DnT Seminar (09/02) @ MOE Edutorium on 19/11/2009

Recommended Reference Books

1. Deconstructing product design : Exploring the Form, Function, Usability, Sustainability, and Commercial Success of 100 Amazing Products
Author William Lidwell and Gerry Manacsa
Publisher Beverly, Mass. : Rockport Publishers, 2009.
NLB (Not ready for loan yet)

1A. Title Universal principles of design : 100 ways to enhance usability, influence perception, increase appeal, make better design decisions, and teach through design
Author Lidwell, William. Kritina Holden, Jill Butler.
Publisher Gloucester, Mass. : Rockport, c2003.
NLB (Central)

2. Design for Environment, Second Edition: A Guide to Sustainable Product Development: Eco-Efficient Product Development

2A. Title Design for environment : creating eco-efficient products and processes
Author: Joseph Fiksel, editor.
Publisher New York : McGraw-Hill, c1996.

3. Title The green imperative : ecology and ethics in design and architecture
Author Papanek, Victor J.
Publisher London : Thames and Hudson, c1995.
NLB (L.K.C Reference ONLY)

4. Title What is product design?
Author Slack, Laura.
Publisher Singapore : Page One, 2006.
NLB (Jurong R./W., Central)

Extra search:

A5. Title Experimental eco- > design : architecture, fashion, product
Author Brower, Cara. Mallory, Rachel, Ohlman, Zachary
Publisher Mies, Switerland : RotoVision, c2009.
NLB (Jurong R./W., Central)

Suggested Websites

• Design Process. Design Stage

http://ahwong.com/comics.html (free PDF)

• The Electronics Club

http://www.kpsec.freeuk.com/index.htm

• Others

http://technologyreview.com/

http://www.economist.com/sciencetechnology/

http://singaporedesignfestival.com/designfest09/

Which one is cheaper, Evian water or petrol?

> Guess you did never think about that
> All these examples do NOT imply that petrol is cheap; it just illustrates how outrageous some prices are. You will be really shocked!
> Think a liter of petrol at $1.60 is expensive? (some time in June 2009, in US$)
> This makes you think, and also puts things into perspective.
> Can of Red Bull, 250ml, $2.95 ... $11.80 per litre!
> Robitussin Cough Mixture, 200ml, $9.95 ..... $199.00 per litre!
> L'Oreal Revitalift Day Cream, 50ml, $29.95 ...... $599.00 per litre!
> Bundy Rum, 1250ml, $51.00 .... $40.80 per litre!
> Visene Eye Drops, 15ml, $5.69 .... $379.00 per litre!
> Britney Spears Fantasy Perfume, 50ml, $29 .... $580.00 per litre!
> And this is the REAL KICKER.
> Evian water, 375ml, $2.95 ...$7.86 per litre! $7.86 for a litre of WATER!!
> And the buyers don't even know the source> (Evian spelled backwards is NAIVE!!)
> Ever wonder why computer printers are so cheap?
> So they can hook you for the ink!!
> Someone calculated the cost of the ink at, you won't believe it but it's true; $1,040 a litre. $1040.00 A LITRE!!!
> So, the next time you're at the pump, be glad your car doesn't run on> water, Red Bull, Robitussin, L'Oreal or, God forbid, Printer Ink
>> MORAL OF THE STORY IS, DO NOT COMPLAIN IF PETROL PRICE INCREASE!!!

Statistics 101

1. Racial Bias

When officers reported knowing the race of the driver in advance, 66 percent of the drivers stopped were black, compared with 45 percent when police reported not knowing the race of the driver in advance, according to the RAND study. (This is a report done in Oakland Police, USA, in 2004)

2. Hit-and-Run Accident (Fictional example proposed by the psychologists Amos Tversky and Daniel Kahneman in the early 1970s)

A certain town has two taxi companies, Blue Cabs and Black Cabs. Blue Cabs has 15 taxis, Black Cabs has 85 (slight variations do exist, e.g. some use 75 instead of 85). Late one night, there is a hit-and-run accident involving a taxi. All of the town's 100 taxis were on the streets at the time of the accident. A witness sees the accident and claims that a blue taxi was involved. At the request of the police, the witness undergoes a vision test under conditions similar to the those on the night in question. Presented repeatedly with a blue taxi and a black taxi, in random order, he shows he can successfully identify the color of the taxi 4 times out of 5. (The remaining 1/5 of the time, he misidentifies a blue taxi as black or a black taxi as blue.) If you were investigating the case, which company would you think is most likely to have been involved in the accident?
Faced with eye-witness evidence from a witness who has demonstrated that he is right 4 times out of 5, you might be inclined to think it was a blue taxi that the witness saw. You might even think that the odds in favor of it being a blue taxi were exactly 4 out of 5 (i.e., a probability of 0.8), those being the odds in favor of the witness being correct on any one occasion.

