galaxy is 100 times further away. So, we can see far more detail in our galaxy than anyplace else. And as you’ll see in a moment, the ability to see detail is key to this experiment.

So, how do astronomers prove that there is a lot of mass inside a small volume? Which is the job that I have to show you today. And the tool that we use is to watch the way stars orbit the black hole. Stars will orbit the black hole in the very same way that planets orbit the sun. It’s the gravitational pull that makes these things orbit. If there were no massive objects these things would go flying off, or at least go at a much slower rate because all that determines how they go around is how much mass is inside its orbit.

So, this is great, because remember my job is to show there is a lot of mass inside a small volume. So, if I know how fast it goes around, I know the mass. And if I know the scale of the orbit I know the radius. So, I want to see the stars that are as close to the center of the galaxy as possible. Because I want to show there is a mass inside as small a region as possible. So, this means that I want to see a lot of detail. And that’s the reason that for this experiment we’ve used the world’s largest telescope.

This is the Keck observatory. It hosts two telescopes with a mirror 10 meters, which is roughly the diameter of a tennis court. Now, this is wonderful, because the campaign promise of large telescopes is that is that the bigger the telescope, the smaller the detail that we can see. But it turns out these telescopes, or any telescope on the ground has had a little bit of a challenge living up to this campaign promise. And that is because of the atmosphere. Atmosphere is great for us; it allows us to survive here on Earth. But it’s relatively challenging for astronomers who want to look through the atmosphere to astronomical sources.

So, to give you a sense of what this is like, it’s actually like looking at a pebble at the bottom of a stream. Looking at the pebble on the bottom of the stream, the stream is continuously moving and turbulent, and that makes it very difficult to see the pebble on the bottom of the stream. Very much in the same way, it’s very difficult to see astronomical sources, because of the atmosphere that’s continuously moving by.

So, I’ve spent a lot of my career working on ways to correct for the atmosphere, to give us a cleaner view. And that buys us about a factor of 20. And I think all of you can agree that if you can figure out how to improve life by a factor of 20, you’ve probably improved your lifestyle by a lot, say your salary, you’d notice, or your kids, you’d notice.

And this animation here shows you one example of the techniques that we use, called adaptive optics. You’re seeing an animation that goes between an example of what you would see if you don’t use this technique – in other words, just a picture that shows the stars – and the box is centered on the center of the galaxy, where we think the black hole is. So, without this technology you can’t see the stars. With this technology all of a sudden you can see it. This technology works by introducing a mirror into the telescope optics system that’s continuously changing to counteract what the atmosphere is doing to you. So, it’s kind of like very fancy eyeglasses for your telescope.

Now, in the next few slides I’m just going to focus on that little square there. So, we’re only going to look at the stars inside that small square, although we’ve looked at all of them. So, I want to see how these things have moved. And over the course of this experiment, these stars have moved a tremendous amount. So, we’ve been doing this experiment for 15 years, and we see the stars go all the way around.

Now, most astronomers have a favorite star, and mine today is a star that’s labeled up there, SO-2. Absolutely my favorite star in the world. And that’s because it goes around in only 15 years. And to give you a sense of how short that is, the sun takes 200 million years to go around the center of the galaxy. Stars that we knew about before, that were as close to the center of the galaxy as possible, take 500 years. And this one, this one goes around in a human lifetime. That’s kind of profound, in a way.

But it’s the key to this experiment. The orbit tells me how much mass is inside a very small radius. So, next we see a picture here that shows you before this experiment the size to which we could confine the mass of the center of the galaxy. What we knew before is that there was four million times the mass of the sun inside that circle. And as you can see, there was a lot of other stuff inside that circle. You can see a lot of stars. So, there was actually lots of alternatives to the idea that there was a supermassive black hole at the center of the galaxy, because you could put a lot of stuff in there.

But with this experiment, we’ve confined that same mass to a much smaller volume that’s 10,000 times smaller. And because of that, we’ve been able to show that there is a supermassive black hole there. To give you a sense of how small that size is, that’s the size of our solar system. So, we’re cramming four million times the mass of the sun into that small volume.

Now, truth in advertising. Right? I have told you my job is to get it down to the Schwarzchild radius. And the truth is, I’m not quite there. But we actually have no alternative today to explaining this concentration of mass. And, in fact, it’s the best evidence we have to date for not only existence of a supermassive black hole at the center of our own galaxy, but any in our universe. So, what next? I actually think this is about as good as we’re going to do with today’s technology, so let’s move on with the problem.

