use German-American tech ambassadors: serial entrepreneurs Petra Vorsteher and Ragnar Kruse receive GABA Award of Excellence By www.prleap.com Published On :: Sun, 02 Jun 2024 20:00:00 PDT Full Article
use Special exhibition "Fairy Tales, Sagas and Symbols" at Liechtenstein NationalMuseum, Vaduz By www.prleap.com Published On :: Tue, 30 Mar 2021 05:00:00 PDT How did the world and life come into being in all its diversity, what is the plan of the supernatural powers that determine destiny, what are the causes of evil, illness and death, and of what extraordinary deeds are there new insights? With its new major exhibition, Liechtenstein NationalMuseum is presenting the topics of fairy tales, myths, legends, fables, and sagas, which form a fundamentally important part of every culture and its collective memory. Full Article
use Hollitzer Publishing House: Oldest Miniature of W.A. Mozart dating from 1766 discovered One of the oldest fan articles in the history of music By www.prleap.com Published On :: Wed, 04 Aug 2021 03:00:00 PDT In 2018, a French round box of candy was discovered in an antique shop in Salzburg. On its lid it portrays a young boy, wearing a wig and a red aristocratic coat. The Belgian Professor Stefaan Missinne spent two years investigating the miniature and the box dating from 1766: Missinne concludes that it is a hitherto unknown French portrait of the 10-year-old Wolfgang Amadeus Mozart. Full Article
use Museums around the world are joining the foundation Ocean us in an unprecedented campaign to fight climate change By www.prleap.com Published On :: Wed, 07 Aug 2024 05:00:00 PDT Under the name "Last Call for Beauty", Ocean us is bleaching famous paintings to raise awareness of the extinction of coral reefs in the world's oceans. Full Article
use Travis Kelce and Patrick Mahomes's houses 'broken into' a day apart By news.sky.com Published On :: Wed, 13 Nov 2024 03:57:00 +0100 The homes of Kansas City Chiefs stars Patrick Mahomes and Travis Kelce were both broken into last month, according to police and media reports. Full Article
use QNX becomes free for non-commercial use, releases Raspberry Pi 4 image By www.osnews.com Published On :: Thu, 07 Nov 2024 21:54:56 +0000 A long, long time ago, back when running BeOS as my main operating system had finally become impossible, I had a short stint running QNX as my one and only operating system. In 2004, before I joined OSNews and became its managing editor, I also wrote and published an article about QNX on OSNews, which is cringe-inducing to read over two decades later (although I was only 20 when I wrote that – I should be kind to my young self). Sadly, the included screenshots have not survived the several transitions OSNews has gone through since 2004. Anyway, back in those days, it was entirely possible to use QNX as a general purpose desktop operating system, mostly because of two things. First, the incredible Photon MicroGUI, an excellent and unique graphical environment that was a joy to use, and two, because of a small but dedicated community of enthousiasts, some of which QNX employees, who ported a ton of open source applications, from basic open source tools to behemoths like Thunderbird, the Mozilla Suite, and Firefox, to QNX. It even came with an easy-to-use package manager and associated GUI to install all of these applications without much hassle. Using QNX like this was a joy. It really felt like a tightly controlled, carefully crafted user experience, despite desktop use being so low on the priority list for the company that it might as well have not been on there at all. Not long after, I think a few of the people inside QNX involved with the QNX desktop community left the company, and the entire thing just fizzled out afterwards when the company was acquired by Harman Kardon. Not long after, it became clear the company lost all interest, a feeling only solidified once Blackberry acquired the company. Somewhere in between the company released some of its code under some not-quite-open-source license, accompanied by a rather lacklustre push to get the community interested again. This, too, fizzled out. Well, it seems the company is trying to reverse course, and has started courting the enthusiast community once again. This time, it’s called QNX Everywhere, and it involves making QNX available for non-commercial use for anyone who wants it. No, it’s not open source, and yes, it requires some hoops to jump through still, but it’s better than nothing. In addition, QNX also put a bunch of open source demos, applications, frameworks, and libraries on GitLab. One of the most welcome new efforts is a bootable QNX image for the Raspberry Pi 4 (and only the 4, sadly, which I don’t own). It comes with a basic set of demo application you can run from the command line, including a graphical web browser, but sadly, it does not seem to come with Photon microGUI or any modern equivalent. I’m guessing Photon hasn’t