Scientific work - in its modern form - has become one of the inventions that allowed progress to progress. Before its form was developed in the 17th century, the results of the work were transmitted privately in letters, ephemerally in lectures, or all in a crowd - in books. There were no places for public discussion of gradual progresses. Leaving on their pages a place to describe individual experiments or small technical advances, journals created chaos from the growing science. Since then, scientists have become like social insects: they are constantly moving progress forward, with a buzz similar to a flock of bees.
The earliest of the works were in some sense more readable than today's ones. They were less specialized, more rectilinear, short and not so formal. Mathematical analysis was invented only shortly before. The entire set of data on the topic under study could fit in a plate on one page. All calculations related to the results were carried out by hand, and they could also be checked.
The more difficult science becomes, the harder it is to report its results. Today's works are longer than ever, and are full of jargon and various symbolic symbols. They depend on a set of computer programs that produce data, erase data, build graphs, process statistical models. And these programs are sometimes so carelessly written and so focused on the result that it also contributes to the crisis of repeatability - that is, the work does not cope with its main task: to report about the discovery made simply enough that someone else can also do it .
Perhaps you should blame the habit of the paper on which the work is printed. Scientific methods evolve with the speed of software; most of all, physicists, biologists, chemists, geologists, and even anthropologists and psychologists are required to master programming languages and packages of
datalogical programs. And at the same time, the main way of communicating scientific results has not changed over the past 400 years. Of course, the work can be spread on the Internet - but it is still text and images located on the page.
What would happen if we today developed a standard of scientific work from scratch? Recently, I spoke with
Bret Victor , a researcher who worked at Apple on early prototypes of the user interface for the iPad, and now directing his own lab in Auckland, California, studying the future of computing systems. Victor has long believed that scientists still do not enjoy all the benefits of a computer. “The situation is not very different from the printing press and the evolution of books,” he said. After Guttenberg, the printing presses were mainly used to reproduce bible calligraphy. Almost 100 years of technical and conceptual improvements were required in order to invent a modern book. "There was a whole period during which people had a new printing technology, and they used it to reproduce old media."
Victor showed what can be achieved when he reworked a journal article written by Dunakn Watts and Stephen Strogatz, “The collective dynamics of networks of small worlds”. He chose it because it is one of the most frequently cited works in all of science, and because it is a model for a clear presentation of information. (Strogats is best known as the author of the column “Elements of Mathematics” in The New York Times).
The work of Watts-Strohats described the key discoveries like most others - with text, pictures, mathematical symbols. And, like most works, these discoveries are very difficult to digest, despite the clear description. The most difficult jobs were those that described the procedures or algorithms, since the reader had to take on the “role of the computer,” as Victor said, to try to keep the picture of what was going on in his mind, following the steps of the algorithm.
After Victor’s reworking, the explanatory text was interspersed with interactive diagrams that illustrated each step. In this version it was possible to trace the operation of the algorithm by example. You could even control him.
Strohats admired option Victor. Later, he told me that he was very sorry that in mathematics for more than one hundred years it has been a tradition to write works as strictly and formally as possible, often even omitting the very visual clues that mathematicians use to make their discoveries.
Stogaz studies nonlinear dynamics and chaos, systems prone to synchronization or self-organization: blinking fireflies, the ticking of metronomes, electrical impulses of heart cells. The key is that such systems work cyclically, and Strohats visualizes this through circular points: when a point returns to the starting point, it is a blinking glowworm or a heart cell trigger. “For almost 25 years, I did small computer animations of dots running in a circle, with colors that signify their frequency,” he said. “The red ones are slow guys, the violet ones are fast ... All these points are spinning on my computer, I have been doing this all day,” he said. I catch patterns in the color dots running across the screen much better than in the 500 time series. In a similar way, I will see little, because in fact it does not look like that at all. I study dynamic processes, so their presentation must also be dynamic. ”
Programs - the carrier is dynamic, but paper is not. In this sense, it seems strange that such studies, like those of Strogats, devoted to dynamical systems, so often spread out on paper, having no advantages in the form of circling dots - since these are the points that helped him to see what he saw, and can help to see this and the reader.
