explain xkcd - User contributions [en]

2170: Coordinate Precision

2021-01-05T20:19:59Z

108.162.229.42: /* Explanation */ Phrasing, grammar

{{comic
| number = 2170
| date = July 1, 2019
| title = Coordinate Precision
| image = coordinate_precision.png
| titletext = 40 digits: You are optimistic about our understanding of the nature of distance itself.
}}

==Explanation==

This cartoon gives increasingly precise latitude and longitude coordinates for a location on the planet Earth. However, a given pair of coordinates covers a trapezoidal region of land, and thus leaves some ambiguity; therefore, greater precision requires an increasing count of decimal places in your coordinates. This comic uses this information to roughly identify how precise a given coordinate length might be.

The increasing precision of coordinates in this cartoon are similar to the increasing magnification in the short documentary {{w|Powers of Ten (film)|"Powers of 10,"}} which can be found [http://www.youtube.com/watch?v=0fKBhvDjuy0 here]. (Also parodied in [[271|#271:Powers of One]]).

The coordinates at [https://tools.wmflabs.org/geohack/geohack.php?pagename=Cape_Canaveral&params=28.52345_N_80.68309_W_type:landmark_region:US-FL_scale:10000 28.52345°N, 80.68309°W] (in {{w|decimal degrees}} form; in {{w|geographic coordinate system}} form using degrees, minutes, and seconds, 28° 31′ 24.4″N, 80° 40′ 59.1″W) are pointing to the {{w|Rocket Garden}} at the {{w|Kennedy Space Center}} in {{w|Merritt Island, Florida}} —specifically, the tip of the [https://www.kennedyspacecenter.com/-/media/DNC/KSCVC/Blog-Images/Rocket-Garden/rocket-garden-with-labels.ashx?h=860&w=1173&la=en&hash=7B9ADC7AFF5370E462AC98D9651945B806B77B2C Delta] rocket.

The sixth entry in the table, with seven digits of precision, includes the caveat that, while your coordinates map to areas small enough on the Earth's surface to indicate pointing to a specific person in a room, "since you didn't include datum information, we can't tell who". This is a reference to the ''{{w|geodetic datum}}'' or ''geodetic system'' — different ways of dealing with the fact that the Earth is neither perfectly spherical nor perfectly an oblong ellipsoid. The various datums do not make much difference at six digits of precision, but at seven, there is enough skew depending on which system is in use that the person in a room you are referring to with the coordinates is ambiguous. It is unstated, but the remaining lines in the table with ever-greater precision suffer from this same issue and are equally ambiguous without datum information.

The final entry, with seventeen digits of precision, suggests that either the user is referring to individual atoms in the much-larger-scale whole-Earth coordinate system, or (perhaps more likely) has not bothered to format the values from the GPS module for viewing in the software UI in any way whatsoever, resulting in a value that is {{w|False precision|meaninglessly precise}} because the measurement wasn't that {{w|Accuracy and precision|accurate}} to begin with. Even if the value is accurate, locating individual atoms by coordinates is not actually useful in most cases, and the motions of multiple systems within our physical world (continental drift, subtle vibrations, {{w|Brownian motion}}, etc.) would render the precise value obsolete rather quickly.

For the decimal places past the 5th on the latitude, the digits given are actually the first part of the decimal expansion of the constant ''e'' (2.7182818284), while for the decimal places past the 5th on the longitude, the digits given are part of the decimal expansion of the constant ''π'' (3.14159265358) starting with the second digit (4).

The title text references how at sufficiently small distances, our understanding of reality itself begins to break down. Smaller than the {{w|Planck length}}, which is more than a quintillion times smaller than the diameter of a proton, the ideals of Euclidean geometry no longer apply and space itself may be composed of a {{w|quantum foam}} where the very geometry of spacetime itself fluctuates, meaning coordinate systems based on an assumption that space doesn't change would no longer work. String theory, on the other hand, assumes that at a short enough distance the world is composed of ten space dimensions, which precludes the use of a two-dimensional coordinate system (not that our “normal” three dimensions don't do so in themselves).

