text:
The Indigenous Experience of Australian Civil Society: Making Sense of Historic and Contemporary Institutions
Hart, Victor G., Thompson, Lester J., & Stedman, Terry (2008) The Indigenous Experience of Australian Civil Society: Making Sense of Historic and Contemporary Institutions. Social Alternatives, 27(1), pp. 52-57.
|PDF (56kB)
In order to protect future citizens from tyranny and to distribute the rewards of a perceived modern civilization, the architects of the Australian constitution sought to institutionalize such principles as liberty, individual rights and democracy. Once established, this Constitution also institutionalized a set of racist principles that have an ongoing impact on civil society in the 21st century. After progressing from its specific illiberal references to race, the Constitution permitted the historic development of government policy based upon certain European liberal ideological values which construct liberty as a white, free-market concept. Indigenous economic priorities have subsequently been perceived as values that must be deleted from society, and Australian policy objectives have been focused by this aim. This paper examines this historically grounded value system and its impact on certain contemporary policy directions. It considers the implications for Indigenous citizenship in Australia and implications for Indigenous citizens.
Impact and interest:
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text:
The Chesterfield Series
Corner Module
Item# NH-46B
Dimensions: 26" Wide x 26" Deep x 32" High
Armless Module
Item# NH-46A
Dimensions: 24" Wide x 26" Deep x 32" High
Item# NH-46C
Dimensions: 24" Wide x 24" Deep x 13" High
Coffee Table
Item# NH-46D
Dimensions: 47" Wide x 24" Deep x 18" High
Neoteric Luxury™ teak furniture is handmade using the highest quality reclaimed teak. Rest assured that the furniture may be left outside in even the harshest weather conditions. For cushions, Neoteric Luxury™ uses the finest quality flow-through outdoor foam and Sunbrella® outdoor fabrics. A wide variety of color choices are possible. Please refer to the "Materials" section for the entire selection of standard Sunbrella® fabric choices and teak finish options. Neoteric Luxury™ also offers customization of most items.
Please contact us with any questions:
305.438.2842 or firstname.lastname@example.com

subset: commoncrawl


text:
Hess Toy Trucks To Continue
While Hess is getting out of the gas station business and ridding itself of its energy trading and marketing businesses it is staying in the toy truck business.
"Following today's news, we want our fans to know that the Hess toy truck, which has been a tradition for 48 years, will continue," posted the company on its Hess Toy Truck Facebook page.
The new truck design is unveiled in the fall to great anticipation at Hess retail locations.
The Facebook post also sounded optimistic that Hess stations aren't closing anytime soon. "Our long-standing commitment to deliver secure supply, competitive prices, and industry-leading service to our customers will not change. Operated by great people, our businesses are strong, profitable and will be well situated for the future," posted Hess.
The oil company says it is shifting focus further into exploration and production. It's also nominating a slate of six independent directors to the company board, rejecting the nominees chosen by Elliott Management. The hedge fund is one of the Hess' largest shareholders and last month accused the board of "poor oversight," saying the company's management was responsible for more than a "decade of failures."
The company was not clear about the fate of its retail locations in today's announcement.
The Associated Press contributed to this story.


text:
The Deal
- $9 for one G-Pass to see the Charlotte Hounds take on the New York Lizards (an $18.50 value)
- When: Saturday, July 20, at 4 p.m.
- Where: American Legion Memorial Stadium
- Seating: Section 16, 21, or 22
- Door time: 3 p.m.
- Parking lots also open at 3 p.m. for tailgating.
- Ticket values include all fees.
- Click here to view the seating chart.

How G-Pass Works: Your G-Pass will be ready to print 48 hours after the deal ends. Print the G-Pass and use it to enter the venue directly; you won't need to redeem at will call. Due to security restrictions, G-Passes cannot be redeemed through the Groupon mobile app.
The Scouting Report
In a match-up that could carry playoff implications, the Hounds clash against the Lizards for the second time this season on July 20. The two lacrosse clubs first met on May 31, a nail-biter that saw the Hounds win in a 14-12 comeback behind a pair of fourth-quarter goals from Matt Danowski. Clutch performances from Danowski have become common. After finishing the 2012 season with the league's sixth-highest points total, the attackman has once again anchored the Hounds offense and is considered among the league's most potent scorers.
Charlotte Hounds
The Charlotte Hounds first introduced their style of slashing, hard-nosed lacrosse in 2012. One of two new Major League Lacrosse clubs that season, the Hounds pounced onto the Carolina sports scene to help the sport grow throughout the region. Prior to home games, crowds gather in the parking lots of American Legion Memorial Stadium to tailgate before heading inside. There, fans find themselves surrounded by history, as the venue was constructed in 1936. In fact, American Legion Memorial Stadium was the first municipal structure in Charlotte capable of accommodating thousands of visitors, and its first speaker was President Franklin D. Roosevelt.


text:
Stores »
A hurricane recipe calls for 1 oz of vodka. I decided to choose Grey Goose.
An ultra smooth vodka made from the purest water in France. It's clean finish makes Grey Goose a favorite at most martini bars.
We are a community of shoppers sharing our best finds from across the web.
© 2017 ThisNext, Inc. ThisNext is a member of BUZZMEDIA Entertainment, a division of BUZZMEDIA.


text:
Sensory-Based Support: Workshop for Parents of Children Birth to 5
Frank D. Lanterman Regional Center
Wednesday, June 11, 2014 from 9:30 AM to 11:30 AM (PDT)
Who's Going
San Francisco, California
London, United Kingdom
Florence, Italy
Event Details
As a parent, have you ever wondered…
- Why does my child move differently from other kids?
- Why does he spin around or bump into things?
- Why does he tune out or seem disturbed in certain environments?
- Why does his mood change rapidly or unpredictably?
- Why won't he touch or taste certain things?
These are all sensory-based struggles that many of our children face. Come attend a two-hour workshop with Katherine Abbey, M.A., OTR/L, Occupational Therapist, to learn more about the cause of some of these challenges as well as various strategies to help our children regulate their bodies and movements, and increase tolerance to sensitivities. Gain ideas you can incorporate in daily life and playtime with your child who is between the ages of birth to 5. There will be a PowerPoint, hands-on activities and discussion.
View flyer for more information
Contact the KYRC at 213.252.5600 or email@example.com for more information.
When & Where
Frank D. Lanterman Regional Center - KYRC Conference Room, First Floor
3303 Wilshire Blvd
Los Angeles,
Wednesday, June 11, 2014 from 9:30 AM to 11:30 AM (PDT)
Add to my calendar
Frank D. Lanterman Regional Center
Koch-Young Resource Center, 213.252.5600 or email@example.com


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Police search for 12 year old boy
COLUMBUS, Ohio (WTVN) --Columbus police are asking for the public's help in locating a 12 year old, considered a "high risk runaway".
Savian Eaton was last seen on Monday at his home in the 1300 block of Stoneridge Drive.
He's described as 5'4" tall, 111 pounds, last seen wearing a last seen wearing a white t-shirt and black & white plaid shorts.
Anyone with information on Savian is asked to call the Columbus Division of Police at 614-645-4545.


text:
Search by
YWCA Family Fun Day: Valentine's Day Event
This event has already taken place. Click here for the latest events.10-02-2013 12:00:00 10-02-2013 12:00:00 America/New_York YWCA Family Fun Day: Valentine's Day Event | 3-5pm Featuring activities like face painting, arts & crafts projects, carnival games, raffle and bake sales, plus, at 4pm, The Brett Band for Kids, an interactive concert that includes a mix of original and classic kids' songs. In the Lower Lounge. Tickets include an entrance to the show, a free pass for the Valentine's Day craft project, and a raffle ticket. Multiple ticket discounts are available. Proceeds will benefit the YWCA Programs and Scholarship fund. For more information or to purchase tickets, please contact firstname.lastname@example.com or call the Development Office at 914-949-6227 x127. http://www.nymetroparents.com/2015neweventinfo.cfm?id=125917 YWCA White Plains & Central Westchester YWCA White Plains & Central Westchester
If you go: Please tell them you saw this event on


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[Date Index]
[Thread Index]
[Author Index]
Re: 'Good' or 'Proper' Mathematica coding habits question
Just highlight whatever cells you want to copy, right click, and choose
copy as > cell expression. This is probably what you did already. The
only problem is making sure not to delete any parts of the cell
expression, such as the list that wraps the entire selection or the
CellGroup head, etc.


