For active fun, take your kids to Bumblebee Play Cafe, one of the largest indoor playgrounds in the area. It has two separate play rooms for different age groups and features an indoor jump pad, a wave slide, a vertical tube climb, and a kiddie basketball court, just to name a few.
Who said rock climbing is just for the big boys? North Wall Rock Climbing Gym in Crystal Lake has a youth climbing club where kids from 5 to 12 years are taught proper climbing techniques. It's an activity that develops skills but also fosters camaraderie. Participants in a youth camp can also learn rappelling and slacklining.
This popular attraction takes fun to new heights—literally. The bounce park is a hit among kids. You can purchase tickets for open play, or book a specific area for children's parties. And if the tots get hungry, there are vendors of food and drinks.
This isn't technically a destination, as Gamin Ride offers a mobile video game theater that serves Huntley and nearby areas. But don't let that fool you – this game arcade on wheels has just about all the gaming consoles you can think of as well as a library of the latest games. They even have 4D-effect cinema screens, so you and your kids can enjoy a truly immersive gaming experience.
If you want to cool off with the kids, give this popular aquatic center a try. Stingray Bay Family Aquatic Center has large swimming pools, water slides, and diving boards for your young ones to enjoy. There's also a volleyball court in the facility if kids want to play out of water.
Donley's Wild West Town is an amusement park and museum rolled into one. Kids can pan for gold or use slingshots just like the people did in the 1800s. A museum clock is adorned with artifacts from the era, which helps young ones appreciate the culture and customs of the time. To cap off the experience, be sure to catch the live Wild West Stunt Show!
Unlike other zoos, this one allows kids to pet and feed the animals. Here, you'll see alpacas, goats, sheep, chickens, and pigs. More exotic creatures such as the great horned owl, foxes, and various reptiles can also be found in the zoo.
Do you want to live in this kid-friendly part of Illinois? Give us a call at 847.669.4010 or send an email to homes(at)huntleyrealty(dotted)com. Our team will help you find the perfect home here. When it comes to Huntley IL real estate, we are your best choice. More buyers and sellers have chosen to work with Huntley Realty than any other real estate office over the past 10 years.
Living in Covington Lakes means living closer to the reinvigorating beauty of nature. This enclave was built between 2006 and 2012 by renowned builder D.R. Horton in Huntley, one of the up-and-coming real estate markets in Illinois.
If you're looking for a single-family home or a townhouse where your family can enjoy expansive green spaces right in your backyard, here's an overview of the development.
As one would expect from a gated community, Covington Lakes offers plenty of space for you and your family. That's why single-family homes here often measure between 2,100 and 2,800 square feet, and typically feature 4 bedrooms and 2 or 3-car garages. Homes sit on lots of up to half an acre.
Properties also have an open floor plan that allows residents to customize the space as they see fit. If your family loves watching movies or cooking, you can make your living room or kitchen bigger to better suit your needs.
The community also offers townhouses that measure 1,350 to 1,546 square feet, with 2 to 3 bedrooms. These homes are ideal for empty nesters or as weekend homes.
It is often a community's amenities that bring neighbors together. Luckily, Covington Lakes offers a lot.
To begin with, the subdivision boasts 50 acres of natural, open space. Here you'll find picturesque ponds where kids can go fishing and a natural conservation area where you can hike or bike for hours. Parks, baseball fields, playgrounds, and picnic areas foster an outdoorsy lifestyle.
Covington Lakes is also close to top-notch schools such as Chesak and Martin Elementary, Marlowe Middle School, and Huntley High School. In fact, many kids just take a bike to school.
Looking to practice your golf swing? Head over to this 130-acre premier golf club that's home to an 18-hole championship course. The five lakes and lush environment make for a truly world-class golfing experience.
In the neighboring community of Lake in the Hills is this nature preserve. Walk its trails and go birdwatching. See if you can spot the great egret, the black-crowned night-heron, and the bluewing teal, just to name a few.
The nearby Deicke Park has charming duck ponds. Three play areas for kids – the so-called discovery zone, a tree house playground, and a sand volleyball pit – are popular. It's also a great place for concerts as well as Easter egg hunts.
Want to call Covington Lakes home? Let Huntley Realty help you find your dream house here. Just call 847.669.4010 or send an email to homes(at)huntleyrealty(dotted)com. When it comes to Huntley IL real estate, we are your best choice. More buyers and sellers have chosen to work with Huntley Realty than any other real estate office over the past 10 years.
Planning to stage your home is planning to have it sold soon. But before you pour time and money into making your home more desirable to buyers, be sure you avoid these common mistakes.
First impressions matter – and this is especially true when it comes to real estate. The first thing potential buyers see when they pull up to view your home is your front lawn. Make sure it's weeded, trimmed, and nicely landscaped – simple solutions guaranteed to make a good first impression. If your front yard is looking a bit worse for wear, get it back to shape ASAP.
Beware of decor and accessories that may turn off buyers. As much as possible, depersonalize the space so it becomes easier for prospects to imagine living in your home. This means personal knick-knacks, family photos, and quirky furniture are best left to storage.
In relation to the above, make sure that your home sticks to a neutral color palette. While you may love the lime green walls of your dining area, other buyers might find the hue too overpowering. Note that color should draw the eye, not overwhelm it—especially in homes that are for sale.
No one likes walking into a cluttered home, especially home buyers. A messy space gives the impression that the current owners are slovenly and don't take good care of their property. Don't let buyers use the mess in your home as a bargaining chip to lowball you. Before showing your home, tidy up. Rid rooms of items that don't belong there like toys cluttering up the kitchen counter; or an exercise machine in the living room.
Good artwork is like fine jewelry: the less you wear, the more it shines. So while it might be tempting to bedeck your home with all the artwork you own, this will only serve to distract the eye. Display art pieces judiciously.
Of course, it's not just what people see in your home that matters—what they smell or don't smell matters a lot, too. Any unpleasant smell must be addressed directly instead of being masked with scented candles and air fresheners. An overly fragrant home will only raise suspicion.
You may think revamping your pool will attract more buyers, but the upkeep of such an amenity might actually drive prospects away. If you do want to renovate your home to make it more attractive, focus on oft-used areas such as the kitchen, bathroom, or bedroom.
Don't assume that successful staging means breaking the bank. Sometimes, even small, cosmetic changes can make your abode look and feel brand new. These include tweaks such as repainting walls, replacing your front door, or installing new lighting.
Need help staging and selling your home? Get in touch with Huntley Realty today by calling 847.669.4010 or sending an email to homes(at)huntleyrealty(dotted)com. When it comes to Huntley IL real estate, we are your best choice. More buyers and sellers have chosen to work with Huntley Realty than any other real estate office over the past 10 years.
Huntley, IL is an ideal suburban community in Northwest Chicago where you can enjoy a tranquil and relaxing lifestyle, along with urban comforts and conveniences. Whether you're a young family, a single professional, or a retiree, you will never run out of things to see and do in the village.
If you love golf, you'll find excellent golf courses just minutes away from where you live. With plenty of wide open spaces and a lush landscape, Huntley is the perfect place to enjoy a day of golf. And even in the winter, you can still indulge in a game or two at a topnotch indoor golf venue.
Check out these places where you can get your golf game on.
Managed by the Huntley Park District, Pinecrest Golf Club features an 18-hole championship golf course that's open to the public, with special discounted rates for Huntley residents.
Built in the early 1970s, the golf course has undergone several renovations and now features five lakes, 63 bunkers, and numerous mature trees that add extra challenge to the game. The facilities include a grass tee driving range, as well as practice greens and sand area. PGA-trained instructors are on hand, and rental carts and clubs are available.
Pinecrest is home to several leagues that organize tournaments and events where members can get together. The beautiful clubhouse has a patio overlooking the 18th green and 10th tee, and includes a fully-stocked pro shop, a restaurant, and a banquet hall that can seat up to 180 guests. The restaurant and banquet hall may be rented for weddings and other private events.
Whisper Creek boasts a highly-rated public golf course built in 2000, with Billy Casper and Greg Nash as architects. While having a distinctly prairie feel, Whisper Creek is a link-style golf course that offers a challenging game for players of all skill levels.
Whisper Creek is a certified Audubon International Cooperative Sanctuary, incorporating protected wetland habitats and native trees and grasses. The picturesque surroundings make golfing here not only challenging but relaxing and pleasurable as well.
The club's practice facility includes both natural and synthetic turf, with 24 hitting bays and a practice putting green.
The prairie-inspired clubhouse has an outdoor seating area and a fully-stocked pro shop. One of the club's unique offerings is the Golfboard – a golf cart designed like a skateboard or a surfboard to add to your golfing fun.
Just because it's snowing or raining outside doesn't mean you can't indulge in a round or two of golf. Tee 2 Green offers a great way to enjoy golf in any season. It has six high-tech golf game simulators featuring 85 golf courses, and come complete with full swing analysis and training and practice modes.
More than just an indoor golf venue, Tee 2 Green is also a sports bar where guests can enjoy great food, a full bar and other games, such as pool, indoor bags, darts, video poker, and more. The facility may also be rented for private events.
Explore your real estate options in Huntley and enjoy a great lifestyle. Contact Huntley Realty here or call 847-669-4010.
Wing Pointe is one of the most sought-after subdivisions in Huntley, IL – and for many good reasons. This peaceful neighborhood boasts beautiful homes, immaculate landscaping, fantastic amenities, and a great location. It has everything you can ask for in a family-friendly community where you can raise your kids in a nurturing environment.
Wing Pointe was developed by The Kirk Corporation in the early 2000s, with homes built from 1999 to 2005. It's one of the most established neighborhoods in Huntley, IL, with property values that have been consistently rising since the recession. Homes for sale in Wing Pointe do not stay on the market for long as buyers are quick to grab the chance to own property here.
Wing Pointe features single family homes with 8 floor plan options and a townhome community called Townes of Wing Pointe. There are 460 single-family homes and 150 townhome units.
The single-family homes in Wing Pointe range in size from 1,207 square feet to 2,659 square feet, with 2 to 4 bedrooms. Home features include a 2- or 3-car garage, finished or semi-finished basements, a large kitchen, a loft, and the much desired open floor plan. Properties come with a large yard, and many have a patio where residents can relax and enjoy the lush green surroundings.
The townhomes at Townes of Wing Pointe range in size from 1,248 square feet to 1,583 square feet. They come with 2 to 3 bedrooms, or 2 bedrooms with a loft that can be converted into another bedroom. These homes feature open floor plans, large kitchens, and the finest finishes.
Wing Pointe is a cozy, self-sufficient community where everything you need is just within walking distance or a quick drive away.
At the northern border of the neighborhood is a small shopping center where you can get dinner at Whichos Tacos or pick up last minute items for your outdoor party at Huntley Food and Liquor. You can also get a quick summer tan at LA Tan, and hours of pampering and grooming at Lotus Spa Nails and Split Ends Hair and Spa.
If you love to shop, Algonquin Commons is the place to go in Huntley. Located less than 5 miles from Wing Pointe, this upscale outdoor mall features top clothing and accessories brands, furniture and home furnishing stores, a grocery store, and many more.
Less than 10 minutes from Wing Pointe, this favorite local destination features water slides, a water play area, competition swim lanes, a café, and more.
This 18-hole championship course is open to the public, with special discounts given to Huntley residents. It also features an excellent restaurant and venues for weddings and other events.
Is Wing Pointe the right neighborhood for you? Learn about your real estate options here. Get in touch with Huntley Realty at this website or call 847-669-4010.
A home is probably the single biggest investment you'll make in life. You'd want to give it the best possible maintenance to ensure it retains its value for a long time and give you good profit when it comes time to sell.
Even with the best of care, however, there's no avoiding the need for repairs as your home gets exposed to the elements and normal wear and tear. The best thing to do is to identify the usual home repair needs and set aside a budget for them.
What are the most common home repairs?
Your HVAC system needs regular maintenance and caring to give you efficient heating and cooling. If your filters are dirty or the motor is in poor condition, the system will need to work harder – and this means higher utility bills. Additionally, the typical lifespan of an HVAC system is around 25 years, and at 15 years, it starts showing signs of wear and old age.
When your toilet tank drains and fills continuously or your faucet drips uncontrollably, it's best to call the plumber immediately to look for the root of the problem.
Of all the parts of your home, the roof is the most exposed to the elements – snow in the winter, the hot sun in the summer, wind, rain, and even pests and bugs. Regular inspections and maintenance are necessary to prevent damages from escalating and make your roof last a long time.
An aging drywall with peeling paint or scratches is an eyesore. Drywall damage can also indicate pests and termites. Maintenance and repairs are needed to keep your interior looking fresh and detect an infestation.
Adjust your budget if you have to spend on major repairs, including a roof replacement, installing a new window, furnace replacement, and others.
If you have the confidence, DIY a few minor repairs, such as re-caulking your bathroom tiles, painting the drywall, or replacing a faucet washer. If the work appears too difficult or dangerous, it's best to let the pros do it. Amateur attempts might worsen the damage, which could cost even more to repair.
Consider the age of your home's components. If your roof is more than 20 years old or if your HVAC just turned 20, you will likely need more repairs and maintenance, or even a complete replacement soon. Adjust your budget accordingly and prioritize these major repairs.
If you're looking to sell a home in Huntley, IL, Huntley Realty can help you get top dollar for it. Contact them here or call 847-669-4010.


