Wednesday, 17 February 2016
World's Longest Palindrome Sentence? 15,139 17,826 words
At 8:02 PM on the 20th of February 2002 it was 20:02 02/20 2002 (if you live in the US), or 20:02 20/02 2002 (if you live in the rest of the world). Either way, it was the best of times, it was the tseb of times, it was a palindromic time. In honor of the event, I wondered if I could create the world's longest palindrome. A search for world's longest palindrome revealed that "In 1980, Giles Selig Hales claimed to have written the world's longest palindrome, which consisted of 58,795 letters." That didn't seem too hard to beat. And in fact, in a few hours I was able to write a program to create a palindrome with 63,647 letters (and later Iupdated the program and got 74,633 letters).
Cognoscenti such as Mark Saltveit, editor ofThe Palindromist, rightfully point out that my creation should not be called a true palindrome, because it makes no sense. But Saltveit says that I am probably safe in calling this "the world's longest palindromic sentence, or the world's longest parody of `A man, a plan.' " I'm satisfied with that assessment.
Jerry Berns has his candidate longest palindrome, consisting of 31,358 words or 119,180 letters, so he's got me beat. His is not in the form of a sentence, but it does have restrictions on how many times a word can be repeated (otherwise you could just do "A radar, a radar, a radar, a radar, ..." and have an infinitely long palindrome).
Luckily for me, I had a better word list: the very nice Moby Word list from Grady Ward (also available at Project Gutenberg), from which I was able to extract the 126,144-word npdict.txt. I thought it would be easy to create a smarter program: I already had a short Python program to look up words in a dictionary given a prefix. All I would have to do is extend it to allow suffix lookup, and implement a search algorithm. Also, importantly, I had an ordinary laptop computer which was at least 1,000 times more powerful than the minicomputer Hoey had in 1984.
The resulting program wasn't too hard to put together: starting at 10:00 PM after the kids were asleep, I thought I might get a long palindrome generated before 02/20 was over. It actually took until 1:00 AM to get something that seemed good (at 1:00 AM), and then in the light of day three more hours to fix two bugs (one reported by Jasvir Nagra and one found by me), and replace a recursive algorithm with a stack to overcome a bug/limitation of Python.
Given that, here's what I was able to come up with, both back in 2002 and more recently:
Commentary: Maybe I'm biased, but I think the palindrome starts out quite strong. "A man, a plan, a caddy" is the basic premise of another fine piece of storytelling. Unfortunately, things go downhill from there rather quickly. It contains truths, but it does not have a plot. It has Putnam, but no logic; Tesla, but no electricity; Pareto, but no optimality; Ebert, but no thumbs up. It has an ensemble cast including Tim Allen, Ed Harris and AlPacino, but they lack character development. It has Sinatra and Pink, but it doesn't sing. It has Monet and Goya, but no artistry. It has Slovak, Inuit, Creek, andItalian, but it's all Greek to me. It has exotic locations like Bali, Maui, Uranus, andCanada, but it jumps around needlessly. It has Occam, but it is the antithesis of his maxim "Entia non sunt multiplicanda praeter necessitatem." If you tried to read the whole thing, you'd get to "a yawn" and stop. Or you might be overcome by the jargon, such as PETN, ILGWU, PROM,UNESCO, and MYOB. Most serendipitous of all is that Steele, who collected severalshorter versions of the Panama oeuvre in a book about a Lisp, shows up in the very last line. Steele and some others have somecomments. You can read the results from top to bottom (if you don't get bored) or you can start in the middle; the letter "y" in "Moray".
Speed: Once I started running my program, it seemed almost too easy. I had it print a message every time it finds a palindrome that is 200 words longer than the last one, and it consistently prints this message every second; so in 3 or 4 seconds it breaks Hoey's record, and in 30 seconds it is over 6000 words. At around 8000 words progress slows to about 1,000 words per minute, and by around 10,000 to 12,000 words progress is sporadic. This is because we are running out of good words: there are 126,000 words in the dictionary, but only about 10% of them are easily reversible. For example, there are 426 words that contain "eq" or "sq", but these are hard to use in a palindrome because there are no words containing "qe" or "qs", and only a few words that end in "q" (and could then be followed by a word starting with "e" or "s".