text:
Lending Library
We have been collecting a few books here and there and are excited to get our library inventory up on the website. Check it out and let us know if you want to borrow a book or have some good reading material lying around that you would like to donate to us.
I am expanding our library as we speak but here are a few of the titles we have available:
- Birthing Ourselves into Being, Baraka Elihu
- Get Me Out: A history of childbirth, Randi Epstein
- Ina May's Guide to Childbirth, Ina May Gaskin
- Birth Sense: A common-sense guide to planning your pregnancy and birth, Janelle Komorowski
- The VBAC Companion: The expectant mother's guide to vaginal birth after cesarean, Diana Korte
- The Birth Partner, Penny Simkin


text: Chicken BBQ July 28, 2013 | 1:00 pm - 4:00 pm Where Lake Delta Fire Department Additional Information There will be a Chicken BBQ Sunday July 28th from 1-4 at Lake Delta Fire Department on Elmer Hill Road in Rome. All proceeds benefit the Fire Department. Category: Food & Wine, Fundraising & Charity Share on Facebook Share on Twitter More Leave a comment Send to a friend! Print this page Pin it! Reddit This! Share on Tumblr! Discuss This Event


text:
Be White, Be Glowing, Be a White Chic!
WhiteChic is a hub for beauty enthusiast wanting to have fair, glowing, and healthy skin.
Effects of Using Glutathione
Helpful topics on what to expect on using injectable or oral glutathiones properly.
Real proofs of our friends and clients who are very satisfied with our products and service.
Contact us
We are eager to know you and answer any of your questions. We will be delighted to always get in touch with you.
What You Need to Know About Injectable Glutathiones
Glutathione is a naturally occurring chemical in the body mostly found in the liver, the eyes, spleen and pancreas. It can also be found in meat and vegetables. This antioxidant serves several functions in our bodies like DNA synthesis or regulation of nitric acid. The levels of glutathione tend to drop as we age and receiving glutathione supplements may correct this. There are several ways of getting glutathione in your system and these are orally, intravenously, nasally or as an inhalant. The most common of these, however is the injectable glutathione.
Another use of glutathione would be in conjunction with some other medication for reducing the effects of chemotherapy on cancer patients. On its own it may reduce the effectiveness of cancer medication so it should not be taken before chemotherapy. In this case, injectable glutathione is only to be taken under a doctor's orders.
Other treatments that involve taking injectable glutathione in its many forms is treatment of Alzheimer's Disease, Parkinsons Disease, Cataracts, glaucoma, liver disease and hepatitis. As a medical supplement, injectable glutathione is used for these diseases and more. It is a very useful supplement in the medical field. It has a few side effects, however and one of these has been used for commercial purposes in the cosmetics industry.
Glutathione is known to have skin whitening properties. This is the main selling point for injectable glutathione on the market today. Many brands make this product for the sole purpose of whitening the skin. Glutathione injectable will do the trick.
Because it is an antioxidant, glutathione is known to protect the body from progressive aging and disease. A study done on the elderly indicated that those with higher levels of glutathione tended to be disease free while those with lower levels had problems like arthritis, heart disease and diabetes. Glutathione in this case may be used to slow the aging effect and provide longevity.
It has had enormous success so far and it is still used today. Since the advancement of technology in recent years has allowed online marketing, you can buy injectable glutathione from trusted websites as opposed to having to look for it in pharmacies.
One has to be very careful when buying injectable glutathione products since there is no guarantee that the contents of the package are not tampered with or genuine. Perhaps the safest place to get the glutathione from this online reseller. If you can find a trusted and certified site to buy the products from, this is a better and quicker option especially if you can't walk very long distances.
The best glutathione injectables are the ones approved by the Food and Drug Association. They are the ones that contain the appropriate levels of injectable glutathione for the use they are intended. The glutathione injectable price is rather high but for the effects desired, it seems to be worth it. As with any other medication, it is advisable to contact a health care professional for advice. In any case, they can give you alternatives and list out all the potential side effects you may get as a result of using it.


text:
FTM-HELP-L ArchivesArchiver > FTM-HELP > 2009-03 > 1236220604
From: "David C Abernathy" <>
Subject: Re: [FTM-HELP] Sleepytime Internet Explorer 7
Date: Wed, 4 Mar 2009 18:36:44 -0800
References: <84BD5360F4F24F61942E02AB275F8853@maggie><D29E2AD7AA104C0987E2F4E21739A469@DavesDesktop><2078AC741C134455B7A9792338C94D62@maggie>
In-Reply-To: <2078AC741C134455B7A9792338C94D62@maggie>
No, you do not need to go "naked" in the wild, but some of the different
programs will take over your machine.
There are also many of things that can upset the operation of ones machines.
Of the things you have listed, I see nothing that should have any affect on
your machine, BUT, I have not used AVG for some time. I have read that are
issues with version 8 of AVG, but I do not know first hand.
Do you have a third party firewall running?
One thing you may try and that is to reset the IE options back to the
To do this, with IE open, "Tools, Internet Options" and then the "Advance"
tab. There near the bottom is a "Reset" button, click it and OK yourself
out. Close IE and then restart up IE and you MAY see some improvement.
David C Abernathy
Email disclaimers
This message represents the official view of the voices in my head.
== All outgoing and incoming mail is scanned by F-Prot Antivirus ==
-----Original Message-----
From: [mailto:]
On Behalf Of Walt Boswell
Sent: Wednesday, March 04, 2009 2:44 PM
Subject: Re: [FTM-HELP] Sleepytime Internet Explorer 7
Oh, I have all the usual goodies, David. There are AVG anti-virus free 8.0,
a firewall (Windows, I think, but I'm not sure about that), Windows Update,
and Windows Defender. I may be missing something, other than my first love,
that is...lo, these many years ago. I wonder where Helen is tonight?
Are you saying that I'm just going to have to live with IE taking the
occasional nap, that I should just let sleeping dogs (now that's a fine word
for IE 7, I'd say) lie? I can't very well do away with my anti-virus and
firewall protection. Can I? That would be rather like refusing a beneficial
flu shot just because I don't like needles. Or something like that. I'll
have to think about this one.
So it goes (Kurt Vonnegut).
This thread:
|Re: [FTM-HELP] Sleepytime Internet Explorer 7 by "David C Abernathy" <>


text:
Colloquia Schedule Spring 2012
Colloquia are on Tuesdays (unless otherwise indicated) at 3:30 pm in RLM 15.216B
"Searching for Clues to the Black Hole-Galaxy Relationship Through Nearby AGN Surveys"
University of Colorado at Boulder
host: Shardha Jogee
Tinsley Visiting Scholar (Stars Group)
"Heavy Element Nucleosynthesis in the Brightest Asymptotic Giant Branch Stars"
Mt. Stromlo Observatory, Canberra, Australia
host: Harriet Dinerstein
"Probing the Cosmic History of Star Formation in Galaxies with the Herschel Space Observatory and CCAT"
University of Colorado at Boulder
host: Shardha Jogee
"New Observational Insights into Cosmic Reionization"
University of Cambridge, Kavli Institute for Cosmology, UK
host: Milos Milosavljevic
"Early Star Forming Galaxies and Reionization"
Steward Observatory, Arizona
hosts: Sally Dodson-Robinson & Shardha Jogee
"Fueling Cosmic Star Formation: The Molecular Gas Mass Density of the Universe"
Virtually all major advances in extragalactic astronomy and our
understanding of galaxy formation and evolution over the past decade
are based on the constraints we obtained on the star formation history
and stellar mass density of the universe. These investigations are
greatly successful in explaining a range of galaxy properties
throughout cosmic times, yet are lacking one fundamental link: a
systematic study of the fuel for star formation, the cause for the
buildup of stellar mass - i.e., constraints on the molecular gas mass
density. I will review the current status of observations of molecular
gas in galaxies back to within a few hundred million years after the
Big Bang. Based on pathfinder studies with the (Expanded) Very Large
Array and the CARMA millimeter array, I will outline the prospects for
the upcoming new generation of large observatories, in particular the
Atacama Large Millimeter Array (ALMA), to provide the first solid
constraints on the gas mass density of the universe. In synergy with
extremely deep studies of the stellar mass and (unobscured) star
formation properties with the largest upcoming optical/infrared
facilities, in particular the Giant Magelllan Telescope (GMT), this
will enable simultaneous studies of the past, present, and future star
formation in galaxies throughout cosmic times.
California Institute of Technology
hosts: Shardha Jogee & Milos Milosavljevic
"Direct Imaging of Exoplanets: Prospects for Comparative Exoplanetology"
Max-Planck Institute for Astronomy, Heidelberg, Germany
host: Anita Cochran
"Understanding Galaxy Evolution in the Early Universe"
University of Texas at Austin
host: Shardha Jogee
"Giant Planets Caught at Formation"
University of Hawaii, Institute for Astronomy
host: Chris Sneden
"The Dark Art of Detecting and Characterizing Planets by Direct Imaging"
NASA, Goddard Space Flight Center
host: Chris Sneden
"Molecular spectroscopy of planet-forming regions: A quest to understand the diversity of planets and planetary systems"
National Optical Astronomy Observatory (NOAO)
host: Sally Dodson-Robinson
Spring Break: 12 - 16 March. No Colloquium scheduled.
No talk scheduled.
"Dark Matter Properties from the Faintest Galaxies"
Stanford University / Kavli Institute for Particle Astrophysics and Cosmology
host: Karl Gebhardt
Antoinette de Vaucouleurs Medalist and Lecturer
"The Carnegie Supernova and Hubble Constant Projects"
Director, Observatories of the Carnegie Institution for Science
host: Dan Jaffe
Antoinette de Vaucouleurs Medalist and Lecturer (visiting: 4/2-4/8)
Public Talk: "A Journey of Discovery: Our Expanding Universe"
Director, Observatories of the Carnegie Institution for Science
host: Dan Jaffe
"The ABCs of Low-Mass Stars"
Boston University
host: TBD
"The History of Massive Galaxy Formation as a Cosmological Tool"
University of Nottingham, UK
host: Shardha Jogee
"Black Holes and Neutron Stars in the Local Universe"
University of Warsaw and University of Texas, Brownsville
host: Milos Milosavljevic
Tinsley Visiting Professor (visiting: 4/23-5/17)
"The First Billion Years of our Universe"
Scuola Normale Superiore, Pisa, Italy
host: Volker Bromm
Texas Cosmology Center Distinguished Visitor
"Constraining Cosmology through the Growth of Structure: New Results from the South Pole Telescope"
University of Chicago
host: Eiichiro Komatsu
PhD Defense Presentation
"Dark Matter Halos and Stellar Kinematics of Elliptical Galaxies"
University of Texas at Austin
PhD Defense Presentation
"An Experiment in Integrated, Guided-Inquiry Science Classes and Implications for Teaching Astronomy"
University of Texas at Austin
PhD Defense Presentation
"Tests of the Episodic Mass Accretion Model for Low-Mass Star Formation"
University of Texas at Austin
Visitors to the Department of Astronomy can find detailed information and maps on our Visiting Austin Page.
Please report omissions/corrections to: G. Orris at firstname.lastname@example.com.