Murat Usanmaz was born in İstanbul, has been involved in playing guitar without any professional support.
Following his graduation from Guitar department of İstanbul University State Conservatory, he studied at the École Normale de Musıque de Paris.
Including many places in Turkey, he played in his concerts in China, Russia, Algeria, Germany, France, Spain, Finland, Italy, Turkmenistan.
Has been placed third at the international guitar contest of Paris prodige-art.
He made the world premiere of the piece 'Adiós Maestro' he wrote for Paco de Lucia on the concert tribute of Paco de Lucia on the International Guitar Festival of Sevilla.
Along his being the first musician who played the first guitar concert of Turkey by Cemal Reşit Ray Guitar Concerto he also gave live into the first performances of many pieces.
In addition to his TV programmes, he performed the several guitar concertos accompanied with various symphony orchestras.
He is playing as a soloist with many symphony orchestras and giving recitals.
He also gives concerts all over the world with his group 'Flamenco de Anadolucia' consisting of Turkish and Spanish musicians. They are playing his own music like a fusion flamenco, Turkish music and Latin jazz.


The 21st annual 2008 Chrysler Jeep Boomsday Festival is here once again, from noon until 10 p.m. Sunday on Neyland Drive and Volunteer Landing in downtown Knoxville.
At 9:30 p.m., watch the nation's largest Labor Day weekend fireworks show along with an original soundtrack provided by Star 102 FM.
The public is also encouraged to drop by participating Buddy's Bar-B-Q locations to pick up free Chrysler Jeep Boomsday Festival glasses with the purchase of a family pack, while supplies last. The glasses will provide viewers with a whole new, spectacular look of the fireworks show.
Admission is free to the public with nominal fees for parking, games, food and beverage. WBIR-TV Channel 10, will air the fireworks display in its entirety during a special one-hour live broadcast from 9 to 10 p.m. on Aug. 31.


Rotisserie chicken and a bottle of Oude Kriek lambic.
Once the holiday season is over, there's still something to look forward to this winter. The first Center City Restaurant Week of 2017 is quickly approaching.
The event will take place on Jan. 22-27 and Jan. 29 through Feb. 3.
During the two weeks, close to 125 Philly restaurants will offer three-course dinners for $35 per person. A few places also offer a three-course lunch special for $20 per person.
The full list of participating restaurants can be found here.
Most reservations can be made through OpenTable. Spots tend to fill up quickly, so booking early is recommended.


Why Tender Evaluator Qualifications are like Driving Licences … 100 years ago!
In the First World War, there were no driving tests. Anyone could drive any vehicle and were assumed competent just because they had done it before. They didn't even need to prove they knew the Road Code.
Today's Tender Evaluators are no different. They're responsible for decisions that spend millions of dollars of our taxpayer money, yet the vast majority have never had to prove their individual competence or their knowledge of procurement rules.
Even qualified Tender Evaluators have, until recently, gained certification primarily by producing a portfolio of work – much of which had been completed with, or even by, others in their procurement departments. The evidence only showed they were involved in procurement – with little focus on quality or individual work.
And because many candidates were required to follow legacy templates and/or instructions from their seniors and therefore had little control over decisions on the tools used, the portfolios did not provide clear evidence of their personal competence.
Getting the qualification took most people years. It was tedious, and it didn't necessarily guarantee that the graduate knew the rules of procurement or was personally and individually competent at the nuts and bolts of procurement – i.e. effective planning, putting together quality RFT documents, and carrying out sound and fair tender evaluations.
The new NZQA Tender Evaluator qualification is changing this. It's great news that the process of getting qualified is faster, more accessible, less tedious, and more robust than previously. And the qualification is valid for all of procurement, not just transport.
Instead of taking years to collate a portfolio of examples that may or may not be good ones, today's candidates can use scenarios for some of their work – so they can prove their individual competence without being hamstrung by legacy tools or hierarchical decisions.
They can move through the qualification at their own pace, fast-tracking if they want to – without having to gather a mountain of workplace examples (good, bad and indifferent), over several years. A couple of outstanding real-life examples, together with the scenario-based assignments, demonstrate they're up-to-speed with best practice far better than the previous methods.
Some of those who have signed up to the new Tender Evaluator Qualification are now close to graduation after just three or four months. They've cut down hundreds of hours of boring document collation into completing a few, sharply targeted assignments and answering questions on them to show-case their practical skills in tendering.
Warning – there will be complaints! This change will no doubt be frustrating for those who expect to have their Certificate handed to them as an honorary qualification (because, according to them, they have been doing this – not necessarily well – for years). However, it will be excellent news for the keenest, the brightest and the most motivated of our procurement professionals.
At last, there's a qualification that's merit-based, founded on demonstration of practical skills, and accessible to anyone with some experience in tendering who's prepared to show-case their individual best practice skills.
Graduates will need to show they can actively apply ethical tendering practices and Government's Rules of Sourcing. They'll need to plan procurement activities thoroughly and answer questions about their procurement activity (to make sure it's their own work). Assessment is now a combination of documented evidence, observation, interview and referee comments – not just centred around documented tender involvement.
If you're keen to get qualified, please drop me a line. I'd love to help you to fast-track your NZQA Level 6 Procurement Qualification so you're qualified for NZTA projects and other procurement contexts.


