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4 On Beach Road
About 4 On Beach Road
Welcome to 4 On Beach
Our very popular 4 on Beach offers spacious, comfortable and laid back self-catering accommodation in a furnished 3-bedroom, first-floor unit situated in Melkbosstrand, conveniently located within walking distance to the beach and restaurants. The unit comprises 3 bedrooms, 3 bathrooms, an open-plan kitchen and dining area with an indoor braai, and a lounge area with full sea views.
The first bedroom contains a double bed and a built-in wardrobe with en-suite.
There is also a seating area with tea- and coffee-making facilities.
The second bedroom contains x2 single beds with amazing sea views. Private bathroom for this room down the corridor.
The third bedroom contains a double bed with a built-in wardrobe. This bedroom has its own en-suite bathroom with a shower and a bath, as well as a private seating area with tea- and coffee-making facilities.
The kitchen is fully equipped with a fridge/freezer, oven, stove, dishwasher, washing machine, microwave, and features a breakfast bar. The open-plan kitchen leads directly to the dining area with indoor braai facilities. The sea view lounge is equipped with a TV, seating for up to 8 guests, and a cupboard with board games.
The unit is ideal for families, groups of friends, water-sport enthusiasts, or business travellers. The location offers easy access to some of Melkbosstrand's popular restaurants, such as Cafe Orca, Damhuis Restaurant, Seafood Lapa, I Love Melkies, and The Hart. The property is approximately a 10-minute walk to the MyCiTi bus link to Big Bay, Bloubergstrand, Table View, Century City and Cape Town. There is a shopping centre opposite the bus terminal for guests convenience.
All welcome!
Beach: White sandy beach for long strolls & exploring. Icy cold water, but amazing waves for surfing & kite surfing. Fantastic location for stand-up paddling & swimming.
Golf: Atlantic Beach Golf Course is a 5 min drive from us.
Family friendly: Across the road from the beach for swimming or exploring. Ice cream house on the beach front. Endless amounts of friends to be made.
Romantic: Come and spoil your other half with our sea view accommodation, long strolls on the beach, days out to Cape Town & Wine Lands. Not to mention our very sought after restaurants.
- Response Rate: 100%
- Enquiry Response Time: 7 hours
- Minimum stay: 1 Days
- Type: Guest House
- Sleeps: 7
- Check-in: 2:00 PM Check-out: 10:00 AM
- Laundry Facilities*
- Braai/Barbecue
- Beach
- Indoor Fireplace
- Hiking
- Wi-Fi
- Credit Card Facilities
- Parking on Premises
- Romantic
- Cosy
- see more
Languages Spoken
- English
- Afrikaans
- No TGCSA Grading
25% OFF Beach Holiday
Stay between 24 Oct 2018 and 30 Nov 2018 and get 25% off.
4 On Beach Road Map
*Distances are shown as the crow flies and not necessarily the actual travelling
Things to do in and around Melkbosstrand
Melkbos Beach
(0.9 km from Melkbosstrand)
The first West Coast beach you will encounter on leaving Cape Town is Melkbos. Perfect for long, lazy walks and safe swimming, Melkbos Beach offers beautiful views of Robben Island and Table Mountain. The sunsets are stunning. Good surfing...
Koeberg Nature Reserve
(5.3 km from Melkbosstrand)
Eskom controls 3000 ha of West Coast around the Koeberg Nuclear Power Station. In keeping with both Eskom's environmental policy and national conservation trends, Eskom has decided to open this property to the public. Grysbok, Steenbok and the...
Dikkop Hiking Trail
(0 km from Melkbosstrand)
The Dikkop Trail is a 13 km circular walk through the dunes and fynbos and a 2 km walk along the beach. The walk is at its most beautiful in spring, when the wildflowers are in bloom.
Atlantic Beach Golf Course
(1.6 km from Melkbosstrand)
The beautiful Atlantic Beach Golf Course is an 18-hole links-style course, just 700 metres from the beach. Complete with lovely views of the ocean and Table Mountain, few courses can match the sheer pleasure of playing this course. This is a full...

subset: commoncrawl


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Sale S1803 Lot 5
LENOX TABLEWARE - To include one Rose pattern bulbous vase; white sugar and creamer with pewter bases, White salt and pepper shaker; small candleholder with gold trim; one Mystic plate with black stamp and one Flower Basket plate with gold border, 8.5", 9" diameter. 7 Pieces total, green stamps on rest, good condition, tallest 8"H.
Sold for $25
© Pacific Galleries. Images, descriptions and condition reports used on this site are original copyright material and are not to be reproduced without permission. For further information telephone 206.441.9990


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On September 23, a group of 12 exotic auto rental agency owners and entrepreneurs gathered in Las Vegas and formed a new industry association, says Ron Sturgeon, newly-elected Chairman of the Exotic Auto Rental Association and owner of DFW ELITE Auto Rental.com.
Pooling marketing resources and expanding opportunities for one of the fastest-growing segments of the U.S. automotive rental business were on the minds of the businesspeople in attendance. As a result, the first order of business for the new association will be a web marketing initiative from the association's home on the web, www.ExoticAutoRentalAssoc.com/.
Sturgeon estimates there are only 40 true exotic auto rental agencies in the U.S., so the turnout for the inaugural meeting comprised about 25 percent of the industry.
At the meeting, founding members of the association created bylaws, a dues structure, elected officers and managers and specified standards for membership. In his role as chairman, Sturgeon outlined an agenda that focused on standardizing the quality of the exotic car rental experience.
John Killand, long-time owner of Rent A Vette in Las Vegas, was elected to serve as secretary for the group and Shane Atwood, owner of Precious Metals Cars in Savannah, Ga., will serve as manager. In addition, Fedor Suica from Showcase Exotic Rentals in Newport Beach, Calif., was elected Treasurer, and Moe Mustafa, owner of Chicago Exotic Car Rentals, was also elected manager.
For additional information, contact Ron Sturgeon at email@example.com, or visit the association's Web site, http://www.ExoticAutoRentalAssoc.com/.


text: In March of 2014, I began a journey I was in no way prepared for… I decided to start a Christian blog. At the time, it wrongly assumed it would be easy. I would simply write a post every now and then, and people would come to my website and read what I wrote. Little did I know all that I would encounter during the next few years. Starting a blog was so much more involved than I had anticipated… but it would also prove to be more rewarding than I could ever have imagined.Read More 4 Reasons to Start a Christian Blog (and 3 reasons not to)


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The Nike Classic Cortez 15 Nylon Women's Shoe remixes a retro running look with a sleek nylon upper and suede detailing. The iconic EVA midsole wedge creates cushioned comfort and an authentic throwback appeal.
Cortez OriginsThe Nike Cortez was Bill Bowerman's first masterpiece, built to be lighter and more weatherproof than any other shoe. In 1972, it put unprecedented cushioning under the fastest feet in the running world and quickly became the most popular training shoe in the USA. It was an unmistakable icon—a walking billboard that told your story and declared your affiliation—and came to thrive with fierce style on the streets of Los Angeles. Since then, no shoe has expanded the definition of a running shoe quite like the Nike Cortez.
Write Your Own Review
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After a repaving project caused motorists to suffer a month of bumper-to-bumper commutes, all lanes on Interstate 15 were expected to be open early today .
"We're happy with the results," said Michelle Booth, a spokeswoman for the Nevada Department of Transportation. "It looks really good, it rides smooth."
Though motorists were mostly thankful that the road was being repaved between Tropicana Avenue and the Spaghetti Bowl, she said others slowed down to yell profanity at crews this weekend as they worked around the clock to get the project done 10 days early.
"We didn't appreciate that," Booth said.
All northbound lanes opened Saturday night, while southbound lanes were choked to one lane much of Sunday until a second southbound lane gradually opened up starting at 8 p.m.
Pole dividers for the express lanes and striping still need to be added, but that won't happen until later this month and is not expected to cause much delay, she said. That job is expected to take three nights between 9 p.m. and 5 a.m. only.
"Those are jobs that are very common," Booth said. "We don't need to close a bunch of lanes for that."
The $6 million repaving project on Nevada's busiest roadway started Sept. 11 and was expected to be finished Oct. 20. The stretch of I-15 hadn't been repaved in 15 years and badly needed the job, Booth said.
"I know it was a burden on the drivers," she said. "We're so glad they cooperated with us, so that we were able to get this job done. People have been really receptive once they drove on it."
Contact reporter Jessica Fryman at firstname.lastname@example.com or 702-383-0264.