So, what I want to tell you, very briefly, is a few examples of the excitement of what we can do today at the center of the galaxy, now that we know that there is, or at least we believe, that there is a supermassive black hole there. And the fun phase of this experiment is, while we’ve tested some of our ideas about the consequences of a supermassive black hole being at the center of our galaxy, almost every single one has been inconsistent with what we actually see. And that’s the fun.

So, let me give you the two examples. You can ask, “What do you expect for the old stars, stars that have been around the center of the galaxy for a long time, they’ve had plenty of time to interact with the black hole.” What you expect there is that old stars should be very clustered around the black hole. You should see a lot of old stars next to that black hole.

Likewise, for the young stars, or in contrast, the young stars, they just should not be there. A black hole does not make a kind neighbor to a stellar nursery. To get a star to form, you need a big ball of gas and dust to collapse. And it’s a very fragile entity. And what does the big black hole do? It strips that gas cloud apart. It pulls much stronger on one side than the other and the cloud is stripped apart. In fact, we anticipated that star formation shouldn’t proceed in that environment.

So, you shouldn’t see young stars. So, what do we see? Using observations that are not the ones I’ve shown you today, we can actually figure out which ones are old and which ones are young. The old ones are red. The young ones are blue. And the yellow ones, we don’t know yet. So, you can already see the surprise. There is a dearth of old stars. There is an abundance of young stars, so it’s the exact opposite of the prediction.

So, this is the fun part. And in fact, today, this is what we’re trying to figure out, this mystery of how do you get – how do you resolve this contradiction. So, in fact, my graduate students are, at this very moment, today, at the telescope, in Hawaii, making observations to get us hopefully to the next stage, where we can address this question of why are there so many young stars, and so few old stars. To make further progress we really need to look at the orbits of stars that are much further away. To do that we’ll probably need much more sophisticated technology than we have today.

Because, in truth, while I said we’re correcting for the Earth’s atmosphere, we actually only correct for half the errors that are introduced. We do this by shooting a laser up into the atmosphere, and what we think we can do is if we shine a few more that we can correct the rest. So this is what we hope to do in the next few years. And on a much longer time scale, what we hope to do is build even larger telescopes, because, remember, bigger is better in astronomy.

So, we want to build a 30 meter telescope. And with this telescope we should be able to see stars that are even closer to the center of the galaxy. And we hope to be able to test some of Einstein’s theories of general relativity, some ideas in cosmology about how galaxies form. So, we think the future of this experiment is quite exciting.

So, in conclusion, I’m going to show you an animation that basically shows you how these orbits have been moving, in three dimensions. And I hope, if nothing else, I’ve convinced you that, one, we do in fact have a supermassive black hole at the center of the galaxy. And this means that these things do exist in our universe, and we have to contend with this, we have to explain how you can get these objects in our physical world.

Second, we’ve been able to look at that interaction of how supermassive black holes interact, and understand, maybe, the role in which they play in shaping what galaxies are, and how they work.

And last but not least, none of this would have happened without the advent of the tremendous progress that’s been made on the technology front. And we think that this is a field that is moving incredibly fast, and holds a lot in store for the future. Thanks very much. (Applause)

• The Royal Swedish Academy of Sciences has decided to award the 2020 Nobel Prize in Physics with one half to Roger Penrose and the other half jointly to Reinhard Genzel and Andrea Ghez.
• Physics Nobel Awarded for Black Hole Breakthroughs

by Louise Elisabeth Glück

We’re all dreamers; we don’t know who we are.

Some machine made us; machine of the world, the constricting family.
Then back to the world, polished by soft whips.

We dream; we don’t remember.

Machine of the family: dark fur, forests of the mother’s body.
Machine of the mother: white city inside her.

And before that: earth and water.
Moss between rocks, pieces of leaves and grass.

And before, cells in a great darkness.
And before that, the veiled world.

This is why you were born: to silence me.
Cells of my mother and father, it is your turn
to be pivotal, to be the masterpiece.

I improvised; I never remembered.
Now it’s your turn to be driven;
you’re the one who demands to know:

Why do I suffer? Why am I ignorant?
Cells in a great darkness. Some machine made us;
it is your turn to address it, to go back asking
what am I for? What am I for?

• Mother and Child
• The 2020 Nobel Prize in Literature is awarded to the American poet Louise Glück “for her unmistakable poetic voice that with austere beauty makes individual existence universal.”

A few years ago, with my colleague, Emmanuelle Charpentier, I invented a new technology for editing genomes. It’s called CRISPR-Cas9. The CRISPR technology allows scientists to make changes to the DNA in cells that could allow us to cure genetic disease.

You might be interested to know that the CRISPR technology came about through a basic research project that was aimed at discovering how bacteria fight viral infections. Bacteria have to deal with viruses in their environment, and we can think about a viral infection like a ticking time bomb – a bacterium has only a few minutes to defuse the bomb before it gets destroyed. So, many bacteria have in their cells an adaptive immune system called CRISPR, that allows them to detect viral DNA and destroy it.