A continuing research program in medium- and high-energy gamma-ray astronomy focuses on increasing our knowledge of the nature and origin of Galactic and extragalactic gamma rays. The work includes instrument development, data analysis, and theoretical studies. Scientific research is in the fields of Galactic diffuse radiation, pulsars, gamma-ray bursts, solar flares, molecular clouds, normal galaxies, active galactic nuclei, and extragalactic diffuse radiation. The results will help us to understand high-energy processes in the Sun, in celestial objects, in the interstellar medium, and in extragalactic space.
The efforts currently concentrate on two projects. The first is participation in the Fermi Gamma-ray Space Telescope mission, involving an international collaboration of particle physicists and astrophysicists. We are involved with many aspects of the Fermi mission, including simulations, development of data analysis techniques, and science analysis. The second is the development of new instrumentation for gamma-ray astrophysics. This work has three thrusts: 1) the Advanced Energetic Pair Telescope (AdEPT) for gamma-ray polarimetery in the 2-200 MeV range. AdEPT is a large volume gaseous time projection chamber with high spatial resolution two-dimensional readout. It is optimized to measure gamma rays interacting via pair production at the highest achievable angular accuracy, limited by the undetectable nuclear recoil, 2) AMEGO, a combination Compton scattering and pair conversion instrument utilizing silicon strips. This instrument is similar in construction to the Fermi Large Area Telescope, but optimized for the 200 keV – 10 GeV energy range, and 3) BurstCube, a CubeSat designed to detect gamma-ray transients such as short gamma-ray bursts in the 10 keV to 1 MeV energy range using Cesium Iodide scintillators coupled to Silicon Photomultipliers.


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Mohylník Pod Chlumem je mohylové pohřebiště z doby lužické kultury z 1. tisíciletí před naším letopočtem nalézající se v lese na úbočí kopce Chlum na katastru obce Semechnice. Mohylník se skládá z 60 mohyl a jeho plocha je prostoupena několika mladšími plochými hroby slezskoplatěnické kultury.

Galerie

Externí odkazy

 bakalářská práce zmiňující mimo jiné i uvedený mohylník

Archeologické lokality v Královéhradeckém kraji
Semechnice

redpajama_set_name: RedPajamaWikipedia


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Egyptian lawyer sues Mohamed Ramadan over 'al-brince' TV series
Egypt IndependentApril 27, 2020
An Egyptian lawyer has filed a lawsuit with the Public Prosecutor against actor and singer Mohamed Ramadan, accusing him of insulting Egyptian values after Ramadan tore up an Egyptian passport on an episode of the TV series "al-brince" (The Prince) currently being broadcast.
In his case, lawyer Ayman Mahfouz said that "Ramadan is working to insult all the symbols of the Egyptian state without punishment."
He added that this scene disgraces the passport as a vital symbol of Egyptian patriotism, and that Ramadan is trying to destroy the values of the country which gave him everything.
Ramadan's action is punishable by a fine between LE10,000 – 30,000, the lawyer said, as it violates a law that forbids the publishing or display of scenes or imagery that could damage the country's reputation.
He explained that this law further punishes with imprisonment and a fine anyone who mocks the publish authorities or interest. The law permits the confiscation of any medium used to commit the crime, be it through art, writing or other methods.
Mahfouz demanded a speedy decision be carried out to punish Ramadan legally, in addition to halting the broadcast of "al-brince".
Egypt Egyptian Passport lawsuit Mohamed Ramadan Passport Ramadan drama

redpajama_set_name: RedPajamaCommonCrawl


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2022 Six Nations
Cronin cleared to play camogie final in ridiculous circumstances
Niall McIntyre
Orla Cronin is free to play in this Sunday's All-Ireland camogie final in nothing short of farcical circumstances.
A last minute and absolutely mind-boggling 'stay of suspension' means that, having failed in her appeal to the camogie association during the week, Cronin, who was red carded for striking Kilkenny's Grace Walsh in the semi-final, will now get her way because the DRA, basically, did not have enough time to make a decision.
That is no mis-print.
Some long-overdue joined-up thinking as Camogie association and GAA start working together
'The DRA has made no finding on the substantive appeal but has granted Orla interim relief to participate in the All Ireland Final today, Sunday 12th September,' was the official line of communication. At this level of competition, that for an explanation is beyond belief.
In effect, the 'interim relief' granted to Cronin means that, hypothetically, she could have committed the most blatant red card offence of all-time in the semi-final but because the appeals process was taken to its last avenue, she would have been set free to play anyway. When you consider that the semi-final was two weeks ago, when you consider that it was a clear red card, when you consider that the verdict was issued less than 24 hours before the game, this whole situation is just ridiculous.
"To miss an All-Ireland final for that is harsh."
Aoife Sheehan says Orla Cronin's sending off was a huge talking point from Cork's thrilling win over Kilkenny. #RTEGAA #TheSundayGame pic.twitter.com/Ft5t3YTD09
— The Sunday Game (@TheSundayGame) August 29, 2021
'An appeal was lodged with the Disputes Resolution Authority (DRA) by Cork player Orla Cronin against the decisions of the Camogie Association's disciplinary process, following a red card in the All Ireland semi-final.
An emergency DRA interim hearing took place on Saturday evening (11th September).
The DRA has made no finding on the substantive appeal but has granted Orla interim relief to participate in the All Ireland Final today, Sunday 12th September.'
Cronin will now probably miss the first three games of next year's national league in a case of the time most definitely being lighter than the crime. Two wrongs don't make a right but the fact that Galway's Emma Helebert should also be suspended for this final will give Cork a degree of justification but for the Camogie association, there could be no justification whatsoever.
Cork Camogie.
Jamie Heaslip delivers Jack Carty reality check, hours before Ireland call-up
Predicting Ireland's starting XV for Wales after Andy Farrell squad announcement
Australia confirms Novak Djokovic is banned from country for three years
"It's an elite level now. We always get fed. We get treated the same way as any county hurling team"
SportsJOE
Galway's energiser bunny gets up from the knocks to bring the O'Duffy Cup home
"Every player will now feel as if they can appeal a decision. It was a clear striking offence" - Jacob calls a spade a spade
Collins a walking example that no sub should be taken lightly
Dervan's ever-lasting commitment to Galway camogie an inspiring thing
Sigerson's striking a sight to behold


