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Why Are Bananas, Nuts, and Crackers the Only Foods That Say 'Crazy'?
An investigation into how three snacks became associated with madness.
by Dan Nosowitz April 13, 2018
Why Are Bananas, Nuts, and Crackers the Only Foods That Say 'Crazy'?
That's one cracked nut. christina_pauchi [Edited]/Deposit Photos
There is an episode from the 1972 first season of the television show M*A*S*H titled "Bananas, Crackers, and Nuts." In it, Hawkeye decides to secure a rest and recuperation break from the war by faking insanity, which he does by, among other things, pretending to be in love with another man. (It's not a good episode in terms of social awareness.) The three foodstuffs in the episode's title are the only three in American English that can also mean "crazy."
It's worth noting that in this article—as in the M*A*S*H episode—we will not be very specific in defining the word "crazy," largely because the terms we're looking at here are not in themselves specific. Calling someone "nuts" isn't exactly a diagnosis. We're also not really examining the history of the way people talk about mental illness. What we're doing is looking at a linguistic blip: How did three, and only three, food-related terms become shorthand for mental illness?
There are reasons, or at least guesses, for the winding path these three terms took. But their etymologies are not related, and show just how weird and broken and non-systematic language can be. To put it in another, definitely worse way: What if….it's language itself….that is bananas, crackers, and/or nuts?
B-A-N-A-N-A-S. Mike Dorner/Public Domain
Let's get started with "banana." The earliest records of the banana plant come from Southeast Asia and Papua New Guinea, but the word probably comes from the West African language Wolof; bananas have been grown in West Africa for thousands of years. The fruit was first brought to the New World in 1516, by Portuguese sailors, where it became widely grown throughout the tropics.
There are a few ideas about how the word banana, and the phrase "go bananas," became a way to indicate craziness. More specifically, though, to go bananas means to lose control; it is a temporary insanity, one that usually has a known cause. You are not born having gone bananas.
The Routledge Dictionary of Modern American Slang and Unconventional English traces the idea of bananas relating to craziness only back to the late 1910s; The Concise New Partridge Dictionary of Slang and Unconventional English roughly agrees, with its own etymology going back to 1924. These sources claim that the crazy banana meaning comes from the phrase "banana oil," which, in flapper slang, meant "nonsense."
Typically, the substance referred to as banana oil is amyl acetate, which is, insanely, used as both a paint solvent and as a flavoring. (It smells strongly, but not precisely, of bananas, which is partly why banana-flavored candies are distinct but not really banana-flavored.) Why did flappers like to use the phrase "banana oil" to mean "nonsense"? Possibly it's related to "snake oil," but I suspect it's also because the word "banana," coming from a language that has not given English very many words, sounds unusual to the ears of English speakers.
In any case, use of the phrase "banana oil" died out for a few decades. But by the early 1960s, using the word "bananas" for something crazy had come back. A 1957 Li'l Abner cartoon used the phrase in roughly the modern way, and it soon caught on in counterculture language. (Tom Wolfe used it a few times.)
An oft-cited alternate explanation is that, when monkeys are presented with a bunch of bananas, they will go crazy in anticipation. Studies indicate that captive primates do like bananas, but not notably more than other fruits; a 1936 study found that the tested monkeys preferred grapes. In the U.S. and Western Europe, both bananas and monkeys are associated with the tropics, and thus with each other; it's likely that the tighter association came from the initial publishing of the Curious George books in the 1940s. In any case I don't really buy it; monkeys are associated with bananas, sure, but in sort of a cute, fun way, not in a way that lends itself to the word "bananas" meaning a lack of self-control. Going bananas is neither cute nor fun.
Absolutely nuts. AntonMatyukha [Edited]/Deposit Photos
The word "nut" is a complete mess; there are several times more definitions of the word than there are letters in it. Here's just a short list of those. A nut can be:
A crazy person.
A hard-shelled fruit-and-seed combo.
A category of various seeds and drupes which are not technically nuts as seen in Definition Number 2.
A testicle.
A piece of metal with a hole in it which is screwed onto a bolt.
Semen (as a noun) or to ejaculate (as a verb).
An enthusiast of something.
A person's physical head.
A person's metaphorical head, or mental state.
A sum of money required to set up a business.
An exclamation roughly equivalent to "darn it!" (Plural only, for this one.)
There are even more than that! (Apparently there's something called a "nut flush" in poker.) In any case, the word "nut" has to be in the running for most possible definitions of a single word in the entire English language.
Several of these definitions come back to the physical description of the botanical nut: a hard, vaguely roundish outer shell with something valuable and/or delicious inside. In this way it's pretty obvious how the word "nut" could be applied to the human skull. To be "nuts about" someone, or something, means that thoughts about that person are thoroughly embedded in your head. That definition dates back, according to some sources, as early as 1785.
Coming later is the idea of nuts as crazy; that use was first seen in 1908, in a newspaper comic strip called Mutt and Jeff. To be "off one's nut" meant to be separated from your head, and thus your senses. That eventually was shortened to the current use, in which someone can simply be "nuts."
Crack-ers. olhaafanasieva/Deposit Photos
The word "cracker," or "crackers," has significantly different definitions depending on which national form of English you speak. For North Americans, as a food, it is a hard, flat, savory baked good. In the U.S., it's also a derogatory word for poor white people, albeit sort of outdated. In the U.K., a cracker is a noisemaking paper cylinder most often seen at Christmas—Americans do not really have this—or a good example of something, as in "that's a cracker of a pudding." And of course no matter where you are, something can be cracked, meaning slightly but not completely broken.
The U.K. also has the option to "drive someone crackers," which is pretty similar in meaning to going bananas, or driving him nuts. It was first seen in soldier reports from World War I, but it's sort of hard to figure out whether these early uses were using the word to mean "crazy." The word is sometimes used to describe things that are loud; think of firecrackers. It's also used to mean "break into," coming from that idea of something that is slightly broken—just broken enough to grant access. You'll see that usage in the word "safecracker."
In any case, it's most likely that the word derived from a peculiar mutation within British English which is commonly associated with public schools. In some instances, nouns and adjectives can be made informal with the addition of the ending -er or -ers. Rugby, or a person who plays rugby, can be altered to "rugger." Instead of being pregnant, you can be "preggers," and instead of eating breakfast, you can eat "brekkers."
I think it's most likely that "crackers" came from this change; the word "cracked," before that point, had been used to indicate craziness. Cracked, in most senses, means appearing almost whole, but in fact being broken. Until very recently—and, in many cases, still today—this was a pretty common understanding of mental illness, if a wildly incorrect and insensitive one. "Unbalanced," "troubled," "disturbed," these are all essentially ways of saying that something is wrong. Cracked, too. It's not a tremendously helpful way of understanding mental illness, as a society, but it is pervasive.
That means, funnily enough, that "driving someone crackers" does not actually have anything to do with the food known as a cracker. Which makes sense! In the U.K., after all, it's called a biscuit.
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Douglaston sells Edge retail space to D.C.-based firm for $40M
Jan.January 06, 2014 01:13 PM
The spacious retail spread at the base of the Edge condominium in Williamsburg will be sold for more than $40 million.
Madison Marquette, a Washington, D.C.-based real estate investment firm, is acquiring the 60,000-square-foot space, Crain's reported. Located west of Kent Avenue at 22 North 6th Street, the retail condo has frontage on both Kent Avenue and North Sixth Street and is already leased to tenants that include CVS, Brooklyn Bodyburn gym, restaurant Fabrica, a bike store, liquor store and preschool.
Jeff Levine, chief executive of the Edge builder Douglaston Development, could not be reached by Crain's for comment. Last year, he told the outlet that he had received "a number of interesting bids" for the retail space.
The purchase marks the latest in Madison Marquette's recent foray into the New York City market. The company paid nearly $85 million for the Center Building, at 33-00 Northern Boulevard in Long Island City, in late 2012.
Crain's was not immediately able to reach Madison Marquette executives for comment. [Crain's] — Julie Strickland
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Yvonne Patterson
August 6, 1934 - October 22, 2021
Yvonne Patterson, age 87, of Rockwall, TX, passed away on October 22, 2021. She was born August 6, 1934, in Paw Creek, NC, to Clarence Mundy and Ada (Perkins) Mundy. Yvonne was a member of Lakepointe Church in Rockwall. Yvonne is survived by her husband of 68 years, Aubrey Q. Patterson; children: Tim Patterson and his wife Janet, Barry Patterson and Greg Raynes, Sheron Tolle and husband Stuart, and Kristi Routen and husband Dan; grandchildren: Matthew Patterson and wife Lyndsey, Jake Patterson and fiancé Katalina Benecke, Emily Tolle, Libby Tolle, Evan Tolle, Conner Routen, and Carson Routen; and sisters: Patsy Bird, and Glenda Diaz and husband Val. She was preceded in death by her parents, brother, and 5 sisters. Yvonne grew up in Charlotte NC, she was one of 9 children. She had 7 sisters and 1 brother. Yvonne had a long career as a Legal Secretary for various law firms in Dallas, Texas. She was a very talented person who could create beauty from anything she touched. She especially enjoyed sewing, painting, gardening, playing the piano, and cooking for her family and friends. After she retired, she became a bear artist making beautiful jointed teddy bears. Her 7 grandchildren were her pride and joy. She and Aubrey were a constant presence at ballgames, recitals, and plays. She was an inspiration to her children and grandchildren who will always be grateful for her constant love and support throughout the years. Funeral services will be held 3:30 pm Friday, October 29, 2021, at Reflections at Rest Haven Funeral Home-Rockwall Location. Interment will follow in Rest Haven Memorial Park. The service will also be live-streamed; please go to www.oneroomstreaming.com and click on the "watch your service" icon and use Event ID: resthavenrockwall and password: N5FUHA
Yvonne Patterson, age 87, of Rockwall, TX, passed away on October 22, 2021. She was born August 6, 1934, in Paw Creek, NC, to Clarence Mundy and Ada (Perkins) Mundy. Yvonne was a member of Lakepointe Church in Rockwall. Yvonne is survived... View Obituary & Service Information
The family of Yvonne Patterson created this Life Tributes page to make it easy to share your memories.
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Ferrari is in ruins - Italian media react to Suzuka
09:53 Tuesday 9 October 2018 by
Martin Macdonald
Lewis Hamilton extended his lead in the 2018 Formula 1 drivers' championship to 67 points ahead of Sebastian Vettel following his comfortable win at the Japanese Grand Prix on Sunday, and with Ferrari once again disappointing, the Italian sports media have not been shy with their criticism.
The pressure was already on for Ferrari heading into Suzuka, as they trailed Mercedes in both the drivers' and constructors' championships, and with Vettel losing ground quickly following a clash with Max Verstappen, the Silver Arrows cruised to victory via Hamilton.
Article continues under video
The Italian sports media have been scathing in their criticism of their home outfit, as well as Vettel.
"Ferrari is in ruins," La Gazzetta dello Sport wrote after the Japanese GP.
"There are strategists who make mistakes, a weak driver who learns nothing from mistakes, a team boss who attacks his team, and a car in decline. Before Monza, you could hardly have imagined such a collapse."
For most of the other outlets, Vettel was the target of their complaints, saying he makes too many mistakes.
"The German adds to his collection of horror mistakes by destroying a fantastic start," Corriere della Sera wrote in reference to the collision with Verstappen.
"These mistakes are an expression of a deep unrest within the four time champion, who is experiencing a crisis of confidence."
La Repubblica agreed, saying:
"While Hamilton reaches for Fangio's record, Ferrari's season fails," it said.
"Vettel chose the worst moment to lose and Ferrari breaks up under team boss Maurizio Arrivabene, who criticises his own people."
Meanwhile, La Stampa believes that the German is a driver no longer capable of making the correct decisions.
"Maybe it's bad luck, but it's also a fact that Sebastian Vettel no longer does anything right," they said.
MORE: Vettel responds to Ferrari quit questions
MORE: Vettel wants Verstappen face-to-face after Suzuka crash
GP fans
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.
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The tally is now at eight scholarship players who have defected from Iowa's program since a historic 12-2 season.
The tally is now eight scholarship football players who have defected from the Iowa program since the historic 2015 season — almost 10 percent of the NCAA-allowed 85 full rides.
Lance Billings became the latest to leave, with that news surfacing Wednesday.
Rivals.com's Blair Sanderson reported that Billings, an incoming freshman in the 2016 class who signed in February, has gone back to Ohio and will not enroll at Iowa.
In a perfect football world, every player who accepts a scholarship offer would turn into a dynamic on-field performer or at least an inspiring teammate.
But expecting perfection among human beings isn't realistic.
Some guys get homesick. Some have a tough time in the classroom. Some see too steep a climb to playing time — that's what happened with Maurice Fleming, who decided after King returned that he would play his fifth year at West Virginia.
The reasons vary. One Hawkeye, Omar Truitt, left to pursue a music career.
A big part of what I think is going on can be gleaned from this year's team book, "Legacy," which I wrote about earlier this summer. The book gets inside the culture of the world's most successful rugby team, the All Blacks of New Zealand.
One important section of the book (the title of which isn't safe for publication) talks about players setting high standards for themselves to ensure that everyone is all-in with a team-first, me-last mentality.
The point is, going in one direction is all-important to earning and keeping one of Kirk Ferentz's 85 scholarships. That's part of what makes Iowa Walk-On U. — where this year's projected starting left tackle (Cole Croston) and left guard (Boone Myers) once paid their own tuition, room and board.
Among the eight departures, only Fleming was in Iowa's pre-spring two-deep. The others would've been lucky to get special-teams work in 2016 — Billings, Truitt, running back Eric Graham, wide receiver Andre Harris, defensive end Terrence Harris, linebacker Justin Jinning and tight end Jameer Outsey.
Suddenly, the 2017 recruiting class projected to be about 16-17 deep could rise to 21-22. Another defensive back opening, for example, certainly won't hurt the push to attract Kobe Boyce, a Texas commitment who was in Iowa City last weekend and is taking a hard look at the Hawkeyes.
Attrition happens. Losing eight in a year is high. But until big-time signees or starters start jumping ship, there's no systemic concern.
Frankly, in the context of a 12-2 season and the recent recruiting surge, this could be a case of strengthening the core 85 ... from the inside.