text:
Getting My decals for cups To Work
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text:
I really enjoyed your writing style and the book was very intriguing. I feel now I have a better understanding of what you all went through before, during, and after the war. I can't tell you how much my appreciation has grown for the sacrifice made whether they truly wanted to or not. Your description and detail made me feel like I was there. And I don't know if this will come of as corny or something you say just to say, but I truly mean it when I say thank you for your service and thank you for telling the story of Company K. I cannot express the gratitude my husband and I have for you writing this book and finding that his great-grandfather (whom he was close to) is included in this book. I am sure many others feel this way. It is a good feeling that through your words the memory of the men of Company K, 335th Infantry, 84th Division will not soon be forgotten.
Regarding William Via, I certainly do understand more of his personality and have an understanding regarding the circumstances around the time he lost his stripes. But, I do still have questions maybe you can offer your opinion or clarify my understanding? I know he didn't seem to want to go into detail on why he was "away like that," but in your opinion do you believe it was out of cowardliness or he somehow got separated and was simply trying to stay alive until he could get back?
Regarding his personality, do you think he was the type of person that once you got to know him he was more personable or friendly? Not as distant that is.
Another question I have is of the circumstances regarding him earning his stripes back. I know he says he went to the first platoon with Prewitt and got them back, but do you know how? Would one earn them back through good conduct or showing ambition?
Jessica McCormack
Message Thread
« Back to index
This board is dedicated to the memory of CAPTAIN LEONARD REED CARPENTER, Company Commander, November 19, 1944 - March 27, 1945.
BOARD HOST: Allan W. Howerton (E-mail: firstname.lastname@example.com)


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We are very pleased to witness that our Athenoxat-1 has reached her 1000 and 1 nights in orbit and continues her journey healthily bringing us many magical images of Earth and the Universe. We always remember the days before Athenoxat launch when we hoped she could be our pride and now our hope has come true.
Athenoxat is a very special bird in her class; she can bring to us the complete view of Earth with day and night images from a global perspective, wide angle and high resolution. She is also the first in her class to readily transmit images for the Radio Amateur community to receive.
To this day we have accumulated much experience in nanosatellites and especially Athenoxat operation. Starting from manual to 24/7 automated operations, and configuring many options and settings for enabling many unexplored features that have brought us new and different experiences as compared to other nanosatellites operation. We hope that Athenoxat-1 will never cease in giving us wonders and thus let more magical journey begin.
Please write to us for any feedback.
A microrocket does not seem complicated if you have a Scanning Electron Microscope (SEM) to look at it, otherwise it appears even simpler as you do not see it at all with naked eye, so most of us cannot relate to it. But now imagine: that rocket has a throat 10 times narrower than a human hair thickness. Something you cannot even see will produce a precise and adjustable thrust of 1mN (nominal at full throttle), just right to maneuver an orbiting nanosatellite.
We produce it by means of photolithography, deep reactive ion etching, anodic bonding and dicing, just like the accelerometers and gyroscopes of your smartphones, airbags and drones.
We start from a thin dish of silicon, because it can be precisely etched by a plasma of very reactive elements (SF6). This means that if such dish is covered by a protective layer patterned with the profile of the nozzle, then such reactive elements will just dig that profile in the silicon.
So, we cover the dish, called "wafer", with a uniform and thin layer of a polymer, by spinning a drop of it on the wafer while is quickly rotating for a few seconds. Then we expose it to ultraviolet light (UV) through a mask that has a transparent image of the nozzle: either multiple microscopic images spaced to cover the whole wafer or few larger images that are projected through a lens system that scales them down to their final microscopic size and then is moved to repeat the exposure on the rest of the wafer.
We develop the polymer with a chemical to remove the area that was exposed to the UV light and we immerse the wafer in quickly alternating cycles of reactive plasma and passivizing Teflon to cover the etched walls so that the etching progresses perpendicularly to the wafer and produces the beautiful high aspect ratio groove that forms the nozzle (Deep Reactive-Ion Etching).
After the etching is completed on both faces, which involves a second exposure aligned to the first one, we bond a glass wafer on the silicon by means of high temperature and voltage. At the end we cut the wafer to release hundreds of micronozzles !
Those are the micronozzles that, firstly designed by CFD and then carefully characterized one by one on our specially made microbalance, have been mounted on POPSAT and have been working in Space for 9 months of micropropulsion experiments.
Please write to us for any feedback.
When we started Microspace, we sketched a Roadmap to define all project steps needed to reach our final goal of Nanosatellites formation flight; that sketch was adopted in the initial European Space Agency (ESA) harmonization documents as early as 2002. Our Microhtrusters are rocket engines, just very, very small. The first step to develop any rocket engine is to calculate its main dimensions for the thrust we want to achieve. This is easy, you can take the Sutton or any other similar book, no need to be "rocket scientist". But this will give you just a couple of diameters and a length, and you would be lucky to achieve half of the maximum possible efficiency. That is why we used Computational Fluid Dynamics (CFD) to simulate the flow in the nozzle as accurately as possible before starting any expensive manufacturing.
CFD is the art of calculating pressures, temperatures, velocities and other flow parameters on small elements of the whole flow domain by means of approximations and interpolations using numerical methods. One of the most used is the Finite Elements Method (FEM), where the flow values are evaluated on nodes of a grid and the flow behaviors are interpolated by means of polinomial shape functions along the grid or integrated in the elements resulting by the grid segments, whereby such functions are expressed by physical laws such as the Navier-Stokes equations (which are a particular case of the 2nd Law of Newton). In our case, compressibilty, viscosity and turbulence have been included in the calculation and a particular formulation of the elements at the walls has been used to consider the boundary layer. Once the domain is modeled, it is meshed with a proper subdivision in Elements of Finite dimension, all equations on all nodes and elements are combined and the resulting matrix is solved, usually by iterations since CFD is highly non linear and hence the matrix cannot be just inverted like for structural, thermal or magnetic problems.
The results are then represented by means of colors or vectors or both and the overall properties of the flow can be integrated over the domain, control volumes or cross sections to understand the performances of the design. Usually many designs need to be attempted before the best shape is identified. As we will explain in another article, many shapes have been simulated and tested to obtain the exact design rules for our special micronozzles. This is how we can achieve the maximum possible efficiency.
Please write to us for any feedback.
As part of celebrating the 2 years of Athenoxat-1 in space, we activated the new type of her data beacon, which is image type. She is now beaconing image thumbnails that she had produced by herself. It was very satisfying to know that the Radio Amateurs community is excited about this new feature. The new beacon type has also enabled Athenoxat-1 to send QSL cards to those who have listened to her before. Scheduled transmissions have been conducted successfully confirmed by the joyful recipients. The above images are the cards that have been transmitted out by Athenoxat.
It is a very interesting, cool and challenging experiment and I think it should continue! Thank you and congratulations to the Athenoxat-1 team.
- Edson PY2SDR (IARU Advisory Panel Region 2)
We, Athenoxat-1 team, are very encouraged by the enthusiasm expressed by the Radio Amateurs community. Mike DK3WN and Roland PY4ZBZ have taken the initiative to build Athenoxat image decoder to help the community reconstruct the images received via radio packets. It is indeed an exciting experience to be able to work and learn together with people across the world who may eventually become our personal friends.
Please write to us for any feedback.
Not many people would have bet it two years ago, so now we are very, very happy to celebrate the second year of Athenoxat-1 in orbit. She has been very good and performing very well to our satisfaction. We are grateful to those who have supported her from the very initial idea conception to realizing and helping her growing to be the today's proudful bird in her class.
We are wishing her always a healthy life and wonderful journey to the 100,000 orbits and more, a smooth sailing to the bright Universe and colorful Eclipse. Hear hear... :)
Please write to us for any feedback.
Field trip! Field trip! Everyone loves field trip, and so do we. We visited a few places and received warm welcome from the community. Everyone was very excited to hear the story of Athenoxat. Interestingly we received similar questions regarding our mother Earth and life in space.
So is it really true that the Earth is flat?
Have you seen aliens by means of Athenoxat?
- Students
We believe Athenoxat and her beautiful experiences and images have inspired the community. It was a really fun trip for us and we are looking forward to doing it again.
Please write to us for any feedback.
We are very happy to celebrate the first year of Athenoxat-1 in orbit! We presented her first year wonderful images in Singapore Science Centre as well as organized our own party hosted by IMDA PIXEL Labs@NDC and kindly sponsored by Ferrari Food + Wine. We were very honored to have been visited by the representatives of Italian Embassy in Singapore. Of course we were also excited meeting our friends at the party. Lots of food and free flow of Bottega Gold !
Telemetry data from Athenoxat shows very good power budget. There is no shortage of memory storage and thousands of images have been produced and downloaded to our ground station in this one year. So we toasted for the continuing good health of Athenoxat-1 and certainly for many more achievements in Nights and Days imaging. Congratulations and Happy Birthday Athenoxat ! We are very proud of you !
Please write to us for any feedback.
Here we are again ! SmallSat 2016 in Logan, USA was a perfect place to present the results of Athenoxat-1 that have been achieved so far, due to the large attendance of small satellites producers and users. We presented during the weekend of Cubesat Workshop focusing on the Remote Sensing capability but also touched on the Horizon Detection capability, of which algorithm has been developed in-house. The algorithm works perfectly, capable of determining the correct Nadir Vector based on the fisheye imaging inputs provided by Athenoxat's secondary payload.
How long is the processing time of the Earth horizon detection and nadir determination?
Is the nadir determination done real-time onboard or in ground station?
How much is the exposure time for the main payload?
Those are the questions we received during our presentation Q & A session. It was very encouraging to know how many people are interested in Athenoxat capability. Perhaps we can collaborate with them in the future. But in the mean time, we really had fun experiencing the conference. Informative presentations, good food, good companies, interesting parties, and beautiful landscape ! And oh, our complete article and presentation can be found here.
Please write to us for any feedback.
Athenoxat-1 is finally in orbit ! She was successfully launched by PSLV rocket C-29 together with the other 5 passengers to the destination of equatorial orbit with 15 degree inclination. Unfortunately due to restriction in photo taking in the launch integration site, we can't show any integration pictures here. But in our free time, we managed to snap some photos of the interesting surrounding of the integration site.
The last few days we had with Athenoxat-1 on Earth were spent carefully and meticulously to check and recheck that all hardware and software settings have been properly configured. Visual inspections as well as health and functional tests were conducted several times to ensure Athenoxat is in her best fit possible. The satellite deployer was also properly measured and tested to ensure it performs correctly as desired. On the last day, we pat goodbye and mounted Athenoxat in her deployer on the rocket head. And lastly we can only wish our Athenoxat may the Universe be with you.
Not long after she was deployed into her orbit, Paulo PV8DX, Mani VU2WMY as well as ourselves confirmed her singing in the Universe telling her name and battery voltage. We were so relieved and excited to start this orbital journey with our beautiful bird. We hope for the best in this mission and may the good Signals be with us all !
Please write to us for any feedback.
It was my first experience attending the famous gathering of Small Satellites including Nanosatellites & Cubesats community. They have chosen one of the most beautiful places that is a small cute town called Logan in the USA. Beautiful scenery certainly influences the spirit of the people. It started with the weekend Cubesat workshop where many cubesat makers presented their interesting work and results. So not to miss the opportunity, we also presented the results of our first Nanosatellite, which is POPSAT, in the SmallSat Conference, which was held on the next several days after the Cubesat workshop.
We were proud to show that our POPSAT is one of the pioneers that has been able to demonstrate the use of micro-propulsion in the nanosatellite class for the attitude control and maneuvering. We have designed and characterized by ourselves the micronozzles in Microspace laboratory. The micro-propulsion is based on Cold Gas system, which in the case of POPSAT, we have used Argon, which is completely safe for the application thanks to its inert, non-flammable and non-toxic properties. The micronozzle itself is based on Silicon, fabricated with the matured MEMS technology. Our in-orbit demonstration with POPSAT shows that our simple cold gas micro-propulsion system is capable of attaining 43 second specific impulse in average, with total delta V of 5 m/sec based on 7.8 bar initial pressure. Here is where our complete article and presentation can be found. In summary, with the successful in-orbit demonstration of POPSAT, we are now able to say that our Micro-Propulsion unit is at the highest Technology Readiness Level !
Besides presenting our POPSAT results, we had good time enjoying the company of others browsing through their most up-to-date technology products. And when the Conference was over, we certainly did not miss the opportunity visiting the nearby Hill Aerospace Museum and it was the right choice before ending our trip in Utah. Till next year then !
Please write to us for any feedback.
Our very first nanosatellite POPSAT-HIP1 is now in orbit, alive and singing ! It was a joyful yet a little nervous moment for us since it was our very first experience in having our hard work launched to space. Yesterday POPSAT was launched to his polar Sun-synchronous orbit by DNEPR rocket together with the other 32 satellites. It was a very valuable experience to be able to visit the launch integration site and meet several other teams from different parts of the World.
Besides ensuring a healthy and functional satellite, our main objective being present in Yasny integration site was to perform propellant filling to the propulsion tank of POPSAT. In this launch, POPSAT was the only Nanosatellite having micro-propulsion unit as a payload. It was not an easy task to begin, but with excellent cooperation between us, our launch agent ISL, and the launcher Kosmotras, all went well. And thanks to Kosmotras, we were allowed to take photos of the rocket parts in the integration room.
Due to the nature of POPSAT's orbit, we could only have our very first contact with him 7 hours from his launch time. Thankfully the presence of Radio Amateurs community made it possible to know the health of POPSAT in orbit just in a couple of hours. Mike DK3WN reported POPSAT strong signal over Germany right after the launch and we were very grateful for that. So from today on, our journey together with POPSAT begins !
Please write to us for any feedback.