Commentary: Unfortunately, I don't have the patience to attempt a witty commentary on this one, but I can detail the history of this version. After a reader sent in a suggestion, I made 4 changes:
This is an example of the venerablelanguage induction problem: given the single sentence "A man, a plan, a canal--Panama" as evidence, what language does it define? It seems clear that it consists of a series of any number of noun phrases. That is,
Commentary: Hoey said he thought that a better word list and a smarter program could get to ten times his 540-word palindrome, using only noun phrases with indefinite articles. I'm pretty sure that will never happen. The problem is a dirth of "a"s. According to Hoey's rules, every phrase must start with the letter "a". That means that either the rest of the word must be an exact reverse of another word (and we know there are 1100 of these) or the phrase must have another "a" in it somewhere, and it must be matched by two or more other phrases. Phrases such as "a man", "a plan" and "a canal" work well because they contain multiple "a"s. Now consider a phrase such as "a biologist". If that appears in the palindrome, then somewhere else the letters "tsigoloib" must appear. But note that those letters must all appear in one word/phrase, because there is no "a", and we only get word boundries at "a"s. And of course, there is no single word that contain those letters. In general, take a word (such as "an asparagus" or "a biologist"), split it into components around the "a"s (yielding ["n", "sp", "r", "gus"] and ["biologist"]). Collect the set of all such segments, from all the phrases in the dictionary. Now go back through the dictionary, and for each word, see if the reverse of each of its components is in this set. So "an asparagus" is good, because its reversed components all appear in the set: "n" appears in many places (including "an asparagus" itself), "ps" appears as a component in "a psalm", "r" appears in many places (such as "a karat"), and "sug" appears in "a sugar". On the other hand, "a biologist" is no good, because the component "tsigoloib" does not appear.
When I first applied this test, I started with the 69,241-word anpdict.txt (containing only noun phrases starting with "a" or "an"). I checked to see whether each reversed component of a phrase appeared anywhere in any other phrase. That eliminated "a biologist", but it let "a zoom" stick around, because the reversed component "mooz" appears in "a schmooze". Doing this level of reduction gets us down to a dictionary of 11,065 phrases. But on reflection I realized that not only does each reversed component have to appear in some word, it must appear as a component of some word. The fact that "mooz" appears in "a schmooze" is not good enough. That would only work if "a zoom" could be followed by the letters "hcsa", which of course it cannot; it must be follwed by the letter "a". Using that stricter test, we get down to only 4,528 noun phrases that are actually usable. So to get a 5,400 word palindrome we would need to start with a bigger dictionary.
Speed: My program consistently generates palindromes of over 2000 words in under 10 seconds using the 4,528 word dictionary. It doesn't go much beyond that.
Cognoscenti such as Mark Saltveit, editor ofThe Palindromist, rightfully point out that my creation should not be called a true palindrome, because it makes no sense. But Saltveit says that I am probably safe in calling this "the world's longest palindromic sentence, or the world's longest parody of `A man, a plan.' " I'm satisfied with that assessment.
Jerry Berns has his candidate longest palindrome, consisting of 31,358 words or 119,180 letters, so he's got me beat. His is not in the form of a sentence, but it does have restrictions on how many times a word can be repeated (otherwise you could just do "A radar, a radar, a radar, a radar, ..." and have an infinitely long palindrome).
How I did it
I knew that Dan Hoey had generated a longish palindrome beginning with "A man, a plan" and ending with "Panama". Another search revealed it was a 540 word versioncreated in 1984. Hoey writes "This was done with the Unix spelling dictionary and a fairly simple-minded program. With a better word list and a smarter program I'm sure the palindrome could be ten times as long."Now if that's not a challenge, I don't know what is.Luckily for me, I had a better word list: the very nice Moby Word list from Grady Ward (also available at Project Gutenberg), from which I was able to extract the 126,144-word npdict.txt. I thought it would be easy to create a smarter program: I already had a short Python program to look up words in a dictionary given a prefix. All I would have to do is extend it to allow suffix lookup, and implement a search algorithm. Also, importantly, I had an ordinary laptop computer which was at least 1,000 times more powerful than the minicomputer Hoey had in 1984.
The resulting program wasn't too hard to put together: starting at 10:00 PM after the kids were asleep, I thought I might get a long palindrome generated before 02/20 was over. It actually took until 1:00 AM to get something that seemed good (at 1:00 AM), and then in the light of day three more hours to fix two bugs (one reported by Jasvir Nagra and one found by me), and replace a recursive algorithm with a stack to overcome a bug/limitation of Python.
