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What channel, time is the NFL game tonight? TV, kickoff, live stream for Chiefs vs Raiders
By Mary OmatigaNov 14, 2021, 8:37 AM EST
The Kansas City Chiefs will battle it out with the Las Vegas Raiders tonight on NBC and Peacock. Live coverage begins at 7:00 p.m. ET with Football Night in America.
NBC Sports has you covered with all you need to know about the game including the TV channel, start time, live stream information, and more.
RELATED: How to watch the Kansas City Chiefs vs Las Vegas Raiders: Live stream, TV info, kickoff time for Sunday
What channel is tonight's Sunday Night Football game on?
Where: Allegiant Stadium in Las Vegas, Nevada
When: Sunday, November 14
Start Time: 8:20 p.m. ET kickoff; live coverage begins at 7:00 p.m. ET with Football Night In America
TV Channel: NBC
Stream live: Watch live on Peacock or with the NBC Sports App
RELATED: 2021 NFL schedule – Dates, times, TV channels for every game in all 18 weeks
Where to live stream Chiefs vs Raiders online tonight
Sunday's game between the Kansas City Chiefs and Las Vegas Raiders can be streamed live on multiple platforms tonight including NBCsports.com, the NBC Sports App and Peacock.
This NFL season, Peacock will stream all of NBC Sports' NFL games including the regular season, playoff games and Super Bowl LVI. More from Peacock's website:
If you have access to NBC via your TV provider, you can watch Sunday Night Football on your TV or with a TV provider login on the NBC Sports app, NBC app, or via NBCSports.com. Check your local listings to find your NBC channel. If you can't find NBC in your channel lineup, please contact your TV provider.
If you don't have access to NBC via your TV provider, you can stream Sunday Night Football on Peacock with a $4.99/month Peacock Premium plan. Sign up here or, if you already have a free Peacock account, go to your Account settings to upgrade or change your existing plan.
RELATED: DeSean Jackson says he's joining the Raiders
Baltimore Ravens at Miami Dolphins, 8:20 pm (FOX, NFL Network, Amazon)
Sunday, Nov. 14
Atlanta Falcons at Dallas Cowboys, 1 pm (FOX)
Jacksonville Jaguars at Indianapolis Colts, 1 pm (CBS)
Cleveland Browns at New England Patriots, 1 pm (CBS)
Buffalo Bills at New York Jets, 1 pm (CBS)
Detroit Lions at Pittsburgh Steelers, 1 pm (FOX)
New Orleans Saints at Tennessee Titans, 1 pm (CBS)
Tampa Bay Buccaneers at Washington Football Team, 1 pm (FOX)
Carolina Panthers at Arizona Cardinals, 4:05 pm (FOX)
Minnesota Vikings at Los Angeles Chargers, 4:05 pm (FOX)
Philadelphia Eagles at Denver Broncos, 4:25 pm (CBS)
Seattle Seahawks at Green Bay Packers, 4:25 pm (CBS)
Kansas City Chiefs at Las Vegas Raiders, 8:20 pm (NBC)
Los Angeles Rams at San Francisco 49ers), 8:15 pm (ESPN)
RELATED: See the 2021 NFL Sunday Night Football schedule here
Be sure to follow ProFootballTalk for breaking news, updates, and much more!
How to watch Super Bowl 2023: TV channel, live stream info, start time, halftime show, and more
By Mary OmatigaJan 31, 2023, 9:17 AM EST
Super Bowl 2023 takes place on Sunday, February 12 at 6:30 PM ET at State Farm Stadium–home of the Arizona Cardinals–in Glendale, Arizona as Jalen Hurts and the Philadelphia Eagles will look to win their second Lombardi Trophy in franchise history and Patrick Mahomes and the Kansas City Chiefs make their third Super Bowl appearance in the last four seasons.
Not only will the match up feature two top seeds for the first time since 2017, but Super Bowl 2023 will be especially monumental because this is the first time that two Black quarterbacks will face each other in the league's biggest game of the year.
RELATED: What to know about the 2023 Pro Bowl – Dates, how to watch/live stream info, AFC, NFC coaches, competition schedule
Super Bowl 2023 will be nothing short of exciting, see below for additional information on how to watch/live stream the game as well as answers to all your frequently asked questions.
How to Watch Super Bowl 2023 – Philadelphia Eagles vs Kansas City Chiefs
Date: Sunday, February 12
Where: State Farm Stadium in Glendale, Arizona
TV Network: Fox
Who is playing in Super Bowl 2023?
The Philadelphia Eagles and the Kansas City Chiefs.
RELATED: What to know about Super Bowl 2023 – Date, location, halftime performance info, and much more
Who is the home team in Super Bowl 2023 and how is it determined?
The Philadelphia Eagles are the home team in Super Bowl 2023. The designated home team alternates each year between the NFC and AFC champions. If it is as odd-numbered Super Bowl, the NFC team is the designated home team. If it as even-numbered Super Bowl, the AFC team is the designated home team.
Which teams have been eliminated from the 2023 NFL Playoffs?
The Seattle Seahawks, Miami Dolphins, Minnesota Vikings, Los Angeles Chargers, Baltimore Ravens, Tampa Bay Buccaneers, Jacksonville Jaguars, New York Giants, Buffalo Bills, Dallas Cowboys, San Francisco 49ers and Cincinnati Bengals have all been eliminated from the 2023 NFL playoffs.
RELATED: 2023 NFL Playoffs scores: Final bracket, recaps, results for every AFC and NFC postseason game
Who is performing the halftime show at Super Bowl 2023?
It was announced in September, that international popstar, entrepreneur, and philanthropist Rihanna will headline the halftime show at Super Bowl 2023.
RELATED: Super Bowl 2023 – What to know about national anthem, pregame performers ahead of Super Bowl LVII
Why does the NFL use Roman numerals?
AFL and Chiefs founder Lamar Hunt proposed using Roman numerals for each Super Bowl to add pomp and gravitas to the game. Roman numerals were, unsurprisingly, used in ancient Rome as a number system. I stands for 1, V for 5, X for 10, L for 50 and C for 100. That's right: In 2066, get ready for Super Bowl C.
Super Bowl V was the first to use Roman numerals. They were retroactively added to the Super Bowl II to IV logos and have been used each year since until 2016. For Super Bowl L, or 50, the NFL tried out 73 different logos before breaking down and using a plain old "50."
The Roman numerals for this year's big game, Super Bowl 57, are LVII.
RELATED: Super Bowl halftime shows – Ranking the 10 best Super Bowl halftime show performances in NFL history
How many Super Bowls have the Eagles won in franchise history?
The Eagles have won just one Super Bowl title in franchise history, however, Super Bowl LVII will be their fourth Super Bowl appearance in franchise history.
RELATED: Philadelphia Eagles Super Bowl History
How many Super Bowls have the Chiefs won in franchise history?
The Chiefs have won two Super Bowls in franchise history (1969 and 2019). Super Bowl LVII will be the franchise's fifth Super Bowl appearance.
RELATED: Kansas City Chiefs Super Bowl History
Who was the first Black quarterback to play in a Super Bowl?
Doug Williams was the first Black quarterback to start and win a Super Bowl. Williams, a product of Grambling State–a historically Black university–achieved the milestone on January 31, 1988 in Super Bowl XXII as the QB for Washington.
RELATED: FMIA Conference Championships – Eagles rout Niners, Chiefs outlast Bengals to set Super Bowl LVII stage
Follow along with ProFootballTalk for the latest news, storylines, and updates surrounding the 2022 NFL season and playoffs, and be sure to subscribe to NFLonNBC on YouTube!
Chiefs Super Bowl history: When is the last time Kansas City made it to, won the Super Bowl?
By Daniel TranJan 31, 2023, 9:00 AM EST
After losing 27-24 in OT to the Cincinnati Bengals in last year's AFC Championship, Patrick Mahomes and the Kansas City Chiefs are back in the postseason for the 8th straight year. The Chiefs are now set to make their third Super Bowl appearance in the last 4 seasons, after a 23-20 win over the Cincinnati Bengals in the AFC Championship game but their history with the NFL's most coveted game is so much more.
RELATED: 2023 NFL Playoffs Schedule – Bracket, game dates, times and TV networks
Super Bowl LVII takes place on Sunday, February 12 at State Farm Stadium in Glendale, Arizona. See below for additional information on how to watch.
Founded in 1960 by Lamar Hunt, the Chiefs started in the American Football League as the Dallas Texans. After winning the 1962 American Football League Championship in the longest championship game in professional football history, Hunt decided to relocate to Kansas City. The team changed its name to the "Chiefs" in honor of Mayor Harold Roe Bartle, who convinced Hunt to move the team to the City of Fountains.
After winning the AFL Championship in 1966, Kansas City represented the American Football League in the AFL-NFL World Championship Game, retroactively known as the first Super Bowl, on January 15, 1967, against the NFL Champion Green Bay Packers. Kansas City played Green Bay close in the first half, but Green Bay scored 21 unanswered points to win the game.
RELATED: When do the 2022 NFL Playoffs start: dates, schedule, playoff format, overtime rules, and more
It wouldn't take the Chiefs long to taste victory in the Super Bowl though – it came just three years later in Super Bowl IV. Though they faced the feared Purple People Eaters of the Minnesota Vikings defense, Kansas City head coach Hank Stram had a plan. He took advantage of Minnesota's aggressive defensive with short passes and trap plays. The Chiefs would prevail 23-7 for Kansas City's first Super Bowl win.
It would be another 50 years until The Kingdom made its return to the Super Bowl, but it would come back armed with some of the most explosive weapons the NFL has ever seen.
When was the Chiefs' last Super Bowl win?
Half of a century went by before the Chiefs earned a Super Bowl berth, but they were back in the 2019 season with a bang in Super Bowl LIV. Led by quarterback Patrick Mahomes, who was coming off an MVP season the previous year, Kansas City made it to the championship game overcoming double-digit deficits in the Divisional Round and AFC Championship Game. They even fell behind by 10 in the Super Bowl against the San Francisco 49ers.
However, the magic wasn't over for the Chiefs. The offense scored 21 unanswered points in the fourth quarter to secure the team's second Super Bowl championship. Kansas City retained most of their core and many expected them back in the championship game in 2021.
RELATED: What are the highest-scoring and lowest-scoring Super Bowls in NFL history?
When was the last Chiefs Super Bowl appearance?
While the team did make it to the Super Bowl in the 2020 season, they ran into an old nemesis. Quarterback Tom Brady was now with the NFC Champion Tampa Bay Buccaneers, but the last time he faced Kansas City was in 2018 as a member of the New England Patriots, who eliminated the Chiefs in the AFC Championship.
He would get the better of them again.
Kansas City could not stop Brady and the Bucs' offensive onslaught. On the other side, Patrick Mahomes couldn't move the ball against a Tampa Bay defense that caught fire in the postseason. The end result was a 31-9 rout with The Buccaneers hoisting the Lombardi Trophy and the Chiefs hoping to get back to the Super Bowl next year.
Chiefs Super Bowl history
1966 season: Lost Super Bowl I vs. the Green Bay Packers, 35-10
1969 season: Won Super Bowl IV vs. the Minnesota Vikings, 23-7
2019 season: Won Super Bowl LIV vs. the San Francisco 49ers, 31-20
2020 season: Lost Super Bowl LV vs. the Tampa Bay Buccaneers, 31-9
Chiefs Super Bowl records and firsts
Tied for fewest touchdowns – 0 (Super Bowl LV)
Hank Stram was the first head coach ever to be "miked for sound" in the Super Bowl (Super Bowl IV)
Lowest attendance for Super Bowl – 24,835 (Super Bowl LV) *due to COVID Pandemic
Lowest attendance, attendance not restricted – 61,946 (Super Bowl I)
Participated in first Super Bowl
First team to come back from three double-digit deficits in the playoffs and win Super Bowl (2019)
Most penalty yards in a half (Super Bowl LV)
How can I watch and live stream Super Bowl 2023?
When: Sunday, February 12, 2023
TV Channel: FOX
Follow along with ProFootballTalk and NBC Sports for NFL news, updates, scores, injuries, and more
RELATED: Who is playing in Super Bowl 2023?
Follow along with ProFootballTalk for the latest news, storylines, and updates surrounding the 2022 NFL Season, and be sure to subscribe to NFLonNBC on YouTube!
How to watch Sunday Night Football on Peacock:
Please note that selection of a Premium plan will result in a charge which will recur on a monthly or annual basis until you cancel, depending on your plan. You can cancel your Premium plan at any time in your Account.
What devices are compatible with Peacock?
Peacock is available on a variety of devices. See the full list here.
In addition to Sunday Night Football, what else can I watch with Peacock Premium?
Premium is your key to unlocking everything Peacock has to offer. You'll get access to all the live sports and events we have, including Premier League and WWE Premium Live Events like WrestleMania. You'll also get full seasons of exclusive Peacock Original series, next-day airings of current NBC and Telemundo hits, plus every movie and show available on Peacock. There is always something new to discover on Peacock Premium.
Read more NFL
Super Bowl 2023: Why the NFL uses Roman numerals for naming and how to read...
Conference Championship week awards: Reddick wrecks SF
Eagles dominate both sides of the ball in NFC Championship