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Axiomatická teorie množin je označení pro teorii, která formalizuje vlastnosti množin takovým způsobem, aby bylo možné pomocí množin zkonstruovat všechny matematické objekty, takže dokazatelná tvrzení této teorie budou přesně odpovídat všem platným matematickým výsledkům ze všech oblastí matematiky (algebra, diferenciální rovnice, geometrie, teorie pravděpodobnosti i všechny ostatní).

Hlavní význam takových teorií je v tom, že staví na velmi solidní základ pojem "dokazatelné matematické tvrzení" a tedy poskytují užitečné vodítko při ověřování, zda nějaký matematický důkaz je korektní.

Nejpoužívanější axiomatická teorie množin je jednak Zermelova-Fraenkelova teorie množin (značení ZF) a dále ZF s přidaným axiomem výběru (ta se značí ZF+AC nebo ZFC). ZFC je všeobecně uznávána jako teorie, která přesně popisuje platné matematické pravdy, tj. matematická věta je pokládána za pravdivou, právě když je dokazatelná v ZFC (dokazatelnost ovšem nelze snadno ověřit, neboť v každém okamžiku existuje mnoho pravdivých hypotéz, které ještě nebyly dokázány nebo ani vysloveny).

Aplikace Gödelových vět o neúplnosti na axiomatickou teorii množin přináší vhledy na podstatu a filosofii matematiky, neboť z ní vyplývá, že sebelepší axiomatika teorie množin bude vždy obsahovat nerozhodnutelná tvrzení (množinu všech matematických pravd nelze popsat žádnou soustavou axiomů) a že pokud teorie, kterou chceme používat k popisu všech matematických pravd, je bezesporná, nelze tuto bezespornost dokázat.

Důvod vzniku
K převážné většině matematických konstrukcí (včetně pokročilých, jako je úplný obal metrického prostoru) stačí intuitivní (naivní) teorie množin, v níž intuitivně pracujeme s množinami jako se souhrny objektů. Tento přístup však vede k rozporům, pokud pracujeme s "příliš velkými" množinami (nejznámější z těchto sporů je Russelův paradox). Vzato do důsledků, naivní teorie množin je sporná a proto v ní lze dokázat cokoli (např. že 1+1=42).

V reakci na tyto rozpory vznikla axiomatická teorie množin, která staví dokazatelnost matematických pravd na pevný základ. Její hlavní přednosti oproti naivní teorii jsou tyto:

1. Neumožňuje Russelův paradox (a další paradoxy naivní teorie množin) tím, že velké souhrny objektů (například "souhrn všech množin") v ní nejsou pokládány za množiny, nýbrž jsou nazývány vlastními třídami a pracuje se s nimi jinak.

2. Nepředpokládá nic kromě přesně vyjmenovaných axiomů (odtud název "axiomatická"). Ani tak samozřejmé skutečnosti, jako že existuje prázdná množina (nebo že k množinám a, b existuje i množina {a,b}) není dovoleno předpokládat, dokud to není dokázáno z axiomů anebo samo není axiomem.

Predikátová logika dává návod, jak prohledáváním nekonečného stromu ověřit dokazatelnost tvrzení z dané množiny axiomů. Existence soustavy axiomů, z nichž plyne každé matematické tvrzení, tedy umožňuje algoritmicky rozhodnout o pravdivosti jakékoli matematické hypotézy (tento algoritmus se nezastaví, pokud je tato hypotéza nerozhodnutelná z axiómů ZFC). To je sice v praxi nepoužitelné, protože počet větví stromu je astronomicky velký, ale přesto je ZFC užitečným vodítkem při diskuzi, zda nějaký argument lze nazvat platným matematickým důkazem.

Proč množiny?
Při konstrukci teorie, která má obsáhnout celou matematiku, není možné do ní přidat všechny druhy objektů – například přidat predikát "tento objekt univerza je přirozené číslo" (podobně, jako GB má predikát "tento objekt je množina") a vložit axiomy, které chování přirozených čísel popisují (např. Peanovy axiomy).

