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David D. Stanton has been at 2 events

HostFollowersTitleDateGuestsLinks
Ingress2,770,254#Interitus XM ANOMALY SERIESStay. Strong. Create. New. Future. Destroy. Breathe. Create.APR 12 Amsterdam http://goo.gl/c2DSS4 SATELLITE SITES Glasgow http://goo.gl/BFBMsS Malaga http://goo.gl/Ganbax APR 26 London http://goo.gl/2ql3ry Flagstaff http://goo.gl/zHlnSuSATELLITE SITES Frankfurt http://goo.gl/8kkOGi Stockholm http://goo.gl/WslonD Colorado Springs http://goo.gl/IQntXSSalt Lake City http://goo.gl/KVRGVS MAY 10 Ishinomaki http://goo.gl/mRTMeX Santa Fe http://goo.gl/oqIpts SATELLITE SITES Beijing http://goo.gl/SFfrpE Seoul http://goo.gl/wFjqcA Helena http://goo.gl/DwX1Dc Madison http://goo.gl/Z4GsXd MAY 17 Melbourne http://goo.gl/BFg59R Kansas City http://goo.gl/5iBAod SATELLITE SITES Auckland http://goo.gl/9OFc4b Brisbane http://goo.gl/u7XBFZ Cheyenne http://goo.gl/WD2eJm Sioux Falls http://goo.gl/BSS5ov JUNE 7 Santiago http://goo.gl/kaKti8 Cincinnati http://goo.gl/23s5go SATELLITE SITES San Jose http://goo.gl/f27qIs San Juan http://goo.gl/0EWlER Asheville http://goo.gl/agdTEx Birmingham http://goo.gl/1ZCZLG #Interitus XM Anomaly Site Satellite Site: Frankfurt2014-04-26 13:00:00863 
Space Fan News!3,911,503Hello Space Fans!Tonight there will be a total lunar eclipse tonight in the Western Hemisphere. +Scott Lewis  will be heading to Cerritos College in Norwalk, CA to do some on-site outreach with Dr. +Thad Szabo. Internet permitting, we'll be attempting to bring in a live feed of the lunar eclipse from LA and hopefully connect with our friends from the +Virtual Star Party  and bring in feeds from there too!If you're in the Los Angeles area, you are more than welcome to join us on site. The event starts at 10:30 p.m. PT and parking is free after 10 p.m.Cerritos College: 11190 Alondra Blvd. Norwalk, CA 90650Parking Lot C-6 off of Studebaker, just south of Alondra Blvd.Not local? That's okay too! Share with us your pictures of the eclipse in the event below! Keep Looking Up!#ScienceEveryday   #Space   #Astronomy   #Eclipse   #LunarEclipse   #BloodMoon  Lunar Eclipse Live!2014-04-15 08:00:00391 

David D. Stanton has been shared in 31 public circles

AuthorFollowersDateUsers in CircleCommentsReshares+1Links
George Clark7,103Circle share with new friendsHi friends follow this circle1 - Include me in your circles2 - Share the circle (Publicly)3 - Add +1 to the post.4 - Leave a comment if you like.I will thankful if you plus and share this circle!I don't wish to offend anyone on the internet, so if you would like to be removed from my shared circles, please send me a private message and I won't share your profile in the future. The only way being shared will affect you is that you will get notifications that people have added you. You are under no obligation to add them back to your circles. If you don't add them back, they will most likely remove you from their circles after some time.#topcircle #circleshareoftheday #sharedcircles  #sharedpubliccircles   #fridaycircle   #themecircle   #mediterranean   #addbackspree   #ripplescircle   #addback   #aahanapriyadarsinee   #peoplescircle   #circleoftheday   #followme   #follow4follow  2014-09-27 10:52:530292437
George Clark5,516Boost your visibility on Google+ - Share the #circle ! To be added to the Circle you have to do these simple steps: 1 - include me in your circles 2 - Click add people and create your circle 3 - share the circle (include yourself) 4 - add +1 to the post#topsharedcircle #circleoftheday #sharedcircle #trustinme #circlesharing #circleshare #circles #circleoftheday #sharedpubliccircles #sharedcircles #share #vipsnowballcircle #sharedcircleoftheday #sharewithyou #followme #followers #followback #circle #googleplus #coolpeople #circleshare #sharedcircles #sharedcircle #sharedcircles #sharedpubliccircles #circleshare #circlesharing #fullcircleshare #addpeople #add #addcircle #socialmedia #dragonseyecircle #VarietyCircle 2014-08-29 06:34:43494191420
Becky Collins10,439Super Science Circle :Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104  #socialmedia  #media  #circles   #circleshare   #circlesharing  #circlecircle   #beckyscircle   #sharedcircles   #sharedpubliccircles  #sharedcircleoftheday  +Becky Collins ?2014-05-31 05:09:154901211
Jack C Crawford86,096Another cool circle.2014-03-22 17:03:555000517
Tiberiu Igrisan448Science (part 1)#science #sciencecircle #sharedcircles  2013-10-14 18:53:04257123
Jane Ellen43,979I call this one my Big Ball-0-Fun.  I started with Dede's Fundies, thank you +Dede Craig King and added smaller circles I had made, along with a science circle from +Ray Sanders ,  and some small circles from +Lynette Young and +Carter Gibson and I don't even know who else.  So I haven't organized circles in two years.  You wanna make sumpin' of it? #sharedcircles   #circleshare  #newbies 2013-09-06 17:42:0642925629
Herb Firestone1,148Sunday Appreciation Circle | My First Shared Circle! Please re-share, comment and plus one if you think this is a good idea for Sundays. #sharedcircles   #sharedpubliccircles   #sunday   2013-03-03 19:39:2511110210
Trever McGhee20,284+Take2seconds to be inspired by this circle of amazing people that +Shaker Cherukuri included me in for appreciation of helping him go from 500 followers to close to 14,000I personally know the majority of the people in this circle and their incredible for what they do to help people and what they bring to the public stream :-))+Take2seconds to add the circle...you won't be disappointed.:-)) ♥ ♥ ♥ :-))I added the circle and now I'm re-sharing it with my pages+Take2seconds  +ShareThis  +2Help Save Lives Below is +Shaker Cherukuri own  words on this circle, from the original post. he shared at 14:46  -  to the public streamSunday Appreciation Circle shareI joined Google Plus on July 15, 2011. However, I did not really get active until January 2012. I was at 500 circlers a year ago. Approaching 14K now. It has been an amazing year on Google Plus.Icing on the cake was the communities. I started two of them: Nuclear Energy and Root Cause Analysis. Thanks for the engagement on my profile and in the two communities.Several folks in this circle shared me in various circles multiple times during the course of this past year. Truly appreciated.Adding this circle will enrich your Google Plus experience. Pass it on for others.2013-02-10 21:43:011174716
Shaker Cherukuri13,662Sunday Appreciation Circle shareI joined Google Plus on July 15, 2011. However, I did not really get active until January 2012. I was at 500 circlers a year ago. Approaching 14K now. It has been an amazing year on Google Plus.Icing on the cake was the communities. I started two of them: Nuclear Energy and Root Cause Analysis. Thanks for the engagement on my profile and in the two communities.Several folks in this circle shared me in various circles multiple times during the course of this past year. Truly appreciated.Adding this circle will enrich your Google Plus experience. Pass it on for others.2013-02-10 20:46:5411041939
Ian Herndon8,223Shared Circle Time! - G+ Community Moderators (4 of x)Re-Share to help moderators easily connect with one another!Now that Google has launched Communities there has been a ton of activity by people to create communities relating to their interests, join ones created by others, and meet other creators in an effort to learn more and more new ways to build and contribute to G+ Communities. +Community Moderators is an example of a page/community dedicated specifically to having a single place where all moderators can join in discussion around just that.I have been hard at work creating Circles that consist of Community Moderators and Owners only. My hope is to be able to help others expand their network of friends to also include like minded people dabbling in the Community space too. In the near future I intend to eventually group these moderator circles into smaller more targeted ones tailored to specific interests. So with that said, here's our circles!G+ Community Moderators & Owners Circle (1 of x) - 12/31/2012https://plus.google.com/u/0/110099838681495349209/posts/ETe6deLAMq2G+ Community Moderators & Owners Circle (2 of x) - 12/31/2012https://plus.google.com/u/0/110099838681495349209/posts/7i2DXeQpknnG+ Community Moderators & Owners Circle (3 of x) - 12/31/2012https://plus.google.com/u/0/110099838681495349209/posts/j1rsi9YGGVgG+ Community Moderators & Owners Circle (4 of x) - 1/12/2013https://plus.google.com/u/0/110099838681495349209/posts/VFUjZcifXPQ#Community   #Moderators   #Owners   #Communities   #Circle   #SharedCircles   #CircleShare2013-01-12 15:28:345005210
Shaker Cherukuri8,427Engagers CircleCircle of folks (few pages) that have actively engaged with me these past few months (re-shared posts, plussed and commented). Moving forward, I will be doing this on a monthly basis.2012-10-30 12:38:3823559837
Shaker Cherukuri6,435My High Engager's Circle. Folks (135 people, 3 pages) that have in the recent past re-shared my posts.Thank You for the support.2012-08-26 18:10:3513825729
David D. Stanton5,770Here is my Geek's Circle: (Note I have just cleaned my G+ to try to remove inactive users.) Enjoy! 2012-06-25 08:47:49501012
David D. Stanton5,770Here is my Science and Technology Circle.... Enjoy! 2012-06-25 08:46:46501105
Alister Macintyre7,220My copy, of this circle of people interested in our Economy and how come it is in a mess, is over 600 people, but I can only share 500.  Some day, I will split the people here into smaller circles of secondary interests, or maybe installments.2012-06-15 03:15:52501314
Robert Kappenhagen151+Charlie Hoover this is Fraser's Science circle (with a few of my own additions) If you want to share it with anyone.2012-03-08 01:47:57295000
Daniel Harrington11,027A Rockin' #Science #Circle - Thanks for Sharing! #circleshare #sciencecircles #scientists #biology #chemistry #physics #astronomy #entomology #marinebiology #archaeology #sciencecircle #sharedcircles #publiccircles2012-03-03 19:45:12337000
Fraser Cain24,647My official, super science circle+Robert Scoble wanted me share my awesome science list. These are people who are active on Google+ and love to talk about science. We've got actual scientists, journalists, bloggers... even an astronaut!If you still don't really get why Google+ is such a great resource, just import this circle, and suddenly you'll see amazing science posts streaming by. Then you'll understand.For those of you wondering how to get on this list, just reply to this share suggesting yourself or someone else who's active and sciency. I'll take a look through your posting history and then add you.For Science!2012-01-17 21:41:532487414188
Imaad Saiyed0"You need more Science in your diet."- +Chris Pirillo.I've gained a lot of new followers in the last month; many have just joined Google+ and have an empty stream. For those of you who are brand new to the service, I want you to understand:The key to enjoying Google+ is to have an active and engaged stream of content. Circle interesting people.To help you out, I'm sharing my carefully curated science circle. This list contains almost 250 people who are active on Google+ and regularly post about science topics. We've got scientists, journalists and science enthusiasts.If you import this circle, you'll see what I'm seeing, and I think you'll get why I like Google+ so much. If you don't import it, you'll see an empty screen and wonder why your friends haven't joined.I try to share this circle once a month or so, with some new faces, and the inactive people removed. So I suggest you import this list into a brand new circle which you can then replace when I send out an update._As always, if I've missed someone, please let me know and I'll be glad to add them for the next round._" Via +Fraser Cain #sharedcircle2012-01-11 06:09:50245200
Suzanne Haggerty13,661PAY IT FORWARD SHARED CIRCLEThe "Pay It Forward" Circle is over 500 people now. G+ only allows me to share 500 with you. If you have a smaller version of this circle, don't forget to add all the new folks in - it's easy and only takes a few seconds.(And a big thank you to those of you who have circled me tonight!)1. ADD CIRCLE 2. ADD YOURSELF3. ADD 1 PERSON TO PROMOTE 4. SHARE CIRCLE Please copy and paste instructions into your Circle Description when sharing, including this sentence. ENJOY & PAY IT FORWARD, everybody gets in.2011-11-30 05:29:12500328
Robby Bowles10,281Science Circle #ScienceSundayI'm going to start off #ScienceSunday today by sharing my science circle. This circle contains scientists, science writers, and many others who post regularly about science related topics. One of my favorite circles! Please share this circle so others can find these science minded individuals!Don't forget to share a #ScienceSunday post today! Post anything related to science and tag it with #ScienceSunday . If you are a photographer, post a science related image and explain why it relates to science to you. If you are not a photographer, simply post anything related to science. We had some great posts last week and a lot of interesting discussion. I look forward to more this week! +Allison Sekuler and myself will be curating this theme each Sunday.2011-11-13 15:01:524216319
Lynne Flynn01 of 2 Occupy Circles +Peter A. Saldaña IIILynne Flynn shared a circle with you.2011-10-29 07:03:42500455
pio dal cin2,936pio dal cin shared a circle with you.2011-10-29 00:41:253051506
Jared Mysko20Got an Occupy Circle in the works. Share and add to it!Jared Mysko shared a circle with you.2011-10-18 03:29:14149345
Robby Bowles5,769Sharing my updated science circle for #ScienceSunday once again. I have added more than 200 people to this circle since its last share. Add these science minded individuals to your circles and reshare this circle so others can find them as well!!Robby Bowles shared a circle with you.2011-10-16 22:53:1137011211
John Alchin79Folks sharing information on Occupy movements worldwide, based on original circle by +marc roundJohn Alchin shared a circle with you.2011-10-16 14:03:51115212
David D. Stanton1,085Friendly Chatty CircleDavid D. Stanton shared a circle with you.2011-10-15 18:02:2254000
Christy Ramsey0This is my first Circle Share! YAY!These are all people who are interactive, witty, snarky, techy or talkative and will definitely liven up your stream. There are photographers, humorists, writers, bloggers, entrepreneurs, and Random-Joes included, so it's a pretty eclectic bunch. But they are all entertaining (at least to me) and are good for interacting and showing appreciation for good quality content.CIRCLE UP!Christy Ramsey shared a circle with you.2011-10-14 14:23:175735611
Daniel Allan0My Standford AI circle, right on 500 :)Daniel Allan shared a circle with you.2011-10-08 20:30:23500301
Peter Bailey1,954Circle Saturday: Top CommentersHere are this week's top commenters. Circle them, because they rule.And make your own so I can circle them :)Speak up if you think I missed you.Peter Bailey shared a circle with you.2011-10-08 10:17:011541419
Peter Bailey1,852Circle Saturday: Top CommentersThese are this week's top commenters. Circle them, because they rule.Peter Bailey shared a circle with you.2011-10-01 10:18:4585813

