Did you know? http://didyouknow.org Fascinating facts and interesting stories about people, places, and history, with top lists and trivia facts. Tue, 20 Sep 2016 13:12:19 +0000 en-US hourly 1 Does tapping a can of fizzy drink really stop it foaming over? http://didyouknow.org/does-tapping-a-can-of-fizzy-drink-really-stop-it-foaming-over/ http://didyouknow.org/does-tapping-a-can-of-fizzy-drink-really-stop-it-foaming-over/#comments Wed, 15 Jun 2016 11:17:30 +0000 http://didyouknow.org/?p=4348 It is one of the distinct sounds of summer: the noise of people tapping the tops of their cans of fizzy drink before opening them. But does this widespread ritual really stop a can of beer or pop from gushing over?

When you open a can of fizzy drink, the refreshing “hiss” is the result of gas bubbles escaping from the liquid as a result of a change in the solubility of the carbon dioxide (CO2) in it. This change occurs due to the pressure inside the can decreasing from ~3 bar (can closed) to 1 bar at atmospheric pressure (can open).

The solubility of CO2 in water reduces from ~4.5g in one litre (33.8oz) of water at ~3 bar, to ~1.5g at atmospheric pressure, something that is described by Henry’s Law.

Before the can is opened, microscopic gas bubbles attach to the inside of it (nucleation). When the can is opened, these bubbles increase in size, due to the decrease in the solubility of CO2. When these bubbles reach a certain size they detach from the inside of the can and rise up to the top of the can due to buoyancy and displace liquid in their path (as shown in Figure 1).

Figure 1: the bubble formation upon opening a bottle of sparkling water.
Images captured specifically for this article.

So what part could tapping the top of the can play in this process? Whether or not this technique actually works is the subject of some debate but there is a theory explaining why it may work. As described earlier, the bubbles in an unopened can nucleate at the walls (Figure 2a) so tapping the can before opening could dislodge some of the bubbles, enabling them to float to the top of the liquid.

When a can is opened, the bubbles expand (Figure 2b) with those deeper within the liquid traveling further than those near the surface, displacing more of the drink and possibly resulting in greater amounts of ejected liquid. A “tapped” can will have fewer of these “deep” bubbles and so less liquid will be dislodged – and possibly sprayed out – than an “untapped” can (Figure 2c).

Figure 2: a possible mechanism for why tapping a can before opening may reduce gushing.
Diagram drawn specifically for this article.

Bubbles also can be dislodged from the side of the can with violent shaking, of course – but this method introduces more turbulence which increases the energy of the system, resulting in more bubbles in the drink and more spraying when opened. Sharply tapping the top of an open beer bottle with another has a similar effect, commonly resulting in a colossal gush of beer foam. This is because pressure waves caused by the impact create tiny “mushroom clouds” inside the bottle that eject huge quantities of liquid as they escape.

Glass and gushing

The debate of tapping aside, the actual material that the container is made from may also reduce gushing. It has been shown that the amount of foam formed when pouring beer into glasses of different “wettabilities” – the extent to which water wets a material – can affect not only the amount of beer head formed but also the size of the bubbles on the inside of the glass. This information is relevant when such bubbles are thought to be the cause of gushing.

Another important factor when it comes to the level of gushing is the stabilization of the bubbles caused by the presence of large molecules in the drink. This is why some beers have long-lived foam heads compared to the short-lived bubbles at the surface of, say, sparkling water. But such foam stabilizing agents are a conversation for another day.

So why not try different ways of opening your fizzy drink – and see how much of it you end up wearing.

Chris Hamlett, Lecturer in Chemistry, Nottingham Trent University. This article was originally published on The Conversation. Read the original article. The Conversation

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Beyond Asimov: how to plan for ethical robots http://didyouknow.org/beyond-asimov-how-to-plan-for-ethical-robots/ http://didyouknow.org/beyond-asimov-how-to-plan-for-ethical-robots/#respond Tue, 07 Jun 2016 10:35:16 +0000 http://didyouknow.org/?p=4328 As robots become integrated into society more widely, we need to be sure they’ll behave well among us.