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Elemental Partners With PerkinElmer, Lands $9M in VC Bucks
Axsome's Depression Drug Meets Phase 3 Goals, FDA Filing Planned
Zafgen's Path Forward Is Reverse Merger With Chondrial Therapeutics
Bill Davenhall
Senior health advisor for Esri
Reinventing Our Visual World, Pixel By Pixel
Wade Roush
@soonishpodcast
Every week I come across news items, tech trends, and useful gadgets and services that I know Xconomy's readers would find interesting, but that don't fit with our usual lineup of hyperlocal news stories about Boston's innovation scene. To create an outlet for such random finds—and, frankly, to get me off Bob and Rebecca's backs about all the cool stories we're missing—we've decided to carve out a bit of space for articles that don't necessarily relate to New England. And here it is: my new weekly column, World Wide Wade. (Please pardon the goofy title, but it fits with my intentions, which are that the column take a very wide, occasionally offbeat view of the technology world.)
On my first couple of outings I'm going to try to tie together a few projects and products relating to the reinvention of the visual Internet. I think we're in the early stages of a radical shift in the types of imagery and image-related tasks that are supported by the Web and software connected to the Web. Anyone who uses a digital camera or even a camera phone ought to be excited about this shift, which is going to make it possible to share, explore, and possibly even inhabit the digital images that we're all capturing in increasing numbers and at increasing resolution. In today's column, I'm going to talk mainly about tools for organizing and viewing still 2-D photographs. In a future column, I'll look at 3-D—and later on, perhaps, at video and animation, which are obviously undergoing their own revolutions.
Finding fun, convenient ways to organize and share our digital photos is a challenge that's been around since the advent of consumer-level digital photography a decade ago. This technology took a big step forward around 2004 with the emergence of Picasa, a snazzy and flexible photo album organizer, and Flickr, a photo sharing service that introduced great social features like photo annotation and tagging. (Picasa eventually became a Google product and Flickr was snatched up by Yahoo.) After that, the new ideas seemed to peter out for a few years. But finally we're starting to see some innovation again.
In fact, I saw some Wednesday night at the Web Innovators Group meeting in Cambridge, where one of the presentations was from Brookline, MA-based Raizlabs, maker of a handsome—indeed, almost too pretty for Windows—PC photo organizing application called PicMe. The freely downloadable software has too many features to list here, so I'll only describe two. First is its beautifully intuitive method of organizing your photos into 3-D stacks, with each stack representing a folder on your hard drive. You can flip through the photos in a given stack using forward and backward arrows, or inspect rows of stacks by scrolling past them in 3-D, as if you were flying over skyscrapers in Manhattan. It's a very nice way to browse through a big photo collection, and is a bit reminiscent of other recent interface innovations such as the Cover Flow feature on iPods and iPhones.
The other nice thing about PicMe is its drag-and-drop method for sharing photos: if you want to e-mail a photo to your mom, just drag it off a stack and drop it on her entry in the contact list on the PicMe screen's left side. If you want to upload a photo (or a whole stack) to your Flickr, Facebook, or MySpace account, just drop it on that entry.
What PicMe demonstrates is that the interface makes all the difference. If you usually upload photos straight from your digital camera into folders on Windows, chances are slim that you're going to go back and lovingly review them later using the clunky Windows Explorer thumbnail display (or even the Finder application on Mac OS X, which is almost as bad). But if your computer can turn your pictures into objects you can almost hold and slide around as if they were 5×7 prints on a big table—or send off to others as easily as if you were slipping them into a mailbox—you're much more likely to enjoy the task. You're probably going to rediscover old photos you'd forgotten about, or decide to share pictures on a whim with others who might enjoy them.
I'm just as excited about two other image-exploration applications called Seadragon and Photosynth, though neither is yet available to use with your personal images, as PicMe is. Both are projects at Microsoft Live Labs, a division of the software giant devoted to building innovative Internet-based software. Seadragon is an interface for zooming in and out on visual information of all sorts, from photographs to entire Web pages, across a huge range of scales and resolutions. Imagine, for example, being able to see an entire edition of a newspaper in a single glance, then have the option of zooming in on just one page, or just one article, or a few lines of text in an advertisement—or even an entire microfilm-like product catalog embedded in that ad.
Or imagine seeing all of your photos in one big spread, and being able to zoom in instantly on any individual photo—or theoretically even further, exploring the world reflected in every raindrop. When you're not dealing with images on physical paper, after all, there's no reason for a limit on how much you can zoom in or out. And that's the whole premise of Seadragon: that our computer interfaces should flexibly scale visual material so that we can browse it at any desired level of detail.
Photosynth, meanwhile, is an interface that's built on SeaDragon but is designed specifically for correlating large groups of photographs into simulated 3-D environments, which then become the interfaces for exploring the individual photos. It's so mind-blowingly cool that I'm going to have to put off a real description until a future column, where I'll have more space to talk about the blurring boundary between still 2-D photography and virtual 3-D environments. In the meantime, if you're interested you should really just go and watch this demo from the May 2007 TED Conference in Monterey, CA. You can also download a preview version of Photosynth (Windows only).
I can't close without mentioning one more imaging project that pushes the boundaries of scale, resolution, and zooming. It's the Gigapan project, which allows people with consumer-grade digital cameras to contribute to a growing collection ultra-high-resolution, 360-degree panoramic images taken at locations around the planet. The trick to making one of these images is to attach a camera to a robotic, tripod-mounted pan-and-tilt drive that precisely aligns it for a series of dozens or hundreds of photographs, then use special software to stitch the images together into giant "gigapixel" panoramas. You can browse some of these images at www.gigapan.org, and for an even more immersive experience, you can see the photographic panoramas overlaid upon their real locations inside Google Earth (a free, downloadable 3-D map browser for Mac and Windows).
It's hard to convey in words the personal excitement I feel when I'm able to use tools like PicMe, Photosynth, or the Gigapan browser to explore photo collections. Such tools liberate our digital photos from the computer folders where they've been languishing and make them into objects we can scrutinize, play with, and redeploy in hundreds of different ways. But then again, I'm someone who tends to feel about my photographs the way Amerigo Vespucci probably did about his maps, or Giambattista Bodoni about his typefaces. Welcome to my world.
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Wade Roush is a freelance science and technology journalist and the producer and host of the podcast Soonish. Follow @soonishpodcast
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3 responses to "Reinventing Our Visual World, Pixel By Pixel"
David Cutler says:
This is great. I look forward to seeing what fun stuff people suggest you write about.
Hey didn't Al Gore invent the World Wide Wade?
I saw the PicMe presentation at WebInno as well and was pretty amazed at the interface that you called: "almost too pretty for Windows". I was even more impressed at the quickness of the client app – I haven't seen something that snappy and quick, that is that visually heavy, well… ever.
Also, the way it addresses a digital file as an almost physical item- seems intuitive and simple- I think it's fair to say that the cover-flow concept is revolutionizing UI.
And the reason I wanted to write in: This is a great idea for a weekly section!


WASHINGTON D.C. - The Capital City Go-Go (17-11) earned their second win in as many games against the Grand Rapids Drive (12-16) at home on Friday night by a final score of 115-106. The Go-Go sealed the win with a scoring flurry late in the fourth quarter.
Dakarai Allen scored 21 points for the Drive, leading them in scoring for the first time this season. Speedy Smith added 18 points and seven rebounds for the visitors, who had eight players register at least six points with leading scorer Marcus Thornton sitting the game out due to a rest day. Jon Horford led the team with nine rebounds off the bench and five players registered at least two assists.
Isaiah Whitehead also chipped in 15 points for Grand Rapids and Todd Withers scored 14, continuing his recent stretch of shooting well from three-point range by going 4-of-6 from downtown.
For the first time this season, the Drive did not register a blocked shot as the Go-Go were persistent in the paint.
The Go-Go were very efficient offensively throughout the game, shooting over 50 percent from the floor and 44 percent from three-point range. Their free throw shooting also played a big part in clinching the victory down the stretch, as they knocked down over 20 of them. The Drive hit as many three-pointers as Capital City managed, but they took almost 10 more attempts to get to their total of 14.
The two teams will rematch in their next action on Sunday afternoon, still on the Go-Go's home court. The action will begin at 3 p.m. EST.