text:
For those portfolios with investment in the energy sector, each day's news seems to bring about sweeping changes in price. One minute, the sector is focused on geopolitical spats between rival nations and oil prices surge. The next, abundant supply projections send prices downward.
It's enough to make your head spin.
However, over the longer term, various supply and demand imbalances bode well for energy prices and stocks in the sector. For investors, ignoring the day-to-day noise and instead focusing on these disparities could be the secret to a good night's sleep and lasting gains.
Growing Demand vs. Shrinking Supplies
Barring any sort of major world conflict or catastrophe, energy prices should continue their steady climb as worldwide demand grows unchecked. While events such as Iran's current threats to close the Strait of Hormuz certainly will have their way with prices in the short term, the longer-term picture supports sustained higher prices. Currently, global oil demand is quickly climbing past 89 million barrels per day, and recent forecasts from a number of research organizations show that number will soon be eclipsed.
The Energy Information Administration's latest projections show that global energy demand will rise by 53% from now until 2035. The bulk of this demand will come from emerging-market nations, who have just begun their "modernization." China alone is projected to see their energy demand surge by 68% in that time frame. New sources of demand — from nations in the ASEAN, India and Latin America — ultimately will put pressures on supplies.
Likewise, in BP's (NYSE: BP) latest energy missive, consumption by non-OECD nations will drive future energy demand growth. Both sets of research show fossil fuels still will be the dominate choice for powering our planet by the 2030s.
And in the face of all this bullish demand data, supplies are shrinking. BP estimates the world will need 16 million barrels per day to replace declining output from existing wells plus cope with demand increases. That's a tall order, considering many of the world's legacy and major fields are now facing dwindling production and reserves. While unconventional fields such as North America's shale formations, Africa's offshore deepwater fields and Arctic drilling will help, the costs associated with these sorts of operations will keep oil prices high. The EIA predicts these factors will see the world confronting average price floors of $108 per barrel oil in 2020 and $125 per barrel in 2035. However, the EIA price forecasts do not account for inflation expectations.
How to Ignore the Noise
With the long-term prognosis for oil demand still rising, investors might want to steer clear of the daily gyrations and focus on the continued supply-and-demand deficits facing the globe. Statistics like that fact that China's energy deficit (across all fuels) will widen by more than a factor of five and India's will more than double are what are really important to portfolios.
To that end, thinking broad might be best. The Vanguard Energy ETF (NYSE:VDE) represents one of the cheapest options for investors in the sector. The fund, which tracks 167 energy heavyweights — including Anadarko Petroleum (NYSE:APC) and Exxon Mobil (NYSE:XOM) — charges an industry-low 0.19% in expenses. The fund has been a solid performer as well, returning 11.8% annually since its inception in 2003. Similarly, the iShares S&P Global Energy Sector (NYSE:IXC) ETF, which includes international energy giants in its mix, can be used as another broad play for the sector.
Finally, I've written before about how the oil services subsector is one of the best ways to play the long-term rise in oil prices. For investors, the iShares Dow Jones US Oil Equipment Index (NYSE:IEZ) and SPDR S&P Oil & Gas Equipment & Services (NYSE:XES) funds are great ways to play the continued increase in energy prices and costs associated with unconventional drilling.
As of this writing, Aaron Levitt did not hold a position in any of the aforementioned securities. However, Levitt may initiate a long position in either IEZ or XES within the next 30 days.


text:
The Motorola V195 has a maximum of 1.6, for instance, while the Samsung Infuse 4G is only 0.2.
Obama is leveraging this to its maximum potential, even more than in 2008.
The wire fraud and mail charges each carry a maximum penalty of 20 years in prison.
Great Britain does not have the death penalty, so life behind bars was the maximum sentence possible.
Bud goes for maximum extraction: he keeps his weed wine in barrel for nine months before bottling it.
How to inflict the maximum of discomfort upon M. Destournelle with the minimum of risk to herself was the question.
Also the present sunspot cycle started its rise to maximum about 1954.
Litaku, Kurrichani, and other similar towns are Sichuana; the Kaffre civilization being said to attain its maximum hereabouts.
The deflection of the centers at the crown was a maximum of 3¼ ins.
The most efficient mixer is the one that gives the maximum product of standard quality at the least cost for production.
maximum max·i·mum (māk'sə-məm)
n. pl. max·i·mums or max·i·ma (-mə)
The greatest possible quantity or degree.
The greatest quantity or degree reached or recorded; the upper limit of variation.
The time or period during which the highest point or degree is attained.
Having or being the greatest quantity or the highest degree attained or attainable.
Of, relating to, or making up a maximum.


text:
Comedian was the only good thing: Norwegian Sky Cruise Review by sillysoul
Overall Member Rating
Comedian was the only good thing
Destination: Bahamas
Embarkation: Miami
We booked this trip for only two reasons. One was just to relax for the weekend, and to try the freestyle cruising. The freestyle cruising is absolutely fantastic. We loved the idea of deciding for ourselves where and when to eat. We also loved the idea of the casual dress code anytime day or night. We have sailed on many other lines and this was our first with Norwegian.
We had a balcony cabin and was surprised how small the cabin was. Barely enough room to walk around the bed. The bathroom was small but that was expected. The balcony itself was small but not bad. I have read reviews where it was stated that the chairs were very small on the balcony. The chairs were fine in size, not uncomfortable and only the table was very small. The bed was hard but not as if it was poured concrete. More We were happy to see upon arrival to our cabin that there was a bottle of wine waiting and delicious chocolate covered strawberries. You are allowed on the ship at noon but your cabin is not ready until two PM. They make an announcement when your cabin is ready. The luggage arrived by four PM. The quickest we ever experienced. The shower was very small and the water temp could not decide between very hot or cold no matter how many times we adjusted the controls. AC was cold and the bathroom worked fine. Housekeeping was fine except for a few things. The mini bar is a waste unless you like to over spend. We were supplied ice but had to ask for water, and that was never replaced. Our attendant either never replaced our water glasses or only left one for two people. We were given a list for fresh fruit to be in our cabin every day. We picked pears and oranges and was given one pear and one orange only one time. Bring your own hair dryer. Ours was terrible and mine only worked by plugging it into the outlet by the desk.
The decor in the ship is still basically all Hawaiian. I did not see any real sign or any refurbishing. The ship seems confused entertainment wise. The hallways had country music and the entertainment was mainly all Latin. Other cruise lines use Reggae and island type music. The too much Latin theme would have made more sense if we were sailing to Puerto Rico. I liked the music don't get me wrong. It just seemed out of place to be an all the time thing.
The musical shows were terrible. The best things to see was the newlywed/not so newlywed show. It was hysterical and very entertaining. It can be very racy and my only beef was parents who felt it was fine to have seven, nine and ten year old children sitting in the front row. They should not have been there at all. The comedian was the hit of the cruise. He was extremely funny and we went to see every show he did. I would highly recommend him. They also had a adult theme game show where couples in teams were asked to do some funny and sometimes risquE things to do.
The staff were all very friendly. We ate at the Il Addaigo (sp?)for dinner and the service was horrible, the food was revolting. Being Italian myself I can honestly say no real Italian would come away raving about it unless they lack taste buds. The buffet was just average. The Crossings was the only place that we had a good dinner with great service. I would rate the food on this ship below average and really not all that good. There was no formal night which was a blessing for us because as I said we just wanted to relax this weekend. Ladies if they wanted to even during the evening can go into any place to eat wearing a sun dress and even flip flops. Many did. Men were asked not to wear shorts at night but many did. It is that relaxing. It was a good mixture of very casual and "just a nice dress, not too dressy". I did not see anyone wear a suit or any formal type dress. The public bathrooms were very clean but very, very small. The casino was very small and way too hot in the evening for me to even stay in. Dazzles to me was a bust. Very small, hot and too many young children during the 18 yrs. and older times. The pools and four hot tubs were fine except for toddlers and small children that were not allowed in them but were, with food in their hands! I guess mom and dad cannot read the signs right on the hot tubs. There were some very unruly children on board never being watched by their parents that were very annoying, including pressing all the buttons in the elevators and throwing balls in areas where they should not be including one man having the ball to hit him in the face and them knocking his drink off his table. Security was very lack on this ship. On other lines security would be at the doors of adult only bars and clubs that would stop kids from going in, not on this ship. They enforced nothing and were basically nowhere to be seen.
I wanted to try this freestyle not just to have a relaxing weekend, (there are much better lines) but the idea of freestyle seemed like it would be ideal for a European cruise. I would be interested to see if any other ships are favorably rated by other passengers. I would not book on this ship again. The AC did break down on the last night but after two hours it was fixed. I forgot one other thing, the White Hot party. They did put on a good show and the fake snow was a good added pleasantry. I would not say it was better than any other line because I have seen better, but it was fun. Less
Published 08/21/08
Cabin review: BA0215 Mid-Ship Balcony
Good balcony,suprisngly small cabin, tiny bathroom.Read All Mid-Ship Balcony (BA) Reviews >>
Read Cruise Critic's Norwegian Sky Review >>
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Hello Everyone ,
I am curious for opinions on the Kyocera Brio and the Sanyo SCP-2700, from people who have some experience(s) with each of those/these mobile phones, because I am trying to decide if I should get the Pre-Owned Sanyo SCP-2700 from Sprint now or should I wait for the Kyocera Brio to be available Pre-Owned from Sprint?
Or will there be some better Dumb Phones/Non-Smart Phones in a Bar/Candy Bar Style with a full Qwerty Keyboard available for Sprint within a years time, and if so what will be the name of those Phones?
There are not many reviews of the Kyocera Brio out at this time, and so I am trying to decide if it is worth waiting for when compared to the Sanyo SCP-2700.
Some things that are important to me are durability, usability, buttons that are easier to read & use, et cetera.
Thank you,
-John Jr
Message was edited by: GoodJohnJunior
Message was edited by: GoodJohnJunior
Have you looked at the ratings and reviews? These are written by other customers and will tell you the good and bad of each phone.
Sanyo - SCP 2700 (refurb) http://community.sprint.com/baw/device-reviews.jspa?deviceId=160
Kyrocera Brio - http://community.sprint.com/baw/device-reviews.jspa?deviceId=3784
Yes I have, but there are only 4 Reviews at this time & one video on YouTube for the Kyocera Brio, and so I am looking for some extra opinions and/or reviews; but thank you.
Having trouble posting or viewing your Private Messages? We made an update to the Community registration process which requires you to validate your email, click here to read more about it.