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Sooners move up to fourth in West Regional, USC in command
May 9, 2014 Ken MacLeod 0 Comments
The 12th-ranked University of Oklahoma women's golf team jumped one spot to fourth place after the second round of the NCAA West Regional in Cle Elum, Wash., Friday. The 24-team tournament is being played at the 6,252-yard, par-72 Tumble Creek Golf Course at Suncadia Resort.
The third-seeded Sooners shot a second-round 295 (+7), good for a two-day 586 (+10), and trail co-leaders USC (No. 1 seed) and Arizona State (No. 2 seed) by eight strokes. No. 4 seed Washington sits in third place, six shots in front of OU.
The low eight teams and low two individuals not on an advancing team from the NCAA West Regional will move on to the 24-team NCAA Championships, which will be held May 20-23 at the Tulsa Country Club in Tulsa, Okla. The Sooners are 20 strokes clear of the elimination line.
Senior Anne-Catherine Tanguay and freshman Alexandra Kaui led the Sooners on Friday, each carding a 1-over-par 73. Kaui, the Big 12 Freshman of the Year, is tied for sixth place out of 126 competitors at even par. Tanguay, who was at 4 under par on the day through 12 holes, is tied for 16th place with a 148 (+4).
Sooner senior Chirapat Jao-Javanil, the 2012 NCAA champion, shot a 75 (+3) on the round and is tied for 11th place at 146 (+2) going into Saturday's final round.
OU senior Emily Collins recorded a second-day 74 (+2) and is tied for 25th place at 150 (+6). Fellow senior Kaitlyn Rohrback shot an 80 (+8) on the round and is tied for 57th place at 154 (+9).
Big 12 Coach of the Year Veronique Drouin-Luttrell said she was happy with how her Sooners battled Friday.
"We had really tough conditions today," Drouin-Luttrell said. "It was cold and rainy, but we played solid again. We have a great game plan going into the final round and will stick to it for tomorrow."
The Sooners will tee off for the final round of the NCAA West Regional starting at 10:36 a.m. CT Saturday. Live stats are available at GolfStat.com.
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redpajama_set_name: RedPajamaCommonCrawl


Phillips Law Group was honored to sponsor and participate in the 2016 Phoenix Walk Like MADD event hosted by Mothers Against Drunk Driving (MADD) on Oct. 22, 2016.
The event, hosted at the Phoenix Zoo, included a 5K walk and a family festival aimed at raising awareness about the devastating effects of drunk driving.
Every day, more than 28 people die in drunk driving accidents, and every 120 seconds, someone is injured in an accident involving a drunk driver.
Each year, MADD organizations throughout the country host Walk Like MADD events and encourage participants to take up the fight against drunk driving. This year, thousands of people in more than 60 cities will participate in local events.
The Phoenix event raised more than $70,000 in online donations and involved more than 500 participants and 60 teams, including a team from Phillips Law Group.
Managing attorney Timothy Tonkin led the way on Saturday and even spoke during the event, featured in the video on this page.
Having seen the devastating impact drunk driving can have, our personal injury attorneys are committed to doing everything we can to help end drunk driving and to help fight for the rights of injury victims.
Thank you to everyone who supported our team's efforts during this event!


Celebrating its 195th anniversary, the House of Bovet is rolling out the new timepiece Virtuoso VIII, with the tourbillon as its accentuated feature. Available in a variety of fine options -ivory, black lacquer and blue aventurine- interested gents can choose from three cases in 18k red-gold, 18k white-gold, and platinum (with customized sub-dial colors).
The high-end timepiece offers an intricate dial and details such as the hand-engraving work, blue screws, and beveling. Virtuoso VIII's design shows off its eye-catching features in its dials, and hints an ode to the House's historic pocket watches. If you have a penchant for form and function, this watch deserves a place in your collection.


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Home News Over 1, 000 unclaimed Nigerian e-passports begging for collection at New York...
Over 1, 000 unclaimed Nigerian e-passports begging for collection at New York consulate
*Okoyen
The consulate general of Nigeria in New York, Mr. Benaoyagha, has said that his office has over 1,000 unclaimed e-passports and appealed to Nigerians to pick them up.
He said in a statement that a backlog of passport and visa applications was constantly being cleared in line with government operational guidelines.
The consul general however denied allegation of shady deals at the consulate saying it adopts the highest standard and best practices obtainable in any other consulate as it relates to e-passport and visa production.
The statement reads: "Despite the pressure and challenges of December rush in New York, occasioned by the temporary lack of e-passport booklets in other Missions in USA, no charge of $200 or any other fee is made by applicants for same-day e-passport service.
"The procedure for timely issuance of passport and visa has been simplified and further streamlined, and well known to the public. We have also worked hard to ensure that New York Consulate never runs short of e-passport booklets to avoid any disruption in our services.
"For the avoidance of doubt, the consulate fully keys into the anti-corruption agenda of the federal government of Nigeria and will, therefore, spare no one in the consulate against whom any allegation of unethical practice can be proven.
"Furthermore, the consulate operates an open-door policy and encourages Nigerians to report any misdemeanor on the part of any of its official to my office. My telephone numbers and email addresses are well publicized for this purpose.
"Besides, a special help-desk has been introduced with dedicated phone lines for applicants to contact officials in the Consulate on any issue for quick response to inquiries without undue delay.
"Similarly, Thebez Global is the only company that handles bio-metric visa processing on behalf of the consulate in the VFS Centre at 145 West 45 Street, New York.
"The consulate therefore wishes to dissociate itself from any other third-party service providers or unauthorized agents in accessing services provided by the consulate general of Nigeria in New York.
"Consequently, any payment made by applicants to any unauthorized third-party service provider should not be misconstrued or translated to mean payment to the Consulate General or its officials.
"As a standard practice, E-Passports are expected to be renewed six months before their expiration. It is sad to note that some Nigerians, who usually book flights far ahead of travel dates, would sometimes forget to apply for passport renewal until the last minute.
"Nigerians are encouraged to be more proactive and desist from putting undue pressure on the officials of the consulate who are sometimes harassed and assaulted for insisting on strict adherence to the appointment dates given to applicants.
"I wish to reiterate the commitment of the consulate general of Nigeria in New York to continued quality services delivery within the limited manpower and resources, and to effectively cover our consular jurisdiction.
"We call on applicants to avoid third-party service providers or agents, as the Consulate does not recognize their services.
"Applicants are urged to apply for Nigerian E-passports and Visas early enough through the official websites: www.nigeriahouse.com or The Nigeria Immigration Service to avoid the last-minute rush that usually overstretches the manpower and facilities in the Consulate."
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Annuals, 15-40 cm; slenderly taprooted. Stems initially erect, later ascending to decumbent (herbaceous), proximally spreading- to deflexed-villous, closely to loosely strigose on distal 1 / 3 - 1 / 2 , eglandular. Leaves basal (often drying translucent, often withering by flowering) and cauline; basal (thin) blades oblanceolate to obovate or spatulate, 10-80(-140) × 5-34 mm, cauline slightly or gradually reduced to distal 1 / 3 of stems (bases clasping), margins usually with 1-4 pairs of teeth or lobes, sometimes entire, faces sparsely short-hirsute to hirsuto-villous, eglandular. Heads (1-)3-10(-20) in diffuse arrays (branches from distal 2 / 3 ). Involucres 2.5-3 × 5-10 mm. Phyllaries in 2-4 series, hirsute to sparsely villous, minutely glandular. Ray florets 95-160(-250); corollas white to bluish, 2.5-4 mm, laminae not coiling or reflexing. Disc corollas 1.7-2 mm. Cypselae 0.6-0.8 mm, 2-nerved, faces sparsely strigose; pappi: outer of setae, inner of 10-13(-15) bristles. 2n = 18. Flowering Feb-May. Brushlands, palm woods, roadsides, disturbed sites; 0-50 m; Tex.; Mexico (Nuevo León, Tamaulipas).


