Selected BotE problems represented in Solve

Here we have the selected problems from bote_problems.html that I am going to represent in Cyc and make Solve solve. The problem numbers refer to those in the original bote_problems.html file.

General Representation Issues

All these questions require finding a number for something. There seems to be two main possibilites --

Countable/discrete things: number of elements in some set.
Number of members of a collection. Is this different from 1?
Continuous things: the exact value for a continuous parameter.

The answer should match with the representation we proposed in the Carve paper. We have the following types of symbolic representations of quantity --
Cyc used to provide high/medium/lowAmountFn. Now they have been replaced with h/m/lAmountOf which works in a funny way. I think this is a consequence of getting rid of attributes. I'll ignore that representation for a while, since I am not sure that it is even stable.

High/Medium/LowValueFn
(isa Canada (HighValueFn Area))
High/Medium/LowValueContextualizedFn
(isa Algeria (HighValueContextualizedFn Area AfricanCountries))

Should the second argument be a PhysicalAmountSlot, in this case, areaOfRegion? That will definitely help in making the inference if somebody asked me what the area of Algeria was.

Set : (cardinality SETORCOL N)
Collection
Group

Why do these make me unhappy? If there is no real reason, then we can represent most of the problems as large conjuncts like this.

(cardinality
       (TheSetOf ?SHIP
           (and
               (isa ?SHIP Ship)
               (owns Iceland ?SHIP)
               (not
                   (isa ?SHIP MilitaryVehicle))
               (vehicleCargoCapacity-Volume ?SHIP
                   (IntervalMinFn
                       (CubicFoot 100000))))) 4)

If the input to solve is a conjunction, what do we want it to do? If the entire query is saved as a node, then its a problem, because since we are doing unification to match a suggestion with the query, there are combinatorial possibilities in the ways in which conjuncts could be arranged (that could be taken care of by canonicalization), but still there is the problem if the query is all conjuncts minus one, the suggestion still might apply, and are we going to write all such possibilites for a suggestion? On the other hand, we can not do that, and when we get a query that is a conjunct, it expands into and-nodes, via an and-suggestion, and now we have primitive queriable forms.