The actual number of longitude digits needed to identify a point to a particular precision depends on its latitude. Near the poles, you need fewer longitude digits than at the equator – starting with one digit fewer at around lat. 85°, past all constantly inhabited human settlements, and with two digits fewer at lat. 89.5°, inaccessible to anyone but polar researchers and the occasional guided tour. The number of latitude digits for some particular accuracy stays essentially the same everywhere.

==Chart==

{| class="wikitable"
|-
! Decimal places
! Resolution*
! In the comic
! Location
! Explanation/notes
|-
| 0
| 110 km (70 mi)
| Something space-related
| Somewhere near the east coast of Florida
| This resolution is enough to point out a large-scale feature like a country, a mountain range, a large lake, or a significant island on a map of the world. It can also be used to tell if certain celestial phenomena are visible from a given location.
|-
| 1
| 11 km (7 mi)
| A specific city
| Cape Canaveral
| Cities typically span a couple kilometers/miles in diameter and are far enough from each other to distinguish them at this resolution. There are exceptions though, and the veracity of this statement depends greatly on the definition of a “city”, which varies by location and history.
|-
| 2
| 1.1 km (¾ mi)
| A neighborhood
| Kennedy Space Center Visitor Complex
|
|-
| 3
| 110 m (360 ft)
| A suburban cul-de-sac
| The Rocket Garden at the Kennedy Space Center
|
|-
| 4
| 11 m (36 ft)
| A particular corner of a house
| Somewhere near the center of the Rocket Garden
|
|-
| 5
| 1.1 m (3½ ft)
| A specific person in a room (given geodetic datum information)
| The [https://www.kennedyspacecenter.com/-/media/DNC/KSCVC/Blog-Images/Rocket-Garden/rocket-garden-with-labels.ashx?h=860&w=1173&la=en&hash=7B9ADC7AFF5370E462AC98D9651945B806B77B2C Thor-Delta] rocket in Rocket Garden
| As the comic notes, the differences between {{w|geodetic datum}}s – different ways to map geodetic coordinates to specific points on the Earth's surface – become large enough that one needs to specify the one in use when supplying coordinates to this degree of precision (or greater, of course). Since the Earth is not a perfect ellipsoid, different parts of the planet conform best to ellipsoids of slightly different proportions, resulting in different coordinates for a specific location; not to mention that locally used datums have local reference points, which means that the local and global standards are slowly drifting away from each other with the tectonical plates.
Note that the comment in the comic concerns only the {{w|North American Datum|NAD 1983}} datum which is fairly close to the international, “one size fits all” standard {{w|WGS-84}}. Other datums may be shifted by tens or even hundreds of meters (yards), making geodetic datum specification necessary for less precise coordinates as well.
|-
| 7
| 1.1 cm (⁷⁄₁₆ in)
| Waldo on a page
| Presumably the very tip of the rocket
| This refers to ''{{w|Where's Wally?|Where's Waldo?}}'', a series of books and magazines containing various scenes (densely packed with people) where one must find Waldo, a character wearing a red and white striped shirt. In the puzzles, he usually stands less than 2 cm (1 in) tall.
Finding Waldo on a page using satellites was also referenced in [[1358:_NRO|#1358]].
|-
| 9
| 0.11 mm (4⅜ thou)
| A specific grain of sand
| rowspan=3 | N/A
|
|-
| 15
| 110 pm (1.1 Å)
| Raw floating point precision or an individual atom
| A double-precision (64-bit) floating point variable stores 52 significant bits (with an implicit 1 in front), so that 180.00000000000000 and 179.99999999999997 may be represented as distinct values. (This is only 14 decimals, however; the larger the integral part, the fewer bits remain to represent the fractional part.) This level of precision is useful for mitigating rounding errors in computations, but this advantage only shows if the last few digits are treated as non-significant and thus, ideally, hidden from view. To work with data that is actually this precise – like tracking individual atoms or representing continental drift up to the second –, one must make allowance for these additional non-significant digits and store the coordinates in ''quadruple'' precision.
To track atoms, however, one needs very sensitive (and expensive) equipment with a severely limited range (according to our current understanding of science and technology). Using a global-scale coordinate system when a micrometer-scale would fit much better is either an abuse of the system and a great waste of memory and computing power, or it means that a significant portion of the Earth's surface has been blanketed by quantum microscopes, which would be an abuse and a waste of many other things as well.{{Citation needed}}
|-
| 40
| 1.1 × 10–11 ym (1.1 × 10–35 m)
| Near (or past) our current understanding of the nature of distance
| This is where the resolution reaches the Planck length (1.6 × 10–35 m). At this scale, the very structure of spacetime (and thus, the notion of distance) may be different than what we know; measuring anything to Planck length precision would necessitate such tremendous amounts of energy in one place that would create minuscule black holes, warping spacetime further (in addition to wreaking havoc with whatever you were trying to pinpoint).
|}
<nowiki>*</nowiki>Since the Earth is not exactly spherical, the actual length of one degree of latitude varies between 110.574 km (68.707 mi) at the equator and 111.694 km (69.403 mi) at the poles, while one degree of longitude is 111.320 km (69.171 mi) at the equator, 55.800 km (34.673 mi) at lat. 60°, and 0 km (0 mi) at the poles.

