text:
secure-multiparty-line-segment-intersection
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Secure Multiparty Computation: Line Segment Intersection Evaluation

Please see: http://toadredcarp.github.io/secure-multiparty-line-segment-intersection/

Video demonstration: https://www.youtube.com/watch?v=n096o-a7_JU

redpajama_set_name: RedPajamaGithub


MIAMI (AP) — A family dispute delayed sentencing Tuesday for a man whose newlywed wife vanished at sea as the couple sailed a catamaran off the Bahamas.
U.S. District Judge Federico Moreno said he needs more information about visitation rights and creation of a trust fund for the couple's young child. Sentencing was reset for May 28.
Bennett, 41, faces up to eight years in prison after pleading guilty to manslaughter in the May 2017 disappearance of Isabella Hellmann, his wife of three months.
GREAT ABACO, Bahamas (AP) — Rafael Campos won The Bahamas Great Abaco Classic in 25-mph wind Wednesday to become the first Puerto Rican champion in Web.com Tour history.
MIAMI (AP) — The U.S. Coast Guard has returned 31 people to dry land after their vessel became disabled in the waters off the Bahamas.
In a statement Monday, the Coast Guard said the pleasure craft Summer Art was reported disabled early Sunday in the waters about 10 miles (15 kilometers) north of Bimini.
A Coast Guard cutter was diverted to the scene. Officials said 31 Haitians aboard the vessel were transferred to Freeport, Bahamas.
GREAT EXUMAS, Bahamas (AP) — Zecheng Dou birdied the final three holes Wednesday for a two-stroke victory in the Web.com Tour's season-opening Bahamas Great Exuma Classic.
MIAMI (AP) — The U.S. Coast Guard is continuing its search for two people missing off a boat off Florida's Atlantic Coast.
The agency said in a news release that they're looking for a 9-year-old Haitian national and a Bahamian national who is a suspected migrant smuggler. They were aboard an 18-foot (5.5-meter) boat that capsized Sunday with 11 people onboard.
Line: Toledo by 4 1/2.
Series Record: FIU leads 2-1.
FIU has an opportunity to post a nine-win season for the first time, and a chance for its second bowl win in program history — the other came in 2010, over Toledo, in the most recent meeting between the schools. Toledo is bidding for a sixth consecutive eight-win season, and could end 2018 on a season-long three-game winning streak.
Fulton County district attorney's spokesman Chris Hopper said in an email Tuesday that prosecutors are working to extradite Don Martin, who is originally from the Bahamas.
Martin fled earlier this month after five days of trial testimony and didn't return for closing arguments.
ELK GROVE VILLAGE, Ill. (AP) — A Chicago suburb's decision to sponsor a nationally televised college football bowl game in the Bahamas has won over some residents and local merchants despite receiving mixed reactions after the announcement last summer.
MIAMI (AP) — FIU running back Shawndarrius Phillips will not accompany the team to the Bahamas Bowl this week, following his arrest on a domestic violence charge.
NASSAU, Bahamas (AP) — Three victories in three countries against fields large and small, strong and weak, couldn't make Jon Rahm's year any better. Nothing could top one win that offered no money, no world ranking points or even a trophy to call his own.
"I don't think there's anything I can do in the game anytime soon that's going to mean more than that," Rahm said.
NASSAU, Bahamas (AP) — Tiger Woods finished the Hero World Challenge on Sunday and headed to Australia to promote the Presidents Cup as the U.S. captain. It's the same schedule he faces next year, with one big difference.
Woods will have 12 players with him, and he could be a playing captain.
BIMINI, Bahamas (AP) — Nausia Woolfolk scored 15 of her career-high 25 points in the second half to help Florida State beat No. 12 Iowa 71-67 on Saturday night in the championship game of the Junkanoo Jam.
BIMINI, Bahamas (AP) — Tynice Martin had 17 points and 11 rebounds, Kysre Gondrezick added 17 points and six assists and No. 25 West Virginia beat Eastern Kentucky 81-39 on Saturday at the Junkanoo Jam.
West Virginia used a 21-3 second quarter to pull away. After a 21-point first quarter, EKU was held to three, six and nine-point quarters.
Naomi Davenport chipped in with 13 points and eight rebounds for West Virginia (4-1). Katrina Pardee scored 12 and Madisen Smith had 11.
BIMINI, Bahamas (AP) — Rennia Davis scored 18 points, Evina Westbrook added 16 and Kasiyanha Kushkituah had 13 as No. 11 Tennessee rallied from a 12-point fourth-quarter deficit before winning 73-69 in overtime over UAB on Saturday.
Perhaps that's why the Cavaliers handled everything that came their way — from fighting through their off-target shooting to tussling with a preseason All-American — well enough to win the Battle 4 Atlantis championship.
BIMINI, Bahamas (AP) — Zaay Green scored eight of her 12 points and Cheridene Green six of her 11 in the fourth quarter when No. 11 Tennessee pulled away for a 78-66 victory over Clemson on Thursday in the Junkanoo Jam.
BOCA RATON, Fla. (AP) — Jailyn Ingram put up 23 points and pulled down 11 rebounds as Florida Atlantic won for the fifth time in six games, holding off Division II-Palm Beach Atlantic, 73-62 on Wednesday night.
The Owls won two of their three games at the Islands of the Bahamas Showcase and now have won three straight. FAU is off to its best start since moving to Division I.
BIMINI, Bahamas (AP) — Trey Burch-Manning scored 20 points with four 3-pointers and South Dakota beat UMBC 58-52 on Monday night in the Bimini Jam.


