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justforbooks · 4 years

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The trackball, a related pointing device, was invented in 1946 by Ralph Benjamin as part of a post-World War II-era fire-control radar plotting system called Comprehensive Display System (CDS). Benjamin was then working for the British Royal Navy Scientific Service. Benjamin's project used analog computers to calculate the future position of target aircraft based on several initial input points provided by a user with a joystick. Benjamin felt that a more elegant input device was needed and invented what they called a "roller ball" for this purpose.

The device was patented in 1947, but only a prototype using a metal ball rolling on two rubber-coated wheels was ever built, and the device was kept as a military secret.

Another early trackball was built by Kenyon Taylor, a British electrical engineer working in collaboration with Tom Cranston and Fred Longstaff. Taylor was part of the original Ferranti Canada, working on the Royal Canadian Navy's DATAR (Digital Automated Tracking and Resolving) system in 1952.

DATAR was similar in concept to Benjamin's display. The trackball used four disks to pick up motion, two each for the X and Y directions. Several rollers provided mechanical support. When the ball was rolled, the pickup discs spun and contacts on their outer rim made periodic contact with wires, producing pulses of output with each movement of the ball. By counting the pulses, the physical movement of the ball could be determined. A digital computer calculated the tracks and sent the resulting data to other ships in a task force using pulse-code modulation radio signals. This trackball used a standard Canadian five-pin bowling ball. It was not patented, since it was a secret military project.

Douglas Engelbart of the Stanford Research Institute (now SRI International) has been credited in published books by Thierry Bardini, Paul Ceruzzi, Howard Rheingold, and several others as the inventor of the computer mouse. Engelbart was also recognized as such in various obituary titles after his death in July 2013.

By 1963, Engelbart had already established a research lab at SRI, the Augmentation Research Center (ARC), to pursue his objective of developing both hardware and software computer technology to "augment" human intelligence. That November, while attending a conference on computer graphics in Reno, Nevada, Engelbart began to ponder how to adapt the underlying principles of the planimeter to inputting X- and Y-coordinate data. On November 14, 1963, he first recorded his thoughts in his personal notebook about something he initially called a "bug," which in a "3-point" form could have a "drop point and 2 orthogonal wheels." He wrote that the "bug" would be "easier" and "more natural" to use, and unlike a stylus, it would stay still when let go, which meant it would be "much better for coordination with the keyboard."

In 1964, Bill English joined ARC, where he helped Engelbart build the first mouse prototype. They christened the device the mouse as early models had a cord attached to the rear part of the device which looked like a tail, and in turn resembled the common mouse. As noted above, this "mouse" was first mentioned in print in a July 1965 report, on which English was the lead author. On 9 December 1968, Engelbart publicly demonstrated the mouse at what would come to be known as The Mother of All Demos. Engelbart never received any royalties for it, as his employer SRI held the patent, which expired before the mouse became widely used in personal computers. In any event, the invention of the mouse was just a small part of Engelbart's much larger project of augmenting human intellect.

Several other experimental pointing-devices developed for Engelbart's oN-Line System (NLS) exploited different body movements – for example, head-mounted devices attached to the chin or nose – but ultimately the mouse won out because of its speed and convenience. The first mouse, a bulky device (pictured) used two potentiometers perpendicular to each other and connected to wheels: the rotation of each wheel translated into motion along one axis. At the time of the "Mother of All Demos", Engelbart's group had been using their second generation, 3-button mouse for about a year.

On October 2, 1968, a mouse device named Rollkugel (German for "rolling ball") was described as an optional device for its SIG-100 terminal was developed by the German company Telefunken. As the name suggests and unlike Engelbart's mouse, the Telefunken model already had a ball. It was based on an earlier trackball-like device (also named Rollkugel) that was embedded into radar flight control desks. This trackball had been developed by a team led by Rainer Mallebrein at Telefunken Konstanz for the German Bundesanstalt für Flugsicherung (Federal Air Traffic Control) as part of their TR 86 process computer system with its SIG 100-86 vector graphics terminal.