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- Diabetic Peripheral Neuropathy Slideshow
- Diabetes and Foot Problems Slideshow
- Diabetic Neuropathy Quiz: Test Your Medical IQ
- Patient Comments: Peripheral Neuropathy - Experience
- Patient Comments: Peripheral Neuropathy - Symptoms
- Find a local Neurologist in your town
Quick GuideDiabetic Peripheral Neuropathy: Improve Diabetes Nerve Pain
What causes peripheral neuropathy?
There are many possible causes of peripheral neuropathy, including:
- Diabetes mellitus
- Shingles (post herpetic neuralgia)
- Vitamin deficiency, particularly B12 and folate
- Alcohol
- Autoimmune diseases, including lupus, rheumatoid arthritis or Guillain-Barre syndrome
- AIDS, whether from the disease or its treatment, syphilis, and kidney failure
- Inherited disorders, such as amyloid polyneuropathy or Charcot-Marie-Tooth disease
- Exposure to toxins, such as heavy metals, gold compounds, lead, arsenic, mercury, and organophosphate pesticides
- Cancer therapy drugs such as vincristine (Oncovin and Vincasar) and other medications, such as antibiotics including metronidazole (Flagyl) and isoniazid
- Rarely, diseases such as neurofibromatosis can lead to peripheral neuropathy. Other rare congenital neuropathies include Fabry disease, Tangier disease, hereditary sensory autonomic neuropathy, and hereditary amyloidosis.
- Statin medications have been linked to peripheral neuropathy, although neuropathy caused by statins only rarely causes symptoms.
While diabetes and postherpetic neuralgia are the most common causes of peripheral neuropathy, often times no cause is found. In these situations, it is referred to as idiopathic peripheral neuropathy.
Sometimes, peripheral nerve entrapments, such as carpal tunnel syndrome, are considered peripheral neuropathies. In these cases, pressure on the nerve rather than a disease state leads to nerve malfunction.


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14 Free Crochet Hat Patterns: Crochet Beanie Hats, Crochet Cap Patterns, and More
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Latest Comments
"I love the idea of crocheting baskets to hold my crochet projects."
"The instructions are incomplete on either page. The outer round is not explained at all."
"This is a great yarn. I have worked with it on a few projects and love how no two items will ever be the same because of the way the yarn changes colors and also thickness randomly. As the designer states, the yarn designs the pattern. You never know what youre getting with it until the very end and it cant be duplicated again."
"To answer panakanics question below As shown in her pattern the designer used the following yarn Large Cowl Hood Red Heart Boutique Unforgettable in Polo Petunia Bernat Vickie Howell Sheep(ish) in Espresso(ish), Taupe(ish), Robin Egg(ish) Small Cowl Red Heart Soft Yarn in Wine and Chocolate Infinity Scarf Bernat Vickie Howell Sheep(ish) in Grey(ish) and Gun Metal(ish)"
"As shown in her pattern the designer used the following yarn Large Cowl Hood Red Heart Boutique Unforgettable in Polo Petunia Bernat Vickie Howell Sheep(ish) in Espresso(ish), Taupe(ish), Robin Egg(ish) Small Cowl Red Heart Soft Yarn in Wine and Chocolate Infinity Scarf Bernat Vickie Howell Sheep(ish) in Grey(ish) and Gun Metal(ish)"
Easy Slouchy Beanie
By: Jenny from jennlikesyarn.com
We are adding the pattern to your Crochet Patterns.
The pattern was added to your Crochet Patterns.
Click here to view your Crochet Patterns.
Using this free crochet hat pattern, you can make an Easy Slouchy Beanie in this beautiful purple color. This is great for anyone to showcase their stylish fashion. The double crochet stitch is used, which allows you to work this pattern up quickly. It's a stylish crocheted hat that will keep your head warm and toasty during the cold winter months. This easy crochet pattern is great for beginners that know how to crochet the magic circle. You'll need some worsted weight yarn and H and G sized hooks in order to completely this project.
If you love these patterns, be sure to subscribe to our newsletter to get amazing crochet patterns like these delivered to your inbox every day!
Crochet HookH/8 or 5 mm hook
Yarn Weight(4) Medium Weight/Worsted Weight and Aran (16-20 stitches to 4 inches)
Are you a visual learner? Check out this video tutorial for a Beginner Crochet Beanie and make your own today!
PLUS: Download our FREE eBook of 14 Free Crochet Hat Patterns: Crochet Beanie Hats, Crochet Cap Patterns, and More
Did You Know:
The notion of the "slouch hat" comes from the brimmed hats of military uniforms worn by many nations for over one hundred years. "Slouch" comes from one side of the brim drooping down on these hats. It's also known as the "Australian bush hat" and it's very recognizable as the hat Theodore Roosevelt wore when he was part of the "Rough Riders" during the Spanish-American War.
While the hats that we consider "slouchy" today don't usually have a brim and aren't associated with the military, the history behind it is interesting. The "slouch" hats or beanies we see today have a droop in the back where the beanie flops down because the pointy end doesn't fit the roundness of the back of the head. These hats are worn by many, but are typically associated with today's "hipster" culture. "Hipsters" could be seen as the movement against mainstream culture, a war of sorts.
The two ideas of "slouch hats" have some relation to each other because they both identify their wearers: military person or hipster. Share your new knowledge the next time you see someone wearing a slouch hat or beanie. Better yet, if you crochet one, you can tell people about your insight into the slouch hat trend.
For more beginner crochet hat patterns, check out our collection of 50 Beginner Crochet Hat Patterns
Do you like slouchy hats or traditional beanies better?
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Hippie Chick
Mar 14, 2017
Slouch is in and anything with slouch in the name is a great selling item on Etsy also. Seems to be very popular with the Millennials for the present time. Dont know how much longer this phase will last, but it seems to be very hot right now. I am sure they will love this great beanie.
paparotsy2011 4133 302
Dec 26, 2016
I have made several of these hats since I found the pattern. I made one as a gift for a co-worker. You'd have thought I gave her a million bucks! She was so excited and it looked fabulous on her. Now I am making them for a children's hospital charity. It's a terrific, easy pattern that crochets quickly! I love this site!
scorekeeper01 1580 827
Dec 26, 2016
How much yarn did you need to buy to make the slouch beanie. Thank you
Dec 23, 2016
Look this hat. I am going to make a few for charity this year in multiple color. I am going to jazz it up by adding buttons, crochet bows and/or crochet flowers.
lyrics587 9192717
Dec 22, 2016
I love this pattern and I have made this hat many times in various colors. This hat is flattering on everybody.
KnittingTherapy201 6
Dec 22, 2016
I've been trying to find a slouchy hat to give as a gift to my sister, but it's being hard to find one that she can use because of her curly hair, and the fact that she always thinks she look like a clown when she put on a hat, Ive been seeing the wonderful comments everybody leaves of these pattern, and how truly simple and easy it is and I was wondering if anyone with the same problem as my sister has try the hat, I really would like to make it for her.
mulberrygalprinces s
Dec 22, 2016
I love the simplicity of this hat. It's very easy to do and works up quickly. You can dress it up by adding different embellishments. And just change the colors to make it more gender accepting. I made my sisters in deep purple with a flower and her husbands in red with a Mario embellishment on his. They don't look at all alike. Thanks for sharing.
Dec 16, 2016
I have made several of these and I love the pattern. It is easy to make it more or less slouchy just by decreasing the number of rows. It looks great in a lot of different colors, I have made blue, purple, red and gray. My teenage daughters and their friends love the look of the beanie! Simply stylish!
Dec 12, 2016
Easy slouchy hat. Beginners, don't let the magic ring deter you, the technique is very easy and versatile. This slouchy makes up quick and is great for gift giving. Most any worsted weight will do because these are not tight fitting.
Dec 09, 2016
I've tried many 'slouchy beanie' - type patterns, and this one is by far my favorite. It is simple and fluid to make with little complication. 5/5 I love it
Nov 12, 2016
I'm giving this Easy Slouchy Beanie a four-star rating because of the color used. This color doesn't appeal to me much. If I were to make this kind of hat, I would make this in earth colors or vibrant colors but not this shade of purple. However, this is the perfect beanie for winter as the double crochets are more compact when finished and can give the wearer the needed warmth and protection on that part of the body during those cold winter months. Thanks for the free pattern.
Dec 07, 2016
In my opinion, having the couple crochets instead of single gives the beanie a more slouchy, looser look versus a tighter single crochet. I think the purple is appropriate for a young girl. -)
Jul 29, 2016
These are my favorite kind of hats to wear in the winter. Can't wait to make it!
Emily Michelle
Jan 22, 2016
This was a great way to learn how to crochet the magic circle. Thanks!
Dec 15, 2015
I love the color of this beanie and the slouchy fit is totally on trend. I can't wait to make it!
collinharris45 079 4738
Sep 25, 2015
I crocheted this hat and it turned out great. I am In love with the style. I had to take off some rows because I thought it fitted my head fine.
Jun 16, 2016
I haven't tried this pattern yet Collin, but am trying to find the perfect yarn color before I start. Was there anything confusing or hard to understand throughout this pattern? Any tips or tricks for someone who hasn't tried this pattern before?
olgabinghamm 99555 63
Mar 11, 2015
I will love this slouchy,can't wait to make it.
Feb 23, 2015
So i was making this hat and it was wayyyy too big for my head..can't I have a lot of hair.. So I took some rows off of double crochets and started the single crochet rows.. Better.
Member 8000804
Jan 14, 2015
It was a bit confusing at first while I worked out how to do the magic circle. After that, it only took a little bit of concentration and persistence!
Mar 06, 2014
I can't find the pattern so be able to save it . Can anyone help .?
wellsmaalik 389705 8
Mar 17, 2014
what you do is click on it where it says Click here for crochet pattern abd then on that site click it where it says looking for more patterns? click here and it will bring you to the pattern
wazupred 6635005
Feb 16, 2014
can't seem to download the pattern
gparenti 4440033
Sep 10, 2013
save this pattern !
kandnstein 6707564
Aug 09, 2013
I have made two of these hats in two days. The pattern is wonderfully easy, even for me. Just pay attention to the first 8? rows, these are the increase rows. After that, it's just double crochet for several more rounds, till you finish with several rows of single crochet as a rim. The pattern is easily adaptable to suit individual tastes. Try to avoid "big" yarn, or you will end up with a huge monstrosity. My first attempt I used soy silk, a little hard to work with, but soft and slouchy. The second hat made with Lion brand cotton ease, my favorite go to yarn. added a row of crossed double crochet for variety. Even if you have never made a hat before, you can make this one!
naniebeth 3487851
Jul 22, 2013
I made this hat with a linen color yarn that I got at Joanne's Fabrics. It made by Joanne's. New I think. It came out a little long and a little tight for my daughter, but absolutely beautiful. It looks like it came from an expensive boutique. Love it and will do another one with a few adjustments. Thank you for the pattern. '
ladyc6 8212991
Jul 13, 2013
TMI Crochet
Mar 08, 2013
going to attempt tonight
Dec 07, 2012
Simple yet chic...I like this :)
rpwailus 1069183
Jul 03, 2012
I see a lot of baby stuff and chochet, I do not crochet and sometimes I do baby things but I need to some stuff for ages 10 and up teens thanks
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Is there any way to do such a thing like robot txt or htaceess ?
No, it's not possible.
The only thing you can do is to obfuscate html and css, this way the ripped html is useless.
Use javascript (document.URL.indexOf) for domain blocking. Use it on several JS across your site structure, then obfuscate to make harder the "clean up" process by rippers. You can also encrypt the values of the allowed domains for a complex solution.
If you include local path as allowed, you will go fun answering supports questions as "my site works on local, but does not when uploaded to my server" (along with the non-purchased badge). Open a beer each time you get this kind of message.
Maybe this helps you: http://perishablepress.com/5g-blacklist-2013/
nicole_89 said
The only thing you can do is to obfuscate html and css, this way the ripped html is useless.
Actually i did something like this in php with the same concept , it only download html not resources