Při takovém přístupu by se množina predikátů a axiomů neustále rozrůstala, například po objevení komplexních čísel, hyperkomplexních čísel apod. S každým rozšířením by se musely znovu dokazovat výsledky o teorii dokázané (například to, že nějaké tvrzení je v této teorii nezávislé).

Proto je zvolen opačný přístup: axiomy popisují vlastnosti skupiny co nejjednodušších objektů, které stačí ke zkonstruování celé matematiky. Ukázalo se, že k tomuto účelu nejlépe slouží množiny; z těch lze zkonstruovat přirozená čísla, reálná čísla, funkce, přímky, topologické prostory atd.

Konstrukce objektů
Jelikož cílem ZF je popsat jedinou soustavou axiomů celou matematiku, není možné postupovat tak, že zavedeme pojem např. "přirozené číslo" a vložíme axiomy o tom, jaké vlastnosti přirozená čísla mají. V takovém případě bychom museli rozšířit množinu axiomů pokaždé, když je v matematice objeven další důležitý pojem (reálné číslo, funkcionál, kategorie...)

Proto ZF vychází z předpokladu, že všechny matematické objekty jsou množiny, a její axiomy poskytují možnost z množin konstruovat množiny složitější. Prvek množin tedy mohou být opět jen množiny.

Matematické objekty, se kterými chceme pracovat, pak ztotožníme s vhodnými množinami – víme, jaké vlastnosti očekáváme od přirozených čísel (například že ke každému číslu existuje číslo o jedničku větší), a proto zvolíme množiny, které odpovídající vlastnost mají.

Uspořádané dvojice
Symbol (a, b) pokládáme za zkratku pro {{a}, {a, b}} .Tato definice splňuje základní vlastnost, kterou od uspořádaných dvojic čekáme:
(a, b) = (c, d) právě když a = c a zároveň b = d.

Přirozená čísla
 Číslo 0 ztotožníme s prázdnou množinou
 Číslo 1 ztotožníme s množinou
 Číslo 2 ztotožníme s množinou
 Číslo 3 ztotožníme s množinou
 Obecně

Formálně: Množinu přirozených čísel definujeme jako průnik všech množin, které obsahují prázdnou množinu a s každým svým prvkem  obsahují i množinu .

Množinu přirozených čísel (včetně nuly) značíme .

Celá čísla

Máme-li definovaná přirozená čísla, pak by se mohlo zdát přirozené reprezentovat záporné číslo  jako . To však nelze, protože pro některá přirozená čísla  by mohlo platit .

Je však možné reprezentovat přirozená čísla (pro ) jako  a záporná čísla  (pro ) jako . Tato definice se nepoužívá, protože by definice sčítání, násobení apod. byla složitější, než u definice následující:

Idea je reprezentovat celé číslo  nekonečnou množinou takových dvojic , že  jsou přirozená čísla splňující . Například

Formálně: Množina celých čísel je definována jako rozklad (tedy množina všech tříd ekvivalence) kartézského součinu  x  podle ekvivalence:
 ~  právě když .

Máme-li definované sčítání a násobení pro přirozená čísla, definujeme je pro celá čísla takto: vyberme libovolný prvek (tzv. reprezentant)  a  čísel, které chceme sečíst. Výsledkem bude třída ekvivalence, která obsahuje dvojici  (tato třída nezávisí na volbě reprezentantů):
 Pro sčítání:
 Pro násobení:
Vzoreček pro násobení lze snadno odvodit roznásobením vztahu

Podobně se postupuje i u dalších matematických operací.

Za pozornost stojí i skutečnost, že totéž číslo (například 2) je reprezentováno jinak jako přirozené číslo než jako celé číslo. Množina přirozených čísel tedy formálně není podmnožinou množiny celých čísel. S podobným jevem se v teorii množin setkáváme velmi často; tento přístup je volen proto, abychom nemuseli změnit reprezentaci množiny, pokud konstruujeme její rozšíření – například kdyby komplexní čísla a kvaterniony (což jsou oboje rozšíření reálných čísel) byly objeveny až poté, co byla ustálena konvence, jak reálná čísla v teorii množin reprezentovat.

Racionální čísla
Každé racionální číslo lze zapsat nekonečně mnoha způsoby jako zlomek, např.:
 3/2 = 6/4 = 300 / 200 = -300 / -200.

Racionální číslo budeme tedy reprezentovat množinou všech takovýchto dvojic .

Formálně: Množina racionálních čísel je definována jako rozklad (tedy množina všech tříd ekvivalence) množiny

podle ekvivalence

 ~  právě když .

V této definici  značí množinu celých čísel definovanou výše a zápis  se týká nuly jako celého čísla, což je formálně jiný objekt, než nula jako přirozené číslo.

Definice sčítání, násobení apod. odvodíme podobným způsobem jako u celých čísel.

Reálná čísla
Reálná čísla je možno definovat několika způsoby, například ztotožnit jejich množinu s množinou všech Dedekindových řezů.

Gödelovy věty a nedokazatelná tvrzení
Gödelovy věty o neúplnosti říkají, že je-li nějaká predikátová teorie bezesporná, rekurzivně axiomatizovatelná a dokazuje základní aritmetické pravdy, pak není úplná a neumí dokázat svoji bezespornost.

V každé teorii, kterou chceme pokládat za popis všech matematických pravd, musí být dokazatelné základní aritmetické pravdy a měl by existovat algoritmus, kterým ověříme, zda dané tvrzení je axiomem; bez takového algoritmu je teorie nepoužitelná k praktickým účelům.

Z toho plyne, že je-li tato teorie bezesporná, pak pro ni platí obě Gödelovy věty o neúplnosti a její bezespornost není nikdy možné dokázat. V její bezespornost matematická komunita pevně věří, protože spor nebyl objeven přes téměř celé století, kdy je tato teorie používána. Pro ZFC, která je běžně přijímána jako popis všech matematických pravd, jsou tedy dvě možnosti:

 ZFC je bezesporná, potom nikdy nebude objeven důkaz sporu i důkaz bezespornosti.
 ZFC je sporná; pokud bude objeven důkaz její bezespornosti, Gödelova druhá věta o neúplnosti dá návod, jak zkonstruovat důkaz sporu.

Dopad na filosofii matematiky

Výše uvedené úvahy nevyužívaly specifické vlastnosti ZFC. Platí o každé rekurzívně spočetné teorii, kterou přijímáme jako popis všech matematických pravd a která umí dokázat základní pravdy aritmetiky (poslední podmínka v zásadě plyne z předposlední).

Z toho plyne, že výše uvedené "vady" ZFC (její neúplnost a nemožnost ověřit její bezespornost) nelze napravit vhodnější volbou jejích axiomů; není tedy možný Hilbertův program. Matematické pravdy tedy nikdy nebudou plně popsány soustavou axiómů.

Bezespornost ZFC je možno snadno dokázat v nějaké silnější teorii (např. Kelleyova-Morseova teorie s axiómem výběru), ovšem to nemá žádnou váhu pro ověření, že je skutečně bezesporná. Kdybychom si byli jisti bezesporností KM+AC, nemuseli bychom ověřovat bezespornost ZFC, která z ní plyne. A pokud si nejsme jisti ani bezesporností KM+AC, tím méně můžeme spoléhat, že každé tvrzení v ní dokazatelné je pravdivé (což je podstatně silnější tvrzení: například PA s přidaným axiomem "PA je sporná" je bezespornou teorií).

Nerozhodnutelná tvrzení v teorii množin mají nejen akademický význam, ale týkají se i "praktičtějších" oblastí matematiky, jako je Matematická analýza (příkladem je Hypotéza kontinua). Bez axiomu výběru je nerozhodnutelná i řada zcela fundamentální faktů pro práci v matematice, například zda je každá funkce Lebesgueovsky integrovatelná a zda je kartézský součin neprázdných množin vždy neprázdný.

Historie

Axiomatická teorie množin se vyvinula během dvacátého století z naivní teorie množin, kterou zavedli Georg Cantor a další.

Naivní teorie množin
Naivní teorie množin vznikla z nutnosti popsat objekty, se kterými pracovala matematická analýza i v jiných matematických disciplínách.

Prvním vážným pokusem o přesný popis těchto objektů byla práce Bernarda Bolzana, jenž zavedl pojem množina a zkoumal vlastnosti nekonečných množin. Na toto téma napsal knihu Paradoxy nekonečna (Paradoxien des Unendlichen), která byla vydána až po jeho smrti.

Opravdovým zakladatelem teorie množin je Georg Cantor, který zavedl pojmy jako potenční množina, ordinál či kardinál. Též dokázal existenci nespočetných množin. K tomu použil zcela nový důkazní prostředek, dnes nazývaný Cantorova diagonální metoda. Později dokázal takzvanou Cantorovu větu tvrdící, že ke každé množině existuje množina o větší mohutnosti – její potenční množina. Používal tuto definici množiny: "Množinou A rozumíme souhrn určitých a rozlišitelných objektů x existujících v naší mysli. Těmto objektům říkáme prvky množiny A.". Tato teorie dosáhla vynikajících výsledků, avšak na přelomu devatenáctého a dvacátého století se v ní objevili antinomie (takzvané paradoxy naivní teorie množin; viz níže).