When the development for the Telefunken main frame TR 440 [de] began in 1965, Mallebrein and his team came up with the idea of "reversing" the existing Rollkugel into a moveable mouse-like device, so that customers did not have to be bothered with mounting holes for the earlier trackball device. Together with light pens and trackballs, it was offered as an optional input device for their system since 1968. Some Rollkugel mouses installed at the Leibniz-Rechenzentrum in Munich in 1972 are well preserved in a museum. Telefunken considered the invention too unimportant to apply for a patent on it.

The Xerox Alto was one of the first computers designed for individual use in 1973 and is regarded as the first modern computer to utilize a mouse. Inspired by PARC's Alto, the Lilith, a computer which had been developed by a team around Niklaus Wirth at ETH Zürich between 1978 and 1980, provided a mouse as well. The third marketed version of an integrated mouse shipped as a part of a computer and intended for personal computer navigation came with the Xerox 8010 Star in 1981.

By 1982, the Xerox 8010 was probably the best-known computer with a mouse. The Sun-1 also came with a mouse, and the forthcoming Apple Lisa was rumored to use one, but the peripheral remained obscure; Jack Hawley of The Mouse House reported that one buyer for a large organization believed at first that his company sold lab mice. Hawley, who manufactured mice for Xerox, stated that "Practically, I have the market all to myself right now"; a Hawley mouse cost $415. In 1982, Logitech introduced the P4 Mouse at the Comdex trade show in Las Vegas, its first hardware mouse. That same year Microsoft made the decision to make the MS-DOS program Microsoft Word mouse-compatible, and developed the first PC-compatible mouse. Microsoft's mouse shipped in 1983, thus beginning the Microsoft Hardware division of the company. However, the mouse remained relatively obscure until the appearance of the Macintosh 128K (which included an updated version of the single-button Lisa Mouse) in 1984, and of the Amiga 1000 and the Atari ST in 1985.

* (Photo) Apple Macintosh Plus mouse

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testblogplzignore · 3 years

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Mathematical concepts needed to understand my calculus of variations post in order

Algebra is the ability to symbolize things and manipulate symbols. I can show you an example by taking two variables $ x $ and $ y $. We can show algebra on these two by adding them together $ x+y $. I can manipulate these symbols by swapping their order (commuting, down below) $ y+x $. Now if I decide to set $ x+y = y+x =0 $ then I can manipulate the symbols further and find that $ x=-y $

What you’re really doing when you do algebra is this

Take

$ x+y $

if you swap the order you’re really doing this

$ x + y -y $

then adding $ y $ to the left side

$ y + x +y -y $

so you get $ y + x $

This also applies to things across an equals sign

$ x+y = 0 $ or

$ x+y-y = 0 -y = -y $

Sometimes you can’t actually switch the order of things as easily so they have words for it (below)

What is a function? A function is anything you want it to be. You can make a function that tells you how many apples are in a box. This function can change by time and if it does then you can tell how many apples are in a box at a given time. You can make a function of distance traveled too. At one point you’re at position $ a $ or your house. You want to go see your friend so you travel a distance to go see him and he’s at his house or point $ b $. If you record where you were everywhere on this journey you’ve created a function of distance as a function of time or $ x(t) $. Another analogy is if you’re traveling in a car you can see both your distance traveled (odometer) and your velocity (speedometer) and both of these are functions of time. Suppose you recorded your speedometer and odometer and recorded the time you took them at. You now have two functions relating distance traveled to time and velocity as a function of time

Now the calculus. The easiest way to comprehend calculus is through graphing or plotting functions and looking at properties of the function. Using the

This picture defines what a derivative and integral are

A derivative is the same as drawing a straight tangent line from a point on a graph. A function’s derivative is a function of the straight lines you draw and tells you what the straight line is for any point you choose. So if I give you the derivative of a function you can tell me how “fast” the original function is going at any point. If the original function is just distance as a function of time or displacement then the derivative is the speed of that function. Hence if you graph the distance something has traveled in a certain amount of time you can see the speed it was traveling by drawing a straight line or taking its derivative. In the case of taking the derivative of displacement you get the velocity it has as a function of time. You can see why velocity is intrinsically related to the distance this way. Mathematically, given a displacement as a function of time $ x(t) $ then the time derivative $ \frac{d}{dt} $ with respect to time ($ dt $) is $ \frac{d}{dt} x(t) $ and is equal to the velocity as a function of time $ \frac{d}{dt} x(t) = v(t) $. Another way to represent this relation/derivative with respect to time is $ \frac{d}{dt} x(t) = \dot{x} $ or Newton notation. More notation explanation will come after

