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The first step in studying the sorts of possible computations (and more interestingly, those things which cannot be computed) is to define exactly what we mean by a “computation.” At a high level, this is easy: a computation is simply a function. Given some input, produce the appropriate output. Unfortunately this is much too general. For instance, we could define almost anything we want in terms of functions. Let $ f$ be the function which..
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Check out my new little automation utility belt app for the keyboard-centric power users. It is hosted on a github project here .
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Check out my new little automation utility belt app for the keyboard-centric power users. It is hosted on a github project here .
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Problem: Prove that for all $ n,k \in \mathbb{N}, k > 1$, we have $$\sum \limits_{i=0}^{n} k^i = \frac{k^{n+1}-1}{k-1}$$ Solution: Representing the numbers in base $ k$, we have that each term of the sum is all 0’s except for a 1 in the $ i$th place. Hence, the sum of all terms is the $ n$-digit number comprised of all 1’s. Multiplying by $ k-1$ gives us the $ n$-digit number where every digit is $ k-1$.
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Problem: Prove that for all $ n,k \in \mathbb{N}, k > 1$, we have $$\sum \limits_{i=0}^{n} k^i = \frac{k^{n+1}-1}{k-1}$$ Solution: Representing the numbers in base $ k$, we have that each term of the sum is all 0’s except for a 1 in the $ i$th place. Hence, the sum of all terms is the $ n$-digit number comprised of all 1’s. Multiplying by $ k-1$ gives us the $ n$-digit number where every digit is $ k-1$.
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Problem: Prove that for all $ n,k \in \mathbb{N}, k > 1$, we have $$\sum \limits_{i=0}^{n} k^i = \frac{k^{n+1}-1}{k-1}$$ Solution: Representing the numbers in base $ k$, we have that each term of the sum is all 0’s except for a 1 in the $ i$th place. Hence, the sum of all terms is the $ n$-digit number comprised of all 1’s. Multiplying by $ k-1$ gives us the $ n$-digit number where every digit is $ k-1$.
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So, Google Plus launched, the first truly viable Facebook competitor. The timing is quite interesting, given Google's recent failures with the Buzz microblogging platform, and the impending Facebook IPO . After a bit of time with Plus, here are some thoughts: Google already knows everything I do, so sharing stuff there feels less risky The UI is pretty and a lot less bloated than Facebook's Messages and comments can be edited, saving fr....
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So, Google Plus launched, the first truly viable Facebook competitor. The timing is quite interesting, given Google's recent failures with the Buzz microblogging platform, and the impending Facebook IPO . After a bit of time with Plus, here are some thoughts: Google already knows everything I do, so sharing stuff there feels less risky The UI is pretty and a lot less bloated than Facebook's Messages and comments can be edited, saving fr....
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Another cache buffers chains latch contention troubleshooting example using LatchProf
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tanelpoder.com
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15 years ago
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eng
One of my blog readers recently dropped me an email noting that he had noticed some cache buffers chains latch contention recently and successfully troubleshooted it with LatchProf . I asked if he’d like to blog about it and here’s the article: http://web.archive.org/web/20111113062613/http://orapsdba.wordpress.com/2011/06/21/another-latchcache-buffer-chains-troubleshooting Cache buffer chains latch contention typically shows up wh..
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Another cache buffers chains latch contention troubleshooting example using LatchProf
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tanelpoder.com
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15 years ago
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eng
One of my blog readers recently dropped me an email noting that he had noticed some cache buffers chains latch contention recently and successfully troubleshooted it with LatchProf . I asked if he’d like to blog about it and here’s the article: http://web.archive.org/web/20111113062613/http://orapsdba.wordpress.com/2011/06/21/another-latchcache-buffer-chains-troubleshooting Cache buffer chains latch contention typically shows up wh..
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Additional Patterns Last time we left the reader with the assertion that Conway’s game of life does not always stabilize. Specifically, there exist patterns which result in unbounded cell population growth. Although John Conway’s original conjecture was that all patterns eventually stabilize (and offered $50 to anyone who could provide a proof or counterexample), he was proven wrong. Here we have the appropriately named glider gun, whose ma..