Part of the CRISPR system is a protein called Cas9, that’s able to seek out, cut and eventually degrade viral DNA in a specific way. And it was through our research to understand the activity of this protein, Cas9, that we realized that we could harness its function as a genetic engineering technology – a way for scientists to delete or insert specific bits of DNA into cells with incredible precision – that would offer opportunities to do things that really haven’t been possible in the past.

The CRISPR technology has already been used to change the DNA in the cells of mice and monkeys, other organisms as well. Chinese scientists showed recently that they could even use the CRISPR technology to change genes in human embryos. And scientists in Philadelphia showed they could use CRISPR to remove the DNA of an integrated HIV virus from infected human cells.

The opportunity to do this kind of genome editing also raises various ethical issues that we have to consider, because this technology can be employed not only in adult cells, but also in the embryos of organisms, including our own species. And so, together with my colleagues, I’ve called for a global conversation about the technology that I co-invented, so that we can consider all of the ethical and societal implications of a technology like this.

What I want to do now is tell you what the CRISPR technology is, what it can do, where we are today and why I think we need to take a prudent path forward in the way that we employ this technology.

When viruses infect a cell, they inject their DNA. And in a bacterium, the CRISPR system allows that DNA to be plucked out of the virus, and inserted in little bits into the chromosome – the DNA of the bacterium. And these integrated bits of viral DNA get inserted at a site called CRISPR. CRISPR stands for clustered regularly interspaced short palindromic repeats. (Laughter)

A big mouthful – you can see why we use the acronym CRISPR. It’s a mechanism that allows cells to record, over time, the viruses they have been exposed to. And importantly, those bits of DNA are passed on to the cells’ progeny, so cells are protected from viruses not only in one generation, but over many generations of cells. This allows the cells to keep a record of infection, and as my colleague, Blake Wiedenheft, likes to say, the CRISPR locus is effectively a genetic vaccination card in cells. Once those bits of DNA have been inserted into the bacterial chromosome, the cell then makes a little copy of a molecule called RNA, which is orange in this picture, that is an exact replicate of the viral DNA. RNA is a chemical cousin of DNA, and it allows interaction with DNA molecules that have a matching sequence.

So those little bits of RNA from the CRISPR locus associate – they bind – to protein called Cas9, which is white in the picture, and form a complex that functions like a sentinel in the cell. It searches through all of the DNA in the cell, to find sites that match the sequences in the bound RNAs. And when those sites are found – as you can see here, the blue molecule is DNA – this complex associates with that DNA and allows the Cas9 cleaver to cut up the viral DNA. It makes a very precise break. So we can think of the Cas9 RNA sentinel complex like a pair of scissors that can cut DNA – it makes a double-stranded break in the DNA helix. And importantly, this complex is programmable, so it can be programmed to recognize particular DNA sequences, and make a break in the DNA at that site.

As I’m going to tell you now, we recognized that that activity could be harnessed for genome engineering, to allow cells to make a very precise change to the DNA at the site where this break was introduced. That’s sort of analogous to the way that we use a word-processing program to fix a typo in a document.

The reason we envisioned using the CRISPR system for genome engineering is because cells have the ability to detect broken DNA and repair it. So when a plant or an animal cell detects a double-stranded break in its DNA, it can fix that break, either by pasting together the ends of the broken DNA with a little, tiny change in the sequence of that position, or it can repair the break by integrating a new piece of DNA at the site of the cut. So if we have a way to introduce double-stranded breaks into DNA at precise places, we can trigger cells to repair those breaks, by either the disruption or incorporation of new genetic information. So if we were able to program the CRISPR technology to make a break in DNA at the position at or near a mutation causing cystic fibrosis, for example, we could trigger cells to repair that mutation.

Genome engineering is actually not new, it’s been in development since the 1970s. We’ve had technologies for sequencing DNA, for copying DNA, and even for manipulating DNA. And these technologies were very promising, but the problem was that they were either inefficient, or they were difficult enough to use that most scientists had not adopted them for use in their own laboratories, or certainly for many clinical applications. So, the opportunity to take a technology like CRISPR and utilize it has appeal, because of its relative simplicity. We can think of older genome engineering technologies as similar to having to rewire your computer each time you want to run a new piece of software, whereas the CRISPR technology is like software for the genome, we can program it easily, using these little bits of RNA.