Given that, here's what I was able to come up with, both back in 2002 and more recently:
Original 15,139 Word Palindrome
Created: | 20 February, 2002 | ||||||||
Words: | 15,319 | ||||||||
Letters: | 63,647 | ||||||||
Phrases: | 12,400 comma-separated noun phrases | ||||||||
Program: | pal.py | ||||||||
Excerpt: | A man, a plan, a caddy, Ore, Lee, tsuba, Thaine, a lair, ... (rest here) ..., Hell, a burial, Aeniah, Tabu, Steele, Roydd, a canal, Panama. | ||||||||
Full palindrome: | here | ||||||||
Storyboard: |
|
Speed: Once I started running my program, it seemed almost too easy. I had it print a message every time it finds a palindrome that is 200 words longer than the last one, and it consistently prints this message every second; so in 3 or 4 seconds it breaks Hoey's record, and in 30 seconds it is over 6000 words. At around 8000 words progress slows to about 1,000 words per minute, and by around 10,000 to 12,000 words progress is sporadic. This is because we are running out of good words: there are 126,000 words in the dictionary, but only about 10% of them are easily reversible. For example, there are 426 words that contain "eq" or "sq", but these are hard to use in a palindrome because there are no words containing "qe" or "qs", and only a few words that end in "q" (and could then be followed by a word starting with "e" or "s".
Latest 17,826 Word Palindrome
Created: | 11 November, 2007 | |||||||||
Words: | 17,826 | |||||||||
Letters: | 74,663 | |||||||||
Phrases: | 14,382 comma-separated noun phrases | |||||||||
Program: | pal2.py | |||||||||
Excerpt: | A man, a plan, a cameo, Zena, Bird, Mocha, ... (rest here) ..., Lew, Orpah, Comdr, Ibanez, OEM, a canal, Panama! | |||||||||
Full palindrome: | here | |||||||||
Storyboard: |
|
- I added the function reversible_words, which finds all pairs of words in the dictionary that are palindromes of other words, such as "Camus" and "Sumac". There all 1100 of these, and adding them all at once helps a little, but not much, because they tend to be found by the search routine anyways.
- The old program would only add a new word that is equal or longer than the missing part on the other side. I added a capability called tryharder to add words that are shorter as well. That is, when I'm looking for a word that starts with "aca", I consider "a caddy" and "a canoe", etc., but this change allows me to also consider "A/C". This helps a little, but it also slows the program down a lot.
- I made the program faster. Profiling showed that reverse was a bottleneck, so I used the [::-1] idiom. I also dump the results to file every 1000 words rather than every 200, until we get near the end.
- I added unit tests, because that's the way things are done these days.
Language Induction
I thought I had leaped past Hoey's 540-word Panama Palindrome by a factor of 30, but when I showed him my palindrome, he said that he was really thinking of sticking with noun phrases of the form "<indefinite article> <noun>."This is an example of the venerablelanguage induction problem: given the single sentence "A man, a plan, a canal--Panama" as evidence, what language does it define? It seems clear that it consists of a series of any number of noun phrases. That is,
S => NP*But from one example, you can't say much more. If we look at the examples from Hoey and Steele, we can see they all start and end the same, so we can say:
S => "A man" "A plan" NP* "A canal" "Panama"But Hoey says that every noun phrase must have an indefinite article:
NP => IndefArt Noun IndefArt => "a" | "an"while I was allowing:
NP => ProperNoun NP => IndefArt Noun IndefArt => "a" | "an"Guy Steele suggested I should also try allowing other noun phrases, such as "two Xs". Gold said the language induction problem can't be solved in general, but others (e.g. Horning, Mooney, Muggleton,de Marcken) have shown that it can be solved probabilistically if you use a probabilistic rather than a strictly logical formalism. With Hoey in mind, I also generated a solution with all indefinite articles:
2,211 Word Palindrome with only indefinite articles
Created: | November, 2003 | |||||||||||||
Words: | 2,211 | |||||||||||||
Letters: | 5,842 | |||||||||||||
Phrases: | 1,106 comma-separated noun phrases | |||||||||||||
Program: | pal2.py with a restricted dictionary | |||||||||||||
Excerpt: | A man, a plan, a casa, a bait, a lag, a malt, ... (rest here) ..., a natl, a mag, a lati, a baas, a canal, Panama! | |||||||||||||
Full palindrome: | here | |||||||||||||
Storyboard: |
|
When I first applied this test, I started with the 69,241-word anpdict.txt (containing only noun phrases starting with "a" or "an"). I checked to see whether each reversed component of a phrase appeared anywhere in any other phrase. That eliminated "a biologist", but it let "a zoom" stick around, because the reversed component "mooz" appears in "a schmooze". Doing this level of reduction gets us down to a dictionary of 11,065 phrases. But on reflection I realized that not only does each reversed component have to appear in some word, it must appear as a component of some word. The fact that "mooz" appears in "a schmooze" is not good enough. That would only work if "a zoom" could be followed by the letters "hcsa", which of course it cannot; it must be follwed by the letter "a". Using that stricter test, we get down to only 4,528 noun phrases that are actually usable. So to get a 5,400 word palindrome we would need to start with a bigger dictionary.