Created 03/22/04

#	Problem, and English worked out solution	Problem, and CycL and other needed knowledge.	Comments
3	How many babies are born in the USA each minute? Population = 300 mil Life expectancy = 75 Assume uniform distribution of people over age # of people 1 yr old = 1/75 * 300 # of babies born per min = 1/70 * 300 * 1/365 * 1/24 * 1/60 mil = 8 per min [US Census website: 1 baby per 8 seconds = 7.5 babies per sec]	(populationDuring UnitedStatesOfAmerica (MonthFn July (YearFn 1997)) 267954764) (lifeExpectancyForGroupInRegion UnitedStatesOfAmerica FemaleHuman (YearsDuration 79.7)) (lifeExpectancyForGroupInRegion UnitedStatesOfAmerica MaleHuman (YearsDuration 72.8)) There is no notion of distribution. Need to make a strategy. Given life expectancy, population, and an age range; the number of people in that range assuming uniform distribution is given by the fraction of people in that age group multiplied by the population. Alternate: (birthRate UnitedStatesOfAmerica 15.25) Thats per thousand per year. Since population = 300mil, that implies 15.25/1000 * 300mil = 15.25 * 300 1000 = 4575000 Per minute = 4575000/36524*60 = 8.7 Query:	The populationDuring statement occurs in many microtheories -- Factbook 1995, 1996, HPKP, Agent Factsheet, etc. How to know which one to pick when that happens? And the time is implicit in question -- maybe now? Male/female implicit?
4	How many K-8 elementary school teachers are in the USA? Given life expectany = 75 and 9 of these years are spent in K-8, the number of kids is approx 1/8 th of the population. Number of kids in K-8 schools = 300/8 mil Assume for every 25 kids there is a teacher Number of teachers = 300/8 * 1/25 = 1.5 million [1.9 million according to Statistical Abstracts, Hoover Business Press]	ElementarySchool -- the collection of all elementary schools. Teacher "K-8 Elementary school teachers" ElementarySchoolTeacher --> USElementarySchoolTeacher (cardinality ElementarySchoolTeacher ?x) Strategy1: find number of students, and number of teachers per student. We need another strategy that says that the number of Using the same logic as in #2, find the number of kids going to K-8 schools.
5	How much is spent on newspapers in USA? 300 mil, Assume 3 per household, 100 mil household. Assume each house buys a newspaper a day. Assume it costs 50 cents Per year money spent = 100 * 365 *0.5 mil = 18 billion [26 billion according to SA, HBP] NewspaperIssue is all the instances of a newspaper on a date. annualSales OBJ PLACE YEAR MONEY annualSales NewspaperCopy UnitedStates 2003 ?sales unitsSold OBJ PLACE TIME NUM cost OBJ PRICE ;; Law of suppy and demand unitsSold OBJ PLACE TIME NUM unitsBought OBJ PLACE TIME NUM unitsBought OBJ PLACE TIME NUM numberOfBuyers OBJ PLACE TIME NUM unitsBoughtPerBuyer OBJ PLACE TIME NUM units	NewspaperSeries: "The collection of all PeriodicalSeries which have NewspaperIssues as subWorks." (priceChargedFor PLACE PRODUCT-TYPE MONEY-RATE) (totalCharge THING MONEY) (relationAllInstance cost Toothbrush (Dollar-UnitedStates 1 3)) OK, cost is the simplest one to use. We need to talk about specific newspapers, and not the brands, so NewspaperCopy Introduce a collection, (genls USNewspaper NewspaperSeries) Now how do we say cost for the whole year? Introduce a predicate (annualCost USNewspapers ?x) :goal (annualCost USNewspaperIssues ?news-cost) :subgoals (unitsSoldPerYear NewsPaperCopy UnitedStatesOfAmerica 2003 ?num) (cost NewsPaperCopy ?price) :result-step (evaluate ?newscost (multfn ?num ?price)) :goal (unitsSoldPerYear NewsPaperCopy UnitedStatesOfAmerica 2003 ?num) :subgoals ( Lets see, how will I ideally do this: (and (isa ?x NewspaperCopy) (isa ?x USNewspaper) (sold	We need to be able to create collections on the fly for these queries, rather than creating new collections like USNewspapers and USDentists, everytime we have a question about US.
6	How many cars are bought in the USA? 300 mil, Assume 3 per household, 100 mil household. Assume 1 car per household Assume a car lives 10 years on an avg So, on an average 1/10th of the cars will be replaced any year = 10 million cars [8 millions in 1997] [133 million cars nationwide in 2000, Stat Abs, 2002]	"cars bought in the usa" "per year" (and (isa ?car Automobile) (buys ?car ?person) (isa ?person UnitedStatesPerson)) Now, either we say per year, or in a specific year. (relationAllInstance age Automobile (YearsDuration 5 50))	Whenever we find an interval, we cant bother to do interval math, just average it to get a scalar?
7	How many dentists are there in US? Assume 1 person makes two visits per year. Assume a dentist sees 10 people a day, or 3650 visits per year Number of visits required per year = 300 mil * 2 Number of dentists = 300 * 2/3650 = 164,000 [160,000 according to SA, HBP]	Dentist