This is the whole problem of scientific communication: today, scientific results are very often found with the help of computers. Ideas are complex, dynamic, they are not easy to cover the inner eye. And at the same time, the most popular tool for sharing results is PDF - literally a simulation of a piece of paper. We can probably come up with something better.
Stephen Wolfram published his first scientific paper at the age of 15 years. By the end of his studies at the institute, he had already published 10 papers, and by the age of 20, in 1980, he had already completed his doctorate in particle physics at the California Institute of Technology. His super-weapon was the active use of a computer in those times when the most serious scientists considered computational work to be inferior. “By that time, I probably used computer algebra the most in the world,” he said in an interview. It was very convenient, I could just carry out all the calculations on the computer. I had a good time, placing especially ornate formulas in my scientific works. ”
With the growth of his research ambitiousness, he increasingly brought existing software to the limits of his possibilities. For one project, he had to use half a dozen different software tools. “I spent a lot of time tying it all together,” he said. “And I decided that I should try to create a single system that would do everything I need - one that could grow forever.” And instead of continuing academic activities, Wolfram decided to create Wolfram Research, and make an ideal computing environment for scientists. The headline in Forbes on April 18, 1988 read: “Physics Whiz Goes Into Biz” [The wizard-scientist hit the business].
In the center of the Mathematica system, as the company called its main product, there is a “notepad” in which you write commands on one line and see the results on another. Write "1/6 + 2/5" and he will give you "17/30". Ask him to multiply the polynomials, and he will submit. Mathematica is capable of mathematical analysis, number theory, geometry, algebra. It has functions for counting chemical reactions and filtering genetic data. Her database has all the pictures of Rembrandt, and she can give you a scatter diagram of his palette over time. The models of orbital mechanics are built into it, and it will be able to calculate how far the F / A-18 Hornet can plan if its engines turn off at an altitude of 10,000 km. The notepad in Mathematica is not just a record of the user's calculations, but a transcript of his conversation with the all-knowing oracle. Wolfram calls carefully written notebooks "computational essays."
The notebook interface was the brainchild of Theodore Gray, inspired by the work with the old code editor for Apple. Most programming environments allow you to execute code line by line or all at once. Apple editor let you select any part of the code and execute it only. Gray brought these basic concepts to Mathematica, and none other than Steve Jobs himself helped to improve the design. Notepad is designed to turn scientific programming into an interactive exercise, in which individual teams can be corrected and restarted tens or hundreds of times, learning from the results of computational experiments, which allows one to come to a deeper understanding of the data.
Especially well notebook copes with its tasks due to the ability to draw graphics, images and beautiful mathematical formulas, despite the fact that all of this dynamically responds to changes in the code. In Mathematica, you can enter a voice recording, apply complex mathematical filters to audio recordings, and visualize the final sound wave. By dragging the parameters with the mouse, you can change its appearance and see which filters are best suited when playing with them. The ability of a package to easily handle so many different computational tasks in one simple interface is the result of "literally human-age work," as Gray says.
The vision underlying the work was repeated many times by Wolfram in his lectures, blog entries, presentations, and press releases. Do not just make good software, but create an inflection point in the very occupation of science. In the middle of the 17th century, Gottfried Leibniz developed a system for recording integrals and derivatives (familiar and dx / dt), which made the complex ideas of mechanical analysis mechanical. Leibniz believed that similar symbols in a wider application could create an “algebra of thoughts.” Since then, logics and linguists have been dreaming of a universal language that can eliminate ambiguity and turn the solution of complex problems into a kind of mathematical analysis.
Wolfram’s career is constantly trying to incorporate all of the world's knowledge into Mathematica, and later to make it available through Wolfram Alpha, the company's “engine of computational knowledge”, behind many of the possibilities to answer questions from electronic assistants like Siri and Alexa. This is Wolfram's attempt to create Interlingua, a programming language that is equally understandable to both humans and machines — algebra of everything.
The task is characteristically ambitious. In the 1990s, Wolfram sometimes teased the public with comments that in the process of creating his company he was working on a revolutionary science project. The wait was growing. Finally, the project arrived: a huge book, as thick as a cinder block, and almost as heavy, with the everlasting title: "
Science of a New Type ."
This turned out to be a detailed study conducted with the help of Mathematica notebooks, surprisingly complex patterns created by the simplest computing processes - cellular automata. The study was conducted just as a matter of research, and in order to understand how simple rules can produce complex phenomena of nature — for example, a tornado or a clam shell pattern. These studies, published by Wolfram without independent editing, were accompanied by constant reminders of their importance.