Paradoxy naivní teorie množin a počátky axiomatické teorie množin

Na přelomu 19. a 20. století byly v naivní teorii množin objeveny antinomie (takzvané paradoxy naivní teorie množin). První se týkaly pouze velmi velkých souborů, jako je množina všech ordinálních čísel (Burali-Fortiho paradox) anebo množina všech množin (Cantorův paradox). Těmto antinomiím se nepřikládal velký význam, neboť se předpokládalo, že zpřesněním práce s tak velkými soubory se odstraní.

Opravdovým problémem se ukázal Russellův paradox, týkající se množiny, která je definována jednoduchou formulí. Russellův paradox se dá popsat takto: "Mějme množinu  všech množin, které nejsou prvky samy sebe. Je tato množina svým prvkem? Obě možné odpovědi vedou ihned ke sporu.

V následujících letech se objevilo ještě několik obdobných problémů; například Richardův paradox týkající se diagonální metody a sémantiky obecného jazyka.

 Počátky axiomatické teorie množin
V roce 1908 Ernst Zermelo v článku Untersuchungen über die Grundlagen der Mengenlehre (česky: Zkoumání základů teorie množin) popsal teorii množin s axiomem extenzionality, axiom dvojice, axiom potenční množiny, axiom sumy, axiom nekonečna, axiom výběru a schéma axiomů vydělení. V roce 1917 Dmitrij Mirimanov schéma axiomů vydělení nahradil obecnějším schématem axiomů nahrazení.

 Jednotlivé systémy
Existuje několik různých systémů axiomatizace teorie množin s různou silou a výsledky. Zde je uvedena jen část z nich.

 Zermelova-Fraenkelova teorie množin

Zermelova-Fraenkelova teorie množin je dnes nejužívanější ze systémů axiomatické teorie množin, která je sama o sobě nebo v některých mírných modifikacích (zejména s přidaným axiomem výběru) používána jako základ pro většinu dalších odvětví matematiky včetně algebry a matematické analýzy. Tento systém nedefinuje třídy, ty jsou jen součástí metajazyka.

Mezi tvrzení nerozhodnutelná v této teorii patří například axiom výběru, hypotéza kontinua, Axiom konstruovatelnosti a Suslinova hypotéza. Všechny výsledky tohoto druhu (že něco nejde z axiomů ZFC dokázat) jsou ovšem formulovány s podmínkou "Pokud je ZFC bezesporná", neboť její bezespornost nelze ověřit.

Je založena na těchto axiomech:
 Axiom extenzionality: Množiny, které mají stejné prvky, se rovnají.
 Schéma axiomů nahrazení: Je-li F(x,y) formule jazyka teorie množin v proměnných x,y, která je navíc zobrazením (tj. pokud F(x,y) a F(x,z), pak y = z) pak každý výrok Pro každou množinu a existuje množina b obsahující právě všechny obrazy prvků množiny a v zobrazení F(x,y)  je axiomem ZF.
 Axiom dvojice: Pro každé dvě množiny a,b existuje množina c obsahující právě tyto dvě množiny.
 Axiom sumy: Pro každou množinu a existuje množina b, která obsahuje právě všechny prvky prvků množiny a.
 Axiom potenční množiny: Pro každou množinu a existuje množina b, která obsahuje právě všechny podmnožiny množiny a.
 Axiom nekonečna:
 Axiom fundovanosti:

 Zermelova-Fraenkelova teorie množin s axiomem výběru

Zkratkou ZFC je označována axiomatická soustava teorie množin, kterou tvoří axiomy Zermelo-Fraeneklovy teorie množin a axiom výběru (zkratka AC – z anglického axiom of choice'').
 Axiom výběru: Na každé množině existuje selektor.

Von Neumannova-Bernaysova-Gödelova teorie množin

Von Neumannova-Bernaysova-Gödelova teorie množin (NBG, též (Von Neumannova)-Gödelova-Bernaysova teorie množin, NGB, GB) se z hlediska své síly příliš neliší od ZF či ZFC – libovolný výrok o množinách je v NBG dokazatelný tehdy a jen tehdy, pokud je dokazatelný v ZF – mluvíme tedy o teorii NBG jako o konzervativním rozšíření teorie ZF (říkáme také, že NBG a ZF jsou ekvikonzistentní). Rozdíl mezi oběma teoriemi spočívá v použitém jazyku a v počtu axiomů. NBG jich má konečný počet díky použití vlastních tříd.

Na rozdíl od ZFC, jejímž objektem jsou pouze množiny, zatímco třídy tvoří pomocný konstrukt na úrovni metajazyka, v NBG jsou množiny i třídy objektem teorie množin – na množiny jsou však kladena (jejich definicí) určitá omezení – jednoduše řečeno množiny jsou právě ty objekty, které jsou prvkem jiného objektu:
 .
Někdy se k axiomům NBG přidává ještě takzvaný axiom výběru či silný axiom výběru. Výsledná teorie se pak značí NBG+AS.

Na rozdíl od ZF neobsahuje (právě díky zavedení tříd jako součásti jazyka teorie množin) NBG nekonečný počet axiomů – nemusí si totiž vypomáhat axiomatickými schématy typu schématu axiomů nahrazení nebo schématu axiomů vydělení.

Je založena na těchto axiomech (malá písmena značí množinové proměnné a velká písmena obecné (třídové) proměnné):
 axiom definice množiny:
 axiom existence množiny:
 axiom extenzionality pro třídy:
 schéma existence tříd:  kde  je formule v níž jsou kvantifikovány pouze množinové proměnné
 axiom dvojice:
 axiom nahrazení:

Kelleyova-Morseova teorie množin

Kelleyova-Morseova teorie množin (označovaná též KM) je teorie silnější než jsou klasické axiomatizace Zermelova-Fraenkelova (ZF) a Von Neumannova-Gödelova-Bernaysova (NGB). V KM je dokazatelná (formální) konzistence ZF.

Axiomatizace KM je velmi podobná axiomatizaci GB, liší se pouze ve schématu existence tříd, kde (na rozdíl od GB) připouští existenci třídy odpovídající libovolné formuli. Tato zdánlivě drobná odlišnost je však příčinou toho, že KM je nesrovnatelně silnější teorií než GB i ZF.

Je založena na těchto axiomech (malá písmena značí množinové proměnné a velká písmena obecné (třídové) proměnné):
 axiom definice množiny:
 axiom existence množiny:
 axiom extenzionality pro třídy:
 schéma existence tříd:  kde  je libovolná formule jazyka teorie množin
 axiom dvojice:
 axiom nahrazení:

New Foundations
New Foundations (NF) je axiomatizace, kterou vyvinul Willard van Orman Quine. Jedná se o zjednodušení teorie typů z knihy Principia Mathematica. Na rozdíl od teorie typů nepoužívá hierarchii typů. Axiomy NF vylučují axiom výběru.

Je založena na těchto axiomech:
 axiom extenzionality: Dva objekty jsou stejné, pokud se skládají ze stejných prvků.
 schéma axiomů vydělení: Množina  existuje, když  je formule logiky prvního řádu, která může být odvozena z dobře definované formule teorie typů odstraněním všech indexů typů (za zajištění toho, že proměnné různých typů nesplynou).

Schéma axiomů vydělení, může být nahrazeno konečně mnoha svými případy. Použití konečné axiomatizace odstraňuje nutnost v definicích zmiňovat typy.

Často se používá ve schématu vydělení koncept vrstvené formule (). (Řekneme, formule  je vrstvená, jestliže existuje funkce) f taková, že všem objektům univerza vrátí přirozené číslo a pro  platí  a pro  platí . Schéma axiomů vydělení pak zní:
 existuje pro každou vrstvenou formuli .

Teorie polomnožin

Teorie polomnožin byla vyvinuta v 70. a 80. letech 20. století Petrem Vopěnkou a Petrem Hájkem. Její axiomatizace je podobná Von Neumannově-Gödelově-Bernaysově teorii množin, ale liší se tím, že umožňuje existenci vlastních tříd, které jsou částí nějaké množiny (). Tato vlastnost umožňuje polomnožinám sloužit jako základ Vopěnkovy alternativní teorie množin

Axiomatizace konečných množin
K některým axiomatizacím teorie množin lze nadefinovat i odpovídající axiomatizace konečných množin.

Například ZFFin získáme ze ZF tak, že axiom nekonečna nahradíme jeho negací. Obdobně se získají NBGFin (respektive KMFin).

Dá se dokázat, že:
 všechny uvedené teorie jsou bezesporné.
 KMFin je ostře silnější než ZFFin.