text:
Barrett hails gutsy Manly after Storm upset
Andrew Marmont NRL.com Reporter
Manly Sea Eagles coach Trent Barrett has hailed his side's determination and resilience after the 24-4 win over Melbourne in an explosive clash at AAMI Park.
The fiery encounter spilled over in the 52nd minute when Storm centre Curtis Scott was sent off for punching Dylan Walker.
Walker was sent to the bin for his part in the fight, as was team-mate Api Koroisau.
Manly lock Jake Trbojevic and Storm winger Josh Addo-Carr also had stints in the bin for professional fouls.
Barrett's side kept their cool despite being down to 11 men in the second half to come away with just their second-ever win at AAMI Park.
"It was a really good win for us," Barrett said.
"It's always really difficult to come to Melbourne and get two points. The last three weeks I've been really happy. I thought we put ourselves in the frame in the last three weeks and got the points against Brisbane and Melbourne.
"To come to Melbourne is a huge effort by our young team. It's the first time a few of them have had a win down here. It was really tough. We had some circumstances thrown at us in that game - down to eleven at one stage - and our blokes handled it really well."
Skipper Daly Cherry-Evans, who laid on tries for Matthew Wright and Tom Trbojevic with grubber kicks, said the team hasn't done anything different apart from trusting their training and methods.
"Outside of the results, not really," he said.
"We trained hard even when we were losing. As Baz mentioned, we were really close against the Knights and then the Roosters. I've felt like we've applied ourselves at training and really bought into the coach's game plans. Over the last couple of weeks, we've executed it perfectly.
"We're starting to build some confidence within our squad. Off the back of that, hopefully keep continue the momentum."
Wright's try early in the second half - where he refused to give up on the chase and touched down inches inside the dead-ball line - typified Manly's effort.
"We're lucky we have a winger that's very good, very instinctive," Cherry-Evans said.
"It was a very big moment and certainly gave us confidence."
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You were in the lair, enjoying the peace that was there. You were reading peacefully. It was nice. Mikey was watching TV not far away and Donnie was in his lab. Raph and Leo were training in the dojo. You let your mind drift from the book you were reading. You thought about the dream you'd had not long ago. It was a nice dream of you and Raph. He'd taken you to the docks at sunset and asked you out there. Of course, you'd said yes. You sighed, wishing you had the courage to confess to him, but you were too afraid of messing up your friendship and making it awkward between you both. You sighed and kept reading your book. Suddenly you heard yelling coming from the dojo. Another than the TV still playing, everything went quiet.
"What was that?" Mikey asked. Donnie came out of his lab.
"What's going on?" He asked.
"I dunno. I'm going to check it out." You said and went toward the dojo. They followed you and you all peeked in. Leo and Raph were fighting, but they were also yelling at each other. Splinter just watched them with a saddened look, allowing them to fight.
"You think you can do everything! Just because your leader doesn't mean you're always right!" Raph yelled.
"I never said that! You're just jealous that I am the leader!" Leo snapped. You were shocked. Donnie and Mikey looked worried too.
"Oh boy." Donnie said worriedly.
"Not this again dudes!" Mikey said to the two of you.
"I would never get jealous of someone like you!" Raph growled.
"Of course you wouldn't! You're too 'strong' for that kind of thing aren't you?" Leo mocked. You were shocked. Leo never did that. This was getting serious. The boys continued to fight each other and Raph lashed out angrily at him. You were stunned as you saw they weren't sparring anymore. They were hurting each other!
"I'm stronger than you!" Raph snapped, his rage boiling over.
"Strength isn't everything! You just want to be on top!" Leo said.
"Like you don't!?" You'd had enough. Not caring if you got hurt, you intervened. Just as Raph was about to hit Leo you jumped in the way. You yelp as you got hit and fell backward.
"(Y/n)!" Leo exclaimed, catching you. Raph looked shocked and afraid.
"I-I didn't mean to!" He said, panicking slightly. Leo glared at him.
"Looks like somebody lost control, again." He growled. Mikey and Donnie just avoided eye contact with Raph and stayed out of it. Splinter seemed interested in where this would go. His eyes were locked on you. You didn't notice. You just glared at Leo.
"Let go." You hissed. He looked surprised, but did as you told. You looked over both of them. Leo's lip was bleeding and he had a bruise on his arm. Raph had a cut on his arm that as bleeding and a bruise to the right under his chin. You saw guilt n his gaze and he growled angrily at himself before taking off out of the lair. You looked at Splinter and he nodded. You hurried after him. You quickly tried to catch up to him. "Raph! Wait!" You called. He stopped and spotted you. He turned away, holding his bleeding arm in one hand.
"Why are you here?" He asked. He didn't sound angry. He sounded sad and was talking quieter.
"I want to make sure you're okay." You said. He turned away again, looking guilty like before.
"Just go back." He said.
"Raph, I wanna help." You said.
"Why? After I..." You frowned. You walked over and looked at his arm.
"Come back with me. I can help you with your arm." You said.
"It's not that bad." He muttered sadly.
"It's enough to need some treatment." You replied.
"(Y/n) why are you trying to help me?" He asked.
"Because I care about you." You said like it was the most obvious thing in the world.
"But I hurt you." He said, his voice having an angry edge to it. You knew it wasn't directed at you. He was mad at himself.
"I'm fine, you aren't." You said. He looked at you somewhat confused.
"I don't understand you." He said.
"You don't have to understand it. I still care about you." You said. "What started it?" You asked. He sighed.
"I lost and lashed out at Leo....again." He muttered the 'again'. You frowned sympathetically at him.
"You wanted to win right?" You said. He growled in annoyance.
"Yes! But it's not just that! It never is! I just-ugh!" He snapped, turning away from you again. You sighed. "They just don't get it." He said.
"I know." You said. He turned stunned.
'I understand why you always do that." You said.
"You want to prove yourself." He looked at you shocked. "You feel like you have to prove yourself. Nobody likes being wrong Raph. Nobody likes being beaten. Some just handle it better than others." You said. You hugged him. He hugged back after a moment.
"You don't have to prove yourself to anyone Raphael." You said. "And winning isn't everything. Nobody does perfectly at anything. No matter how many times you win or lose, you're just as important. And no matter what, I'll be here for you." You said. He stared at you. He smiled.
"Thanks." He said. You smiled.
"Let's get back okay?" You said.
"Not yet." He said. "I would rather nobody be watching when I do this." Before you could say anything, he smashed his lips into yours. You were shocked, but you let him lead as you kissed back. It was short and sweet, but it was perfect. When he broke it he was smiling like an idiot. "H-heh. I-I didn't think you would-"
"Shut up and kiss me again." You said. He was shocked. He grinned.
"Anything for my girl." He quickly pulled you in closer and kissed you again, more roughly this time. Your arms wrapped around him and you gladly kissed back with just as much affection. He deepened the kiss and you grinned a bit as he played with your tongue. Your grip tightened a little and so did his. He broke it and said, "I love you." before quickly diving back into the kiss. You felt your heart speed up and your body was tingling with excitement. When it broke you smiled.
"I love you too." You replied. He held you close to him and pecked your cheek.
"Ya shoulda told me sooner sweetheart." He said. You blushed.
"I didn't know how you felt." You replied.
"Heh, same here." He replied. You smiled and hugged him. "So...I guess were dating then?" You chuckled.


Hi everyone, just want to know is there any free tool that I can use to transfer videos, music, photos, etc from my iPhone or iPod to my PC for backup? I do not want to delete the files on my iOS devices, but they have no any spare space to add the new media contents?
I bought a new laptop and I want to make a backup on transferring my music from iPhone to PC, but I don't know how to do it, please help me.
As is known to all, iPhone works not only as a phone to call somebody, but also it is a great media player with a good quality of sound, and iPhone users can download or enjoy music in iTunes or the other third party music app. Meanwhile, the users are very interested in making some music collection to share with their friends, the music is extremely important for them, and perhaps hundreds of music downloaded on their iPhone, so if you get your iPhone lost or all the music files have been gone after a crash of your iPhone, somehow it means that you need to spend a lot of time to research in the music app. Therefore, backup music from iPhone to PC has become more and more important cause you don't know if you might encounter the bad situation like losing data in your iPhone life. Thus, in this article, we'll recommend you a world's first completely free iPhone data transfer software - EaseUS MobiMover, which supports to transfer everything from iPhone to the computer, and sync files from computer to your iPhone and vice versa. Please follow the steps below to have a try.
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text:
// typeinfo/SnowRemovalRobot.java
// (c)2017 MindView LLC: see Copyright.txt
// We make no guarantees that this code is fit for any purpose.
// Visit http://OnJava8.com for more book information.
import java.util.*;

public class SnowRemovalRobot implements Robot {
  private String name;
  public SnowRemovalRobot(String name) {
    this.name = name;
  }
  @Override
  public String name() { return name; }
  @Override
  public String model() { return "SnowBot Series 11"; }
  private List<Operation> ops = Arrays.asList(
    new Operation(
      () -> name + " can shovel snow",
      () -> System.out.println(
        name + " shoveling snow")),
    new Operation(
      () -> name + " can chip ice",
      () -> System.out.println(name + " chipping ice")),
    new Operation(
      () -> name + " can clear the roof",
      () -> System.out.println(
        name + " clearing roof")));
  public List<Operation> operations() { return ops; }
  public static void main(String[] args) {
    Robot.test(new SnowRemovalRobot("Slusher"));
  }
}
/* Output:
Robot name: Slusher
Robot model: SnowBot Series 11
Slusher can shovel snow
Slusher shoveling snow
Slusher can chip ice
Slusher chipping ice
Slusher can clear the roof
Slusher clearing roof
*/