The more you run into Wolfram, the more it resembles his style. In an article about him from 1988, Forbes tried to get to the roots of this phenomenon: “As Harry Wolfe, the former director of the prestigious Advanced Research Institute (in Princeton), where Wolfram was one of the youngest senior researchers at 23, said, he had "Cultivated difficulties in the character, supported by a sense of loneliness, isolation and uniqueness."
When one of Wolfram's assistants announced a significant mathematical discovery at the conference, which was a key part of the “Science of a new type”, Wolfram threatened to condemn it in the event of publication of the work. “In no serious research group, the junior researcher will not be allowed to talk about what the senior is doing,” he said at the time. Other scientists criticized Wolfram’s massive book for being based on other works, but did not mention them. “He hints that he is the author of the main ideas that have been the central idea of the theory of complex systems for the last 20 years,” one of the researchers told Times Higher Education magazine in 2002.
The self-praise of Wolfram seems all the more surprising since it is completely unnecessary. His achievements speak for themselves - if he would allow them to do it. Mathematica achieved success almost immediately after launch. Users have long been waiting for such a product; at universities, the program has become as prevalent as Microsoft Word. Wolfram also used a steady income to hire additional engineers and experts in various industries, feeding more and more information to his insatiable program. Today Mathematica knows about the anatomy of the foot and the laws of physics, about the music, the systematics of coniferous trees and the main battles of the First World War. Wolfram himself helped to teach his program to the archaic Greek notation.
All this knowledge is “computable”. If you want, you can mark the location of the
battle on the Somme by x, and y indicates the daily precipitation in 1916 within a radius of 50 km from this place, and Mathematica will calculate if more deaths occurred during the First World War during rain.
"I noticed an interesting trend," wrote Wolfram in a blog post. - Choose any area X, from archeology to zoology. Then it will be associated with "computational X", which either already exists or is only being born. And this is considered the future of this field. "Wolfram argues that the better specialists in these areas will master computational methods, the more the field of what is being opened will expand. The notepad in Mathematica can become an accelerator of science, since it can give rise to a new style of thinking." , - he says, - as the same transition occurs that took place in the 17th century, when people had the opportunity to read mathematical records. This becomes a form of communication with a very important feature - the possibility new launch.
The idea is that this kind of “scientific work” can have the same dynamism that Strohats and Viktor wanted to have — interactive charts interspersed with text — with the added advantage that all the code that generates these charts and all the data will be available to the reader. who can review them and play with them. “Honestly, when you write something so simple and understandable in the Wolfram language in a notebook, there is no place for deception. There is what is, and it works the way it works. There is no way to adjust the result, ”says Wolfram.
To write a paper in a Mathematica notebook means to reveal the results and methods of your work; and scientific work, and everything you did to write it. As a result, it will be easier for readers not only to understand it, but also to reproduce (or not reproduce). When millions of scientists around the world make their contribution to science gradually, the only way to turn all this work into something important will be to enable others to reliably build something based on these contributions. “This is what scientific work made in the form of computational essays can accomplish,” said Wolfram.
Wolfram says he is surprised that computational essays have not gained popularity. He recalls his work with Elsevier, a giant of scientific publications, in the early 1980s. “Elsevier hired me to consult about something like" what the future of scientific publications will look like. " This was before the appearance of Mathematica notebooks, but he pushed them to talk about from the same area. “A few years ago I again talked with someone from the company's management. And at that meeting, I realized - oh my God, I told you exactly the same thing 35 years ago! “
I talked to Theodore Gray, who left Wolfram Research in order to become a writer. He said that his work on the notepad in particular was motivated by his sensations, which had already been well formed by the 1990s, “that, obviously, all the scientific communication and all the technical works that used any data or mathematics or modeling or graphics or schemes or something like that, do not need to publish on paper. This was quite obvious by 1990, “he said.
"For the past 29 years, the fact that, with the exception of some people who understood this, the community as a whole has not taken this approach, is perceived with horror and surprise," he said. “It’s literally impossible to calculate how much is lost, how much time is wasted, how many results are misunderstood or incorrectly presented.”
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