Activity

Average numbers for the latest posts (max. 50 posts, posted within the last 4 weeks)

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Top posts in the last 50 posts

Most comments: 1

2014-11-08 15:37:34 (1 comments, 0 reshares, 0 +1s)Open 

X-Men mind control becomes a reality



Most reshares: 1

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2014-11-22 12:56:35 (0 comments, 1 reshares, 1 +1s)Open 

As usual, Stephen Colbert nails it.

Most plusones: 2

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2014-11-19 12:54:25 (0 comments, 0 reshares, 2 +1s)Open 

Still waiting for the OTA...
It's almost been a week since Lollipop's official release. I'm too embarrassed to use my phone in public now. All those people judging me for having a Nexus 5 without the latest from Android. I could try keeping a gallery of Lollipop screenshots to help keep the illusion that Google hasn't completely abandoned me. I would try flashing it but it just doesn't feel right. I want my update to come straight from Android's majestic servers. I want to see the rainbow that will appear outside my window ending at my phone when my time has come. I bet you didn't know every rainbow you've seen since the 12th has been someone getting the Lollipop OTA. I guess I'll just have to stay inside until Lollipop comes my way... if it ever does. #Android #Nexus #Lollipop #Trololollipop

This post may or may not be an exaggeration.

Latest 50 posts

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2014-11-22 12:56:35 (0 comments, 1 reshares, 1 +1s)Open 

As usual, Stephen Colbert nails it.

As usual, Stephen Colbert nails it.___

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2014-11-22 12:56:10 (0 comments, 0 reshares, 0 +1s)Open 

Here's what famous paintings look like recreated in Minecraft: http://on.mash.to/1r6lFSs

Here's what famous paintings look like recreated in Minecraft: http://on.mash.to/1r6lFSs___

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2014-11-22 12:54:19 (0 comments, 0 reshares, 1 +1s)Open 

Circuit Diagram of TV Remote Jammer using 555 Timer


Resource Link: http://buff.ly/1EU5KPh

Circuit Diagram of TV Remote Jammer using 555 Timer


Resource Link: http://buff.ly/1EU5KPh___

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2014-11-22 12:53:49 (0 comments, 0 reshares, 0 +1s)Open 

I hope @stellerstories comes out with an Android app in the near future...

I hope @stellerstories comes out with an Android app in the near future...___

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2014-11-22 12:45:51 (0 comments, 0 reshares, 1 +1s)Open 

___

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2014-11-22 12:15:33 (0 comments, 0 reshares, 0 +1s)Open 

Let me know what covers you'd like me to do next! Thankyou so much for your incredible kind support. Love you all so much! THANK YOU!!! 

Let me know what covers you'd like me to do next! Thankyou so much for your incredible kind support. Love you all so much! THANK YOU!!! ___

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2014-11-22 12:10:07 (0 comments, 0 reshares, 0 +1s)Open 

Bravo!

Bravo!___

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2014-11-22 11:52:17 (0 comments, 0 reshares, 0 +1s)Open 

Bravo! FUS DU RAH!!

Bravo! FUS DU RAH!!___

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2014-11-22 06:34:34 (0 comments, 0 reshares, 1 +1s)Open 

Interview of Andrew Ng, the "deep learning" expert who defected from Google to Baidu. "We're on track to close out the year with 96 people in this office, employees plus contractors. We're still doing the 2015 planning, but I think we'll quite likely double again in 2015. We’re creating models much faster than I have before so that's been really nice. Our machine-learning team has been developing a few ideas, looking a lot at speech recognition, also looking a bit at computer vision. Baidu's performance at speech recognition has already improved substantially in the past year because of deep learning. About 10% of our web search queries today come in through voice search. Large parts of China are still a developing economy. If you're illiterate, you can't type, so enabling users to speak to us is critical for helping them find information."

Interview of Andrew Ng, the "deep learning" expert who defected from Google to Baidu. "We're on track to close out the year with 96 people in this office, employees plus contractors. We're still doing the 2015 planning, but I think we'll quite likely double again in 2015. We’re creating models much faster than I have before so that's been really nice. Our machine-learning team has been developing a few ideas, looking a lot at speech recognition, also looking a bit at computer vision. Baidu's performance at speech recognition has already improved substantially in the past year because of deep learning. About 10% of our web search queries today come in through voice search. Large parts of China are still a developing economy. If you're illiterate, you can't type, so enabling users to speak to us is critical for helping them find information."___

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2014-11-20 14:07:33 (0 comments, 0 reshares, 0 +1s)Open 

LG G Watch R Review!: http://youtu.be/W6xQgFBM2kI

Out of my four Android wear watches this thing is definitely my favourite! I highly recommend it to anyone wanting to get a cutting edge smartwatch. 

LG G Watch R Review!: http://youtu.be/W6xQgFBM2kI

Out of my four Android wear watches this thing is definitely my favourite! I highly recommend it to anyone wanting to get a cutting edge smartwatch. ___

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2014-11-19 22:19:33 (0 comments, 0 reshares, 0 +1s)Open 

___

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2014-11-19 18:53:57 (0 comments, 0 reshares, 1 +1s)Open 

___

2014-11-19 13:04:51 (0 comments, 0 reshares, 1 +1s)Open 

SuperSU v2.24 BETA - moar testing!