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Sundaramurthy, H (1978) Validity of axis transfer technique for pitch damping measurements AIAA-78-833. In: 10th Aerodynamic Testing Conference.Full text available as:
Download (1018Kb)
Results of some experimental investigations undertaken to verify the validity pitch damping measurements on high fineness ratio configurations are presented. Free oscillation tests on three half models of fineness rations 10 and 25 were conducted at Mech numbers between 0.7 and 1.2 with three different axes of oscillation. The measured pitch damping derivatives for two axes user used to compute the derivative for the third axis. Comparison between the transferred and the measured derivatives was in general, good for Mach numbers 1.1 and 1.2
|Item Type:
|Conference or Workshop Item (Paper)
|Uncontrolled Keywords:
|Axis transfer technique
|AERONAUTICS > Aerodynamics
|Depositing User:
|Mrs Manoranjitha M D
|Date Deposited:
|09 Mar 2006
|Last Modified:
|24 May 2010 09:40
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text:
Robin Roberts allegedly says it was nothing serious as to why she was in the hospital again. However, she just was not feeling well and we suppose her physicians wanted to make sure she was alright. It's good for all of you ladies to realize there is nothing wrong with getting check-ups, especially after feeling a little ill.
As you know, Good Morning America's host, Robin Roberts had already went through a surgical procedure, more than once. However, we also know she is a woman of faith, one who does not give up, regardless of her previous diagnosis. Therefore, we believe Robin Roberts' life is a testimony and God will make sure she will be fine and have a healthy long life. God bless her and in the meantime, we will continue to keep her in our prayers.
Read more articles like this one @AToast2Wealth.com
Watch Video


text: Twin Cam Sam - Unregistered September 12, 2010 9:34 AM Fairplay to Ogier, a good result, but great shame for Petter. Would have been great to see him take the first win for a privateer for 16 years. Shame for him to be slowed by a mechanical problem on the final day. He's still got the chance to overhaul Latvala to finish 3rd in the drivers championship which would be an incredible achievement. So, when is Mr Wilson going to wake up and get over the fact that Petter walked away from his 5 year deal with Ford a few years ago. He's tried and failed to sign Ogier, he's looking at trying to sign Sordo who is'nt in the same league as Solberg, or nearly as big a star. I don't understand his lack of plain logic ? I was reading this week that Citroen's Norwegian importer has seen sales increase by 67% since Solberg switched to Citroen. I cannot for the life of me understand why Malcolm Wilson doesn't swallow his pride and get Petter signed up. Ford Motor Company should overule him, and take the decision out of his hands. 14 agree 1 disagree


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Column: District 518 planning for students with special needs
By DEB STOLL, District 518
WORTHINGTON — It may be November, but senior students are already focused on May — graduation, and what is next in life. Students are being asked, "What do you want to be?" "What do you want to do after graduation?" "Do you need to begin your planning, apply for a program and make some decisions?"
These inquiries from adults are often difficult for students to answer, but parents, teachers, principals and counselors are there to help navigate and prepare students for the complexities of life after high school. This is also true for students with special needs; there are numerous people to help and guide students with their decisions.
The Individuals with Disabilities Education Act (IDEA) directs schools to provide "Secondary Transition Planning" for special education students, which is simply preparing for the future.
Beginning in 9th grade or no later than age 14, all students on an Individual Education Plan (IEP) must have a transition assessment, which begins the process of assisting the students to examine their interests, strengths and aspirations. In many schools in Minnesota, the transition process begins at the middle school level — as it's never too early to encourage students and their families to think about the future and begin to plan.
Secondary Transition Planning is the development of a plan to prepare students for life after high school and includes preparing for postsecondary education/training, employment and independent living. This proposal is created by a team that understands the student's disability, keeping in mind the student's strengths, occupational aspirations and academic achievement. The team, which includes the student and parents, examine which skills would be beneficial for the student to gain/learn while still in school in order to reach their potential and be successful in life.
The plan often includes training in the areas of life skills, self-determination (making choices appropriate for self), self-advocacy (having a voice in decisions) and independence skills (taking care of self), keeping in mind that students with disabilities should practice these skills on their own behalf to the best of their abilities. Additionally, the schools work closely with community agencies to assist the student with the goals of the plan.Often Vocational Rehabilitation Services, Community Services, and other key agencies combine their efforts to support the student and team in the decisions for after high school. These pooled efforts repeatedly have amazing results and students find the support goes beyond their graduation, receiving continuous backing into adulthood.
Planning ahead is always a good idea, and Transition Planning services by schools are designed to guide special education students and parents to prepare for the future. Whether graduates are non-disabled or disabled students, early planning is important and can play a vital role in helping students achieve their goals.
If you would like to learn more, the Minnesota Department of Education has information on Secondary Transition Planning along with an excellent document, "Planning Guide for Students Entering Postsecondary Programs." Visit http://education.state.mn.us/MDE/Welcome/index.html.
Deb Stoll is assistant director of special education for District 518.