10	What is the weight of solid garbage thrown away by American families each year? 100 million households. Averaging 1 to 2 pounds per day? 200 million pounds? Another way -- 10 lbs of garbage/week (for a family of 4) 10 lbs of recyclable materials/week (for a family of 4) total: 20 lbs of trash/week (for a family of 4) 50 weeks/year . 20 lbs of trash/week = 1,000 lbs of trash/ year The answer is: about 1,000 lbs of trash/year	Missing knowledge: Garbage-OfficeRefuse is a subset of #$Garbage-Generic.
11	How much time would be saved nationwide by increasing the speed limit from 55 to 65 mph? 3 people per household, 1 car per household => 100 million cars. How much is everyone driving? For an average person, 20 miles a day, plus 1000 miles of longer trips => ~ 10,000 miles per year. [Well, SA says about 12000 miles per year on an average vehicle] Total miles driven = 100 billion. Time saved = 100/10 = 10 billion hours 8760 hours in an year, say 10,000 = 1 million years. Well per person, its 10,000/300 = 30 hours.
18	How many uranium atoms must undergo fission to supply electricity to an average household for one day? (number of uranium atoms) 1 fission results in 200 Mev = 200 * 10^9 1.6 10^-19 = 3.2 * 10^ -11 J (1 ev = 1.6 * 10 ^-19 J) 1 J = 1/3.2 * 10^11 fissions 1 W = 3 * 10^10 fissions per sec Average power consumption of a house: 10 cents per kWH. Monthly bill of a household = 50 Perday $2 = 20 kWH
32	How much tea is there in China? 1 billion people. 5 cups a day. 5 gms a cup. Lets say they stock an years worth of supply. 25 billion grams = 25 million kilos per day In an year, 365 * 25 ~ 10 billion kilos
33	Annual cost of healthcare in USA? The insurance companies cant be making a loss, so this gives an upper bound = 300 mil * 1000 = 300 billion. No, there is medicare and other things.
34	How much paper does the New York Times use in a week? circulation of NYT size of a newspaper/amount of paper in it. population of NY ~ 10 mil 3 mil families, 1/3 of them buy paper, say 1 mil NYT issues sold 1ft * 1ft * 0.5 inch 1ft * 1ft * 2 inch sunday 1/2 mil cubic feet per week. If stacked 10 ft high, need 100,000 sq ft. roughly 300ft * 300ft -- football field.
35	How many hotdogs sold in a baseball season at Wrigley Field? there are 80 home games/season attendance: 35,000 people/game (usually sold out) 1 hot dog/person (some people buy more than one, some don't buy any) (80 games/season) . (35,000 people/game) . (1 hot dog/person) = 2,800,000 hot dogs/person The answer is: about 3,000,000 hot dogs/season.
36	How much gasoline is used by a car per year? Or maybe total amount of gas used? the average capacity of a gas tank: 12 gallons/1 filling 1 filling/week 8 additional fillings/year for vacation times (52 weeks/year) . (1 filling/week) . (12 gallons/filling) + (8 fillings/year) . (12 gallons/filling) The answer is: about 700 gallons/ year. (What do we get if we go in another way?) an average person drives: 15,000 miles/year an average car's efficiency: 20 miles/gallon (15,000 miles/year) / (20 miles/gallon) = 750 gallons/year The answer is: about 700 gallons/year.
37	How many chopsticks are used in japan per year? population: 127,214,499		On an average, 23 to 25 billion disposable chopsticks are used every year in Japan (around 200 per person). Of this, 90 percent is imported and 10 percent is made domestically. If put end to end, the chopsticks will l stretch from Tokyo to the southern city of Fukuoka in Kyushu! These disposable chopsticks are about 8" long and between 1/4" and 1/8" thick. We'll assume that the cross-sectional area of 10 pairs is one square inch, with machining lossses. Let's say that our tree is a foot across and has 100 square inches cross-section. Let's say it's 50 feet high and (throw in some more machining losses as I think we've been a bit tight so far) we can get one chopstick length per foot. So we can get 5010010 = 50,000 pairs of chopsticks from one tree. Then, Japan is about the size of the UK, so we'll assume it's got 50m people. Say 40m off them use disposable chopsticks and they use 2 pairs a day for 300 days a year - that's 24,000,000,000 pairs or 4,800,000 trees.
38	Whats the total volume of blood in the world?
39	What is the flow rate of the Mississippi river?
40	What is the average speed of an automobile including all the overhead (maintenance, looking for parking, cleaning, etc)? Of a bicycle?
41	How much electric power is used by american households in a year?
42	What is the heat output of a human being?
43	How much flow is needed for a 1000 MW hydroelectric power plant?
44	How much coal is needed for a 1000 MW coal-fired plant?
45	How much area is needed for a 1000 MW solar power generator?
46	How much uranium is needed for a 1000 MW nuclear plant? Amount of solid waste produced?