==Transcript==
:[Single panel containing a table with two columns for "Lat/Lon Precision" and "Meaning" and a caption above the table.]
:Caption: What The Number of Digits in Your Coordinates Means

:[Row 1]
:Lat/Lon: 28°N, 80°W
:Meaning: You're probably doing something space-related

:[Row 2]
:Lat/Lon: 28.5°N, 80.6°W
:Meaning: You're pointing out a specific city

:[Row 3]
:Lat/Lon: 28.52°N, 80.68°W
:Meaning: You're pointing out a neighborhood

:[Row 4]
:Lat/Lon: 28.523°N, 80.683°W
:Meaning: You're pointing out a specific suburban cul-de-sac

:[Row 5]
:Lat/Lon: 28.5234°N, 80.6830°W
:Meaning: You're pointing to a particular corner of a house

:[Row 6]
:Lat/Lon: 28.52345°N, 80.68309°W
:Meaning: You're pointing to a specific person in a room, but since you didn't include datum information, we can't tell who

:[Row 7]
:Lat/Lon: 28.5234571°N, 80.6830941°W
:Meaning: You're pointing to Waldo on a page

:[Row 8]
:Lat/Lon: 28.523457182°N, 80.683094159°W
:Meaning: "Hey, check out this specific sand grain!"

:[Row 9]
:Lat/Lon: 28.523457182818284°N, 80.683094159265358°W
:Meaning: Either you're handing out raw floating point variables, or you've built a database to track individual atoms. In either case, please stop.

{{comic discussion}}

[[Category:Space]]
[[Category:Geography]]
[[Category:Programming]]

Talk:835: Tree

2014-06-17T14:10:34Z

108.162.229.42:

I didn't really look too closely, but it seems to be based on Red-Black trees (Red Green in the case of Christmas): http://en.wikipedia.org/wiki/Red_black_tree

Then again it could just be a color scheme. [[Special:Contributions/132.3.25.79|132.3.25.79]] 12:35, 23 April 2013 (UTC)Tyler

The title text doesn't really make sense - removing the root of a heap is a very common practice for a variety of applications. In fact, you almost always want to process heaps by removing the root. [[User:Ciotog|Ciotog]] ([[User talk:Ciotog|talk]]) 14:05, 2 March 2014 (UTC)
: It is common, ok. And, in fact, Billy WILL process the heap by removing the root. It makes however sense, since all heaps must be "refreshed" after you remove the root. While it takes small time for a computer, it can be lengthy for a human. And it would be probably better an unsorted array of presents, so Billy can open any present without effecting any effect (see Comic 326) --[[Special:Contributions/108.162.229.42|108.162.229.42]] 14:10, 17 June 2014 (UTC)

1331: Frequency

2014-02-18T00:08:05Z

108.162.229.42: /* Explanation */

{{comic
| number = 1331
| date = February 17, 2014
| title = Frequency
| image = frequency.png
| titletext = This comic shows estimated average frequency. I wanted to include the pitch drop experiment, but it turns out the gif format has some issues with decade-long loops.
}}

Today's comic is animated. While we prepare a gif for the wiki, click on the date above the comic to see the animated version.
==Explanation==
{{incomplete|Incomplete.}}
This comic shows a number of common events, arranged in a grid. Each of the events flashes with their average frequency.

For example, statistically a child is born somewhere on the world approximately every 0.24 seconds, or four times per second. Therefore the tile "One birth" blinks about 4 times per second.