seen a ton of work since its golden days two decades ago, which might explain why it’s not here. There’s also a list of current open source ports, which includes chunks of toolkits like GTK and Qt, and a whole bunch of other stuff. Honestly, as cool as this is, it seems it’s mostly aimed at embedded developers instead of weird people who want to use QNX as a general purpose operating system, which makes total sense from QNX’ perspective. I hope Photon microGUI will make a return at some point, and it would be awesome – but I expect unlikely – if QNX could be released as open source, so that it would be more likely a community of enthusiasts could spring up around it. For now, without much for a non-developer like me to do with it, it’s not making me run out to buy a Raspberry Pi 4 just yet. Full Article QNX
use 37. Blogger: User Profile: Nathan By www.blogger.com Published On :: Blogger is a free blog publishing tool from Google ... Push-Button Publishing. Nathan. My Blogs. Team Members. Simplyukgadgets. User Stats. On Blogger Since ... Full Article
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use 18. [wxperl-users] Free Casino Slot Mac. - Ford - org.perl.wxperl ... By markmail.org Published On :: 2009-01-26T01:46:28+00:00 Simply Uk Gadgets, siti di Simply Uk Gadgets, informazioni su Simply Uk Gadgets ... Simply UK Gadgets Disclaimer Statement. Eliminate irritating pop-up ... Full Article
use Even Small Business Owners Can Use These Tax Breaks By www.small-business-software.net Published On :: Tue, 1 Jul 2014 09:00:00 -0400 Two recent news clips caught my attention. One involved a company trying to avoid the IRS. The other involved the IRS trying to avoid trouble. Taken together, I can see how a small business owner might cynically ask if a small business has a fighting chance as far as taxes. complete article Full Article
use The Most Obnoxious And Overused Startup Jargon By www.small-business-software.net Published On :: Thu, 30 Apr 2015 09:00:00 -0400 From Silicon Valley to Silicon Alley, mind-numbing startup jargon is stopping for no one. It winds up in TED Talks, pitch meetings and every tech journalist’s inbox in between. complete article Full Article
use 6 Best Tools That Small Business Owners Could Use to Promote Their Business Online By www.small-business-software.net Published On :: Mon, 8 Aug 2016 09:00:00 -0400 Marketing a business online can be a bit tricky with cost being a concern to most business owners. Some have to work with a low budget with most opting to find a free way to market their trade online. There are tons of free tools businesses can turn to when it comes to marketing online. With that in mind, it may all boil down to where to start and which tool is best used first. The tools mentioned range from actual sites to free tools integrated with their marketing plans. Below are some of the tools that companies can consider using. complete article Full Article
use Here is How Businesses Use Technology to Boost Productivity By www.small-business-software.net Published On :: Mon, 30 Jan 2017 09:00:00 -0500 Interconnectivity is at the core of our digital universe, and with tech advancements, staying on top of trends is critical to career success. With 86 percent of U.S. adults1 18-29 owning a smartphone, most students, recent grads and longtime employees are seasoned in adopting new technologies. Preparing for the future of automation and digital security can help jobseekers adapt to the future of tech. As you consider your career goals in todays digital world, there are four things to ask yourself. complete article Full Article
use 3 Ways Entrepreneurs Are Making IoT More User-Friendly By www.small-business-software.net Published On :: Tue, 26 Sep 2017 13:51:54 -0400 The Internet of Things (IoT) is a rapidly evolving technology sector. As the popularity of connected devices increases with consumers, the number of entrants into the market grows. But rapid growth and iteration have had some unintended consequences in the IoT space, especially when it comes to usability. IoT More Friendly Full Article
use 10 Tips for Building a Customer Focused Business By www.small-business-software.net Published On :: Mon, 2 Oct 2017 09:00:00 -0400 For tips on keeping your business customer focused and more, check out this recent content from members of the online small business community. complete article Full Article
use To Be Successful, Stop Making Excuses and Face Your Fears By www.small-business-software.net Published On :: Wed, 17 Jan 2018 16:48:19 -0500 Do you constantly find yourself making excuses? Do you try to ignore the toxic work environment you’re in? Are you in denial about your exercise and health regimen? Whatever it might be, if you want to be successful, you have to identify these things and face challenges head-on. complete article Full Article