Do you think the witness was reliable?

However, the facts are quite different. Based on the data supplied, the probability that the accident was caused by a blue taxi is only 0.41. That's right, the probability is less than half. It was more likely to have been a black taxi.

How do you arrive at such a figure? Use Bayes Theorem.
Compute the product
P(blue taxi) x P(witness is right),
and divide the answer by the sum
[P(blue taxi) x P(witness is right) + P(black taxi) x P(witness is wrong)].
Putting in the various figures, this becomes the product 0.15 x 0.8 divided by the sum [0.15 x 0.8 + 0.85 x 0.2], which works out to be 0.12/[0.12 + 0.17] = 0.12/0.29 = 0.41.

To look at the problem from another angle:
For the 15 blue taxis, he would (correctly) identify 80% of them as being blue, namely 12. (In this hypothetical argument, we are assuming that the actual numbers of taxis accurately reflect the probabilities.)
For the 85 black taxis, he would (incorrectly) identify 20% of them as being blue, namely 17.
So, in all, he would identify 29 of the taxis as being blue.
Thus, on the basis of the witness's evidence, we find ourselves looking at a group of 29 taxis.
Of the 29 taxis we are looking at, 12 are in point of fact blue.
Consequently, the probability of the taxi in question being blue, given the witness's testimony, is 12/29, i.e. 0.41.

You see, sometimes, our intuitions can be so wildly misleading!

For the case of 15 blue taxis and 75 black taxis, the probability of the same witness of correctly identifying a blue taxi was 12/27 = 0.44.

Blackjack - The Game of 21

First of all, I am not promoting gambling here. I am definitely against gambling, whether or not money is involved. I am promoting the understanding of probability.

How is Blackjack or 21 played?

Each player plays his hand independently against the dealer. At the beginning of each round, the player places a bet in the "betting box" and receives an initial hand of two cards. The object of the game is to get a higher card total than the dealer, but without going over 21 which is called "busting", "breaking", or many other terms. (The spot cards count 2 to 9; the 10, jack, queen, and king count as ten; an ace can be either 1 or 11 at the player's choice). The player goes first and plays his hand by taking additional cards if he desires. If he busts, he loses. Then the dealer plays his or her hand. If the dealer busts, he loses to all remaining players. If neither busts, the higher hand total wins. If a player ties with the dealer the hand is a "push" and the player's bet is returned.

What do you think is the cut-off point for the dealer representing the casino?

The answer is 17! Yes, 17 Again! (Not the movie though)

If the dealer has less than 17, he must hit. If the dealer has 17 or more, he must stand (take no more cards), unless it is a "soft 17" (a hand that includes an ace valued as "11," for example a hand consisting of Ace+6, or Ace+2+4). With a soft 17, the dealer follows the casino rules printed on the blackjack table, either to "hit soft 17" or to "stand on all 17's."

The Number Sense - Benford's Law

"Would you like to try a bet?

Open a book (any book) at random and note the first digit that your encounter.

If this digit is either 4, 5, 6, 7, 8, or 9, you win $10.

If this difit is either 1, 2, or 3, I win $10. "

Do you think your winning odds (chances) are higher than mine?

I read this in the booked " The Number Sense: How the Mind Creates Mathematics" by Stanislas Dehaene. (Published in 1999, p. 113)

If we keep on playing for a long period, say the running time of a typical movie (2 hours), you would almost always lose. We shall look at the statistics researched by many scientists and mathematicians.

Benford's law (named after physicist Frank Benford), also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.

Measurements of real word values are often distributed logarithmically (or equivalently, the logarithm of the measurements is distributed uniformly).

This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). The result holds regardless of the base in which the numbers are expressed, or the units the measurements are taken, although the exact proportions change.

Income tax controllers use them to check those who are dishonest about their declaration. Benford's Law is also employed to check possible fraud cases in general election, e.g. 2009 Iranian Election.

The Numbers Behind Numb3rs - Making and Breaking Codes

What keeps your password safe?

