![]() At the climate summit in Paris 2015 (COP21), well-known environmental organizations such as Greenpeace made a point of delivering a bright and hopeful message, praising the deal as an important breakthrough. Even if emotions such as fear, anxiety, despair or depression may exist among activists, hope is still indispensible, mediating the other emotions so as to motivate action (Gardner 2017, Kleres & Wettergren 2017). In regard to climate activism in particular, researchers have pointed to the centrality of the emotion of hope in mobilizing and sustaining activism (e.g. As Klein points out in the quote above, pessimism should probably be "saved for better times" if you want to stop bad things from taking over entirely. Don't people need hope in order to become activists? It's a well-known saying that people don't join movements because of pessimism. In post-apocalyptic environmentalism we encounter a new paradox. Order to enable us to avoid it, Dark Mountain instead exemplifies what I've called a new post-apocalyptic form of environmentalism which sees catastrophe as something that's already here: as already having happened, as ongoing or as unvaoidable. Rhetoric, pointing to the threat of a future, global catastrophe only in Whereas much environmentalism until now has employed an apocalyptic … Giving up hope, to me, means giving up the illusion of control and accepting that the future is going to be improvised, messy, difficult. They hope desperately that they can keep control of the way things are panning out. I find that people who talk about hope are often really talking about control. We need to imagine a future which can’t be planned for and can’t be controlled. This may sound a strange thing to say, but one of the great achievements for me of the Dark Mountain Project has been to give people permission to give up hope. In a debate with fellow enviornmentalist Wen Stephenson, Kingsnorth expresses it as follows: Instead, the group insists that accepting loss and honestly confronting the fact that the catastrophe can no longer be avoided is a liberating act. The fundamental gesture of Dark Mountain consists, I believe, in giving up hope that "the world can be saved". Dark Mountain is a hugely interesting group of writers, artists and activists who came together in 2009 to put words on the experiences of loss accompanying the decay and collapse of civilization. I'd like to use these remarks about hope as a way of approaching and making sense of two books I've read recently, Paul Kingsnorth's Confessions of a Recovering Environmentalist and Other Essays (2017) and Walking on Lava: Selected Works for Uncivilised Times (2017), an anthology of texts produced by the Dark Mountain collective (of which Kingsnorth is a co-founder). To the extent that such statements are meant to induce a feeling of hope. ![]() Reflect on statements about optimism (and pessimism) as well, at least Yet despite this difference, the paradoxical quality of hope often seems to Hope, by contrast, is to see the future as openĪnd thus calling for action (Solnit 2006 also Ehrenreich 2009:3, Weber-Nicholsen 2002:183). Rebecca Solnit puts it well when she writes that both optimism and pessimism are set views of the future and both provideĮxcuses for inactivity. Hope is aįeeling not wholly under our conscious control, while optimism is aĬognitive assessment. I realize of course that hope isn't the same as optimism. L’optimisme, laissons le pessimisme pour des temps meilleurs.')” Optimism we’ll save pessimism for better times.' ('L’heure est à Here's what Naomi Klein wrote after Trump's election: ”To quote a popular saying on the French left, 'The hour calls for The curious thing is that both statements ring true, and that's the paradox. A seemingly opposite viewpoint is offered by the Salvage magazine: "Hope is precious it must be rationed". It is also the last resort” (quoted in Jensen 2004: 256). When asked by an interviewer if he had hope in view of the ecologicalĭisaster, Paul Shepard replied: "Of course I have hope. Perhaps there is no pure hope, no hope without an element of hopelessness? But conversely, isn't it true that one sometimes experiences how giving up hope can be a cure against hopelessness? In that sense, every incidence of hope is causeįor pessimism. Of something bad, something that we want to escape. Indeed, the very presence of hope testifies to the existence There is a logic connecting hope and hopelessness, two emotions that constantly seem to invite each other. ![]() Writing this I recall Walter Benjamin's words at the end of his essay on Goethe - “Only for the sake of the hopeless are we given hope”. ![]() No emotion lends itself so well to paradoxical formulations as hope.