use 10 Helpful Insights to Help You Make Use of Video and Better Communicate with Customers By www.small-business-software.net Published On :: Fri, 23 Feb 2018 09:00:08 -0500 Video is a medium that gives your small business lots of different options for communicating and sharing information with customers. But it can be sort of overwhelming for some small businesses. Arielle Kimbarovsky of CrowdSpring offers some suggestions for businesses looking to make the most of video in a recent post. complete article Full Article
use The Seven Factors Lenders Use To Measure Small Business Credit By www.small-business-software.net Published On :: Fri, 30 Mar 2018 09:00:47 -0400 Why does qualifying for a small business loan have to be such a mystery? According to a CB Insights study, cash flow issues are the second most common reason startups fail, accounting for 29% of failures. In many cases, access to capital would make a big difference. Yet the loan application process is notoriously opaque for small business owners. Research from the Federal Reserve Bank of New York shows the average small business owner spent 26 hours searching and applying for credit, contacted three financial institutions and submitted three credit applications. Despite this time-consuming work, only half of small-business applicants end up being approved for the loan amount they applied for. complete article Full Article
use It is Going to Get Easier to Make Money the Next 5 to 10 Years, and It is Because of These 5 Technologies By www.small-business-software.net Published On :: Fri, 20 Apr 2018 09:00:21 -0400 As an entrepreneur and an angel investor, I get really excited about the future of personal finance. As new technologies develop, from cryptocurrencies to virtual wallets, I see advantages for businesses. I also see opportunities for everyday Americans and our families to make--and keep--more of our own money. In meetings with financial technology startups, I am seeing so many incredible new developments on the horizon. Any innovation that improves how we live, shop, and pay sets off alarm bells--of the good kind--in my friendly neighborhood Certified Financial Planner brain. Here is a sneak peek of why I think the next five to 10 years are going to make making money easier for all of us. It is thanks to these five emerging technologies: complete article Full Article
use 5 Highly Effective Negotiation Tactics Anyone Can Use By www.small-business-software.net Published On :: Wed, 16 May 2018 09:08:11 -0400 Want to be a better negotiator? Here are some simple tips. 1. Listen more than you talk. It is easy to go into a negotiation focused only on what you'll say, especially when you are nervous. The goal of a negotiation is not just to get what you want, but also to help the other side get what they want. (Otherwise, how will you ever strike a deal?) To do that, you need to actually know what the other side wants -- which means you have to listen. Finding common ground means knowing common ground exists. complete article Full Article
use How to Create a User-Intent SEO Strategy By www.small-business-software.net Published On :: Fri, 5 Oct 2018 09:26:50 -0400 Behind every Google search, there is an intention. People are looking for something in particular when they are searching the web -- the answers to their problems, information about the services available to them or sources for the product they want. If you want your business to be discovered by users on the web, your content needs to be optimized for user intent. Since Google can recognize user intent, it displays pages in search results that are most relevant to what the user is looking for. Because of this, understanding user intent and creating content with the user's intent in mind is essential to improving the relevance of your website pages and improving SEO. complete article Full Article
use Use This 5-Step Process to Set and Achieve Your Sales Goals By www.small-business-software.net Published On :: Wed, 13 Mar 2019 09:02:35 -0500 Step 1: Set meaningful goals. People do nott achieve goals unless the goals are meaningful to them. Sure, every seller has a quota for this year, but so what? If you want to maximize your motivation to achieve the goals, you must know why achieving it is important to you. To do that, go beyond your one-year quota-focused goal. complete article Full Article
use 59% of Small Businesses Use Video for Advertising, Survey Finds By www.small-business-software.net Published On :: Fri, 7 Jun 2019 12:35:57 -0400 A new report finds that a good number of small businesses (29%) are spending somewhere in the sweet spot of ($750-$2499) monthly to get the data needed for good online advertising results. WordStreams Online Advertising Landscape in 2019 report also found that only 10% of the respondents had a monthly advertising budget less than the low end plateau for effectiveness of $750 monthly. complete article Full Article