Odkazy

Poznámky

Reference

Teorie množin

redpajama_set_name: RedPajamaWikipedia


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› Articles › Medical › Neighborhood › Mt. Sinai To Lower Manhattan: DROP DEAD!
Mt. Sinai To Lower Manhattan: DROP DEAD!
admin May 3, 2017 Articles, Medical, Neighborhood
By Arthur Z. Schwartz
HOSPITAL BED CRISIS: Arthur Schwartz's 95-year-old mother waited 10 hours for a room at NYU Langone, as Mount Sinai/Beth Israel continues to cut services. Photo by
Arthur Z. Schwartz.
The best way to learn about the state of our health care is to get sick, or to be responsible for the care of a loved one, and experience it first hand. I had a heart attack in January and learned firsthand how important the survival of Beth Israel is. But, last week, I got another important reminder.
My mom, who just turned 95, and is an active, vibrant person who still goes to work every day, had an outpatient procedure at NYU Langone last week. Something went wrong, and in mid-surgery she was rushed to the Emergency Room. I ran up there, entered the doors where the patients were, and almost fell over. My mother was on a portable bed, with an IV, but she wasn't in one of the bays, which were built to give patients privacy. She was lined up, along with about 25 other people, also on beds, outside of the bays (which were also full), much like cars lined up to enter the nearby Midtown Tunnel. The photo tells the story. I was there to advocate for my mother in this terribly overcrowded situation. However, those without a family member just lay and wait. This was just a normal Wednesday afternoon, not the day of a bus or train accident, or a mass shooting, or a building explosion.
My mom had to be admitted "for observation." It took over 10 hours to get her into a room, in the Step Down ICU area, which she shared with three other people. By the next morning, upset about being treated in a cattle car, my mom signed herself out "against doctor's orders." She preferred to recuperate at home. She is strong and ambulatory, so she walked herself out the door and into a cab.
This is bad enough. Just imagine what happens when Beth Israel closes, and its current emergency room, with 700 beds waiting for patients, and its full panoply of operating rooms (except for the Cardiac Surgery Unit, which they have closed), disappears. It will be a disaster!
On April 6th, probably in response to the last three issues of WestView, Mount Sinai/Beth Israel had a public meeting to explain what was going on. They repeatedly assured those present that "nothing had closed," which was a lie, and that there would be, in the end, no reduction in services. They presented a map of Manhattan south of 34th Street, with lots of dots, and explained the various outpatient "urgent care" facilities, which they were going to open. They also discussed how they will expand outpatient services at their Union Square East location, and how their new planned Emergency Room/70-bed hospital, at the corner of 2nd Avenue and 14th Street, would absorb all the inpatient needs now served by a nearly 800-bed hospital.
State Senator Brad Hoylman asked the hospital representatives whether they had done a "needs study" before deciding on a plan. They said "NO." City Council Member Corey Johnson noted that they were building a two-story hospital on a plot of land where they could build six stories. The speaker said that they would build up if there was a need. Corey's response was: "There is a need! You should do it from the start."
Despite the lack of a study, or meaningful community notice, the NYS Health Department has approved the closure of six major parts of Beth Israel, including the Cardiac Surgery Unit and the Maternity Ward. Clearly, Mount Sinai/Beth Israel plans to close the hospital piece by piece, so that there is no way to argue, at the four-year mark, that there is anything to save.
On May 4th, at 6pm, at Local 32BJ, SEIU, at 25 West 18th Street, a Town Hall will occur to explore how to stop Mount Sinai, how to save our health care, and what you can do. Key demands, which will come out of the meeting include:
NO MORE NYS Health Department approvals for closures without a comprehensive health needs and impact study;
A call to the Mayor and City Council to fund such a study, to be performed with the assistance of the affected Community Boards;
A transparent process to be implemented by the NYS Health Department and Governor Cuomo so that applications affecting public health are publicly reviewed (It is harder to get permission to have a sidewalk café, or a liquor license, than to close a hospital);
A call to the Governor to support the creation of a single- payer health insurance system in NYS, which is key to preventing the mass closure of hospitals in the State (the legislature is just two votes short of approval for this type of system).Arthur Z. Schwartz is the Democratic District Leader for Greenwich Village, and a founder of Progressive Action of Lower Manhattan, a chapter of the New York Progressive Action Network.
Arthur Z. Schwartz is the Democratic District Leader for Greenwich Village, and a founder of Progressive Action of Lower Manhattan, a chapter of the New York Progressive Action Network.
"Each Day Catches Fire": Revisiting the Latvian Poet Imants Ziedonis
Valid Anxiety in West Village Residents About Heart Attack Care


text:
The Great Rebellion: A History of the Civil War in the United States, Volume 1
By J. T. Headley
TYLER'S POSTION.
white tops--the dark looking ambulances—winding columns of cavalry now bursting into view, and now lost in deep shadows-combined to form a scene of thrilling interest. Not a drum or bugle cheered the march-a deep silence, broken only by the heavy rumbling of artillery carriages, or the muffled tread of the advancing host, rested on forest and valley. The divisions, separating like the rays of a fan, moved off to their respective positions. Hunter and Heintzelman took the same road until they came to the turn off to the ford where the latter was to be dropped. Hunter then kept on alone. It was evident that the battle was to be lost or won by these two divisions, fourteen thousand strong. The rest of the army was only to keep the enemy in front occupied till they were seen coming down the opposite bank, then the general advance was to take place, for the battle was assuredly won. The Sabbath morning broke warm and pleasant, and at six o'clock Tyler was in front of the enemy's centre, and soon a thirty pound rifled Parrott gun--the signal agreed on-y which he was to announce he was in positionawoke the morning echoes, and the shell bursting in mid air announced to the chemy that the decisive hour had come. The duty assigned him was to threaten the bridge which here crossed the stream till the appearance of Hunter's and Heintzelman's divisions on the other side coming down the stream, when he was to move across to their support. He had reached his position at half-past five, and hence had ample time to survey that of the enemy on the farther side. The latter was posted on hights that rose in regular slopes from the shore, broken into knolls and terraces, crowned here and there by earthworks. The woods that interfered with his cannon ranges had all been cut away, and his guns had a clean sweep of every approach. On our side the descent was more gradual, and covered with a dense forest. A lookout was stationed in a tree that overlooked the surrounding country, from which
THE FLANKING DIVISIONS.
he could observe the progress of the flanking columns under Hunter and Heintzelman. Hour after hour this division stood thus on the ridge that overlooked Bull Run and the bridge, doing nothing except now and then sending a shell from its thirty-two pound Parrott gun at bodies of infantry and cavalry that far inland could be detected moving in the direction of Hunter's and Heintzelman's divisions.
Colonel Richardson, with his brigade (detached for the time-being from the fifth division in reserve under Miles) took the position at Blackburn ford, still farther down the stream, to threaten a passage there. While Tyler was to wait the appearance of Hunter and Heintzelman across the stream before commencing his attack, Richardson, below him, was to wait the thunder of Tyler's artillery as the signal for him to move on the ford. It will thus be seen that but one division (Tyler's) and one brigade (Richardson's) were on the stream, while the two divisions of Hunter and Heintzelman were to open the battle—the other two being out of the fight-Miles' in reserve at Centreville, and Runyon's protecting the communications with Vienna. The whole interest, therefore, centred on the two former divisions, and from little after sunrise every eye was strained in the direction they were expected to appear, and every ear open to hear the thunder of their artillery. These two columns, as before remarked, moved steadily along the same road, on their unknown journey up the stream and back of it, until they came to the place designated for Heintzelman to turn off to the left to the ford where he was to cross.
But the road laid down on the map,
and which he was to take was found to have no existence in fact, and so he kept on after Hunter; and about eleven o'clock came to Sudley's Springs ford, where the latter had just crossed with the exception of one brigade which was then entering the water. It was ten miles from Centreville to this place and the soldiers before reaching it
THE ENEMY'S FLANK TURNED
had become much exhausted. The enemy had got information of this movement, and from high points of observation large masses of troops could be seen moving rapidly towards the threatened point. The roar of artillery soon announced that Hunter was engaged with the enemy. Heintzelman immediately pushed forward his division, but finding it slow work to get it over in a body, he ordered the regiments to break off and cross separately. The men, however, suffering from thirst, stopped to drink and fill their canteens which delayed the march. McDowell, having stationed himself where he could the most quickly receive reports from the different divisions, had at length flung himself on the ground to get a little rest, as he was suffering from illness. At half-past ten a courier dashed up to him, and announced that Hunter was across Bull Run. He immediately sprang to the saddle, and galloped off to accompany the column on which the fate of the day depended. The brave Porter, the gallant Burnside, and the chivalrous Sprague were in the advance of Hunter, driving the enemy steadily before them. Soon Heintzelman appeared also on their left, and the amazed enemy saw their position turned. The advancing columns were at last seen from the lookouts at Tyler's position, and huge columns of smoke rising in the summer air and waving to and fro in the sunlight showed where the encountering hosts were struggling for victory. Then all along that sluggish stream, for five miles in extent, the artillery opened, and the columns were put in motion. Tyler's left wing swept forward, the famous Irish regiment, sixteen hundred strong, leading the van. With the quick-step at first, then the double-quick, they, with shouts that shook the field, flung themselves forward, skirting with their glittering steel the edge of the forest. Coats, haversacks, everything that could impede their progress were cast loose. Meagher galloped at their head, and shouting, "Come on, boys; you have got
your chance at last," led them fiercely on the foe. The Seventy-ninth Highlanders, the Thirteenth New York, and Second Wisconsin, followed. It was now high noon, and the battle began to rage with terrible fury. Hunter had been wounded, but his and Heintzelman's divisions kept on their terrible way, steadily pushing the enemy before them. Rickett's battery, after losing nearly every man at the guns, fell into the hands of the enemy. Out of the woods volumes of smoke writhed fiercely upwards, telling where bodies of infantry struggled for the mastery-regiments on the doublequick streamed across the open meadows, and the next moment, like two thunder clouds charged with lightning, burst in flame on each other, while the incessant roar of cannon shook the earth. The surrounding inhabitants grew pale with affright, and the deafening reverberations rolled sullenly away, till they broke with a muffled sound over Fairfax and Alexandria, and even Washington itself, blanching the cheeks of listeners, and filling their hearts with yague fears. Those stationed near Tyler's position listened with intense eagerness to Hunter's and Heintzelman's charges in the northern woods, and ever and anon cheers were heard mingling with the roar of artillery. Some regiments flinched through want of proper officers, and Rickett's battery was lost by the cowardly flight of the Fire Zouaves who had boasted of the deeds they would perform beforehand. Others came gallantly into the fight for a while, but soon broke and fled in dismay; a few stood firm until all was lost. The Second Minnesota, ordered to the extreme right, moved for a mile across the field of battle at the quick and double-quick, and drew
up within close pistol shot of a superior foe. Heintzelman was everywhere present—now in talking distance of the foe, and now dashing amid the wavering battalions to steady them. Where such men as he, and Porter, and Burnside, and Sprague led, there could not but be deeds of heroism;
and where such batteries as Griffin's, and Rickett's, and the Rhode Island, were directed by their respective commanders, the harvest of death was reaped fast. By little after noon these two flanking divisions had worked their desperate way down the farther banks of Bull Run until they were opposite Tyler's position at the Stone bridge. The enemy hurried up regiment after regiment to arrest the reversed tide of battle, but all in vain. Tyler, sending forward reinforcements across the stream, brought help io the exhausted, thirsty troops which had been marching and fighting ever since two o'clock in the morning of this hot July day. Sherman and Keyes led their brigades gallantly forward, and by two o'clock the battle was to human view won. Many of the enemy were already in full flight—the whole army borne back a mile and a half—and Beauregard was preparing to retreat to his lines at Manassas Junction, when clouds of dust, rising in the distance, told him that reinforcements were hurrying to his relief. As Blucher stole away from Grouchy at Wavres, to decide the fate of the battle of Waterloo, so had Johnston beguiled Patterson, and pushing his troops forward by railroad, had now come to make a Waterloo defeat to the Federal arms. Hunter and Heintzelman, after their long march and long fight without rest or food, and part of the time without water, now found a fresh enemy approaching on their right flank, and partly in their rear. It matters not whether this was the cause of the panic that followed or not, it made the loss of the battle certain. Ten thousand fresh troops thrown suddenly on these two divisions, that had been marching and fighting without any respite for thirteen hours, could have but one result. It must be remembered that those thirteen hours told heavier on our raw troops, fresh from the counting house and workshops, than twenty-four would have done on old soldiers. An orderly retreat might have been effected but for the panic, nothing more.