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Additional Patterns Last time we left the reader with the assertion that Conway’s game of life does not always stabilize. Specifically, there exist patterns which result in unbounded cell population growth. Although John Conway’s original conjecture was that all patterns eventually stabilize (and offered $50 to anyone who could provide a proof or counterexample), he was proven wrong. Here we have the appropriately named glider gun, whose ma..
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Additional Patterns Last time we left the reader with the assertion that Conway’s game of life does not always stabilize. Specifically, there exist patterns which result in unbounded cell population growth. Although John Conway’s original conjecture was that all patterns eventually stabilize (and offered $50 to anyone who could provide a proof or counterexample), he was proven wrong. Here we have the appropriately named glider gun, whose ma..
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Cellular Automata There is a long history of mathematical models for computation. One very important one is the Turing Machine, which is the foundation of our implementations of actual computers today. On the other end of the spectrum, one of the simpler models of computation (often simply called a system) is a cellular automaton. Surprisingly enough, there are deep connections between the two. But before we get ahead of ourselves, let’s se..
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Cellular Automata There is a long history of mathematical models for computation. One very important one is the Turing Machine, which is the foundation of our implementations of actual computers today. On the other end of the spectrum, one of the simpler models of computation (often simply called a system) is a cellular automaton. Surprisingly enough, there are deep connections between the two. But before we get ahead of ourselves, let’s se..
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Cellular Automata There is a long history of mathematical models for computation. One very important one is the Turing Machine, which is the foundation of our implementations of actual computers today. On the other end of the spectrum, one of the simpler models of computation (often simply called a system) is a cellular automaton. Surprisingly enough, there are deep connections between the two. But before we get ahead of ourselves, let’s se..
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I just noticed that Jonathan Lewis has announced that he’s writing a new Oracle (fundamental) internals book , due to be out in November. So, I’m happy to add to Jonathan’s announcement, that I’m the tech reviewer of that book! After all the hard work on the Exadata book , I didn’t want to hear about working on any book again (even if it’s just tech reviewing work), but as this is Jonathan’s book, about exactly these topics I love and..
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I just noticed that Jonathan Lewis has announced that he’s writing a new Oracle (fundamental) internals book , due to be out in November. So, I’m happy to add to Jonathan’s announcement, that I’m the tech reviewer of that book! After all the hard work on the Exadata book , I didn’t want to hear about working on any book again (even if it’s just tech reviewing work), but as this is Jonathan’s book, about exactly these topics I love and..
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In May I received the IOUG Select Journal Editor’s Choice Award for my Systematic Oracle Latch Contention Troubleshooting article where I introduced my LatchProfX tool for advanced drilldown into complex latch contention problems (thanks IOUG and John Kanagaraj !). As the relevant IOUG webpage hasn’t been updated yet, I thought to delay this announcement until the update was done – but I just found an official enough announcement (pr..
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In May I received the IOUG Select Journal Editor’s Choice Award for my Systematic Oracle Latch Contention Troubleshooting article where I introduced my LatchProfX tool for advanced drilldown into complex latch contention problems (thanks IOUG and John Kanagaraj !). As the relevant IOUG webpage hasn’t been updated yet, I thought to delay this announcement until the update was done – but I just found an official enough announcement (pr..
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Google+ - Google’s newest attempt to delve into the world of social networking on a scale that it hasn’t done before. Orkut looked promising but enthusiasm died, Google Wave flopped (even though I quite liked it originally, I never used it after the first day), Google Buzz fizzled out. I hope that Google+ will be the hit in Google’s track record of social networking misses.
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Tutto comincia con una normale riunione tra programmatori, magari dedicata all’analisi di un nuovo intrigante progetto software. I toni inizialmente tranquilli all’improvviso si alzano e quello che doveva essere un incontro di routine si trasforma rapidamente in qualcos’altro. La discussione, ora vivace e concitata, diventa un vero e proprio alterco. Sedie penne e matite vengono spostate freneticamente, le voci si sovrappongono l’un l’altra..