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![]() ![]() JOURNEY THROUGH SPACE AND TIME Battle across 11 crazy worlds, from Ancient Egypt to the Far Future, and beyond. ![]() Earn coins, piñatas, and more to top the leaderboards, level up through Leagues, and become the ultimate garden guardian. Enter Arena and compete against other players to get the highest score on unique levels. Boost your plants to ensure those zombies are lawn-gone! COMPETE AGAINST OTHERS IN ARENA Think your zombie-bashing strategy is the best? Put your planting skills to the test when you face other players in Arena. Power up attacks, double-down defenses, speed up planting time, and even gain entirely new abilities. Go toe-to-missing-toe with a massive array of zombies at every turn, like Jetpack Zombie and Mermaid Imp – you’ll even have to protect your brain from rampant Zombie Chickens! GROW POWERFUL PLANTS Earn Seed Packets as you play and use them to fuel your potent plants. 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How to Download and Install Plants vs Zombies™ 2 Mod APK 10.8.1.How to download Plants vs Zombies™ 2 Mod APK for free?.Is Plants vs Zombies™ 2 Mod APK safe to use?.Feature Of Plants vs Zombies™ 2 Mod APK. ![]() Overusing our search engine with a very large number of searches in a very short amount of time.Using a badly configured (or badly written) browser add-on for blocking content.Running a "scraper" or "downloader" program that either does not identify itself or uses fake headers to elude detection.Using a script or add-on that scans GameFAQs for box and screen images (such as an emulator front-end), while overloading our search engine.There is no official GameFAQs app, and we do not support nor have any contact with the makers of these unofficial apps. Continued use of these apps may cause your IP to be blocked indefinitely. This triggers our anti-spambot measures, which are designed to stop automated systems from flooding the site with traffic. Some unofficial phone apps appear to be using GameFAQs as a back-end, but they do not behave like a real web browser does.Using GameFAQs regularly with these browsers can cause temporary and even permanent IP blocks due to these additional requests. If you are using the Brave browser, or have installed the Ghostery add-on, these programs send extra traffic to our servers for every page on the site that you browse, then send that data back to a third party, essentially spying on your browsing habits.We strongly recommend you stop using this browser until this problem is corrected. The latest version of the Opera browser sends multiple invalid requests to our servers for every page you visit.The most common causes of this issue are: ![]() Your IP address has been temporarily blocked due to a large number of HTTP requests. ![]() It doesn’t have a touchscreen, but the subtle touch panel on top makes it easy to flick between photos. We think Aura frames have the slickest software out there, and the Carver is no exception. It helps that the screen can adjust automatically to ambient conditions and go impressively bright, aided by a semi-matte finish. Its 10.1-inch display isn’t as sharp as the slightly pricier Carver Luxe, but we found its 1280x800 panel fine in testing, with pleasant colors and good viewing angles. ❌ You want a portrait frame: The Carver is only designed to stand in landscape orientation and the screen image can’t be rotated.Ĭlassier than most competitors, the Aura Carver stands out with an embossed border and angular, free-standing design. ❌ You want complete control: By favoring simplicity over deep customization, the Aura Mason offers limited room for manual control. In contrast, the metal-effect variant is both excessively reflective and a serious fingerprint magnet, distracting from what is otherwise a sharp and capable Wi-Fi frame. One final note: in matte black, the bezel is sizeable but understated. You can also connect with friends to easily add their snaps to your frame. You can create playlists using photos from your smartphone, or sync with Google Photos to display AI-generated smart albums. One of our favorite things about this frame is how straightforward it is to load photos using the app. Controlled via a physical remote (or the virtual replica in the app), the frame proved responsive and pretty intuitive during our review, even if the high resolution means text can appear small. The option to wall-mount is also a useful one.