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ARC stands for Advance Review Copy. An ARC reviewer receives a free copy of a book for an honest review. You can sign up for my ARC team by filling out the form below.
– All reviews MUST be posted to Amazon within 14 days of receipt. Anywhere else is optional.
– For those who are already members of the newsletter, after you sign up you'll be sent to a Subscription Confirmation page. That's the verification page to show you've been added to the ARC list.
– Since the goal of the ARC sign up is to gather loyal reviewers, the ebook page will be checked on the 14th day to verify that a review was posted. You don't have to notify me when you post a review. Reviewers who have been inactive for 2 consecutive book launches will be removed from the ARC team.


text:
Rendang is a fragrant meat dish originally served in Indonesia. However its rich spicy flavour made it so popular that it is also commonly served in Singapore.
Beef rendang is one of Daniel's favourite Singapore cuisine and a
must-have when we visit. However he has high expectations of this dish.
While he's happy to eat rendang anywhere, my aunt's homemade from
scratch rendang is his favourite. No restaurant or hawker has come close
to replacing Daniel's favourite. How much of it is sucking up? To be
honest I have no idea since a simple request of rendang often results in
a wide spread of all his favourite dishes for dinner the next day – all
cooked by my aunt.
Rendang is something I've never (and maybe never) cooked from
scratch. The list of ingredients scares me to death and the actual
cooking time required tests my patience. Most importantly, I have no
confidence in recreating anything as close as my aunt's rendang – not
even 50% as close. Therefore, it is one of those dishes that I'm happy
to use premix paste for.
I found Prima Taste's Rendang at an Asian supermarket in town and
decided to give it a try. I had my fears. It takes less effort than
cooking from scratch but I hate ruining dinners. What if it tastes
Thankfully, my two hours effort of cooking this dish didn't go to
waste. It was flavoursome, creamy enough (add just enough water to
immerse the meat but not make the rendang watery) and the meat turned
out tender.
I'll admit that it is not like my aunt's rendang but it's excellent
quality given that it's from premix paste! I love rendang when it's
"dry" because it means that the meat has soaked up lots of the spices.
The ones that have too much gravy left over tend to be diluted and less
satisfying. I also love adding potatoes to my rendang and then serving
the dish with a bowl of steaming hot white rice. As a kid I've always
loved to mash my potatoes, mix them with rice and rendang (or any
curry!). That to me is a good dinner.
Note: Recipe can be found here.


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What effect would U.S. inflation have on other currencies?
They would rise relative to the dollar
They would fall relative to the dollar
No effect
I'm not sure
Which of the following high-risk/high-reward investments have you invested in recently?
Private Equity
Foreign Currencies
Small cap stocks
None of the above
Have you ever heard about trading in the foreign currencies market?
Yes, I already trade foreign currencies
Yes, I am interested in trading
Yes, I want to know more
No, I am not interested
The differences of currency markets over traditional investment markets offer you an exciting, new market that you will not find anywhere else.


text:
Welcome to the online extension of Excellence in Government 2014. You may watch any of the sessions and access additional resources once you have registered.
Excellence in Government's mission is building the agency of the future. As workforce demographics shift and businesses develop new ways of managing and measuring performance, the federal government must be poised to respond — and to compete in the new landscape of work. These sessions will look at:
- Talent & Hiring - Global and U.S. workforce demographics are changing. With a new, more diverse generation on employees entering government, how can agencies recruit and grow top talent?
- Culture & Training - The culture of an organization is vital to employee retention. How are federal leaders building agencies and departments with great culture? How are they developing talent that supports that culture?
- Data & Performance - The future of work is data-driven. From decision-making to performance management, how are government agencies leveraging metrics, big data, and technology to improve employees work and program outcomes?
- The New Workplace - The rising workforce works in non-traditional ways. How are agencies leveraging flex schedules, mobile offices, and green buildings to build a workplace of the future?
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Announcing the Spare Parts Newsletter
Each week, I come across a bunch of awesome stuff that doesn't make it on to the blog. I've started a free weekly email, the Spare Parts Newsletter, as a place to share things like:
- Links to interesting articles and videos.
- New tools and techniques.
- Interesting stuff that's not about web development.
- A summary of the articles on my site from the last week.
Sound interesting? Sign up for free here.