An integral is the area under the function on a graph. A function’s integral is also a function (usually) and it represents the area underneath the original function. So If I give you the integral of a function then you can tell me how much area was underneath that function. If I give you a function that measures your speed or velocity as a function of time and you take the integral of it then you have the distance traveled as a function of time. Another way to think of an integral integrating a function is adding up what that function is doing between two points. Mathematically, given a function of velocity $ \dot{x} (t) $ then the integral $ \int $ with respect to time ($ dt $) is $ \int \dot{x}(t) dt $ and is equal to the distance as a function of time $ \int \dot{x}(t) dt = x(t) $

Some calculus notation is $ \dot{} $ is the time derivative $ \frac{d}{dt} $ and came from Newton hence Newton notation. Usually the $ dt $ or $ dx$ is just telling you the variable you’re taking the derivative or integral of is. $ \prime $ notation is the derivative $ \frac{d}{dx} $ which is not specific to time and is called Leibniz notation. An integral takes the form $ \int $ for finding the total area under a function or $ \int_a^b $ for finding the area under the graph between two points for a function. There is also a concept known as a partial derivative $ \frac{\partial}{\partial x} $ and is only there for functions dependent on more than one thing, e.g. $ f=f[x,y(x),z(x)] $ or $ f=f(t, x, \dot{x}) = f[t, x(t), \dot{x} (t)] $ in the case of my calculus of variations post. It takes the derivative with respect to a single variable and completely ignores any other variable

A function is differentiable if its derivative is defined at every point This is just a property of some functions and those functions are defined as differentiable. Another way to think about this is if you draw out or graph a function can you draw a straight tangential line at every point on the function?

These next two aren’t calculus but are important concepts when doing university math and above

Distribution or distributing is the ability to apply one thing to everything it is being applied to Trying to use a different word to describe this but mathematically it’s the same thing as $ 2 \cdot(3+4) = 2\cdot3 + 2\cdot 4 $. This applies to calculus just like it does to multiplication

Commutation or commuting is the ability to change the order of things Mathemtically $ 1+2 = 2+1 $. This also applies to calculus

Extremizing or maximizing/minimizing is the way to make a function exhibit its maximum or minimum value. Like how you throw a ball up into the air and you see it only went so high. Taking the extrema of the path that ball travels (displacement) is the peak height it reached. It can also mean making something take the shortest possible path

The derivative of a function when set to zero maximizes/minimizes the function The explanation for when the derivative is zero finding the extrema (maximum/minimum points) of a function is if you look at where a function on a graph has its highest and lowest points and draw a tangent line it will be a horizontal line which is where the derivative is zero (horizontal line has a “slope” of 0). In relation to the picture if you take a parabola of the form $ f(x) = ax^2 + bx +c $ then its maximum or minimum (hence extrema) can be found by taking the first derivative and setting it equal to zero (where the tangent line is horizontal). It should be mentioned that $ a$, $b$, and $c$ are constants

$ \frac{d}{dx} f(x) = \frac{d}{dx} ( ax^2 + bx +c ) $

Distributing as I mentioned above

$ \frac{d}{dx} f(x) = \frac{d}{dx} ax^2 + \frac{d}{dx} bx + \frac{d}{dx} +c $

By the power rule (below) and the next point

$ \frac{d}{dx} f(x) = 2ax + b + 0$

$ \frac{d}{dx} f(x) = 2ax + b $

Which is a straight line. You can find the maximum or minimum extremely easy by doing this and if you remember high school math it was relatively extremely painful to find it. This way you just set $ f’(x) = 0 $ and see that $ x = - \frac{b}{2a} $. This is actually the first term in the quadratic formula