Īs with other Nixplay frames, the settings menu offers no shortage of customisation options, from colour adjustments to the sensitivity of the motion sensor. ![]() At 9.7 inches, we also felt it struck a good balance: with a flexible stand that works in portrait or landscape, the frame fits on most shelves, yet still gives images space to be seen. Our tests found it vibrant, too, with deep blacks and enough brightness to beat the reflective coating. Nixplay’s 2K Smart Digital Photo Frame features one of the sharpest screens on the market, offering lots of detail. ❌ You like easily readable text: Because of the high resolution, menu text can appear small, making it difficult to read at a distance. ❌ You hate fingerprint marks: In matte black the bezel is understated, but the metal-effect version is super reflective and easy to smudge. The best high-resolution digital photo frame Read our in-depth Aura Mason Luxe review. ![]() The cost of the Mason Luxe may seem high for a 10-inch photo frame, but after our tests, we conclude the quality of the software and hardware justifies the expense. You can invite friends and relatives to send photos to the frame, and everyone in this inner Aura circle can “like” and comment on the images, creating a cosy sort of private social network. There’s also a social side to the Aura Mason Luxe. We found that color is natural-looking and well-saturated too, so you can be sure you’re seeing a fair representation of the photos you fling its way. Pixel density is so high they look sharp and detailed even when you get your face right up to the screen. Its 4:3 aspect display is perfect for not just adding some color to your room with your photos, but to actually get an up-close look at them. It’s stylish, has greater character to its design and, most important of all, the screen is excellent in most respects. The Aura Mason Luxe is a clear cut above most other photo frames. ❌ You have a limited budget: Clever software and a high-quality screen mean the Mason Luxe comes with a relatively high initial outlay. ❌ You want an offline frame: Because photos are stored on Aura’s service, the Mason Luxe must be connected to your Wi-Fi at all times. Once you’ve selected your favorite, you’ll find links to the best deals beneath each entry. If you need more in-depth suggestions, check out our guide on how to buy a digital photo frame. If you’re not sure where to start, scroll to the end for expert buying advice to help you choose the right frame. Whatever your expectations, you’ll find something to fit the bill below. Our guide spans a wide variety of frames, ranging from simple models to high-end frames with features to match. Whether you want to display a slideshow of family portraits, vacation snaps or your own photography, you’ll find a fitting option in the list below. Or if your budget is a little tighter, the Aeezo Portrait 01 offers excellent value. That said, if you’re prepared to spend more on a sharper display, the Nixplay 2K is worth a look. 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Optional: Tap Edit cover to edit the default cover picked by Instagram (a frame from the first Story in your collection). Then, tap Next in the top right corner of the screen.Ĥ. Scroll through your Story archive and select the Stories you want to include in your highlight. Open your Instagram account in the mobile app and click “New” in the highlights section below your bio.Ģ. Follow these step-by-step instructions to create a highlight (and if you already have a highlight set up, skip this part). To create an Instagram highlight cover, first you need to have an Instagram highlight. How to create an Instagram highlight cover Highlight covers aren’t essential, but they do provide your profile with a polished look-and they make a great first impression for people visiting your Instagram page for the first time. In the example below (indicated by the blue rectangle), a fashion brand uses highlights to feature important information-a sizing guide, care info, new launches, etc.-and each highlight has a cute floral highlight cover. It’s like a book cover, but for your highlight. Instagram Stories can only be viewed for 24 hours, but adding a Story to a highlight gives it a permanent spot on your profile.Īn Instagram highlight cover is a photo or graphic that appears above the highlight name on your profile page. What is an Instagram highlight cover?Īn Instagram highlight is a collection of Instagram Stories that a user has saved under a certain category. Optimize your profile and set your brand apart from the competition. Download your free pack of 40 customizable Instagram Stories Highlights Icons now. ![]() Most of the time, I don’t have homemade chicken broth on hand. No burning myself on hot pieces of chicken required! Pressure Cooker Chicken Noodle Soup: The Broth–and a boost. Instead, I chop the chicken, put it in the soup, and when the cook time is done, I can eat. Cut them while they are too hot to handle. To save time, I cut my chicken thighs into bite-size pieces before they go into the pot.