use A Harvard Study Found That 27 Top-Performing CEOs Use These 6 Strategies to Manage Their Time By www.small-business-software.net Published On :: Fri, 16 Aug 2019 13:17:40 -0400 Time is said to be spent or invested. But without time management, it can also be squandered. Is your to-do list constantly growing? Do you feel like there are not enough hours in the day to meet your family, work and social obligations? For a business leader, time management is especially problematic given their magnitude of responsibilities and limited hours in the day. Lost time is not only never found again, but not managing it strategically harms the executive's well-being, effectiveness and organizational performance. My team and I had the opportunity to lead coaching sessions for executives of public and private companies worth billions. And one thing is clear-- how you manage your time leads to success or failure. complete article Full Article
use Abdominal Pain Causes By Location By www.medicinenet.com Published On :: Wed, 20 Apr 2022 00:00:00 PDT Title: Abdominal Pain Causes By LocationCategory: Doctor's & Expert's views on SymptomsCreated: 7/12/2013 12:00:00 AMLast Editorial Review: 4/20/2022 12:00:00 AM Full Article
use Federal Court Orders EPA to Re-examine Whether Roundup Causes Cancer By www.medicinenet.com Published On :: Mon, 20 Jun 2022 00:00:00 PDT Title: Federal Court Orders EPA to Re-examine Whether Roundup Causes CancerCategory: Health NewsCreated: 6/20/2022 12:00:00 AMLast Editorial Review: 6/20/2022 12:00:00 AM Full Article
use Psychosis Risk Rises When People Abuse 'Speed' By www.medicinenet.com Published On :: Tue, 15 Feb 2022 00:00:00 PDT Title: Psychosis Risk Rises When People Abuse 'Speed'Category: Health NewsCreated: 2/15/2022 12:00:00 AMLast Editorial Review: 2/15/2022 12:00:00 AM Full Article
use Oral Health: 19 Habits That Cause Bad Teeth By www.medicinenet.com Published On :: Tue, 8 Feb 2022 00:00:00 PDT Title: Oral Health: 19 Habits That Cause Bad TeethCategory: SlideshowsCreated: 1/27/2012 12:00:00 AMLast Editorial Review: 2/8/2022 12:00:00 AM Full Article
use Aromatherapy Diffuser Market Set for Strong Growth: Projected to Reach $3.45 Billion by 2030 By www.emailwire.com Published On :: Fri, 01 Nov 2024 00:00:00 -0700 (EMAILWIRE.COM, November 01, 2024 ) Aromatherapy Diffuser Market was valued at USD 1.87 Bn in 2023 and is expected to reach USD 3.45 Bn by 2030, at a CAGR of 9.17 % during the forecast period Aromatherapy Diffuser Market overview: The aromatherapy diffuser market has witnessed significant growth... Full Article
use ***** Prime Aviation Ltd, Gatwick, Ashdown House (rank 19) By www.gigaalert.com Published On :: Mon, 10 Oct 2016 13:26:39 +0100 Prime Aviation Ltd, Ashdown House in Gatwick London Gatwick Airport, Phone 01293 567667 with Driving directions Full Article
use ***** Prime Minister Narendra Modi wants farmers to slash use of ... (rank 24) By www.gigaalert.com Published On :: Sat, 15 Aug 2020 02:36:13 +0100 New Delhi: Prime Minister Narendra Modi has urged farmers to significantly cut their use of urea to boost income and soil health, and said his government was constantly striving to prop up rural India with steps such as the ₹1 lakh crore agriculture infrastructure fund, for which he launched the financing facility on Sunday. Modi also released ₹17,000 crore to the bank accounts of 85 ... Full Article
use ***** Greenhouse gas emissions (GHG) verification Aviation, Airports ... (rank 21) By www.gigaalert.com Published On :: Sun, 22 Oct 2023 23:30:30 +0100 Verifavia. Verifavia, part of the Normec Group, is a worldwide independent environmental accredited verification, certification and auditing body for aviation, airports and maritime transport. In particular, Verifavia performs independent emissions verification audits for ICAO's CORSIA, EU ETS , UK ETS , Swiss ETS and ACA to aircraft operators ... Full Article
use North side of Crystal Pier is my latest habit. I’ve gotten applause for a ride once. Been hooked on my flippers by a fisherman twice. Been told I was thought to be a seal once. That’s so far this year. Different years, different adventures. By artlung.com Published On :: Sun, 03 Nov 2024 00:53:42 +0000 from Instagram https://instagr.am/p/DB48I-gSloZ/ via IFTTT Full Article general IFTTT swim2024 via-instagram
use Whooping cough vaccine does not prevent disease - it causes more severe outbreaks By www.newmediaexplorer.org Published On :: 2012-08-20T18:57:25+01:00 This is a reasoned argument by Joanna (Why I Don't Vaccinate My Children) posted on Erwin Alber's VINE facebook page which was started in 2009, to help parents make an informed choice on behalf of their children. Image credit topnews.ae Joanna responds (below) to a lady who published an article saying that unvaccinated children are the cause of recent increased pertussis (whooping cough) outbreaks in areas where vaccination is actively pursued...... Full Article