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Crooked Debbie Wasserman Schultz Gone
How about this news as the on-ramp to the Democrat's convention. Who wanted crooked Debbie Wasserman Schultz gone?
I guess the Democrats can only save ONE female rat, so the Jewish chick got the boot. Can't scuttle the ship over yet another incompetent Liberal woman. Regardless, top Democrats wanted Wasserman Schultz gone
The Democrats had already quarantined the new virus of WikiLeaks Wasserman Schultz, when they put her on lockdown at the convention. How 'bout them optics, when the head of the DNC isn't allowed to speak?! Wasserman-Schultz was to open and close the convention, and that's it. No speeches.
There is so much dirt between Wasserman Schultz and crooked Hillary Clinton, a fleet of Caterpillar dump trucks couldn't handle it all. These two wenches conspired against ALL Democrats, and particularly the Jewish socialist Bernie. They did this in an effort to elect the crime boss named Hillary Clinton to the highest office in the land.
If they Democrats were smart, they would have dumped Clinton months ago, as they certainly had enough chances. It was only a matter of time for the shoe to fall, and who knew it would rain Jimmy Choos.
Thank GOD for WikiLeaks, or America would not know the little we know now. Can you even imagine what is yet to be discovered?! It's no wonder Wasserman Schultz stepped down.
The Florida congresswoman's resignation came from severe pressure from top Democrats. Her resignation is a result of the release of leaked emails showing DNC staffers favoring Hillary Clinton over Bernie Sanders in the party's 2016 primary contest. But there is so much more that can and will come of the leaks.
After Wasserman-Schultz made her announcement that she was leaving, pro-Sanders supporters cheering during a demonstration in Philadelphia.
In her statement, Wasserman Schultz said that she remains committed to seeing Clinton elected president. To quote Malcolm X: "By any means necessary!"
Supposedly crooked Debbie talked with Obama and Clinton before making her announcement.
"Going forward, the best way for me to accomplish those goals is to step down as Party Chair at the end of this convention…As Party Chair, this week I will open and close the Convention and I will address our delegates about the stakes involved in this election not only for Democrats, but for all Americans,"
Since when have Democrats been for "all" Americans? Democrats have their agendas, and they only care about what enriches them personally.
This news is a prelude to much worse for the Democrats. I'm convinced WikiLeaks will confirm much more of our suspicions about the Clintons and other high-ranking Democrats. This will likely become a worldwide conspiracy.
For now, Conservatives can gloat in the fall of a Democrat scoundrel. She should be in jail, and let's hope that people who donated to the Sanders campaign sue the Democrats for fraud.


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Professor Camacho: Twitter Trump Ban Does Not Violate Free Speech
KHSL-CHANNEL 12 (CHICO) -- Action News Now asked if a professor at San Francisco State University if this violates free speech.
"Companies like Facebook and Twitter have terms of services that people agree to," said Professor Melissa Camacho, an associate professor at San Francisco State University.
Professor Camacho says in the past few years, Twitter and Facebook have been trying to crack down on disinformation while still trying to let people to speak freely.
"From a media perspective, no, it's not censorship," said Professor Camacho.
"You're not being banned from saying anything. You are being banned because you violated the contract of service."


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Russell Jeffrey "Jeff" Blackburn – Lafayette
September 25, 1956 – July 13, 2016
Russell Jeffrey "Jeff" Blackburn, 59, of Lafayette, was born into eternal life at 11 pm on Wednesday, July 13, 2016 in Bedford.
Born September 25, 1956 in Lawrence Co., he was the son of Russell and Marilyn (Trisler) Blackburn. He married Dolly Moutardier on August 20, 1977. He was an engineer for Duke Energy for forty years. He was a member of the Linnwood Church of Christ. Jeff was an active member in the March of Dimes campaign and Habitat for Humanity. Lovingly known as Peffy, Gimpy, Uncle Jeff, and Colonel Clodd. He was a longtime "Survivor" enthusiast with fifteen years of "Survivor" audition tape submissions.
Survivors include his wife, Dolly, of Lafayette; a son, Corey Blackburn of Lafayette; a daughter, Emily Griffith and husband, Steve, of Indianapolis; two granddaughters, Isla and Mazo Griffith; his parents, Russell and Marilyn Blackburn; a sister, Julia Wimmer and husband, Dave, ofZionsville; two brothers, Jody Blackburn and wife, Becky of Mitchell, and Jay Blackburn and wife, Irma, of Bedford; lots of nieces and nephews, great nieces and nephews.
He was preceded in death by his grandparents.
Funeral services will be conducted at 10 am on Tuesday, July 19th in the Elmwood Chapel of the Day & Carter Mortuary. Burial will follow in the Old Union Cemetery. Visitation will be from 2 pm to 8 pm on Monday, July 18th at the Day & Carter Mortuary.
Ivan Ducker – Bloomington
Ivan Ducker, of Bloomington, died Friday, July 15, 2016 at Meadowood in Bloomington.
Arrangements are pending at the Day & Carter Mortuary.
Treasa Stalcup – Bedford
Treasa Stalcup, 83, of Bedford, died at 5:12 am on Friday, July 15, 2016 at Johnson Christian Village.
Russell Jeffrey Blackburn – Bedford
Russell Jeffrey Blackburn, 59, of Bedford, died Wednesday, July 13, 2016.
Grant Cole King – Bedford
Grant Cole King, infant son of Steve and Nicole (Bowmer) King, died at 7:05 am on Monday, July 11, 2016 at Methodist Hospital in Indianapolis.
Survivors include his mama and daddy, Nicole L. and Steve M. King, of Bedford; two brothers, Matthew B. King and Kane A. Fishel; papaw, Victor Bowmer; E, Kellie Todd; mamaw, Subrena Terrell; papaw, Kevin Terrell; uncles, Michael Bowmer and Eric King; great grandparents, Margaret Bowmer, James Allgood, Margaret King and Phillip King.
He was preceded in death by papaw, Darrell King and great grandpa, Walter Bowmer, Sr.
Graveside services will be conducted at 3:30 pm on Wednesday, July 20th at Port Williams Cemetery with John Lee officiating. Burial will follow. Visitation will be from 2 pm to 3 pm on Wednesday, July 20th at the Day & Carter Mortuary.
The family asks that friends consider memorial contributions be made to Methodist Hospital Labor & Delivery.
Previous Story: July 14, 2016
Next Story: July 16, 2016


Do you need to catch a flight to Melbourne? Check out our domestic flights to Melbourne. If Melbourne is not your closest airport, then here are all our flights to Bangkok from Philippines and flights to Thailand.
The nearest train station to Melbourne airport is Broadmeadows which is 6 kms away.
31 airlines operate the route from Melbourne to Bangkok. They include Austrian, China Airlines, Virgin Australia, Vietnam Airlines, Hong Kong Airlines, Bangkok Airways, Singapore Airlines and more.
From Bangkok to Melbourne is 7,332 kilometres.