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Easiest Caramel Popcorn
- 1 10-ounce bag of marshmallows
- 1 cup margarine or butter
- 1 cup brown sugar
- 3-4 bags microwave popcorn (about 20-25 cups)
- Heat the sugar and butter in a large microwave-safe bowl in the microwave until melted.
- Stir and add the marshmallows; microwave for 1-2 minutes, until melted.
- Stir to combine, then pour over popcorn, stir to coat, and let cool.
Recipe Courtesy Of: fabulesslyfrugal.com/easiest-caramel-corn-ever
Parmesan Herb Spiced Popcorn
- 4 tablespoons butter
- 2 teaspoon Italian seasoning
- 1 teaspoon garlic powder
- 1 teaspoon sea salt
- 8 cups popped popcorn
- 1/2 cup grated parmesan cheese
- In a small sauce pan, melt the butter over medium heat.
- Add the Italian seasoning, garlic powder and sea salt and stir to combine.
- Pour the spiced butter mixture over the popped corn.
- Add the grated Parmesan and toss to combine.
- Add salt if needed.
Recipe Courtesy Of: whatsgabycooking.com
S'mores Popcorn
- 1 bag of microwave popcorn (unbuttered)
- 1 bag (2 cups) milk chocolate chips
- 2 cups mini marshmallows
- 2 cups graham cracker pieces and crumbs
- Spread popcorn evenly on parchment paper.
- Crush graham crackers to make 2 cups of crumbs.
- Melt chocolate chips and a small scoop of shortening (if desired, to thin chocolate) in the microwave.
- Drizzle over popcorn.
- Sprinkle mini marshmallows and graham cracker crumbs over popcorn.
- Repeat process until all chocolate and marshmallow/graham cracker is gone.
- Allow to cool and then enjoy!
Recipe Courtesy Of: www.bombshellbling.com/category/edible-crafts
Easy Sriracha Lime Popcorn
- 8 cups BOOMCHICKAPOP sea salt popcorn (or popcorn of your choice)
- 4 Tbsp melted butter
- 2-3 Tbsp sriracha
- 1 tsp lime zest
- 1/2 Tbsp lime juice
- Garnish with minced cilantro if desired
- Melt butter.
- Stir in additional ingredients.
- Toss popcorn in butter mixture and serve!
Recipe Courtesy Of: www.thechunkychef.com


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- 284 Visitors


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You can't let the light of love in if your walls are shutting it out.
It is normal to be nervous about opening up to current or potential partners. However, you're not doing your love life any favors by never letting anyone in.
Relationship coach Jasbina Ahluwalia offers insight on what causes you to be so cautious and how to let your guard down. She says that one of the biggest reasons we build a wall is the fear of rejection.
In order to let your wall down, you must face your fear of rejection and realize your self worth. Build up your self worth in order to bring down your walls. Watch the video above for tips on how to let down your walls and let love in.


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C. S. Bennett (1887)
Posted By: Pat Hochstetler (email)
Date: 10/27/2007 at 16:41:08
Winterset Madisonian - January 27, 1887
Winterset, Iowa
page 4
Our Chip Basket
By a telegram from C. S. Beerbower, to his father, Mr. S. Beerbower, we learn that C. S. Bennett, a son-in-law of G. A. Beerbower, of Lincoln township, died in Florida, Monday the 24th instant. His home was in Cedar Rapids, and he had gone south in the hope of recovering his health.
Madison Obituaries maintained by Kent Transier.
WebBBS 4.33 Genealogy Modification Package by WebJourneymen


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This is a PRIVATE website owned by John Skakel. Contact us HERE
Cemeteries Office Staff have asked that users NOT contact them with questions directly.
Remember. Family, Friends, Historians, etc can add information in any page. Family photos. Details of the person's life. Details of the family "Tree". etc. Just email for details. Please see "Contact us"
William A. Johnston
Jane (McMaster) Johnston
Baby Johnston
George Johnston
William J. Johnston
William Johnston
Margaret Ann (McMaster) Johnston
Margaret Melissa Johnston
Gladys Lorain Bowels
Cemetery Lot Number...1786 E & W
Location: Center East Front, Rows 7 & 8
William A. & Jane Johnston
Main stone, Full view
William A. Johnston
3/30/1819 - 2/21/1903, Aged 84 Yrs.
His Wife,
Jane (McMaster) Johnston
7/**/1830 - 10/2/1890, Aged 60 Yrs.
William A. Johnston
Footstone "Father"
Jane (McMaster) Johnston
Footstone "Mother"
Unmarked; Baby Johnston, George Johnston, William J. Johnston, William Johnston, Margaret Ann Johnston, Margaret Melissa Johnston and Gladys Lorain Bowels, see index page.


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I agree - the law must be followed. So many got easy with the Obama way - no laws followed. So wrong. So lets get back to normal and start arresting those that don't obey.
Employers will be charged for obeying the LAW
sostwinch #21
Montecresto1 #22
Pretty sure the State AG said he was going to do that.


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Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold
© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. F, ch. 4.3, p. 101
Section 4.3.3. Use of fusion proteins
aLaboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0560, USA
Fusion proteins have been frequently used in a variety of applications (reviewed by Nilsson et al., 1992), such as preventing proteolysis, changing solubility and increasing stability. They have also been used – although less frequently – for crystallization. The disadvantage in the context of crystallography is that the length and flexibility of the linker chain often introduce mobility of one protein domain relative to the other, which can impede, rather than enhance, crystallization.
Donahue et al. (1994) were able to determine the three-dimensional structure of the 14 residues representing the platelet integrin recognition segment of the fibrinogen γ chain by constructing a fusion protein with lysozyme, which was then crystallized from ammonium sulfate. Kuge et al. (1997) successfully obtained crystals of a fusion protein consisting of glutathione S-transferase (GST) and the DNA-binding domain (residues 16–115) of the DNA replication-related element-binding factor, DREF, under crystallization conditions similar to those used for GST alone.
In many cases, a fusion protein is made to aid in the isolation and purification of the target protein, and the intervening linker is engineered to contain a proteolytically susceptible sequence. However, subsequent cleavage to separate the two proteins can introduce the possibility of accidental proteolysis elsewhere in the protein. This was observed with a fusion protein between thioredoxin and VanH, a D-lactate dehydrogenase, where attempts to remove the carrier resulted in non-specific proteolysis and VanH inactivation (Stoll et al., 1998). Fortunately, cleavage was unnecessary, and conditions were identified under which the authors were able to crystallize the intact fusion protein.
A novel approach to crystallizing membrane proteins is provided by the fusion protein in which cytochrome was inserted into a central cytoplasmic loop of the lactose permease from Escherichia coli (Privé et al., 1994). Although crystals have not yet been reported, the cytochrome attachment provides increased solubility together with the ability to use the red colour to assay the progress of crystallization trials.
ReferencesDonahue, J. P., Patel, H., Anderson, W. F. & Hawiger, J. (1994). Three-dimensional structure of the platelet integrin recognition segment of the fibrinogen γ chain obtained by carrier protein-driven crystallization. Proc. Natl Acad. Sci. USA, 91, 12178–12182.
Kuge, M., Fujii, Y., Shimizu, T., Hirose, F., Matsukage, A. & Hakoshima, T. (1997). Use of a fusion protein to obtain crystals suitable for X-ray analysis: crystallization of a GST-fused protein containing the DNA-binding domain of DNA replication-related element-binding factor, DREF. Protein Sci. 6, 1783–1786.
Nilsson, B., Forsberg, G., Moks, T., Hartmanis, M. & Uhlén, M. (1992). Fusion proteins in biotechnology and structural biology. Curr. Opin. Struct. Biol. 2, 569–575.
Privé, G. G., Verner, G. E., Weitzman, C., Zen, K. H., Eisenberg, D. & Kaback, H. R. (1994). Fusion proteins as tools for crystallization: the lactose permease from Escherichia coli. Acta Cryst. D50, 375–379.
Stoll, V. S., Manohar, A. V., Gillon, W., Macfarlane, E. L. A., Hynes, R. C. & Pai, E. F. (1998). A thioredoxin fusion protein of VanH, a D-lactate dehydrogenase from Enterococcus faecium: cloning, expression, purification, kinetic analysis, and crystallization. Protein Sci. 7, 1147–1155.