The table below lists all the events and their duration / frequency. Some events make reference to other comics.

The title text refers to the {{w|Pitch drop experiment}} which measures the flow of a piece of pitch over many years. At room temperature, tar pitch flows at a very slow rate, taking several years to form a single drop. The title text jokes that Randall tried to include a tile that flashes about once every {{w|decade|ten years}}, but the tiles are all {{w|Animated GIF|animated GIFs}} and the file format does not support animations that long.

{| class="wikitable sortable"
!Picture
!Text
!Period (seconds)
!Frequency (per minute)
!Frequency (per year, N/I = not interesting)
!Explanation
|-
|[[File:heartbeat.gif]]
|Heartbeat||0.86||70||32,785,200||
|-
|[[File:birth.gif]]
|One birth||0.24||250||131,490,000||
|-
|[[File:death.gif]]
|One death||0.56||107||56,360,000||
|-
|[[File:wikipedia.gif]]
|Someone edits Wikipedia||0.67||90||47,100,000||
|-
|[[File:vibrator.gif]]
|Someone buys a vibrator||2.99||20||10,550,000 ||
|-
|[[ File:car china.gif ]]
|China builds a car||1.89||32||16,700,000||
|-
|[[ File:car japan.gif ]]
|Japan builds a car||4.01||15||7,870,000||
|-
|[[ File:car germany.gif ]]
|Germany builds a car||5.8||10||5,440,000||
|-
|[[ File:car us.gif ]]
|The US builds a car||6.95||8.6||4,540,000||
|-
|[[ File:car elsewhere.gif ]]
|Someone else builds a car||1.03||58||30,640,000||
|-
|[[ File:kiss.gif ]]
|A European Union resident has their first kiss||5.53||11||5,700,000||
|-
|[[ File:fire dept.gif ]]
|A US fire department puts out a fire||23||2.6||1,370,000||
|-
|[[ File:holeinone.gif ]]
|Someone hits a hole-in-one||180||20 times per hour||175,320||A {{w|hole in one}} is a feat in {{w|golf}} in which the player hits the ball directly from the tee into the cup with one shot.
|-
|[[ File:turnsignal1.gif ]]
|My turn signal blinks||0.94||64||N/I||See below
|-
|[[ File:turnsignal2.gif ]]
|The turn signal of the car in front of me blinks||0.9||67||N/I||This, together with the previous item, forms a reference to [[165: Turn Signals]].
|-
|[[ File:earthquake1.gif ]]
|Earthquake (magnitude 1)||2.43||25||13,000,000||
|-
|[[ File:earthquake2.gif ]]
|Earthquake (magnitude 2)||24.26||2.5||1,300,000||
|-
|[[ File:earthquake3.gif ]]
|Earthquake (magnitude 3)||242.6||15 times per hour||130,000||
|-
|[[ File:earthquake4.gif ]]
|Earthquake (magnitude 4)||2426||1.5 times per hour||13,000||
|-
|[[ File:parliament toilet.gif ]]
|A member of the UK parliament flushes a toilet||10.06||6||3,140,000||Note that probably during the daytime in Britain such a toilet is flushed 8.5 times per minute, while at night it is flushed only 1 time per minute.
|-
|[[ File:flight.gif ]]
|An airline flight takes off||0.93||65||34,000,000||
|-
|[[ File:book mockingbird.gif ]]
|Someone buys ''To Kill a Mockingbird''||42.05||1.4||750,000||“{{w|To Kill a Mockingbird}}” is a famous novel by {{w|Harper Lee}}.
|-
|[[ File:cat mockingbird.gif ]]
|Someone's pet cat kills a mockingbird||1.82||33||17,340,000||Whereas the previous item references the well-known book “To Kill a Mockingbird”, this one talks about {{w|Mockingbird|mockingbirds}} being literally killed (in this case, by cats). There are 45 million mockingbirds in the world;[http://animaldiversity.ummz.umich.edu/accounts/Mimus_polyglottos/] this means that according to Randall, cats kill 39% of mockingbirds in one year, i.e. in 2.5 years they are able to kill all mockingbirds (excluding the ones that are born in the meantime).
|-
|[[ File:phoenixshoes.gif ]]
|Someone in Phoenix buys new shoes||1.08||56||29,200,000||Since {{w|Phoenix metropolitan area|metro Phoenix}} has 4,200,000 inhabitants, according to Randall people in Phoenix buy 7 pairs of shoes per capita per year.
|-
|[[ File:phoenix.gif ]]
|Someone in Phoenix puts on a condom||2.05||29||15,390,000||
|-
|[[ File:keys.gif ]]
|Someone locks their keys in their car||2.43||25||13,000,000||
|-