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Network Theory (Part 14)
We've been doing a lot of hard work lately. Let's take a break and think about a fun example from chemistry!
The ethyl cation
Suppose you start with a molecule of ethane, which has 2 carbons and 6 hydrogens arranged like this:
Then suppose you remove one hydrogen. The result is a positively charged ion, or 'cation'. When I was a kid, I thought the opposite of a cation should be called a 'dogion'. Alas, it's not.
This particular cation, formed from removing one hydrogen from an ethane molecule, is called an 'ethyl cation'. People used to think it looked like this:
They also thought a hydrogen could hop from the carbon with 3 hydrogens attached to it to the carbon with 2. So, they drew a graph with a vertex for each way the hydrogens could be arranged, and an edge for each hop. It looks really cool:
The red vertices come from arrangements where the first carbon has 2 hydrogens attached to it, and the blue vertices come from those where the second carbon has 2 hydrogens attached to it. So, each edge goes between a red vertex and a blue vertex.
This graph has 20 vertices, which are arrangements or 'states' of the ethyl cation. It has 30 edges, which are hops or 'transitions'. Let's see why those numbers are right.
First I need to explain the rules of the game. The rules say that the 2 carbon atoms are distinguishable: there's a 'first' one and a 'second' one. The 5 hydrogen atoms are also distinguishable. But, all we care about is which carbon atom each hydrogen is bonded to: we don't care about further details of its location. And we require that 2 of the hydrogens are bonded to one carbon, and 3 to the other.
If you're a physicist, you may wonder why the rules work this way: after all, at a fundamental level, identical particles aren't really distinguishable. I'm afraid I can't give a fully convincing explanation right now: I'm just reporting the rules as they were told to me!
Given these rules, there are 2 choices of which carbon has two hydrogens attached to it. Then there are
choices of which two hydrogens are attached to it. This gives a total of 2 × 10 = 20 states. These are the vertices of our graph: 10 red and 10 blue.
The edges of the graph are transitions between states. Any hydrogen in the group of 3 can hop over to the group of 2. There are 3 choices for which hydrogen atom makes the jump. So, starting from any vertex in the graph there are 3 edges. This means there are edges.
Why divide by 2? Because each edge touches 2 vertices. We have to avoid double-counting them.
The Desargues graph
The idea of using this graph in chemistry goes back to this paper:
• A. T. Balaban, D. Fǎrcaşiu and R. Bǎnicǎ, Graphs of multiple 1,2-shifts in carbonium ions and related systems, Rev. Roum. Chim. 11 (1966), 1205.
This paper is famous because it was the first to use graphs in chemistry to describe molecular transitions, as opposed to using them as pictures of molecules!
But this particular graph was already famous for other reasons. It's called the Desargues-Levi graph, or Desargues graph for short:
• Desargues graph, Wikipedia.
Later I'll say why it's called this.
There are lots of nice ways to draw the Desargues graph. For example:
The reason why we can draw such pretty pictures is that the Desargues graph is very symmetrical. Clearly any permutation of the 5 hydrogens acts as a symmetry of the graph, and so does any permutation of the 2 carbons. This gives a symmetry group , which has elements. And in fact this turns out to be the full symmetry group of the Desargues graph.
The Desargues graph, its symmetry group, and its applications to chemistry are discussed here:
• Milan Randic, Symmetry properties of graphs of interest in chemistry: II: Desargues-Levi graph, Int. Jour. Quantum Chem. 15 (1997), 663-682.
The ethyl cation, revisited
We can try to describe the ethyl cation using probability theory. If at any moment its state corresponds to some vertex of the Desargues graph, and it hops randomly along edges as time goes by, it will trace out a random walk on the Desargues graph. This is a nice example of a Markov process!
We could also try to describe the ethyl cation using quantum mechanics. Then, instead of having a probability of hopping along an edge, it has an amplitude of doing so. But as we've seen, a lot of similar math will still apply.
It should be fun to compare the two approaches. But I bet you're wondering which approach is correct. This is a somewhat tricky question, at least for me. The answer would seem to depend on how much the ethyl cation is interacting with its environment—for example, bouncing off other molecules. When a system is interacting a lot with its environment, a probabilistic approach seems to be more appropriate. The relevant buzzword is 'environmentally induced decoherence'.
However, there's something much more basic I have tell you about.
After the paper by Balaban, Fǎrcaşiu and Bǎnicǎ came out, people gradually realized that the ethyl cation doesn't really look like the drawing I showed you! It's what chemists call 'nonclassical' ion. What they mean is this: its actual structure is not what you get by taking the traditional ball-and-stick model of an ethane molecule and ripping off a hydrogen. The ethyl cation really looks like this:
For more details, and pictures that you can actually rotate, see:
• Stephen Bacharach, Ethyl cation, Computational Organic Chemistry.
So, if we stubbornly insist on applying the Desargues graph to realistic chemistry, we need to find some other molecule to apply it to.
Trigonal bipyramidal molecules
Luckily, there are lots of options! They're called trigonal bipyramidal molecules. They look like this:
The 5 balls on the outside are called 'ligands': they could be atoms or bunches of atoms. In chemistry, 'ligand' just means something that's stuck onto a central thing. For example, in phosphorus pentachloride the ligands are chlorine atoms, all attached to a central phosphorus atom:
It's a colorless solid, but as you might expect, it's pretty nasty stuff: it's not flammable, but it reacts with water or heat to produce toxic chemicals like hydrogen chloride.
Another example is iron pentacarbonyl, where 5 carbon-oxygen ligands are attached to a central iron atom:
You can make this stuff by letting powdered iron react with carbon monoxide. It's a straw-colored liquid with a pungent smell!
Whenever you've got a molecule of this shape, the ligands come in two kinds. There are the 2 'axial' ones, and the 3 'equatorial' ones:
And the molecule has 20 states… but only if count the states a certain way. We have to treat all 5 ligands as distinguishable, but think of two arrangements of them as the same if we can rotate one to get the other. The trigonal bipyramid has a rotational symmetry group with 6 elements. So, there are 5! / 6 = 20 states.
The transitions between states are devilishly tricky. They're called pseudorotations, and they look like this:
If you look very carefully, you'll see what's going on. First the 2 axial ligands move towards each other to become equatorial.
Now the equatorial ones are no longer in the horizontal plane: they're in the plane facing us! Then 2 of the 3 equatorial ones swing out to become axial. This fancy dance is called the Berry pseudorotation mechanism.
To get from one state to another this way, we have to pick 2 of the 3 equatorial ligands to swing out and become axial. There are 3 choices here. So, if we draw a graph with states as vertices and transitions as edges, it will have 20 vertices and 20 × 3 / 2 = 30 edges. That sounds suspiciously like the Desargues graph!
Puzzle 1. Show that the graph with states of a trigonal bipyramidal molecule as vertices and pseudorotations as edges is indeed the Desargues graph.
I think this fact was first noticed here:
• Paul C. Lauterbur and Fausto Ramirez, Pseudorotation in trigonal-bipyramidal molecules, J. Am. Chem. Soc. 90 (1968), 6722–6726.
Okay, enough for now! Next time I'll say more about the Markov process or quantum process corresponding to a random walk on the Desargues graph. But since the Berry pseudorotation mechanism is so hard to visualize, I'll pretend that the ethyl cation looks like this:
and I'll use this picture to help us think about the Desargues graph.
That's okay: everything we'll figure out can easily be translated to apply to the real-world situation of a trigonal bipyramidal molecule. The virtue of math is that when two situations are 'mathematically the same', or 'isomorphic', we can talk about either one, and the results automatically apply to the other. This is true even if the one we talk about doesn't actually exist in the real world!
This entry was posted on Saturday, October 15th, 2011 at 3:12 am and is filed under chemistry, mathematics, networks.	You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
22 Responses to Network Theory (Part 14)
15 October, 2011 at 4:00 am
This is how cations and dogions interact:
Jacques Distler says:
And why are the ligands treated as distinguishable? Does somebody paint numbers on them?
Surely one chlorine atom is indistinguishable from another, and these should be treated as identical particles.
Yeah, I raised the same issue for the ethyl cation.
I haven't been able to find out if chemists actually do take treat the atomic nuclei as indistinguishable particles in numerical simulations of molecules this size, and how much of a difference it actually makes. They talk about the Desargues graph, but I haven't seen them discuss this issue.
If the chlorines have enough internal degrees of freedom (all those electrons) and they're interacting with enough other stuff in a hot and messy environment, like some phosphorus pentachloride in liquid form, it's possible that symmetrizing (or antisymmetrizing) the wavefunction with respect to the chlorine nuclei has a pretty negligible.
Here's a puzzle for beginners (not you) who are interested in this issue.
In actual water, the two lone protons in the H2O are indistinguishable fermions, so we should antisymmetrize the wavefunction with respect to interchanging them.
But we can imagine a world where there were two different particles with the same mass and charge as a proton—say, a proton and a 'schmoton'. Then we could make a chemical called 'pseudowater', where instead of using two protons for the H's in our H2O, we used a proton and a schmoton. Then we would not antisymmetrize the wavefunction with respect to interchanging them.
Puzzle 2. What would be the easiest way to tell the difference between a molecule of water and a molecule of pseudowater, experimentally?
Of course we actually can make water using one ordinary hydrogen atom and one deuterium atom. This is called semiheavy water. And here again, we don't antisymmetrize the wavefunction. But it's easy to tell the difference between semiheavy water and ordinary water, either by weighing it or noticing that it melts and boils at a lower temperature than ordinary water. So, I need to invent 'pseudowater' to make my question more interesting.
Digressing somewhat: in the liquid state, molecules of water trade protons with each other quite often. So, liquid semiheavy water is not stable: it rapidly turns into a mixture of 25% ordinary water, 25% heavy water and 50% semiheavy water. The same thing would happen with pseudowater. This complicates my question a bit more than I want, which is why I spoke of 'a molecule of pseudowater' instead of a liter of pseudowater. But in a low-density gas, I think water molecules don't trade their protons so quickly.
Digressing further, I just discovered that rats can taste the difference between ordinary water and heavy water!
I knew that large eukaryotic organisms (like people and rats) will die if all they drink is heavy water. But I hadn't known that rats actually avoid the stuff:
• Inglis J. Miller Jr. and Gregory Mooser, Taste responses to deuterium oxide, Physiology & Behavior 23 (1979), 69-74
Abstract: Substitution of deuterium oxide (D2O) as the solvent in taste stimuli elicits neural responses which differ from ordinary water (H2O). Previous reports have shown that D2O is toxic to many animals and rats avoid drinking it when offered H2O simultaneously. In the current study, summated responses were recorded from the chorda tympani nerves of rats after NaCl, KCl, sucrose and quinine were applied to the tongue in solutions of either D2O or H2O. Both solvents were used as the adapting or rinse solution in separate series. On tongues adapted to H2, D2O elicited mean responses which were equivalent to 29% of the response to 0.1 M NaCl. The threshold concentration of D2O in H2O was between 25% and 50%. Solutes in D2O yielded responses which were greater than corresponding solutions of H2O when adapting rinse was H2O. Adaptation to D2O diminished the responses to D2O solutions of NaCl, KCl and sucrose but not quinine. This observation suggests that some portion of the augmented response to stimuli in D2O is due to the solvent itself. The taste of water has been examined by both electrophysiological methods and by behavior, but none of the mechanisms espoused for its effect seem adequate to explain the response to D2O. Water structure at the interface between molecular components of the cell membrane and the bulk phase of the surrounding medium is considered as a locus for disparity in the taste responses to D2O and H2O in the rat.
I don't know if people can taste the difference between ordinary water and heavy water. I supposed I'd have heard it if they could. But maybe only special people, like trained wine tasters, can do it?
Digressing still further, I got the following very interesting email a while ago, from somebody who'd been unable to find Greg Egan's address:
Dear Mr. Egan,
I recently read, with pleasure, several of your books. I particularly enjoyed "Diaspora". I also note that on your website you have the following erratum regarding the isotopically substituted biosphere on Swift:
"The difficulties of either creating a biosphere, or modifying an existing one, to use heavy water are not addressed. Certainly, the chemistry of heavy water is sufficiently different from that of normal water that a complete substitution would be fatal to most organisms in Earth's biosphere. Life based on heavy water might well be possible, but it would not be a simple matter to make the substitution."
As a protein NMR spectroscopist by trade, I deal with isotopically substituted organisms on a regular basis. It seems that single-celled microorganisms tolerate 100% heavy water substitution. However, to achieve near 100% substitution of protium with deuterium in all cellular metabolites and macromolecules, a perdeuterated carbon source is needed. For protein NMR sample preparations, it is routine to completely substitute at least one of major elements in the molecule (commonly N or C) with a heavier isotope 15N or 13C. This is done by producing proteins biosynthetically in E. coli cultures, grown in chemically defined media that contain isotopically substituted compounds: 99% – 15N ammonium salts as sole nitrogen source and 99% – 13C glucose as sole carbon source. Occasionally, 15N , 13C and 2H substituted samples are prepared (I've done this myself) by using 99.9% D2O as solvent for medium, and 13C,2H-glucose as a sole carbon source. E. coli grow slowly in D2O compared to H2O, but they do grow. I was told that ~98% of 1H is substituted with 2H in samples produced this way.
Now, bacteria are among simpler forms of life. Eukaryotic organisms, such as yeast and algae, can also grow in 99% D2O (again, used in production of isotopically labeled samples for NMR). While complete substitution with heavy water is fatal to higher organisms and their cell cultures, it seems that amino acids completely substituted with 15N and (or) 13C are tolerated well enough in animal cell cultures. And apparently mass-spectroscopists produce living rats with 15N substitution, by using algal feedstock with >98% 15N. These are meant to study cellular protein composition and modifications under pathological versus normal conditions, so presumably (I do not know how rigorously has this been tested) rats suffer no ill effects from the isotopic substitution itself.
I do not know how much of this is news to you, and certainly none of the above contradicts your statement that for present terrestrial biosphere substitution with heavy water would not be a simple matter, but I hope you found it somewhat interesting.
Good luck with upcoming "Orthogonal" books.
Algirdas Vėlyvis
Andrew Taube says:
The short answer is that for nuclei heavier than H, there is very little impact from nuclear exchange for molecular structure calculations. In fact, there is relatively little impact from assuming that nuclei are classical! The idea is that the nuclei, being so much more massive than the electrons, are sharply peaked about classical positions (at least at the temperatures relevant to chemistry). For many of the things that chemists care about, It turns out this classical nuclei approximation is really good. At room temperature, the thermal wavelength of a proton is about 0.4 Angstrom, a good bit smaller than internuclear distances in a stable molecule.
Note that fully taking into account nuclear quantum effects and exchange has philosophical implications as well–it would completely change the concept of molecular structure and destroy the idea of isomers (same nuclei, different spatial arrangement). Here's one recent summary about those issues:
• Brian Sutcliffe, Permutational symmetry and molecular structure calculations, Collect. Czech. Chem. Commun. 70 (2005), 657-676.
For protons, there can be relatively substantial effects from the quantum nature of the proton, but even then one often ignores exchange, assuming that the nuclei are sufficiently localized (overlap between single particle proton functions is approx. zero) as to make the correction to the energy due to exchange negligible:
• Benjamin Auer and Sharon Hammes-Schiffer, Localized Hartree product treatment of multiple protons in the nuclear-electronic orbital framework, J. Chem. Phys. 132 (2010), 084110.
For high accuracy dynamics, taking into account permutation invariance is important:
• Bastiaan J. Braams and Joel M. Bowman, Permutationally invariant potential energy surfaces in high dimensionality, International Reviews in Physical Chemistry 8 (2009).
What a wonderfully erudite answer, Andrew! Thanks for all those references: I was trying to find some, but I wasn't having much luck. I'm very relieved that I can study phosphorous pentachloride fairly accurately without (anti)symmetrizing over the chlorine nuclei wavefunctions, because I was going to whether I could or not—I just wanted an excuse to play around with dynamics on the Desargues graph!
My 'water versus pseudowater' puzzle is surely too easy for you, so I'm glad you didn't address it directly… I hope some other readers, perhaps less knowledgeable in physical chemistry, take a crack at it!
People are posting important comments about how to save the world, so I feel a bit silly posting another one about heavy-water-drinking rats, but I feel it's good to put all this esoteric information in one place.
Over on Google+, Bruce Head wrote:
I'm reading The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements by Sam Kean, and he has the following anecdotes about heavy water:
[György] Hevesy [Hungarian radiochemist and Nobel laureate] helped determine how quickly the human body recycles an average water molecule (nine days) by volunteering to drink special "heavy" water, in which some hydrogen atoms have an extra neutron, and then having his urine weighed each day … [he also] performed heavy-water experiments on goldfish as well as himself, and he ended up killing a number of them.
Gilbert Lewis also used heavy water in a last-ditch effort to win the Nobel Prize in the early 1930s. Lewis knew that Harold Urey's discovery of deuterium – heavy hydrogen with an extra neutron – would win the Nobel Prize, as did every other scientist in the world, including Urey. (After a mostly lackluster career that included ridicule from his in-laws, he came home right after discovering deuterium and told his wife, "Honey, our troubles are over.")
Lewis decided to hitch himself to this no-miss prize by investigating the biological effects of water made with heavy hydrogen. Others had the same idea, but Berkeley's physics department, headed by Ernest O. Lawrence, happened to have the world's largest supply of heavy water, quite by accident. The team had a tank of water it had been using for years in radioactivity experiments, and the tank had a relatively high concentration of heavy water (a few ounces). Lewis begged Lawrence to let him purify the heavy water, and Lawrence agreed – on the condition that Lewis give it back alter his experiments, since it might prove important in Lawrence's research, too.
Lewis broke his promise. After isolating the heavy water, he decided to give it to a mouse and see what happened. One queer effect of heavy water is that, like ocean water, the more you drink, the more throat-scratchingly thirsty you feel, since the body cannot metabolize it. Hevesy ingested heavy water in trace amounts, so his body really didn't notice, but Lewis's mouse gulped all the heavy water in a few hours and ended up dead. Killing a mouse was hardly a Nobel Prize-worthy exercise, and Lawrence went apoplectic when he learned a lousy rodent had peed away all his precious heavy water.
Geoffrey Irving says:
Your comment that it's tricky to know whether to apply stochastic or quantum mechanics raises an interesting question: what are the equations that smoothly transition between the two based on the level of external noise? Is it possible to write these down in a universal way that isn't too dependent on the type of noise, or would a different level of noise be required for each state?
I'm sure people have studied this question, at least for some particular examples of quantum systems. I haven't read the literature on this subject. But in the particular case of a system whose states are the vertices of the Desargues graph:
if we seek a solution that's compatible with all 240 symmetries of the Desargues graph, it's almost unique. The symmetries constrain the problem enormously!
I'd been planning to talk next time about the classical and quantum versions of this problem, but I could also talk about the almost unique way of interpolating between the classical and quantum cases. And if I do, you'll see this particular way of interpolating works pretty generally. But I don't know how physically reasonable it is, in general.
linasv says:
I'd be interested in knowing the answer to Geoffrey Irving's question. I've been interested in a certain generalization: for any graph, one can define a Markov process; for any graph, you can replace that by a quantum process. Briefly, the edges, instead of being probabilities of transition, become unitary matrices. The verticies are then points in projective spaces (i.e. point in the space on which U(n) acts). So, for example, a one may define a "quantum finite automata" by applying the above steps to a normal probabilistic finite automata. (see wikipedia for details).
Likewise, given any symmetric space, and a collection of symmetries that act on it, you can generalize Markov by making the points of the graph be elements in the symmetric space, and the edges be valued among the symmetries.
So, given this rather abstract presentation, I find that Geoffrey Irving's question is in fact quite interesting. Answering it would seem to shed light on the details of decoherence. I only wish I had the time to ponder such things :-(
p.s. sorry if above was already discussed in earlier posts; I am going back now to read them…
linasv wrote:
I'd be interested in knowing the answer to Geoffrey Irving's question. I've been interested in a certain generalization: for any graph, one can define a Markov process; for any graph, you can replace that by a quantum process. Briefly, the edges, instead of being probabilities of transition, become unitary matrices.
I plan to talk about these things, at least a little. It actually sounds like you mean 'Markov chain' rather than 'Markov process' here. A Markov chain occurs in discrete time while a Markov process occurs in continuous time. So, to specify a Markov chain we give a transition probability for each pair of states, while to specify a Markov process we give a 'probabilistic rate of transition' for each pair of states. For a Markov chain the matrix of transition probabilities is a stochastic matrix, while for a Markov process the matrix of rates is an infinitesimal stochastic matrix, also known as an 'intensity matrix'.
All these concepts were explained more clearly than I'm doing it now back in Part 11. And, they all have quantum analogues, as explained in Part 12.
Don't feel bad: I'm happy to review things. That's the only way to keep new people jumping on board. I don't want what I'm doing to only be comprehensible to people who have been following all along!
Anyway, from a graph we can get 4 things in a completely natural way: a Markov chain, a Markov process, and the quantum analogues of those two. We can also get a 1-parameter family of continuous-time dynamical systems interpolating between the Markov process and its quantum analogue. I haven't thought about trying to doing that in the discrete-time case.
I'm beginning to see what I should talk about in my next post(s)! Thanks!
I hope someone tackles this puzzle, which is really rather fun:
I also hope someone tackles my pseudowater puzzle. It was buried in distracting remarks about rats and heavy water, so here it is in a nutshell:
Puzzle 2. Suppose there were a substance called 'pseudowater', exactly like ordinary H2O except that the Pauli exclusion principle didn't apply to the nuclei of the two hydrogen atoms. What would be the easiest way to tell the difference between water and pseudowater?
(If you have trouble answering ill-defined counterfactual questions, assume in Puzzle 2 that hydrogen nuclei can be made of two different particles, protons and schmotons, which have the exact same mass, charge, etcetera but differ in some internal degree of freedom. 'Pseudowater' is HH'O, where H is ordinary hydrogen, and H' is hydrogen with a schmoton replacing the usual proton.)
Interesting. Are you talking about spin isomers? I would expect a measurable mass difference between the two spin isoforms.
Hi, Walter – hope all's well!
You got it. If I were talking about H2 instead of H2O, that article you linked to on spin isomers of hydrogen would be exactly right. But—for no particularly good reason—my question was about H2O.
In fact, I got a bit mixed up… it turns out I understand the answer for H2 a lot better than the answer for H2O. So let me see if I can explain it for H2.
There are two kinds of H2 molecules: orthohydrogen, where the spins of the two protons are lined up, and parahydrogen, where they are anti-aligned:
Since the two protons are identical fermions, the wavefunction of the hydrogen molecule has to change sign when you switch them.
In orthohydrogen the protons' spin state is symmetric: it doesn't change when you switch them. So their position state must change sign when you switch them. This means that their total orbital angular momentum can't be 0: if it were, it would be invariant under rotations, so it wouldn't change sign when you switch the two protons! But it can be 1, or in fact any odd integer.
On the other hand, in parahydrogen the protons' spin state is antisymmetric: it changes sign when you switch them. That's not obvious from the picture above, which shows one with spin up and the other with spin down. That's a defect of the picture! In reality, their spin state is
So, it's antisymmetric. That means their position state must not change sign when you switch them. That means the the total orbital angular momentum of the protons can be 0, or in fact any even integer.