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A Most Merry and Illustrated Explanation
(With a Merry Theorem of Proof Theory Thrown In)
If you flick on the tube today, in addition to the ubiquitous but misnamed reality shows, 24-7 sports events, jackass judges on amateur hours, over-decibilized sitcoms, and boring but chic comedy shows, you might stumble across a program about the achievements of mankind. Although increasingly rare, they are there.
But even those programs tend to shoot for the melodramatic. Not too long ago, you could lean back, press the remote, and suddenly you found a show about the lives of two mathematicians, Kurt Gödel and Georg Cantor (pronounced "GAY-org", but we'll call him "George"). Lamenting how their amazing discoveries drove them crazy, the stone faced narrator spoke with melancholy monotone how George went near insane grappling with the concept of infinity, and Kurt's mental stability deteriorated as he grappled with how George's problem lead to non-provable truths.
Although not really a bad introduction to the work of these two fellows (and of two more), this show definitely suffered from the Definciency of the Tube. First, there was a misplaced cause-and-effect message. Yes, both men had mental problems which ultimately became true mental illness. But it's highly questionable that their work was the primary cause. We also come away from the program hearing that Kurt and George had made discoveries of near mystic profundity shaking the very foundations of truth and the mind of man. Now that might be pushing it a bit, although what Kurt and George did was important.
Oh, yes, it's probably not fair to expect a TV show to go into the technical details of what George or Kurt did. But on the other hand the only way to decide how profound their discoveries are is to see exactly what they did. Now admittedly Kurt's work is very mathematical and in its original form nearly incomprehensible. However, what George did is not difficult to understand at all so we'll talk about that. Whether what George did is profound is a personal opinion, but it is undeniably one of the slickest mathematical tricks ever invented, a discovery that was totally glossed over in the program.
George's discovery - one of many - was to come up with the diagonal argument. Although George used it mostly to talk about infinity, it's proven useful for a lot of other things as well. The best of its applications is to prove there are things can't be proven. Ultimately that's what Kurt did, but we'll get to that at the end.
George's interest was not infinity per se. What he was doing was developing set theory. Remember how you were always bored because every book of math you had in school started off with sets? And you didn't see what the heck it had to do with any of the following chapters? Well, you can blame George for that.
But in developing set theory, George came across the need to precisely develop the notion of infinite sets. After all if you want to talk about counting numbers, integers, and the points on a line, you have to know about infinity. George found there was a way to do this precisely and unambiguously.
George decided to start off simple: pick the counting numbers. Now George and everyone knew there is a never ending supply of those.
The symbolism is pretty clear. You can pick any number, no matter how large, add 1 to it, and you'll always have another number. This property then defines the infinity of the counting numbers. And if an infinite set has members that can be put into a one-to-one correspondence with counting numbers, then George said that set was countably infinite.
George, though, found there were some oddball properties of a countably infinite set. For instance, some subsets of countably infinite sets are also countably infinite. For instance, you'd think there would be only half as many even numbers as counting numbers. But George showed you can put the counting and even numbers into the one-to-one correspondence. So the two sets have the same number of elements.
But this type of diagram isn't good enough for "rigorous" mathematical articles. A more "rigorous" way to state there are the same number of even numbers as counting numbers is to state you can create a new set or ordered pairs, P, defined by:
P = { (n, 2n) where n = 1, 2, 3, ...}
The key point is that for any integer, n, you have both a counting number - which is n - and its double, 2n, which is a unique even number. So there is a one-to-one correspondence between counting numbers and the even numbers, and half of a countable infinity is still a countable infinity!
Another weird property is that if you combine a countably infinite set to another countably infinite set, the new set is also countably infinite. Take the natural numbers (ergo, 1, 2, 3, etc.). Group them with zero and the negative numbers (-1, -2, -3, ...) and what you have is the set of integers. But you can prove the number of integers is the same as the number of counting numbers simply by setting up the following one-to-one correspondence. And although it's a little more complex, George showed that the fractions - rational numbers - are also countably infininte.
This can be put a bit more formally as:
|Odd Numbers:
|(n - 1)/2
|Even Numbers:
Now this formulation would probably pass muster in a mathematics journal. But if you want an even more formal representation, you can define the set P containing the ordered pairs:
P = (n, (-1)(n+1)n/2 - [(1 - (-1)(n)])/4)
where n = 0, 1, 2, 3, ...
which is the same as the more familiar algebraic notation:
f(n) = (-1)(n+1)n/2 - [(1 - (-1)(n)])/4
which simply means if you start with a integer, n, and start counting up, it will produce an alternative positive/negative integer list. Start with zero and you'll ending up pairing all integers with the counting numbers like that shown above.
(Like the commercials say, try this formula. It really, really works.)
So you can more than double the number of a countable infinity and still have a countable infinity! The part is the same as the whole and the whole is the same as the part! Very strange but rigorous from a mathematical point of view.
(At this point, we have to admit that although we have shown the formulas for the one to one correspondence of counting numbers and the other sets, we have not actually proven the formulas are correct. This would require a process called mathematical induction. It can be a bit tricky but not so tricky that the average person can't understand it. For a Most Merry and Illustrated essay with an introduction to induction click here.)
What stamped George as a great mathematician is he realized he didn't have to worry about the strange results (although some of his colleagues did). He just accepted them, and with them he invented the concept of cardinality. Essentially the cardinality is simply the size of a set.
For finite sets determining cardinality is simple. That's just the number of elements in the set. For infinite sets, though, it's a bit more abstract. Two sets (and this includes finite sets) have the same cardinality as long as their elements can be paired off in a one-to-one correspondence. Therefore all countably infinite sets - the even numbers, odd numbers, integers, fractions or whatever - also share the same cardinality. Since infinity is not a number, George designated the cardinality of a countably infinite set by the a symbol called aleph null, ℵ0
So far so good. But then George found not all infinities were created equal.
One property of sets is that you can make sets of sets. Take the set { 1 , 2 , 3 }. Now take all combinations of the numbers and put them in sets. What you have is:
{ 1 } , { 2 }, { 3 }, { 1 , 2 } , { 1 , 3 } , { 2 , 3 } , { 1 , 2 , 3 }
Notice that there are 7 sets. In other words, if you have a set with three members you can make 7 sets or 23 - 1 sets. To make it nice and easy, mathmeticians say the empty set {} - that is a set with nothing in it and most often represented by φ - should also be counted as a subset. That makes of eight sets from a set of three elements. So if you have a set of n elements you have a total 2n subsets.
Now put all these sets into still another set and call it the power set of the original set. A power set of a set S is represented by writing by 2S.
So for our set { 1 , 2, 3 } the power set is :
2{ 1 , 2, 3 } = { { 1 } , { 2 }, { 3 }, { 1 , 2 } , { 1 , 3 } , { 2 , 3 } , { 1 , 2 , 3 }, φ }
OK, but what about the set of counting numbers? How many sets can you make from a countably infinite set?
Well, if you go by the formula we came up with above, then it should be 2 taken to the power of ℵ0. But what the heck number is that? I mean a number to the infinity power should be infinity, right? Can't we just say it's infinite too, and say the cardinality of the power set of the natural numbers is ℵ0 as well?
But if the set of counting numbers has the same cardinality of its power set, then the two sets can be put into a one-to-one correspondence. But that raises a more general question. Are there infinite sets that cannot be put into a one-to-one correspondence. For instance, can the counting numbers be put into a one-to-one correspondence with the real numbers?
Now the real numbers not only include counting numbers, integers, fractions (¼ ½, ¾, etc.), but also the irrational numbers like the square root of 2, and our friend pi (3.141592653589793238462643383279502884197, etc., etc.). But at the same time, we remember you can combine a countably infinite set with a countably infinite set and still have a countable infinite set. So could the set of real numbers also be countably infinite? This is where George came up the diagonal argument.
George's proof, we should mention, is an indirect proof. You start off assuming the opposite of what you want to prove. Then you reason (correctly) until you find a contradiction with something you know is true. Once you do that, logicians tell us, then what we wanted to prove in the first place - that is, the opposite of our assumption - is correct.
The diagonal argument relies of being able to represent real numbers as we did in school. You put a decimal point someplace and then put a string of numbers afterwards. That way you can represent intergers, fractions (repeating and non-repeating), and irrational numbers by the same notation
|Type of Number
|Non-repeating fraction
|Repeating fraction
|Irrational Number
|1.414213562373095048801688724209698078569671875 .........
OK. For our indirect proof, we'll start off assuming you can put all the real numbers into one-to-one correspondence with all the natural numbers. To make things simpler, though, we'll restrict our lists to the real numbers between 0 and 1. If they can't be put into a one-to-one correspondence with natural numbers, then the rest of the points on an infinite line sure can't either.
A partial list of the one-to-one corresondence might look something like the following table. Again this isn't to be take too literally but is simply a hypothetical example.
Place in List
But this won't help us prove the theorem. What we need is a more more general representation, all the better to reason with. So what we do is dream up a symbolic list. Ergo:
|Place in List
|0.d11d12d13d14d15d16d17d18d19 ....
|0.d21d22d23d24d25d26d27d28d29 ....
|0.d31d32d33d34d35d36d37d38d39 ....
|0.d41d42d43d44d45d46d47d48d49 ....
|0.d51d52d53d54d55d56d57d58d59 ....
|0.dn1dn2dn3dn4dn5dn6dn7dn8dn9 ....
In other words, write a zero with a decimal point followed by a series of numbers that goes on forever. Remember if - and it's a big if - the real numbers can be put in one-to-one correspondence with natural numbers, then such a list of pairings does exist. It doesn't matter if it would take forever to write it down and we don't know what it is.
But consider this. What happens if we do write such a list - that is we pair the counting numbers with a unique real number? Then we show that there is another number that cannot be in the list? Well, then we've found our contradiction. And that means our initial assumption - that there is the one-to-one correspondence of natural and real numbers - can't be true.
