[LINK] Numbers limit how accurately digital computers model chaos
Numbers limit how accurately digital computers model chaos SEPTEMBER 23, 2019 https://phys.org/partners/university-college-london A study published today in Advanced Theory and Simulations, shows that digital computers can not reliably reproduce the behaviour of 'chaotic systems' which are widespread. Professor Peter Coveney, Director of the UCL Centre for Computational Science and study co-author, said: "Our work shows that the behaviour of the chaotic dynamical systems is richer than any digital computer can capture." “Chaos is more commonplace than many people may realise and even for very simple chaotic systems, numbers used by digital computers can lead to errors that are not obvious but can have a big impact. Ultimately, computers can't simulate everything." The team investigated the impact of using floating-point arithmetic—a method standardised by the IEEE and used since the 1950s to approximate real numbers on digital computers. Digital computers use only rational numbers, ones that can be expressed as fractions. Moreover the denominator of these fractions must be a power of two, such as 2, 4, 8, 16, etc. There are infinitely more real numbers that cannot be expressed this way. In the present work, the scientists used all four billion of these single-precision floating-point numbers that range from plus to minus infinity. The fact that the numbers are not distributed uniformly may also contribute to some of the inaccuracies. First author, Professor Bruce Boghosian (Tufts University), said: "The four billion single-precision floating-point numbers that digital computers use are spread unevenly, so there are as many such numbers between 0.125 and 0.25, as there are between 0.25 and 0.5, as there are between 0.5 and 1.0. It is amazing that they are able to simulate real-world chaotic events as well as they do. But even so, we are now aware that this simplification does not accurately represent the complexity of chaotic dynamical systems, and this is a problem for such simulations on all current and future digital computers." The study builds on the work of Edward Lorenz of MIT whose weather simulations using a simple computer model in the 1960s showed that tiny rounding errors in the numbers fed into his computer led to quite different forecasts, which is now known as the 'butterfly effect'. The team compared the known mathematical reality of a simple one-parameter chaotic system called the 'generalised Bernoulli map' to what digital computers would predict if every one of the available single-precision floating-point numbers were used. They found that, for some values of the parameter, the computer predictions are totally wrong, whilst for other choices the calculations may appear correct, but deviate by up to 15%. The authors say these pathological results would persist even if double-precision floating-point numbers were used, of which there are vastly more to draw on. "We use the generalised Bernoulli map as a mathematical representation for many other systems that change chaotically over time, such as those seen across physics, biology and chemistry," explained Professor Coveney. "These are being used to predict important scenarios in climate change, in chemical reactions and in nuclear reactors, for example, so it's imperative that computer-based simulations are now carefully scrutinised." The team say that their discovery has implications for the field of artificial intelligence, when machine learning is applied to data derived from computer simulations of chaotic dynamical systems, and for those trying to model all kinds of natural processes. More research is needed to examine the extent to which the use of floating-point arithmetic is causing problems in everyday computational science and modelling and, if errors are found, how to correct them. Professor Bruce Boghosian and Dr. Hongyan Wang are at Tufts University, Medford, Massachusetts, United States (Dr. Wang now works at Facebook in Seattle). Professor Peter Coveney of UCL is speaking at an event tomorrow in the Science Museum on the future of quantum computing. ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On 24/09/2019 5:10 pm, Stephen Loosley wrote: > Numbers limit how accurately digital computers model chaos > Gee, do these people not know how to research their subject. Michael V Berry wrote about this subject in 1978 and was quoted by Nassim Taleb in the Black Swan. "On a billiard table, if you know a set of basic parameters concerning the ball at rest, can compute the resistance of the table (quite elementary), and can gauge the strength of the impact, then it is rather easy to predict what would happen at the first hit. The second impact becomes more complicated, but possible; and more precision is called for. The problem is that to correctly compute the ninth impact, you need to take account the gravitational pull of someone standing next to the table (modestly, Berry's computations use a weight of less than 150 pounds). And to compute the fifty-sixth impact, every single elementary particle in the universe needs to be present in your assumptions! An electron at the edge of the universe, separated from us by 10 billion light-years, must figure in the calculations, since it exerts a meaningful effect on the outcome. (p. 178)" The cause is non-linearity not chaos. Chaos is the result. The problem is not just the accuracy of the numbers used to represent real values, but any source of error, perturbation or simplification. -- Regards brd Bernard Robertson-Dunn Canberra Australia email: b...@iimetro.com.au ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
https://en.wikipedia.org/wiki/Butterfly_effect "In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.[1]" Jevan. On Tue, 24 Sep 2019 07:10:16 + Stephen Loosley wrote: > The study builds on the work of Edward Lorenz of MIT whose weather > simulations using a simple computer model in the 1960s showed that tiny > rounding errors in the numbers fed into his computer led to quite different > forecasts, which is now known as the 'butterfly effect'. -- Volunteer Work Only (but you can make money) MIT SE (UC), GradDip IT (UC), BSc (ANU), GradCert Rsch Methods & Des (UC) I am here for online friends, hobbies, volunteer or paid work, working on business ideas, preferably a friend, activity partner, staff or freelancer/contractor at the same place or website where I work or on my team of paid staff, or my manager, who is an adult female age 18+ who has any disability (physical or mental). I am age 47 male and receive Centrelink Disability Support Pension due to my schizophrenia and aspergers. I am also interested in paid work however I am not usually successful to obtain that. I work from home wherever possible, otherwise I am able to come into the workplace anytime I choose during your working hours without any notice/appointment. Me: Computing Researcher, Self Employed, Innovation, Management, Canberra Australia. Interests: Especially things involving the use of a computer. Creating, Doing, Improvising, Analysing for Improvement: Computer Programming Open Source including C#/VB.NET, CSS, HTML, Javascript, MS Visual Studio, My/MS Sql, PHP, Wi! nForms, W PF. My interests are making, collaborating, and managing people to make: 3d animation, Acting Improvisations, Audio Podcasts, Business & Startups, Chat, Collaborations, Creative Writing & Poetry, Creativity, Dancing, Debating, Decisions, Digital Art, Discussion of Topics, Electronic Music Composition/Creation (FL Studio), Engineering, Entrepreneurs, Friends, Graphic Design, Ideas, Information Analysis, Innovation, IT Tuition, Jazz Piano, Jazz Singing Male Baritone & Choir & Karaoke, Leadership, Management, Mathematics, Meetings, PC Support, Phone Talk (if done from my home), Photography, Physics, Public Speaking, Reading online science magazines and emails, Research, Science, Web Design, YouTube Videos. Friendship with adults via phone, Email, Online Chat, anything we can make and send each other and collaborate on. Note: For our interactions, collaborations, hobbies, volunteer work, etc to turn out successful, it may be necessary for there to be a financial cost to me in o! rder for you or your organization to make it work, so let me know what you suggest. Web: http://www.jevan.com.au/ Tel: (02) 6152 8010 (or +61 2 6152 8010) LinkedIn: http://www.linkedin.com/in/jevanpipitone Facebook: http://www.facebook.com/jevanpipitone GitHub: http://www.github.com/jevanpipitone Twitter: http://www.twitter.com/jevanpipitone Photo of Jevan Pipitone: http://www.jevan.com.au/images/JevanPipitoneWebcamImage-ForEmailSignature-Latest.jpg Canberra, Australia ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
[LINK] Names to Fly on NASA's Next Mars Rover