So once a double-stranded break is made in DNA, we can induce repair, and thereby potentially achieve astounding things, like being able to correct mutations that cause sickle cell anemia or cause Huntington’s Disease. I actually think that the first applications of the CRISPR technology are going to happen in the blood, where it’s relatively easier to deliver this tool into cells, compared to solid tissues.

Right now, a lot of the work that’s going on applies to animal models of human disease, such as mice. The technology is being used to make very precise changes that allow us to study the way that these changes in the cell’s DNA affect either a tissue or, in this case, an entire organism.

Now in this example, the CRISPR technology was used to disrupt a gene by making a tiny change in the DNA in a gene that is responsible for the black coat color of these mice. Imagine that these white mice differ from their pigmented litter-mates by just a tiny change at one gene in the entire genome, and they’re otherwise completely normal. And when we sequence the DNA from these animals, we find that the change in the DNA has occurred at exactly the place where we induced it, using the CRISPR technology.

Additional experiments are going on in other animals that are useful for creating models for human disease, such as monkeys. And here we find that we can use these systems to test the application of this technology in particular tissues, for example, figuring out how to deliver the CRISPR tool into cells. We also want to understand better how to control the way that DNA is repaired after it’s cut, and also to figure out how to control and limit any kind of off-target, or unintended effects of using the technology.

I think that we will see clinical application of this technology, certainly in adults, within the next 10 years. I think that it’s likely that we will see clinical trials and possibly even approved therapies within that time, which is a very exciting thing to think about. And because of the excitement around this technology, there’s a lot of interest in start-up companies that have been founded to commercialize the CRISPR technology, and lots of venture capitalists that have been investing in these companies.

But we have to also consider that the CRISPR technology can be used for things like enhancement. Imagine that we could try to engineer humans that have enhanced properties, such as stronger bones, or less susceptibility to cardiovascular disease or even to have properties that we would consider maybe to be desirable, like a different eye color or to be taller, things like that. “Designer humans,” if you will. Right now, the genetic information to understand what types of genes would give rise to these traits is mostly not known. But it’s important to know that the CRISPR technology gives us a tool to make such changes, once that knowledge becomes available.

This raises a number of ethical questions that we have to carefully consider, and this is why I and my colleagues have called for a global pause in any clinical application of the CRISPR technology in human embryos, to give us time to really consider all of the various implications of doing so. And actually, there is an important precedent for such a pause from the 1970s, when scientists got together to call for a moratorium on the use of molecular cloning, until the safety of that technology could be tested carefully and validated.

So, genome-engineered humans are not with us yet, but this is no longer science fiction. Genome-engineered animals and plants are happening right now. And this puts in front of all of us a huge responsibility, to consider carefully both the unintended consequences as well as the intended impacts of a scientific breakthrough.

Thank you.

(Applause)

(Applause ends)

Bruno Giussani: Jennifer, this is a technology with huge consequences, as you pointed out. Your attitude about asking for a pause or a moratorium or a quarantine is incredibly responsible. There are, of course, the therapeutic results of this, but then there are the un-therapeutic ones and they seem to be the ones gaining traction, particularly in the media. This is one of the latest issues of The Economist – “Editing humanity.” It’s all about genetic enhancement, it’s not about therapeutics. What kind of reactions did you get back in March from your colleagues in the science world, when you asked or suggested that we should actually pause this for a moment and think about it?

Jennifer Doudna: My colleagues were actually, I think, delighted to have the opportunity to discuss this openly. It’s interesting that as I talk to people, my scientific colleagues as well as others, there’s a wide variety of viewpoints about this. So clearly it’s a topic that needs careful consideration and discussion.

BG: There’s a big meeting happening in December that you and your colleagues are calling, together with the National Academy of Sciences and others, what do you hope will come out of the meeting, practically?

JD: Well, I hope that we can air the views of many different individuals and stakeholders who want to think about how to use this technology responsibly. It may not be possible to come up with a consensus point of view, but I think we should at least understand what all the issues are as we go forward.

BG: Now, colleagues of yours, like George Church, for example, at Harvard, they say, “Yeah, ethical issues basically are just a question of safety. We test and test and test again, in animals and in labs, and then once we feel it’s safe enough, we move on to humans.” So that’s kind of the other school of thought, that we should actually use this opportunity and really go for it. Is there a possible split happening in the science community about this? I mean, are we going to see some people holding back because they have ethical concerns, and some others just going forward because some countries under-regulate or don’t regulate at all?

JD: Well, I think with any new technology, especially something like this, there are going to be a variety of viewpoints, and I think that’s perfectly understandable. I think that in the end, this technology will be used for human genome engineering, but I think to do that without careful consideration and discussion of the risks and potential complications would not be responsible.