$ x = \frac{ -b \pm \sqrt{b^2-4ac}}{2a} = \frac{-b}{2a} \pm \frac{ \sqrt{b^2-4ac}}{2a} $

So the way you find the roots from the quadratic formula is by looking at the extremum then adding or subtracting a certain value depending on the constants to land on the x axis. There is only one extrema because a parabola is a polynomial that only goes up to $ ax^2 $ and its derivative is is a straight line with only one value when its derivative is zero

Taking the derivative of something independent of what you’re taking the derivative with respect to is always zero. A constant is an example of this The explanation for the derivative of something independent is the fact that derivatives measure the rate of change of a variable and if what you’re differentiating doesn’t have that variable it can’t possibly be changing with respect to that variable.

Zero times anything is still zero by definition

The derivative

$ \frac{d}{dx} x= \frac{\partial}{\partial x} x = 1 $

The explanation for the derivative of a single variable $ x $ or $ x^2 $ is called the power rule which is described by

$\frac{d}{d x} x^n=n x^{n-1} $

When $ n =1 $ it simplifies to $ \frac{d}{dx} x= \frac{\partial}{\partial x} x = 1 $

The fundamental theorem of calculus says that taking the integral of a function with the function being the derivative to what you’re taking the integral to equates to the function itself. Mathematically,

$ \int \frac{d}{dx} f(x) dx = f(x) $

$ \int f’(x) dx = f(x) $ Leibniz notation

$ \int \dot{x}(t) dt = x(t) $ Newton notation

So if you take the derivative of displacement with respect to time you get velocity. If you take the integral of velocity with respect to time then you get dispalcement

Other math you might not understand is just notation and operation. For instance

$ \big[ x \big]_{a}^{b} $ is saying evaluate $ x$ at $x=a $ and $ x=b $ which takes the form

$ \big[ x \big]_{a}^{b} = \Big[b-a \Big] $

In integral notation you integrate from point $ a $ to point $b$ as per $ \int_a^b $

If you understood at least parts of this post you can nonironically say you understand very important theories in calculus. Sure you might not understand the math but the big take away from calculus classes is what taking the derivative and integral actually means. Do you think math is more fun now that it’s about the concepts instead of symbols? Maybe

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kristablogs · 4 years

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Goats get us. Or at least, our hand gestures.

These goats seem to be happy together (Christian Nawroth/)

It was like greeting an old friend. Each morning, without fail, Nadia, a snowy white goat with pink transparent ears, would heartily greet Christian Nawroth when he entered the goat pen. Even if Nawroth had an appointment with another goat, Nadia always made her presence known. “I’d say, ‘Hi, Nadia, how are you doing?’ and we’d cuddle a bit,” says Nawroth.

Nadia is one of 141 goats residing at Buttercups Sanctuary for Goats, located in Kent, England. From 2015 through 2016, they were mildly interested participants in Christian Nawroth’s studies of goat and human communication, motivated mostly by the possibility of pasta and cuddles from researchers. The study, recently published in Frontiers of Psychology on May 19, 2020, aims to shed light on animal cognition tests typically administered on dogs, cats, and apes, and bring them to livestock animals—in particular, the goat, which has been Nawroth’s focus for the past five years. Together with Alan McElligott, an animal behavior researcher at the University of Roehampton in the UK, Nawroth wants to redefine how we interact with farm animals, especially when it comes to factory farms, where the majority of the world’s 450 million goats are kept.

Each morning, Nawroth and his two assistants carried two buckets, one filled with pasta, the other empty, to the goat pen. They’d rendezvous with one goat at a time in a walled area with video cameras, and stretch the capacity of goats to understand human gestures.

First, goats had to pass a pre-test before they could participate in the study. Some of them lacked motivation, or were unable to choose the right bucket, and those animals wouldn’t be suited to being subjects in a cognition test. With a pool of twenty selected goats—including Annie, Dingle, Gilbert, Pooky, Vern, Jimmy, Leo, Ralph, and Sticky—Nawroth and his team conducted a series of tests.