Speed: My program consistently generates palindromes of over 2000 words in under 10 seconds using the 4,528 word dictionary. It doesn't go much beyond that.
Peter Norvig, 20:02 02/20 2002 | See some comments on this page...subscribe |
1 millions disclosed English on earth
The Vocabulary.com Top 1000
May 19, 2011 By Vocabulary.com (NY)
The top 1,000 vocabulary words have been carefully chosen to represent difficult but common words that appear in everyday academic and business writing. These words are also the most likely to appear on the SAT, ACT, GRE, and ToEFL.
To create this list, we started with the words that give our users the most trouble and then ranked them by how frequently they appear in our corpus of billions of words from edited sources. If you only have time to study one list of words, this is the list.
To create this list, we started with the words that give our users the most trouble and then ranked them by how frequently they appear in our corpus of billions of words from edited sources. If you only have time to study one list of words, this is the list.
- considerdeem to beAt the moment, artemisinin-based therapies areconsidered the best treatment, but cost about $10 per dose - far too much for impoverished communities.
— Seattle Times (Feb 16, 2012) - minuteinfinitely or immeasurably smallThe minute stain on the document was not visible to the naked eye.
- accordconcurrence of opinionThe committee worked in accord on the bill, and it eventually passed.
- evidentclearly revealed to the mind or the senses or judgmentThat confidence was certainly evident in the way Smith handled the winning play with 14 seconds left on the clock.
— Reuters (Jan 15, 2012) - practicea customary way of operation or behaviorHe directed and acted in plays every season and became known for exploring Elizabethan theatrepractices.
— BBC (Feb 16, 2012) - intendhave in mind as a purpose“Lipstick, as a product intended for topical use with limited absorption, is ingested only in very small quantities,” the agency said on its website.
— BusinessWeek (Feb 15, 2012) - concernsomething that interests you because it is importantThe scandal broke out in October after former chief executive Michael Woodford claimed he was fired for raising concerns about the company's accounting practices.
— BBC (Feb 15, 2012) - commitperform an act, usually with a negative connotationIn an unprecedented front page article in 2003 The Times reported that Mr. Blair, a young reporter on its staff, had committed journalistic fraud.
— New York Times (Feb 15, 2012) - issuesome situation or event that is thought aboutAs a result, the privacy issues surrounding mobile computing are becoming ever-more complex.
— Time (Feb 16, 2012) - approachmove towardsSpain’s jobless rate for people ages 16 to 24 isapproaching 50 percent.
— New York Times (Feb 15, 2012) - establishset up or foundA small French colony, Port Louis, was established on East Falkland in 1764 and handed to the Spanish three years later.
— BBC (Feb 16, 2012) - utterwithout qualificationNo one can blame an honest mechanic for holding a wealthy snob in utter contempt.
— Ingersoll, Robert Green - conductdirect the course of; manage or controlScientists have been conducting studies of individual genes for years.
— BusinessWeek (Feb 15, 2012) - engageconsume all of one's attention or timeWe had nearly two hundred passengers, who were seated about on the sofas, reading, or playing games, or engaged in conversation.
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— New York Times (Feb 11, 2012) - scarcedeficient in quantity or number compared with the demandMeanwhile, heating oil could grow more scarce in the Northeast this winter, the Energy Department warned last month.
— New York Times (Jan 21, 2012) - policya plan of action adopted by an individual or social groupInflation has lagged behind the central bank’s 2 percent target, giving policy makers extra scope to cut rates.
— BusinessWeek (Feb 15, 2012) - straightsuccessive, without a breakAfter three straight losing seasons, Hoosiers fans were just hoping for a winning record.