"INSPIRED BY OUR TRIPS TO SAN MIGUEL DE ALLENDE, MEXICO & EUROPE, WE'VE CREATED OUR GARDEN AND OUR SHORT TERM RENTALS TO REFLECT A PLACE OF BEAUTY AND PEACE AND ARE EXCITED TO SHARE THEM WITH TRAVELERS! CHOOSE FROM THE COTTAGE OR THE 1 BEDROOM UNIT.
BE SURE TO SCROLL DOWN TO SEE A SAMPLING OF OUR REVIEWS ."
Beautifully appointed 1 Bedroom UNIT, 1 Full Bath Rental; a duplex really, as only the kitchen wall is shared with one other unit in a free standing space. Cottage is featured in gallery.
With a neutral palette, Venetian plaster walls, hardwood floors, travertine in kitchen and bath, crown moulding, recessed lighting, fresh new linens, and king bed, this is a sunny, simple, uncluttered and quiet unit.
What's included in the vacation rentals: Equipped with just what one would need for a short term rental; full kitchen, new "antique white" dishes, stainless steel pots and pans, etc., wi-fi, HBO, cable, DVD player, and stereo.
What a wonderfully tranquil place right in the middle of the city. It was a great place from which to explore Santa Monica on foot. We loved the place, both the apartment but especially the garden area that required a lot of hard work to establish & maintain - it was so peaceful & pleasing to the senses. Cara was a total delight to work with & was extremely responsive to our communications. We would definitely stay there again. The king sized bed was very comfortable, the windows provided for terrific air circulation & all the amenities that we needed were there. The place was very clean & ready for use as stipulated. We can't wait to stay at one of Cara's other Airbnb at a different location in California. The apartment was a great value.
I just loved your private feedback and included it here! It was a joy having you at Secret Garden Santa Monica. We have had vacation rentals here for the best part of 20 years and have truly enjoyed our experience providing reasonably priced accommodations for travelers in a beautiful tranquil setting. Thank you Paul it was a delight. Cara, your communications was great even prior to our arrival that I figured it would be a great place to stay & that proved to be true. Your excellent & quick responses after we were there continued to be excellent. We loved that place, both the apartment but especially the garden area that you & Lori have worked so hard to establish & maintain. What a wonderfully tranquil place right in the middle of the city. It was a great place from which to explore Santa Monica on foot. You were a delight to do business with - love your apparent entrepreneurial spirit combined with great customer service.
Amazing find! A lovely apartment with access to a beautiful and peaceful garden, yet very close to everything in Santa Monica. Well-equipped kitchen and well-appointed living room and bedroom. Cara is a gracious hostess and was very helpful in providing easy check-in as well as suggestions for activities, restaurants, etc. 'Hard to go wrong on selecting this rental.
Cara's place was wonderful. Spacious, comfortable, well equipped (even access to a washer and dryer), Cara's apartment was a perfect respite at the end of the day. From the booking to our check out, Cara was in quick communication with me which made the travel totally stress free. Further, Santa Monica's public bike access made everything easily accessible. We biked to the beach, to restaurants, and to our son's apartment. We will definitely seek to stay at Cara's the next time we are in LA. AND before I sign off, the king sized bed was so comfortable. I would recommend Cara's apartment to everyone. Thank you, Cara.
I absolutely love this place! The gardens are beautiful! Charming little cottage. A short walk to the beach. I will definitely be back!
Casey ! We loved having you at Secret Garden Santa Monica!!
Cara is a superb host - checking in with us and making our stay quite comfortable. The location is ideal for Santa Monica and the gardens are truly enchanted. It was a lovely apartment, roomy and bright and clean, and we look forward to staying there again soon. It is a little oasis in the middle of a busy city.
This is a perfect place to stay on a Santa Monica visit! Not only is there a charming garden making the city seem far away, it is within walking distance of the Wednesday Farmers' Market, great restaurants and beach. We had everything we needed, including a comfortable king bed. We especially appreciated the dual bedside table lamps, with adjustable dimmer controls. Cara proved an exceedingly responsive host, who provided lots of good information about the area. As our daughter lives in Santa Monica, we will be back, and this will be our first choice place to stay.
Really enjoyed my 3 night stay at Cara's place. It is a very nice apartment in a great location, very central. Cara was always responsive and helpful. Would like to stay here again... Recommend Cara's place.
This place is amazing, my fiancé & daughter and I loved it. Its in a nice neighborhood surrounded by tons off stores, restaurants, and close to the beach, but when your home you still feel secluded in the garden which was amazing. The bed is super comfy, and the home is fully furnished. There is a co op market just up the street if you want to stay in and cook. Communication was great from prior to booking all the way through the vacation. i highly recommend staying here.
We had an exceptional stay at Cara's place over the Memorial Day weekend. It was in a great location, within walking distance to the Promenade and beach, but also in a quiet neighborhood that made for a very relaxing stay. Cara also provided us with thoughtful extras (i.e. water, chocolate, coffee, etc.), and the communication prior and during our stay was excellent. I would recommend that anyone looking for a relaxing, convenient stay in Santa Monica and visit to L.A. should contact Cara immediately. Thanks again, Cara!
Ram, you were a delight to host, thanks so much for the fabulous review, we really appreciated your stay!
We had an amazing stay at Cara's!! The garden is GORGEOUS and it's walkable to all of Santa Monica!
Kelsey! So happy to have had you there! Thank you so much for your stay!
I booked Cara's property for my brother and sister in law and they both were very pleased. They said the property is beautiful just like in the pictures. They also appreciated that the property was in walking distance to several places they needed to go to. Cara was fantastic! The reservation was made with ease and the communication was great, we appreciated that she kept in touch with us. Thank you, Cara, again for being a great host. After listening to how much my family enjoyed your property, I hope to visit your property myself one day!
We enjoyed a week at Cara's apartment, and it was wonderful. The garden is truly magical & I am going to really miss it. The apartment has everything we needed for a relaxing stay, and Cara was always only a text message away if we had questions. The neighborhood is great, we walked all over the place and checked out some of Cara's recommendations- the Pono Burger is my new favorite. If you are looking for a quiet place to relax in bustling LA, Cara's place is perfect. We would love to come back and stay here again!
Lovely having you and so happy it all worked out.
This is a very charming well-located guest suite in a quiet and convenient location overlooking a beautiful garden complete with a gurgling fountain. Although it comes with a parking space,it's a very easy walk to many locations and to the beach. It is sunny and immaculate with a very comfortable bed and bedside reading lights. It has a full kitchen with a table for 2 and a very large closet in the bedroom. A lovely place to enjoy your morning coffee or afternoon tea looking out over the flowers and palm trees. There is a strong and fast wi-if connection. Just be aware that access is up an outdoor stairway,as the unit is above a garage. There is a pay for use washer and dryer on the property. Cara is extremely helpful and responds quickly to any questions . We highly recommend this property.
We had a wonderful one month stay at the Enchanting Garden! The moment I stepped into the garden I was captivated by the fragrant blooming flowers and the tranquil feeling of the surroundings. Our "cottage" was exactly like the pictures posted. I felt as if I had been there before. The cottage was equipped with everything we needed to make our stay comfortable and relaxing. We loved the neighborhood because it was located to shops, restaurants, and the beach. We walked everywhere; we hardly ever drove our car. The available parking spot was a huge convenience. The icing on the cake was the wonderful owners/landlords. They are sweet, warm, and friendly people that we hope to see again! Our stay was perfect! Thank you Cara!!
The Enchanting Garden apartment is as wonderful as the pictures show. The unit is extremely quiet despite being only 0.9 miles away from the 3rd Street action. There are many other details that Cara has added that are not highlighted enough on the ad. The king bed is a dream with fresh new linens, the bathroom is beautifully renovated with fresh new towels, the kitchen is very well equipped and Cara even provided water, coffee, tea and fresh flowers from the garden. The entire place was very clean. Our car had parking, which is an added bonus. Cara is a wonderful host that is extremely prompt in responding to any messages while we were booking this unit. She checked in with us during our stay to make sure we didn't have any questions or issues. We look forward to another opportunity to stay in this unit and would highly recommend it to anyone staying in the area.
The attention to details and how beautiful everything was.
It was great. Keep it up!
We had a wonderful 2 month stay at the Walk everywhere garden cottage. This place is truly amazing. We spent a lot of time in the garden enjoying peaceful atmosphere, flowers, butterflies and birds. If you are lucky you may also spot 2 friendly squirrels coming to the garden sometimes. Also I heard owl sometimes at night but never managed to spot it. We often had breakfast in the garden. Garden around makes you feel like staying out of the city when in reality it's walking distance from promenade, beach and many great restaurants and shops. The cottage had everything we need to make our stay comfortable. Another great thing about this place is a dedicated parking spot. So we never had to care about where to park our car. What made this place really special for us is the details. Every little space in the garden and cottage if filled with charm and every other day we noticed something new about this place like a little angels statues hidden in the green plants or the drawing on the wall in one of the rooms that has a little colibri birds that looks same as colibri birds flying in the garden. Cara has a perfect sense of style and you will see it in every inch of the property. Cara is a perfect host. She is very kind, friendly and flexible. Always ready to help make our stay better. I would definitely recommend this place to all my friends. Thank you Cara!
Loved having your beautiful little family on the garden! Thank you so much for your stay; I simply cannot say enough about what a lovely couple you are and how precious and beautiful the little one is! Please stay in touch!
Charm of the place and exceptional care and kindness of the host.
Charlotte you were a wonderful guest! I meant to leave a lovely review for you but think it got past the due date! I have an inquiry out to AIRBNB about it! 31 days is never enough time to enjoy perfect guests as yourself! THANK YOU !!!!!
The cottage was so clean and welcoming! The furnishings were lovely and comfortable and the kitchen and everything (and more!) for what we needed. Thank you SO much again for making an exception to your stay rule and allowing us to come just for the weekend!
Gracias por todo el cariño y compañía que me habéis dado. Nos vemos en España. Aunque yo, volveré.
Wir hatten das große Glück und konnten uns eine Woche lang wie zuhause fühlen! Fotos und Beschreibung sind absolut zutreffend. Die Wohnung ist mit sehr viel Liebe und Geschmack hochwertig eingerichtet, alles was man braucht ist vorhanden. Die Vermieterin sehr herzlich und eine wunderbare Gastgeberin. Sie antwortet auf Mails oder SMS aus Deutschland umgehend (natürlich den Zeitunterschied beachten ;-). Der Garten ein kleines verwunschenes Refugium mit mehreren Sitzplätzen. Die Lage ist zentral und dabei nachts aber ruhig. Mit dem Auto ist man in ein paar Minuten überall - Supermarkt, Fußgängerzone, Ocean-Boulevard, Strand und Santa Monica Pier. Mit einem Fahrrad wäre das auch keine Thema. Wir waren zu zweit dort und empfanden es als perfekt so - es könnte aber noch eine dritte Person im Wohnzimmer auf der Couch schlafen. Ich habe schon viele Ferienhäuser und -Wohnungen gemietet, diese steht dabei ganz weit oben auf der Rangliste. Da ist es verständlich, das wir gerne irgendwann wiederkommen möchten!
Claudia, so wonderful to meet you! THANK you for your kind words and I appreciate having it in German. Any referrals should contact me directly! THANKS so much!
We loved the charming apartment!
The apartment was perfect and the wonderful garden made you feel as if you were in a resort area vs. an urban setting. All the details that the owners thought of added to our comfortable stay. It truly is better than the pictures.
We stayed here on our honeymoon and had a truly lovely time. A beautiful apartment and really made you feel at home. Cara was on holiday but Eric made sure we were comfortable and was always helpful and friendly. Thank you for a lovely place to stay. Perfect for what we needed.
Amazing !! A little paradise !
It was my first experience with airbnb and it was perfection !! This place is amazing, Cara is so kind and quick to answer any question. It really felt like home. The secret garden is a little paradise, so beautiful! If you want to cook, the kitchen is perfect, you have everything you need. The bed is wonderful, I want the same in my home !! Very easy parking at the back of the house, so convenient in LA! The location is perfect, near the beach but very quiet and safe at night. There are a lot of shopping, cafe, bar and restaurants without taking the car! Thank you so much Cara, my vacations were perfect thanks to you! I hope to come back soon because there are so many things to do and see ! ....... C etait ma premiere experience avec airbnb et ce fut parfait ! L endroit est superbe, Cara est tres sympathique et rapide pour repondre aux eventuelles questions. Je me suis senti comme a la maison et le jardin secret est un petit paradis ! Si vous voulez cuisiner, l endroit est parfait et tres bien fournit. Le lit est hyper confortable, je veux le meme chez moi!! Le parking est tres facile, a l arriere de la maison, tellement pratique a LA! le quartier est parfait, pres de la plage tout en etant calme et rassurant la nuit. Il y a pleins de shopping, bar, cafe et restaurants dans les environs, sans meme avoir a prendre la voiture! Grace a Cara mon sejour fut parfait et j espere revenir bientot car il y a tellement de choses a voir et a faire dans cette ville !
Ceci fut ma première expérience avec Airbnb et je suis vraiment ravie. Cara est une hôte exceptionnelle, très accueillante et accommodante. L'appartement, correspondant parfaitement à la description, est très agréable et confortable. Le jardin est sublime et très reposant. L'appartement est très bien situé dans Santa Monica et à distance raisonnable de la plage et des commerces que nous pouvions rejoindre à pied. La voiture est obligatoire à L.A. et le parking est un véritable plus. Le quartier est résidentiel et très calme ce qui est agréable après une journée de visite dans la région de L.A. Nous avons passé un très bon séjour chez Cara et nous relouerons surement chez elle lors de notre prochain séjour à Santa Monica.
Words cannot describe just how utterly fantastic this apartment is, and that's even before I mention the breath-taking surrounds. We stayed for 4 nights. Cara met us upon arrival and was the nicest most genuinely helpful person. We were immediately put at ease by the warmth of her welcome. Cara provided a folder of highly useful information about the local area, not to mention her giving us the time to explain where to go and what to do. As you walk up to the apartment you stroll through a beautifully set out, well manicured cottage garden. The smells and vibrant colours, sound of water from the fountain and heavenly inviting seating area greet you on your way up to the apartment. We stayed in the upstairs apartment. My husband is extremely picky when it comes to staying anywhere besides home. He would say he has a very high standard of expectations and I can tell you he was not disappointed. The pictures of the interior cannot give you a true sense of the high quality finish completed by Eric, Cara's husband. Don't be fooled by the pictures, there is ample space for two in the apartment. The bedroom has the most storage space we have ever had, you can fit two large suitcases in the sliding wardrobe along the wall and as many clothes as you can ever wear. This is no mean feat considering my husband and I came to California from Ireland for a three week visit. The bathroom may feel a little compact but it is so well laid out it is not an issue. The shower is powerful and spotless. Cara provides shampoo and shower gel which is a nice touch. The apartment was nice and cool during our stay and not once did we hear a single noise from any of the neighbours, and we had the windows open all the time! We had access to bikes which we used to cycle down to the beach (about a 5 min cycle). There is one parking spot allocated at the rear of the apartment if you cannot park on the street. We loved sitting in the kitchen in the morning eating our breakfast and looking out at the beautiful view of the garden, it was really hard to believe you're in a big city when staying in the apartment. We met Cara a few times during our visit and spent some time chatting to her and we felt like her friend rather than someone we were renting an apartment from. She was always available to text if we had any questions. We met her husband Eric who tends to be around from time to time maintaining the property. A very nice, friendly laid back guy. We will definitely be back!
Declan, thank you for the excellent review! We thoroughly enjoyed having the two of you and would be honored to have you again anytime! Wishing one day to find ourselves in your beautiful Ireland ! Best to you both!
Note: This review refers to the cottage on the property At the end of April we spent four great weeks in Cara's cottage. It's located in a beautifully landscaped garden and very well equipped. We didn't miss anything in kitchen, bathroom or living room, also Wi-fi is available. The interior is very tastefully decorated with attention to detail. It has a small veranda with direct access to a private garden which leads to the courtyard garden, a wonderful place to start the day with a cup of coffee. The location is also good, you reach Santa Monica Pier within 15 minutes by walking. There are well stocked supermarkets with organic food in the vicinity, perfect for cooking in the fully equipped kitchen. Proprietress Cara is very helpful and friendly without being intrusive. We would come back any time, thank you Cara!
So wonderful having you at the cottage! Thanks so much for this beautiful review! Even since you were there we have changed up several things there, including the bathroom vanity. It's such a little jewel this cottage; helps you imagine Santa Monica 100 plus years ago! I hope you both return! Thanks again so very much!
Wonderful stay at the beautiful Secret Garden!
We had an amazing time staying here - the Tuscany garden area outside is gorgeous and very well manicured! The apartment itself was also nicely designed and very clean with the most comfortable bed I have ever slept in outside of my house! I was at ease and instantly felt stress melt away - exactly what I needed on a much needed vacation! The location was very quiet and tranquil - perfect. The beach is 12 blocks away, 3rd street promenade is 9 blocks away, very short walk or bike ride away. I have already told my mother about this place and will recommend to all friends and family that choose to enjoy Santa Monica!
Very peaceful accommodation. Within easy reach of shops, restaurants and walking distance to 3rd street and promenade. The apartments has a very welcoming feel to it and is fully equipped with all your needs. The host is extremely helpful.
Cara's apartment is absolutely beautiful, the perfect place for a quiet and romantic getaway! It is at the back of a stunning central garden that can be accessed by guests. There is off street parking which is super convenient and the apartment itself is furnished beautifully. It's a few short blocks, 9 perhaps, to the center of downtown and about 12 blocks from the beach and the famous Santa Monica pier but you may choose to drive/taxi for the evening time, (or bike) and even then it is only a $5 - $10 taxi ride. Some amazing restaurants nearby and, generally a great buzz about the place. Cara herself is a delight! She met us onsite to exchange the keys and give us a tour and a run down of everything we needed to know, she even had some drinks chilling in the fridge for us!! Everything was simple and easy with great communication all along the way. I would absolutely recommend Cara's apartment and if I am ever in the area again would definitely return. Thank you, Cara, for your amazing hospitality!
We had a great time in Cara's house. The place is so cute, the bed is so comfortable, the kitchen is complete and Cara is a wonderful host! There is a beautiful garden where I spent my time just enjoying the flowers. We had four very good weeks there!
I'd never used a service like AirBnB before, so at first I was a little bit concerned that my experience at Cara's place would lack the professional touches provided by a hotel. What I realized the moment I crossed the threshhold was that this was far better than a hotel. I felt instantly comfortable because of the home-like environment. The place was exactly as advertised--clean, quiet and convenient to everything I wanted to see in Santa Monica. The gorgeous garden was a huge plus. My local family members who visited were very impressed. I'd definitely recommend this place and would stay there again the next time I'm in Santa Monica.
I cannot say enough about Cara and what a warm welcome I received! From the moment I walked through the beautiful garden and was greeted by her cheerful smile and gracious presence, I felt at home! She and her husband have created a very charming and special place tucked away in a quiet neighborhood only a few blocks from the ocean. Cara was so generous with her time in sharing with me her favorite places to check out in Santa Monica.
We had such a wonderful stay in Cara's beautiful house in Santa Monica! Cara was so welcoming when we arrived, gave us some great tips about the area and made us comfortable and excited for our stay! Her apartment was gorgeous, clean and in a perfect location - a 10 minute walk to trendy restaurants, shopping, the grocery store and the beach/pier. We can't wait to return to Santa Monica and hopefully stay in this beautiful little oasis!
We had a great time visiting Santa Monica and this apartment overlooked Cara's garden bursting with flowers, herbs and birds. It was in a good location for walking to the beach and shops and the king size bed put our bed at home to shame. We will be back!
This is a fantastic place to stay in Santa Monica. It's convenient as it's a short walk to the pier, close to a supermarket but comes with a parking space so makes it a great place to use as a base to explore LA. The apartment was even nicer than the pictures and an absolute haven - especially the garden! The kitchen is well equipped so it's perfect if you want a rest from eating out. Cara is a great host and goes out of her way to make sure you have everything you need. I would definitely recommend this place to friends visiting California!
Our stay in Santa Monica was excellent and Cara made sure we were able to enjoy it to the fullest. The neat apartment is really close to the beach and many interesting locations can be reached very quickly. The documentation Cara provided also contained many tips on activities, restaurants etc. The place really is as beautiful as depicted on the photos with an amazing garden.
We had the most amazing time at the secret garden cottage, it just felt like home even though that is thousands of miles away!! The garden is an oasis and the rooms are beautifully decorated. It's not often you visit somewhere and the reality is BETTER than the photos! The cottage is just a 10 minute walk to the beach and there are loads of restaurants within a 5 min walk. Cara herself greeted us when we arrived and she was lovely and emailed us to check we were ok and happy with the apartment, so sweet. Without a doubt, worth every penny and we would love to stay again.
We are so happy we found Cara´s apt and her secret garden – it´s a jewel! It´s very stylish, calm and clean and everything you need for a stay is available, such as toilet paper, different kinds of hairdryers, iron and even fully equipped kitchen, spices included! The king size bed is very comfortable and there are plenty of wardrobes and storage places. We were only two adults, but there is an extra bed/sofa in the living room – not as luxurious as the one in the bedroom though. We especially appreciated the amazing, well-designed Tuscan garden – we had every breakfast and some dinners there and really enjoyed the peacefulness and the relaxed atmosphere. The location is perfect; you can walk to 3rd St Promenade and all the shops and restaurants around, the pier and the beaches. We had some long, lovely morning walks and on our way back home we had cappuccino at Starbucks or Coffee Bean… Yum! Cara herself is very friendly and helpful and a perfect host. She was immediately ready to help if we needed anything, but let us be undisturbed as much as we wanted. If you want you can meet very nice neighbors in the garden, but you can also enjoy it all by yourself if you want. So, if you are looking for an oasis in the big city this is the right place!
As you know, we loved having you! Thank you for the lovely review!!!
LOVED Cara's beautiful apartment in Santa Monica. She hosted my parents and they were both thrilled with their first AirBNB experience. When I dropped by, the apartment was very clean and nestled in the most lovely garden. My parents emphasized that they would love to stay again in the future. Thank you for providing them with such a wonderful experience!
The garden was beautiful and we enjoyed spending time there most mornings. The birding was great with lots of hummingbirds. The rooms were well appointed and supplied with most everything we needed. The keyless entry was very convenient. Cara was a most pleasant and helpful hostess. She responded immediately to any questions or requests. And most important of all, the bed was comfortable.
Cara's apartment was really lovely - clean, bright, airy and comfortable, with a very pretty garden. Everything that we needed was provided, even beach towels. Arrival & departure were very easy due to the keypad lock on the door, but we did get to meet Cara on our arrival to show us a few things. There was parking for what Cara calls a 'small' car. It was an easy 15-20 min walk to the 3rd street promenade (a lovely shopping area) and on to the beach. For Jewish visitors, like ourselves who stayed there for the holidays, the apartment is two blocks from the Chabad so very conveniently located.
Hi Cara. Glad we stayed at your cottage. Loved the garden, your taste in décor and that it was well stocked with the essentials. You were an attentive host. Thanks.
Cara's apartment is absolutely beautiful, the perfect place for a quiet and romantic getaway!! It is one of five apartments in a small quadrangle with a stunning central garden that can be accessed y guests. There is off street parking at the rear which is super convenient and the apartment itself is furnished beautifully. Its an 12 block walk to the beach and famous Santa Monica pier but you may choose to drive/taxi of an evening time - still, its only $5-10 ride.Some amazing restaurants nearby and, generally,a great buzz around the place. Cara herself is a delight! She met us onsite to exchange the keys and give us a tour and run down of everything we needed to know... she even had some drinks chilling in the fridge for us!! The entire experience was simple and quick with great communication the whole way along. I would absolutely recommend Cara's apartment and if I am ever in the area again would definitely return. Thank you Cara for your amazing hospitality!!