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Based on extensive research, this lays out the thinking of the most successful Network Computing knowledge experts, those who are adept at continually innovating and seeing opportunities.
This is the first place to go for Network Computing innovation - INCLUDED are numerous real-world Network Computing blueprints, presentations and templates ready for you to access and use.
Also, if you are looking for answers to one or more of these questions then THIS is the title for you:
Is cloud computing network computing or not? Is network computing really adding value to research? What actually is cloud network computing and how does this service work? Is computer networking and network computing the same thing? If not, what's the difference? What are some examples of BOINC (Berkeley Open Infrastructure for Network Computing) software being used for commercial purposes? How can I find server software for a Net Computer (NC100) Multi-User Network Computing Terminal? Virtual Network Computing:What is the Screens application for iOS like? Virtual Network Computing:How can I configure RealVNC viewer so as it never disconnects? What technological or other breakthrough has made cloud computing possible today? What is the difference between cloud computing and network computing concepts like a WAN? I have to make a presentation on virtual network computing. Where can I find the best information or data about it?


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Previous work on mathematical models of cultural evolution has mainly focused on the diffusion of simple cultural elements. However, a characteristic feature of human cultural evolution is the seemingly limitless appearance of new and increasingly complex cultural elements. Here, we develop a general modelling framework to study such cumulative processes, in which we assume that the appearance and disappearance of cultural elements are stochastic events that depend on the current state of culture. Five scenarios are explored: evolution of independent cultural elements, stepwise modification of elements, differentiation or combination of elements and systems of cultural elements. As one application of our framework, we study the evolution of cultural diversity (in time as well as between groups).
1. Introduction
In social science and the humanities, there is a long tradition of describing complex culture [1–4], and of exploring the evolution of culture and cultural systems [5–10]. An important observation about human culture is that it evolves in a seemingly open-ended manner which, among other things, includes the potential for the appearance of cultural elements of increasing complexity and refinement, and to form systems of culture [6,10]. Our aim in this theoretical paper is to develop a theory of cultural accumulation and explore how the cumulative aspect of culture may contribute to cultural diversity. To achieve this aim we will conceptualize cumulative culture in a way that lends itself to mathematical formalization.
The basic units of our theory will be cultural elements and dependencies between such elements. By a cultural element we here mean anything that may or may not be present in a given human society at a given time, like a tool or artefact, a method, an idea, a piece of knowledge. Dependencies refer to relationships between elements, such that the presence of one cultural element affects the likelihood that another element appears or disappears.
Dependencies between cultural elements seem to us to constitute the core of what cumulative culture is about. Other conceptualizations of cumulative culture in the literature seem to be special cases that are too limited. For instance, it has been proposed that cumulative culture is a culture that cannot be created within a single generation [11,12], which excludes cultural progress that proceeds in several steps within a single generation, and also begs the question why some culture cannot be created at such a high speed. Another example is the metaphor of cumulative culture as a ratchet [13] or as an irreversible process [10,14], which excludes the possibility that a cultural element can be lost and creates a one-dimensional image of progress. Dependencies between cultural elements, on the other hand, may describe not only refinement or progress, but also differentiation, combination of elements, substitutability (different solutions to the same problem), loss, and so on. Indeed, we propose that such 'multi-dimensional' aspects of cumulative culture are at the root of cultural diversity between societies. Specifically, we claim that accumulation of culture leads to diversity only if there are rich branching possibilities (differentiation and combination) or mutually inhibiting cultural elements, such that if one is present it inhibits the appearance of the other. We discuss these aspects in detail below.
Isaac Newton's famous statement that 'If I have seen further it is only by standing on the shoulders of giants' [15] could serve as a motto for our theory of cumulative cultural evolution. The general implication of this motto is that in order for human culture (of which science and mathematics are prime examples) to become increasingly sophisticated, it is not necessary that increasingly intelligent and creative individuals are born [16]. As knowledge, methods, ideas and tools cumulate, a new innovator who has no more talent than his predecessors can still come up with an innovation that is superior to what any predecessors have produced, precisely because he already has access to the contributions these predecessors made. In our theory we conceptualize this in probabilistic terms; a certain cultural element x may be very unlikely to appear, or even impossible, without the presence of some other cultural element y; when y appears (for whatever reason), the subsequent appearance of x may suddenly become highly likely.
The individuals of society are not explicitly represented in our models, despite the obvious fact that human agency is central in developing and transmitting culture. The virtue of an agent-less model is of course its simplicity, and the justification for making this simplification lies in Newton's statement. Although Newton was an exceptional scientist and mathematician, there is no reason to believe that the development of, say, differential calculus would not have happened without him; indeed, building on Descartes' work on analytical geometry, Newton's contemporary Gottfried Wilhelm Leibniz independently came up with an equally good solution to the problem of developing what is known as differential and integral calculus. To put it in general terms, the reason an agent-less model makes sense is that the innovations made in a society at a given time seem to be related much more strongly to the society's current culture than to its specific individuals. The framework we are proposing could be extended to include individual agents and thereby account for the degree to which a cultural element is established in a society (see §8). However, for the qualitative phenomena that we will discuss, it is sufficient to consider cultural elements as either present or absent in the society.
With these ambitions and limitations, our models are very different from the previous work on modelling cultural evolution. Such work has typically focused on how a predefined set of cultural elements may compete and spread in a population [17–21]. A smaller number of models allow accumulation of new cultural variants, but only along a single dimension [19,22–25]. These models are all individual-based, and the object is often to explore coevolution of genes and culture [26–28]. Whereas coevolutionary models consider how culture both influences and is influenced by genetic evolution, we are here interested in the impact of culture on its own evolution.
In the following, we will give a precise formulation of our theoretical framework, and then present a series of models exploring how different types of dependencies lead to cumulative cultural evolution that results in very different levels of cultural diversity between societies.
2. A framework for describing how the past influences the future in cumulative culture
It seems to us that almost every part of modern human culture (words, constructions and artefacts, behaviours, social organization, etc.) would have been alien to prehistoric humans. This illustrates that most cultural elements are not part of any ready-made human repertoire but instead come into existence in a particular population at some particular point in time. Here we will use the term 'appearance' for all such events, by which we mean that a cultural element is established in the population to the extent that it can influence further cultural change. Thus, we take a macroscopic approach in which we consider cultural elements that are present at the level of a cultural group (the framework can be extended to individual-based models by tracking the state of each individual rather than the population as a whole; cf. [29]).
The framework we develop here has two main features: it describes cultural evolution as (i) a stochastic process that (ii) at any point of time is partially dependent on the current cultural state. To say that a process is stochastic means that events occur with some probability, thus capturing the notion that cultural evolution is not completely predictable. Nor is cultural evolution completely unpredictable; the more we know about the current state of the world, the more accurately we can predict the coming events. In other words, future cultural evolution is not independent of the past.
There are many ways in which a current cultural element, say y, can influence the evolution of another cultural element, say x. For instance, if x can be obtained as a modification of y (possibly in combination with other cultural elements), then clearly x is much more likely to appear if the precursor y is present; the precursor could then either be replaced or remain and contribute to diversity. There are also more indirect types of influence, such as an element of general knowledge or an attitude that promotes or inhibits the appearance of x. An innovation may depend on more than just a single precursor and be subject to many indirect influences. This leads us to the notion that cultural elements often interact in larger cultural systems, which we will briefly explore in one of our models.
As a first step towards gaining a general understanding of processes of cumulation of complex culture, we will ignore the precise nature of the relationships between different cultural elements and only consider, in the abstract, how the probabilities of appearances and disappearances change when new elements appear or current elements disappear. From this perspective, there are only three ways in which y can influence the appearance of an element x that is currently not present: y may either facilitate or inhibit the appearance of x, or have no effect at all, i.e. be neutral or independent. These basic influences are described and exemplified in table 1. Disappearances of cultural elements follow the same logic: if x is already present then its disappearance may be either promoted or inhibited by y, or be independent of y.
The probability of x appearing may of course depend on more than one other element. Indeed, it may depend on a large number of cultural elements as well as the current natural environment. To make possible a general description of such multiple dependencies, we will use the concept of a current state of the world. We will usually use the symbol S to denote the current state of the world.