Yes, another beta update. The test procedure and question is the same as for v2.23, so please read that post: https://plus.google.com/113517319477420052449/posts/jGoDoPPZUdT

During testing of v2.23 it became apparent a few calls still didn't work right. Investigating that issue lead me to the conclusion that the calls that were actually fixed in v2.23, would stop working the next (minor) Android update, due to new security commits in AOSP.

v2.24 should circumvent that, as well as fix additional calls (namely: am). In theory app compatibility should be the same or better as v2.23, but please test all your apps again to see if everything still works.

And yes, for those who keep asking, the new docs relating to SuperSU and Lollipop are underway and hopefully will be released in the next day or two.

SuperSU v2.24 BETA - moar testing!

Yes, another beta update. The test procedure and question is the same as for v2.23, so please read that post: https://plus.google.com/113517319477420052449/posts/jGoDoPPZUdT

During testing of v2.23 it became apparent a few calls still didn't work right. Investigating that issue lead me to the conclusion that the calls that were actually fixed in v2.23, would stop working the next (minor) Android update, due to new security commits in AOSP.

v2.24 should circumvent that, as well as fix additional calls (namely: am). In theory app compatibility should be the same or better as v2.23, but please test all your apps again to see if everything still works.

And yes, for those who keep asking, the new docs relating to SuperSU and Lollipop are underway and hopefully will be released in the next day or two.___

2014-11-19 13:04:27 (0 comments, 0 reshares, 0 +1s)Open 

+Google+ Developers - Anyone have a good automatic way to clean up my circles? I have hit the 5000 limit and want to remove those who dont post. I want to follow active users.

+Google+ Developers - Anyone have a good automatic way to clean up my circles? I have hit the 5000 limit and want to remove those who dont post. I want to follow active users.___

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2014-11-19 13:02:41 (0 comments, 0 reshares, 1 +1s)Open 

I'm more than impressed ..
Now, that I know how these glass sculptures have been done .. I think, I'm going to start collecting them. 

#Crafting   #GlassSculpture  

I'm more than impressed ..
Now, that I know how these glass sculptures have been done .. I think, I'm going to start collecting them. 

#Crafting   #GlassSculpture  ___

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2014-11-19 13:02:14 (0 comments, 0 reshares, 0 +1s)Open 

Wal-Mart got scammed into selling PS4 consoles for $90

Ouch...

But, y'know... If I could, I would.

Wal-Mart got scammed into selling PS4 consoles for $90

Ouch...

But, y'know... If I could, I would.___

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2014-11-19 13:00:43 (0 comments, 0 reshares, 1 +1s)Open 

Tip: If you aren't already using it, download the Google Now Launcher after you get the Lollipop upgrade.

It'll give you the new 5.0-level app drawer and other Lollipop-style visuals that won't show up with the old stock Android launcher.

Worth at least checking out as part of your Lollipop experience!

[https://play.google.com/store/apps/details?id=com.google.android.launcher]

Tip: If you aren't already using it, download the Google Now Launcher after you get the Lollipop upgrade.

It'll give you the new 5.0-level app drawer and other Lollipop-style visuals that won't show up with the old stock Android launcher.

Worth at least checking out as part of your Lollipop experience!

[https://play.google.com/store/apps/details?id=com.google.android.launcher]___

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2014-11-19 12:54:25 (0 comments, 0 reshares, 2 +1s)Open 

Yeah, Gotta get taht Lollipop +Cyanogen Inc. +CyanogenMod 

Still waiting for the OTA...
It's almost been a week since Lollipop's official release. I'm too embarrassed to use my phone in public now. All those people judging me for having a Nexus 5 without the latest from Android. I could try keeping a gallery of Lollipop screenshots to help keep the illusion that Google hasn't completely abandoned me. I would try flashing it but it just doesn't feel right. I want my update to come straight from Android's majestic servers. I want to see the rainbow that will appear outside my window ending at my phone when my time has come. I bet you didn't know every rainbow you've seen since the 12th has been someone getting the Lollipop OTA. I guess I'll just have to stay inside until Lollipop comes my way... if it ever does. #Android #Nexus #Lollipop #Trololollipop

This post may or may not be an exaggeration.___Yeah, Gotta get taht Lollipop +Cyanogen Inc. +CyanogenMod 

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2014-11-19 12:19:15 (0 comments, 0 reshares, 0 +1s)Open 

Brilliant news!

Let’s Encrypt — Mozilla, Cisco, and Akamai to offer free HTTPS/SSL certificates for the Entire Web http://thn.li/scdh___Brilliant news!

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2014-11-19 12:18:31 (0 comments, 0 reshares, 1 +1s)Open 

H/T +martin shervington 

Google's new mobile friendly tool - robot.txt

In case you missed it, Google has just launched a #mobilefriendlytool to test if your website is suitable for mobile.

Although it seems a little buggy, it is still how Google sees your website and so hugely important for organic traffic.

We had a few sites that failed this test even though they were responsive and very mobile friendly. The cause - was a robot.txt blocking Google Bot from a graphic file. It took 1 minute to fix, and so here is me hoping for an surge of website visitors from organic mobile search.

The tool has been added to our website healthcheck here:
http://jeyjoo.com/blog/how-good-is-your-website-free-website-healthcheck

Here is a link to the mobile friendly tool:
https://www.google.com/webmasters/tools/mobile-friendly

#seotips #plusonly  ___H/T +martin shervington 

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2014-11-19 12:15:55 (0 comments, 1 reshares, 0 +1s)Open 

50 G+ Tips / 117 G+ Answers / 123 G+ How-To / 20 Google Tips
50 Google+ Tips
Create A Killer Hovercard: goo.gl/ifDhJW
Sharing to Circles vs. Publicly: goo.gl/1qr0YO
Google+ Communities: goo.gl/NC21Ly
Share Your G+ Posts on Other SM : goo.gl/QeefiD
Report Issues With G+ or Suggest Ideas: goo.gl/FywX2c
Create A "Save For Later" Circle: goo.gl/PmBRWf
Add A Large Image To Your Post: goo.gl/lVr3yj
The Various G+ Keyboard Shortcuts : goo.gl/7BaxMs
Share Someone Else's G+ Post : goo.gl/DYJo3U
Create A Mini Blog on G+: goo.gl/zEVIOM
Host A Google+ Hangout: goo.gl/2P0n0Q
Leave A Wake of Value-Add In Your Path: goo.gl/lpCzaD
Take Control Of Your G+ Notifications: goo.gl/WHU0p3
SEO Your Google+ Posts: goo.gl/oYb6J1
How To Find Things On G+: goo.gl/rY18uQ
Formatting For Beautiful, Engaging Posts:... more »

50 G+ Tips / 117 G+ Answers / 123 G+ How-To / 20 Google Tips
50 Google+ Tips
Create A Killer Hovercard: goo.gl/ifDhJW
Sharing to Circles vs. Publicly: goo.gl/1qr0YO
Google+ Communities: goo.gl/NC21Ly
Share Your G+ Posts on Other SM : goo.gl/QeefiD
Report Issues With G+ or Suggest Ideas: goo.gl/FywX2c
Create A "Save For Later" Circle: goo.gl/PmBRWf
Add A Large Image To Your Post: goo.gl/lVr3yj
The Various G+ Keyboard Shortcuts : goo.gl/7BaxMs
Share Someone Else's G+ Post : goo.gl/DYJo3U
Create A Mini Blog on G+: goo.gl/zEVIOM
Host A Google+ Hangout: goo.gl/2P0n0Q
Leave A Wake of Value-Add In Your Path: goo.gl/lpCzaD
Take Control Of Your G+ Notifications: goo.gl/WHU0p3
SEO Your Google+ Posts: goo.gl/oYb6J1
How To Find Things On G+: goo.gl/rY18uQ
Formatting For Beautiful, Engaging Posts: goo.gl/mnfP5d
How To Disable Comments & Shares: goo.gl/Bkc6Mp
Attract More Comments With Gifs & Image Posts: goo.gl/VGcNhl
Start A Conversation With Someone : goo.gl/VXOVmy
Create An Event Using G+: goo.gl/IUFmlP
Enable Automatic Hash-tagging: goo.gl/MuoV9h
Don’t Give Up At The First Hurdle: goo.gl/2zdPQ8
The Benefits of Link Shorteners: goo.gl/pwfGXo
Understanding Ripples & Using Them To Your Advantage: goo.gl/Z47kxp
What Not To Do On G+ (Part 1): goo.gl/IdP51J
Edit Posts - Did You Know You Could Do That?: goo.gl/aFsKU9
Choose The Best Link Thumbnail For Your Post: goo.gl/wXTSh4
Start Building Your Author Rank: goo.gl/4427P3
Link G+ To Your Content With Authorship Tags: goo.gl/Rn4GGJ
Curate & Streamline Circles for Awesome News Streams: goo.gl/e8lNhh
Use Eye-Grabbing Headlines: goo.gl/p45IPK
Use Google Drive With Google+: goo.gl/zpwHHC
Track Circle Shares With CircleCount: goo.gl/TXfe2j
Be Awesome With AutoAwesome: goo.gl/Inq2bX
Build Your Following By Watching Hangouts: goo.gl/Rjgrhi
Overcome Difficulties With Plus-Mentioning People: goo.gl/nQsT9T
Write Posts That People Are Actually Looking For: goo.gl/D8NwGh
Use ‘The Google+ Effect’ To Improve Your Twitter Experience: goo.gl/hLE1Ia
Learn How To Use Images Appropriately & Legally: goo.gl/D3dzCc
Learn To Schedule Posts With +Do Share:  goo.gl/1BUcrN
Build A Community Around Your Passion: goo.gl/IsFrHg
Optimise Your Profile/Page/Community For Search: goo.gl/YMblJF
Share Beyond Your Circles & GPlussers: goo.gl/ryHWHQ
Blocking & Muting People - As Simple As It Sounds?: goo.gl/wqsXnN
Extend The Life Of Your Best Posts: goo.gl/tGw9g7
Merge Multiple Google+ Profiles Together: goo.gl/sRKzp8
Using Your About Tab More Effectively: goo.gl/sNqUDQ
Posting Multiple Photos Per Post: goo.gl/sM32aP
Use Google+ ...Every Day: goo.gl/fS0tIq
What Not To Do On Google+ (Part 2): goo.gl/3ahoO4
(by +Rick Eliason)