Either Nawroth or one of assistants would sit on a chair between the two buckets, and point toward the bucket filled with pasta with the arm closest to it, and record whether the goat would approach the correct bucket within sixty seconds. In the second test, the experimenter pointed with the arm farther away from the pasta bucket. In the last round, the experimenter sat closer to the empty bucket and pointed toward the filled bucket. Nawroth not only wanted to test goats on their ability to understand human pointing gestures, but also if they had a strong sense of referentiality, meaning the ability to extend the pointing finger over an increased distance toward the desired object—in this case, a bucket full of delicious ready-to-eat pasta.

As mentioned in the study, dogs are superstars when it comes to understanding human gestures, including pointing. Using this study, Nawroth hoped to dig deeper into the mechanisms behind which goats, an extremely understudied species, may respond to those same gestures. After a year of data collection, Nawroth and his team discovered that goats succeeded in seeking out the right bucket when the experimenter sat exactly in between the buckets. However, they didn’t do quite as well when the experimenter sat further away from the reward bucket. Nawroth found that goats understand us more than we originally thought.

These tests, however, did not always go as planned. While Nawroth tried to make his research pen “goat-proof,” the goats managed to surprise him. They nibbled on camera cables, even knocked over and smashed some video cameras in their excitement to reach the pasta. Some of the taller goats preferred ‘salad’ over pasta. Trees lined the walled pen, and the dangling leaves were too tempting. “Some of them managed to smash the walls of the test arena,” says Nawroth, by jumping on top of the walls to reach the leaves. “Although there is pasta, they go for the leaves above my head.”

Nawroth educating a goat (Christian Nawroth/)

Born in Germany, Nawroth began his career as a biologist researching invertebrates, mostly ants. After receiving his Masters in Biology at the University of Wuerzburg, where he studied great apes, he took a PhD position at the University of Halle-Wittenberg in Agricultural Sciences, which is where he first began livestock research in 2010 on pigs. When he encountered goats for the first time, he knew he was there to stay. Nawroth’s bearded face over our Zoom call brightens when I ask him whether he’d consider returning to the study of great apes. He shakes his head. “My fate has been written out,” he says.

But why goats? According to Nawroth, they’re more curious and less fearful than pigs. They don’t flock as much as sheep, and are more confident when isolated with humans. Nawroth is devoted to the study of livestock animals—cattle, pigs, chickens, goats, and sheep—because he believes they don't receive the attention they deserve when it comes to scientific research. “We usually attribute farm animals with lesser intellectual capacities than we do for companion animals like dogs and cats,” says Nawroth. “Some use derogative terms, like stupid goat or filthy pig.” The lack of exposure to these animals can exacerbate our antipathy. While 78 million dogs live in American homes, livestock animals aren’t an integral part of most people’s lives—they often spend their entire life on a factory farm.

Even subtle differences like eye positioning make our hearts melt more for dogs than goats. Dogs are predators—they’re designed to track prey with forward-facing, sharply focused eyes, and they frequently make eye contact with other dogs to coordinate hunting. Livestock are traditionally prey, so their eyes are positioned on either side of the head in a unilateral position, which gives goats a 300-degree view to watch out for predators, according to Nawroth. This makes it difficult for a goat to appear like they’re looking straight into your eyes, unlike a dog or cat.

Nawroth hopes to bridge the distance between humans and goats by increasing our understanding of how their minds work. “Given the fact that we house billions of them in industrial settings that aren’t suitable to keep them in a happy state, it’s important to have a diverse set of approaches to improve their wellbeing,” says Nawroth.

Samantha Pachirat works as the Director of Education and Strategic Initiatives at Farm Sanctuary, a nonprofit organization that advocates for the welfare of livestock animals, including goats. At the nonprofit’s two sanctuaries, which house eighty-one rescued goats, the animals live as part of a herd and frolic on a specially built playground and jungle gym. “We have the chance to get to know them as individuals,” says Pachirat.