A good service provider (e.g. a bank) will not store customers' passwords. The reason is simple. If someone hacks into the computer of the servic provider, he would easily get the passwords should they be stored in the computer.

How to prevent this from happening?

Your bank does not store your password, but rather a hashed version. When you log onto your bank account, the bank's computer compares the hashed version of the password you type in with the entry stored in its hashed-password profile.

The hashed version, denoted by H, is actually a function of your password, let's call it input x.

To make the hashed version secure, the function H(x) should have the following properties:
1. For any input x, it should be easy to compute H(x) ;
2. Given H(x) , it should be computationally infeasible to find x(inverse function);
3. All values produced by H, say y, should have the same bit-length; (y, if different from your password x are "collisions"). This is to prevent some different bit-length input y, which produces H to gain access.
4. It should be computationally infeasible to find y that collides with x, i.e. H(x) = H(y).


Note: "computationally infeasible" means it would take the fastest computers more than a human life to carry out the procedure to completion. That is to say, even someone hacks into the stored H(x) , he would not be able to obtain your password, x.

The Numbers Behind Numb3rs - DNA Profiling

DNA profiling (also called genetic fingerprinting) is a technique to identify individuals on the basis of their respective DNA profiles. Although 99.9% of human DNA sequences are the same in every person, enough of the DNA is different to distinguish one individual from another. DNA profiling uses repetitive ("repeat") sequences that are highly variable, called variable number tandem repeats (VNTR). VNTRs loci are very similar between closely related humans, but so variable that unrelated individuals are extremely unlikely to have the same VNTRs.

a. The FBI's CODIS System: based on 13 loci (including Virginia's 8-loci); total of 3,000,000 in the database;
b. Virginia Division of Forensic Science: based on 8 loci; total of 101,905 offender profiles (as of November 1999) in the database;
c. Arizona: based on 13-loci; total of 65,000 offender profiles in the datase.

The probability that someone would match a random DNA sample at any one site (locus, pl. loci) is roughly 1 in 10.

The probability that someone would match a random DNA sample at 8 loci is __________.

The probability that someone would match a random DNA sample at 9 loci is __________.

The probability that someone would match a random DNA sample at 13 loci is __________.

Case Study: USA v. Raymond Jenkins
At first, the DNA profiling was done against Virginian database of 8-loci. The likelihood of an accidental match is roughly 101,905 x 1/100,000,000 = 1/1,000. Considered quite high, Jenkins was released from custody.
Later, more evidence was found and another DNA profiling was performed against the FBI's database of 13-loci. The likelihood of an accidental match is roughly 3,000,000x 1/10,000,000,000,000 = 1/3,000,000. Considered extremely rare, Jenkins was then arrested and charged with second-degree murder.

The Database Match Calculation:
Suppose an DNA sample is sent to Arizona for DNA profiling with 13 loci and 65,000 DNA profiles in the database,
what is the probability of there being a 9-locus match?
Given that the probability that someone would match a random DNA sample at any one locus is roughly 1 in 10.

(1) For 9-locus DNA profiling, the probability for a 9-locus match is _________________.

(2) Out of 13 loci, there are ________________ different ways of having 9-locus match.

(3) Hence, finding a match on any 9 loci of the 13 is 715 / 1,000,000,000.

(4) If any one profile is picked in the database, the proability of a second profile not matching on 9 loci is 1- 715/10^9.

(5) The probability of all 65,000 entries not matching on 9 loci is (1- 715/10^9)^65,000. Using Binomial Theorem, this is approximately 1- 65,000x715/10^9.

(6) The probability of there being a 9 loci match is thus 1- (1- 65,000x715/10^9) = 65,000x715/10^9 = 0.05 = 5%.

In fact, an actual analysis of the Arizona database uncovered 144 individuals whose DNA profiles matched at 9 loci, 144/65,000 = 0.22% (differed from the theoretical 5%, why?), one pair matched at 11 loci and one pair matched at 12 loci. The 11 and 12 -locus matches turned out to be siblings, hence not random.

Extension: Brithday Problem (23, >50%). In a class of 40, the probability of two students share the same birth date is as high as 85%. Surprised?!

Amazing Art - Upside Down

Below are the collections of "The Upside-Downs of Little Lady Lovekins and Old Man Muffaroo" by Gustave Verbeek in 1905. Yes! 1905!

What do you see from the drawing on the left?

...

...

...

...

...

An island with trees and a man in a boat?