In 1942, science fiction writer Isaac Asimov attempted to lay out a philosophical and moral framework for ensuring robots serve humanity, and guarding against their becoming destructive overlords. This effort resulted in what became known as Asimov’s Three Laws of Robotics:

  1. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
  2. A robot must obey the orders given it by human beings except where such orders would conflict with the First Law.
  3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Laws.

Today, more than 70 years after Asimov’s first attempt, we have much more experience with robots, including having them drive us around, at least under good conditions. We are approaching the time when robots in our daily lives will be making decisions about how to act. Are Asimov’s Three Laws of Robotics good enough to guide robot behavior in our society, or should we find ways to improve on them?

Asimov knew they weren’t perfect

Isaac Asimov. Image Rowena Morrill/GFDL, CC BY-SA

Asimov’s “I, Robot” stories explore a number of unintended consequences and downright failures of the Three Laws. In these early stories, the Three Laws are treated as forces with varying strengths, which can have unintended equilibrium behaviors, as in the stories “Runaround” and “Catch that Rabbit,” requiring human ingenuity to resolve. In the story “Liar!,” a telepathic robot, motivated by the First Law, tells humans what they want to hear, failing to foresee the greater harm that will result when the truth comes out. The robopsychologist Susan Calvin forces it to confront this dilemma, destroying its positronic brain.

In “Escape!,” Susan Calvin depresses the strength of the First Law enough to allow a super-intelligent robot to design a faster-than-light interstellar transportation method, even though it causes the deaths (but only temporarily!) of human pilots. In “The Evitable Conflict,” the machines that control the world’s economy interpret the First Law as protecting all humanity, not just individual human beings. This foreshadows Asimov’s later introduction of the “Zeroth Law” that can supersede the original three, potentially allowing a robot to harm a human being for humanity’s greater good.

0. A robot may not harm humanity or, through inaction, allow humanity to come to harm.

Asimov’s laws are in a particular order, for good reason.
Randall Munroe/xkcd, CC BY-NC

Robots without ethics

It is reasonable to fear that, without ethical constraints, robots (or other artificial intelligences) could do great harm, perhaps to the entire human race, even by simply following their human-given instructions.

The 1991 movie “Terminator 2: Judgment Day” begins with a well-known science fiction scenario: an AI system called Skynet starts a nuclear war and almost destroys the human race. Deploying Skynet was a rational decision (it had a “perfect operational record”). Skynet “begins to learn at a geometric rate,” scaring its creators, who try to shut it down. Skynet fights back (as a critical defense system, it was undoubtedly programmed to defend itself). Skynet finds an unexpected solution to its problem (through creative problem solving, unconstrained by common sense or morality).

Catastrophe results from giving too much power to artificial intelligence.

Less apocalyptic real-world examples of out-of-control AI have actually taken place. High-speed automated trading systems have responded to unusual conditions in the stock market, creating a positive feedback cycle resulting in a “flash crash.” Fortunately, only billions of dollars were lost, rather than billions of lives, but the computer systems involved have little or no understanding of the difference.

Toward defining robot ethics

While no simple fixed set of mechanical rules will ensure ethical behavior, we can make some observations about properties that a moral and ethical system should have in order to allow autonomous agents (people, robots or whatever) to live well together. Many of these elements are already expected of human beings.

These properties are inspired by a number of sources including the Engineering and Physical Sciences Research Council (EPSRC) Principles of Robotics and recent work on the cognitive science of morality and ethics focused on
neuroscience, social psychology, developmental psychology and philosophy.

The EPSRC takes the position that robots are simply tools, for which humans must take responsibility. At the extreme other end of the spectrum is the concern that super-intelligent, super-powerful robots could suddenly emerge and control the destiny of the human race, for better or for worse. The following list defines a middle ground, describing how future intelligent robots should learn, like children do, how to behave according to the standards of our society.