use The abuse of a college education By www.sellingwaves.com Published On :: 2005-02-01T19:25:38-05:00 “Perhaps you’re familiar with “the tragedy of the commons,” a social dilemma outlined by the late biologist Garrett Hardin in a famous 1968 essay of the same name. The dilemma is that when individuals pursue personal gain, the net result for society as a whole may be impoverishment. (Pollution is the most familiar example.) Such thinking has fallen out of fashion amid President Bush’s talk of an “ownership society,” but its logic is unassailable.” That response seems like a pretty damn obtuse interpretation of the essay, simply because the essay is nothing if not a plea for the creation of property rights. Furthermore, while it is true that Hardin claims that pursuing individual gain leads to group catastrophe, the word “when” in the paragraph above implies that there are times when the individual doesn’t, whereas Hardin claims that individuals basically always pursue their own interest, which is the problem in high-density situations where some amout of coordination is necessary. However, upon re-reading it, I realize that for Hardin property rights only forms a part of a wished-for imposition of coercive measures which will prevent individuals from pursuing personal gain at the expense of their environment. Which makes sense, because property rights, for all this may get lost in the ceaseless ideological wrangling today, are themselves forms of state-imposed coercion. Dismiss the semi-metaphysical nonsense in Locke and Kant about gaining “just propriety” over an object by making a visible mark on it. Think about it: animals control exactly as much “property” as they can defend; cheetahs peeing on trees only works because they will fight to defend what they have claimed. By contrast, think about who adjudicates the (in theory) incontestable property rights: the authorities, i.e. in our society, the State. The corollary of this, of course, is that nationalized or federal property is not “public property,” in the sense of property owned by the public—quite the contrary. The dichotomy between it and “private property” is spurious. “Public property” is simply property owned by the government. This no doubt seems obvious and intuitive, but based on the foolishness I cited above, it bears repeating that property rights, whether granted to others by the government or to itself, are not opposed to coercive state power but are in fact the very essence of it. That fact is perhaps more apparent in regards to so-called “intellectual property.” As a marginal note, Hardin’s essay, despite the pithiness of its central analogy, is rather dispiriting insofar as it takes Hegel’s statement that “Freedom lies in the recognition of necessity” as its motto and guiding spirit. That formulation is, as I believe I have said before, perfectly monstruous. Freedom means nothing if it is not the absence of restriction, and it is perhaps a sign of the evasive confusion of priorities in Western culture that one would pretend to celebrate this value in such a way while in fact describing its opposite. Freedom is not an act or a thought, but rather a set of conditions under which action and thought occur. This is the same idealistic debasement of the language that has turned love into a deed: making love. Full Article
use Abuse? I'll show you abuse! By www.sellingwaves.com Published On :: 2005-02-05T02:19:38-05:00 Note to Curt: Just because the state claims the authority to apprehend and punish rapists doesn’t mean that apprehending and punishing rapists is a form of state coercion. Nor is the notion that rape is bad an example of state coercion. Depending on your perspective, this is either a moral truth derived from God/reason/whatever or a widely-accepted social convention. Similarly, the notion that one can own property is (again, depending on your perspective) either morally necessary or a widely-accepted social convention that seems to work pretty well (here I’m dispensing with Communists and other fools who have nothing intelligent to say on the matter). Either way, the fact that the state claims ultimate authority to adjudicate property disputes does not make private property a form of state coercion. (Further reading) Full Article
use "...you just get used to them" By www.sellingwaves.com Published On :: 2005-02-13T04:37:18-05:00 “Young man, in mathematics you don’t understand things, you just get used to them.” —John von Neumann1 This, in a sense, is at the heart of why mathematics is so hard. Math is all about abstraction, about generalizing the stuff you can get a sense of to apply to crazy situations about which you otherwise have no insight whatsoever. Take, for example, one way of understanding the manifold structure on SO(3), the special orthogonal group on 3-space. In order to explain what I’m talking about, I’ll have to give several definitions and explanations and each, to a greater or lesser extent, illustrates both my point about abstraction and von Neumann’s point about getting used to things. First off, SO(3) has a purely