BG: There are a lot of technologies and other fields of science that are developing exponentially, pretty much like yours. I’m thinking about artificial intelligence, autonomous robots and so on. No one seems – aside from autonomous warfare robots – nobody seems to have launched a similar discussion in those fields, in calling for a moratorium. Do you think that your discussion may serve as a blueprint for other fields?

JD: Well, I think it’s hard for scientists to get out of the laboratory. Speaking for myself, it’s a little bit uncomfortable to do that. But I do think that being involved in the genesis of this really puts me and my colleagues in a position of responsibility. And I would say that I certainly hope that other technologies will be considered in the same way, just as we would want to consider something that could have implications in other fields besides biology.

BG: Jennifer, thanks for coming to TED.

JD: Thank you.

(Applause)

The 2020 Nobel Prize in Chemistry has been awarded to Emmanuelle Charpentier and Jennifer A. Doudna “for the development of a method for genome editing.”

Man is by nature a social animal; an individual who is unsocial naturally and not accidentally is either beneath our notice or more than human. Society is something that precedes the individual. Anyone who either cannot lead the common life or is so self-sufficient as not to need to, and therefore does not partake of society, is either a beast or a god. – Aristotle

• Erikson’s stages of psychosocial development
• Erik Erikson was a student of Anna Freud, the daughter of Sigmund Freud.

© Guest Editors’ Introduction: The Top 10 Algorithms

An algorithm is a sequence of finite computational steps that
transforms an input into an output. (Cormen and Leiserson, 2009)

Algos is the Greek word for pain. Algor is Latin, to be cold. Neither is the root for algorithm, which stems instead from al-Khwarizmi, the name of the ninth-century Arab scholar whose book al-jabr wa’l muqabalah devolved into today’s high school algebra textbooks. Al-Khwarizmi stressed the importance of methodical procedures for solving problems. Were he around today, he’d no doubt be impressed by the advances in his eponymous approach.

Some of the very best algorithms of the computer age are highlighted in the January/February 2000 issue of Computing in Science & Engineering, a joint publication of the American Institute of Physics and the IEEE Computer Society. Guest editors Jack Don-garra of the University of Tennessee and Oak Ridge National Laboratory and Fran-cis Sullivan of the Center for Comput-ing Sciences at the Institute for Defense Analyses put togeth-er a list they call the “Top Ten Algorithms of the Century.”

“We tried to assemble the 10 al-gorithms with the greatest influence on the development and practice of science and engineering in the 20th century,” Dongarra and Sullivan write. As with any top-10 list, their selections—and non-selections—are bound to be controversial, they acknowledge. When it comes to picking the algorithmic best, there seems to be no best algorithm.

1946: Metropolis Algorithm for Monte Carlo

John von Neumann, Stan Ulam, and Nick Metropolis, all at the Los Alamos Scientific Laboratory, cook up the Metropolis algorithm, also known as the Monte Carlo method.

Monte Carlo methods are the only practical choice for evaluating problems of high dimensions.

1947: Simplex Method for Linear Programming

George Dantzig, at the RAND Corporation, creates the simplex method for linear programming.

The Simplex method relies on noticing that the objective function’s maximum must occur on a corner of the space bounded by the constraints of the “feasible region.”

1950: Krylov Subspace Iteration Methods

Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.

The importance of iterative algorithms in linear algebra stems from the simple fact that a direct approach will require \( O(N^3) \) work. The Krylov subspace iteration methods have led to a major change in how users deal with large, sparse, nonsymmetric matrix problems.

1951: The Decompositional Approach to Matrix Computations

Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations.

Introducing the decompositional approach to matrix computations revolutionized the field.

1957: The Fortran Optimizing Compiler

John Backus leads a team at IBM in developing the Fortran optimizing compiler.

The creation of Fortran may rank as the single most important event in the history of computer programming: Finally, scientists (and others) could tell the computer what they wanted it to do, without having to descend into the netherworld of machine code. Although modest by modern compiler standards—Fortran I consisted of a mere 23,500 assembly-language instructions—the early compiler was nonetheless capable of surprisingly sophisticated computations. As Backus himself recalls in a recent history of Fortran I, II, and III, published in 1998 in the IEEE Annals of the History of Computing, the compiler “produced code of such efficiency that its output would startle the programmers who studied it.”

1959: QR Algorithm for Computing Eigenvalues

J.G.F. Francis of Ferranti Ltd., London, finds a stable method for computing eigenvalues, known as the QR algorithm.

The QR Algorithm for computing eigenvalues of a matrix has transformed the approach to computing the spectrum of a matrix.

1962: Quicksort Algorithm for Sorting

Tony Hoare of Elliott Brothers, Ltd., London, presents Quicksort.

Hoare’s algorithm uses the age-old recursive strategy of divide and conquer to solve the problem.