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news, act-politics, andrew barr, act labor, labor leader, chief minister, who will succeed andrew barr, act election, act election 2020
Whether Labor wins or loses the ACT election on Saturday, it will have pretty big questions to answer. Who could take Andrew Barr's spot as the leader? If he loses, Barr has made it clear he'll make way for someone else to take the party's top job. But there have also been lingering questions about whether he would see the term through if Labor wins. Barr has maintained he plans to stick it out (pending any family or health emergency). But the hot contest among Labor candidates in his seat of Kurrajong suggests some could be running in the hope his seat becomes vacant in some part of the next four years. Former Barr-advisor Jacob Ingram has been campaigning non-stop for almost a year. Meanwhile, CMFEU-backed CPSU ACT secretary Maddy Northam has some heavyweight backing from Senator Katy Gallagher. It is true there's an outside chance Labor or the Greens could take another member from the Liberals in that seat. It has become more progressive from a redistribution, and Liberal Candice Burch would be the most likely casualty. But it remains, at best, an outside shot. So it leaves the question - who is Barr's most likely successor, and does the party have the talent to fill that hole? Up until 2019, Barr's logical successor was Meegan Fitzharris. She held two high-profile ministerial portfolios - health and transport - and had a warmth and likability that has evaded many of the current members. She was extremely popular in her seat of Yerrabi, raking in the second highest individual Labor vote after Barr. But she suddenly quit in 2019, leaving a big hole in the party's talent department. However, it did make way to develop a few potential future leaders - the right's Chris Steel and the left's Rachel Stephen-Smith. Both appear to be the strongest contenders. Of course the logical successor for Barr would be deputy Chief Minister Yvette Berry. She may have the support of the left for the top job and is among the most experienced members of cabinet. But there is a real uncertainty about how she would deal with the pressures of the top job, coming across as gaffe-prone to say the least. The government has been mostly lauded for its response to the coronavirus pandemic, striking a balance between public health and economic recovery. But it was Berry's handling of the schools closures early on in the pandemic that caused the most widespread public backlash. And for good reason - it featured confusing messaging and contradictory statements. Then there is Steel - a close Barr associate and the right's most likely next candidate for chief minister. In his mid-30s, Steel is young and relatively inexperienced, entering the Assembly in 2016. At times he still appears wooden and unsure of himself. He took over the transport portfolio from Fitzharris in 2019 during challenging times when the disastrous new bus network threatened to derail the government's messaging and campaign. Steel has managed to steady the ship and probably neutralised the issue just enough in time for the election. Stephen-Smith has emerged as the left's top contender, on merit at least, finding her feet as a minister during the coronavirus crisis. She was promoted straight to the ministry when she was elected in 2016, but has come into prominence since taking the health portfolio from Fitzharris. After a nervous start, she has come to shine in her role during the pandemic and appears more confident and consultative. The right's Tara Cheyne, a backbencher, was probably the most unlucky MLA during the reshuffle caused by Fitzharris' departure. Despite being the logical next choice, the need for a minister in the important seat of Yerrabi and one from the party's left faction meant she missed out in favour of the low profile Suzanne Orr. There is clearly a fear amidst the party of what life without Barr would look like. Many simply don't believe they have the depth of talent necessary. Unlike the 2016 election, this time around it's unlikely Labor will gain any new blood. It would require tossing out an incumbent or picking up an extra seat. Labor is an outside chance of picking up a third seat from the Liberals in Kurrajong. The party has also claimed it's in with a chance to get a third seat in Brindabella, but that also looks unlikely in reality. If an incumbent were to be replaced by a new Labor member the most likely seat could be Brindabella, where Mick Gentleman and Joy Burch faced a tough pre-selection battle, coming in second and third. Unaligned candidate Taimus Werner-Gibbings came in miles ahead of them during the pre-selection vote. Burch and Gentleman had faced calls to depart to make way for some new "fresh" talent to regenerate Labor. There were even some murmurings among the more disaffected members that it would be better for Labor to lose the election so it could have some generational change. So going into Saturday's election, ACT Labor's biggest long-term challenge may not actually be at the ballot box.
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SUBSCRIBER | OPINION
October 13 2020 - 11:30AM
Who is ACT Labor leader Andrew Barr's successor?
Daniella White
ACT Chief Minister Andrew Barr. Picture: Sitthixay Ditthavong
Whether Labor wins or loses the ACT election on Saturday, it will have pretty big questions to answer.
Who could take Andrew Barr's spot as the leader?
If he loses, Barr has made it clear he'll make way for someone else to take the party's top job.
But there have also been lingering questions about whether he would see the term through if Labor wins.
Barr has maintained he plans to stick it out (pending any family or health emergency).
But the hot contest among Labor candidates in his seat of Kurrajong suggests some could be running in the hope his seat becomes vacant in some part of the next four years.
Former Barr-advisor Jacob Ingram has been campaigning non-stop for almost a year.
Meanwhile, CMFEU-backed CPSU ACT secretary Maddy Northam has some heavyweight backing from Senator Katy Gallagher.
It is true there's an outside chance Labor or the Greens could take another member from the Liberals in that seat.
It has become more progressive from a redistribution, and Liberal Candice Burch would be the most likely casualty.
But it remains, at best, an outside shot.
So it leaves the question - who is Barr's most likely successor, and does the party have the talent to fill that hole?
The leadership players
Up until 2019, Barr's logical successor was Meegan Fitzharris. She held two high-profile ministerial portfolios - health and transport - and had a warmth and likability that has evaded many of the current members.
MLA Meegan Fitzharris quit in 2019. Picture: Elesa Kurtz
She was extremely popular in her seat of Yerrabi, raking in the second highest individual Labor vote after Barr.
But she suddenly quit in 2019, leaving a big hole in the party's talent department.
However, it did make way to develop a few potential future leaders - the right's Chris Steel and the left's Rachel Stephen-Smith.
Both appear to be the strongest contenders.
Of course the logical successor for Barr would be deputy Chief Minister Yvette Berry.
She may have the support of the left for the top job and is among the most experienced members of cabinet.
But there is a real uncertainty about how she would deal with the pressures of the top job, coming across as gaffe-prone to say the least.
The government has been mostly lauded for its response to the coronavirus pandemic, striking a balance between public health and economic recovery.
But it was Berry's handling of the schools closures early on in the pandemic that caused the most widespread public backlash.
And for good reason - it featured confusing messaging and contradictory statements.
Deputy Chief Minister Yvette Berry. Picture: Elesa Kurtz
Then there is Steel - a close Barr associate and the right's most likely next candidate for chief minister.
In his mid-30s, Steel is young and relatively inexperienced, entering the Assembly in 2016. At times he still appears wooden and unsure of himself.
He took over the transport portfolio from Fitzharris in 2019 during challenging times when the disastrous new bus network threatened to derail the government's messaging and campaign.
Steel has managed to steady the ship and probably neutralised the issue just enough in time for the election.
Stephen-Smith has emerged as the left's top contender, on merit at least, finding her feet as a minister during the coronavirus crisis.
She was promoted straight to the ministry when she was elected in 2016, but has come into prominence since taking the health portfolio from Fitzharris.
After a nervous start, she has come to shine in her role during the pandemic and appears more confident and consultative.
The right's Tara Cheyne, a backbencher, was probably the most unlucky MLA during the reshuffle caused by Fitzharris' departure.
Despite being the logical next choice, the need for a minister in the important seat of Yerrabi and one from the party's left faction meant she missed out in favour of the low profile Suzanne Orr.
A need for new talent
There is clearly a fear amidst the party of what life without Barr would look like.
Many simply don't believe they have the depth of talent necessary.
Unlike the 2016 election, this time around it's unlikely Labor will gain any new blood.
It would require tossing out an incumbent or picking up an extra seat.
Labor is an outside chance of picking up a third seat from the Liberals in Kurrajong. The party has also claimed it's in with a chance to get a third seat in Brindabella, but that also looks unlikely in reality.
If an incumbent were to be replaced by a new Labor member the most likely seat could be Brindabella, where Mick Gentleman and Joy Burch faced a tough pre-selection battle, coming in second and third.
Unaligned candidate Taimus Werner-Gibbings came in miles ahead of them during the pre-selection vote.
Burch and Gentleman had faced calls to depart to make way for some new "fresh" talent to regenerate Labor.
There were even some murmurings among the more disaffected members that it would be better for Labor to lose the election so it could have some generational change.
So going into Saturday's election, ACT Labor's biggest long-term challenge may not actually be at the ballot box.
Discuss "Who is Barr's successor? Win or lose, Labor faces some tough leadership questions"