įor me, it saves time because I don’t have to remove hot, cooked chicken thighs from the pressure cooker. Most recipes for chicken soup call for you to cook the chicken breasts or thighs whole and then cut it up after the soup has cooked. The flavor tastes so much better than chicken breasts that I bet you’ll love it! Cook Fast, Eat Well Tip: Cut the Chicken Before You Begin That said, I encourage you to try chicken thighs at least once. The chicken gets cut so small that texture isn’t really an issue. However, if you want to use chicken breasts, this is a great recipe for them. So you’ll rarely see me call for boneless chicken breasts on this site. Chicken breasts tend to get rubbery cooked in a pressure cooker. There’s enough fat to keep the chicken moist and tender under pressure. And I wouldn’t have it any other way.Īs I mentioned in the recipe for pressure cooker burrito bowls, boneless, skinless chicken thighs are my favorite cut of chicken to use in a pressure cooker. Not this recipe! This recipe makes a soup that’s loaded with pieces of tender chicken. And it always seemed like those cans of soup had one, maybe, of those bits in them. My favorite spoonfuls involved bite-sized pieces of tender chicken. Even as a kid, I remember thinking there wasn’t enough chicken in the Chicken Noodle Soup. I grew up eating Campbell’s chicken noodle soup which, if memory serves, was made up mostly of mushy noodles and salt. Pressure Cooker Chicken Noodle Soup: The Chicken Oh, and about that container, make sure the lid snaps on tight or your entire fridge will smell like onions. When you’re ready to make the soup, just throw them into the hot oil. (Mince the garlic right before you use or it will lose some flavor.) Store the chopped vegetables in a covered container in the fridge. You can save cooking time by chopping up the onions, carrots, and celery the night before. When sautéd, onions and garlic taste less sharp and the carrots have a lovely sweet flavor that you don’t get if you just throw them into the pot raw.Īs much as I like shortcut cooking, sautéing the vegetables is one step I wouldn’t skip. It sounds like it wouldn’t make much of a difference but it does. Sautéing brings out different flavors than cooking raw vegetables in the soup. I mean, the vegetables will cook anyway, right? Since the soup cooks so quickly, it’s tempting to skip the sauté step. This soup starts by sautéing vegetables in just a splash of olive oil. Pressure Cooker Chicken Noodle Soup: The Vegetables Because, let me tell you, I think a good 40% if my winter diet consists of soup–and a lot of that is chicken noodle soup. This is why we’re friends.Īs much as I love a pot of soup simmering on the stove, I love that I can make classic chicken noodle soup in just minutes in my pressure cooker. She agreed that classic chicken noodle soup is the best chicken noodle soup. It adds a nice flavor without taking over. My reply: “Nothing fancy! Chicken, egg noodles and enough onions, carrots, celery, and garlic to make it taste good. ![]() The other day my friend Michele asked what I put in my chicken noodle soup. This pressure cooker chicken soup recipe takes only 10 minutes to cook but tastes like it’s been simmering all day. Musk is clearly out of his competence when he claims that supersonic electric airplanes are viable, even with the progress in battery technology to be expected in the next few decades. Going supersonic means crossing a drag peak, but beyond that the maximum possible lift to drag ratio is well below that at subsonic speed and decreases again with increasing Mach number. The best lift to drag ratio is achieved in subsonic flight. A Pitot tube on the vertical tail measures a pressure of 2.96x104 N/m2. ![]() If you only want to go fast, the current limit with electrical propulsion and already rather generous assumptions is somewhere around Mach 2.įlying higher does not reduce the thrust requirement since the same lift has to be generated. transonic: adjective being or relating to speeds near that of sound in air or about 741 miles (1185 kilometers) per hour at sea level and especially to speeds slightly below the speed of sound at which the speed of airflow varies from subsonic to supersonic at different points along the surface of a body in motion relative to the surrounding air. A high-speed subsonic Boeing 707 airliner is flying at a pressure altitude of 12 km. However, the energy requirements for doing so will require an energy density of the batteries which is several magnitudes above what is currently possible. Supersonic speed helps to fly high - while subsonic designs run into the coffin corner, supersonic flight helps to maintain high dynamic pressure even at altitude. We had this discussion before, and indeed solar-electric propulsion helped to reach record altitudes: The AeroVironment Helios set a record at 29,524 m which will be hard to break. The composition