118 Google+ Help Tips
Profile, Photos, Auto Backup: goo.gl/w9ffcT
Whom Should You Circle?: goo.gl/RoNPvA
Make use of Google+ tours: goo.gl/c5RZFy
Photos: goo.gl/fF6lth
Save posts, articles and ideas on G+: goo.gl/WSN8Ov
3 steps to more privacy on your G+ profile: goo.gl/u3I3Wv
Actively managing your community membership: goo.gl/TVymDg
How to explore and join Communities: goo.gl/zL2pl3
How to send feedback on G+: goo.gl/VvLWoX 
Make Your G+ Photos “Auto Awesome”: goo.gl/UdahMn
Automatically share your blog posts to Google+: goo.gl/sHDbhm
Ways to use Google+ photo editing: goo.gl/Byk90r
Let hashtags find fun posts for you: goo.gl/MWWD4i
Make your Communities happier and healthier: goo.gl/DoByrf
Do More with Your Photos From Auto Backup: goo.gl/f9WFRJ
Search your own photos -> goo.gl/VB3ZEU
How to delete your Auto Backup photos -> goo.gl/oTO6Eq
Google Photos app is one-tap access to your Google+ Photos: goo.gl/jJ2Dma
How to post publicly, to your circles, or to a community: goo.gl/5NTmUo
Share an album with someone not yet on G+: goo.gl/M9RJDR
How to restore photos from Trash: goo.gl/hpgp3c
How to adjust the mix of posts in your Home stream: goo.gl/4XCqy4
Follow your favorite YouTube channel on Google+: goo.gl/RgsI55
Assign a G+ Page Manager: goo.gl/ccGqji
Getting started on Google+: goo.gl/scpl11
Turning on Auto Backup on Android: goo.gl/tEMs9F
Formatting a Google+ Post: goo.gl/va50H0
Start a scheduled Hangout on Air: goo.gl/nWc3Fk
Grow your following on G+: goo.gl/0GII5U
Use Q&A in your Hangout: goo.gl/X5ZMNA
Select your stream based on your circles: goo.gl/mmoFVb
Produce your Hangout with Control Room: goo.gl/CmktPj
Article Rendering: goo.gl/3ogWrA
See more posts from your favorite communities: goo.gl/QPT3VS
Mastering the art of Hangouts on Air: goo.gl/WEjUik
How to leave a Google+ community: goo.gl/ya1hUS
How to Get Rid of Junk in Your G+ Home Stream: goo.gl/X0tUoW
Seeing Junk in What's Hot?  Clean Up Your Circles!: goo.gl/PQHRKq
Why Your Community Posts Might Be Flagged As Spam: goo.gl/3sJd18
Why Are My Private Posts in Google Search Results?: goo.gl/QOAxKx
How to Set Your Profile Picture: goo.gl/mXqE6y
How to add text to an image already in a G+ album: goo.gl/qrOQau
Ensure Images from Your Website "Full Bleed": goo.gl/ebV15t
To Mute or To Block? That is the Question!: goo.gl/CVZXin
Dealing with Google+ Notification Overload: goo.gl/kwHHyu
Why You Can Only Post to One Google+ Community at a Time: goo.gl/KBiCDl
Circles, Your Circles, and Extended Circles: How Sharing and Notifications Work: goo.gl/iLEfsl
Google+ Tips Collection: goo.gl/Th3hV0 What's Hot and Recommended: How Posts Get Selected: goo.gl/jNlTMT
Using Photo Sphere on your device: goo.gl/JO8Xa9
Deleting Business Pages, How "Google feedback" works, Transferring to another Google Account: goo.gl/ZaaZEo
Public view of profile, Updating page information and Managing circles: goo.gl/MzAj9B
Lost in Translation, 2 Many Accounts, Added You Back: goo.gl/asV6wy
Focus on Communities and a Google+ Update: goo.gl/wtWrTC
Deleting Google+ Photos, Who Follows You On Google+, Hangout Invitations: goo.gl/9XzCdk
Profiles & Pages, Public posts to Communities, Private Communities: goo.gl/eUY0E0
Photos, Profile, Custom URL: goo.gl/TpR3I8
Frozen Auto Backup, Auto Backup on Multiple Devices, and Changing Cover Photos: goo.gl/MTfErM Auto-Backup and Page Ownership: goo.gl/OsWeL0
Connect G+ page to website, Retrieving deleted pics and videos, Add links to G+ business page: goo.gl/OIFJbS
Spam, Stories, Profiles: goo.gl/5GMoG5 
Pages and Communities: goo.gl/pRmH6D
Page Managers, Duplicate account, Hangouts Help: goo.gl/rtbKqR
HOA invites, Autobackup management, YouTube Migration to Brand Page: goo.gl/vBq5lz
Communities, Pages, and Photos: goo.gl/SWvj5D
Community sharing preferences, reporting spammers and mobile stream not loading: goo.gl/CACcc1
Followers, Cover Banner, Brand Pages: goo.gl/7oeSw8
Getting more followers, deleting an old local page: goo.gl/0pj1yi
Autobackups, Custom URL’s and +1’s and viewcounts: goo.gl/uhZuTU
Pages, Names, and Photos: goo.gl/S3c3k4
How To Get Help, Stories privacy, Google+ Page: goo.gl/az1T3K
Photo Privacy, Finding All Your +1s, and Pages Without Profiles:  goo.gl/TbCuZ0 Profile/Page Clarification, Google+ Auto-backup, Circling Limits: goo.gl/3Cw5s4
Circles, Google maps listing for business, different types of Hangouts: goo.gl/mXNh1W
Google+ Posts notification emails , “Avis” tap , Merge G+ local page with G+ business page: goo.gl/GuiKTe
Engagement, Photos to albums, Larger images in posts: goo.gl/NYAi2k
Creating Community From Mobile, Upgrading To Full Size Auto Backup: goo.gl/dCb3y0
Page views, Hoffsome photos, Home page filters: goo.gl/LDe1Ji
Apps, Extended Circles, and Hashtags: goo.gl/9aoNg1
Profile Verification, What’s Hot list, Access Auto Backup photos: goo.gl/WCR0Xy
Page ownership, Privacy, Personalized URLs: goo.gl/Myy5ha
Community Pinned Posts, Preventing Circle Adds, Images in Web Shares: goo.gl/XH4d6P Ignore/Mute a conversation, Commenting on YouTube, Google+ Hashtags: goo.gl/f7aQaj
Gmail notices, Circles, and Photo AutoBackUp: goo.gl/dPfFp8 
Google Plus pages, Using A Business page to +1 and share from the web, Formatting GPlus posts: goo.gl/mysxFK
Visibility of private posts, Merging profile with Google Apps, Deleting Google Local photos: goo.gl/jxRdlt
Public posts, picture tagging, and privacy: goo.gl/4uIOcF
Managing Google+ Business Page, Google+ backing up pictures, Transferring Google+ custom URLs: goo.gl/o0TcG9
Restore, Backup, and Business: goo.gl/KVbTeZ
Your Posts and Membership in a Community, Turning Off Community Posts in Profile, Vanity URLs: goo.gl/V3OgfJ
Contacts, YouTube, and Auto Awesome Movies: goo.gl/9pFZU3
Pages, pages, and more pages: goo.gl/kVxIhd
Photos, Videos: goo.gl/4KrntW 
Downloading your photos, Google+ Local Pages, Authorship: goo.gl/CpvL6u
Migrating to a new account, Post visibility, Profiles & Pages: goo.gl/gTMhZc
Auto Backup, E-mail notification, Change E-mail Account: goo.gl/84yhdq
Custom URL Changes, YouTube Comments Explained, Managing a Business Page: goo.gl/9faF4o
Random People, Cover Photos, That’s My Face: goo.gl/4MhWMz
Custom URLs, Photo upload settings: goo.gl/ceVyyZ 
Images, Blogger Comments, Archived Hangouts: goo.gl/hj7Gru 
Names, endorsements, newbies: goo.gl/ox2zTD
Community Abandonment, Business Pages,  Notification Exhaustion: goo.gl/ajNwnN 
Getting noticed, protecting youth, & photo editing: goo.gl/99Fhn7 
Adblock Plus, Google Places, G+ Page/YouTube: goo.gl/1DJ6mP
Hangouts without webcams, local business listings, and resharing posts: goo.gl/sPIAQl
Events, Communities, and Monetization: goo.gl/65ewNH 
Upload videos from Google+ straight into YouTube, Auto Backup of pictures from mobile: goo.gl/yDC3nF
Recover pictures back to my phone or tablet, change the privacy settings on old posts, search the posts for a single community: goo.gl/hZO2xK
Post to Circles and to a community at the same time, Who can see my post when I make them Public: goo.gl/FiCzoM 
Google+ Support Firefox, What time zone shows up on Events, Can non-Gmail users become G+ users: goo.gl/wzuOoI 
Faces, Photos, and Plusses: goo.gl/gM3NTn
Notifying circles, Google+ training resources, Finding hangouts, Securing your Google+: goo.gl/87NHjk
Communitues, Commenting, Hangout Request, and Email Notifications: goo.gl/9JsanF
Webmasters, Geotags , Notifications , and +1's: goo.gl/zSCX9T 
+1 activity posts, Why can’t I post to Communities and Circles/Public at the same time, Why can't I add more people to my circles: goo.gl/tpDzuK 
Searching, Filtering, Boxes, and Histories: goo.gl/203smg
Photo and video privacy, removing yourself from circles, migrating circles from Profile to Page: goo.gl/G1Nx2U
How to Choose Photos When Sharing Links: goo.gl/SrGZmp
See your Google+ stream in chronological order: goo.gl/94N6IX
(by +Google+ Help)