In short, parahydrogen can have total angular momentum zero, but orthohydrogen can't—it has to be 'rotating'. This means the ground state of parahydrogen has lower energy. And the energy difference is significant; according to the Wikipedia article divided by Boltzmann's constant is about 175 kelvin.
If instead we had a 'pseudohydrogen' molecule HH' built from a proton and a schmoton and two electrons, it would still come in 'ortho' and 'para' forms, but the argument I sketched would no longer apply. So, either form could have any total angular momentum it wanted: 0, 1, 2,…
So for a pseudohydrogen molecule, unlike an ordinary hydrogen molecule, the ground state energy of the para form would equal that of the ortho form.
Now, what about water? How would pseudowater differ from water?
So nobody is willing to try this puzzle? What a bunch of wimps! I won't make fun of you if you try to answer it and make a mistake. But I'll definitely make fun of you if you don't even try!
David Corfield says:
With precisely 5 minutes this morning for such fun activity as answering Azimuth puzzles, can't we establish for Puzzle 1 an isomorphism between the states and transitions of the trigonal bipyramidal molecule and those of the ethyl cation? Whether an atom is in the axis of the former corresponds to whether it's in the pair end of the latter.
With precisely 5 minutes this morning for such fun activity as answering Azimuth puzzles…
I'm sorry you're so busy these days! Anyway, you've done more than your share of answering Azimuth puzzles—I think you answered all the Network Theory puzzles until your current state of overwork overtook you. So I would never make fun of you for not trying this one. It's all the other people who're in trouble.
… can't we establish for Puzzle 1 an isomorphism between the states and transitions of the trigonal bipyramidal molecule and those of the ethyl cation?
That's indeed the best way to do it. After all, so far I've basically defined the Desargues graph to be the graph of states and transitions for the ethyl cation. Sure, I showed you a picture of it too—but it's hard to do much with that.
Whether an atom is in the axis of the former corresponds to whether it's in the pair end of the latter.
Hey, that sounds promising. In case someone didn't follow that, David seems to be hinting that the split of chlorines into 3 equatorial ones and 2 axial ones in this trigonal bipyramidal molecule:
is analogous to the split of hydrogens into a group 3 and a group of 2 in this ethyl cation:
If so, the next step would to make sure that this analogy sets up a 1-1 correspondence between the states in the two problems, and also the transitions.
Consider the transitions, for example. Does a hydrogen hopping from one carbon to another in the ethyl cation correspond to a 'pseudorotation' of the trigonal bipyramidal molecule? Remember, pseudorotations are a bit funky. They work like this:
James Griffin says:
Fascinating, I'm considering sending the post to my graph theory students. As for the validity of distinguishing between different identical particles: my approach would be to say that of course you're allowed to distinguish between them, just as long as you remember the symmetries.
One thing I've always wondered is when in a given physical situation with such a symmetry, which is the right quotient? The usual one, or the homotopy one? Let's say the symmetry is finite, indeed it could be just a single reflection. Can one ever see the homology of in a physical system?
Another question I have is about the construction of these graphs. Why have we stopped at edges? Could there be 2-cells?
… I'm considering sending the post to my graph theory students.
If you do, you might tell them that the Desargues-Levi graph is a close relative of the Petersen graph, which they may already know. The Petersen graph is the universal counterexample to all dumb guesses in graph theory:
The Desargues-Levi is the 'bipartite double cover' of the Petersen graph, formed by replacing each Petersen graph vertex by a pair of vertices and each Petersen graph edge by a pair of crossed edges.
I think I used to know how you could get the Petersen graph directly from thinking about the ethyl cation. Maybe just treat the two carbons as indistinguishable?
As for the validity of distinguishing between different identical particles: my approach would be to say that of course you're allowed to distinguish between them, just as long as you remember the symmetries.
Well, Distler's point was that the Hilbert space of quantum states of phosphorus pentachloride (for example) is smaller than I made it sound.
One thing I've always wondered is when in a given physical situation with such a symmetry, which is the right quotient? The usual one, or the homotopy one?
People mainly discuss this issue in the treatment of 'gauge' symmetries in classical field theory. The traditional approach was to take the usual quotient, but it's starting to seem that the homotopy quotient is right. A good example is whether you should use the moduli space of elliptic curves when studying about strings whose worldsheet has genus 1, or the moduli stack. The moduli space is an ordinary quotient, while the moduli stack is a homotopy quotient. As I explained back in "week125" of This Week's Finds, the Picard group of the moduli stack of elliptic curves is , and this is related to the magic role of the numbers 12 and 24 in this theory—for example, how the vacuum energy is -1/24, which is part of why the theory is only consistent in 24 + 2 = 26 dimensions.
Heh. I'm not doing the n-category schtick anymore. But if we were studying something like a 2d random field theory, instead of a Markov process or Markov chain (where there's just 1 dimension, namely time), that could be natural.
Thank you for the thorough reply, I'll need a little time to digest all that. As for the 2-cells, I was more influenced by group (co)homology than n-category theory. Essentially the idea in my head was that if it were possible to move two hydrogens at once, then there may be a 2-cell whose boundary records the equivalence between the moves which move only one hydrogen at once.
The simplest example I can come up with is cyclopropane (C3H6, a triangle of carbon molecules) with two hydrogens removed, although I have no idea how stable this would be! I think the graph would have 54 vertices and 144 edges and an action of . The 2-cells depend on the model of how hydrogens are allowed to move, but assuming they're only allowed to skip over the bonds (rather than over the centre of the triangle) then there are are number of squares attached, perhaps 24.
A Math Puzzle Coming From Chemistry « Azimuth says:
Let's try this chemistry puzzle again…
Network Theory (Part 15) « Azimuth says:
Last time we saw how to get a graph whose vertices are states of a molecule and whose edges are transitions between states. We focused on two beautiful but not completely realistic examples that both give rise to the same highly symmetrical graph: the 'Desargues graph'. […]
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text:
7 best ultra marathons in the world
By Let's Do This, October 7, 2019
Ultra marathons are any running events that at the very minimum go further than the marathon distance of 42.2km. The problem is that there is no upper limit. As a result, there are now some insanely challenging events held across the globe. The distance isn't the only problem either, as competitors are asked to wrestle with mountains, rain-forests, deserts, or extreme weather conditions.
Since they're events that allow you to experience the world in a unique way, we've chosen the best ultra marathon from all 7 continents (yes, even Antarctica), and added a couple of runners up so you can explore your options.
Find your next ultra marathon
Africa: Comrades Marathon
The route:
Durban to Pietermaritzburg (or Pietermaritzburg to Durban, depending on the year)
87km/54 miles uphill or 90 km/56 miles downhill in a 12 hour time-limit
Takes in 'The Big Five' hills with a highest elevation of 2,850ft/870m above sea level
Run it for:
This is the world's oldest and largest ultramarathon. It was first run in 1921, and has been completed by over 300,000 runners. The current field allows for 27,500 participants. It is famous for its vibrant atmosphere and support, with school children and local folk bands cheering you along the way. The race is run in the spirit of 'Ubuntu', which can be translated as 'humanity towards others'.
Runners up:
Marathon des Sables, Morocco: 251km in the Sahara Desert
Namib Race, Namibia: 250km in the Skeleton Coast National Park
Antarctica: The Last Desert
A variety of locations on the Antarctic Peninsula, potentially including King George Island, Deception Island, and Paradise Bay
250km multi-stage event
Each night sleeping on the expedition ship
This is the only multi-stage footrace in Antarctica. The main challenges in the polar desert are the conditions of extreme cold, high winds and sheer landscapes. Varying snow, ice and weather conditions cause the course to change each year, often at late notice. The chance to tread in the footsteps of ancient explorers and to see a variety of wildlife including whales, penguins, and seals in the untouched wilderness makes this event a rare and life-changing experience.
Runner up:
The Arctic Ice Marathon and 100k
Asia: La Ultra – The High
In the Great Himalayan range of India, starting from the Nubra Valley towards the Indus River, and finishing in the Morey Plains of the Changtang plateau
333km/207 miles in 72 hour time limit. Including three 17,500ft+ mountain passes.
Most of the run is done with 50% less oxygen than at sea level. Add in to that fluctuating temperatures from -12 to 40 degrees celsius, and you'll get a good idea of what sort of brutality your body will be put through. The three climbs to Khardung La, the world's highest motorable pass at 5,359m, will push your physical and mental endurance beyond almost any other sports race. Under 59% of competitiors complete the race; can you be one of them?
The Grand Raid Reunion/Diagonale des Fous (translated as 'Diagonal of Mad Men'): 100 miles at La Reunion Island, in the Indian Ocean, with 9,643m elevation
Gobi March, 250km in the Gobi Desert of Mongolia
Australasia/Oceania: Ultra-Trail Australia (UTA)
In the Blue Mountains National Park in New South Wales
100km/62.1 miles (there is a 50km option as well)
In a country that boasts some of the world's most spectacular scenery and wildlife, the Blue Mountains National Park is the most beautiful region of the lot. The World Heritage Area makes for a stunning ultra marathon, steeped in aboriginal history. Not for the faint hearted, the course involves an elevation gain of 4,400m, but the sense of achievement upon completing this challenge is immense. It is a hugely popular ultra, with many participants signing up to do it again.
Tarawera Ultra: 100 miles exploring the lakes, forests and waterfalls of New Zealand
Kepler Challenge: 60km through Fiordland National Park, NZ.
Europe: Ultra-Trail du Mont-Blanc (UTMB)
Following the route of the Tour du Mont Blanc in France, Italy, and Switzerland. Based in Chamonix, France.
171km/106 miles, single-stage race with a total elevation gain of 10,040m/32,940ft
This is one of the most challenging footraces in the world, especially in terms of elevation gained in such a short time, and is on many experienced ultra runners' bucket lists. The winners of this race complete the course in around 20 hours, running through the night. Only about 60% of competitors complete the race in any given year, as the race includes mountainous climbs and demanding descents, but there are also stunning Alpine views throughout. Since it crosses between three countries, this could be one of the only ultras where you need your passport with you!
Spartathlon, Greece: 153 miles/246km in under 36 hours from Athens to Sparta, in the footsteps of Pheidippides.
Dragon's Back Race, Wales: 315km in 6 days, with average daily climbing of 3,100m
North America: Western States Endurance Run
Sierra Nevada Mountains, California. Starting in Squaw Valley and ending at Auburn's Placer High School.
161km/100 miles single-stage event, with cumulative elevation gain of 18,090ft/5,500m
This is known as one of the world's toughest single-stage endurance races, taking on the rugged ranges and canyons of California. The race is also famous for its mythology: it started in 1974, when a man's horse went lame before a 24-hour race, so he ran it on foot instead (18 minutes inside the time limit!). Nowadays, runners compete for one of the legendary belt-buckles: bronze for finishing in under 30 hours, silver for finishing in under 24 hours.
Badwater Ultra: 135 miles around Death Valley and the Inyo mountains, with temperatures up to 54 degrees celsius.
Hardrock Endurance Run: 100 miles in 48 hours on Southern Colorado's San Juan Range
South America: The Jungle Ultra
In the Amazon Rainforest of Manu National Park, Peru from the Andes mountains to the Madre de Dios River
230kms in five stages with humidity above 77%
This is a chance to explore a relatively unspoilt area of the steaming jungle, taking in cloud forests, mountains, and valleys. There will be arduous undergrowth, deep mud and river crossings to navigate, heavy rain throughout the challenge, and you might even run under nightfall. This is a wild course, where you will have to be almost entirely self-sufficient, so it is a test of endurance in the most extreme conditions. Being surrounded by a variety of rare wildlife will make for an incredible experience though.
Atacama Crossing, Chile: 250km in 7 days in the Atacama desert
Half Marathon des Sables, Peru: 120km in 3 days through the Ica desert
The list of best ultra-marathons in the world:
Comrades Marathon (Africa)
The Last Desert (Antarctica)
La Ultra – The High (Asia)
Ultra-Trail Australia (Australasia/Oceania)
Ultra-Trail du Mont-Blanc (Europe)
Western States Endurance Run (North America)
The Jungle Ultra (South America)
Categories: Running, Trail Running, Trail Running, Ultramarathons
5 best sprint triathlon events
7 Ultra Marathon training tips