In fact, it turns out our mysterious new number is very easy to write. Call it m and define it as:
m = 0.(d11+1)(d22+1)(d33+1)(d44+1)(d55+1)(d66+1).....(dnn+1)....
In other words. take the diagonal elements of the original list - that is, take d11, d22, d33, d44, d55 and all the rest - and then add one to them. Then line them up after a zero and a decimal point. This is a real number, and if our assumption that the real numbers and counting numbers have a one-to-one correspondence it true, then that number will be somewhere in our original list.
(Strictly speaking, what we do is slightly more complicated. If dmm is 0 through 8, then we substitute dmm + 1 for dmm. But if dmm = 9, the dmm becomes 0).
All right. Just where does this number fit in the list? It can't be the first place because the first number after the decimal point is d11, not (d11+1). It can't be the second place either since the second number is d22, not (d22+1). Third place? Nope. That has d33 not (d33+1).
It's the same for any number you pick. There is no place in the whole lousy list where you can put the new number, m. That is, for any natural number n the new number cannot be put in the list since the original list had dnn and our new number has (dnn+1).
And the consequence? If the real numbers and rational numbers were in a one-to-one correspondence, then any number we come up with should have been in the list. But we have a number that is not and can never be in the list. That's our contradiction. So our assumption you can put the two sets into the correspondence is incorrect.
At this point it's tempting to say, "Well, you can add one to a countably infinite set and still have a countably infinite set. So we'll advance every number by one place, and stick in the new number. So now we have our one to one correspondence with the counting number.
Well, that doesn't work either. You can still take the new diagonal, add one to each number, and come up with a number that's not in our new list. You can't win, and the real numbers and counting numbers cannot be put in a one-to-one correspondence. We'll elaborate some more on why you can't expand the list later.
But consider this point. If the real numbers and counting numbers cannot be put in a one-to-one correspondence and we are coming up with extra numbers, then there are more real numbers than counting numbers. That means there's too many real numbers to count. Now that means we have two types of infinity. One is countable (the natural numbers) and the other is uncountable.
Calling a spade a spade, George called this new and uncountable infinity an uncountable infinity. And it turns out that a lot of sets are uncountable: the number of points on a line, the number of points on a plane; stuff like that. Since this infinity is larger than the earlier infinity, George called this infinity, aleph one, ℵ1.
How are these two alephs related? Well, do you remember the power set of natural numbers? George believed that that if the cardinality of a countable infinity is ℵ0 then the cardinality of an uncountable set ℵ1 is:
ℵ1 = 2ℵ0
This equation represents what George called the continuum hypothesis. He also believed that there were no infinities between these two numbers. That is, there is no set whose cardinality is between the cardinality of integers and the cardinality of the real numbers.
Despite George's efforts to prove the continuum hypothesis he had no luck in doing so. That's because it can't be proven. The continuum hypothesis is instead independent of the other axioms of set theory. That was shown by the work of two men. In 1940, Kurt Godel showed the continuum hypothesis cannot be disproven with the axioms. Then in 1963 Paul Cohen proved they can't be proven either.
That means the continuum hypothesis is like Euclid's fifth proposition. It is independent of the other axioms. If you want, you can create a set theory where the continuum hypothesis is true. Or you can create a set theory where it is not.
The point to remember is the counting numbers are a subset of the real numbers, and the two sets are not equal. Ergo, there are more real numbers than counting numbers and ℵ1 is larger than ℵ0.
The diagonal argument bothers a lot of people, and you will find many spittle flinging diatribes on the Fount of All Knowledge (i. e., the Internet) that attempt to prove it is wrong. All of these objections - regardless of how much mathspeak they use - are erroneous and can be distilled down to simple but subtle misunderstandings.
A common error we mentioned before is to believe you can indeed bump-up-the-numbers and slip in the new diagonal number. And as we pointed out, slipping in a new number only leads to a never ending goose chase since you can always create a new diagonal that's not in the list. But some people reason that because you can engage in a wild goose chase, then that means the real and countable numbers are indeed the same size. This belief, though, is due to a misunderstanding of proper reasoning using an indirect proof.
Remember, our premise was all real numbers could be assigned uniquely to every counting number. But then you found a real number that could not have been assigned to one of the real numbers. So you found a contradiction. This, then, invalidates your premise. So if you now say you can bump the numbers up to establish a one-to-one correspondence, you are saying you can do what you just proved impossible.
The crucial point is that any contradiction derived in an indirect proof invalidates the premise, which in turn was the opposite of what you are trying to prove. Finding just that one extra number proves there is not a one-to-one correspondence between the reals and the counting numbers - and that there are more real numbers. Saying you can bump up a number to prove George was wrong actually means you've proven George was right.
But yes, you say, you found a contradiction. But that only means some assumption is false. Who knows? Maybe, there is another fundamental flaw in arithmetic that really caused the contradiction - not the assumption of a one-to-one correspondence between the reals and the counting numbers. What about that?
Well, in the next section we will show that there is a proof which, though it may seem indirect, is in fact, not. Instead we will devise an effective method, to generate unique real numbers each of which will be assigned to every counting number. We will then prove there are real numbers that cannot be assigned to natural numbers.
There is another characteristic about the proof that bothers people but they find hard to articulate. This problem is that in the diagonal proof you first define a pairing of the natural numbers and real numbers. That is you have a set of pairs of a natural number and a real number. Then once you do that, you not only create another pair of numbers, but a pair that is defined from the set you just created. Then it looks like you assume this new pair of numbers is in the original list!
Creating a set and then defining a new element that is based on the original set and is in the original set is disturbingly similar to how you produce Richard's Paradox (first described in 1905 by Jules Richard). Not only that, but we read that defining new elements from an infinite set and then placing the new elements in the original set is exactly what renders Richard's and other paradoxes invalid. So why is the diagonal proof valid and Richard's Paradox is not?
Actually there are two reasons. Remember that Richard's paradox creates an ordered list of English sentences, each sentence defining a number (actually Jules wrote in French). The paradox next creates a sentence based on the properties of the entire list and then claims this new sentence belongs with the original sentences. So Richard's paradox improperly mixes definitions of the numbers themselves with the properties about the numbers. George did not do that.
But more importantly George is not assuming or placing the new pair of numbers in the old set. He is simply identifying a real number and asking if that number is in the original list and then proving it is not. It's actually irrelevant that he created the new number by adding 1 to the diagonal. He could have pulled a number out of his - ah - hat as long as he could prove it wasn't in the original list. Using the diagonal method just happened to be the simplest method to do this. Any number that can be shown not to be in the original list shows us that the belief that natural and real numbers can be paired is incorrect. And it is incorrect.
Strangely, you'll find there are people who believe the diagonal argument is wrong because the proof uses dots when writing a series of numbers 1, 2, 3, ..., n, ...., etc. For some reason they triumphantly point out the dots - particularly at the end - mean you can always slip in as many counting numbers you need for any number of real numbers.
Fortunately that objection is totally erroneous because the dots are simply a simplification of more rigorous notation, an objection disposed of quite easily by using the more rigorous notation as we will not proceed to do.
The diagonal proof is, we will restate, accomplished by first writing a function that maps every counting numbers with a unique real number. For the two sets of numbers to be the same size, then every real number must have a corresponding natural number.
All right. We'll add the rigor here and point out that our function is formally an ordered pair of numbers, something anyone with middle school math is familiar with. The first number is a unique natural number and the second number of the pair is a unique real number. Our function is the set of all such ordered pairs.
So to begin George's proof completely without dots, we now define a set of ordered pairs:
A bit of explanation may be in order. What the formula above means is we have defined a set of all ordered pairs (x, yx) where x is a member of the natural (counting numbers). This means that there are as many ordered pairs as counting numbers.
The second element of the ordered pair yx is defined as:
The part of this equation, yxi, is in turn defined as:
yxi = RND( {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} )
That is, yxi is simply a single digit from 0 to 9 but randomly selected.
Knowing that the capital letter Sigma, Σ represents summation, we see that yx is a number represented by a decimal point followed by a random infinite series of the digits from 0 to 9. Ergo, the ordered pair (x, yx) has a counting number for the first number and a real number for the second.
First we need to deal with the pesky requirement that yx values are unique. But fortunately we don't need to have some algorithm to weed repeats out since there can be no repeats. A little minor reflection tells us that no two values of yxi are identical.
Alas, for those for whom the reflection does not yield immediate gratification, consider two numbers. Call them, yr and ys. We will define them as we did yx but sum over a finite number, k, of randomly chosen digits.
For instance, if k = 10, then yr and ys could be.
yr = 0.4408754017
ys = 0.8598501984
Now of course if we kept trying we would eventually end up with two values that happen to be equal. But just what is that probability? That is, yr and ys will be the same?
yr = 0.5200845709
ys = 0.5200845709
Well, that's easy enough to calculate. Since we have k digits (here k = 10), the probability that two series of digits of length k are equal is given by:
That is, if, we have two series of numbers that are 2 digits long, the odds that the numbers are equal is 0.01. If they have three digits, then the odds are 0.001 they will be the same. With 10 digits (as we have in our example) we have a probability 0.0000000001.
So if yr and ys have an infinite number of digits:
This means that with our definition of yx with an infinite number of random digits after the decimal point, no two yx values will be the same. Ergo, each yx will be unique.
(Note: We emphasize that is not true if k is a finite number. Then if you create enough yx values, then eventually you'll find two that are the same. That's the famous Birthday Problem but generalized.)