Google+ 123 How-To
How to put a village on the map: goo.gl/ABUA2J
The Art of Managing a Google + Brand Page: goo.gl/wg0RjW
How to add in a shared circle on Google+: goo.gl/scCBPr
How to change your cover photo on Google+: goo.gl/Baxb5Z
How to change your profile picture on Google+: goo.gl/atDLKB
How to find the 21 digit ID of a Google+ Profile or Page: goo.gl/vGLWie
Socialize – adding and engaging with people from your area: goo.gl/Ek4Rx7
Optimize – helping people find your Google+ Page: goo.gl/7UYL0x
Localize – how to get yourself on the Map with Google: goo.gl/zOJGzw
How to reach more people with your Google+ content: goo.gl/bX8Q8k
A Guide to Collaborative Working using Google software and tools: goo.gl/cifIq7
Personal Branding using Google+, an A-Z Guide: goo.gl/ou75bk
Want to add in a delivery radius to a ‘Storefront’ Business?: goo.gl/9KXmh7
Google Pages for Businesses who ‘deliver as well’: goo.gl/iSU948
How to Integrate Google+ into Your Editorial Calendar: goo.gl/SmTF4d
How to stop showing YouTube tab on your Profile: goo.gl/9z0djW
Make your Google+ Page or Profile a Destination: goo.gl/4JE8h5
How to import your Linkedin Contacts to Google+: goo.gl/MraUx3
How to rename a Google+ community: goo.gl/d7dqOn
Who can see your Google+ posts?: goo.gl/f80hCh
How to use Google Plus Communities for outstanding Customer Service: goo.gl/eVY3NY
Can you turn off the plus ones on Google+?: goo.gl/U9mGQ8
How to share circles between Profiles and Pages: goo.gl/275uYK
A Guide to Google Plus Polls: goo.gl/mxqmJL
Google Plus and Social SEO Facts and Evidence: goo.gl/uqGTmn
Google Plus Marketing Case Study Teaser: goo.gl/LpKjIO
How to share a blog post from a website as a Google Plus page, not a profile: goo.gl/KYGgKi
The value of using tools on Google Plus: goo.gl/mhUvh0
What are extended circles on Google+? And why should we care anyway: goo.gl/k5YcgC
How to delete a Google+ Business Page: goo.gl/qNNGqD
Anatomy of a Time Stamp Post: goo.gl/ZAyoge
The Power to ‘Recommend’ on Google Plus: goo.gl/FFIOjc
Google Business View: Step Inside the Sage Group Headquarters: goo.gl/DQYBJT
10 brilliant things you can do with Circloscope: goo.gl/4XzFn5
How to Use Clean Google+ URLs & the Google+ Canonicals: goo.gl/RTYbOl
‘Google+ for Business’ Presentation: goo.gl/imhF5W
Discover Google Plus: goo.gl/5AXCsk
A Complete Guide to Google Pages: goo.gl/J0PwN7
Google Plus Marketing Stats: goo.gl/gG6ESY
Google Plus ‘Explore’ and Hangouts: goo.gl/wYW8JA
Google Plus Marketing Circles and Communities: goo.gl/Dy9NJ1
Google Plus Marketing Profile and Pages: goo.gl/a74DQg
Google Plus Posts: goo.gl/iabGnJ
A Complete Guide to Google+ Marketing: goo.gl/Q218qw
10 brilliant things you can do with CircleCount.com: goo.gl/zlFDHZ
Google Plus Analytics and Insights: goo.gl/rSCNu2
Google Plus SEO: Trust, Reputation and Authority: goo.gl/3cs1zi
How to create a ‘plus post ad’ within Google Adwords: goo.gl/B1Uu9s
Social Media Marketing and the Power of Google Plus: goo.gl/IMFMpn
How to REALLY build a community on Google Plus: goo.gl/jel8DH
The ‘View Count’ Feature on Google Plus explained and explored: goo.gl/dPdNNE
Organizational Analysis on Google Plus: goo.gl/RiyaQm
Google Plus – Frequently Asked Questions: goo.gl/pVN6UB
Social, Search and Site – how to use Google+ to make it all work together: goo.gl/V03LZF
Google Chrome Extensions – as Suggested by the Google+ Community:  goo.gl/YTT3JG
Lights, Camera, Produced Hangouts: goo.gl/IYXIt7
A Guide to Google Maps Business View: goo.gl/OvgTr5
Complete Guide to Google Hangouts for Businesses and Individuals: goo.gl/eBldKf
Content is King; Community is Kingdom: goo.gl/TFbaUG
Planning Your Social Media Marketing Strategy, using Google Plus: goo.gl/D9XZ34
Content Creation Tools: goo.gl/10lUbC
Hashing Out Google Plus Hashtags: Uncover Their Hidden Powers: goo.gl/NBxOm9
Free Google Plus Training Materials: goo.gl/ZmjtHs
A guide to Google Plus notifications: goo.gl/ChhCPi
Google Plus Coaching, Training, Consulting Directory: goo.gl/l96JIA
How to create a private Google Hangout-on-Air (VIDEO): goo.gl/Dhh3X8
Google Plus For Business and Individuals: goo.gl/LQ0qD3
Getting your Google Plus Brand Page ready for +Post Ads: goo.gl/p9Es89
How to build niche email lists using Google+: goo.gl/OPKfZt
What is Content Marketing? And how to use Google+ to do it brilliantly: goo.gl/aeWLVX
How to use content marketing for high visibility in Google Search: goo.gl/PP0zyU
6 Circles every Google Plus business page should have: goo.gl/XtqfRO
How to create a Google+ Community: goo.gl/VDZVJn
Beginners Guide to Google Plus: goo.gl/6C7ibF
Google Plus Custom URLs: goo.gl/oOuACS
How does Google Plus influence online behavior?: goo.gl/LSNPa5
How to use Google+ for Social SEO: goo.gl/FY82rB
A Complete Guide to Google Pages: goo.gl/txD0RX
Google+ and YouTube comment integration: goo.gl/ChSu7N
A Complete Guide to Google Helpouts: goo.gl/ryqKAR
How to make a Google Plus Page: goo.gl/e2dgFq
Should you choose a ‘Profile’ or a ‘Page’ on Google Plus?: goo.gl/oqsVZ0
Google Plus Tips Guide: goo.gl/7MiUZA
Shortcuts: goo.gl/dg07uL
How to resume from a position ‘down stream’ and receive more content too: goo.gl/5jiYVC
Viewing the profile as if from other’s perspectives: goo.gl/dshbLq
Changing your profile circle settings: goo.gl/X82l3B
How to filter searches on Google Plus: goo.gl/Uiml5D
How to subscribe and receive emails of new content: goo.gl/71RMUq
Showing or hiding posts to communities on your Profile or Page: goo.gl/K0Osma
How to submit feedback on Google+: goo.gl/nC1Kw7
Where to mute or block a profile: goo.gl/3fLO5b
Customise your hangout settings (part 1): goo.gl/ZyztlQ
Customise your hangout settings (part 2): goo.gl/EGBR18
How to change the flow of content from communities in your stream: goo.gl/sduvMX
Top fans on YouTube–circles: goo.gl/3dP9vS
How to turn notifications on or off: goo.gl/gvsWQb
How to change the flow of content from circles in your stream: goo.gl/11HQxz
Adding people to circles from ripples: goo.gl/hJ2u3d
Mute posts you no longer want to hear from: goo.gl/VQ8JRQ
Create a private community with categories for future posts: goo.gl/BMdkRT
How to find channel settings and monetization on Youtube: goo.gl/tsMGBV
Changing your photo settings: goo.gl/m5hfK4
Share public for maximum reach: goo.gl/txbTzL
Change settings on who can interact with you: goo.gl/4yQKKp
Flipping the Google Plus cards: goo.gl/9t6WUB
Choosing to notify a circle by email: goo.gl/Sq96Y8
How to create a new circle from activity on a post: goo.gl/P18Ji0
How to disable comments and reshares before you post: goo.gl/nJjpu0
How to open a new link by dragging and dropping: goo.gl/7PZfB7
How to embed a Google Plus post into a website: goo.gl/wQbrT4
Google+ Page Manager Circle Tip: goo.gl/SuZ4Y4
Using Google Plus communities to work on projects: goo.gl/mexhiA
Analyzing your Google+ Page Content using SNA: goo.gl/ZHJ1WD
What is Google Drive? – a complete user guide: goo.gl/RCWUh0
Gain social reach by adding shared circles to circlecount.com: goo.gl/6WqYrZ
Refining Google Plus Search Using Filters: goo.gl/lO4EcL
Google Circles Management Tips: goo.gl/858xNX
Connect Google account to YouTube: goo.gl/rOF3Jf
Add a thumbnail to your YouTube videos: goo.gl/sAAHoa
Google+ Plus Training Modules: goo.gl/n8QBpQ
Google Apps for Business: http://goo.gl/gG7cUv
Google Plus Cover Photo and Design Tips: goo.gl/r9HP9m
(by +Plus Your Business!)

20 Awesome Google Tips
Your Personal Google Search Trends History: goo.gl/agMWXD
Google Chrome: goo.gl/ynciWj
Search like a Pro: goo.gl/dkUgf4
Google Doodles: goo.gl/s65qHq
Google Alerts: goo.gl/uaY3Oj
Google Docs: goo.gl/UYSdiV
Shorten Your Links with Google: goo.gl/UvWmpP
Back in time with Google Maps: goo.gl/5dqv60
Google Location History:  goo.gl/oJ0kbl
Google Dashboard: goo.gl/3KmiFM
YouTube Playlists: goo.gl/1lgkmM
Google Translate: goo.gl/VFmYGn
Google Calender: goo.gl/PmkIoM
Google Trends: goo.gl/7i6GW4
Secure your Google account: goo.gl/7tNJvL
Android Device Manager: goo.gl/rHtCqm
Make money with Google Adsense: goo.gl/37M90D
Advertising with Google Adwords: goo.gl/y0RRAe
Google Chrome & Search Tricks: goo.gl/mj2vst
15 Awesome Gmail Tricks: goo.gl/vLHyBd
Google Plus - Series Finale: goo.gl/37l2Q7
(by +Daniel Futerman)

Google+ Resources:
. Google+ Support: support.google.com/plus/
. Google+ Help Community: goo.gl/NpiOEf
. Circle +Google+ & +Google+ Help 

More: Discover Google(+) -> http://goo.gl/eIJTNs

#Google #googleplustips #googlenow #gonegoogle   #tiptuesday #tipstuesday___

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2014-11-19 11:56:28 (0 comments, 0 reshares, 0 +1s)Open 

IBM's new email app learns your habits to help get things done

IBM's new email app learns your habits to help get things done___

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2014-11-19 11:49:13 (0 comments, 0 reshares, 0 +1s)Open 

Exec: Samsung to release device with flexible display next year

According to a senior Samsung executive, Korea's digital dominator is planning to release a flexible device by the end of next year.