text:
New Marriott offshoot brand hotel headed for the canal
J. Elias O'Neal April 18, 2019 5
AC Hotel by Marriott is set to rise on about 0.8 acres near Byrd and Virginia streets. (Photos courtesy KM Hotels)
A Henrico-based hotelier is making its first splash in the city with plans for an eight-story hotel downtown.
KM Hotels is planning to construct the state's first AC Hotel by Marriott on part of a nearly 2-acre site at 1300 E. Byrd St., along the south side of the Kanawha Canal.
Plans call for the 150-room hotel to rise next door to the Lady Byrd Hat Factory building and across Virginia Street from the Vistas on the James condominium building.
The project also would include 10 residential condominium units, a 4,000- to 5,000-square-foot rooftop restaurant that the group is negotiating to be run by Chris Tsui's EAT Restaurant Partners, and about 3,700 square feet of retail space along the canal side of the building.
A view of the proposed AC Hotel by Marriott from Kanawha Canal. Renderings courtesy nbj Architecture.
Launched in the U.S. by Marriott International in 2013, AC Hotel is the chain's latest boutique concept for business travelers and visitors.
There are 53 AC Hotels operational throughout several large and midsized metros, with Marriott planning to establish 75 additional locations nationally in the coming years.
"It has a similar feel to the Quirk Hotel … with upscale European design and amenities," said Mayur Patel, KM Hotels' president and chief operating officer. "It will serve the higher-tiered, millennial corporate clients traveling into Richmond."
Pending city approval, construction would begin in the first quarter of 2020, Patel said, with a delivery date in late spring or early summer 2021.
Plans call for a two-story parking deck via East Byrd Street with 78 parking spaces, Patel said. The hotel's lobby will be located on the ground floor and include pedestrian access to Kanawha Canal.
All of the hotel's rooms and condos will be located on six levels above the parking deck and lobby area, Patel said, each with views of either the James River or Kanawha Canal. A similar conference room also is planned for the property that will have views of the canal.
Looking to help enhance the Canal Walk experience, Patel said his firm has proposed an idea to allow the city to construct a bike ramp on its property along Virginia Street that would connect the Virginia Capital Trail with the Canal Walk. The group also is working with the city to reconfigure the Byrd and Virginia streets intersection.
All of the hotel's rooms and condos will have views of either the James River or Kanawha Canal.
Other hotel amenities include a 24-hour fitness center, and a breakfast bar and lounge.
Land deal in the works
KM Hotels is under contract with North Falls Acquisitions LLC, a business entity comprised of Fountainhead Properties' Tom Papa and WVS Cos.' Jason Vickers-Smith and Richard Souter, to purchase about 0.8 acres of the 1.8-acre tract at 1300 E. Byrd St. for an undisclosed amount.
Andrew Condlin, an attorney with Richmond-based law firm Roth Jackson who is representing KM Hotels, said the firm will close on the property once city officials approve the project.
The project also is under review by the Architectural Review Board of Venture Richmond, a process necessary for owners of property along the riverfront that are planning new construction.
A cost estimate for the project was not released.
As part of the agreement, Condlin said North Falls plans to raze the existing 22,000-square-foot warehouse building to make way for the hotel.
North Falls originally had the entire parcel under contract with local developer Charles Macfarlane, who had planned a 10-story, 144-room Hyatt Place hotel on much of the site.
But a lengthy legal dispute over access to Pope's Alley, a 35-foot-wide private alley owned by North Falls and an entity owned by Richmond-based Fulton Hill Properties developer Margaret Freund, ultimately killed the project.
Both sides voluntarily withdrew their claims last summer without resolving the matter.
AC Hotel will not require access to Pope's Alley for the project to be developed.
The property falls within the Downtown Civic and Cultural District (DCC) and the B-4 Central Business District zoning, which allows the development to take place without a rezoning, Condlin said.
KM Hotels operates hotels under several flags, including Candlewood Suites, Fairfield Inn & Suites and Hampton Inn, throughout Virginia, West Virginia, Texas, New Jersey, Kentucky, Maryland, Alabama and Washington, D.C.
KM Hotels is constructing a five-story, 91-room hotel at 101 and 103 N. Carter Road in Ashland. (Courtesy Hilton)
The company has been busy in metro Richmond, most recently breaking ground on a new Tru by Hilton hotel in Ashland.
A 119-bed Residence Inn also is under construction on the former Skilligalee restaurant site at 5416 Glenside Drive in Henrico County by KM Hotels, and it is remodeling the Holiday Inn Express at 2000 Staples Mill Road. It also recently converted the remaining Red Carpet Inn, which sits next door to the future Tru by Hilton in Ashland, into a Red Roof Inn.
Given the city's continued business growth, Patel said launching Virginia's first AC Hotel in Richmond was a good match.
"Downtown's progressing demand generators will help revitalize the Canal Walk and our growing city," Patel said.
POSTED IN Commercial Real Estate, Featured, News
About the Author: J. Elias O'Neal
J. Elias O'Neal was a BizSense reporter from 2016 through early 2020. Please send current news tips on the real estate and restaurant beats to BizSense reporter Mike Platania at [email protected] or call 804-554-6872.
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In order to foster transparent, civil conversation, please include your full name when posting comments.
Matt Klaman
The canal has so much potential but ultimately falls flat with a severe lack of energy after work hours (it's used primarily by walkers/runners). This hotel, given the canal-front retail shown in the rendering, can play a large role in boosting that energy. Would loved to see more parking, so it can be utilized by nearby businesses and area visitors, but that's tough to do with the canal there and no real means to go underground. I ask (not like my opinion matters) for two things with this project: 1. They fill the retail with something other than a handful… Read more »
Reply to Matt Klaman
I like to see better screening *windows vs. open screen on this side) of the parking garage on the canal side of the building but this is a great project.
Matt Faris
Reply to Michael Dodson
The windows add a significant cost to the ventilation and fire suppression systems. I'm guessing that has a lot to do with the open parking space.
sam nelson
Another great project by KM Hotels. The 10 residential condominium units are out-of-the-box thinking for Richmond and a good idea. I look forward to enjoying the rooftop restaurant. I think how far the CBD has come in 25 years. This hotel continues that progression. Best Wishes to Mike and all of KM Hotels.
Bruce Anderson
Looks like a great project that will add more dynamism to the neighborhood. Good luck to KM Hotels.