|[[ File:amelia.gif ]]
|A Sagittarius named Amelia drinks a soda||7.79||7.7||4,000,000||This frequency is taken from the number of persons called {{w|Amelia_(given_name)|Amelia}} ([http://howmanyofme.com/ est. 82,572 people in the U.S.]), the number of persons born under the astrological sign of {{w|Sagittarius (astrology)|Sagittarius}} (~1/12th of the population, i.e. approximately 6881 Amelias in the U.S.) and the frequency of soda (soft drinks) being drunk (216 liters per person per year in the U.S.[http://www.nationmaster.com/graph/foo_sof_dri_con-food-soft-drink-consumption]). According to our figures, 6881 Amelias drink 1,44 million liters of soft drinks per year in the United States alone, which means that Randall's figures only account for American Amelias (drinking 356 cc or 12 fl. oz. of soda in each drink).
|-
|[[ File:dogbite.gif ]]
|A dog bites someone in the US||7.01||8.6||4,500,000||
|-
|[[ File:bike.gif ]]
|Someone steals a bicycle||24.93||2.4||1,265,000||
|-
|[[ File:eagle.gif ]]
|A bald eagle catches a fish||2.69||22||11,700,000||
|-
|[[ File:bottles.gif ]]
|50,000 plastic bottles are produced||1.27||2.36 million bottles||1.24 trillion||
|-
|[[ File:recycled.gif ]]
|50,000 plastic bottles are recycled||4.64||646,552 bottles||340 billion||27% of the plastic bottles manufactured get recycled
|-
|
|A bright meteor is visible somewhere||1.15||52||N/I||
|-
|
|Old Faithful erupts||5640 (94 minutes)||15 times per day||5,595||{{w|Old Faithful}} is a geyser in {{w|Yellowstone National Park}} in the US, that tends to erupt every 65 or 91 minutes. XKCD's period of 1h 34m falls between the [http://geysertimes.org/getGeyserInfo.php?geyserID=2 mean and median of recent Old Faithful eruptions] and corresponds to a [http://geysertimes.org/getSingleEruption.php?id=645135 February 16, 2014 eruption].
|-
|
|A fishing boat catches a shark||0.83||72||38,000,000|| [[1326: Sharks]]
|-
|
|Someone in the US is diagnosed with cancer||18.99||3.2||1,660,000|| [[881: Probability]]
|-
|
|Someone in the US dies from cancer||54.34||1.1||580,000|| [[881: Probability]]
|-
|
|Someone adopts a dog from a shelter||15.6||3.8||2,000,000||
|-
|
|Someone adopts a cat from a shelter||21.3||2.8||1,5000,000||
|-
|
|Someone gets married||0.75||80||42,000,000||
|-
|
|Someone registers a domain||0.64||94||49,300,000 ||
|-
|
|Someone in the US buys a house||6.22||9.6||5,000,000||
|-
|
|Someone in the US gets a tattoo||2.06||29||15,300,000||
|-
|
|The star PSR J1748-2446AD rotates 1,000 times||1.4||43,000 rotations||N/I||{{w|PSR J1748-2446ad}} is the fastest spinning {{w|pulsar}} known.
|-
|
|Someone lies about their age to sign up for Facebook||4.32||14||600,000 per month||To sign up for Facebook, [https://www.facebook.com/help/210644045634222 the user must claim to be at least 13 years old]. This is a reflection of the U.S. {{w|Children's Online Privacy Protection Act}}.
|-
|
|Someone breaks an iPhone screen||0.93||65||34,000,000||
|-
|
|A Little League player strikes out||1.23||49||N/I||{{w|Little League Baseball|Little League}} is a system of local youth baseball and softball competitions. A {{w|strikeout}} is a situation in baseball and softball.
|-
|
|Someone has sex in North Dakota||1.38||43||22,900,000||Since {{w|North Dakota}} has 723,000 inhabitants (ranked the 48th state), and if we estimate the sexually active population as 80% (and if ''someone'' means ''a couple)'' this means that people in North Dakota have sex 79.1 times a year. It is estimated that 3.93% of the world population has sex on a given day;[http://geography.about.com/od/culturalgeography/a/geographyofsex.htm] Randall's rate for North Dakota is 17.3% which is not low.
|-
|
|Justin Bieber gains a follower on Twitter||4.73||13||556,000 per month||{{w|Justin Bieber}} is a Canadian pop music singer whose [https://twitter.com/justinbieber Twitter account] is extremely popular
|-
|
|Someone in Denver orders pizza||1.27||47||2,000,000||
|}