A bird with someone in its mouth?

See coloured version here.

Another example here. The cartoon can be read upright and upside down.

One more example here. (Click View upside down )

Scott Kim's Inversions - Symmetry

You may not have heard of him. But you will surely be amazed by his works.

Scott Kim is an American puzzle and computer game designer, artist, and author. He created hundreds of other puzzles for magazines as well as thousands of puzzles for computer games.

He had an early interest in mathematics, education, and art, and attended Stanford University, receiving a BA in music, and a PhD in Computers and Graphic Design. In 1981, he created a book called Inversions, words that can be read in more than one way. His first puzzles appeared in Scientific American in Martin Gardner's "Games" column. He is one of the most well-known masters of the art of ambigrams.

Selected recent works of Scott Kim:

Joy to the World (The snowflakes are special.)

Alphabet Tessellation (Amazing!Click on any letter to start tessellating.)

Fantasy (Scott Kim is true someone.)

GALLERY of his recent works
CLASSROOM ACTIVITIES for teachers
CLASSROOM GALLERIES of inversions by students
LINKS to other ambigram artists

DIE DIE MUST ...

Fair 6-sided dice are used in the questions.

(1) Throwing 1 die, what is the probability of getting a 6?


(2) Throwing 2 dice, what is the probability of getting a sum of 6?


(3) Throwing 3 dice, a sum of 10 is more likely or a sum of 9?


Do NOT peep the answers before you attempt the questions!

No... No... No... PEEPS YET...

...........................................................................................................
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.
.
.
.
.
............................................................................................................

Answers:
(1) 1/6
(2) Tabulate the results, you can see there are 5 times of sum 6 out of the total 36 outcomes. So it is 5/36.
(3) 9: (621) (531) (522) (441) (432) (333)
10: (631) (622) (541) (532) (442) (432)
Do they have the same chance? Not really.

Let's see. For example, (6 2 1) there are 6 different ccombinations 126, 162, 216, 261, 612, 621.
If we do that, we find that there are 27 ways of getting 10 and 25 ways of getting 9. Hence, 10 is more likely to appear.

SingAPool - Lesson Learned from Virginia Lottery

Lottery Principle:

Lottery organisations like Singapore Pools raises money because on average the cost of each ticket is more than the return of it. For example, the cost of a ticket is $1 and the return of it by winning something (including all the prizes) is 50 cents. On average, one loses 50 cents for every ticket he buys.

In 1992, some investors noticed that the Virginia Lottery violated this principle. The lottery involved picking 6 numbers from 1 to 44. They are C(44, 6) - a combination, or 7,059,052 ways (about 7 million) of choosing 6 numbers from a group of 44. The jackpot was $27 million, and with the 2nd, 3rd, 4th prizes included, the pot grew close to $28 millmion, or $27,918,561 to be exact. Therefore, each ticket has an approximate value of $28m / 7m = $4 (or $3.95). However, the cost of each ticket was just $1. To put simply, if one buys all the more than 7 million different combintions, he will have a net profit of $21 million ($28m pot - $7m cost).

The Australian investors quickly found 2,500 small investors in Australia, New Zealand, Europe and the United States willing to put up an average of $3,000 each. If the scheme works, each will have an average net profit of about $10,000.

Risks in the scheme:
1. They were not the only ones buying the tickets; they would have to share the winning pot.
(However, the statistics was on their side: in the 170 times the lottery had been held, there were 120 times with no winners, only 40 times with a single winner and just 10 times with two winners. The expected return is 120/170 *$28m + 40/170*$14m + 10/170*$9m = $23m, or more than $3 per ticket, net profit $2 per ticket on average.)
2. Time for filling in the slips. Each slip was good for 5 tickets. They had 1.4 milion slips to fill out.
As they only had 72 hours before the deadline, they hired grocery-store employees working on shifts to sell as many tickets as possible. In the end, they own managed to purchase 5 million out of more than 7 millions, 0r 70%.
3. Payment for the tickets bought. Luckily, some chain store accepted back checks for 2.4 million tickets, or about 50% of the tickets they bought.
4. Time for checking the prizes. This was not really a problem as the lottery gave 1 ~ 3 months of collecting the prizes won. It was just hard searching work. It took them days to come forward with the winning tickets.
5. Legal or illegal: Luckily, the officials concluded that they had no valid reason to deny the group's winning.

Really interesting and exciting true story!

Warning: The golden rule is NEVER EVER GAMBLE!