3) How much oil is consumed in the US? This is a timely and relevant question since the "Gulf crisis" and subsequent war six years ago.

Solution: Where do you begin such an estimate? Well, the use of oil (or its byproducts) with which you are probably most familiar is the use of gasoline in your car or your family's car. Approximating your gasoline consumption will be a good starting point. Then estimating the number of cars in the country will give the next bit of necessary data. A factor for other motor vehicles will be needed also, i.e. trucks, buses, airplanes. Finally a guess at the amount of gasoline produced by each gallon or barrel of crude oil will be needed. What about heating oil, oil for generating electricity, and other petroleum products like plastics?

To begin the oil consumption estimation consider a single personal automobile. If you own one (or have noticed what family or friends spend on gasoline), then you know that a typical fuel tank holds on the order of 10 gallons (and gas costs over $1.20 per gallon as of Jun.11,1997). Furthermore such cars run about 200 or so miles on 1 tank, so that the "mileage" or fuel efficiency is about 20 miles per gallon (20 mpg). How many miles does a typical car cover in one year? There is obviously a lot of variation, but a typical distance (that the I.R.S. assumes average for auto expenses on the income tax forms) is 10,000 miles. Hence for 1 car the consumption is

10,000 miles
________________ = 500 gal in 1 year.
20 miles/gal

Next we need an estimate of how many cars are in use in the US. The population is about 250 million and perhaps 1 in 3 drive a car; say 100 million cars for simplicity. Then all passenger cars consume 500 x 100x10⁶ = 5x10⁴ x 10⁶ = 5x10¹⁰ gallons of gasoline in 1 year. Now a barrel of oil is defined as 42 gallons, so assuming that most of the crude oil becomes gasoline we obtain

5x10¹⁰ gal/yr 50x10⁹
___________ = ______ = 1.2x10⁹ bbl/yr ,
42 gal/bbl 42

or in terms of barrels per day we have

1.2x10⁹ bbl/yr 12x10⁸
____________ @ ______ = 3x10⁶ bbl/day.
365 day/yr 4x10²

So 3 million barrels per day is our estimate, without taking account of trucks, buses, airplanes, heating oil and electricity generation. We also have not allowed for the fact that not all of the barrel of crude oil becomes gasoline, perhaps 2/3. Also a factor of 2 is probably appropriate for other motor vehicles (which are less numerous but travel further and are much less efficient) and another factor of 2 for heating and electricity. Multiplying all of these additional factors, 3/2 x 2 x 2 = 6, times the 3 million gives 18 million barrels per day.

Is that reasonable? Looking in an Almanac for 1995, which has petroleum consumption figures for 1993, we see that some 17 million barrels per day is the total figure. Not bad at all, considering how rough the approximations had to be!

To connect all of this to recent history, note that about 45% of that consumption is supplied by imports. OPEC countries produced about 18 million barrels per day, so the US must have bought about half of all the OPEC oil. With Iraq and Kuwait oil being roughly 20% of OPEC's production before the Gulf War, that means that about 10% of the US's normal supply was stopped with the embargo on Iraq(as of Sept.'90). How did that 10% affect the consumption? We know that the price of gasoline went up by some 40% shortly thereafter (but settled down again within a few months after the war), but did consumption decrease with the reduced supply? Or did oil production increase? How did this jibe with comments in the media about oil production at the time?