Sorting is a central problem in many areas of computing so it is no surprise to see an approach to solving the problem as one of the top 10. Quicksort is one of the best practical sorting algorithm for general inputs. In addition, its complexity analysis and its structure have been a rich source of inspiration for developing general algorithm techniques for various applications.

1965: Fast Fourier Transform

James Cooley of the IBM T.J. Watson Research Center and John Tukey of Princeton University and AT&T Bell Laboratories unveil the fast Fourier transform.

Easily the most far-reaching algo-rithm in applied mathematics, the FFT revolutionized signal processing. The underlying idea goes back to Gauss (who needed to calculate orbits of asteroids), but it was the Cooley–Tukey paper that made it clear how easily Fourier transforms can be computed. Like Quicksort, the FFT relies on a divide-and-conquer strategy to reduce an ostensibly \( O(N^2) \) chore to an \( O(NlogN) \) frolic. But unlike Quick- sort, the implementation is (at first sight) nonintuitive and less than straightforward. This in itself gave computer science an impetus to investigate the inherent complexity of computational problems and algorithms.

Mozart could listen to music just once and then write it
down from memory without any mistakes. (Vernon, 1996)

FFT is an algorithm “the whole family can use.” The FFT is perhaps the most ubiquitous algorithm in use today to analyze and manipulate digital or discrete data. The FFT takes the operation count for discrete Fourier transform from \( O(N^2) \) to \( O(NlogN) \).

1977: Integer Relation Detection

Helaman Ferguson and Rodney Forcade of Brigham Young University advance an integer relation detection algorithm.

Some recently discovered integer relation detection algorithms have become a centerpiece of the emerging discipline of “experimental mathematics” — the use of modern computer technology as an exploratory tool in mathematical research.

1987: Fast Multipole Method

Leslie Greengard and Vladimir Rokhlin of Yale University invent the fast multipole algorithm.

The Fast Multipole Algorithm was developed originally to calculate gravitational and electrostatic potentials. The method utilizes techniques to quickly compute and combine the pair-wise approximation in \( O(N) \) operations.

• The Best of the 20th Century: Editors Name Top 10 Algorithms, By Barry A. Cipra, a mathematician and writer based in Northfield, Minnesota.
• The Top10 Algorithms From The 20th Century, Alex Townsend, Cornell University

Problem

189. Rotate Array

Follow up

• Try to come up as many solutions as you can, there are at least 3 different ways to solve this problem.
• Could you do it in-place with O(1) extra space?

Java

Using Reverse

© Approach 4: Using Reverse

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class Solution {
    public void rotate(int[] nums, int k) {
        final int N = nums.length;
        if (k >= N)
            k = k % N;
        reverse(nums, 0, N - 1);
        reverse(nums, 0, k - 1);
        reverse(nums, k, N - 1);
    }

    private void reverse(int[] nums, int start, int end) {
        int temp;
        for (int i = 0; i < (end - start + 1) / 2; i++) {
            temp = nums[start + i];
            nums[start + i] = nums[end - i];
            nums[end - i] = temp;
        }
    }
}

Submission Detail

• 35 / 35 test cases passed.
• Runtime: 0 ms, faster than 100.00% of Java online submissions for Rotate Array.
• Memory Usage: 39.4 MB, less than 97.56% of Java online submissions for Rotate Array.

brute force

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class Solution {
    public void rotate(int[] nums, int k) {
        int temp;
        final int N = nums.length;
        if (k >= N)
            k = k % N;
        for (; k > 0; k--) {
            temp = nums[N - 1];
            for (int i = N - 1; i > 0; i--) {
                nums[i] = nums[i - 1];
            }
            nums[0] = temp;
        }
    }
}

Submission Detail

• 35 / 35 test cases passed.
• Runtime: 183 ms, faster than 22.49% of Java online submissions for Rotate Array.
• Memory Usage: 39.4 MB, less than 96.24% of Java online submissions for Rotate Array.

© Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne

Types of analyses

• Best case - Lower bound on cost.
• Worst case - Upper bound on cost.
• Average case - “Expected” cost.

Order-of-growth classifications

notation

Tilde notation

• Estimate running time (or memory) as a function of input size N
• Ignore lower order terms

1.4 Analysis of Algorithms

Stop Translating in Your Head.
Learn to Think in English.

To be honest, it is an easy but time taking process. Although I’m not a native speaker but still I know it is pretty difficult in the beginning when we try to think in English.

Think in single words

When

When your mind is clear and you’re not busy, one to two times a day.

How

If you’re just starting to learn English, don’t worry—it’s never too early to start thinking in English. You can begin as soon as you know even a small number of vocabulary words.