(a) Conditional probability functions of appearance and disappearance
As a means to capture the totality of dependencies of future culture on the present culture, we introduce the following pair of mathematical objects: These are mathematical functions that for any cultural element x and any state of the world S return the conditional probability that x will appear, respectively, disappear (within some given short time period) given that the world is in state S. We will presently discuss how to mathematically represent the state of the world.
We want to emphasize that these probability functions can account not only for any dependencies of the current state of the world but also for other aspects that affect appearance and disappearance, such as cultural transmission and functionality. For instance, ceteris paribus, a cultural element that is difficult for individuals to acquire would have a lower appearance probability and a higher disappearance probability; similarly, a useful cultural element would typically have a higher appearance probability and a lower disappearance probability than a similar but useless element.
(b) Starting conditions and cultural seeds
A special case to consider is the situation where there exists no culture yet. It seems to us that almost all cultural elements are such that they can arise only in the presence of other cultural elements. In other words, only a very limited set of cultural elements are such that they can possibly appear from a situation where there is no previous culture. We will call such elements cultural seeds. In our models we will always assume that there is a limited number m of possible cultural seeds. The starting conditions of the cumulative process are defined by the set of cultural seeds and the probabilities for their respective appearances. These conditions will obviously affect the start of the cumulative process; for instance, higher probabilities of appearance of cultural seeds will lead to faster initial accumulation. However, initial conditions may also influence long-term evolution, for instance, by favouring one cultural system over another through path dependence. (We will discuss this further in §7.)
(c) Representing the state of the world
In principle, the variable S in the conditional probability function should specify every single detail of the world that can potentially affect the probability of appearance or disappearance of a cultural element x. This might include cultural factors as well as genetic and environmental factors. In practice, though, we need to specify models where S captures only the most relevant aspects of the world. In the present paper we will only deal with cultural states, but it would be just as easy to incorporate genetic or environmental influences (e.g. if one wanted to model that iron-based artefacts are more likely to appear in an environment where iron ore is easily accessible).
To describe cultural states we shall use the formalism of set theory. A state is defined as a set of elements (listed within curly brackets), so that for instance S = {y, z} means that S consists of elements y and z. States change when new elements are added or old elements are removed. We will denote the addition of a single element x to a set S by S + x. Thus, for the example above we would have S + x = {x, y, z}. Similarly, we will denote the removal of an element by the minus sign, so that in our example we would have S − y = {z}. The number of elements in a set S is denoted by |S|, so in our example we have |S| = 2.
(d) An example of complex cumulative cultural evolution
As an example of how our framework might apply in practice, consider the proof of the Four-Colour Conjecture (4CC), a long-standing conjecture in mathematics stating that the regions of any map can be coloured using at most four colours so that no two regions sharing a border have the same colour [30]. The problem was first proposed by Francis Guthrie in 1842 and eventually gained wide attention among mathematicians. A proof of the conjecture was published by Alfred Kempe in 1879, but 11 years later it was shown, by Percy Heawood, to contain a crucial error. The conjecture withstood the continued attacks of many mathematicians for another century until it was proved by Kenneth Appel and Wolfgang Haken in 1977. By combining new ideas of their own with an idea developed in the 1960s by Heinrich Heesch (which itself built on Kempe's work), Appel and Haken succeeded in reducing the conjecture to a large but finite number of cases that were verified case-by-case using a computer. Thus, when Appel and Haken finally proved the 4CC they benefitted from several achievements by other people. In order to describe some core aspects of this instance of cultural evolution within our framework, we define four states of the world: We claim that the probability of the appearance of a correct proof of the 4CC ought to increase as the state of the world changes from S0 to S3: The interpretation of these inequalities is as follows. First, an innovation (the proof of 4CC) is more likely to happen if there is an explicit idea that such an innovation may be possible (the 4CC itself). Second, an innovation that is a combination of several parts is more likely if some part already exists (Heesch's idea). Third, a labour-intensive innovation is more likely if there exists adequate labour-saving tools (computers).
(e) Combinations, components and facilitators
The above example illustrates two main ways in which a pre-existing cultural element y can influence the likelihood of the arrival of a new cultural element x. One possibility is that the new cultural element x is a combination where y is a component (like Heesch's idea is a part of Appel and Haken's proof). To express that x is a combination of y and z we may write where ○ denotes the operation by which the parts have been combined. The above example also shows how an element may facilitate the appearance of x without itself being part of x. The computers were necessary to carry out the proof but are not a component of the proof itself.
Generally, we will say that an element y facilitates the appearance of another element x if, for all relevant states of the world, it holds that Pr(+x |S + y) > Pr(+x|S); similarly, y inhibits the appearance of x if Pr(+x|S + y) < Pr(+x|S).
(f) Representing dependencies between cultural elements as a graph
Relationships between elements are often effectively illustrated using a graph with vertices and edges representing elements and relationships, respectively. We will draw edges with closed arrowheads for facilitating relationships, while open arrowheads signify inhibiting relationships; no edge means no relationship (i.e. independence).
The graphs in figure 1 represent some specific models that we will investigate. We have chosen these examples to illustrate a diversity of cases. To explore the extent to which cultures tend to diverge or remain similar, we define the similarity of two cultural states as the proportion of all elements present in either state that are shared by both states. See appendix A for details.
3. Independent cultural elements
A number of recent models have studied the evolution of independent cultural elements (figure 1a; [29,31–34]). Although these models allow accumulation of elements over time, they are not strictly models of cumulative culture in the sense of this paper because the appearance of new elements is neither facilitated (nor inhibited) by the existence of other cultural elements. In our framework, this means that the probabilities of appearance and disappearance of a cultural element are constants: 3.1and 3.2From the point of view of our framework, this is the baseline case where there are no other possible elements than the cultural seeds themselves (i.e. all elements are accessible from a culture-less state). Throughout this paper we denote the number of cultural seeds by m. Hence, in this model there are only m elements that are at all possible.
Let nt denote the expected number of elements present at time t. The expected number of elements present at time t + 1 can be computed as 3.3where the first term accounts for the disappearance of a fraction qdis of elements that exist at time t, and the second term is the expected number of elements that appear, out of the m − nt that do not exist at time t. Assuming that there are no elements at time 0, we have n0 = 0 and equation (3.3) has the unique solution 3.4As t grows, the number of elements approaches the equilibrium value 3.5
Figure 2 illustrates how the expected number of elements varies over time. Although the expected number develops smoothly from 0 to the equilibrium value, simulated evolutionary trajectories present chance fluctuations in both the number of elements and which elements are present at a given time. Nevertheless, if the probability of appearances is significantly higher than the probability of disappearances, then the equilibrium number of elements will be close to m (saturation) and hence any two cultures will tend to become quite similar (figure 3). Indeed, assuming that both cultures are characterized by the same two parameters, qapp ≫ qdis, we can obtain an explicit solution. In this case, the formula for the expected cultural similarity at time t, (A 3) in appendix A, simplifies to 3.5which at equilibrium takes the value 3.6
Here we see clearly that the expected cultural similarity is close to 1 if qapp ≫ qdis. The same saturation phenomenon also implies that culture will be rather static, as typically almost all m possible elements will be present at any given time once equilibrium is reached.
4. Stepwise modification
There are few formal studies that consider culture as more than a collection of independent elements. To our knowledge, the only relatively well-studied case is that of an ordered succession of elements, representing successive modification of an ancestral element (figure 1b). For example, tools such as hammers may be arranged in a succession of increasing functionality [6]. Element 0 of the succession would describe lack of hammers, element 1 very crude hammers such as unmodified stones, and so on. Alternatively, a succession can represent the stepwise development of a one-dimensional quantitative trait (e.g. the length of a spear), which is most efficient at some particular value [19,22]. We here consider the former case for illustration. Formally, we write xi for the element at position i, and we assume that it can appear if the preceding element xi−1 exists: 4.1As above, each element has an independent probability qdis of disappearing. In this model, progress along the dimension is linear in time, provided qapp > qdis (figure 4a). This is the only possible path of cultural evolution, hence this model also produces considerable similarity between independently evolved cultures (figure 3).
It is easy to modify the model so that at any given time, the best of all present variants have a lower disappearance probability than inferior variants, which might be more realistic. However, in simulations we have found that such a modification does not lead to any qualitative change in results.
5. Differentiation
In models of culture as an ordered succession, each element can be elaborated upon along a single dimension only. Typically, however, cultural elements can be modified in many ways. Hammers, for instance, can be specialized to serve different purposes, with an increase in the diversity of hammer types as well as an increase in the efficiency of each type. Such an increase in diversity can be referred to as cultural differentiation.