~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.

TOTO: Choose 6 numbers from 1 to 45.

(1) How many different combinations are there? Ans: 8,145,060.

(2) Each combination (6 numbers) costs 50 cents. How much does one pay for all combinations? Ans: $4,072,530.

(3) This coming TOTO jackpot is $5,500,000 (estimated).

The Roulette Wheel

Joseph Hobson Jagger (1830–1892) was a British engineer, known as "The Man Who Broke the Bank at Monte Carlo" (a song composed and written for Jagger).

How did he manage that?

In 1873, Jagger hired six clerks to secretly record the outcomes of the six roulette wheels at the Beaux-Arts Casino at Monte Carlo, Monaco. He discovered that one of the six wheels showed a clear bias, in that nine of the numbers (7, 8, 9, 17, 18, 19, 22, 28 and 29) occurred more frequently than the others. He therefore placed his bets and quickly won a considerable amount of money, £14,000 (equivalent to around 50 times that amount, or £700,000 in 2005). Over the next three days, Jagger gained £60,000 in earnings with other gamblers. In response the casino rearranged the wheels, which threw Jagger into confusion. After a losing streak, Jagger finally recalled that a scratch he noted on the biased wheel wasn't present. Looking for this telltale mark, Jagger was able to locate his preferred wheel and resumed winning. Counterattacking again, the casino moved the metal dividers between numbers around daily. Over the next two days Jagger began to lose and he finally gave up. But he took his remaining earnings, two million francs, then about £65,000 (around £3,250,000 in 2005), and left Monte Carlo never to return.

Do you see the effect of a biased wheel? The same effect goes to throwing a die. A perfect 6-sided die shows a fair chance of 1 - 6, i.e. 1 in 6 chance.

Warning: this occured in the old times; with the modern machines, one is never possible to beat the casinos. Plus, the casino CCTV watches one's every move. Do you think one can easily and hopefully safely walk out of the casino? The golden rule is NEVER EVER GAMBLE!

Interesting Events

(1) In 1965, aged 90, with no living heirs, Calment signed a deal to sell her former apartment to lawyer André-François Raffray, on a contingency contract. Raffray, then aged 47, agreed to pay her a monthly sum of 2,500 francs until she died, an agreement sometimes called a "reverse mortgage". Raffray ended up paying Calment more than the equivalent of $180,000, which was more than double the apartment's value. After Raffray's death from cancer at the age of 77, in 1995, his widow continued the payments until Calment's death. (Whitney, Craig R. (5 August 1997). "Jeanne Calment, World's Elder, Dies at 122". New York Times.)

Fact: Calment died 45 years later than Raffray. Therefore, the Raffrays did not gain anything from the contract, but ended up paying 45 years of a monthly sum of 2,500 francs. What a LOSS!

(2) The former American football star and actor, O. J. Simpson,was brought to trial for the 1994 murder of his ex-wife Nicole Brown Simpson and her friend Ronald Goldman. Simpson was acquitted in 1995 after the longest jury trial in California history.

Simpson hired a high-profile defense team led by Johnnie Cochran and F. Lee Bailey. Cochran persuaded the jurors that there was reasonable doubt about the DNA evidence (then a relatively new type of evidence in trials) - including that the blood-sample evidence had allegedly been mishandled by lab scientists and technicians.

Later, both the Brown and Goldman families sued Simpson for damages in a civil trial. On February 5, 1997, the jury unanimously found there was a preponderance of evidence to find Simpson liable for damages in the wrongful death of Goldman and battery of Brown. In its conclusions, the jury effectively found Simpson liable for the death of his ex-wife and Ron Goldman. On February 21, 2008, a Los Angeles court upheld a renewal of the civil judgment against Simpson.

Fact:

- Why Simpson was not brought to justice in the first criminal trial?

- Because he hired a strong defense team. The team presented that "4 million women are battered annually by husbands or boyfriends in US; yet in 1992, according to FBI reports, a total of 1,432 (1 in 2,500) were killed by their husbands or boyfriends" and therefore they concluded that "few men who beat their domestic partners go on to murder them".

Well. The last statement by the defense team was true. But it was not relavent. The point here is rather the probability that a battered wife who was murdered was murdered by her abuser. According to the FBI report , of all the battered women murdered in US in 1993, some 90% were killed by their abuser. This statistic was not mentioned in the trial.