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VP of International & Enterprise, oDesk
Matt brings to oDesk over a decade of executive operating experience in both start-ups and Fortune 500 companies. Previously, as a member of the executive team at Accolo, Inc., a recruiting services and technology firm, he grew the business from one employee into one of the top 50 companies on the Inc 500 list. He also co-founded a boutique strategic consulting firm for ramping early-stage companies, and started his career in investment banking at JPMorgan Securities. Matt puts his finance, operations and strategy expertise to work in driving oDesk's International and Enterprise market growth. Matt holds an MBA from Vanderbilt University. He also graduated with a Bachelor of Science degree in Economics, magna cum laude, from Vanderbilt University.
Fireside chat with oDesk, Gidsy, Uber & Oliver Jung
You Can Always Get What You Want: oDesk and Uber Discuss On-Demand Access to Services.


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Q: JS: Sending POST to server, getting no response I am sending a Postman POST to a LDAP Server. When I use the GET response for one function it works; however, when I use the POST for another function that involves client.binding. I get no response, "Could not get any response" after 1 minute of waiting. I am using http, with no proxy.

GET that works:
   IAMserver.get('/account/list', function(req,res){
        //list accounts for a compangy. seraches everyhting under provided compagny node.
        let enterprise = req.jwtPayload.enterprise || "Enterprise";
        var opts = {
            //filter: 'cn='+base,
            filter: '(objectclass=person)',
            scope: 'sub'
        };
            console.log(result);
            console.log('status: ' + result.status);
            respondWithJSON(200, 0, "Success", res, entries);

POST that doesn't work:
IAMserver.post('/account/modify', function(req,res){
    if(req.jwtPayload.entityData == null || req.jwtPayload.entityData == {}){
        respondWithJSON(400, 400, "No entity data provided or data was not JSON encoded.", res);
        return;
    }
    //Check if exists already.
    aSearch(req.jwtPayload.cn).then(
    //exists
    function(result){
        //Bind to admin account.
        client.bind(adminCred, adminPass, function(err){
            if(err){
                respondWithJSON(500,500, err.message, res);
                return;
            }
        });
        //define modifications
        let changes = new ldap.Change({
            operation: 'replace',
            modification: req.jwtPayload.entityData
        });
        //try to modify.
        client.modify('cn='+req.jwtPayload.cn+',ou=Enterprise,dc=abc,dc=com', changes, function(err){
            if(err){
                respondWithJSON(500, 500, err.message, res);
                return;
            }
            respondWithJSON(200, 0, "Changes executed correctly.", res);
        });
    },
    //Doesn't exist, can't modify.
    function(result){
        respondWithJSON(200,1, "Failure. "+result.message, res);
    });
});

redpajama_set_name: RedPajamaStackExchange


We've pulled together our top picks to help you find the perfect gift for your Mum on Mothering Sunday, (psst… that's Sunday 26th March).
Treat your Mum to the fragrance that makes life more beautiful this Mother's Day. Incarnated by Julia Roberts, La Vie Est Belle is a feminine fragrance created with a mix of precious ingredients.
Let Mum put her feet up and have a pamper session with Liz Earle's Glow Getter kit from Boots. Including a range of skin-loving complexion-balancing must-haves, this gift will leave her skin feeling touchably soft and visibly glowing.
For a bold, statement gift- this stunning heart locket from Beaverbrooks is perfectly on trend with its vintage-inspired style and rose gold finish. With beautiful detail and swirling strands of plated sterling silver, this locket will make your Mum feel extra special this Mother's Day.


Welcome to BusinessKitbag.com. Here you'll find hand-picked online products and services for your small business, whether you are just starting out, or have been in business for some time.
A small business owner has to be a jack-of-all-trades to get everything done. New skills and knowledge must be acquired, often quickly, to move forward with plans or deal with issues that arise unexpectedly.
There are many excellent tools, applications, and services which are available online to assist with almost every aspect of business, however, there are countless thousands of these, and finding the right ones to help your business is time consuming, often confusing, and hit-and-miss at best. Search results, reviews, and commentary often have a US-centric bias, making the job of finding resources suitable for UK conditions even harder.
We have been small business owners, and found researching these options took up time we didn't have. We decided to create BusinessKitbag.com as a resource for people like us: small business owners in the UK. We've done the trawling, reading, questioning, and testing – from a UK small business perspective – and filtered down our findings into information that you can quickly digest to find what you need.
All of the products we feature are highly rated and recommended by independent experts and product users through services such as Trustpilot, Feefo, Software Advice, and GetApp.
These cloud based services will offer you flexibility in how and where you work, help you work more efficiently, with greater productivity and will lead to increased profitability. Who doesn't need that?
We are always on the hunt for the best deal for your B2B software or service, see our deals page for our latest discounts and offers brought to you by our partners. Please sign up for us to keep you informed as and when new offers are released.
Work smarter not harder using these great software products and services and take your business to the next level.
Know an online product or service you think we should list on BusinessKitbag? Get in touch at [email protected].


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The Science of Speed
The Science of Speed, produced for the National Science Foundation (NSF) and written and hosted by Diandra Leslie-Pelecky, explains the scientific principles that are so essential to the NASCAR experience. Viewers learn how science makes cars powerful, agile, fast and safe--and how these same principles affect their own cars.
You can't win NASCAR races without getting the science right. NASCAR teams push science to its limits to eke out the tenths or hundredths of a second that separate the winner from the also-rans. This video series uses the elements of NASCAR to show that a racecar really is a science experiment on wheels.
Episode 1. Drag & Drafting
Engine power is constrained at superspeedways like Daytona and Talladega, so teams use aerodynamics to gain an advantage. Teams adjust their cars to minimize drag, but then it's up to the drivers to find 'the draft' and to trust the drivers behind them to literally "bump" them into Victory Lane.
View video (5:29 min.)
Episode 2. Car Safety
Conservation of energy explains how NASCAR's new car helped driver Michael McDowell walk away from a scary crash at Texas Motor Speedway in 2008.
Episode 3. Friction & Heat
Friction always creates heat. Brakes and tires depend on friction to work, but more friction isn�t always better. In the engine, friction is never good and engine builders use everything from oil to high-tech coatings to get a little extra horsepower.
View video (5:527 min.)
Episode 4. Grip
There's one thing every driver always want more of: Grip. Grip is the frictional force that holds the tires on the track, but crew chiefs like Steve Letarte describe it as a 'warm and fuzzy feeling' when you have it. Whether mechanical or aerodynamic, more is always better.
Episode 5. Sound
"Loud is fast" Brian Vickers tells us, and speed is one reason racecars don't have mufflers. Experiencing a NASCAR race means feeling the roar of the engines as well as hearing them. It's all good--as long as you�ve got your ear protection.
Episode 6. Tires & Pressure
NASCAR tires don't have "air pressure" because they're filled with nitrogen. The culprit responsible for increasing tire pressure during a race is friction. Using dry nitrogen gas helps the team predict how hot the tire will get and how much the pressure will "build" during a race.
Episode 7. Turning
Anyone can go fast straight: The challenge is turning. It takes more than ten thousand pounds of force to get a racecar around Turn 3 at Texas Motor Speedway at 180 mph. All that force comes from four tiny patches of rubber--the only thing keeping the car on the track and out of the wall.
Episode 8. Power
850 horses all lined up--that's how much power a NASCAR Sprint Cup engine has. The engine's job is to convert the energy in fuel to speed. NASCAR engines do it faster and more efficiently than passenger car engines.
Episode 9. Balance
A racecar driver is like Goldilocks: The car always seems to be too loose or too tight. Getting the right balance is hard because the weight of the fuel changes and the tires wear during each green-flag run. Understanding the science is how crew chiefs make the car "just right".
Episode 10. Momentum & Time
Increasing the time of a collision from a tenth of a second to two tenths of a second can make a huge difference in the number of G's a driver experiences. The car, the track, seat belts, and seat construction spread out the force of impact and save lives.
Episode 11. Load Transfer
NASCAR corners are divided into three parts because the car's grip changes in different parts of a turn. The higher center of gravity in the new car challenges crew chiefs to minimize weight shift around a turn. Equipment like the seven-post rig helps, but the ultimate test is on the track.
Episode 12. Firesuits
"Frightening" is how Jeff Gordon describes fire, even though he knows he's protected head to toe (and right down to his underwear) by fire-resistant Nomex fabric. Firesuits and the associated gear don't just protect drivers from fire, though--they decrease the rate of heat transfer, giving the driver a little more time to move somewhere cooler.