of the atmosphere does not change too much with altitude, so it is the low atmospheric density which limits maximum altitude. That electric propulsion needs no oxygen is of little help for flying high. I mean somehow there must be limits, otherwise we could just fly higher and higher and fly with 0 thrust and still maintain mach 2 (not talking about space flight here)? These provide reasonable bases for inputs to models. ![]() Would that mean the power or thrust requirement to maintain mach 2 would only be 3.4%? Or is induced drag becoming significant at that point? Or maybe it would even stall at mach 2 if flying 40km high? Emission inventories have been developed for the current subsonic and projected supersonic and subsonic aircraft fleets. Meaning the resistance at 40km would only be 3.4% compared to 18.3km. While technology will definitely advance, it is still not prescriptible to cruise at the most critical part of the transonic regime where the drag divergence is maximum. ![]() Air density at 18.3km is 0.115 kg / m^3, at 30km it's 0.018 kg / m^3 and at 40km it is 0.0039 kg / m^3. thereby obtaining a Mach 0.95 subsonic cruise during the first lower altitude cruise-climb. Instead of mach 2 cruising at 18300 meters, assume it would climb to 30km, or even 40km. Question: is there some kind of limit for altitude and TAS? I mean suppose the Concorde would be retrofitted with batteries and electric fans. His logic seems to be: electric (fan?) propulsion doesn't need oxygen -> can go higher -> less friction -> need less power and thrust to maintain airspeed compared to traditional jet Assuming we have sufficiently energy-dense batteries, where would the limits be in terms of speed and altitude. With this, the waves merge together to form into shock wave which then travels at the speed of sound at Mach 1 which is equivalent to 1,235 km/hour or (767 miles per hour).So I was thinking about Elon Musk's supersonic electric jet idea. It is usually rated at 20 C (68 F), and is about 343 metres per second (1235 km/h 1125 ft/s 767 mph). These sound waves then pass at the speed of sound and when the object rises, the waves are compressed together as they can't pass out from each other's path fast. Sonic speed is the speed of sound in dry air. When an aircraft travels in the air, it creates sound waves both at the front and the rear of the plane. For the lowest subsonic conditions, compressibility can be ignored. When a supersonic aircraft is flying at a low altitude, the sonic boom caused by it may lead to slight tremors similar to earthquakes shaking buildings and shattering glasses. Subsonic conditions occur for Mach numbers less than one, M 1. ![]() The sonic boom causes a large amount of sound energy and sounds like an explosion to the human ear. Sometimes the sonic boom created by supersonic aircraft is so loud that it may cause damage to some structures. Sonic boom phenomenon occurs when an aircraft breaks the sound barrier and travels faster than the speed of sound. ![]() The moral of the story for you is simple, don't buy a Land Rover product, this is our recommendation after driving them on/off for 20-years. ![]() Moral of our story will be to drive these for another 3 years, and trade them in for Ford, Toyota (Lexus) or Jeep. The Dealership has been super responsive and helpful while the work on a DFT (Dealer Facilitated Trade) for the Discovery (but no promises). But, once again I am sitting on two vehicles that have lost a significant amount of their value and I'm back and forth to the service facility. We have serious mixed emotions, the Land Rover products are awesome in the snow, off-road and as daily haulers. ![]() The Range Rover Sport is having the brake issues and software issues and has enjoyed about 8 days in the shop. So, after racking up 7,000 miles and 5 months, the Discovery has been in the shop 18 days, major brake issues (sticking), software issues, and AEB issues. After, NEVER having … any issues with Toyota or Lexus for 4-years, we made the decision to go back to Land Rover and give the company the benefit of the doubt and purchased a 2018 Discovery (new from dealer) and 2018 Range Rover Sport (new from dealer) and both in cash. The base SE is the more affordable option, but in this comparison, you’ll see the different features and performance specs for both vehicles in order to help you make. The mapping on this website is provided by external mapping providers and is for general information purposes only.We've owned Land Rover products for nearly 20 years, and 5 years ago we left for Toyota (we purchased a 4runner and a Lexus SUV) because the frustrations of owning a Land Rover were interrupting our life (the service manager and Land Rover and I used to joke, that I should park the cars at the dealership, because