Goats and humans can also form lasting relationships, just like Nadia and Nawroth. Fifteen years ago, Pachirat says an intern named Dan D’Eramo joined the sanctuary and started a long-standing bond with Simon, an infant goat who had recently fallen sick. To Simon’s dismay, he had to be isolated in a veterinary hospital for several days. Simon cried every night. D’Eramo moved into the hospital room and stayed with Simon for several nights until the little goat was well enough to return to the herd. Simon never forgot. For the next fifteen years, they remained close friends. Whenever D’Eramo came back for a visit, Simon followed him everywhere around the sanctuary. “Simon made many goat friends, but he never forgot Dan,” says Pachirat.

One of the goats in the study (Christian Nawroth/)

The organization, based in upstate New York and southern California, works a three-pronged approach to improving the lives of farm animals throughout the United States, from saving abused livestock animals and keeping them in sanctuary, to educating students and launching advocacy campaigns, including lawsuits against corporations and the United States Department of Agriculture.

1.5 million goats are slaughtered for meat in the United States each year, often on high speed slaughter lines. Most goats are killed at only three to five months old, just a fraction of their natural lifespan, which is between fifteen and eighteen years, according to Farm Sanctuary. Goats kept for dairy are kept continually impregnated through artificial insemination so that they continue producing milk. Male kids, seen as useless in the dairy industry, are often killed immediately after birth. “Their lives are just dollar signs to the industry,” says Pachirat. “It’s dispensable life.”

This is where science steps in. Farm Sanctuary provides financial support for scientific research, including Christian Nawroth’s. “Science is telling us what we see living out on a daily basis,” says Pachirat. “It’s powerful. Science is a powerful tool for helping to elevate our understanding and appreciation for these animals.”

“Understanding how they perceive the environment will help us better understand how to design these environments,” says Nawroth. With the onset of COVID-19, Pachirat hopes that a deeper, intimate understanding of livestock animals, including goats, will force the country to reckon with its meat industry. To recognize the “scale and how gruesome some of the methods are” is the first step, she says. “We are working to raise awareness about it. It’s really a symptom of everything that’s wrong.” Pachirat works within the classroom (although now remotely) to educate grade school students on the lives of farm animals. This coming Tuesday, she will teach kindergarten through fifth grade class all about goats via video call.

In the next few months, Nawroth, now stationed at the Leibniz Institute for Farm Animal Biology, in Dummerstorf, Germany, wants to probe even further into the mind of the goat. Do they know what gravity means? Do they have expectations when it comes to objects falling? Do they know that objects that vanish out of sight, perhaps behind a closed door, might still exist? While research lingers at a stand-still due to the pandemic, Nawroth continues to plan for the day he can reenter the goat pen.

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scootoaster · 4 years

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Goats get us. Or at least, our hand gestures.

These goats seem to be happy together (Christian Nawroth/)

Nadia is one of 141 goats residing at Buttercups Sanctuary for Goats, located in Kent, England. From 2015 through 2016, they were mildly interested participants in Christian Nawroth’s studies of goat and human communication, motivated mostly by the possibility of pasta and cuddles from researchers. The study, recently published in Frontiers of Psychology on May 19, 2020, aims to shed light on animal cognition tests typically administered on dogs, cats, and apes, and bring them to livestock animals—in particular, the goat, which has been Nawroth’s focus for the past five years. Nawroth’s goal is to redefine how we interact with farm animals, especially when it comes to factory farms, where the majority of the world’s 450 million goats are kept.

Nawroth educating a goat (Christian Nawroth/)

Samantha Pachirat works as the Director of Education and Strategic Initiatives at The Farm Sanctuary, a nonprofit organization that advocates for the welfare of livestock animals, including goats. At the nonprofit’s two sanctuaries, which house eighty-one rescued goats, the animals live as part of a herd and frolic on a specially built playground and jungle gym. “We have the chance to get to know them as individuals,” says Pachirat.

One of the goats in the study (Christian Nawroth/)

1.5 million goats are slaughtered for meat in the United States each year, often on high speed slaughter lines. Most goats are killed at only three to five months old, just a fraction of their natural lifespan, which is between fifteen and eighteen years, according to the Farm Sanctuary. Goats kept for dairy are kept continually impregnated through artificial insemination so that they continue producing milk. Male kids, seen as useless in the dairy industry, are often killed immediately after birth. “Their lives are just dollar signs to the industry,” says Pachirat. “It’s dispensable life.”