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Tutto comincia con una normale riunione tra programmatori, magari dedicata all’analisi di un nuovo intrigante progetto software. I toni inizialmente tranquilli all’improvviso si alzano e quello che doveva essere un incontro di routine si trasforma rapidamente in qualcos’altro. La discussione, ora vivace e concitata, diventa un vero e proprio alterco. Sedie penne e matite vengono spostate freneticamente, le voci si sovrappongono l’un l’altra..
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Knowing what you want to achieve before thinking of how to achieve it – a query optimization example
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tanelpoder.com
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15 years ago
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eng
Today I received a question which was a good example of systematic problem solving approach. It was about getting a long-running query to run faster. It took a long time as the correlated subquery in the query was not unnested, was re-visited many times, causing the whole subquery subtree in the plan to be executed again and again). The main part of the question was this: Is there a way to avoid “NOT IN” conversion to “NOT EXISTS” by o..
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Knowing what you want to achieve before thinking of how to achieve it – a query optimization example
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tanelpoder.com
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15 years ago
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eng
Today I received a question which was a good example of systematic problem solving approach. It was about getting a long-running query to run faster. It took a long time as the correlated subquery in the query was not unnested, was re-visited many times, causing the whole subquery subtree in the plan to be executed again and again). The main part of the question was this: Is there a way to avoid “NOT IN” conversion to “NOT EXISTS” by o..
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A mate of mine was looking at a previous article I wrote about Decoding CAPTCHA’s where I pointed people to the following article (PDF) http://la2600.org/talks/files/20040102/Vector_Space_Search_Engine_Theory.pdf He was having some difficulty understanding it so I thought I would write up a very simple explanation of what’s actually happening in the vector space. The vector space isn’t actually that complicated, but getting your hea..
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caption id=“attachment_40030” align=“alignleft” width=“300” caption=“The Quantum Thief by Hannu Rajaniemi”] [/caption]I finished reading The Quantum Thief (affiliate link) by Hannu Rajaniemi, but this will not be a book review. Mostly because I need to read it again before I can honestly feel confident about reviewing this thing. I feel that even though I grasped most of the concepts of how the world works and the individual technologi..
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App Harbor is a great new cloud hosting service, which I’ve been trying out over the last few weeks. It deploys straight from source code…
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App Harbor is a great new cloud hosting service, which I’ve been trying out over the last few weeks. It deploys straight from source code…
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In the wake of this brief description of my component binding system, I was asked to provide more details on its implementation. This article is my best attempt to do so! This is a tale of intrigue, excitement, and wonder, in which I try to implement a component-entity system in C#, and stumble upon a remarkable paradigm that merges components with data binding. Note: If you don't have at least a vague concept of component-entity desi..
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Mockups for paintings Makehuman figures imported into SketchUp I’ve been playing around with the Golden Open acrylics a lot lately and preparing a bunch of small and not-so-small supports for new paintings. After trips to MOMA and the Chicago Art Institute’s Architecture and Design room, I’m fired up to try more content using SketchUp as a planning tool for dreamy, sci-fi spacious otherscapes. While playing around with this I ....
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Mockups for paintings Makehuman figures imported into SketchUp I’ve been playing around with the Golden Open acrylics a lot lately and preparing a bunch of small and not-so-small supports for new paintings. After trips to MOMA and the Chicago Art Institute’s Architecture and Design room, I’m fired up to try more content using SketchUp as a planning tool for dreamy, sci-fi spacious otherscapes. While playing around with this I ....
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Thoughts on using Twitter to shrink the size of large classrooms, foster discussion and make class more enjoyable.
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How to Clean Your Dirty Smartphone (Without Breaking Something)
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justingarrison.com
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15 years ago
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eng
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Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
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Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
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Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
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Community Service Mathematics is supposed to be a process of discovery. Definitions, propositions, and methods of proof don’t come from nowhere, although after the fact (when presented in a textbook) they often seem to. As opposed to a textbook, real maths is highly non-linear. It took mathematicians quite a lot of fuss to come up with the quadratic formula, and even simple geometric conjectures were for the longest time the subject of hot ..
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