Look around you. What do you see? In your head, try to name each object in your surroundings.

Charles Thomas tells his students to name the things that they see around them, wherever they are.

“As you continue with this, it becomes more of a habit, so things are going to pop up into your head – computer, telephone, chair, desk. Whatever it is…wherever you are.”

Start with nouns and then add in verbs, he suggests.

He says you can also do this at home when you wake up and before you go to sleep.

“I’ve had students tell me that they label everything in their room or their apartments so that these English words, kind of, stick in their heads.”

Narrate your day, Describe your day

When

When your mind is clear and you’re not busy, one to two times a day.

How

A narrator is someone who tells or reads the story. In books, the narrator is the part without dialogue, which describes what’s happening. Many movies—especially documentaries—use narrators to explain certain parts. Now you get to pretend to be the narrator in your life, as if your life were a movie!

Your daily life narration might sound something like this: “It’s morning. She wakes up and rubs her eyes, preparing to face the day. She yawns as she makes herself a cup of coffee, and wonders what she should wear today.”

Thomas asks his beginning-level students to describe their day using the simple present verb form. So, they would think to themselves things like, “I put on my shirt” and “He drives the bus.”

For example, you might tell yourself, “When I leave the house, I’m going to get an iced coffee. Then, I’ll take the train to class. I’m studying with Paola today. She said she booked a study room at the library for 2 p.m.”

Make up conversations, Talk to yourself in English

This is a great way to practice what you might say in a real conversation.

When

When you’re alone and not busy, once a day.

How

Of course, when you speak to other people you don’t just tell them about your day. Conversations come in many different topics, so you’ll want to practice conversations as well.

For example, if you’re planning to go to a restaurant soon you can practice a conversation with the waiter. Think of both the waiter’s parts and yours. Your conversation might look something like this:

Waiter: “Hello, and welcome to our restaurant. Do you know what you’ll be ordering?”

You: “I’m not sure yet. What do you recommend?”

Waiter: “If you like seafood, our fish of the day is fantastic.”

You: “Great, I’ll have that, then.”

You can try the conversation in different ways, and seeing how differently it turns out each time.

Get creative

When

Every time you don’t know how to say something in English.

How

So you’re sitting in your car and practicing your English. That’s great! But what do you do when you can’t think of how to say a word? Instead of interrupting a conversation to pull out a dictionary app, it’s time to get creative.

For example, if you’re trying to explain to someone that you lost your key, but can’t remember the word “key,” you can tell them instead that “I can’t open my door because it’s locked,” or “I can’t get into my house, I lost the thing you use to unlock the door.”

Both sentences don’t use the word “key,” but they’re both clear enough to be understood.

Build your vocabulary

When

Every time you think in English.

How

You know that word you couldn’t remember earlier? (The words you don’t know, which cause you to get creative in #4.) As soon as you can, write down the “definition” in English or the word in your native language. Carry around a little book or use a note app on your phone. Every time you can’t think of a word (or don’t know a word) in English, write it down. At the end of the day, look up these words in English and write them down. This will help you fill in the gaps in your vocabulary.

Now that you have a long list of new words, what can you do with them? The first step is to use them in conversations (and your thoughts). A good way to do this is by grouping the words into chunks. Choose a group of around five words every morning, and use them throughout the day. This will help you remember them in the long run.

Something else you can do with your growing vocabulary list is move them to the digital world. Wordnik is a website where you can look up a word and see real examples of it being used. You can also make a list of words here. Add your new words and learn how to use them. As you internalize these new words you can move from your “vocabulary” list to a “learned words” list.

The Dictionary website (and apps) also lets you add words to a list of favorites, as does the Vocabulary website. Use these websites and lists!

Use an English to English dictionary, Don’t use a bilingual dictionary

When

Every time you look up a word.

How

When you feel more comfortable thinking in English, make sure to do this in your daily life whenever possible. This includes looking up words in an English to English dictionary (with definitions in English). The less you translate, the easier it will become to just think and speak in English.

Think in sentences, Learn vocabulary in phrases, not single words

Our brains are pattern-matching machines that remember things put into context. If I can’t come up with any context examples, I check out Cambridge Advanced Learner’s Dictionary or google it.

For example, if you are sitting in a park, you can tell yourself things like, “It’s such a beautiful day” and “People are playing sports with their friends.”

Once this becomes easy, you can move on to more difficult sentences.

Hinshaw sometimes uses this exercise to think about what he wants to say to people in Spanish.

“I definitely try to say these sentences in my head or try to put the words together without thinking too much about if it’s absolutely correct.”

Describe unknown words

Another exercise that both Thomas and Hinshaw suggest is describing in your mind objects you don’t know the words for.