redpajama_set_name: RedPajamaCommonCrawl


text:
Comparative study of selegiline plus L-dopa-carbidopa versus L-dopa-carbidopa alone in the treatment of Parkinson's disease
Ann Neurol. 1995 Jan;37(1):95-8. doi: 10.1002/ana.410370117.
T Brannan 1 , M D Yahr
1 Department of Neurology, Mount Sinai School of Medicine, New York, NY 10029.
DOI: 10.1002/ana.410370117
The long-term effect of selegiline (L-deprenyl) in the treatment of Parkinson's disease has not been clearly delineated. We report on a group of patients whose treatment was initiated with selegiline (n = 43) and then subsequently included L-dopa-carbidopa (Sinemet) and in whom an extended period of observation was carried out; they are compared to a group of patients whose treatment consisted of L-dopa-carbidopa alone (n = 39). In each, serial observations of the parkinsonian state and the response to treatment on a yearly basis for a period of 5 years were performed. No significant difference in the Hoehn-Yahr stage or in the motor subscores of tremor, rigidity, bradykinesia, and gait-posture was found between the two groups, nor was there a significant difference in the incidence of fluctuating responses or dyskinesias. The group that received combination therapy required less L-dopa than did the group that received L-dopa-carbidopa alone during the first 3 years of treatment and a similar trend was evident in years 4 to 5. We conclude that minimal benefits accrued to the parkinsonian patients from long-term use of selegiline. No clinical evidence to support the claim of "neuroprotective" properties was found. Selegiline's major usefulness is to modify the fluctuating therapeutic response seen with L-dopa-carbidopa.
Antiparkinson Agents / administration & dosage*
Carbidopa / administration & dosage
Carbidopa / adverse effects
Carbidopa / therapeutic use*
Drug Combinations
Levodopa / administration & dosage
Levodopa / adverse effects
Levodopa / therapeutic use*
carbidopa, levodopa drug combination