==Transcript==
:[Repetitive events are written in grey and arranged in a grid. Each statement pulses to black and then returns to grey at an interval characteristic of the named event.]

{| style="text-align:center;"
|- style="vertical-align: top; background-color:#eeeeee;"
|Heartbeat (0.86 sec)
|One birth (0.24 sec)
|One death (0.56 sec)
|Someone edits Wikipedia (0.67 sec)
|Someone buys a vibrator (2.99 sec)
|- style="vertical-align: top;"
|China builds a car (1.89 sec)
|Japan builds a car (4.01 sec)
|Germany builds a car (5.8 sec)
|The US builds a car (6.95 sec)
|Someone else builds a car (1.03 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|A European Union resident has their first kiss (5.53 sec)
|A US fire department puts out a fire (23 sec)
|Someone hits a hole-in-one (180 sec)
|My turn signal blinks (0.94 sec)
|The turn signal of the car in front of me blinks (0.9 sec)
|- style="vertical-align: top;"
|Earthquake (magnitude 1) (2.43 sec)
|Earthquake (magnitude 2) (24.26 sec)
|Earthquake (magnitude 3) (242.6 sec)
|Earthquake (magnitude 4) (2426 sec, 42 min)
|Member of the UK Parliament flushes a toilet (10.06 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|An airline flight takes off (0.93 sec)
|Someone buys ''To Kill a Mockingbird'' (42.05 sec)
|Someone's pet cat kills a mockingbird (1.82 sec)
|Someone in Phoenix buys new shoes (1.08 sec)
|Someone in Phoenix puts on a condom (2.05 sec)
|- style="vertical-align: top;"
|Someone locks their keys in their car (2.43 sec)
|A Sagittarius named Amelia drinks a soda (7.79 sec)
|A dog bites someone in the US (7.01 sec)
|Someone steals a bicycle (24.93 sec)
|A bald eagle catches a fish (2.69 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|50,000 plastic bottles are produced (1.27 sec)
|50,000 plastic bottles are recycled (4.64 sec)
|A bright meteor is visible somewhere (1.15 sec)
|Old Faithful erupts (5640 sec, 94 min)
|A fishing boat catches a shark (0.83 sec)
|- style="vertical-align: top;"
|Someone in the US is diagnosed with cancer (18.99 sec)
|Someone in the US dies from cancer (54.34 sec)
|Someone adopts a dog from a shelter (15.6 sec)
|Someone adopts a cat from a shelter (21.3 sec)
|Someone gets married (0.75 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|Someone registers a domain (0.64 sec)
|Someone in the US buys a house (6.22 sec)
|Someone in the US gets a tattoo (2.06 sec)
|The star ''PSR J1748-2446ad'' rotates 1,000 times (1.4 sec)
|Someone lies about their age to sign up for Facebook (4.32 sec)
|- style="vertical-align: top;"
|Someone breaks an iPhone screen (0.93 sec)
|A little league player strikes out (1.23 sec)
|Someone has sex in North Dakota (1.38 sec)
|Justin Bieber gains a follower on Twitter (4.73 sec)
|Someone in Denver orders a pizza (1.27 sec)
|}

{{comic discussion}}
[[Category:Dynamic comics]]
[[Category:Charts]]

1331: Frequency

2014-02-17T11:16:11Z

108.162.229.42: /* 1. Changed the two occurences of one birth from 'five times per second' to 'four times per second', as 0.24 second is about 1/4 second. 2. Removed 's' from 'seconds' for time < 2 seconds in the table. */