A culture that evolves by differentiation of existing elements can be represented as a branching tree that originates from one of the cultural seeds (figure 1c). At any time during the differentiation process, any element can potentially differentiate into one or more new versions. Here we assume that all such differentiation events occur independently of each other with probability qapp. Thus, any element x that is not a cultural seed has a unique (direct) predecessor, π(x). Only elements that are currently present can differentiate, so similar to the previous model of successive modifications we have 5.1
The difference from the previous model is that an element may become the direct predecessor of more than one new element. In our simulations, we have set the number of potential successors to two. Under our usual assumption that each element has an independent probability qdis of disappearing, the expected path of cultural evolution is exponential growth in the number of elements, provided that qapp is sufficiently larger than qdis (see [34] for a related model and empirical examples of exponential cultural growth). An interesting observation is that individual runs of the model show considerable variation in the time of onset of accumulation but thereafter grow in a quite regular manner (figure 4b). Exactly which elements appear among the many possible choices, however, is a matter of chance. This results in little similarity between independently evolved cultures (figure 3).
6. Combinations
We now consider a model in which new cultural elements can be formed by a combination of the existing elements. For instance, a food y and a spice z can be physically combined to produce a dish x = y ○ z. However, by combination we also refer more broadly to any cultural element that can arise only if two (or more) component elements are present (such as the combination of mathematical ideas with computer technology in the the proof of the 4CC, as discussed earlier).
For simplicity, we assume here that only pairwise combinations can be formed, and that any two elements can be combined in only one way (y ○ z = z ○ y). However, we will assume that the order of successive combinations is crucial for the result. For example, cooking foodstuff y with technique z and then adding foodstuff w results in the dish (y ○ z) ○ w, which is generally different from the dish (y ○ w) ○ z obtained by first combining the raw foodstuffs y and w and then cooking with technique z.
As usual, we will assume that there are m cultural seeds that can be invented directly from a culture-less state. Any other element can only be formed as a combination of two other elements, and can appear only if both components are present: 6.1As in our previous models, we assume a constant disappearance probability of qdis.
Cultural growth in this model is very fast, even faster than the exponential growth we saw in the model of cultural differentiation. The reason is that the number of elements that can be invented by pairwise combinations of n elements is of the order of n2, while the number of elements that can be invented by differentiation is proportional to n.
Figure 4c shows the expected number of elements, computed as an average over 100 simulations. Similar to the case of differentiation above, in individual runs of the model, growth is initially erratic but becomes very regular after a few elements have appeared. At this stage, losses become negligible compared with the very high number of innovations that can appear by combining elements.
Figure 3 illustrates the average similarity of two independently evolving cultures. During the initial stages of growth, expected similarity increases owing to the relatively high probability of the cultures inventing the same cultural seeds and some of the simplest combinations. After growth picks up, however, the likelihood that the two cultures invent the same complex combinations is very small, hence similarity between cultures tends to drop quickly towards zero.
Finally, figure 5b illustrates the growth in complexity, defined as the number of evolutionary events (creations of cultural seeds and combinations of elements) necessary to create a certain cultural element. Thus, the complexity of a cultural seed is 1, the complexity of y ○ z is 3, etc. As shown in the figure, the average complexity increases rapidly.
7. Cultural systems
In all previous models, the appearance of a given cultural element has depended on at most one or two others. In this section, we consider the cultural evolution of 'systems' of culture, in the sense of sets of interdependent cultural elements.
We first consider a model in which the probability that a cultural element appears depends on all elements in the culture. Here we assume that there is a set of N potential cultural elements, each of which may stand in either a facilitating or inhibiting relationship with any other element (as discussed in §2). For instance, a technology for melting iron ore may facilitate the appearance of iron tools; the practice of keeping an animal species for companionship may inhibit consumption of its meat.
To construct a simple model, let us say that an element x is inhibited in cultural state S if S contains more inhibitors than facilitators of x, and assume that x can appear in state S only if it is not inhibited in this state: 7.1We also assume, as usual, that an element has a fixed probability qdis of disappearing at each time step. The outcome of this model depends on the probability that elements facilitate or inhibit each other. When few inhibiting dependencies exist, most elements can appear in most cultural states, resulting in cultures with most of the m possible elements being present. In turn, this results in a high level of similarity between independently evolved cultures (figure 8). When the probability of inhibiting dependencies increases, cultures evolve to contain a smaller number of elements, and consequently are more different from each other.
Dependencies between cultures can also, potentially, influence the disappearance of elements. For instance, we may assume that an element that is facilitated in state S cannot disappear from that state: 7.2An influence of cultural state on the disappearance of elements may give rise to new phenomena, among which rivalling systems and combinations of independent systems.
(a) Rivalling systems
Figure 6 shows the dependencies between eight cultural elements represented as a graph in which edges represent facilitating relationships, and absence of edges represents inhibiting relationships. In this graph, we can identify two cultural systems: A = {1, 2, 3, 4} and B = {5, 6, 7, 8}. By this we mean that elements within A typically facilitate each other and inhibit elements outside A, and the same goes for B. Neither system, however, is perfectly free from conflict. For instance, within system A elements 3 and 4 inhibit each other and facilitate outsiders 5 and 6, respectively. Nevertheless, we expect cultural evolution to establish either system A or system B. Which of these two systems becomes established is a matter of chance events in the beginning of the evolutionary process.
In 1000 simulations of this example, using the appearance and disappearance rules equations (7.1) and (7.2), the culture ended up in system A 406 times and in system B 594 times. Thus, owing to the strong influence of cultural state on the appearance and disappearance of elements, the similarity between two independently simulated cultures was always either 0 or 1.
(b) Combinations of independent systems
When there are also neutral relationships between elements, collections of several smaller cultural systems can emerge and coexist independently of each other. An example is given in figure 7. Here, there are four identifiable systems: C = {1, 3}, D = {2, 4}, E = {5, 7} and F = {6, 8}. Systems C and D are mutually exclusive, as are systems E and F. However, the first two systems are independent of the second two. In this situation, we therefore expect any of the four possible combinations of systems (CE, CF, DE and DF) to become established with equal probability.
In summary, complex webs of positive and negative dependencies between potential cultural elements will give rise to emergent cultural systems or collections of systems. Characteristics of such systems are that: (i) they are highly path-dependent, so that different cultural groups may develop very different cultural systems despite the same initial potential for culture; and (ii) the systems consist of elements that are on the whole mutually supporting but where some conflict between elements may be unavoidable (e.g. elements 3 and 4 in system A in figure 6).
8. Discussion
In this paper, we have developed a theoretical framework for exploring cumulative cultural evolution. It is based on the simple idea that the existing cultural elements can facilitate or inhibit the appearance of new elements as well as the disappearance of present elements (table 1). With many cultural elements, the set of interdependencies can become arbitrarily complex (e.g. norms about what can be eaten can influence farming, breeding, household practices, etc., and can be influenced by religion and other traditions), so that evolution can only be understood if the whole system is studied together.
By describing how different cultural states influence the appearance and disappearance of cultural elements, we can explore long-term cumulative cultural evolution as a succession of appearance and disappearance events. By studying a series of different scenarios, we have shown in this paper that the nature of dependencies between cultural elements has dramatic effects on the pattern of cultural evolution. For example, when any given element facilitates the appearance of several similar elements, we observe a process of cultural differentiation in which the number of elements grows exponentially in time. In contrast, if elements can vary only along a single dimension, we observe linear growth. We stress that both the description of dependencies between elements and the process of cultural evolution that emerges from such dependencies lend themselves naturally to mathematical formulation. Indeed, they would be very difficult to explore without mathematics.
The results we have derived here raise many questions for future work. Below, we first discuss our results on the evolution of cultural diversity, then we discuss some open issues.
(a) The evolution of cultural diversity
The expression 'cultural diversity' can refer to several phenomena. Thus in developing a theory of cultural diversity we can ask many distinct questions, such as:
(1) Why do different cultures exist, and what determines how many different cultures are there?
(2) Given that distinct cultures exist, what governs their similarities and differences?
(3) What determines the number of cultural elements within a culture?
(4) What determines the diversity of cultural elements within a culture, in terms of similarities and differences between the elements?
(5) What determines the extent to which individuals within a cultural group carry the same or different cultural elements?