Here is a cool article from Frontiers in Psychology: Consciousness Research that looks at what our current knowledge of neuroscience shows us about the process of Zen meditation. There is a lot of geeky neuroscience stuff, but it's well-written enough for novices in neurobiology to grasp the meanings.
Zen Buddhist meditative practices emphasize the long-term, mindful training of attention and awareness during one's ordinary daily-life activities, the shedding of egocentric behaviors, and the skillful application of one's innate compassionate resources of insight-wisdom toward others and oneself. This review focuses on how such a comprehensive approach to training the brain could relate to a distinctive flavor of Zen: its emphasis on direct experience, with special reference to those major acute states of awakening that create deep transformations of consciousness and behavior. In Japanese, these advanced states are called kensho and satori. Ten key concepts are reviewed. They begin by distinguishing between the concentrative and receptive forms of meditation, noticing the complementary ways that they each train our normal "top–down" and "bottom–up" modes of attentive processing. Additional concepts distinguish between our two major processing pathways. The self-centered, egocentric frame of reference processes information in relation to our body (our soma) or to our mental functions (our psyche). The other-centered frame of reference processes information anonymously. Its prefix, allo- simply means "other" in Greek. Subsequent concepts consider how these useful Greek words—ego/allo, soma/psyche—correlate with the normal functional anatomy of important thalamo ↔ cortical connections. A plausible model then envisions how a triggering stimulus that captures attention could prompt the reticular nucleus to release GABA; how its selective inhibition of the dorsal thalamus could then block both our higher somatic and psychic cortical functions; so as to: (a) delete the maladaptive aspects of selfhood, while also (b) releasing the direct, all-inclusive, globally-unified experience of other. Two final concepts consider how the long-term meditative training of intuitive functions relates to certain kinds of word-free spatial tasks that involve insightful creative problem-solving.
Only those contents of consciousness can be developed that correspond to the organization of the brain.
These words by Hess suggest that the following pages will invoke neurophysiological explanations, not loose metaphysical notions. That said, this review proposes that neuroscientists and Zen trainees can learn a few things from each other's models of consciousness. What does Zen training emphasize during its long-term approach to meditation? First, the mindful training of attention and awareness during one's ordinary daily life activities. Second, shedding the layers of maladaptive habits, overly self-centered attitudes and behaviors that waste time and energy. Third, enhancing one's innate, intuitive resources of insight-wisdom. Fourth, applying these fresh insights skillfully, with increasing compassion, both toward all other beings and one's own well-being.
These emphases are part of a long path of brain training that can lead toward more adaptive traits of character. The path emerges along that broad interface between two crucial domains, self and other. The former represents the distinctive interior consciousness of our personal self. The latter refers to that other consciousness representing the environment outside our skin. An important aspect of this path is epitomized in the historical account of a man, originally called Siddhartha. The records indicate that his behavior was substantially transformed after he emerged from a major state of awakened consciousness. Thereafter, he would be known as the "enlightened" one, the Buddha.
During the four decades since Hess died, the neurosciences have continued to learn more about the organization of the brain. Still, some readers may question: is it appropriate in this special issue of Frontiers for a neurologist to speculate about how such an acute episode could have transformed a 35-year old man like Siddhartha? On the other hand, only secular explanations will be tentatively proposed. They will address fundamental issues at the crucial interface between self and other. In order to focus on such an interface, this review leaves to other contributors the complex topic of correlating meditation with neuroimaging data. Left to its closing pages is the discussion of subtle incremental deconditionings of the maladaptive self, and a consideration of how such changes could emerge along a continuum of practical intuitive, creative, problem-solving traits. A glossary at the end helps to define useful terms.
The next pages summarize aspects of 10 key conceptual issues that are raised either in four books previously published or the one now in press. The Zen approach to training specifically targets unwarranted self-centeredness. It studiously avoids first-person references. This principle is not possible to achieve in this kind of review which necessarily refers to the author's several publications.
The first concepts summarize Zen meditative practice in terms of psychological phenomena. Later concepts suggest principles of neural organization that govern important physiological mechanisms. These mechanisms are involved both during our normal modes of ordinary consciousness, and in our normal modes of ordinary subconscious processing. Moreover, many of their phenomena surface in the foreground of the kinds of advanced extraordinary states of consciousness that are often called "awakening" or "enlightenment." The Japanese terms for these brief states are kensho and satori. Samples of frontier research will later be cited which appear to have fertile interdisciplinary implications.
This meditative approach trains attention by focusing body and mind on the ongoing, mindful perception of each present moment as it really exists right now. Gradually, an increasingly calm awareness becomes the setting for the emergence of more subtle introspective memory skills. These are automatic "recollections". They serve useful, self-correcting ends. (Austin, 2011, pp. 95–96, 98). Their subconscious meta-cognitive memory functions were always inherent in the original meaning of the ancient Pali term, sati. A newly-coined word, "remindfulness," can serve a useful purpose. It simply acknowledges this involuntary, helpful overview memory capacity. (Austin, 2011, pp. 94–98) When Emerson pointed to the surge of this natural, insightful, affirmative mode of "guidance," he used the apt phrase, "lowly listening" to describe its remindful qualities (Austin, 2011, p. 145).
One doesn't "learn" Zen meditation in just a few days or weeks. The major target during the early months and years is one's self-centered I-Me-Mine complex and its unfruitful, maladaptive, emotional attachments. (Austin, 1998, pp. 43–47, 50–51; Austin, 2006, pp. 13–14) Long-term monastic training goes on to address the diverse existential, instinctual, and emotional aspects of the personality that cause unnecessary suffering. None of these ingrained egocentric attitudes surrender without a struggle. During meditative retreats (Austin, 1998, pp. 138–140), trainees benefit from many opportunities both to endure their own liabilities and to uncover their innate assets, while being guided by an authentic teacher (Austin, 1998, pp. 119–125; Austin, 2006, pp. 64–69).
A. Neuroscience research has identified two basic network systems of attention operating at the cortical level. (Austin, 2009; Corbetta and Shulman, 2011; Kubit and Jack, 2013, pp. 29–34). Here, in a provisional sense, several aspects of their functional anatomy may be summarized when using such terms as dorsal and ventral, upper and lower, "top–down" and "bottom–up," more voluntary and more involuntary.
Research in meditators indicates that our dorsal attention system for top–down attention becomes more involved during the narrowly focused, concentrative meditative practices. (Austin, 2009, pp. 39–43) In contrast, the ventral attention system orients itself reflexively toward the subtler forms of bottom–up attention and global awareness. These become cultivated more gradually during the other kinds of meditative practices that are more openly receptive.
B. Neuroscience research has also made major contributions to the neural correlates of self/other issues. Two major processing pathways have been identified, also dorsal and ventral in their early course. These networks provide consciousness with two anatomically separate versions of "reality" that are soon blended seamlessly (Austin, 2009, pp. 53–64). Our self-consciousness is most familiar with the "feeling" of the first version. Figure 1 illustrates how the dorsal pathway can tap into the specialized touch and proprioceptive resources inherent in the parietal lobe. This overlapping is convenient, because these senses of touch and proprioception help us manipulate important tangible items located inside that lower field of space lying nearest our body.
The figure helps to appreciate that this upper, occipito-parietal, egocentric processing pathway follows a trajectory that is closest to, and overlaps, those same lateral and superior cortical regions which also represent the body schema of our somatic, physical self. So, can this upper pathway be described as asking only a one-word question: "Where?" No. A hungry person, seeing an apple within reach, instantly refers all lines of sight from this apple back to his or her own physical axis of self in order to grasp it. Therefore, this upper pathway seems poised to ask a much longer question. This highly practical question is structured in terms that correspond with the three dimensions of our personal space: "Where is that apple in relation to Me and My body?" (Austin, 2009, pp. 54–55, 58–59).
The ventral pathway relies on other specialized refinements, those associated with its capacities for seeing and hearing. Notice the lower origin of this other cortical pathway. It begins in the inferior occipito-temporal region and extends toward the inferior frontal region. Such a trajectory confers a very different, allocentric perspective. (Austin, 2009, pp. 55–74) Allo, from the Greek, simply means "other." Why is the existence of this hidden other-referential pathway so unfamiliar to us? Because such a silent "frame of reference" begins to operate anonymously. It asks the question, "What is that object?" Instantly, subconscious pattern-recognition skills identify that object. Simultaneously, other skills decode what that object means. (Austin, 2009, pp. 130–149) When Freud coined the useful diagnostic term, agnosia, he could then apply it to the isolated loss of visual meaning caused by a discrete lesion which had damaged a patient's temporal lobe (Austin, 2009, pp. 130–135).
Our ordinary conscious processing remains unaware that it is deploying a seamless blend of these two complementary—upper and lower—categories of spatial reference. (Austin, 2009, pp. 57–58) Such ignorance vanishes when the entire upper version drops out. Zen parlance applies the following metaphor of selfless "emptiness" to this abrupt release from all former attachments to the intrusive self: "The bottom falls out and releases its bucket-full of water." (Austin, 2009, pp. 191–193) Now the lower version's allocentric processing stands unveiled. Its innate subconscious capacities, perceived in isolation, are revealed for the first time. This "awakening"—this fresh perspective of "real" reality, infused with instant recognition and meaning—is an awesome surprize. (Austin, 2006, p. 361–371).
C. Neuroscience research has also begun to attach a shorthand term, "default network," to a large consortium of heterogeneous regions. The three largest regions occupy the medial prefrontal cortex, the medial posterior parietal cortex, and also the lateral cortex of the angular gyrus. Included within this triad and its several extensions are representations of both intrinsic, autobiographical and topographical association functions. (Austin, in press) The more rostral parts of this coalition contribute to an impression of personal sovereignty: our self as the sole psychic agency, its operations consistent with those of a private, autonomous I-Me-Mine. (Austin, 2009, pp. 74–75) Yet if each such mental notion about our personal self is to lodge in memory as a coherent event, it helps to encapsulate it within the context of some particular local scene. (Austin, 1998, pp. 390–391) These topographical, scenic details are essential if this locale is to serve as the "frame" enabling each event memory later to be used for purposes of navigation. (Austin, 2009, pp. 72–74) Only when each intimate episode is anchored both in one particular place in our own environment, and in one particular moment of our own "time frame" can these separate episodes become organized into a detailed, useful, lifetime, personal narrative.
Figure 1. Egocentric and allocentric attentive processing; major differences in their efficiencies. This view contrasts our top–down dorsal egocentric networks with those other networks representing our ventral allocentric, bottom–up pathways. The reader's vantage point is from a position behind the left hemisphere, looking at the lower end of the occipital lobe. This person's brain is shown gazing up and off to the left into quadrants of scenery. The items here are imaginary. The baby and the hammer are within reach, in the space down close to the person's body. The scenery above and the tiger are off at a distance, out of reach. Starting at the top of the brain are the two modules of the dorsal, top–down attention system: the intraparietal sulcus (IPS) and the frontal eye field (FEF). They serve as the attentive vanguards linked with our subsequent sensory processing and goal-oriented executive behavior. Notice how they are overlapped by the upward trajectory of the upper parietal → frontal egocentric (E) system. This is a self-referential system. Its arching red pathway is shown as beginning in the upper occipital region. Notice that a similar red color also surrounds the lower visual quadrants containing the baby (at left) and the hammer (at right). Why? To indicate that this dorsal, "northern" attention system attends more efficiently—on a shorter path with a lesser "wiring cost"—to these lower visual quadrants. This enables our parietal lobe senses of touch and proprioception to "handle" easily such vitally important tangible items down close to our own body. In contrast, our two other modules for cortical attention reside lower down over the outside of the brain. They are the temporo-parietal junction (TPJ) and the regions of the inferior frontal cortex (IFC). During bottom–up attention, we activate these two modules of the ventral attention system chiefly on the right side of the brain. There, they can engage relatively easily the networks of allocentric processing nearby (A). The green color used to represent these lower temporal → frontal networks is also seen to surround the upper visual quadrants. Why? This is to suggest the ways this lower ("southern") pathway is poised globally to use its two different specialized systems of pattern recognition. One is based on our sense of vision, the other on our sense of audition. Both serve not only to identify items off at a distance from our body but also to infuse them instantly with meaningful interpretations. The yellow FG in parenthesis points to this lower pathway's inclusion of the left fusiform gyrus. This region, hidden on the undersurface of the temporal lobe, contributes to complex visual associations, including our sense of colors.