This is where science steps in. The Farm Sanctuary provides financial support for scientific research, including Christian Nawroth’s. “Science is telling us what we see living out on a daily basis,” says Pachirat. “It’s powerful. Science is a powerful tool for helping to elevate our understanding and appreciation for these animals.”

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ds4design · 8 years

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Polymath Stephen Wolfram Defends His Computational Theory of Everything

Stephen Wolfram seems to see himself as Newton upgraded with programming chops and business savvy, but it’s not hubris if you back it up. As he points out on his website, he published papers on particle physics in his mid-teens, earned a Ph.D. in physics from Caltech when he was 20 and won a MacArthur “genius” grant at 22. In his late 20s he invented and began successfully marketing Mathematica, software for automating calculations. Wolfram contends that Wolfram Language—which underpins Mathematica and Wolfram|Alpha, a knowledge engine he released in 2009—represents a “new paradigm for computation” that will enable humans and machines to “interact at a vastly richer and higher level than ever before.” This vision dovetails with the theme of Wolfram’s 2002 opus A New Kind of Science, which argues that simple computer programs, like those that generate cellular automata, can model the world more effectively than traditional mathematical methods. Physicist Steven Weinberg called the book an interesting “failure,” and other scientists griped that Wolfram had rediscovered old ideas. Critics have also accused Wolfram of hyping his computational products.* Yet Wolfram, when I saw him speak last fall at “Ethics of Artificial Intelligence,” exuded confidence, suggesting how Wolfram Language might transform law and politics. We recently had the following email exchange.–-John Horgan

Horgan: Can you summarize, briefly, the theme of A New Kind of Science? Are you satisfied with the book’s reception?

Wolfram: It’s about studying the computational universe of all possible programs and understanding what they can do. Exact science had been very focused on using what are essentially specific kinds of programs based on mathematical ideas like calculus. My goal was to dramatically generalize the kinds of programs that can be used as models in science, or as foundations for technology and so on.

The big surprise, I suppose, is that when one just goes out into the computational universe without any constraints, one finds that even incredibly simple programs can do extremely rich and complex things. And a lot of the book is about understanding the implications of this for science.

I’ve been very happy with the number and diversity of people who I know have read the book. There’ve been thousands of academic papers written on the basis of it, and there’s an increasing amount of technology that’s based on it. It’s quite amazing to see how the idea of using programs as models in science has caught on. Mathematical models dominated for three centuries, and in a very short time, program-based models seem to have become the overwhelming favorites for new models.

When the book came out, there was some fascinating sociology around it. People in fields where change was “in the air” seemed generally very positive, but a number of people in fields that were then more static seemed to view it as a threatening paradigm shift. Fifteen years later that shift is well on its way, and the objections originally raised are beginning to seem bizarre. It’s a pity social media weren’t better developed in 2002, or things might have moved a little faster.

Horgan: Can the methods you describe in A New Kind of Science answer the question of why there is something rather than nothing?

Wolfram: Not that I can see so far.

Horgan: Can they solve "the hard problem"? That is, can they explain how matter can become conscious?

Wolfram: One of the core discoveries that I discussed in the book is what I call the Principle of Computational Equivalence—which implies that a very wide range of systems are equivalent in their computational sophistication. And in particular, it means that brains are no more computationally sophisticated than lots of systems in nature, and even than systems with very simple rules. It means that “the weather has a mind of its own” isn’t such a primitive thing to say: the fluid dynamics of the weather is just as sophisticated as something like a brain.

There’s lots of detailed history that makes our brains and their memories the way they are. But there’s no bright line that separates what they’re doing from the “merely computational.” There are many philosophical implications to this. But there are also practical ones. And in fact this is what led me to think something like Wolfram|Alpha would be possible.

Horgan: The concept of computation, like information, presupposes the existence of mind. So when you suggest that the universe is a computer, aren't you guilty of anthropomorphism, or perhaps deism (assuming the mind for whom the computation is performed is God)?

Wolfram: The concept of computation doesn’t in any way presuppose the existence of mind... and it’s an incorrect summarization of my work to say that I suggest “the universe is a computer.”