redpajama_set_name: RedPajamaGithub


The machine includes an immersion blender and a. or getting too hot and burning off the THC, this unit does it perfectly. And unlike the stovetop method of pot infusion, the Magical Butter Machine.
It's the first time I've dipped my toe into the 'cooking with beans' pool and I'm kicking myself for putting it off for so long! We were seriously blown away by these Peanut Butter & Chocolate Chickpea Cookie Bars. As I mentioned, they contain no butter, no flour, no refined sugar yet taste absolutely decadent and indulgent.
Inside Natali Leduc's studio space (a converted barn in North Saanich), the acrid smell of burning metal. you'll get a laugh," said Leduc. Burning Man, the famous desert festival held yearly in.
Rohit Nair tells you how to be a star in the kitchen – and a super-saver in the household – by rustling up stuff you'd normally have to run to the supermarket for Blenders are amazing. they're ripe.
So I never had smoke ever coming from a blender but my. Those black flakes are the flakes from the bottom or the attachment for the blade.
I have had my Black and Decker blender for two or three years. cooker spewing black smoke and the smell of electrical fire was filling the entire apartment.
The wind was blowing through Malibu's Decker Canyon on the day Millie Decker stepped out onto her back porch and heard the distant clatter of helicopters. Moments later, several wide-bellied prop.
I've had a burning smell before when using a cheap blender with a. and stripped, producing a burning smell and lots of little black pieces.
My blender when I use it produces a weird burnt plastic smell but there is no discernible damage or loss of function any ideas what this smell is.
So if your appliance is suddenly greeting you with a burning smell during. Another frequent cause of a pressure washer emitting a burning smell may be a.
Sony Pictures Entertainment said it will relocate a 1,150-square-foot double-decker trailer being used by Will Smith during filming of "Men in Black III" because of. about the eyesore — and the.
I purchased my Healthmaster Blender approximately 4 years ago. It was a lot of money. The very first time I used it there was a burning smell. So I reread all of. Within a few uses I noticed a.
What could cause a battery hedge trimmer to have white smoke come out of it?. A quick google search confirms that this can occur with Black & Decker hedge trimmers, although it does not appear to be wide spread. Because you didn't provide the model it isn't possible to give you a more specific reason why it has failed. There will be a.
Its throat had been slit, and it had just been dumped, rather unceremoniously, on the hard-packed black earth. chilli sauce. The smell of charred flesh drifted over from an enclosure of timber and.
Blender burning Smell ~ Don't burn out your Blender Motor when you are making Smoothies!! Tips on how to prevent your blender motor from burning out!
"There are days in the summer when the heat and the rush-hour fumes hang over the stationary black cabs and double-decker buses. "the smell hits you like a wall while you're still in your seat. A.
(Photo Credit: Gilles Bonugli Kali) For Burning Man 2018. immersion blender, food processor, etc. For that we purchased a 3.5kw propane generator and used up about 400 lbs of propane during the.
Read consumer reviews to see why people rate Black & Decker 2-Slice Toaster. I noticed was that the first few times I used it, there was a burning plastic smell.
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Jun 22, 2007 · We are in need of a new blender, our one right now has started to smell like the rubber is burning. We make smoothies every morning for breakfast, so we are looking for a blender that can crush ice and frozen fruit on a daily basis. My el cheapo black and decker blender does not blend the celery well at all. Nothing like a gross.
Absolutely no way your Instagram account doesn't have at least one highly posed photo of you holding a cup of black coffee over a pure white. in the process and sent off this horrible burning bin.
Utterly addictive, this bright and spicy salsa combines vine-ripened tomatoes, onions, garlic, Serrano chiles, cilantro and fresh lime. Unlike most salsas, which are raw, the vegetables in this recipe are roasted — a technique that intensifies the flavor of the tomatoes, mellows the onions and garlic, and adds a light touch of smokiness.
Get the best Pogen's Gingersnaps recipe on the ORIGINAL copycat website! Todd Wilbur shows you how to easily duplicate the taste of famous foods at home for less money than eating out.
The smell of. can have coarse, medium or fine grind. For my grinding purposes, I use a simple hand held grinder (Black-n-Decker) with blades. Coffee experts prefer using a burr grinder (it's on my.
Vacuum Repair: 3 Common Problems. Depending on the problem — like loss of suction or a burning smell while vacuuming — a simple fix could get your vacuum working again. (Photo by Katelin Kinney) Vacuum not working? Before you buy a new one, check for these common issues.
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Its throat had been slit, and it had just been dumped, rather unceremoniously, on the hard-packed black earth of the burning area at Atwemonom. thinks it's safe to eat bushmeat: "We don't think.
Published: 2017-11-22 | There can be several reasons why white smoke comes from your Philips Airfryer. Please find out here how we can help you.
My blender has a bit of black dust at the bottom after I use it, It wasn't long after the black dust began that it started making a burning smell.
A food blender is a popular and useful kitchen appliance. in the blender jar and trying to chop them with a low motor speed can cause the motor to burn out.
Some 170 people scrambled off an outbound British Airways jet today at the Las Vegas airport after an engine caught fire, sending 14 people to the hospital with injures mostly suffered escaping the.
Do this in a ventilated space if possible; depending on the oven, you'll smell fumes in the first. its internal temperature. The Black+Decker TO1332SBD 4-Slice Toaster Oven was the most.
Series that exist because of this rule Edit Advertising Edit. Some of the items sold by such catalogues as Skymall and The Bradford Exchange would never exist were it not for this trope. This editor's personal favorite is the wall-sculpture Night Flight.Depending on your point of view, it's either awesome on top of awesome or actually kind of impressive in terms of sheer ridiculousness.
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Buy BLACK+DECKER FusionBlade Set of 2 BPA-free Personal Blender Jars with. Motor almost immediately started giving off a burned plastic smell that.
"Do not buy the Black & Decker GT524 520w Electric." Written on: 11/07/2009 by hiitsphil (1 review written) Do not buy the Black & Decker GT524 520w Electric Hedge Trimmer, I used it twice third time burning smell and then dead BandQ wont replace as its a year old having purchased it last summer.
The stainless steel blade has two tips versus four on the best cheap blenders. The 48-ounce glass jar displays cup measurements along the side and can accommodate hot liquids. The lid has a 1-ounce removable cap for measuring and dribbling in ingredients.
This one from Black+Decker is a great option with. are swiftly becoming the new candle. They smell amazing, light up, and can be left running continuously for hours without worrying about burning.


text:
Q: How to to transform a String of Property Names into an object's Property Values Many of my classes have a DisplayName property using string interpolation, for example:
  DisplayName = $"{CutoutKind} {EdgeKind} {MaterialKind}";

where each element in {} is a class Property Name.
What I would like to do is to retrieve the String being interpolated from the database, something like
displayName = SomeFunction(StringFromDatabase, this);

Where StringFromDatabase is a variable, value set from the database,  = "{CutoutKind} {EdgeKind} {MaterialKind}"
However I want to do this without using reflection
Is there some different way of achieving what I want?

A: Doing this at runtime without using reflection would mean that a generic solution is not possible. You would have to write different method for each class you want to support. A very simple version:
static string SomeFunction(string format, MyClass instance)
{
    return format.Replace("{CutoutKind}", instance.CutoutKind.ToString())
                 .Replace("{EdgeKind}", instance.EdgeKind.ToString())
                 .Replace("{EdgeKind}", instance.MaterialKind.ToString());
}

Or a slightly more sophisticated version:
Dictionary<string, Func<MyClass, string>> propertyGetters =
    new Dictionary<string, Func<MyClass, string>>
    {
        { "CutoutKind", x => x.CutoutKind.ToString() }
        { "EdgeKind", x => x.EdgeKind.ToString() }
        { "EdgeKind", x => x.MaterialKind.ToString() }
    };

static string SomeFunction(string format, MyClass instance)
{
    return Regex.Replace(@"\{(\w+)\}",
        m => propertyGetters.HasKey(m.Groups[1].Value)
                 ? propertyGetters[m.Groups[1].Value](instance)
                 : m.Value;
}

But if you decide you don't want to have to write this kind of method for each class, here's a simple generic version using reflection:
static string SomeFunction<T>(string format, T instance)
{
    var propertyInfos = typeof(T)
        .GetProperties(BindingFlags.Public | BindingFlags.Instance)
        .ToDictionary(p => p.Name);
    return Regex.Replace(@"\{(\w+)\}",
        m => propertyInfos.HasKey(m.Groups[1].Value)
                 ? propertyInfos[m.Groups[1].Value].GetValue(instance, null)
                 : m.Value;
}