How can any three-pound brain normally maintain such a life story, packed with notions that its omni-self is truly an ongoing, functioning agency? Not surprisingly, the early PET studies showed that the coalition of self-referential regions required an especially active ongoing metabolism even during seemingly "resting" conditions. Functional MRI signals arising from this consortium became even more activated (above such arbitrary "baselines") when researchers assigned discrete self-referential tasks to their normal subjects. (Austin, 2006, pp. 204–207; Austin, 2009, pp. 75–76, 266–267) Subjects who tried to meditate in thought-free silence in the scanner discovered how much their "monkey-mind" wandered during the so-called "resting" state of quasi-"baseline" consciousness.
Importantly, fMRI signals from these same (mostly medial) intrinsic networks were acutely reduced (below baseline) at the instant that a sudden external stimulus event captured a subject's attention. Further fMRI research revealed a second important finding: the activity of these chiefly medial, self-referential cortical regions varied inversely with the activity of the lateral attention regions. (Austin, 2009, pp. 98–108) These separate self and attention regions co-participated—but in opposite directions—in the peaks and valleys of a slow, spontaneous, endogenous rhythm. This reciprocal rhythm required no external stimulus. It recurred slowly—around three times a minute—on its own largely independent cycle (Austin, 2011, pp. 32–34).
The Swiss physiologist, Walter Hess, was co-awarded the Nobel Prize in 1949. His pioneering research documented the dynamic switching capacities that lurked in the deep central diencephalic regions of the brain (Austin, 1998, pp. 190, 194, 232, 635–636). Extensions of that research make plausible today's hypothesis that some regions in the axial core of the brain—in and around the thalamus—might qualify as the deep origins for these reactive and spontaneous shifts that occur up in the recent cortical fMRI data. After all, these are fast and slow, switchings on and switchings off. They are enlisting separate cortical regions that make crucial commitments either to attention or to the representations of the self. Moreover, these regions respond not only within both hemispheres simultaneously, but also in a reciprocal manner (Austin, 2006, pp. 197–198, 427–428). Were Hess alive today, he would surely be encouraging neuroscientists to identify which basic mechanisms organize these two remarkable anticorrelated physiological feats.
The annals of Zen demonstrate more than an early, historical emphasis on the mindful training of attention and awareness (Austin, 1998, pp. 69–73). They also document numerous examples during which a sudden external stimulus—like the unexpected "CAW" of a crow—served not only to instantly capture attention but also to precipitate states of awakening (Austin, 1998, pp. 452–457; Austin, 2006, pp. 303–306; Austin, 2009, pp. 109–117; Austin, 2014, Chapters 5, 6). So, one wonders: could Siddhartha's legendary "awakening," two and a half millennia ago, also represent a comparable event? Indeed, it was said that this state of enlightenment was triggered, before dawn, when he looked up and saw the brilliant "morning star" (Austin, 2011, pp. 77, 209). The ancient astronomers were familiar with this bright celestial object. They recognized the obvious fact that it traveled on a path, unlike a star. They gave the name, Venus, to this distinctive planet whose brilliance still lights up our Eastern sky before sunrise.
Explicit statements about selflessness entered the Buddha's earliest discourses. Examples of no-self sentences are found in two of the ancient Udana sutras: "When no you remains, then this, just this, will be the end of your suffering." "Getting free of the conceit that "I am" is truly the ultimate happiness." (Austin, 2014, Chapter 1; Austin, 2011, vi) Scientists have reason to be skeptical: could any rigorous common ground ever link old Buddhist legends with neurobiology? (Austin, 1998, pp. 1–7, 677–683). On the other hand, might what neuroscience is learning about the neurophysiological origins of selfhood help explain how selflessness could occur?
Intricate interactive circuitries merge thalamic functions with those of our cortex (Austin, 2006, pp. 167–176). What is special about the three limbic nuclei in the front of our dorsal thalamus? Why could they play a crucial role in modulating these to-and-fro, rapidly oscillating connections between thalamus and cortex? Because these are the three thalamic nuclei poised to relay over-emotionalized messages from our limbic system up to pertinent parts of our self-referential cortex and to receive reverberations from them. Indeed, these three limbic nuclei interact with most of those same medial cortical association regions that item 3C had just singled out. Recall that these key regions of neocortex appear to be organized in a manner that can represent major attributes consistent with the autobiographical aspects of our psychic self that are linked to its topographical memories (Austin, 2009, pp. 87–94) (Please see Figure 2).
Figure 2. Thalamocortical contributions to the dorsal egocentric and ventral allocentric processing streams. This composite view shows the pathways (normally bi-directional) which connect the thalamus with the cortex. For convenience in viewing, only left-sided structures are shown. These connections supply key regions both on the outside and inside of the left hemisphere. Pathways predominate from all five nuclei in the dorsal tier of thalamic nuclei. Up front are the three limbic nuclei. The medial dorsal (MD) thalamic nucleus projects to the prefrontal cortex, both to its medial (MPFC) and to its outer, dorsolateral (DLPFC) surfaces. The deep medial area of cortex in the back of the brain is shown enlarged at the top right. Here, the projections from the two other adjacent dorsal nuclei of the limbic thalamus can also be seen reaching this medial cortical surface (dashed lines). Thus, the anterior thalamic nucleus projects to the posterior cingulate cortex (PCC) (a major connection hub), and the lateral dorsal nucleus (LD) projects to the retrosplenial cortex (RETROSPLEN), a major memory-based resource for recollection. Down at the bottom right, one path leads up from the dorsal pulvinar (DPUL) to the angular gyrus (ANG) on the outer cortical surface. Dashed lines indicate that a second path from this dorsal pulvinar leads up to the precuneus (PRECUN) on the medial parietal surface. Other projections from the lateral posterior (LP) nucleus supply the superior parietal lobule (SPL), our major somatosensory association region. These connections help to anchor each person's subliminal sensory impression: I exist as an independent, tangible, physically-articulated body schema. Relatively few pathways are shown emerging from the thalamus to serve the lower, allocentric processing stream. However, messages from the ventral pulvinar (VPUL) would pass first through the region of the fusiform gyrus (FG) on the undersurface of the temporal lobe. These associations ramify, to become further refined on their way forward and upward through the other-referential networks in the rest of the temporal lobe that lead on toward the frontal lobe. The figure shows three important GABA inhibitory nuclei, artificially detached at the bottom. They are the reticular nucleus, the zona incerta (ZI), and the anterior pretectal nucleus (APT). Two sensory relay nuclei of the thalamus are also shown at the bottom right. The lateral geniculate nucleus (LG) relays visual data to the occipital cortex. The medial geniculate nucleus (MG) relays auditory information to the auditory cortex. The superior colliculus (SC) in the midbrain relays its reflexive visual and related polymodal messages quickly through both the dorsal and ventral pulvinar to the cortex. Its counterpart, the inferior colliculus, plays a similar auditory role. Not shown are two somatic sensory relay nuclei in the ventral tier. These medial and lateral divisions of the ventral posterior nucleus lie in front of the ventral pulvinar. They relay sensation from the head and body, respectively. cingulate gyrus (CG).
Figure 2 illustrates which limbic nuclei and cortical regions are organized to become co-activated either during an acute surging emotional overload or during subsequent un-checked ongoing ruminations (Austin, 1998, pp. 347–352, 567–570; Austin, 2006, pp. 239–265, 396–398; Austin, 2009, pp. 223–247; Austin, 2011, pp. 160–162). They include: (a) the medial dorsal nucleus and its several connections with the medial prefrontal cortex in particular; (b) the anterior thalamic nucleus and its connections, including those with the posterior cingulate cortex in particular; (c) the lateral dorsal nucleus and its connections with the event-memory-linked topographical and navigational functions of the retrosplenial cortex.
The thalamus serves as an important "pacemaker" for the brain. All of our sensations ascend through its nuclei (except for smell) on their way up to our cortex. Yet these bi-directional thalamo ↔ cortical connections, over-simplified here in Figures 1, 2, only hint at some explanations for how we might normally represent our omni-self's ordinary perceptions, emotions, and its journal entries into long-term memories. The question remains: how could a brain drop off the deep layers of the maladaptive self during the awakened states of kensho and satori?
A thin layer of nerve cells caps the rounded contours of the thalamus (Austin, 1998, pp. 267–271, 591, 605; Austin, 2006, pp. 176–178). This is the reticular nucleus. Existing fMRI data don't list it. Do not be misled. Its neurons release GABA (gamma aminobutyric acid), a powerful inhibitory neurotransmitter. Could this GABA play a "self-annihilating" role? Yes. How? By virtue of its selective capacities to readjust the synchrony of our usual thalamo ↔ cortical oscillations (Minn, 2010; Austin, 2011, pp. 35–37). Included in this selectivity are the capacities to dissociate visual functions in the ventral and dorsal streams (Austin, 2014, Chapter 11).
A simple analogy helps illustrate how the release of GABA might shift our waking consciousness away from its usual, dominant self-centered role. Try on a set of active, noise-canceling headphones. They generate a profile of sound-wave oscillations. These are 180° out of phase with those frequencies causing undesirable background noise. When the headphones are switched on, their selective tuning accomplishes two goals simultaneously: you hear the music coming through clearly; you block out the loud rumble of distracting traffic noise.
The reticular nucleus does not act alone. It has two, lower level, extra-reticular inhibitory allies (Austin, 2006, pp. 178–179) (Figure 2). The zona incerta releases its GABA on higher-order thalamic nuclei (including the medial dorsal nucleus). The anterior pretectal nucleus projects to both the medial dorsal and lateral dorsal nuclei of the limbic thalamus. It also stands poised to modulate the diversity of relevant functions among the somatosensory, intralaminar, and other nuclei that are included within the ventral and medial thalamus (Sherman and Guillery, 2013).
An Instructive Zen "Mini-Koan": Which Direction Do You Face, When You Want to Move Straight "Ahead"?
Most self-orientations operate automatically. A covert motivation urges our first leaning forward. Instantly—too fast for thought—it commits us to "head" in one particular direction (Austin, 2006, pp. 106–108). If such subconscious systems are to resolve the riddle posed above, they first need to "know" where our own head is already located, and be capable of using visual information from our eyes that confirms the direction toward which the rest of our face is assumed to be pointing.
In short, we're using a subconscious, direction-sensitive, personal "behavioral compass" (Austin, 2006, pp. 172–174). Why might two nuclei of the limbic thalamus (anterior [dorsal] and lateral dorsal) be assigned some role in establishing this covert behavioral compass? Perhaps because this subcortical network does more than add to our static notions of being a private, interior self. Perhaps it could also be preparing us to lean, move, and navigate. How? By accessing subconscious links to hidden memories, to reconstructions of past events that had "taken place," as we say, in the scenery outside our skin. We had encoded useful personal/local details during these remote prior events (Austin, 1998, pp. 390–391; Austin, 2009, pp. 259–260). These had served to frame the topographical signature representing each new, memorable spatial environment.
Item 5 explained how the five nuclei of the dorsal thalamus contribute to the normal overly-dominant egocentric attitudes of our psyche and soma. Item 6 then drew attention to selective capacities of deep inhibitory systems. It suggested that these GABA systems could have the potential to dissolve one's psychic and somatic association functions from the field of consciousness during kensho. The words, anatta, no-self, and non-I are among the standard terms used to describe the resulting selfless attributes of this advanced state (Austin, 2009, pp. 118–121). This abrupt dissolution at the core of the sense of self is noteworthy for two reasons. It can help explain why the deep roots of primal fear also drop out of kensho's field of waking consciousness, as does all personal sense of the passage of time (achronia) (Austin, 2006, pp. 378–383; Austin, 2009, pp. 193–196).
What other networks could remain active in a brain during kensho? What evidence offers a potential explanation for the fresh impression of unity that prevails throughout the whole "new" field of conscious experience? Leading the list of candidates would be the brain's lower allocentric pathways. Their "other" frame of reference is not a new category of experience. This anonymous perspective had always been there, its contributions playing only a hidden, subordinate role. (A in Figure 1) Now liberated from the dominant subjectivities of the former intrusive self, these other-referential resources could be openly expressed in an undiluted, disinhibited manner. Such a release from prior suppression could then be further enhanced in the course of a disinhibitory rebound (Austin, 2006, pp. 416, 418, 421).
• In empty anonymity, this now-unveiled other-referential mode is liberated into the foreground of consciousness, reifying the perfection of the whole mental field with a meaningful global objectivity beyond reach of mere words (Austin, 2006, pp. 329–333, 383–387).