By +Matthew Benson 

Exec: Samsung to release device with flexible display next year

According to a senior Samsung executive, Korea's digital dominator is planning to release a flexible device by the end of next year.

By +Matthew Benson ___

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2014-11-19 11:48:55 (0 comments, 0 reshares, 1 +1s)Open 

___

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2014-11-19 11:45:20 (0 comments, 0 reshares, 0 +1s)Open 

Cyanogen Inc and Micromax announce plans to launch a Cyanogen OS powered smartphone in India

Post by +Robert Triggs 

Cyanogen Inc and Micromax announce plans to launch a Cyanogen OS powered smartphone in India

Post by +Robert Triggs ___

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2014-11-19 11:44:28 (0 comments, 0 reshares, 0 +1s)Open 

Here’s a fascinating astronomy blog that takes on some big topics. This particular posting tells of antarctic lichens that seem to have adapted well to  Mars-like conditions.  It’s a superficial report, but amazing in its tentative implications.  

http://beyondearthlyskies.blogspot.com/2014/10/adaptation-of-antarctic-lichens-to.html

Here’s a fascinating astronomy blog that takes on some big topics. This particular posting tells of antarctic lichens that seem to have adapted well to  Mars-like conditions.  It’s a superficial report, but amazing in its tentative implications.  

http://beyondearthlyskies.blogspot.com/2014/10/adaptation-of-antarctic-lichens-to.html___

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2014-11-19 11:20:10 (0 comments, 0 reshares, 0 +1s)Open 

It's been an amazing road to where we are today. What's been the most memorable moment for you in Cyanogen's history?

It's been an amazing road to where we are today. What's been the most memorable moment for you in Cyanogen's history?___

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2014-11-19 11:16:09 (0 comments, 0 reshares, 0 +1s)Open 

Fleksy beats its own world record and enjoys the success by announcing permanent price drop

By +Joseph Hindy 

Fleksy beats its own world record and enjoys the success by announcing permanent price drop

By +Joseph Hindy ___

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2014-11-19 11:07:29 (0 comments, 0 reshares, 0 +1s)Open 

Moving from iOS to Android? We’ve written our own step-by-step guide to make sure you feel right at home on the OnePlus One http://bit.ly/SwitchtoOnePlus

Moving from iOS to Android? We’ve written our own step-by-step guide to make sure you feel right at home on the OnePlus One http://bit.ly/SwitchtoOnePlus___

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2014-11-19 11:06:57 (0 comments, 0 reshares, 0 +1s)Open 

Bright Spiral Galaxy M81
One of the brightest galaxies in planet Earth's sky is similar in size to our Milky Way Galaxy: big, beautiful M81. This grand spiral galaxy can be found toward the northern constellation of the Great Bear (Ursa Major). This superbly detailed view reveals M81's bright yellow nucleus, blue spiral arms, and sweeping cosmic dust lanes with a scale comparable to the Milky Way. Hinting at a disorderly past, a remarkable dust lane actually runs straight through the disk, to the left of the galactic center, contrary to M81's other prominent spiral features. The errant dust lane may be the lingering result of a close encounter between M81 and its smaller companion galaxy, M82. Scrutiny of variable stars in M81 has yielded one of the best determined distances for an external galaxy—11.8 million light-years.

Image Credit: Subaru Telescope (NAOJ), HubbleS... more »

Bright Spiral Galaxy M81
One of the brightest galaxies in planet Earth's sky is similar in size to our Milky Way Galaxy: big, beautiful M81. This grand spiral galaxy can be found toward the northern constellation of the Great Bear (Ursa Major). This superbly detailed view reveals M81's bright yellow nucleus, blue spiral arms, and sweeping cosmic dust lanes with a scale comparable to the Milky Way. Hinting at a disorderly past, a remarkable dust lane actually runs straight through the disk, to the left of the galactic center, contrary to M81's other prominent spiral features. The errant dust lane may be the lingering result of a close encounter between M81 and its smaller companion galaxy, M82. Scrutiny of variable stars in M81 has yielded one of the best determined distances for an external galaxy—11.8 million light-years.

Image Credit: Subaru Telescope (NAOJ), Hubble Space Telescope; 
Processing & Copyright: Roberto Colombari & Robert Gendler

+Astronomy Picture of the Day (APoD) 

#NASA   #Space   #Astronomy   #Hubble   #Galaxy  #Spiral #M81  #UrsaMajor #Cosmos  #Universe #APoD___

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2014-11-19 11:06:42 (0 comments, 0 reshares, 1 +1s)Open 

Lucky this little guy fell where he did. Check out those peepers!

#owlsarebadass   #owlsdayeveryday  

Lucky this little guy fell where he did. Check out those peepers!

#owlsarebadass   #owlsdayeveryday  ___

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2014-11-19 11:06:09 (0 comments, 0 reshares, 0 +1s)Open 

With Android Lollipop, Android Wear, and a bit of Android TV now safely on the road, Google gets to train its real road warrior, the Android Auto. Google is now opening the doors for Android developers to start tweaking their apps to provide support for…

With Android Lollipop, Android Wear, and a bit of Android TV now safely on the road, Google gets to train its real road warrior, the Android Auto. Google is now opening the doors for Android developers to start tweaking their apps to provide support for…___

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2014-11-19 11:03:18 (0 comments, 0 reshares, 0 +1s)Open 

+The MagPi issue 28 is out - get your fantastic, free, fan-produced magazine while it's fresh! Featuring a FUZE BASIC arcade game tutorial, the first in a series on open source computer vision, a fab beginner feature introducing the Arduino and Arduberry, and much more!

+The MagPi issue 28 is out - get your fantastic, free, fan-produced magazine while it's fresh! Featuring a FUZE BASIC arcade game tutorial, the first in a series on open source computer vision, a fab beginner feature introducing the Arduino and Arduberry, and much more!___

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2014-11-19 09:42:41 (0 comments, 0 reshares, 1 +1s)Open 

Lets do it!

Lets do it!___

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2014-11-18 04:39:12 (0 comments, 0 reshares, 0 +1s)Open 

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2014-11-18 04:15:15 (0 comments, 0 reshares, 0 +1s)Open 

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2014-11-18 04:04:23 (0 comments, 0 reshares, 1 +1s)Open 

Very cool animation of the UK's flight traffic! :)

Very cool animation of the UK's flight traffic! :)___

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2014-11-15 16:20:28 (0 comments, 0 reshares, 0 +1s)Open 

Oneplus One (bacon) - Lolipop

This would not be possible without CyanogenMod's support.

#LiquidSmooth

Oneplus One (bacon) - Lolipop

This would not be possible without CyanogenMod's support.

#LiquidSmooth___

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2014-11-15 16:20:10 (0 comments, 0 reshares, 0 +1s)Open 

Week 48: Pre-orders Prep, JBL E1+, Time Lapse Graffiti
http://bit.ly/OPWeek48

Week 48: Pre-orders Prep, JBL E1+, Time Lapse Graffiti
http://bit.ly/OPWeek48___

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2014-11-15 16:19:24 (0 comments, 0 reshares, 0 +1s)Open 

Attention all Agents and #IngressRecruits : we have collected some of our favorite #Ingress  tips, guides, and resources created by other Agents and added them to our Help Center. Visit our page to see what we've found: https://support.google.com/ingress/answer/6130976?hl=en&ref_topic=3261456

More is out there, so let us know in the comments of other great resources you've created!

Attention all Agents and #IngressRecruits : we have collected some of our favorite #Ingress  tips, guides, and resources created by other Agents and added them to our Help Center. Visit our page to see what we've found: https://support.google.com/ingress/answer/6130976?hl=en&ref_topic=3261456

More is out there, so let us know in the comments of other great resources you've created!___

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2014-11-15 16:18:48 (0 comments, 0 reshares, 0 +1s)Open 

Some have questions on private keys & storage in our U2F implementation. If you do, please read today's blog 'Yubico's take on U2F key wrapping' 

Some have questions on private keys & storage in our U2F implementation. If you do, please read today's blog 'Yubico's take on U2F key wrapping' ___

2014-11-15 16:17:32 (0 comments, 0 reshares, 0 +1s)Open 

In the last decade, technology has changed a lot about how we work. Tell us: what's changed the most for you in the last 10 years?

In the last decade, technology has changed a lot about how we work. Tell us: what's changed the most for you in the last 10 years?___

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2014-11-15 15:35:08 (0 comments, 0 reshares, 0 +1s)Open 

The purpose of today’s post is to make your head explode with simple arithmetic. If you’re reading this, I’ll bet that you feel pretty confident in your ability to add and subtract, and that you have an excellent grasp of a complicated concept like “three.” 

So OK, let’s start out with a simple challenge: Explain to me what “three” means. Define it.

If you give me an answer like “one plus two,” then OK, smarty-pants – define “one,” “two,” and “plus.”

Try this for a bit, and look up some definitions, and you may realize that an idea which seems blindingly obvious is actually fairly hard to put into words. And that’s important, because if we want to do mathematics, or things that depend on it like “building bridges that don’t fall down,” then we generally want to be able to start by defining our basic concepts, and if we can’t evendefine three, then what hope have we got of ... more »

The purpose of today’s post is to make your head explode with simple arithmetic. If you’re reading this, I’ll bet that you feel pretty confident in your ability to add and subtract, and that you have an excellent grasp of a complicated concept like “three.” 