An example would be if you couldn’t think of the word “garage,” Thomas says.

“If you’re looking at your house and you see your garage, but you can’t think of the name in English, you can say, ‘The place inside where I put my car.’ Or you can say, ‘It’s next to my house. I keep things there.’”

He says you can also use shorter phrases, such as “It’s similar to…” or “It’s the opposite of…”

Hinshaw says doing this can help learners of any language. As a Spanish learner, he does it himself.

Take notes

Hinshaw suggests writing down just five to 10 new words and phrases each day.

Keeping a notebook, he says, helps you remember the situation that you needed that word or phrase for. This makes it easy to recall when you are in such a situation again.

Practice it daily

Thomas says do a little every day.

“So when you’re doing it every day, over and over again, little by little, that’s the key. Because, when you make things a habit, then it just pops up into your mind without thinking and then, before you know it, really, you’re thinking in English.”

Get an English-speaking friend or partner

Travel

• Do You Think in English? Here’s Why You Should, Plus 6 Steps That Show Exactly How to Start
• Train Your Brain to Think in English
• How can I start thinking in English in my mind?
• Stop Translating in Your Head & Learn to Think in English
• 6 Ways to Think in English
• Learn How to Think in English

© Inspiring quotes for English learners

These inspiring quotes will help you stay motivated to improve your English every day. It’s easy to get discouraged after a bad grade on a test or a particularly difficult lesson. It is hard to learn a new language, and more importantly, it takes time, effort, and practice. But even when the task seems hard, it’s never impossible, as these inspiring quotes will tell you. So change tactics, try something new, and keep on learning English!

An investment in education pays the best interest. — Benjamin Franklin

Anyone who stops learning is old, whether at twenty or eighty. — Henry Ford

Education costs money, but then so does ignorance. — Sir Claus Moser

Education is not preparation for life. Education is life itself. — John Dewey

Get over the idea that only children should spend their time studying. Be a student as long as you still have something to learn, and this will mean all your life. — Henry Doherty

I am always doing that which I cannot do in order that I may learn how to do it. — Pablo Picasso

I am always ready to learn although I do not always like being taught. — Winston Churchill

I hope that in this year to come, you make mistakes. Because if you are making mistakes, then you are making new things, trying new things, learning, living, pushing yourself, changing yourself, changing your world. — Neil Gaiman

I learned the value of hard work by working hard. — Margaret Mead

If the goal you’ve set for yourself has a 100 percent chance of success, then frankly you aren’t aiming high enough. — Benny Lewis

If you hold a cat by the tail you learn things you cannot learn any other way. — Mark Twain

If you’re determined to learn, no one can stop you. — Zig Ziglar

It is good to have an end to journey toward, but it is the journey that matters in the end. — Ernest Hemingway

Knowledge is of no value unless you put it into practice. — Anton Chekhov

Live as if you were to die tomorrow. Learn as if you were to live forever. — Mahatma Ghandi

Never discourage anyone who continually makes progress, no matter how slow. — Plato

Self education is the only kind of education there is. — Isaac Asimov

The noblest pleasure is the joy of understanding. — Leonardo da Vinci

Theory is knowledge that doesn’t work. Practice is when everything works and you don’t know why. — Herman Hesse

There are no foreign lands. It is the traveller only who is foreign. — Robert Louis Stevenson

There are no secrets to success. It is the result of preparation, hard work, and learning from failure. — Colin Powell

You can be discouraged by failure, or you can learn from it. So go ahead and make mistakes, make all you can. Because, remember that’s where you’ll find success - on the far side of failure. — Thomas Watson

You can get help from teachers, but you’re going to have to learn a lot by yourself, sitting alone in a room. — Dr. Seuss

You don’t learn to walk by following rules. You learn by doing, and by falling over. — Richard Branson

You’ll never know everything about anything. — Julia Child

Start to Freelance

• Upwork
• Fiverr

Coding Contests

• Topcoder
• HackerEarth
• Coderbyte
• Project Euler
• CodeChef
• Codeforces
• Sphere Online Judge (SPOJ)
• Google Code Jam
• CodingBat
• Codility
• HackerRank
• InterviewBit

Record and Sell Online Courses

• Udemy
• BitDegree
• Udacity
• Skillshare

YouTube Channel

Start a Podcast

Sell an Ebook

• Amazon Kindle Direct Publishing

Start to Write

• Medium

• Side Gigs That Will Make You Money as a Programmer in 2020 - An unbiased look at revenue streams every programmer can use to boost their income
• How to Make Extra Money as a Programmer - There are plenty of opportunities to expand your income beyond your day job
• 8 Side Income Ideas For Programmers