What seems to vanish in kensho's fresh perspective? Certainly not the world in 3D. What vanishes is only the former self's intrusive sense of sovereignty over it. When the former egocentric self no longer remains the "owner" of its ongoing perceptions, then the environment opens up to reveal percepts that are experienced with utmost "objectivity" (Austin, 1998, pp. 43–47, 263–267, 591–621; Austin, 2006, pp. 327–356, 414–432; Austin, 2009, pp. 85–94; Austin, 2011, pp. 163–165).
Do not conclude that the gradual diminution of the ego during decades of authentic Zen training will remove that pragmatic sense of self which enables one to resolve life's complexities by adapting to them in an increasingly mature, realistic, matter-of-fact way. Rather is the training oriented toward dissolving those negative, neurotic distortions of ego defenses imposed by one's overconditioned self-centered attachments (Austin, 1998, pp. 34–36). Longitudinal multidisciplinary studies will be required in order to specify which precise sequences of neural mechanisms need to mature in order for genuine wisdom and compassion to evolve. This caveat holds both for the kinds of decades-long research required to study normal control populations (Vaillant, 2012) or a carefully-matched cohort of long-term meditators (Austin, 2006, pp. 352–356, 399–401; Austin, 2009, pp. 221–262).
A different model of organization and reorganization is proposed for that alternate state of consciousness termed internal absorption (Austin, 1998, pp. 469–479; Austin, 2010). Internal absorption represents a preliminary state, one not uncommon during the early years among trainees who mediate regularly. Paradoxical phenomena enter its intensified awareness: vision "sees" into a vast, pitch-black ambient space; audition "hears" the "sound of absolute silence," perception loses every physical sense of self from head to toe. In a quest for preliminary explanations of internal absorption, its agenda of 16 descriptors again leads us to the frontiers of neuroscience research.
A plausible model for such sensate phenomena can also begin on the basis of a GABA blockade (Austin, 1998, pp. 589–590; Austin, 2006, pp. 313–322; Austin, 2009, pp. 98). This inhibition could be applied to the lowermost regions in the back of the thalamus. (Please refer to Figure 2) Inhibition down here could prevent impulses from rising up to the cortex through the lowermost ventral sensory relay nuclei. They include the lateral geniculate, medial geniculate, ventral posterior medial and lateral nuclei, respectively.
Carl Jung (1875–1961) understood the key role of intuition. It supplies, he said, that "superior analysis, insight or knowledge which consciousness had not been able to produce" (Jung, 1969; Austin, 1998, pp. 545–553). Could long-term meditative training do more than cultivate a person's attention and affirmative traits of character? Could it also influence subconscious, intuitive mechanisms that subtly enhance a person's flexible creative problem-solving behavior? (Austin, 2003, 2014, Chapter 14).
Two recent experiments by Strick et al. (2012) are germane. The 63 meditators in their first experiment had completed 6 months to 5 years of prior Zen practice. In the evening, between 6 and 9pm, one group (led by a Zen master) then meditated for 20 min. The second Zen group served as controls. They relaxed at the same time, without meditating, also for 20 min. Both groups then went to individual cubicles. There they performed three sets of five Remote Associates Tests using a computer screen. (For example, given three words, search your associations for that one fourth word which they all share in common.) The subjects who had just meditated solved more test items (7.00) than did those who had merely relaxed (5.94), p = 0.02.
In the second experiment, the response times of 32 Zen meditators were measured during similar word association tests. Again, the subjects who had just meditated solved more Remote Associates Test items than did their controls (6.82 vs. 4.87), p < 0.01. They also solved them faster (taking only 13.22 vs. 16.37 s), p < 0.05. In addition, the groups were then asked to free associate to a new collection of different questions. However, in this instance, each of the 20 questions might have not just one, but three or four possible answers. (e.g., "Name one of the four seasons.") Moreover, this time—before each question—a priming word-answer appeared subliminally on the screen (e.g., "Summer"). No subject could "see" this hidden, priming word consciously, because it lasted only 16 ms.
Now the question was: could meditation unveil any of their subconscious sensitivities? If so, would this hidden awareness enable the subliminal priming word to reshape the answer? The meditators' answers did match the hidden priming words at the p = 0.06 level, just short of statistical significance. In contrast, the relaxed control group showed no priming effect.
The Remote Associates Test is often interpreted as a task for verbal creativity that combines an initial divergent search with convergence functions. Therefore, the experiments suggest that these particular Zen meditators (tested in the evening) showed evidence consistent with an enhancement of creative processing after having meditated (Austin, 2009, pp. 125–130, 154–188). Why should researchers in the future specify the hours during which they conduct their cognitive experiments? Because many normal subjects may not reach their performance maximum for working consciousness until the later hours between 7 and 9 pm (Austin, 1998, pp. 338–347). In this regard, Shannon et al. (2013) made an intriguing observation. In normal subjects, the medial temporal regions show greater local fMRI connectivities in the morning hours. In the evening hours, more connections open up that will link the frontal and parietal neocortex with the striatum and brain stem.
In their study of creativity, Colzato et al. (2012) interpreted this Remote Associates Task as a way to index the competence of convergent thinking, and assessed the productivity of divergent thinking with the Alternate Uses Task. Their 19 meditators had been practicing mixtures of concentrative and receptive forms of meditation for an average of 2.2 years. The task for each subject was to spend only 35 min a day (on each three separate days) either in concentrative meditation, or in receptive meditation, or in a baseline control condition. The data suggested that 35 min of focused meditation (only) did not sustain convergent thinking processes toward a single solution, but that a separate 35 min of receptive meditation did support divergent thinking processes.
Our normal ordinary, intuitive quests for meaning become successful only when we repeatedly apply subtle convergent and divergent attentive processing mechanisms with appropriate flexibility. Many of these flexible interactions integrate the functions of fronto-temporal and fronto-parietal lobe networks in particular (Austin, 2009, pp. 130–173). However, diverse phenomena unfold quickly during advanced alternate states of consciousness. They present unusual blendings of different attributes. The two sentences condensed in item 8 suggest that the flash of selfless insight-wisdom (Skt: prajna) is extraordinary for two reasons. First, for the way it dissolves self-centered processing; second, for the way it liberates other functions that are consistent with enhanced modes of allocentric attentive processing (Austin, 2009, pp. 178–188, 199–214). The egocentric vacancy in the core of the psyche leaves an extraordinary impression: all root origins of selfhood and deep natural survival angsts seem to have dropped off. This acute, ineffable release from the deepest instincts of primal fear is especially liberating (Austin, 1998, pp. 569–570; Austin, 2006, pp. 232–237, 357–387; Austin, 2014, Chapter 14).
Insight happens. Insight is not driven by logic-tight sequences of deliberate thought. For centuries, Zen masters emphasized that advanced degrees of insight (Skt: prajna) played a key transforming role in the Buddhist meditative Path. The masters also warned their trainees: steer clear of those heavy burdens imposed by word language, ruminating thoughts, and fixed conceptual barriers (Austin, 2009, pp. 150–152; Austin, 2014, Chapters 3, 6, 8). Does any contemporary research into the pros and cons of language appear to support such an orthodox empirical stance?
The first task for the normal subjects studied by Bergen et al. (2007) was straightforward: listen to words that would be spoken in the form of simple, short, recorded sentences. The whole meaning of each sentence hinged on where, in space, each event could have taken place. The two possibilities were either higher up, or lower down, in the extrinsic environment. For example, in some sentences the subjects could hear an up-word ("sky") being spoken. Other sentences would specify a down-word ("grass"). The subjects' next task was a simple visual discrimination: they indicated by a button press whether they saw a circle or a square. Each visual target appeared either at a higher, or lower place on the computer screen. They could see each ◦ or □ clearly, during a long 200 ms interval. Some subjects took 30 ms longer to signal this discrimination. What caused this slowing? Why had they hesitated? Notably, the delay occurred when they saw either this square, or this circle, in that very same—upper, or lower—location, the same place which had just been inferred by that up-or-down word-language inserted into the prior sentence. When did these prior spatial nouns or verbs cause the greater interference delays? When both the visual and the auditory processing converged during those tasks that were chiefly referable to the upper visual fields. Figure 1 suggests that these upper visual fields are represented by the lower occipital ↔ temporal lobe pathways.
How do words interfere with other brain functions? Could word entanglements that arise among language networks (perhaps especially in our left hemisphere) sometimes compete for neural resources with nearby intuitive processing mechanisms? Could such obstacles, acting either directly or indirectly, block the free-flowing access to adjacent networks that might otherwise help us express innate degrees of selfless, insight-wisdom?
In this regard, a different kind of experiment has examined the ways the right and left hemispheres function in normal subjects (Chi and Snyder, 2011, 2012). In these studies, the brain is being stimulated by the gentle flow of direct current. This technical approach is called transcranial direct current stimulation (tDCS). This direct current is delivered at low amperage to the scalp over the right and left anterior temporal regions, simultaneously. However, the left anterior temporal scalp electrode serves as the negative pole (–). This cathodal pole tends to hyperpolarize the resting potentials of nerve cells in the underlying left anterior temporal lobe. This makes these left nerve cells less excitable. In contrast, the right anterior temporal scalp electrode serves as the + pole. This anodal pole tends to depolarize the resting potentials of the underlying nerve cells on the right side. What is the net result of these modulations? Notice that this result generates the asymmetrical expression of temporal lobe functions. Those pathways on the right side become more readily excitable. Those on the left side—the side dominant for language—become less excitable (Austin, 2014, Chapter 13).
These normal subjects received transcranial direct current stimulation to the scalp in this manner for only 10–17 min. Next they were challenged to solve either some difficult "matchstick" tests (Austin, 2009, pp. 183–184) or to solve another, very difficult, "connect-the-9-dots" test. In brief, the data showed that tDCS substantially improved the subjects' creative problem-solving performance for up to the next hour beyond that which occurred either in the sham controls, or when the directions of current flow were reversed. These results have implications both for the kinds of complications introduced by our words and for the nature of the kinds of insights we use during creative processing.
It turns out that old Greek words, plus a few old words used in Zen, overlap with concepts recently evolving in neuroscience. The results can be mutually illuminating if their correlations are interpreted with appropriate caution. A longitudinal perspective is essential. Thirty-five year old Siddhartha had devoted six long years to a rigorous spiritual quest before he happened to glance up before dawn at that legendary morning star (Austin, 1998, pp. 7–8).
Is it feasible to attempt to develop a theoretical neural basis for such an "awakening" of insight-wisdom? The 10 topics just reviewed in this condensed version are the latest sample emerging from several decades spent exploring testable hypotheses (Austin, 1998, xvi; Austin, 2006, xvi; Austin, 2009, xvi; Austin, 2011, pp. 169–177). Some of these have the potential to clarify thorny issues increasingly important to meditators, researchers, and to society in general (Austin, 2012, in press).
Achronia: A state of consciousness lacking all sense of time, resulting in the impression of eternity.
Allocentric: Other-referential. The term serves as a useful contrast to our dominant mode of egocentric (self-centered) consciousness. Additional terms emphasize the anonymity implicit in allocentric processing. They include: stimulus-centered, object-centered, observer-independent.
I-Me-Mine: A descriptive psychological construct. It helps define the personal self in operational terms.
Kensho: Seeing into the essence of reality. The beginning of true long-term meditative training; a prelude to the depths of satori.
Koan: An enigmatic statement serving as a device for concentration.
Limbic thalamus: The three most rostral nuclei in the dorsal thalamus: the medial dorsal, anterior, and lateral dorsal nuclei. They are intimately connected both with the limbic system and with particular regions of the overlying cortex.
Prajna (Skt): The flashing insight-wisdom of enlightenment.
Remindfulness: The overview intuitive functions that tap into memory to provide us with subconscious forms of affirmative guidance. These normal recollection functions are implicit in an ancient Pali word, sati, that is usually translated only as mindfulness.
Reticular nucleus of the thalamus: The thin outer layer of GABA nerve cells capping the dorsal thalamus in particular. It plays a pivotal, normal inhibitory role in shaping our thalamo ↔ cortical interactions.
State: A temporary condition involving mentation, emotion, or behavior.
Trait: A distinctive ongoing quality of attitude, character or behavior. Traits can be transformed incrementally in the course of long-term meditative training, especially when reinforced by deep insightful states of awakening.
Zen: A form of Mahayana Buddhism which emphasizes a systematic approach to meditative training and to the development of character. Its two major schools—Rinzai and Soto—developed in China when Indian Buddhism evolved in the cultures of Taoism and Confucianism, and later spread to Japan.