So OK, let’s start out with a simple challenge: Explain to me what “three” means. Define it.

If you give me an answer like “one plus two,” then OK, smarty-pants – define “one,” “two,” and “plus.”

Try this for a bit, and look up some definitions, and you may realize that an idea which seems blindingly obvious is actually fairly hard to put into words. And that’s important, because if we want to do mathematics, or things that depend on it like “building bridges that don’t fall down,” then we generally want to be able to start by defining our basic concepts, and if we can’t even define three, then what hope have we got of defining more complicated things like “differential equations?”

Today I’m going to walk you through the answer to this seemingly simple question. This was actually the product of decades of very hard work by very intelligent, albeit somewhat eccentric, individuals. (If you want to read about their story, I highly recommend the book Logicomix by Apostolos Doxiadis and Christos Papadimitriou. Fair warning: the phrase “mad as a bag of clams” will apply.) Rather than giving you the fully technical answer (the book that ultimately put a lot of this on a sound footing, Principia Mathematica, takes until page 83 of volume 2 to finally prove Proposition 110.643, “1+1=2,” a fact which they note is “occasionally useful”), I’ll try to boil it down to its simplest concepts – but what you’re going to get below is the real mathematics, not the kiddie version. By the time we’re done, you’ll know why 1+1=2.

Sets and relationships

The first big insight that let us answer these questions was that, while it can be really messy to define “three,” one thing that we can define is the notion of a set of items. I’ll skip the very technical definition of a set (see the notes below if you want it), but it basically consists of some simple notions: two sets are the same if every element of one is an element of the other, and vice-versa; there is an empty set, which has no elements; if you have a set, then any collection of elements from that set is also a set; so is the union of two sets, or the intersection of two sets, or the set containing just that set. Basically, a set is a careful way to describe the idea of “here are a bunch of objects, in no particular order.”

Another thing that we can define is relationships between things. (And since the only things we’ve defined so far are sets, we’ll talk about that a lot) You can probably think of lots of relationships between objects in daily life: “is the same as,” (a relationship between all sorts of things) “is less than,” (a relationship between numbers) “is the mother of,” (a relationship between people), “has just eaten.” (A relationship between me and my dinner) A relationship is a statement about a pair of objects which can be either true or false. 

Now, there are some special kinds of relationships out there, and they have special names. A reflexive relationship is a relationship that is always true about any object and itself. For example, “is the same as” is reflexive: every object is the same as itself. Ditto “is as big as” for anything that has a size. On the other hand, “is less than” isn’t reflexive: in fact, no number is less than itself. Likewise, no person is her own mother. (Although this isn’t true for every family relationship: I'm my own Grandpa) 

A symmetric relationship is one that always works both ways: if A has this relationship to B, then B always has this relationship to A. “Is the same as” is symmetric; if A is the same as B, then B is the same as A. Likewise “is married to,” among people. On the other hand, “is less than” isn’t symmetric: if A is less than B, then B isn’t less than A! 

A transitive relationship is one such that if A is related to B, and B is related to C, then A is related to C. Being equal to, or being less than, is transitive: if A < B, and B < C, then we immediately know that A < C, too. But “eats” isn’t transitive, as a relationship between animals: wolves eat deer, and deer eat grass, but wolves generally don’t eat grass. 

Why did I just tell you about these three kinds of relationship? Because it turns out that something very magical happens when you find a relationship which is reflexive, symmetric, and transitive. Such a relationship is called an “equivalence relationship,” because “equals” is the most famous example. What’s magical about equivalence relationships is that you can use them to divide up all of the objects in the world. To see how, let’s take a concrete example: the relationship “is a blood relative of” among people. You can see that it’s an equivalence relationship, because everyone is a blood relative of themselves; if Alice is a blood relative of Bob, then Bob is one of Alice; and if Alice is Bob’s relative, and Bob is Christie’s, then Alice is Christie’s relative as well. 

Pick any one person to begin with, say Alice. Our first person forms her own group.

Now pick a second person, Bob. If Bob is a blood relative of Alice, then he goes in her group; if he isn’t, then he starts his own group.

Pick a third person, Christie. If Christie is a blood relative of Alice, she goes in Alice’s group; if she’s a blood relative of Bob’s, she goes in his group; and if she’s neither, she starts her own group. There’s no possibility that she could be both, because if she were a blood relative of both Alice and Bob, then Alice and Bob would also be blood relatives, so they would have been in the same group!

Keep doing this until you’ve put all of the people into groups. What are these groups? Well, if you pick any two people in the same group, they’re blood-related, and if you pick any two people in different groups, they aren’t blood-related. You’ve just divided the entire world into families: every person is in exactly one group, and two people are related to each other if and only if they’re in the same group. This kind of division is called a partition.

Partitions are useful, because these groups – we call them “equivalence classes” sometimes – are now objects that we can talk about much like we talked about the individuals. For example, say there’s some other relationship – “has red hair” – which has the property that, if two people are blood related, then they have the same hair color. We don’t even require the reverse property, that people who aren’t blood related have different hair color; maybe everyone in this world has red hair. This is a property of people, but we can use the partition to say that it’s also a property of families: after all, if two people are in the same family, they’re blood-related, and so if one has red hair, then the other does. That means that if anyone in a family has red hair, everyone in that family does. So we can say that “the family has red hair:” a property of individuals is also a property of these groups. 

We can give these families names, if we want, or we can just name them after any element we pick: “Alice’s family.”

Comparing apples and oranges

Now, let’s do some real magic. Here is a relationship for you, a relationship between sets: “has as many items as.” Be careful! This sentence sounds simple, but I actually almost cheated you, because I never explained what “as many as” means. The definition we want is:

If we have two sets A and B, then A has as many items as B if there is a way to pair up every element of A with an element of B, so that none are left over on either side.

Makes sense, right? This is how you would (say) compare apples and oranges. Let’s define that pairing up a bit more closely: this means that I have some rule that, given any element of A, tells me which element of B it’s paired with. Being a pairing means that every element of A gets mapped to a different element of B. Having nothing left over on the A side means that every element of A gets a mapping. Having nothing left over on the B side means that every element of B is mapped to by some element of A. 

If we want to write this in math-speak, incidentally, we give this rule a name, say “f,” and we say that if x is in A, then f(x) (pronounced “f of x”) is the element of B that it’s paired with. We write “f: A → B” (“f maps A to B”) to say that every element of A gets mapped, and the result is always an element of B. “f is one-to-one” means that every element of A gets mapped to a different element of B; “f is onto” means that every element of B gets mapped onto. 

I claim that this definition is actually what we normally think of as meaning “as many as.” For example, let’s say that I have two sets, namely a bucket of apples and a bucket of oranges. To make a pairing between them, I will line up the apples and oranges in two rows. “f” pairs an apple with the adjacent orange. “f is one-to-one” means that every apple is next to one orange, not two. If f weren’t one-to-one, then I might have put one apple next to a giant pile of oranges, which doesn’t really tell me anything about how many oranges I have. “f is onto” means that every orange is next to one apple; if it weren’t, then I might have a bunch of oranges left over, and again I have no idea how many oranges I have. But if f is one-to-one and onto, then every apple is next to exactly one orange, and that can only happen if I have exactly as many apples and oranges.

As it happens, “has as many items as” is an equivalence relationship. Let’s prove it.

Slightly harder part. If you slow down for these paragraphs until you understand them, the rest will seem a lot easier.

First of all, it’s reflexive: for any set A, A has as many items as A does. This may seem idiotically obvious, but given that “three” turned out not to be so obvious, let’s be careful this time. What we’re really claiming is that for any set A, there’s a way to pair the items of A with the items of A which is one-to-one and onto. I choose the pairing “f(x) = x” – that is, I will pair each item of A with itself. (Note: this pairing is really not rocket science) It’s one-to-one, because if I pick two different elements of A, x and y, then f(x) = x and f(y) = y which are, therefore, different. It’s onto because if I pick any element x, then f(x) = x, which means that x was paired with – lo and behold! – itself. Therefore! I know that every set has as many items as it does.

Yes, that proof was a bit silly. OK, let’s up the ante: our relationship is symmetric. If A has as many elements as B, then B has as many elements as A. How do we know this? Well, if A has as many elements as B, then there is some pairing f: A → B which is one-to-one and onto. (By our definition of “has as many elements as”) So I will now define a new pairing g: B → A by the rule: if y is in B, then let g(y) be the element of A which f mapped onto y. (That is, g is the same pairing as f, only in the opposite order) That is, g(y) is the element of A such that f(g(y)) = y.

Is g even well-defined? Well, we know that f is onto, so every element of B was f of something in A. And we know that f is one-to-one, so we know that this element of B was f of exactly one thing in A. So it’s true that for every item in B, there is exactly one item in A that our f-rule paired with it, and that shall be our definition of g.

The statement “g is one-to-one” then means that g pairs every item of B with a different item of A – or a bit more explicitly, if x and y are two different elements of B, then g(x) and g(y) are two different elements of A. We want to prove that: if x ≠ y, then g(x) ≠ g(y). How do we know it? g(x) and g(y) are both elements of A, by definition, so we can apply the f-rule to them and get back elements of B. Now imagine that g wasn’t one-to-one: x and y are different, but g(x) = g(y). Since those two are the same, obviously f(g(x)) must be the same as f(g(y)). (If you apply the rule to the same thing twice, you get the same result) But we know what that combination is, because it’s just the definition of g! f(g(x)) is x, and f(g(y)) is y. That means that x and y are the same, which is a contradiction! Therefore we know that g must be one-to-one.

The statement “g is onto” means that every item of A is g of something in B. I can even tell you what it is: if x is in A, then it’s g of f(x). How do I know this? Go back to the definition of g: “g(y) is the element of A such that f(g(y)) = y.” That means that g(f(x)) is the element of A such that f(g(f(x))) = f(x). (Got that? f of g of f of x – that is, start with some x, then apply rule f to get an element of B, then apply rule g to get an element of A, then apply rule f again to get another element of B) Now, what we have here is a statement that f of two different things are the same – but we know that f is one-to-one, which means that if f of one thing is the same as f of another, then the two things themselves must be the same. If we apply that to our messy equation above, that means that g(f(x)) = x – which is exactly what we wanted to prove! Every item x is g of something, namely f(x).