Based on the superfluid hydrodynamic equations and scaling theory, we numerically study the collective excitations of superfluid Fermi gases in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein Condensate (BEC) of molecules in a linearly ramped trap. The effects of controllable parameters,including the velocity and amplitude of the linearly ramped trap, and the anisotropy of the trap on the excitations are studied in detail. Through the spectral analysis and data fitting, the frequencies of the collective modes in the zero-amplitude limit induced by the linearly ramped isotropic and anisotropic traps along the BCS-BEC crossover are presented, respectively, which are in agreement with theoretical results previously obtained. Our work may provide a reference to experiments on collective excitations in the future.


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'Gods Of Jade And Shadow' Spins A Dark, Dazzling Fairy Tale
'Gods of Jade and Shadow' by Silvia Moreno-Garcia
Novelist and NPR contributor Silvia Moreno-Garcia's new fantasy, Gods of Jade and Shadow, is at its witty, compelling, and merciless best when it is fully rooted in its setting, a perfectly organic combination of 1920s Jazz Age Mexico and the Mayan mythological text, the Popol Vuh. The plot of the book is simple: A young woman, Casiopeia Tun, is suffering Cinderella-esque deprivation in the house of her grandfather, a wealthy rural landholder in the Yucatán. She stumbles upon a locked chest containing (most of) the dismembered body of one of the Lords of Xilbalba, a Mayan god of death called Hun-Kamé, and frees him — becoming spiritually linked to him in the process. Hun-Kamé has been deposed from his throne by his twin brother, Vucub-Kamé, and Casiopeia finds herself first an unwilling and then an active participant in his quest to take revenge and reclaim his standing as the ruler of Xilbaba.
So far, so fairy-tale — though the pleasure of seeing Mayan mythology underlying what at first seems to be a straightforward rendition of the Cinderella trope adds immediate interest to Moreno-Garcia's work. Nevertheless, for the first few chapters of Gods of Jade and Shadow, the dominant tone is that of the basic fairy-tale retelling, and while Casiopeia's anger, frustration, and family entanglements are all well-drawn, they are nothing particularly special. The book comes into itself the moment Casiopeia is entangled with Hun-Kamé, and Moreno-Garcia takes her, and the reader, on a whirlwind tour of a 1920s Mexico vivid with jazz, the memories of revolution, and gods, demons, and magic which are both indigenous and foreign-born.
Casiopeia and Hun-Kamé travel from Casiopeia's small Yucatán town to the rural "big city" of Merída — and then on to Veracruz, Mexico City, and Baja California, acquiring Hun-Kamé's stolen magic (and body parts) as they go. But the real fascination of their journey is the relationship between them: Hun-Kamé is using Casiopeia's mortal life force to remain present in the world of men, but the process is both killing her and making him less of a god of death and more a young man. Casiopeia is rightfully angry at what Hun-Kamé demands of her; but they develop a complex, shifting, and deepening understanding of one another. Their travels are not merely those of an underprivileged and oppressed young woman finding her place in the wide and exciting world of the Jazz Age — nor are they the (expected) version of a love story, where the devotion of a mortal woman redeems and saves the heart of a god.
This is not your European mythological landscape, after all. And the Xilbalba of Gods of Jade and Shadow is not even slightly defanged — it is a place of blood sacrifice, hungry ghosts, despair and confusion. Hun-Kamé is merciless, as death is; his twin, Vucub-Kamé, is both merciless and cruel. (Vucub-Kamé's cooption of the will, desires, and eventually body of Casiopeia's unpleasant cousin Martín is one of the more disturbing threads woven through the novel. His plans to reinstitute human sacrifice across the Mesoamerican peninsula are actually less upsetting in comparison.)
Moreno-Garcia's book is a dispatch from a universe where indigenous American legends have always been part of the lexicon of fantasy. That universe gets closer to being ours every day, and we are better for it.
At the end of a quest, or a fairytale, the hero must make a choice: usually selfishness or selflessness, safety and power or love. Casiopeia, even before she experiences the emotional and physical excoriation of walking the Black Road through Xilbaba for Hun-Kamé's sake, has already made her choice. Confronted with the option of either having a version of Hun-Kamé who has come to love her, or losing him entirely in exchange for both keeping her promises to him and freeing herself, her cousin, and possibly all of Mexico from Vucub-Kamé's plans, she chooses like a hero, like an adult. Like a woman who sees a future for herself that she might build even beyond the first flush of love and freedom.
Gods of Jade and Shadow does not offer easy or simple answers. It dazzles, instead, showing the reader a world that seems entirely inevitable, a Mexico of the 1920s that would naturally be infused with Precolumbian magic — a magic which evolves and changes with colonization and modernity, and is as current, vital, and strange as any more expected mythological underpinning for a story about figuring out how to be a woman, a free spirit, and an ethical person in a rapidly changing world. It is effervescent and surprising. Like Rebecca Roanhorse's Navajo-based Sixth World fantasy series (the most recent of which is Storm of Locusts), Moreno-Garcia's book is a dispatch from a universe where indigenous American legends have always been part of the lexicon of fantasy. That universe gets closer to being ours every day, and we are better for it.
Arkady Martine is a speculative fiction writer, a Byzantinist, and a city planner — the latter two as Dr. AnnaLinden Weller. She tweets @ArkadyMartine.


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Ask DMU
Staggering Suicide Statistics
Suicide is not a topic we all like to talk about. But recent incidents have brought more attention to this unfortunate event that's often linked to severe depression. At Divine Mercy University, we strive to educate our students and the general public of ways to prevent suicide and provide adequate mental health services. Recently, we hosted an on-campus lecture entitled "How to Understand Suicide and its Aftermath: From a Scientific & Faith Perspective," presented by Melinda Moore, Ph.D., a Licensed Psychologist and Assistant Professor in the Department of Psychology at Eastern Kentucky University. Her interest in Posttraumatic Growth emerged from her own experience with suicide and the changes that experience created within her allowing for her current career path and personal interests and relationships. Watch the recording of the suicide lecture to learn how a faith-based approach to mental disorders can help save lives. We also wanted to share suicide prevention resources with you, in the case that you or someone you know may need help:
Crisis Text Line: Text HOME to 741741
In our psychology and counseling programs, we teach students how to act effectively in situations where de-escalation, negotiation, and crisis intervention are needed, such as suicide attempts. The courses also train students on the best ways to diagnose and treat common psychological problems to prevent severe disorders from developing. Sign up to learn more.
My School Bus Rode Past a Suicide Scene
This blog post was written by Ebony Shamberger, a marketing associate at Divine Mercy University. I remember the day like it was yesterday. I was on the school bus nodding off to sleep, trying to play catch up from studying the night before, when the bus made a sudden stop. The jolt of the bus woke me up as my peers started complaining about being late to school. (As if the good ol' cafeteria food would hit the spot). "What is going on? Why did she just stop like that?" said a high school girl. From the front of the bus, we could hear the driver talking on the two-way radio. "I can't drive them through this. What am I supposed to do?" she said nervously. I couldn't make out what was said on the other end, but all of a sudden the driver stood up and commanded everyone to close their eyes. All I could think was – what is the big deal? Is she afraid to drive us to school all of a sudden after having been on our route for nearly half the school year? So many thoughts and questions crossed my mind. "Do you see that? There's a body hanging from the playground," someone yelled from the front-end of the bus. I eased up from my seat to look out the window. And all I could see was a light shining on what looked like the shadow of a teenage body that dangled from the monkey bars. It wasn't even 7am and I already felt like I had knots in my stomach, which didn't usually come until after lunchtime from the greasy fries I just had to have. The darkness of the early morning didn't make the situation any less terrifying as we slowly rode past the neighborhood playground that was now a crime scene. That was the first time I witnessed the fatality of a mental health illness and I didn't even know. It wouldn't be until I worked for Divine Mercy University that I would realize that at a young age my very own peers were dealing with issues that they didn't think they'd be able to live with. So they'd take their own life not to bear the burden of bullying, peer pressure, addiction and so many other psychological detriments. If only someone was able to recognize that this young person was displaying suicidal behaviors and was able to guide her to a counselor or psychologist. If only she was told that her inherit nature as a human being, seen in the likeness of God, was enough to keep her on Earth a little longer. Despite all the "if onlys," "shouldas," "couldas," and "wouldas," there's still a chance that people, with their innate human kindness and caring heart, can save the next person from a premature death and learn how to cope with everyday challenges. It could be as simple as directing them to the National Suicide Prevention Lifeline (1-800-273-8255) or gaining skills to become a mental health professional. Regardless, of how you'd like to help save the next life on the path of destruction, just remember, every life is worth living. And, just knowing that a parent, friend or love one has to find their child hanging from monkey bars, overdosed on opioids or leaving a note behind after imitating "13 Reasons Why," is reason enough to become a vessel of healing for those suffering in the world. Learn how you can become a mental health professional today.
About DMU
Divine Mercy University (DMU) is a Catholic graduate university of psychology and counseling programs. It was founded in 1999 as the Institute for the Psychological Sciences. The university offers a Master of Science (M.S.) in Psychology, Master of Science (M.S.) in Counseling, Doctor of Psychology (Psy.D.) in Clinical Psychology, and Certificate Programs.
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Divine Mercy University is accredited by the Southern Association of Colleges and Schools Commission on Colleges (SACSCOC) to award masters and doctorate degrees. Questions about the accreditation of Divine Mercy University may be directed in writing to the Southern Association of Colleges and Schools Commission on Colleges at 1866 Southern Lane, Decatur, GA 30033-4097, by calling (404) 679-4500, or by using information available on SACSCOC's website at https://www.sacscoc.org.