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Q: Vieta's formula for quartic complex polynomial? I am trying to reproduce the steps of a paper that gives the two principal complex roots of the following equation:
$$ a_{11}z^4 + \left( 2a_{12}+a_{66} \right) z^2 + a_{22}=0 \, , \tag{1}\label{1}$$
where $a_{11},\, a_{12},\, a_{22},\, a_{66} \in \Re$. After formulating it, the author states that

it has been proven that, except for the following special cases
a) $a_{22}=0$ ,
b) $a_{22}=2a_{12}+a_{66}=0$ ,
a) $a_{11}=0$ ,
d) $a_{11}=2a_{12}+a_{66}=0$ ,
the roots of \eqref{1} are either complex, or purely imaginary
numbers.

He then goes on to say that the principal roots (and I think he defines them by the ones with a positive imaginary part) of the equation have the following relationships:

$$ z_1 z_2 = -\sqrt{\frac{a_{22}}{a_{11}}}\, , \tag{2}\label{2}$$
$$ z_1^2+z_2^2=-\frac{2a_{12}+a_{66}}{a_{11}}\, , \tag{3}\label{3}$$
$$ i\left( z_1+z_2 \right) = -\sqrt{\frac{2a_{12}+a_{66}}{a_{11}}+2\sqrt{\frac{a_{22}}{a_{11}}}}\, . \tag{4}\label{4}$$

I don't know how he obtains the relationship in \eqref{4}. I think I get that he obtains the first two ones from Vieta's formula applied to the biquadratic equation, and considering that, in the rest of the paper, whenever he takes a square root of these complex solutions, he takes the negative one (for physical significance). To put this last sentence into equations, let us define $x=z^2$; then the roots of
$$ a_{11}x^2 + \left( 2a_{12}+a_{66} \right) x + a_{22}=0 \, , \tag{5}$$
satisfy that
$$ x_1+x_2=-\frac{2a_{12}+a_{66}}{a_{11}} \tag{6}\, , $$
from where \eqref{3} is obtained, and
$$ x_1 x_2 = \frac{a_{22}}{a_{11}}\, ; \tag{7}\label{7}$$
applying the definition of the complex square root stated before, \eqref{7} transforms into \eqref{2}:
$$ \left(z_1z_2 \right)^2= \frac{a_{22}}{a_{11}} \Rightarrow -z_1z_2 = \sqrt\frac{a_{22}}{a_{11}}\tag{8}\, . $$
Finally, he writes:

[t]he two principal roots, $z_1$ and $z_2$, can be solved using equations \eqref{2} to \eqref{4}. The solution is:
$$ z_1=\frac{i}{2}\left[ \sqrt{ \frac{2a_{12}+a_{66}}{a_{11}} +2\sqrt{\frac{a_{22}}{a_{11}}} }  +  \sqrt{ \frac{2a_{12}+a_{66}}{a_{11}} -2\sqrt{\frac{a_{22}}{a_{11}}} }  \right] \, ,\tag{9} \label{9}$$
$$ z_2=\frac{i}{2}\left[ \sqrt{ \frac{2a_{12}+a_{66}}{a_{11}} +2\sqrt{\frac{a_{22}}{a_{11}}} }  -  \sqrt{ \frac{2a_{12}+a_{66}}{a_{11}} -2\sqrt{\frac{a_{22}}{a_{11}}} }  \right] \, .\tag{10} \label{10}$$

My questions are: how to get \eqref{4}? And, then, how does he get \eqref{9}, \eqref{10} from \eqref{2} to \eqref{4}?
Excuse my complex algebra illiteracy if the answer is obvious.

A:
  I have solved the above question. You can see in the image below

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