Computation is just about following definite rules. The concept of computation doesn’t presuppose a “substrate,” any more than talking about mathematical laws for nature presupposes a substrate. When we say that the orbit of the Earth is determined by a differential equation, we’re just saying that the equation describes what the Earth does; we’re not suggesting that there are little machines inside the Earth solving the equation.

About the universe: yes, I have been investigating the hypothesis that the universe follows simple rules that can be described by a program. But this is just intended to be a description of what the universe does; there’s no “mechanism” involved. Of course, we don’t know if this is a correct description of the universe. But I consider it the simplest hypothesis, and I hope to either confirm or exclude it one day.

Horgan: What's the ultimate purpose of the Wolfram Language? Can it fulfill Leibniz's dream of a language that can help us resolve all questions, moral as well as scientific? Can it provide a means of unambiguous communication between all intelligent entities, whether biological or artificial?

Wolfram: My goal with the Wolfram Language is to have a language in which computations can conveniently be expressed for both humans and machines—and in which we’ve integrated as much knowledge about computation and about the world as possible. In a way, the Wolfram Language is aimed at finally achieving some of the goals Leibniz had 300 years ago. We now know—as a result of Gödel’s theorem, computational irreducibility, etc.—that there are limits to the scientific questions that can be resolved. And as far as moral questions are concerned: well, the Wolfram Language is going in the direction of at least being able to express things like moral principles, but it can’t invent those; they have to come from humans and human society.

Horgan: Are autonomous machines, capable of choosing their own goals, inevitable? Is there anything we humans do that cannot—or should not—be automated?

Wolfram: When we see a rock fall, we could say either that it’s following a law of motion that makes it fall, or that it’s achieving the “goal” of being in a lower-potential-energy state. When machines—or for that matter, brains—operate, we can describe them either as just following their rules, or as “achieving certain goals.” And sometimes the rules will be complicated to state, but the goals are simpler, so we’ll emphasize the description in terms of goals.

What is inevitable about future machines is that they'll operate in ways we can't immediately foresee. In fact, that happens all the time already; it's what bugs in programs are all about. Will we choose to describe their behavior in terms of goals? Maybe sometimes. Not least because it'll give us a human-like context for understanding what they're doing.

The main thing we humans do that can't meaningfully be automated is to decide what we ultimately want to do.

Horgan: What is the most meaningful goal that any intelligence, human or inhuman, can pursue?

Wolfram: The notion of a “meaningful goal” is something that relies on a whole cultural context—so there can’t be a useful abstract answer to this question.

Horgan: Have you ever suspected that God exists, or that we live in a simulation?

Wolfram: If by “God” you just mean something beyond science: well, there’s always going to be something beyond science until we have a complete theory of the universe, and even then, we may well still be asking, “Why this universe, and not another?”

What would it mean for us to “live in a simulation”? Maybe that down at the Planck scale we’d find a whole civilization that’s setting things up so our universe works the way it does. Well, the Principle of Computational Equivalence says that the processes that go on at the Planck scale—even if they’re just “physics” ones—are going to be computationally equivalent to lots of other ones, including ones in a “civilization.” So for basically the same reason that it makes sense to say “the weather has a mind of its own,” it doesn’t make any sense to imagine our universe as a “simulation.”

Horgan: What's your utopia?

Wolfram: If you mean: what do I personally want to do all day? Well, I’ve been fortunate that I’ve been able to set up my life to let me spend a large fraction of my time doing what I want to be doing, which usually means creating things and figuring things out. I like building large, elegant, useful, intellectual and practical structures---which is what I hope I’ve done over a long period of time, for example, with Wolfram Language.

If you’re asking what I see as being the best ultimate outcome for our whole species---well, that’s a much more difficult question, though I’ve certainly thought about it. Yes, there are things we want now---but how what we want will evolve after we’ve got those things is, I think, almost impossible for us to understand. Look at what people see as goals today, and think how difficult it would be to explain many of them to someone even a few centuries ago. Human goals will certainly evolve, and the things people will think are the best possible things to do in the future may well be things we don’t even have words for yet.