This second event is actually related to Bayer's Theory. A few more linked cases are HIV test report, or urine test report against drug uses for athletes (e.g. Mary Decker Slaney).

Students Lying to Teachers

It’s sad, but many students lie to teachers and get away with it. That’s why I love to read about stories where teachers catch the students red-handed.

Here’s one story I especially enjoyed:

"My dad heard this story on the radio. At Duke University, two students had received A’s in chemistry all semester. But on the night before the final exam, they were partying in another state and didn’t get back to Duke until it was over. Their excuse to the professor was that they had a flat tire, and they asked if they could take a make-up test. The professor agreed, wrote out a test and sent the two to separate rooms to take it. The first question (on one side of the paper) was worth 5 points, and they answered it easily. Then they flipped the paper over and found the second question, worth 95 points: ‘Which tire was it?’ What was the probability that both students would say the same thing? My dad and I think it's 1/16. Is that right?"

Source: excerpted from Marilyn vos Savant (IQ 228, the highest recorded around the world), Parade Magazine, 3 March 1996, p 14.

Besides being a nice story, the situation raises some interesting questions in game theory.

The answer is no. It's not right. If the students were lying, the correct probability of their choosing the same answer is 1/4.

Again, let's look at the sample space. (response of Student 1, response of Student 2)
{ (RF, RF); (RF, LF); (RF, RR); (RF, LR);
(LF, RF); (LF, LF); (LF, RR); (LF, LR);
(RR, RF); (RR, LF); (RR, RR); (RR, LR);
(LR, RF); (LR, LF); (LR, RR); (LR, LR) }
4 /16 = 1/4

Alternatively, we can look at the situation this way. Student 1 can choose anything. Suppose he chooses RF, then Student 2 has a probability of 1/4 getting RF.

Of course, this is based on the assumption that both students are lying and their choices are independent and importantly, they have equal chances to choose one of the four wheels.

In reality, people prefer RF tire (58%), with the other three tires of similar probability, LF (11%); RR(18%); LR(13%). (Source: Introduction to probability By Charles Miller Grinstead, James Laurie Snell, p.40)

Example of Conditional Probability

There are two children in a family.

[1] What is the chance of having at least one girl in this family?

Sample space { (B, B); (B, G); (G, B); (G, G)}

Obviously: the answer is 3/4.

[2] What is the chance of having two girls given that one of the children is girl?

You may argue that since one child is G, there is only one left to look at. The chance of that child's being a G is 1/2, hence the probability of having both girls is 1/2.

Is this correct? Let us look at our sample space.

Sample space {(B, G); (G, B); (G, G)}

Obviously: the answer is 1/3.

The mistake in earlier reasoning is this. We don't know which one is a G, the first child or the second.

Looking back at the second question: What is the chance of having two girls given that one of the children is girl? We have two events: A = both girls; B = one of them girl

P(AB) = P(A intersect B) / P(B) = (1/4)/(3/4) = 1/3
where P(A intersect B) = P(A) in this case.

People v. Collins

The People of the State of California v. Collins was a 1968 jury trial in California, USA that made notorious forensic use of mathematics and probability.

Bystanders to a robbery in Los Angeles testified that the perpetrators had been a black male, with a beard and moustache, and a caucasian female with blonde hair tied in a ponytail. They had escaped in a yellow motor car.
After testimony from an "instructor in mathematics" about the multiplication rule for probability, the prosecutor invited the jury to consider the probability that the accused pair, who fitted the description of the witnesses, were not the robbers. Even though the "instructor" had not discussed conditional probability, the prosecutor suggested that the jury would be safe in estimating:
Black man with beard (A) 1 in 10
Man with moustache (B) 1 in 4
White woman with pony tail 1 in 10
White woman with blonde hair 1 in 3
Yellow motor car 1 in 10
Interracial couple in car 1 in 1000
By multiplying the probability of all events, the chance of a couple fitting all these distinctive characterisistics are 1 in 12 milllions.
The jury returned a verdict of guilty.

Appeal:
Black man with beard (A) 1 in 10
Man with moustache (B) 1 in 4

The argument on events A and B was "most men with a beard also have a mustache". So if you observe a Black man with beard, the chances are no long 1 in 4 that the man you observe has a mustache.

The population of the crime area was several millions, which means that there could be 2 or 3 couples with the description.

Probability

If two events, A and B, are independent, then the probability that both A and B will occur is equal to the product of their individual probabilities.