— Seattle Times (Feb 15, 2012) - stockcapital raised by a corporation through the issue of sharesIn other words, Apple’s stock is cheap, and you should buy it.
— Forbes (Feb 16, 2012) - apparentclearly revealed to the mind or the senses or judgmentBut the elderly creak is beginning to become apparentin McCartney’s voice.
— Time (Feb 16, 2012) - propertya basic or essential attribute shared by members of a classOwing to these magic properties, it was often planted near dwellings to keep away evil spirits.
— Parsons, Mary Elizabeth - fancyimagine; conceive of; see in one's mindFor a time, indeed, he had fancied that things were changed.
— Weyman, Stanley J. - conceptan abstract or general idea inferred from specific instancesAs a psychologist, I have always found the concept of speed dating fascinating.
— Scientific American (Feb 13, 2012) - courtan assembly to conduct judicial businessWhen Brown pleaded not guilty to assaulting Rihanna, their violent past came out in court.
— Slate (Feb 16, 2012) - appointassign a duty, responsibility or obligation toIn 1863 he was appointed by the general assembly professor of oriental languages at New College.
— Various - passagea section of text, particularly a section of medium lengthHis interpretation of many obscure scripturalpassages by means of native manners and customs and traditions is particularly helpful and informing.
— Sheets, Emily Churchill Thompson - vainunproductive of successAn attempt was made to ignore this brilliant and irregular book, but in vain; it was read all over Europe.
— Various - instancean occurrence of somethingIn many instances large districts or towns would have fewer representatives than smaller ones, or perhaps none at all.
— Clarke, Helen Archibald - coastthe shore of a sea or oceanMartello towers must be built within short distances all round the coast.
— Wingfield, Lewis - projecta planned undertakingThe funds are aimed at helping build public projectsincluding mass transit, electricity networks, water utility and ports, it said.
— BusinessWeek (Feb 17, 2012) - commissiona special group delegated to consider some matterThe developers are now seeking approval from the landmarks commission.
— New York Times (Feb 16, 2012) - constanta quantity that does not varyIn 1929, Hubble independently put forward and confirmed the same idea, and the parameter later became known as the Hubble constant.
— Nature (Nov 15, 2011) - circumstancesone's overall condition in lifeThe circumstances leading up to the shootings was not immediately available.
— Chicago Tribune (Feb 19, 2012) - constituteto compose or representOil and natural gas constituted almost 50 percent of Russian government revenue last year.
— BusinessWeek (Feb 19, 2012) - levela relative position or degree of value in a graded groupOnly last month did the men’s and women’s unemployment rates reach the same level.
— New York Times (Feb 19, 2012) - affecthave an influence uponThe central bank will start distributing low-interest loans in early March to individuals and small- and medium-sized companies affected by the flooding.
— BusinessWeek (Feb 19, 2012) - instituteset up or lay the groundwork forCorporations have to be more and more focused oninstituting higher labor standards.
— Washington Post (Feb 7, 2012) - rendergive an interpretation ofBut authorities had rendered the weapon and the explosive device inoperable, officials said.
— Chicago Tribune (Feb 17, 2012) - appealbe attractive toTo get traditional women’s accessories to appeal to men, some designers are giving them manly names and styles.
— New York Times (Feb 19, 2012) - generatebring into existenceQualities such as these are not generated under bad working practices of any sort.
— Hungerford, Edward - theorya well-substantiated explanation of some aspect of the worldTesting that theory begins Saturday night, as the Capitals take on Tampa Bay in another important contest.
— Washington Post (Feb 18, 2012) - rangea variety of different things or activitiesLike American community colleges, admission at an open university is not competitive, but the schools offer a range of programs, including doctoral degrees.
— Time (Feb 19, 2012) - campaigna race between candidates for elective officeAt the same point in 2004 — as an incumbent facing re-election — Mr. Bush had taken in about $145.6 million for his campaign.
— New York Times (Feb 18, 2012) - leaguean association of sports teams that organizes matches"When I broke into the big leagues until a month ago, Gary kept in touch," Mets third baseman David Wright said.
— Seattle Times (Feb 17, 2012) - laborany piece of work that is undertaken or attemptedMore labor is entailed, more time is required, greater delay is occasioned in cleaning up, and the amount of water used is much greater.
— Hoskin, Arthur J. - conferhave a meeting in order to talk something overMs. Stewart said Mrs. Bachmann conferred with her family and a few aides after her disappointing showing on Tuesday evening.