algebraic definition as the set of all real (that is to say, the entries are real numbers) 3 × 3 matrices A with the property ATA = I and the determinant of A is 1. That is, if you take A and flip rows and columns, you get the transpose of A, denoted AT; if you then multiply this transpose by A, you get the identity matrix I. The determinant has its own complicated algebraic definition (the unique alternating, multilinear functional…), but it’s easy to compute for small matrices and can be intuitively understood as a measure of how much the matrix “stretches” vectors. Now, as with all algebraic definitions, this is a bit abstruse; also, as is unfortunately all too common in mathematics, I’ve presented all the material slightly backwards. This is natural, because it seems obvious that the first thing to do in any explication is to define what you’re talking about, but, in reality, the best thing to do in almost every case is to first explain what the things you’re talking about (in this case, special orthogonal matrices) really are and why we should care about them, and only then give the technical definition. In this case, special orthogonal matrices are “really” the set of all rotations of plain ol’ 3 dimensional space that leave the origin fixed (another way to think of this is as the set of linear transformations that preserve length and orientation; if I apply a special orthogonal transformation to you, you’ll still be the same height and width and you won’t have been flipped into a “mirror image”). Obviously, this is a handy thing to have a grasp on and this is why we care about special orthogonal matrices. In order to deal with such things rigorously it’s important to have the algebraic definition, but as far as understanding goes, you need to have the picture of rotations of 3 space in your head. Okay, so I’ve explained part of the sentence in the first paragraph where I started throwing around arcane terminology, but there’s a bit more to clear up; specifically, what the hell is a “manifold”, anyway? Well, in this case I’m talking about differentiable (as opposed to topological) manifolds, but I don’t imagine that explanation helps. In order to understand what a manifold is, it’s very important to have the right picture in your head, because the technical definition is about ten times worse than the special orthogonal definition, but the basic idea is probably even simpler. The intuitive picture is that of a smooth surface. For example, the surface of a sphere is a nice 2-dimensional manifold. So is the surface of a donut, or a saddle, or an idealized version of the rolling hills of your favorite pastoral scene. Slightly more abstractly, think of a rubber sheet stretched and twisted into any configuration you like so long as there are no holes, tears, creases, black holes or sharp corners. In order to rigorize this idea, the important thing to notice about all these surfaces is that, if you’re a small enough ant living on one of these surfaces, it looks indistinguishable from a flat plane. This is something we can all immediately understand, given that we live on an oblate spheroid that, because it’s so much bigger than we are, looks flat to us. In fact, this is very nearly the precise definition of a manifold, which basically says that a manifold is a topological space (read: set of points with some important, but largely technical, properties) where, at any point in the space, there is some neighborhood that looks identical to “flat” euclidean space; a 2-dimensional manifold is one that looks locally like a plane, a 3-dimensional manifold is one that looks locally like normal 3-dimensional space, a 4-dimensional manifold is one that looks locally like normal 4-dimensional space, and so on. In fact, these spaces look so much like normal space that we can do calculus on them, which is why the subject concerned with manifolds is called “differential geometry”. Again, the reason why we would want to do calculus on spaces that look a lot like normal space but aren’t is obvious: if we live on a sphere (as we basically do), we’d like to be able to figure out how to, e.g., minimize our distance travelled (and, thereby, fuel consumed and time spent in transit) when flying from Denver to London, which is the sort of thing for which calculus is an excellent tool that gives good answers; unfortunately, since the Earth isn’t flat, we can’t use regular old freshman calculus.2 As it turns out, there are all kinds of applications of this stuff, from relatively simple engineering to theoretical physics. So, anyway, the point is that manifolds look, at least locally, like plain vanilla euclidean space. Of course, even the notion of “plain vanilla euclidean space” is an abstraction beyond what we can really visualize for dimensions higher than three, but this is exactly the sort of thing von Neumann was talking about: you can’t really visualize 10 dimensional space, but you “know” that it