P(A intersect B) = P(A)*P(B), given that A and B are independent.

Now your time to try:

Suppose
(A) a married person has 1 in 50 chance of getting divorced each year;
(B) a police officer has 1 in 5,000 chance of being killed on the job each year.

What is the probability of a married police officer will be divorced and killed in the same year?

Think it carefully. Tricky?!

Fun Logic

Which is greater:

(A) the number of 6-letter English words having "n" as their 5th letter or
(B) the number of 6-letter English wrods ending in "ing" ?

You don't have to survey Oxford English Dictionary to get a correct answer.

A or B? How?

Explanation on "The Drunkard's Walk", p.28.

TTTTT what is next, T or H? (2 - Films)

Today's stories are on people who select possible blockbusters before a film is produced.

Sherry Lansing, who ran Paramount with great success for many years, had helped Paramount win many Best Picture awards, including Forrest Gump, Braveheart and Titanic. Then Lansing was dumped by Paramount after " a long stretch of underperformance at the box office". During Lansing's last 6 years, the market shares of Paramount Motion Pictures Group were 11.4, 10.6, 11.3, 7.4, 7.1, 6.7. Her boss, Sumner Redstone panicked and she decided to leave.

Sherry Lansing was lucky at the beginning and bad luck at the end. One the other hand, we have Mark Canton. Canton was criticized for be "incapable of distinguishing the winners from the losers". He left when he departed films such as Men in Black ($589m), Air Force One ($315m), Anacoda ($137m).

What do we learn from these two stories?

Let me explain it this way. Say you are good at math and your average score is 80/100. Does that mean you won't score 60 or even below? Is this string of scores possible: 90 92 80 72 61 85? What would your teacher or parent think after they know the scores 90 92? What would your teacher or parent think after they know the scores 90 92 80 72 61?

My point is clear. We can't tell your true performance from one or two tests. However, over the long run, the average of your scores does tell us something.

Now, can you make a guess of what I mean by the title of this post?

Source: The Drunkard's Walk: How Randomness Rules Our Lives (Leonard Mlodinow, available at Kinokuniya)

TTTTT what is next, T or H? (1 - Writers)

Everyone will be rejected in some way at some time.

Stories of some now-famous but then-unknown writers.

Judy Blume received “nothing but rejections” for two years. “I would go to sleep at night feeling that I’d never be published. But I’d wake up in the morning convinced I would be. Each time I sent a story or book off to a publisher, I would sit down and begin something new. I was learning more with each effort. I was determined. Determination and hard work are as important as talent.”

“After spending six years writing the first instalment of her “Harry Potter” novels, J.K. Rowling was rejected by 9 publishers before London’s Bloomsbury Publishing signed her on.” (IMDB)

Shockingly, The Diary Of Anne Frank received the following rejection comment: “The girl doesn’t, it seems to me, have a special perception or feeling which would lift that book above the curiosity’ level.” The book was rejected 16 times before it was published by Doubleday in 1952. More than 30 million copies are currently in print, making it one of the best-selling books in history. (Rotten Rejections)

Margaret Mitchell’s Gone With The Wind was rejected 38 times.

Source: Writers and rejection: don’t give up!

Question No. 2876 (Adapted from ScienceNet):

What is "pi"? What does it stand for?

In mathematics, "pi" is defined as the ratio between the circumference of a circle and its diameter(pi = circumference / diameter).

You may find Ask Dr. Math. interesting.

Some of the interesting mathematics questions posted at ScienceNet

Question No. 14317 :Why are there 360 degrees in a circle? Why not say 100 degrees?

Question No. 14557 :Is there a way to TRISECT an angle?

Question No. 19863 :How is radian useful in our daily lives? Why can't degree always be used?

Question No. 20128 :How does a 7,9,10,12,20-gon look like?

Mr Sun: what do you notice about the change in the shape of the polygons?

Designed for Kids / Life / Living / People ...