redpajama_set_name: RedPajamaStackExchange


text:
Ben Blum-Smith Mathematics January 9, 2010 July 19, 2010 12 Minutes
Happy New Year y'all! I'm looking forward to writing some real posts soon – this one's just for fun. (Maybe they all are?) My first effort at catching up on my blog reading was to read the last eight posts from f(t). Kate gives us a post on her favorite theorem, including the proof. It turns out to be Cantor's diagonal proof of the nondenumerability of the reals. I really enjoyed it and got excited to catalogue some of mine.
Here's a top-10 list. It's a little capricious. But I'll stand behind each of these theorems being amazing. They span a lot of levels, from early elementary school thru graduate level stuff. Partly, especially for the lower-level ones, I'm making a case that these guys deserve more respect than they typically get. Below the list I put some comments on each. I got kinda technical toward the end, and I feel a bit self-conscious about that. I'll be excited if you read any of this but definitely feel free to stop, and then give me sh*t about it, when I get too abstruse.
I. The commutativity of multiplication. (I'm not kidding. I think this is dope. More below.)
II. a÷b (division) = a/b (fraction)
III. The Pythagorean theorem.
IV. Every rational number has a terminating or repeating decimal expansion.
V. If a is a root of a polynomial p(x), then x-a divides p(x).
VI. The fundamental theorem of calculus.
VII. Every prime of the form 4n+1 is a sum of squares in exactly one way.
VIII. Every element of SOn is a composition of rotations in orthogonal planes.
IX. A function C->C that is analytic in a neighborhood has a convergent Taylor expansion equal to itself in that neighborhood.
X. The fundamental theorem of Galois theory.
I. The commutativity of multiplication
Most students and teachers I know treat this as so trivial and obvious that I must be some sort of ridiculous person to dignify it with the word "theorem." But seriously now. When they told you what 5×7 was, depending slightly on your teacher, it was something like "five 7's." (This is the language used by my first grade teacher Judy Lazrus. She was amazing, but this isn't especially an example of that.) 7+7+7+7+7. That means 7×5 is 5+5+5+5+5+5+5. Is it obvious that these are going to come out the same?
NO, it's NOT. Not even to me, and I've had a lot of time to get used to it. Certainly not to a six year old. There really is a theorem in here. If you've worked with kids who are first learning about multiplication, you know this.
A formal, utterly rigorous proof would begin with something like the Peano axioms and build up addition and then multiplication in a formal way from scratch. This is cool, but I have a different proof in mind. It's less formal; less "rigorous" by professional standards; however, it's the one that gives this theorem such import to me, it's totally convincing, and it's accessible to a six-year-old. You probably already know it; perhaps it's how you convinced yourself multiplication really is commutative way back when; but I think it deserves special attention.
Represent 5×7 as an array – five rows of 7 dots:
Now interchange the roles of the rows and columns. Instead of seeing the array as a stack of rows, one on top of the other, see it as a line of columns, side by side. Each column is formed with one dot from each row, so the size of each column equals the number of rows, while the number of dots in each row becomes the number of columns. 5 rows of 7 becomes 7 columns of 5. So 5×7 = 7×5. The same argument could be used with any pair of natural numbers: mxn = nxm.
Why am I making a big deal of this? Two reasons. One is that learning multiplication's commutativity is something that happens very early in a typical math education, and this is a chance for students who are just beginning their mathematical journey to have a taste of real mathematics – an elegant, powerful argument giving a totally convincing proof of an unexpected result. The other is that the particular method of proof here (interchanging rows and columns) is one with great power, whose usefulness extends well beyond high school. For example, this is the idea behind the proof of Burnside's formula in group theory, or the proof in number theory that the number of partitions of n with at most k parts equals the number with each part at most k, and many other advanced results. I love the idea of putting an idea of this vast power and scope into the hands of tiny children.
I can't back this one up quite as well – I don't even know how to state this claim in precise mathematical language, and I can't give you anything I would consider a proof. But I know there's something surprising in here because I've watched a lot of kids be surprised by it.
When I learned division in school, I learned that 10÷2 means the number of 2's that are needed to add up to 10. 10/2 means what you get if you accumulate ten halves. These are definitely not the same thing. In the former case, I am imagining stacking up 2's till I get to 10. The answer, five, is counting boxes of 2. I'm thinking about whole things, and the 5 is counting boxes of more than 1 whole thing. There's certainly no fraction anywhere in sight – everything is whole. In the latter, the 5 is constructed from gluing together 10 halves. When I imagine it I can still see the glue. Such a difference in visual images – why is the number coming out the same?
I think there are a lot of ways to get convinced, and unlike my first theorem I'm not attached to a specific argument. What I feel sure of is that as kids come to learn about division, and fractions, this identity deserves a lot of thought, and offers something to get excited about.
III. The Pythagorean theorem
You know it, y'all, this thing is amazing. I think the Pythagorean theorem is for many of us one of the great missed opportunities of our math education. Because most adults can recite it like a mantra but only a very few people (one is my former roommate Thierry – big ups to your middle school math teacher, Thierry!) recall it with any of the awe it deserves.
This is the earliest example I can think of in the curriculum of a really surprising connection between algebra and geometry. Somehow right-anglyness is precisely captured by sum-of-squaresiness and vice versa. Somehow "right triangle" is a geometrical picture, and "a^2+b^2=c^2" an algebraic description, of precisely the same underlying mathematical structure. I think that's amazing. I'm still not over it.
I have three favorite proofs:
a) Euclid's. Not very accessible to the kiddies but has the virtue of actually partitioning the square on the hypotenuse into two parts equal in area to the squares on the legs.
b) The one where you put four copies of the triangle inside a square of side length a+b and if you arrange them one way the remaining area is c^2 and if you arrange them another way it's a^2+b^2. Here's a picture.
c) The one where you draw an altitude from the hypotenuse, like this, and then work from the similarity of the three triangles.
There are a zillion other proofs. There are books and books. One I'm very excited about, by Bob & Ellen Kaplan (who wrote Out of the Labyrinth, which I was also very excited about), is called Hidden Harmonies: The Lives and Times of the Pythagorean Theorem and is due out in August. Part of what I love about this theorem is the amazing diversity in the ways it is proven.
Okay now I have to speed through the rest:
The awesome Larry Zimmerman says that a good math problem "has a future." Meaning that the ideas in the problem have a reach that extends to other problems, possibly to other whole domains of mathematics. My excitement about the proof of commutativity of multiplication, above, has to do with this. Likewise, this theorem. First of all, it's a handy characterization of rationals, and looks ahead in a natural way to interesting calculus-laden questions having to do with convergence of series, especially geometric series. But maybe even more important to me is the proof, which involves the division algorithm and the pigeonhole principle. Both of which spin off great showers of mathematical consequences…
One of which is this! The division algorithm generalizes in a natural way from the natural numbers…
b divided by a has a remainder less than a
…to polynomials (techically, polynomial rings over a field):
p(x) divided by q(x) has a remainder which is a polynomial of degree less than q.
Because of this, we get this awesome connection between the behavior of a polynomial as a function (for what x is p(x) equal to zero?) and its behavior as an object to be factored (what other polynomials divide p(x)?)
The converse is less startling to me – if x-a is a factor of p(x), then when x=a, x-a=0, so p(x)=0 at x=a. The interesting part is the result I stated – all we have to know is p(a)=0 to know x-a is a factor. And as I mentioned, this comes from the division algorithm:
p(x) / (x-a) has a remainder of degree lower than x-a – i.e. a constant.
So p(x) = (some polynomial)*(x-a) + const.
If p(a) = 0, then evaluating this equation at a gives
0 = (some polynomial, evaluated at a)*0 + const.
The constant must be 0, i.e. the remainder must be 0, i.e. x-a is a factor of p(x). Boom!
VI. The fundamental theorem of calculus
Oh my goodness. Don't even get me started. How am I trying to do this quickly? If the pythagorean theorem felt like it was connecting disparate realms (the geometry of a right angle and the algebra of a^2+b^2=c^2), the fundamental theorem of calculus is connecting disparate planets. If f tells you about g's speed, then g tells you about f's… area? WHAT??? I need to move on because I'm going to wax poetical all night long if I don't stop. This was the theorem that sealed the deal between me and math.
I have a thing for when you're confused about some question about really familiar, concrete objects and you eventually answer it by considering it in the broader context of really fanciful, crazy objects. All three of these theorems represent for me the wierd power of complex numbers and other crazy abstractions to answer questions that are about real numbers. (In the first case, natural numbers.)
There are proofs of Fermat's theorem about primes of the form 4n+1 being sums of squares that don't involve complex numbers, but the proof I relate to the most certainly does. I just wrote it out but then I realized that it is kind of technical so I'm putting it at the end as an appendix. I don't know if the theorem about SOn has proofs that don't involve complex numbers but the proof I know certainly and powerfully does. A sketch of it is at the end too.
The Taylor expansion is a slightly different but related story for me. It used to confuse me that functions like sin x and e^x are equal to their Taylor expansion everywhere, but then there is that funky example: f(x)=e^-(1/x^2) if x isn't 0 and f(x)=0 if x is 0
This function is continuous and differentiable for all real x. At x=0, it and all its derivatives are 0. So its Taylor expansion at 0 is identically 0. But the function itself is totally not 0 at all. What the hell?
Once again, broadening out into the complex plane explains everything. The function f(x) = e^-(1/x^2) isn't defined at x=0. When you're just looking at the real line, it looks like you can plug the hole with f(0)=0 and everything will be smooth and nice. But if you look at the whole complex plane, x=0 is an essential singularity of f. f's behavior in the neighborhood of 0 is actually completely bananas. They fooled us by only showing us a tiny, well-behaved slice when they showed us the real line. If a function is really continuous and differentiable in a whole complex neighborhood, it will equal its Taylor expansion there. Whew!
X. The fundamental theorem of Galois theory