text:
Q: OpenGL instanced rendering not working, only one instance appears I am writing a mini OpenGL program with instancing in it. But when I ran the code, only one instance was shown. I thought that it should be easy, but I failed. Here is the code:
    #include <stdio.h>
    #include <stdlib.h>
    #include <GL/glew.h>
    #include <GLFW/glfw3.h>
    #include <iostream>
    #include <GL/glut.h>
    #include <vector>
    #include <fstream>
    #include <string>
    #include <glm/glm.hpp>
    #include <glm/gtc/matrix_transform.hpp>
    #include <vector>

    #define WIDTH  1280
    #define HEIGHT 720

    static const std::string vertexShader =
        "#version 330 core\n"
        "in vec3 position;\n"
        "in vec3 color;\n"
        "in ivec3 Glob_pos;\n"
        "uniform mat4 MVP;\n"
        "out vec3 ToFragColor;\n"
        "void main(){\n"
        "   gl_Position = MVP * vec4(vec3(Glob_pos) + position,1.0);\n"
        "   ToFragColor = color;\n"
        "}\n";

    static const std::string fragmentShader =
        "#version 330 core\n"
        "in vec3 ToFragColor;\n"
        "uniform vec3 Cam;\n"
        "out vec3 out_color;\n"
        "void main(){\n"
        "   out_color = ToFragColor;\n"
        "}\n";

    static const GLfloat CUBE_VERT[12*3*2*3] = {

        -1.0f,-1.0f,-1.0f,  1.0f, 0.0f, 1.0f,
        -1.0f,-1.0f, 1.0f,  0.0f, 0.0f, 1.0f,
        -1.0f, 1.0f, 1.0f,  0.0f, 1.0f, 1.0f,

         1.0f, 1.0f,-1.0f,  1.0f, 1.0f, 1.0f,
        -1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 1.0f,
        -1.0f, 1.0f,-1.0f,  0.0f, 1.0f, 1.0f,

         1.0f,-1.0f, 1.0f,  1.0f, 1.0f, 0.0f,
        -1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 0.0f,
         1.0f,-1.0f,-1.0f,  1.0f, 0.0f, 0.0f,

         1.0f, 1.0f,-1.0f,  1.0f, 1.0f, 1.0f,
         1.0f,-1.0f,-1.0f,  1.0f, 0.0f, 1.0f,
        -1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 1.0f,

        -1.0f,-1.0f,-1.0f,  1.0f, 0.0f, 1.0f,
        -1.0f, 1.0f, 1.0f,  0.0f, 1.0f, 1.0f,
        -1.0f, 1.0f,-1.0f,  1.0f, 1.0f, 1.0f,

         1.0f,-1.0f, 1.0f,  1.0f, 1.0f, 0.0f,
        -1.0f,-1.0f, 1.0f,  0.0f, 1.0f, 0.0f,
        -1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 0.0f,

        -1.0f, 1.0f, 1.0f,  1.0f, 1.0f, 1.0f,
        -1.0f,-1.0f, 1.0f,  1.0f, 0.0f, 1.0f,
         1.0f,-1.0f, 1.0f,  0.0f, 0.0f, 1.0f,

         1.0f, 1.0f, 1.0f,  1.0f, 1.0f, 1.0f,
         1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 1.0f,
         1.0f, 1.0f,-1.0f,  0.0f, 1.0f, 1.0f,

         1.0f,-1.0f,-1.0f,  0.0f, 0.0f, 1.0f,
         1.0f, 1.0f, 1.0f,  1.0f, 1.0f, 1.0f,
         1.0f,-1.0f, 1.0f,  1.0f, 0.0f, 1.0f,

         1.0f, 1.0f, 1.0f,  0.0f, 1.0f, 1.0f,
        -1.0f, 1.0f, 1.0f,  1.0f, 1.0f, 1.0f,
         1.0f,-1.0f, 1.0f,  0.0f, 0.0f, 1.0f,

                //TOP
         1.0f, 1.0f, 1.0f,  1.0f, 1.0f, -1.0f,
         1.0f, 1.0f,-1.0f,  1.0f, 0.0f, -1.0f,
        -1.0f, 1.0f,-1.0f,  0.0f, 0.0f, -1.0f,

         1.0f, 1.0f, 1.0f,  1.0f, 1.0f, -1.0f,
        -1.0f, 1.0f,-1.0f,  0.0f, 0.0f, -1.0f,
        -1.0f, 1.0f, 1.0f,  0.0f, 1.0f, -1.0f

    };

    GLuint LoadShaders();

    void setup(GLuint programID);
    void render(GLuint programID);
    void computeMatricesFromInputs(GLFWwindow* window);

    GLuint vao, vbo, ib;
    GLuint MatrixID;
    GLuint CamID;

    //For model view matrix calculation
    glm::vec3 CamLoc = glm::vec3(0,0,-5);
    glm::mat4 Projection = glm::perspective(glm::radians(45.0f), (float) WIDTH / (float)HEIGHT, 1.0f, 1000.0f);
    glm::mat4 View = glm::lookAt(
        CamLoc,
        glm::vec3(0,0,0),
        glm::vec3(0,1,0)
    );
    glm::mat4 Model = glm::mat4(1.0f);
    glm::mat4 mvp = Projection * View * Model;
    glm::vec3 direction;
    float horizontalAngle = 3.14f;
    float verticalAngle = 0.0f;
    float initialFoV = 45.0f;
    float speed = 3.0f;
    float mouseSpeed = 0.005f;
    float mtimeScale = 0.1f;
    float ktimeScale = 1.0f;
    float FoV = initialFoV; //- 5 * glfwGetMouseWheel();
    double lastPos[] = { 0,0 };
    const glm::vec3 null = glm::vec3(0,0,0);
    //For model view matrix calculation -- end

    std::vector<int> instanceObj;

    int main(int argc, char **argv){
        glutInit(&argc, argv);
        glfwInit();

        glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
        glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
        glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);

        GLFWwindow* window;
        window = glfwCreateWindow(WIDTH, HEIGHT, "DearDaniel's OpenGL", NULL, NULL);

        glfwMakeContextCurrent(window);

        glewExperimental = true;
        glewInit();

        glfwSetInputMode(window, GLFW_STICKY_KEYS, GL_TRUE);

        GLuint programID = LoadShaders();
        MatrixID     = glGetUniformLocation(programID, "MVP");
        CamID        = glGetUniformLocation(programID, "Cam");

        glEnable (GL_DEPTH_TEST); glDepthFunc (GL_LESS);
        glEnable(GL_CULL_FACE); glCullFace(GL_BACK);

        glClearColor(0.0f, 0.0f, 0.4f, 0.0f);

        glfwSetInputMode(window, GLFW_CURSOR, GLFW_CURSOR_DISABLED);

        setup(programID);

        do{
            glUseProgram(programID);
            computeMatricesFromInputs(window);
            render(programID);
            glfwSwapBuffers(window);
            glfwPollEvents();
        } while( glfwGetKey(window, GLFW_KEY_ESCAPE ) != GLFW_PRESS && glfwWindowShouldClose(window) == 0 );

        glDeleteProgram(programID);

        return 0;

    }

    GLuint LoadShaders(){

        GLuint VertexShaderID = glCreateShader(GL_VERTEX_SHADER);
        GLuint FragmentShaderID = glCreateShader(GL_FRAGMENT_SHADER);

        char const * VertexSourcePointer = vertexShader.c_str();
        glShaderSource(VertexShaderID, 1, &VertexSourcePointer , NULL);
        glCompileShader(VertexShaderID);

        char const * FragmentSourcePointer = fragmentShader.c_str();
        glShaderSource(FragmentShaderID, 1, &FragmentSourcePointer , NULL);
        glCompileShader(FragmentShaderID);