Here we have mainly considered questions (2) and (3). Our analysis has highlighted a number of factors, summarized in table 2, that influence both the number of elements in a culture and the extent to which two independently evolved cultures share common elements. The first factor is the number of branching possibilities, that is, the possibilities to create new cultural elements from the existing ones (e.g. by differentiation or combination). If there are plenty of such possibilities, we have seen that cultures tend to become larger and less similar to each other (figures 3 and 5). Figure 4 also shows that, when many innovations are possible, cultural elements accumulate longer histories, i.e. they arise from many evolutionary steps. Table 2 also points to the complementary influences of facilitation and inhibition on cultural diversity, the former promoting amount of culture, the latter promoting difference between cultures. Mutual facilitation makes it more likely that similar sets of elements eventually appear in different cultures, even if the cultures initially contain different elements. Mutual inhibition increases cultural differences because different cultures may establish different subsets of mutually incompatible elements (figure 8).
A third source of cultural diversity is chance. Because the appearance and disappearance of elements have stochastic components, we generally observe random variation both in the time of appearance of specific elements and in what elements actually appear. Some effects of chance can be appreciated by contrasting average paths of cultural evolution with single simulation runs in figure 4. When many possibilities for innovation exist, and in the presence of inhibitory dependencies between elements, chance is particularly important in choosing which of the many possible paths a particular culture actually takes. This means that any two cultures are unlikely to take exactly the same path (multilinear evolution) [10]. Even in the presence of random factors, however, there can be surprising regularities. One example is the regular growth in the amount of culture in the model of cultural differentiation, reminiscent of a steady rate of genetic change in genetic evolution, the 'molecular clock' metaphor [35].
It is possible to extend our framework to address questions (4), (5) and (1) above. To tackle question (4) we need to define a measure of similarity between cultural elements, e.g. similarity in function, appearance or history. Similarity measures based on different criteria may sometimes agree, though not always (cf. analogy and homology in genetic evolution) [35]. For instance, two hammers that are derived from the same, pre-existing hammer will often be similar in function, appearance and, of course, history. Once a measure of similarity between cultural elements is defined, it is possible to use it within our framework to study the similarity of evolved cultural elements. Whether this can be a fruitful line of research is a question for future work.
Question (5) concerns how culture is distributed among individuals in a group. Although we have not considered how individuals carry culture, it seems clear that maintaining a large culture requires individuals to specialize, i.e. each to carry a different subset of the culture (this follows from the simple fact that each individual has limited memory). Thus conditions that favour a large culture are also expected to foster within-group cultural diversity, i.e. specialization. We also point out that specialization itself may favour cultural growth, because if individuals do not need to carry all of the group's culture they may have more resources to create new culture within their specialization.
Question (1) is akin to asking how different biological species evolve, and what determines their number and abundance. Cultural diversity in this sense, therefore, may be quantified using measures of biodiversity [36]. A true understanding of how such cultural diversity evolves, however, requires significant theoretical developments, which lie beyond our present scope. Note that questions (1) and (5), while seemingly at opposite ends of a spectrum ranging individuals to cultures, may actually be strictly inter-related. The reason is that a complete understanding of how distinct cultures emerge requires the understanding of how cultural differences develop between individuals. Addressing questions (1) and (5) requires a refinement of our framework in which the appearance and disappearance of traits is tracked at the level of individuals [29,37].
(b) Causes of the appearance and disappearance of cultural elements
We have assumed in our models that cultural elements appear and disappear solely based on their dependencies on other elements. In reality, many other factors contribute. For instance, the appearance and disappearance of a cultural element are influenced by its functionality. For example, many combinations of cultural elements seem unlikely to appear simply because they can serve no function (think of the possible combinations of 'pasta', 'tomato sauce', 'hammer' and 'computer'). Introducing such cultural selection based on function may or may not change the general patterns of growth analysed above. Consider, for instance, the model of cultural accumulation along a single dimension. If some elements are much more efficient than others (e.g. a certain length for a spear), and if function is the main determinant of element's appearance and disappearance, we expect evolved cultures to consist mostly of the few efficient elements; we no longer expect the number of elements to grow linearly in time once the functional elements have appeared [19]. Some of our results, however, appear more robust. For example, consider the model of cultural differentiation and suppose that only a fraction of the elements that can be derived from any given element is functional. We still expect an exponential increase in the number of elements, albeit at a slower rate. Thus, a system in which cultural elements can differentiate would still produce more diversity than a system that develops along one dimension only, and less diversity than a system in which cultural elements can combine.
We have also left out the effect of environmental variation and genetic factors on cultural evolution. The environment can be incorporated in the 'state of the world' so that, for example, a cultural element may be more likely to appear in one environment than in another. Similarly, genetic predispositions may influence appearance and disappearance probabilities. For instance, facilitation and inhibition between cultural elements could be viewed as reflecting the impact of evolved mental structure. An extension of our framework to individuals would enable the study of the interplay between individual genetic variation and cumulative cultural evolution.
(c) Cultural complexity
The greatest challenge in studying the evolution of cultural diversity lies perhaps in the complexity of cultural systems. We have only touched upon this topic in our last model, but our framework can cover a wider range of cases where processes of refinement, differentiation, combination, facilitation and inhibition, which we have studied separately, occur simultaneously.
We believe that an advantage of our approach in the study of complex culture is a stronger focus on creativity and cultural history, compared with most current theory which emphasize social learning as the main force in cultural evolution [11,19,27]. Social learning (in a broad sense) can explain how culture is maintained in time (including why some elements may be more easily retained), but the most spectacular feature of human cultural evolution is the open-ended process of creation of novel, often increasingly complex culture. Although individual creativity has been the subject of much investigation [16,38], very little is clearly understood about how creativity shapes long-term cultural evolution. We believe that a framework like ours is helpful, possibly even necessary, for real progress to be made on this topic.
There are many steps left to be taken, for which our framework can be a starting point. For instance, the issue of the consequences of human intentionality could be explored through studies of the interaction between different kinds of cultural elements, such as ideas (about what is possible), opinions (about what is important) and goals (for what to achieve).
Another obvious route to go is to incorporate more fine-grained aspects about the population to make it possible to deal with issues like specialization and subcultures within groups, and interactions between cultural groups.
Our models also point to the importance of what we have called 'cultural seeds', i.e. cultural elements that can appear in the absence of pre-existing culture. It may very well be the case that there does not exist a very large set of cultural elements that are all essentially independent of each other and that can evolve from a situation without any culture. Theoretical and empirical explorations of this issue are, to our knowledge, extremely limited, with the possible exception of ideas within structural anthropology [39].
(d) Conclusion
We sought to capture in a clear formal framework what we believe is the essence of cultural accumulation: the unlimited potential for innovation and the complex dependencies between cultural elements. Our approach offers, to our knowledge for the first time, a way to model at least some of the complexity of cumulative cultural evolution beyond the ideas of a simple accumulation of elements or one-dimensional improvement. To be really useful, however, our approach must be connected productively to empirical observations of cultural dependencies, cultural evolution and cultural history. We believe that this is possible through investigations of actual trajectories of cultural evolution and studies of relationships between cultural elements. As an example of empirical data that are relevant here, it has been shown that the number of cultural elements in some domains has grown exponentially [34], suggesting that differentiation has been a major underlying process in these cases. One example of empirical studies we would like to see done is analyses of absence of particular elements in cultural systems in terms of presence of inhibiting elements.
There has so far been little common ground between mathematical theory of cultural change and mainstream work on cultural change in anthropology and other social sciences [10]. Our framework may help to strengthen the connection, as the evolving cultural systems presented here could be used to model many existing notions within the human sciences (e.g. within the fields of ethnicity, sex and gender, social norms, world views and subsistence systems) about how various ideas and practices may support or be in conflict with each other.
We thank Kevin Laland for many insightful comments. Work was supported by European Commission grant FP6-2004-NEST-043434 (CULTAPTATION). S.G. is on leave of absence from the university of Bologna.
One contribution of 14 to a Theme Issue 'Evolution and human behavioural diversity'.
- This journal is © 2011 The Royal Society
Appendix A
To quantify cultural diversity, we define the similarity of two cultural states as the proportion of all elements present in either state that are shared by both states. Formally, if X and Y are the sets of elements representing the two states, and assuming that at least one is not empty, then their similarity is defined as A 1where x is a random element drawn uniformly from the set of all possible elements (assumed to be finite). If the cultural states X and Y arise from a stochastic process, they are themselves random variables, and we define their expected similarity by Then we have A 2Assuming that states X and Y have evolved independently of each other, the last expression can be rewritten as A 3Thus, we can calculate the expected similarity between cultures if we know the probability that an element is part of a cultural state.