I'm not even going to state this one. I could use avoiding the technicalities as an excuse, but the real reason is that I'm avoiding spoilers. The F. T. of G. T. is the punchline of an amazing mathematical journey. The way I learned it kind of killed it. The teacher stated it, showed us examples, and then spent a few classes proving it. Then, it was applied to the problem it had originally come into being to deal with (the insolubility of the quintic). I had been told the answer before I had asked the question, as it were. I feel a sense of loss that I never got to see it shimmering in the distance as I searched. This spring I'm teaching an informal course on group theory, hopefully culminating in Galois theory, for some teacher friends. I'm gonna do my darndest to bring out the fundamental theorem in an organic, motivated and natural way. I'll let you know how it goes.
Appendices:
Proof that an odd prime p is a sum of 2 squares if and only if p has the form 4n+1.
Let p be a prime. If p=a^2+b^2 then p factors in the ring of Gauss integers – it equals (a+bi)(a-bi). Likewise, the only way for p to factor in the ring of Gauss integers is (a+bi)(a-bi). (This is because if (a+bi) is a factor of p, say p=(a+bi)(c+di), then its conjugate (a-bi) is too, and (a+bi)*(a-bi) is a real factor of p^2, so it is 1, p or p^2. But if it were 1 or p^2, the factorization p=(a+bi)(c+di) would be trivial – in the first case, a+bi would be a unit, in the second case, c+di would. So if (a+bi) is really a nontrivial factor of p, then p=(a+bi)(a-bi).) So p is a sum of squares if and only if p stops being prime when you venture out into the ring of Gauss integers.
I.e. p is a sum of squares if and only if (p) is not a prime ideal of Z[x]/(x^2+1).
I.e. p is a sum of squares if and only if Z[x]/(x^2+1,p) is not an integral domain.
I.e. p is a sum of squares if and only if Fp[x]/(x^2+1) is not an integral domain.
I.e. p is a sum of squares if and only if x^2+1 factors in Fp[x].
I.e. p is a sum of squares if and only if -1 is a square in the field Fp.
Now the multiplicative group of Fp is cyclic and order p-1, and (if p>2) -1 has order 2 in this group, so if g is a generator for the group, -1=g^[(p-1)/2]. -1 is a square if and only if the exponent is even, i.e. if p-1 is a multiple of 4.
So if p is a prime >2, it is a sum of squares if and only if p-1 is a multiple of 4, in other words if p has the form 4n+1.
The uniqueness of the representation as a sum of two squares follows from the fact that Z[x]/(x^2+1) is a unique factorization domain, which comes from the fact that it has a Euclidean division algorithm (big ups to the division algorithm again!). Thus p only factors one way: p=a^2+b^2=(a+bi)(a-bi). If p=c^2+d^2 too, then p would =(c+di)(c-di) too, but this contradicts unique factorization.
Outline of proof that any element of SOn is a composition of rotations in orthogonal planes:
Take an element P of SOn and regard it as having complex entries, even though they're really real. Then P is unitary, so by the spectral theorem for unitary operators, it has an orthonormal basis of eigenvectors (which may be complex). The eigenvalues all have absolute value 1, their product is 1, and the complex ones come in conjugate pairs because P's entries, and hence the coefficients of its characteristic polynomial, are real. Consider the subspace A of C^n spanned by a pair of eigenvectors associated to a pair of conjugate eigenvalues. Then consider the subspace A' of A consisting of strictly real vectors (i.e. A' is A intersect R^n). A' is a plane, and the restriction of the action of P to A' is a rotation. (This step takes some doing.) Other similar subspaces constructed as A' was are all orthogonal to it since the basis of eigenvectors is orthonormal. If there are real eigenvalues, they are all 1 or pairs of -1s since the product of all eigenvalues is det P=1. Every pair of -1s gives a rotation thru pi in yet a new orthogonal plane, and the 1's represent fixed subspaces. Thus the net effect of P is a composition of orthogonal rotations.
One corollary is the amazing fact that the composition of two rotations in 3-space about completely different axes, is a rotation! This is a corollary because in 3-space there isn't room for 2 orthogonal planes – that would require 4 dimensions. So every element of SO3 is a rotation in a single plane. Since SO3, as a group, is closed, composing 2 rotations must give a new element of SO3 which must also be a rotation.
Published January 9, 2010 July 19, 2010
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14 thoughts on "Favorite Theorems"
Kate Nowak says:
I made it all the way to VII before I got lost! Do I get a 70?! I pass! Woo!
Incorporating a classroom proof for I. would require third grade teachers who don't pee their pants at the mention of the word "proof." I know they're out there. Just frightfully thin on the ground.
I'm always amazed at how II comes as a serious shock to kids in Algebra 2.
Now I need you to package up some of your enthusiasm and sell it on Amazon so I can buy some and take a hit on Wednesday mornings.
jd2718 says:
I'm calling II a definition.
Now, VII, I didn't know that, and it is cool. But aren't there a bunch of similar true statements?
I still like prime factorization being unique (down to order). Way underrated.
benblumsmith says:
Re: VII – yes, definitely. In a way it's just the solution of one very specific problem in diophantine analysis: for what p does x^2 + y^2 = p have a solution? You could just as well ask for what p does x^2+5y^2=p have a solution, or any number of similar or not-so-similar problems. Historically I think it was an early discovery in this family – I know it's attributed to Fermat. It stands out for me because the result feels simple and relevant to me – I care about primes and squares, and don't typically see them as all too related, so this relationship strikes me as deep and unexpected.
You know, uniqueness of factorization was on my first draft of the list and at the last second I replaced it with the one about rational numbers having repeating or terminating decimals. I love both those theorems as expressions of the power of the division algorithm.
Susan B. says:
A quite delectable one I discovered recently is an enumeration of the positive rationals in which each rational occurs exactly once, already expressed in lowest terms. I wish I could find the original paper–the authors really knew how to tell a story. They presented the method initially as the solution to an apparently unrelated problem.
Another favorite of mine is Urysohn's Lemma in point-set topology.
I guess the enumeration was more clever than just doing the usual diagonal thing and skipping the fractions not in lowest terms? (I.e. 1/1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 5/1, …?) If you find it I'd love the reference.
I've never studied Urysohn's lemma but its name rang a bell and I realized that I'd seen a painting about it by artist-mathematician Lun-Yi Tsai, who creates these awesome paintings of mathematical ideas.
Aha, found the link!
Click to access recounting.pdf
Yes, it is more elegant than the usual enumeration, in my opinion.
That painting is awesome!
Yes, that enumeration is gorgeous! I can't decide if my favorite part is the connection to the counting problem, or the (shockingly simple) proof that every reduced fraction occurs exactly once in the tree.
John A Arkansawyer says:
But nothing proved by induction. That seems a shame to me.
Mmmm… good point.
I think this might be because inductive proofs often feel… less explanatory, to me, somehow? Like, proving that the nth triangular number is n(n+1)/2 can be done via induction, with a straightforward computation:
Base case: 1(2)/2 = 1
Induction step: (n-1)(n-1+1)/2 + n = n(n+1)/2
(I vaguely remember doing this when I first learned what induction was.)
But this proof doesn't make me feel it. I'd prefer a more geometric argument (like cutting an n x (n+1) array of dots in half along a diagonal) or a more combinatorial one (count the number of handshakes possible among n+1 people in 2 ways: first person shakes n hands, next shakes n-1, …, so total shakes = n+(n-1)+…+1 = nth triangular number; or, all n+1 folks shake n hands, but this counts each shake two times, so total shakes = n(n+1)/2). I feel like I get more insight out of these arguments.
But this is fickle taste. Much props to induction's power and scope, which can't be denied. So, let me nominate another great theorem, which is proved by induction:
The Spectral Theorem from linear algebra.
José Hugo says:
I tried to find a way to explain to kids why the order in which two numbers are multiplied does not affect the result, and I found only that way good enough 😀
Other approach that I thought, but resigned to elaborate, was that:
5 x 3 = 3 + 3 + 3 + 3 + 3
3 x 5 = 5 + 5 + 5
as both the number of terms as the value of each term are different, it's not evident if the results are equal or not
but if one number is subtracted from the other and the difference is zero, then they are equal
we can use
3 + 3 + 3 + 3 + 3 – 5 = 2 + 2 + 2 + 2 + 2
5 + 5 + 5 – 3 = 4 + 4 + 4
in the first case:
3 + 3 + 3 + 3 + 3 – 5 – 5 – 5 = 0
so they are equal
But I think the rows and columns argument is much better.
By the way, very nice this post! Thanks for it.
Gregory says:
Concerning II. The easiest way I can think of to make this equality clear is to show that 1/n simply signifies a quantity wich taken n times equals 1. Then for every natural number k, k=k*1 = ((1/n)*n)*k = (1/n)*nk. Thus k contains nk such quantities, so k times more than 1. Thus 1/n is k-times smaller part of k, than it was of 1. So, to get n-th part of k we must multiply 1/n by k and we get k/n. It's just an exposition of the fact, that the same fraction of greater number is itself greater by the same coefficient (and vice versa). So, for example 5-th part of 7 is 7/5 (7 times greater than 5-th part of 1, which is 1/5).
The other way to show that m:n is the same as m/n might go like this. For case when mn. Sorry for my English.
The other way to show that m:n is the same as m/n might go like this. For case when m<n. Let a=m and b=n-m. We have 'a' quantities and want do distribute them into 'a+b' equal quantities. 'a+b' is greater than 'a', so clearly resulting quantities will be smaller than this at hand. What we have to do is to take from each initial quantity (there are 'a' of them) some part of it (the same from each), such that the sum of this parts divided by 'b' (number of "spots" we must "fill in"), would be equal to what's left from some our initial quantity after we took from it aforementioned part.
So, let 'k' be '1/b' of that supposed part. Then from our initial quantities we take sum of parts which equals 'a*(b*k)' and divide it between 'b' spots. So every spot is a quantity 'a*k' and – from assumption – equals every quantity which has left after we've substracted from initial quantities aforementioned parts. Before we did that every such quantity was greater by b*k, so it was a*k + b*k = (a+b)k. Our new quantities equal a*k. So "new" to "old" is: ak/(a+b)k = a/a+b = m/n.
In very similar way we could show that equality holds for m>n. Sorry for my English and many post (i looks like there is some limitation concerning number of signs in one post).
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DANNEMANN ET AL./AJHGWe humans may have our Neanderthal and Denisovan ancestors to thank for some innate immune genes, according to two studies published in The American Journal of Human Genetics this week (January 7). Two independent groups have found genomic evidence to suggest that present-day people inherited versions of several toll-like receptors (TLRs) that recognize pathogens through the interbreeding of human ancestors with Neanderthals and Denisovans.
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