Here’s a bit of fun .. https://www.nasa.gov/feature/jpl/deadline-closing-for-names-to-fly-on-nasas-next-mars-rover It's the final boarding call for you to stow your name on NASA's Mars 2020 rover before it launches to the Red Planet. The Sept. 30 deadline for NASA's "Send Your Name to Mars" campaign gives the mission enough time to stencil the submitted names — over 9.4 million so far — on a chip that will be affixed to the Mars 2020 rover. This rover is scheduled to launch as early as July 2020 and expected to touch down on Mars in February 2021. The Mars 2020 rover represents the initial leg of humanity's first planned round trip to another planet. With this robotic scientist weighing 2,300 pounds (1,040 kilograms), the Mars 2020 mission will search for signs of past microbial life, characterize the planet's climate and geology, collect samples for future return to Earth, and pave the way for human exploration of the Red Planet. "As we get ready to launch this historic Mars mission, we want everyone to share in this journey of exploration," said Thomas Zurbuchen, associate administrator for NASA's Science Mission Directorate in Washington. "It's an exciting time for NASA as we embark on this voyage to answer profound questions about our neighboring planet, and even the origins of life itself." The opportunity to send your name to Mars, which opened on May 21, 2019, comes with a souvenir boarding pass and "frequent flyer" points. This is part of a public engagement campaign to highlight missions involved with NASA's journey from the Moon to Mars. Miles (or kilometers) are awarded for each "flight," with corresponding digital mission patches available for download. More than 2 million names flew on NASA's InSight mission to Mars, giving each "flyer" about 300 million frequent flyer miles (nearly 500 million frequent flyer kilometers). You can add your name to the list and obtain a souvenir boarding pass to Mars here: https://go.nasa.gov/Mars2020Pass The Microdevices Laboratory at JPL will use an electron beam to stencil the submitted names onto a silicon chip with lines of text smaller than one-thousandth the width of a human hair (75 nanometers). At that size, millions of names can be written on a single dime-size chip. The chip will ride on the rover under a glass cover. NASA will use Mars 2020 and other missions, including to the Moon, to prepare for human exploration of the Red Planet. Charged with returning astronauts to the Moon by 2024, the agency intends to establish a sustained human presence on and around the Moon by 2028 through NASA's Artemis lunar exploration plans. The Mars 2020 Project at JPL manages rover development for SMD. NASA's Launch Services Program, based at the agency's Kennedy Space Center in Florida, is responsible for launch management. Mars 2020 will launch from Cape Canaveral Air Force Station in Florida. ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On 25/09/2019 1:16 am, Jevan Pipitone wrote: > https://en.wikipedia.org/wiki/Butterfly_effect > > "In chaos theory, the butterfly effect is the sensitive dependence on initial > conditions in which a small change in one state of a deterministic nonlinear > system can result in large differences in a later state.[1]" Which is a bit of a simplification. When you use numerical methods to solve dynamic non-linear system equations, every iteration has initial conditions. This means that reducing the iteration time actually increases the potential for error. Scientists and engineers hate non-linearity. Unfortunately the world is essentially non-linear. > Jevan. > > > On Tue, 24 Sep 2019 07:10:16 + > Stephen Loosley wrote: > >> The study builds on the work of Edward Lorenz of MIT whose weather >> simulations using a simple computer model in the 1960s showed that tiny >> rounding errors in the numbers fed into his computer led to quite different >> forecasts, which is now known as the 'butterfly effect'. -- Regards brd Bernard Robertson-Dunn Canberra Australia email: b...@iimetro.com.au ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On 25/9/19 9:29 am, Bernard Robertson-Dunn wrote: Scientists and engineers hate non-linearity. Unfortunately the world is essentially non-linear. A quibble about language. (I'm enjoying the conversation). All mathematics involves intellectual models / mind-stuff. Mathematics is not, and not of, the real world. Statements like "the world is essentially non-linear" blend words that apply in the two distinct spaces of the mind and the real-world. Some scientists and engineers 'know all that'. But the media, and the public, are very prone to confusion, because they've never heard Einstein's dictum 'God doesn't