What we have done, here, is not set up a premise for an indirect proof. Instead, we have defined an effective method for generating unique real numbers, each of which can be assigned to a unique counting number. What follows, though, may appear similar to our earlier indirect proof is actually a direct or constructive proof.
Now at this point we have to wonder. So far we've generated an infinite number of real numbers each having an infinite number of digits. Now the point to note is that if there are the same number of real numbers as counting numbers, then there cannot be any more real numbers than the ones we have created. And if we can find at least one more real number, then the two sets do not have the same number of elements and there are more real numbers than counting numbers.
And you'll probably guess how we'll do that. Yes, we'll just take our previously defined ordered pairs, (x, yx) and keeping in mind that yx is built up from a series of digits, yik, we'll write the following ordered pair:
Here yii is digit i from number yn of our previously (and hypothetically) defined set of ordered pairs. As before if yii = 9, then we take yii + 1 = 0, not 10.
(Note: For you sticklers for exactness, that means we actually define the ordered pair, as { n, Σmod( [yii + 1] / 10) } )
All right. Can the ordered pair be in our original set? Or rather what value of n can we select so is equal to some yx of our original ordered pairs?
Since no digit is equal to itself plus 1, there is no such n. Furthermore, no matter how we change the real numbers assigned to the counting numbers, substituting new reals for the old ones, shifting numbers up and inserting new ones - doesn't help. The number defined as yii + 1 - or more exactly as mod( [yii + 1] / 10) - will always be an extra number not in the original list. So you will always have more real numbers than counting numbers.
But (the holdouts continue to say), how can this be an effective method for assigning the counting numbers to a unique real number? Because each real number is an infinite series, you could never write it down. So you can't assign a real number to each counting number because it would take forever to do so. Clearly, the holdouts shout triumphantly, George didn't prove anything, and his claim that there are two infinities is as chimerical as having two political parties that can put partisan politics aside for the good of the country.
But sadly, we must point out that this is indeed an effective method. That is it is if you understand what infinity really means.
Saying something "goes on forever" isn't really a proper definition of infinity. That's because "going on forever" is simply a way of saying something is infinite. So this (vague) definition of infinity simply says something is infinite if it is infinite.
So a better way to define an infinite series is that no matter what number I pick, there is always a number that's higher in rank. Or equivalently, a list is infinite if you cannot name a counting number that does not have an associated member of the series. So for any counting number, I can determine the xth digit of the associated real number simply by generating a random number from 0 to 9. I don't have to write down the whole series.
But if you do that then I can tell you the corresponding digit of a number not in the list. I simply by adding one to your random number.
So we'll summarize what we've said about why George's proof is correct.
So what have we done? Well, our effective method for assigning real numbers fulfills the requirement for Step 1. The diagonal method - adding 1 to the diagonal element - fulfills the requirement of Step 2 and Step 3. So being able to bump up the numbers in the list is completely irrelevant to the validity of the proof.
To put it another way, if someone says George is wrong, then the burden is on them to prove that if you assign a unique real number to the counting numbers you can't create a new number. But by adding 1 to the diagonal element, you can always create that number.
Soddy, old chaps, George was right. You can't enumerate the real numbers, there are more real numbers than there are natural numbers, integers, or rational numbers, and there's nothing we can do about it.
In any case, we now have the diagonal argument. And we've proven that there are more real numbers than counting numbers. But now what can we do with it?
Well, how about proving there are more truths in the universe than we can prove? The diagonal argument has let us do that. But first we need to decide what it means to prove something. And to do that we need to know what we mean by a theorem.
In math or logic, when you want to prove something you have to start with a set of premises. In math these are axioms or previously proven theorems. Then by deductive reasoning you arrive at your conclusion.
Now if you do this right, each step of your reasoning is either an axiom, a previously proven theorem, or a new statement derived (correctly) from one or more of the previous steps. Eventually (if you're correct) then the last step in your line of reasoning will be the final conclusion you want. That last line is the theorem. The whole list of symbols from top to bottom is your proof.
The simplest and most boring "proof" in the history of mankind began with Aristotle. But it shows the difference between a proof and a theorem.
|All men are mortal.
|Socrates is a man.
|Socrates is mortal.
In this case the theorem is the final sentence. "Socrates is mortal." That's what you have proven. The proof is the list of sentences that lead to the final statement.
In essence then a proof is a list of statements arrived at by a given set of rules. Whether the theorem is in English or another "natural" language or is written symbolically doesn't matter. What's important is a proof has a finite number of steps and so uses finite number of symbols.
Now it is true that the number of symbols is open ended. If you don't want to use English you can use mathematical and logical symbols. In that case, you can have an unlimited number of variables which can be written as x0, x1, x2, ... and so on forever. But at most we can only use a countably infinite number of symbols. So any theorem must be shorter than a countably infinite number of steps and the limit of symbols is likewise countably infinite.
So no matter how many theorems we prove, books we write, or politicians give speeches, the symbols used will always make at most a countably infinite list. So at most there are only a countably infinite number of mathematical theorems and so only a countably infinite set of proofs.
So now as the $500 an hour psychiatrist said after a year of twice a week sessions, we can begin, yes?
OK. Let's take the set of natural numbers and make the power set. That is make all possible subsets of the natural numbers.
Then pick a number, any number. We'll pick the number "1". Then for every subset it will be either true or false that "1" is a member of that particular set. So there is at least one true mathematical statement associated with each subset of the natural numbers.
But wait. How many truths do we have? Well, since the number of subsets of the natural numbers is uncountably infinite, there must be an uncountable number of true mathematical statements.
But remember what we said above? We only have a countable number of theorems. So there are not enough theorems to prove all the true mathematical statements.
Yes, Virginia, there are true mathematical statements that can't be proven.
How about that?
Metalogic: An Introduction to the Metatheory of Standard First Order Logic , Geoffrey Hunter, University of California Press, (1973).
As hard as it is to believe, there are many people who think that the CooperToons Merry Histories and Educational Essays are written in a spirit of sarcasm and in fact are satires of scientific, philosophical, and theological writings. But a quick perusal of Geoffrey's book (just the first chapter for crying out loud) will show you that the proof given in such painful length and detail above is essentially that which Geoffrey gives us with much less wind.
Geoffrey's book is intended for people who have some introduction to formal logic but otherwise its for the layman who is interested in going beyond the "Socrates is mortal" type schtick. As he points out, if you take a logic course in college they usually end before you get to studying the interesting stuff.
An alternative proof, by the way, to show there are true statements with no proof is to realize you have specifiable sets which can be expressed as a formula, and there are other sets which cannot be specified as a formula.
For instance the set of even numbers, E, is defined as:
E = {x: x = 2n where n = 1, 2, 3, ...}
This is read as "The set E is the set of all x such that x = 2n where n = 1, 2, 3, ...
So in general a set, S, is specifiable if you can write it like:
where P(x) is a formula you can plug x into and get a member of the set.
Now you can only prove an element is in a set if the set is finite - which means you can check each element if you have the time - or if you have a formula for determining if the element satisfies the equation. But there are only a finite number of formulas or at best a countably infinite number of formulas. As we showed there are uncountably infinite sets, there are sets without an associated formula and yet are infinite. So you there are some sets where you can't tell if a given number is a member or not - even though it is. So once more we have more true mathematical statements than we have proofs.
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text:
State regulation of newspapers would violate human rights laws, a key adviser to the Leveson Inquiry declared yesterday.
Shami Chakrabarti came out against the report's recommendations that the press might have to be shackled.
Lord Justice Leveson, who conducted the inquiry into Press standards in the wake of the phone-hacking scandal, wants newspapers to set up an independent regulator backed by law – and calls for compulsory regulation if that body fails.
But Ms Chakrabarti, head of pressure group Liberty, says that would violate Article 10 of the European Convention on Human Rights which guarantees free speech and is enshrined in Britain's Human Rights Act.
One of six assessors who worked with the judge on the inquiry, she said: "In a democracy, regulation of the press and imposing standards on it must be voluntary."
A compulsory statute to regulate media ethics in the way the report suggests would violate the Act, and I cannot support it."
She stressed there was a huge difference between her view and the proposed reforms.
She explained: "Leveson doesn't want compulsory regulation of the press but says if they don't play ball, politicians may have to consider it. That is where I get off the bus."
PM David Cameron has rejected a prop-osed Leveson Law regulating the press but agreed to draft up the judge's recommendations to prove they would be unworkable.
Chancellor George Osborne yesterday backed Ms Chakrabarti, telling the Andrew Marr show: "Shami Chakrabarti spoke very powerfully about the risks of legislation."
The Government also yesterday rejected an ultimatum by Ed Miliband to agree new laws regulating the press within weeks.
The Labour leader backs the Leveson Report in full and demanded the Government accept it by Christmas or face a Commons vote in the New Year. He said: "In the next two to three weeks, we have got to have a resolution."
And Shadow Culture Secretary Harriet Harman revealed Labour had begun work drafting its own law.
But Mr Osborne said the parties should continue talking to find a consensus on the recommendations.
Shadow Chancellor Ed Balls even hinted at divisions within Labour when he said: "I'm somebody who was always very sceptical about imposing statutory legislation on the press but that's not what Leveson did."
Meanwhile, actor Hugh Grant, 52, who was caught in a car with an LA prostitute in 1995 and has led recent calls for press reform, branded Mr Cameron's position "very close to disgraceful".
But amid the growing furore, it emerged around 2,000 editors had agreed to sign up to a new independent press watchdog.