Whew. You can see that this one was a bit trickier.

The next proof is that “as many as” is transitive – that is, if A has as many elements as B, and B has as many elements as C, then A has as many elements as C. I’m going to apply the famous Math Teacher’s Cheat here and say that if you really want to understand this, you should sit down with a piece of paper and work it out yourself. You can use all of the same tricks that I just used above, and if you can prove it correctly, then you will really understand how equivalence works.

End of the hard part. Back to numbers! Let’s define three!

So what we just proved is that “has as many items as” is an equivalence relationship. That means that we can use the partitioning trick that we worked out earlier with it, and divide all of the sets in the world up by how many things they have – that is, into “families” which all have the same number of items. A set of three apples and a set of three oranges would be in the same family, but they would be in a different family from a set of four armadillos or a set of twelve black holes. 

And just like above, we can name these families. “Three” is the name of the family of all the possible sets that have as many items as, say, a set of three apples.

That’s the actual definition of three.

Wait! you say, having heard this story before. You just used three to define three! And I don’t think you ever actually defined any apples, just sets!

You clever fellow. Let’s be more careful.

We know that there is an empty set, a set with no elements at all. Let’s call it ∅. (That’s the standard symbol for it, and it’s pronounced “the empty set.”) This set must belong to some family, and we shall name that family Zero. (For reasons which will shortly become clear, I’ll give this set another name as well, “0.”)

Since that is a set, we also know that {∅} is a set. That means “the set which contains exactly one element, namely the empty set.” That is, this is a set of other sets, and it has exactly one thing in it, which is the only other object we had lying around, namely ∅. Fine! It’s a set.

It can’t be in the same family as ∅ is, though, because there’s no way to pair them up. {∅} has exactly one element in it, namely ∅, but what do I pair it with? ∅ has no elements in it, by definition. So the pairing can’t possibly be onto. So this set is in a new family, which we shall name One. And we’ll name this set “1,” since it’s the first element of One that we’ve met.

What other sets can we build? Well, we could make {{∅}}, namely the set that contains exactly one set, that being the set that contains the empty set. This set belongs in the same family as {∅}, though: the pairing is simply to pair {∅} with ∅. Both of those sets have one element, or rather, One element. This set doesn’t get a special name; it’s just {{∅}}, or {1}, to use the other name.

But we can also take the union of two sets, and this is where things start to look really absurd. {∅, {∅}} is also a set. That is, this is a set which has two elements, namely ∅ and {∅}. This one, you will quickly figure out, doesn’t go in either Zero or One, because (for example) if I paired up the ∅ of {∅, {∅}} with the ∅ of {∅}, then there would be nothing left over to pair the {∅} with. We have met our first element of Two: “2,” a.k.a. {∅, {∅}}, a.k.a. {0, 1}.

You can see where this is going to go. Our first element of Three will be the set {∅, {∅}, {∅, {∅}}}, “3,” a.k.a. {0, 1, 2}. And we’ll get Four, Five, and so on as well. We have just defined the counting numbers. 

In fact, we also just figured out how to add one to any number, because each of our “numbers” is just the list of lesser numbers: 1 is {0}, 2 is {0, 1}, 3 is {0, 1, 2}, and so on. To add one to x, you simply take the union (combine the sets) of x with the set {x} itself: that is, to add one to 2, you just combine {0, 1} with {2} to get {0, 1, 2}, better known as 3.

And lo and behold, we have just proven that 1 + 2 = 3! 

I want you to stop for a moment and feel very proud of yourself for having proven something known to small children. Knowing something is easy: knowing why something is true is not so easy.

What we just did was this: We figured out what a set of things was. We figured out that there are relationships which can compare sets, and that special kinds of relationships – “equivalence relationships” – act a lot like “equals,” so you can divide up all of the sets in the world into families which share those properties. Then we realized that “has as many items as” is one of these equivalence relationships, and so you can divide up all the sets in the world into families which have the same number of elements: a family of sets with no elements, a family of sets with one element, a family of sets with two elements, and so on. And that’s what “two” actually means: a set has two items if it has as many items as our “Standard Two.” 

The next step – adding any pair of numbers – is pretty easy. (To add 3 and 2, just say that 2 = 1 + 1, and so 3 + 2 = 3 + 1 + 1, which we already understand) Beyond this comes a rather clever trick to define subtraction, and then multiplication (with rows of identical items), division (using the same trick as subtraction), fractions, and the most subtle and tricky of all, decimals. We can even use these methods to define “infinity” and talk about its behavior. But I’ll save those for another day, as we’ve only just stepped out from the rabbit hole, and even Alice waited before her second venture through the looking glass.


A final note: Less than an hour after I finished writing this, I received news of the death of Alexander Grothendieck, a brilliant mathematician, one of the founders of the field of algebraic geometry, and the inventor of the “clever trick” defining subtraction with which the next part of this would have to open. His mathematical work was at the foundation of a great deal of the modern cutting edge of physics, including a good deal of my own research in my physics days. Among his most important work was bringing category theory into the mainstream of mathematics; category theory essentially takes the ideas above, of kinds of mapping, equivalence, relations of relations, and so on, to their widest possible conclusion. I would like to dedicate this article to his memory, and hope that it may be the first step for some people to go and visit the great intellectual landscapes that he opened.

–––––––––––––––––––– 

If you want more on a similar line, my older article "Counting to Infinity" is about how to use the same method to define what infinity really means. It's a bit lighter-weight than this one. https://plus.google.com/+YonatanZunger/posts/BtHzUPFz4te

If you want to know the careful definition of a set, you should read http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory . This was one of those subjects that people thought was “really obvious” until Bertrand Russell pointed out that if you did the “really obvious” thing, you could define “sets” like “the set of all sets which don’t contain themselves,” which quickly led to paradoxes and confusion. Zermelo and Fraenkel finally laid out a careful definition of sets which doesn’t lead to paradoxes, and in fact works. It turns out that you need seven rules to do so, and there are two other famous “optional rules” – optional in that set theory actually makes sense with or without them. These two optional rules are the “Axiom of Infinity” (that roughly says, “infinite sets exist”) and the “Axiom of Choice.” 

The Axiom of Choice roughly says that for any set, there exists a way to pick an element from it, a statement which seems sort of obvious until you realize that for infinite sets, it isn’t. For example, the rule “pick the smallest element” works great for “the set of positive integers” or “the set of real numbers between 0 and 1, inclusive,” but it doesn’t work very well for “the set of real numbers greater than zero,” because there isn’t a smallest element: if you pick any number greater than zero, half that number is smaller than it is. In fact, it turns out that despite how obvious it seems, the Axiom of Choice has some really weird consequences, such as the Banach-Tarski Theorem: you can prove that there’s a way to slice up a solid sphere into five pieces, and then rearrange those pieces to get two spheres, each identical to the original! This requires infinitely fine cuts, so it isn’t (alas) applicable to gold bullion. The main use of the Banach-Tarski Theorem is to make mathematicians’ heads explode, and to demonstrate just how weird the consequences of the Axiom of Choice really are. (Once their heads have exploded, they can be rearranged into the brains of two identical mathematicians, which is useful for math departments on a tight staffing budget)

The image is "Three," by Grant Hutchinson (https://www.flickr.com/photos/splorp/59231687), a photograph of graffiti by an unknown artist.___

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2014-11-15 03:38:35 (0 comments, 0 reshares, 0 +1s)Open 

Our co-founder Carl unveils more about the OnePlus secret recipe in this interview with Forbes: http://bit.ly/OPForbes

Our co-founder Carl unveils more about the OnePlus secret recipe in this interview with Forbes: http://bit.ly/OPForbes___

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2014-11-15 03:37:52 (0 comments, 0 reshares, 1 +1s)Open 

The giant black hole at the center of the Milky Way may be producing mysterious particles called neutrinos. If confirmed, this would be the first time that scientists have traced neutrinos back to a black hole.
The evidence for this came from three NASA satellites that observe in X-ray light: the Chandra X-ray Observatory, the Swift gamma-ray mission, and the Nuclear Spectroscopic Telescope Array (NuSTAR).  

Read more: http://go.nasa.gov/1u6kfe6 

The giant black hole at the center of the Milky Way may be producing mysterious particles called neutrinos. If confirmed, this would be the first time that scientists have traced neutrinos back to a black hole.
The evidence for this came from three NASA satellites that observe in X-ray light: the Chandra X-ray Observatory, the Swift gamma-ray mission, and the Nuclear Spectroscopic Telescope Array (NuSTAR).  

Read more: http://go.nasa.gov/1u6kfe6 ___

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2014-11-13 11:31:01 (0 comments, 0 reshares, 0 +1s)Open 

Amazon details how it does networking in its data centers

https://gigaom.com/2014/11/12/amazon-details-how-it-does-networking-in-its-data-centers/

Amazon details how it does networking in its data centers

https://gigaom.com/2014/11/12/amazon-details-how-it-does-networking-in-its-data-centers/___

posted image

2014-11-09 14:47:50 (0 comments, 0 reshares, 1 +1s)Open 

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2014-11-08 18:58:25 (0 comments, 0 reshares, 0 +1s)Open 

The Flash Mob These Soldiers Filmed In Afghanistan Is Too Awesome For Words!
Read more at http://blog.thebreastcancersite.com/soldier-flash-mob-afghanistan/#eerYt6fShMdsRlrO.99


http://blog.thebreastcancersite.com/soldier-flash-mob-afghanistan/

The Flash Mob These Soldiers Filmed In Afghanistan Is Too Awesome For Words!
Read more at http://blog.thebreastcancersite.com/soldier-flash-mob-afghanistan/#eerYt6fShMdsRlrO.99


http://blog.thebreastcancersite.com/soldier-flash-mob-afghanistan/___

2014-11-08 15:37:34 (1 comments, 0 reshares, 0 +1s)Open 

X-Men mind control becomes a reality



X-Men mind control becomes a reality

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