they spent more time in the shop than in my garage). The entry-level 2020 Range Rover SE starts at 90,900 MSRP in comparison to the 2020 Range Rover HSE starting price of 95,950 MSRP. Please contact your local authorized Land Rover Retailer for availability and prices. Some vehicles are shown with optional equipment and retailer-fit accessories that may not be available in all markets. The Discovery‘s lightweight aluminum body is impressively strong an attribute that helps reduce body flex and thereby lessen interior creaks and rattles. The information, specification, engines and colors on this website are based on European specifications and may vary from market to market and are subject to change without notice. The 2020 Land Rover Discovery offers all the luxury and off-road capability of the larger Range Rover line, but with a more modern chassis and more fuel-efficient engines. Some features may vary between optional and standard for different model year vehicles. Jaguar Land Rover Limited is constantly seeking ways to improve the specification, design and production of its vehicles, parts, options and/or accessories and alterations take place continually, and we reserve the right to make changes without notice. This is a very dynamic situation, and as a result imagery used within the website at present may not fully reflect current specifications for features, options, trim and color schemes. Please contact your local authorized Land Rover Retailer for detailed specifications. The global shortages of semiconductors and other materials are currently affecting vehicle build specifications, option availability, and build timings. Important note on imagery & specifications. © 2023 Jaguar Land Rover North America, LLC SiriusXM, Pandora and all related logos are trademarks of Sirius XM Radio Inc. All fees, content and features are subject to change. ![]() Availability of some services and features is subject to device capabilities and location restrictions. Visit for most current service area information. Available in the 48 contiguous United States, D.C., and Puerto Rico (with coverage limits and capable receiver). See the SiriusXM Customer Agreement & Privacy Policy at for full terms and how to cancel, which includes online methods or calling 1-86. If you decide to continue service, the subscription plan chosen will automatically renew and be charged according to your chosen payment method at the then-current rates. 2020 2020 Land Rover Discovery Change year or car 52,300 starting MSRP 32 Shop Now Key specs Base trim shown SUV Body style 18 Combined MPG 7 Seating capacity 195.1 x 73 Dimensions. Your SiriusXM service will automatically stop at the end of your trial unless you decide to subscribe. Some features may not be available while driving.Īll SiriusXM services require a subscription, sold separately by SiriusXM after the trial period. *SiriusXM with 360L: Radio features, content, and display may vary by vehicle. While the 5.3L V8 found in our tester is perfectly serviceable, the approximately three-ton Tahoe should be fitted with the larger engine option. Article content Driving the 2023 Chevrolet Tahoe This advertisement has not loaded yet, but your article continues below. Chevrolet blamed its cancellation on flagging sales but this author thinks the powertrain ate voraciously into the truck’s profit margin and an embarrassing sojourn through corporate bankruptcy surely didn’t help matters. At present, there are no hybrid or electric options on any Tahoe trim, though an effort was made about 15 years ago in the form of a (very) mild hybrid which was offered for a short time. The only battery in this brute is a lead-acid lump under the hood which starts it in the morning. Third-row passengers are treated to 10 extra inches of legroom, meaning the Way Back is almost as roomy as the other rows and suitable for more than just children and Wizard of Oz extras. ![]() Overall cargo room is up 30 percent to a gargantuan 3,482 litres (123 cubic feet). New suspension geometry makes better use of interior room, contributing to nearly 26 feet of cargo space behind the third row – a measure up by two-thirds compared to the last-gen Tahoe. Article contentĪs for interior space, the Tahoe is virtually unchallenged in its category. Anyone navigating their condo’s underground car park will need to be mindful of posted clearance signs since the Tahoe stands 1.93 m tall (75.8 inches) and inches 2057 mm wide (81 inches, not including its elephant ear mirrors). For perspective, this full-size SUV is nearly five feet longer than a Mini Cooper and has more than two feet on the common Honda Civic found at every Canadian street corner. After its redesign a couple of model years ago, the Tahoe grew to an overall length of 5.35 metres (210.7 inches or 17.5 feet), making it the longest Tahoe ever built and one of the lengthiest new vehicles on the road today. ![]() The Tahoe Z71 on these digital pages purports to offer a dose of off-road swagger to accompany its handsome face and commodious cabin.