looks pretty much like regular 3 dimensional space with 7 more axes thrown in at, to quote Douglas Adams, “right angles to reality”. Okay, so the claim is that SO(3), our set of special orthogonal matrices, is a 3-dimensional manifold. On the face of it, it might be surprising that the set of rotations of three space should itself look anything like three space. On the other hand, this sort of makes sense: consider a single vector (say of unit length, though it doesn’t really matter) based at the origin and then apply every possible rotation to it. This will give us a set of vectors based at the origin, all of length 1 and pointing any which way you please. In fact, if you look just at the heads of all the vectors, you’re just talking about a sphere of radius 1 centered at the origin. So, in a sense, the special orthognal matrices look like a sphere. This is both right and wrong; the special orthogonal matrices do look a lot like a sphere, but like a 3-sphere (that is, a sphere living in four dimensions), not a 2-sphere (i.e., what we usually call a “sphere”). In fact, locally SO(3) looks almost exactly like a 3-sphere; globally, however, it’s a different story. In fact, SO(3) looks globally like , which requires one more excursion into the realm of abstraction. , or real projective 3-space, is an abstract space where we’ve taken regular 3-space and added a “plane at infinity”. This sounds slightly wacky, but it’s a generalization of what’s called the projective plane, which is basically the same thing but in a lower dimension. To get the projective plane, we add a “line at infinity” rather than a plane, and the space has this funny property that if you walk through the line at infinity, you get flipped into your mirror image; if you were right-handed, you come out the other side left-handed (and on the “other end” of the plane). But not to worry, if you walk across the infinity line again, you get flipped back to normal. Okay, sounds interesting, but how do we visualize such a thing? Well, the “line at infinity” thing is good, but infinity is pretty hard to visualize, too. Instead we think about twisting the sphere in a funny way: You can construct the projective plane as follows: take a sphere. Imagine taking a point on the sphere, and its antipodal point, and pulling them together to meet somewhere inside the sphere. Now do it with another pair of points, but make sure they meet somewhere else. Do this with every single point on the sphere, each point and its antipodal point meeting each other but meeting no other points. It’s a weird, collapsed sphere that can’t properly live in three dimensions, but I imagine it as looking a bit like a seashell, all curled up on itself. And pink. This gives you the real projective plane, . If you do the same thing, but with a 3-sphere (again, remember that this is the sphere living in four dimensions), you get . Of course, you can’t even really visualize or, for that matter, a 3-sphere, so really visualizing is going to be out of the question, but we have a pretty good idea, at least by analogy, of what it is. This is, as von Neumann indicates, one of those things you “just get used to”. Now, as it turns out, if you do the math, SO(3) and look the same in a very precise sense (specifically, they’re diffeomorphic). On the face of it, of course, this is patently absurd, but if you have the right picture in mind, this is the sort of thing you might have guessed. The basic idea behind the proof linked above is that we can visualize 3-space as living inside 4-space (where it makes sense to talk about multiplication); here, a rotation (remember, that’s all the special orthogonal matrices/transformations really are) is just like conjugating by a point on the sphere. And certainly conjugating by a point is the same as conjugating by its antipodal point, since the minus signs will cancel eachother in the latter case. But this is exactly how we visualized , as the points on the sphere with antipodal points identified! I’m guessing that most of the above doesn’t make a whole lot of sense, but I would urge you to heed von Neumann’s advice: don’t necessarily try to “understand” it so much as just to “get used to it”; the understanding can only come after you’ve gotten used to the concepts and, most importantly, the pictures. Which was really, I suspect, von Neumann’s point, anyway: of course we can understand things in mathematics, but we can only understand them after we suspend our disbelief and allow ourselves to get used to them. And, of course, make good pictures. 1 This, by the way, is my second-favorite math quote of the year, behind my complex analysis professor’s imprecation, right before discussing poles vs. essential singularities, to “distinguish problems that are real but not serious from those that are really serious.” 