— New York Times (Jan 4, 2012) - grantallow to haveHe had been granted entry into the White House only for the daily briefing, later that afternoon.
— New York Times (Feb 17, 2012) - dwellthink moodily or anxiously about somethingBut it is hardly necessary to dwell on so normal an event.
— Vinogradoff, Paul - entertainprovide amusement forThe first Super Bowl in 1967 featured college marching bands entertaining the crowds at halftime.
— Reuters (Feb 6, 2012) - contracta binding agreement that is enforceable by lawContracts with utilities will be signed starting next month, he said.
— BusinessWeek (Feb 16, 2012) - earnestcharacterized by a firm, humorless belief in one's opinionsToo much praise cannot be given to the earnest and efficient missionaries who founded and have maintained this mission.
— Miller, George A. - yieldgive or supplyIt is a very important honey plant, as it yields an exceptionally pure nectar and remains in bloom a long time.
— Parsons, Mary Elizabeth - wanderto move or cause to move in a sinuous or circular courseWhile each animal wandered through the maze, its brain was working furiously.
— New York Times (Feb 16, 2012) - insistbe emphatic or resolute and refuse to budgeInterior Department officials insisted that they had conducted an extensive scientific inquiry before moving ahead with the spill response plan.
— New York Times (Feb 17, 2012) - knighta person of noble birth trained to arms and chivalryThe knight was gallant not only in war, but in love also.
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— Chicago Tribune (Feb 19, 2012) - conventiona large formal assemblyLast year, the industry’s main trade convention, the Inside Self-Storage World Expo, organized workshops in Las Vegas focusing on lien laws and auction sales.
— New York Times (Feb 17, 2012) - skillan ability that has been acquired by trainingHe says many new drivers are terrified of motorway driving because they do not have the skills or confidence needed.
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— BusinessWeek (Feb 1, 2012) - compelforce somebody to do somethingBut the flames grew too large, compelling firefighters to call off the rescue.
— New York Times (Feb 18, 2012) - ventureproceed somewhere despite the risk of possible dangersClearly he would not venture to descend while his enemy moved.
— Strang, Herbert - territorythe geographical area under the jurisdiction of a stateOn Friday, West Africa regional group Ecowas condemned the rebels, urging them to end hostilities and surrender all occupied territory.
— BBC (Feb 18, 2012) - tempera characteristic state of feelingOscar Wilde, to do him justice, bore this sort of rebuff with astonishing good temper and sweetness.
— Anonymous - bentfixed in your purposeThe business-oriented constituency of the Republican Party, Jacobs said, has been weakened by a factionbent on lowering taxes and cutting spending.
— BusinessWeek (Feb 17, 2012) - intimatemarked by close acquaintance, association, or familiarityThe female spider can choose when to cut offintimate relations by eating her partner, or kicking him out.
— Scientific American (Jan 31, 2012) - undertakeenter upon an activity or enterpriseAn autopsy has reportedly been undertaken but the results are not expected for several weeks.
— The Guardian (Feb 13, 2012) - majoritymore than half of the votes in an electionRepublicans need just four seats in the Senate to take control as the majority party.
— Reuters (Feb 7, 2012) - assertto declare or affirm solemnly and formally as trueIn your talk you asserted the pill's risks of blood clotting, lung artery blockage, heart attack and stroke are minimal.
— Science Magazine (Feb 18, 2012) - crewthe men and women who man a vehicleSeveral pilots and crew members would have to escape at once, while safety divers watched, ready to rescue anyone who became stuck.
— New York Times (Feb 6, 2012) - chambera natural or artificial enclosed space"Today," said the old man, "you must push through with me into my most solitary chamber, that we may not be disturbed."
— Carlyle, Thomas - humblemarked by meekness or modesty; not arrogant or prideful“Challenging yourself, playing up against stronger, tougher, and overall better competition will keep youhumble.”
— Washington Post (Jan 17, 2012) - schemean elaborate and systematic plan of actionSome companies in the Globe District of Arizona have started extensive underground schemes for mining large tonnages very cheaply by "caving" methods.
— Hoskin, Arthur J. - keendemonstrating ability to recognize or draw fine distinctionsNot one of his movements escaped her keenobservation; she drank in every shiver.
— Wingfield, Lewis - liberal....subscribe for more...funny comedy at www.YouTube.com/drcrazie
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