īigger than ever, really. ![]() Consumer-grade examples of the Tahoe provide similar benefits for the proletariat and are offered in a range of trims from a cloth-upholstered base LS to zooty High Country. No way I'd do the whole season like that though. Turned out pretty great, but took an hour or 2. So I made English subtitles for E01, by machine translating existing German and Portuguese subs and using the 'original' German for reference. No English subtitles available for S04 of Rita (danish). Just in the last few days I've had these subtitle-related issues: I wish there was a site where you could put money towards english subs for things!! I guess judging the quality wouldn't be so easy etc. BBC or SBS shows non-english movies/series I guess. ![]() I imagine doing it will also get you really close to understanding how the movie is built up. the viewers may accept someone saying "fuck that", but seeing it written down "- Fuck that" feels awkward.Īnd that's probably also why people are doing it in their spare time, perhaps after having seen a bad job from the official movie. And there's also the issue of difference between spoken and written language, e.g. you can't translate a strong exclamation word into something too soft. Imagine also facing translation issues - where you not only are trying to roughly hit the same meaning and connotations, but also need to stay relatively close to the acting, e.g. Now what do you cut?Īnd this is just for subtitles in the same language. Sometimes, if it's a quick back and forth, you even have to leave out some of the dialogue. There's a limited space and time budget - people need to be able to read the thing without spending too much time focusing on it. Try writing subtitles yourself, and you'll probably see why. > Both are in English, so I don't see why they can't just transcribe what's being said. In many ways, correlation and covariance are more fundamental than convolution - they are closely and directly related to the inner product.Īnd the only reason to use the FFT here is convenience (i.e., it is fast and simple to compute), but the correlation/convolution property applies to many "transform domains" - Laplace, Z, Cosine, Sine, and a few others (all of which are closely related among themselves, but only a few easy to compute numerically). (I don't think 5 year olds heard of Pearson's correlation coefficient or convolutions, but. Which means, if you have an efficient way to compute convolutions (and you do, through FFT), you have an efficient way to compute correlations. Now, correlation is just like convolution except one series is flipped around on the time axis. What he is looking for is maximal correlation between two binary series (think "Pearson's r or r-square correlation coefficient"). It has nothing to do directly with FFT, which is why it is confusing: So finally to solve the problem, we get the pointwise product sequence S = fourier(videoSpeech) \* fourier(subtitle), do the inverse fourier transform on it invFourier(S), and maximize invFourier(S)(i) over i. ![]() It's relevant here because it "turns convolution into multiplication": fourier(videoSpeech)(i) \* fourier(subtitle)(i) = fourier(conv(videoSpeech, subtitle))(i). The discrete fourier transform is a function that takes a sequence and gives another sequence. So we can rephrase this problem as, find the index i which maximizes the value of the convolution sequence. Mathematically, conv(videoSpeech, subtitle)(i) = sum( videoSpeech(t)\* subtitle(t-i)). This is the definition of a convolution: the convolution of two sequences gives a new sequence where the value at index i is this sum above where one of the sequences is shifted by i. We can express the goodness of alignment as the number of matching 1's, aka the sum over all times t of videoSpeech(t) \* subtitle(t). ![]() We can imagine padding the sequences out on either side with 0's, and consider the alignment task as shifting the subtitle sequence left and right in time until we get the best alignment with the 1's in the videoSpeech sequence. We have the videoSpeech sequence, and the subtitle sequence - each is a vector, indexed by time, of 0's and 1's indicating whether there is speech in that time. Lets start by seeing how this is a convolution. (note that \* means multiplication, there doesnt seem to be a way to escape an asterisk) ELI5: You can turn this problem into finding the best "convolution index", and fourier transforms make computing convolutions cheaper. |
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