play dice with the world'. Worse still, many scientists and engineers fall into the habit of loose language, and trap their own thinking into the assumption that model = system. Here's an (inevitably flawed) attempt to avoid loose language: Various kinds of mathematical models can be used to represent various real-world systems, and can achieve varying levels of approximations of real-world behaviour and outcomes. We (all) believe that a wide array of physical phenomena are being approximated with workable error-factors (e.g. tides, and met forecasts in relatively stable conditions). In some circumstances, physical phenomena are being approximated with incredibly small error-factors (e.g. solar system mechanics, as indicated by moon and Mars landings). Models of real-world systems of large scale (many entities) and high complexity (many inter-relationships among many entities) have notoriously large error-factors, and have error-factors that vary enormously depending on the circumstances and that defy attempts at prediction. A new round of AI enthusiasm is prancing its nonsense around the world. And this one has associated with it a wave of artefact-autonomy. Unless we use our language very carefully, we're inviting: (a) simplistic scientists and engineers, and feeble-minded marketers, to over-believe and over-sell, and deliver horrible outcomes (of which Robodebt is merely a harbinger) (b) the media and the public will put up with the nonsense for a period of time, but public backlash will in due course wash away the hubris, and with it not just the badly-conceived and harmful models and artefacts, but also some that are of value to humankind -- Roger Clarkemailto:roger.cla...@xamax.com.au T: +61 2 6288 6916 http://www.xamax.com.au http://www.rogerclarke.com Xamax Consultancy Pty Ltd 78 Sidaway St, Chapman ACT 2611 AUSTRALIA Visiting Professor in the Faculty of LawUniversity of N.S.W. Visiting Professor in Computer ScienceAustralian National University ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On Wed, 2019-09-25 at 10:35 +1000, Roger Clarke wrote: > But the media, and the public, are very prone to confusion, because > they've never heard Einstein's dictum 'God doesn't play dice with > the world'. Einstein was apparently wrong with is "Der Herrgot wuerfelt nicht". As Bohr said in response "Der Herrgott tut nichts ausser wuerfeln" - "God does nothing BUT play dice". Regards, K. -- ~~~ Karl Auer (ka...@biplane.com.au) http://www.biplane.com.au/kauer http://twitter.com/kauer389 GPG fingerprint: 8D08 9CAA 649A AFEF E862 062A 2E97 42D4 A2A0 616D Old fingerprint: A0CD 28F0 10BE FC21 C57C 67C1 19A6 83A4 9B0B 1D75 ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On 25/09/2019 10:35 am, Roger Clarke wrote: > Models of real-world systems of large scale (many entities) and high > complexity (many inter-relationships among many entities) have > notoriously large error-factors, and have error-factors that vary > enormously depending on the circumstances and that defy attempts at > prediction. Non-linearity rears its ugly head when it comes to predictions. It is a characteristic of non-linear systems that any errors will grow exponentially, the only question is How Quickly? Your reference to moon and Mars landings is a little off target. Engineers did what engineers always do when faced with non-linearity - they wrap the prediction system in a negative feedback loop. By definition a negative feedback loop tries to minimise the error between target state and actual state. If the target state is a moving state, then it's called goal seeking. > > A new round of AI enthusiasm is prancing its nonsense around the > world. And this one has associated with it a wave of artefact-autonomy. > > Unless we use our language very carefully, we're inviting: > (a) simplistic scientists and engineers, and feeble-minded marketers, > to over-believe and over-sell, and deliver horrible outcomes > (of which Robodebt is merely a harbinger) My experience is that "simplistic scientists and engineers, and feeble-minded marketers", get into trouble when they make predictions outside their areas of expertise. Which is why Health IT has been less than successful. Technologists do not understand the problems of healthcare but they insist on implementing their solutions. > > (b) the media and the public will put up with the nonsense for a > period of time, but public backlash will in due course wash away > the hubris, and with it not just the badly-conceived and