2 As a side note, calculus itself is a prime example of mathematical abstraction. The problem with the world is that most of the stuff in it isn’t straight. If it were, we could have basically stopped after the Greeks figured out a fair amount of geometry. And, even worse, not only is non-straight stuff (like, for example, a graph of the position of a falling rock plotted against time) all over the place, but it’s hard to get a handle on. So, instead of just giving up and going home, we approximate the curvy stuff in the world with straight lines, which we have a good grasp of. As long as we’re dealing with stuff that’s curvy (rather than, say, broken into pieces) this actually works out pretty well and, once you get used to it all, it’s easy to forget what the whole point was, anyway (this, I suspect, is the main reason calculus instruction is so uniformly bad; approximating curvy stuff with straight lines works so well that those who who are supposed to teach the process lose sight of what’s really going on). Full Article
use use cheat instead of man By oksoft.antville.org Published On :: 2022-07-04T08:53:57Z wget github.comgunzip cheat-linux-arm64.gzchmod 770 cheat-linux-arm64./cheat-linux-arm64mv cheat-linux-arm64 /usr/local/bin/cheat#use cheat tar or cheat wget to get more info Full Article
use Use focus mode using Android phones By oksoft.antville.org Published On :: 2023-01-01T03:59:21Z Settings > Digital Wellbeing and parental controls. Tap your preferred Focus Mode or create your own by selecting Add. Select Start to start using that Focus Mode. Full Article
use User Defined Property By oksoft.antville.org Published On :: 2023-01-09T08:52:28Z You can create User Defined Property in libreoffice writer. File – Properties – Custom Properties – Add Property – Set the type: Date) – Set the value.To use this property goto Insert – Field – More Fields – DocInformation – Custom. Full Article
use The Gophers Go to the Haunted House By storiesmykidslove.blogspot.com Published On :: 2014-04-12T14:43:18.398-07:00 The Gophers visit the Graveyard of Terror and get a little bit more for the price of admission than the other guests at the Haunt....Enjoy this special October edition of Bedtime Stories My Kids Love.No worries, the Adventures of the Man in the Can will continue in November.MP3 File - Click Here to Download Podcast Full Article bedtime bedtime stories Bedtime Stories My Kids Love bedtime story Gophers graveyard ghoul kidsafe safe
use List Of Brands Available In The UK That Use Monsanto Products. By nancythroughthelookingglass.blogspot.com Published On :: Sat, 06 Jul 2013 19:03:00 +0000 Complete list of UK Brands that use Monsanto products, so these companies products probably contain Genetically Modified ingredients. Boycott all these companies for the good of your health! This site is very useful too called "How To Avoid GM Foods". And also check out "GM Watch" And if you are in the USA watch the video at the bottom of the post for a full list of products you should be boycotting too. Betty Crocker Cadbury Campbells Capri Sun Carnation Coca Cola Quakers Green Giant Heinz Hellmanns Nestle Spam Kellogs Knorr Kraft Lipton Minute Maid Ritz Crackers Ocean Spray Pepsi Pilsbury Power BarPringles Proctor and gamble Quaker Ragu Weight Watchers Schweppes Uncle Bens Unilever Full Article genetically modified gm list of uk gm foods monsanto
use La France est non fumeuse By poypoye.over-blog.com Published On :: Tue, 01 Jan 2008 13:45:32 +0100 PARIS (Reuters) - L'interdiction de fumer dans tous les lieux publics a pris effet mardi en France mais un délai de tolérance de 24 heures, 1er janvier et réveillon obligent, a offert aux fumeurs un ultime répit. L'entrée en vigueur de la loi sur le tabac... Full Article
use Réforme de la "carte famille nombreuse" By poypoye.over-blog.com Published On :: Fri, 11 Apr 2008 10:11:00 +0200 Après le bouclier social, la fin des 35h qui permette de gagner moins (puisque non majorées à 25 %), les suppressions de postes de fonctionnaire (mais surtout pas dans les ministères !), la suppression de la pub sur France Télévision, qui ne gênait personne... Full Article
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use La Chine et les pays d'Am�rique latine et des Cara�bes b�n�ficieront de perspectives plus prometteuses au cours des dix prochaines ann�es By chine.in Published On :: 2024-11-13T09:56:49+01:00 Guid�e par la diplomatie des chefs d'Etat, la communaut� d'avenir partag� Chine-pays d'Am�rique latine et des Cara�bes b�n�ficiera de perspectives plus prometteuses durant la d�cennie � venir, a d�clar� mardi un porte-parole du minist�re chinois des... Full Article Chine
use Chine : croissance vigoureuse du secteur de la livraison express en octobre By chine.in Published On :: 2024-11-13T20:14:44+01:00 Le secteur chinois de la livraison express a enregistr� une expansion rapide en octobre, avec une acc�l�ration significative du taux de croissance des affaires, selon un indice de l'industrie publi� mercredi par le Bureau national des postes. ... Full Article livraison express