Source:
National Library English 745.2083 RIC -[ART]
Designed for Kids a complete sourcebook of stylish products for the modern family
by Phyllis Richardson

• Eco Cradle
• Tripp Trapp Chair
• Splash, Chow
• Play Tables / Seating / Storage / Toys & Arts
• Dado Cubes
• Spaceframe Sculpture Kit
  

More Books on Design

Designed for kids a complete sourcebook of styli Richardson, Phyllis. 2008
Designed for life Ellison, Michael. 2002
Designed for living Davidson, Avelyn. 2003
Designed for london 150 years of transport desig Green, Oliver. 1995
Designed for people 2008
Designed for pleasure the world of edo japan in 2008
Designer (Singapore) Periodical 2001

DnT Seminar (09/01) @ Zhonghua Sec on 06/05/2009

Engaging Pupils in Design Thinking

Suggested Websites:

Design Process, Design Stage

• Science and Technology/Engineering


• Journal of Industrial Teacher Education


• That Squiggle of the Design Process


• ThinkGenealogy > Tag: Design

• Problem Solving with a Design Attitude

• Design Guide

Fun Design

• YeDuo (叶朵) Shape Borrowing
• Do More Idea
• Black Blum

Mathematics in the Movies

Numb3rs (2005)
A CBS TV series starting its third year, where David Krumholtz plays Charlie Eppes, a "world class" mathematician who helps his brother Don, an FBI agent played by Rob Morrow, solve crimes.

Proof (2005)
Leaving the Wilbur Theater in Boston after seeing the play Proof, a theatergoer remarked "This is the year of mathematicians." Proof is now a movie (Directed by Miramax, staring Gwyneth Paltrow and Anthony Hopkins), adapted from David Auburn's Tony and Pulitzer winning play. Three of the four main characters are mathematicians. The father character is loosely based on John Nash, but the story is fiction and takes a very different path from A Beautiful Mind, focusing on the daughter.

A Beautiful Mind (2001)
All those Hollywood spy cliches turn out to be a brilliant device to let us see what happens from from John Nash's perspective.

A list of more movies collected by a Harvard Professor

GMC Publications (Wood)

Books

WOODWORKING

Basics
Celtic
Furniture
General Projects
Pyrography
Routing
Scroll Saw & Intarsia
Slipcase Sets
Techniques
Tools
Woodcarving
Woodturning
Workshop

Making Furniture: Projects and Plans (Paperback)
by Mark Ripley (Author)

Furniture Making: Plans, Projects and Designs (Paperback)
by Kevin Ley (Author)

Making Authentic Craftsman Furniture: Instructions and Plans for 62 Projects (Dover books on woodworking & carving) (Paperback)
by Gustav Stickley (Author)

Magazines

+ Furniture & Cabinet Making
+ Woodcarving
+ Woodturning
+ Woodworking
Plans & Projects

Useful Design & Technology Websites [Knowledge]

• Mechanisms

1. CABARET Mechanical Theatre (UK)
2. Flying Pig (UK)
3. Martin Smith Automata (UK)
4. The Puppetry Home Page (US)

• Electronics

1. New Wave Concepts
2. Doctronics (UK) - PCB

• Structures
• Plastics

• General (related t0 DnT textbook topics)

1. FOSS WEB (Electronics, Force & Motion)
2. Technology Student (Comprehensive information)
3. Design Technology (Key Stage)
4. DT Online (Mechanisms, Electronics, Structures)

Useful Design & Technology Websites [General]

• How Stuff Works

A deep understanding on how stuff works.

• The drawings of Leonardo da Vinci

Most, if not all, of da Vinci's sketches.

• My Sketch Book (Little Red Dot - Singapore)

Some local political cartoon sketches.

• Isometric Grid Paper

Choose type of graph paper: Isometric Graph Paper

• Orthographic Grid Paper (Engineering)

Choose type of graph paper: Engineering Graph Paper

Useful Design & Technology Websites [Ideation & Development]

Ideation & Development

• I New Idea Homepage

This is an amazing site, which presents the up-to-date design ideas. The ideas are very interesting and innovative, and sometimes "weird". They are also classified into different categories for easy search. Not so lastest ideas are archived.

• Red Dot Online

Red Dot Publications

Some of the Red Dot Design Yearbooks are available at the Lee Kong Chian Reference
Library (Central Library near City Hall MRT) under the Call Numer English 745.2 RDDY
(2006 to 2008). Yearbook 2006 is also available at NIE library NK1160 Red (Level 4).

• Design Council - Better by Design (Channel 4, UK) (showcasing some common projects)

• Design London TV Channel (Quite a number of Videos)

• IFC Singapore (Furniture)

• 100 Chairs in 100 Days by Gamper Martino (Video clips available at YouTube)

• IKEA online catalogue 2010

• "after2 - humble beginnings" A collection of furniture prototypes, NAFA
• S U S T A I N A B L E T E C H N O L O G Y E D U C A T I O N P R O J E C T