harmful > models and artefacts, but also some that are of value to humankind Sometimes. This was published today: Why the Myth of Period Syncing Won’t Go Away https://www.theatlantic.com/family/archive/2019/09/period-syncing-almost-definitely-isnt-real/598714/ "For decades, researchers have been poking holes in the study that introduced the concept of “menstrual synchrony.” Many people believe in it anyway." ... "For a phenomenon that’s highly unlikely to be real, period syncing has enjoyed an impressively long life in the popular imagination. Every now and again, news stories and listicles pop up to inform the public that no, actually, period synchronization as a result of prolonged proximity is not a thing, but the fictional story lines and offhand jokes persist nonetheless." How does all this relate to non-linearity? Sometimes you only have to be a little bit wrong to totally stuff things up. -- Regards brd Bernard Robertson-Dunn Canberra Australia email: b...@iimetro.com.au ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On Wednesday, 25 September 2019 10:35:44 AEST Roger Clarke wrote: > All mathematics involves intellectual models / mind-stuff. > Mathematics is not, and not of, the real world. Now that's a very brave assertion IMO. It can also be argued the reason why mathematics allows us to model the real-world so successfully is that it's a generalisation derived from the world we see around us. That's why the number "zero" was late to be recognised, for example. The most beautiful equation of all is perhaps Euler's formula: e^(iϑ) = cosϑ + i sinϑ where 'e' is the base of natural logarithms, 'i' is the square-root of -1, 'ϑ' is any angle, and ^ means to-the-power. If ϑ=pi this reduces to the wondrous equality e^(i pi) = 1 which is a relation between transcendental numbers. But even that doesn't imply that mathematics comes from some spiritual other-world. > But the media, and the public, are very prone to confusion, because they've > never heard Einstein's dictum 'God doesn't play dice with the world'. On Wednesday, 25 September 2019 11:31:38 AEST Karl Auer wrote: > Einstein was apparently wrong with is "Der Herrgot wuerfelt nicht". As Bohr > said in response "Der Herrgott tut nichts ausser wuerfeln" - "God does > nothing BUT play dice". Karl, you beat me to it. However another explanation was recognised very early. It involves a seemingly far-out idea that all possible outcomes occur at any given moment, leading to a spectrum of realities or world-lines, and this results in quantum uncertainty at very small scales. It a form of multiverse. > A new round of AI enthusiasm is prancing its nonsense around the world. And > this one has associated with it a wave of artefact-autonomy. > Unless we use our language very carefully, we're inviting: > (a) simplistic scientists and engineers, and feeble-minded marketers, to > over-believe and over-sell, and deliver horrible outcomes (of which Robodebt > is merely a harbinger) > (b) the media and the public will put up with the nonsense for a period of > time, but public backlash will in due course wash away the hubris, and with > it not just the badly-conceived and harmful models and artefacts, but also > some that are of value to humankind Hear, hear! > And an excellent one too. David L. ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
Re: [LINK] Numbers limit how accurately digital computers model chaos
On 25/09/2019 3:11 pm, David wrote: >> All mathematics involves intellectual models / mind-stuff. >> Mathematics is not, and not of, the real world. > Now that's a very brave assertion IMO. It can also be argued the reason why > mathematics allows us to model the real-world so successfully is that it's a > generalisation derived from the world we see around us. That's why the > number "zero" was late to be recognised, for example. It may be brave, but IMO Roger's assertion is totally justifiable. As you state, mathematics is a language, a model, of the real world. It may exist on its own in the real world (you can get a degree in the subject), but like any other language, its use is as a representation or reality, validated by experiment. And when you put numbers (data) in a model, it can become more than a generalisation, it can become highly specific - Apollo 11 on its journey to the moon and back. -- Regards brd Bernard Robertson-Dunn Canberra Australia email: b...@iimetro.com.au ___ Link mailing list Link@mailman.anu.edu.au http://mailman.anu.edu.au/mailman/listinfo/link