        GLuint ProgramID = glCreateProgram();
        glAttachShader(ProgramID, VertexShaderID);
        glAttachShader(ProgramID, FragmentShaderID);
        glLinkProgram(ProgramID);

        glDetachShader(ProgramID, VertexShaderID);
        glDetachShader(ProgramID, FragmentShaderID);

        glDeleteShader(VertexShaderID);
        glDeleteShader(FragmentShaderID);

        return ProgramID;
    }

    void setup(GLuint programID) {
        glGenVertexArrays(1, &vao);
        glBindVertexArray(vao);
        glGenBuffers(1, &vbo);
        glBindBuffer(GL_ARRAY_BUFFER, vbo);
        glBufferData(GL_ARRAY_BUFFER, 12*3*2*3*sizeof(int), CUBE_VERT, GL_STATIC_DRAW);
        glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 6 * sizeof(float), (void*)                  0);
        glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 6 * sizeof(float), (void*)(3 * sizeof(float)));
        glGenBuffers(1, &ib);
        glBindBuffer(GL_ARRAY_BUFFER, ib);
        glVertexAttribPointer(2, 3,   GL_INT, GL_FALSE, 3 * sizeof(  int), (void*)                  0);
        glEnableVertexAttribArray(0);
        glEnableVertexAttribArray(1);
        glEnableVertexAttribArray(2);
        glVertexAttribDivisor(2, 1);
        glBindVertexArray(0);
    }

    void render(GLuint programID) {
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
        glBindVertexArray(vao);

        glBindBuffer(GL_ARRAY_BUFFER, ib);
        instanceObj.clear();
        for (int i = 0; i < 32; i+=2)
            for (int j = 0; j < 32; j +=2)
                for (int k = 0; k < 32; k +=2) {
                        instanceObj.push_back(i);
                        instanceObj.push_back(j);
                        instanceObj.push_back(k);
        }
        glBufferData(GL_ARRAY_BUFFER, sizeof(int)*instanceObj.size(), &instanceObj[0], GL_STATIC_DRAW);

        glUniformMatrix4fv(MatrixID, 1, GL_FALSE, &mvp[0][0]);
        glUniform3f(CamID, CamLoc.x, CamLoc.y, CamLoc.z);
        glDrawArraysInstanced(GL_TRIANGLES, 0, 36, 16*16*16);
        glBindVertexArray(0);
    }

    void computeMatricesFromInputs(GLFWwindow* window){

        static double lastTime = glfwGetTime();
        double currentTime = glfwGetTime();
        float deltaTime = float(currentTime - lastTime);
        double xpos, ypos;

        glfwGetCursorPos(window, &xpos, &ypos);

        float hori = horizontalAngle + mouseSpeed * float( xpos - lastPos[0] ) * mtimeScale;
        float vert = verticalAngle   + mouseSpeed * float( ypos - lastPos[1] ) * mtimeScale;
        horizontalAngle = hori;
        if (vert > -3.14f/2.0f && vert < 3.14f/2.0f) verticalAngle = vert;

        lastPos[0] = xpos;
        lastPos[1] = ypos;

        direction = glm::vec3 (
            cos(verticalAngle) * sin(horizontalAngle),
            sin(verticalAngle),
            cos(verticalAngle) * cos(horizontalAngle)
        );

        glm::vec3 right = glm::vec3(
            sin(horizontalAngle - 3.14f/2.0f),
            0,
            cos(horizontalAngle - 3.14f/2.0f)
        );

        glm::vec3 up = glm::cross( right, direction );

        if (glfwGetKey( window, GLFW_KEY_UP ) == GLFW_PRESS)    CamLoc += direction * deltaTime * speed * ktimeScale;
        if (glfwGetKey( window, GLFW_KEY_DOWN ) == GLFW_PRESS)  CamLoc -= direction * deltaTime * speed * ktimeScale;
        if (glfwGetKey( window, GLFW_KEY_RIGHT ) == GLFW_PRESS) CamLoc += right * deltaTime * speed * ktimeScale;
        if (glfwGetKey( window, GLFW_KEY_LEFT ) == GLFW_PRESS)  CamLoc -= right * deltaTime * speed * ktimeScale;

        Projection = glm::perspective(glm::radians(FoV), 4.0f / 3.0f, 0.1f, 100.0f);

        View = glm::lookAt(
            CamLoc,           // Camera is here
            CamLoc+direction, // and looks here : at the same position, plus "direction"
            up                  // Head is up (set to 0,-1,0 to look upside-down)
        );

        lastTime = currentTime;

        mvp = Projection * View;

        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 4; ++j) {
                printf("%f ", mvp[i][j]);
            }
            printf("\n");
        }

    }

I used the following command to compile my code:
   g++ miniGL.cpp -Wall -std=c++11 -L/usr/local/lib -pthread -lGLEW -lGLU -lGL -lglut -lglfw3 -ldl -lrt -lXrandr -lXxf86vm -lXi -lXinerama -lX11 -lXcursor -lglfw -o ogl

I was meant to render 16*16*16 cubes onto the screen, but only one has shown. I spent more than ten hours for debugging. Now I gave up and shamelessly seeking for help.

A: You have to use glVertexAttribIPointer, when defining the array of generic vertex attribute data, for the vertex attrbute in ivec3 Glob_pos;.
glVertexAttribPointer is for floating point attributes only (integral data will be converted to floating point).
See the Khronos group reference page for glVertexAttribPointer:

For glVertexAttribPointer, if normalized is set to GL_TRUE, it indicates that values stored in an integer format are to be mapped to the range [-1,1] (for signed values) or [0,1] (for unsigned values) when they are accessed and converted to floating point. Otherwise, values will be converted to floats directly without normalization.
For glVertexAttribIPointer, only the integer types GL_BYTE, GL_UNSIGNED_BYTE, GL_SHORT, GL_UNSIGNED_SHORT, GL_INT, GL_UNSIGNED_INT are accepted. Values are always left as integer values.

Note, probably Glob_pos is never set and has always the same, but undefined value.

Since you don't use glGetAttribLocation to get the attribute indices for the vertex attributes (position, color, Glob_pos), you should use Layout Qualifiers:
layout (location = 0) in vec3 position;
layout (location = 1) in vec3 color;
layout (location = 2) in ivec3 Glob_pos;

redpajama_set_name: RedPajamaStackExchange


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Analyzing LRAD (NASDAQ:GNSS) & Technicolor (NASDAQ:TCLRY)
Critical Contrast: Daqo New Energy (NYSE:DQ) and United Microelectronics (NYSE:UMC)
Envestnet (NYSE:ENV) Posts Quarterly Earnings Results, Beats Estimates By $0.02 EPS
Posted by Lisa Pomrenke on Nov 11th, 2019
Envestnet (NYSE:ENV) issued its earnings results on Thursday. The business services provider reported $0.60 earnings per share (EPS) for the quarter, topping the consensus estimate of $0.58 by $0.02, Briefing.com reports. Envestnet had a negative net margin of 1.72% and a positive return on equity of 9.15%. The firm had revenue of $236.08 million for the quarter, compared to analysts' expectations of $233.02 million. During the same quarter last year, the business earned $0.53 earnings per share. The business's revenue was up 16.2% on a year-over-year basis.
NYSE:ENV traded up $1.24 during trading hours on Friday, hitting $64.44. The company had a trading volume of 762,836 shares, compared to its average volume of 327,360. The company has a market capitalization of $3.28 billion, a PE ratio of 51.55, a price-to-earnings-growth ratio of 2.80 and a beta of 1.76. The stock has a 50-day moving average price of $59.77 and a 200 day moving average price of $64.58. Envestnet has a 52 week low of $46.57 and a 52 week high of $73.94. The company has a debt-to-equity ratio of 0.61, a current ratio of 0.54 and a quick ratio of 0.54.
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In related news, CFO Peter D'arrigo sold 5,000 shares of Envestnet stock in a transaction on Wednesday, October 30th. The shares were sold at an average price of $62.50, for a total value of $312,500.00. Following the sale, the chief financial officer now owns 57,747 shares in the company, valued at $3,609,187.50. The transaction was disclosed in a document filed with the SEC, which is accessible through this hyperlink. Also, insider William Crager sold 18,500 shares of Envestnet stock in a transaction on Monday, August 12th. The shares were sold at an average price of $58.13, for a total transaction of $1,075,405.00. Following the completion of the sale, the insider now owns 243,512 shares in the company, valued at approximately $14,155,352.56. The disclosure for this sale can be found here. In the last quarter, insiders sold 117,375 shares of company stock worth $6,795,807. 4.97% of the stock is currently owned by company insiders.
Several brokerages have recently issued reports on ENV. Zacks Investment Research cut shares of Envestnet from a "hold" rating to a "sell" rating in a report on Tuesday, August 13th. DA Davidson raised their target price on shares of Envestnet from $67.00 to $74.00 and gave the stock a "buy" rating in a report on Friday. Buckingham Research cut their target price on shares of Envestnet from $71.00 to $68.00 and set a "neutral" rating on the stock in a report on Friday. Finally, ValuEngine cut shares of Envestnet from a "buy" rating to a "hold" rating in a report on Thursday, August 8th. One equities research analyst has rated the stock with a sell rating, four have assigned a hold rating, six have given a buy rating and one has given a strong buy rating to the stock. Envestnet presently has an average rating of "Buy" and an average price target of $74.00.
About Envestnet
Envestnet, Inc, together with its subsidiaries, provides intelligent systems for wealth management and financial wellness in the United States and internationally. It operates through Envestnet and Envestnet | Yodlee segments. The company's product and services suites include Envestnet | Enterprise, which provides an end-to-end open architecture wealth management platform, as well as sells data aggregation and reporting, data analytics, and digital advice capabilities; Envestnet | Tamarac that provides trading, rebalancing, portfolio accounting, performance reporting, and client relationship management software; Envestnet | Retirement Solutions, which offer a suite of services for advisor-sold retirement plans; and Envestnet | Portfolio Management Consultants that provide research, due diligence, and consulting services to assist advisors in creating investment solutions for their clients, and patented portfolio overlay and tax optimization services.
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Photo Gallery | Art by You!
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