  • If robots (and other AIs) increasingly participate in our society, then they will need to follow moral and ethical rules much as people
    do. Some rules are embodied in laws against killing, stealing, lying and driving on the wrong side of the street. Others are less formal but nonetheless important, like being helpful and cooperative when the opportunity arises.
  • Some situations require a quick moral judgment and response – for example, a child running into traffic or the opportunity to pocket a dropped wallet. Simple rules can provide automatic real-time response, when there is no time for deliberation and a cost-benefit analysis. (Someday, robots may reach human-level intelligence while operating far faster than human thought, allowing careful deliberation in milliseconds, but that day has not yet arrived, and it may be far in the future.)
  • A quick response may not always be the right one, which may be recognized after feedback from others or careful personal reflection. Therefore, the agent must be able to learn from experience including feedback and deliberation, resulting in new and improved rules.
  • To benefit from feedback from others in society, the robot must be able to explain and justify its decisions about ethical actions, and to understand explanations and critiques from others.
  • Given that an artificial intelligence learns from its mistakes, we must be very cautious about how much power we give it. We humans must ensure that it has experienced a sufficient range of situations and has satisfied us with its responses, earning our trust. The critical mistake humans made with Skynet in “Terminator 2” was handing over control of the nuclear arsenal.
  • Trust, and trustworthiness, must be earned by the robot. Trust is earned slowly, through extensive experience, but can be lost quickly, through a single bad decision.
  • As with a human, any time a robot acts, the selection of that action in that situation sends a signal to the rest of society about how that agent makes decisions, and therefore how trustworthy it is.
  • A robot mind is software, which can be backed up, restored if the original is damaged or destroyed, or duplicated in another body. If robots of a certain kind are exact duplicates of each other, then trust may not need to be earned individually. Trust earned (or lost) by one robot could be shared by other robots of the same kind.
  • Behaving morally and well toward others is not the same as taking moral responsibility. Only competent adult humans can take full responsibility for their actions, but we expect children, animals, corporations, and robots to behave well to the best of their abilities.

The nature of morality and ethics

Human morality and ethics are learned by children over years, but the nature of morality and ethics itself varies with the society and evolves over decades and centuries. No simple fixed set of moral rules, whether Asimov’s Three Laws or the Ten Commandments, can be adequate guidance for humans or robots in our complex society and world. Through observations like the ones above, we are beginning to understand the complex feedback-driven learning process that leads to morality.

By Benjamin Kuipers, Professor of Computer Science and Engineering, University of Michigan. This article was originally published on The Conversation. Read the original article.The Conversation

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9 lesser known facts about Australia http://didyouknow.org/9-lesser-known-facts-about-australia/ http://didyouknow.org/9-lesser-known-facts-about-australia/#respond Wed, 04 May 2016 14:31:10 +0000 http://didyouknow.org/?p=4293 The Commonwealth of Australia is the sixth largest country (after Russia, Canada, China, the USA, and Brazil) in the world, occupying the Australian continent and surrounding islands, the largest of which is Tasmania (68,401 km²). At 7 692 024 km², Australia accounts for five percent of the world’s land area of 149 450 000 km².

Many who dream to go there might think of it as too far, too expensive to get there or too unknown, even uninteresting. There are koalas, kangaroos, summer heat, the ocean and what else?

Travel Ticker offers you 9 little-known and exciting facts about this distant and beautiful country.


1. Australians almost never leave a tip.

Australians almost never leave a tip. But with valid reason, as explained by Peter Baskerville on Quara.

Australians do, however, tip for instances of particularly good service.

2. Canberra became Australia’s capital as a compromise between Sydney and Melbourne.

Australians couldn’t decide which of their two largest cities should be made the capital city. So, in 1908, it was decided to build a completely new capital city on a site of a smallish settlement between these two rival cities.

Construction of the capital in 1913 along the banks of the Molonglo river. At midday on 12 March 1913, the city was officially given the name Canberra.

Canberra is 280 km (170 miles) south-west of Sydney and 660 km (410 miles) north-east of Melbourne.

3. Australia is home to the world’s most venomous snake.

The inland taipan – also known as the “fierce snake” – is the world’s most venomous snake. Its venom is specially efficient to kill warm-blooded species. One byte possesses enough venom to kill at least 100 people.

They grow up to 2,5 metres (8.2 feet) long, with an average length of 1.8 m (6 ft). According to Wikipedia, it is an “extremely fast and agile snake which can strike instantly with extreme accuracy.”

Fortunately, they are quite shy and are found mainly in the remote semi-arid regions of central east Australia, away from the usual travel destinations.

Inland taipan snake

Inland taipan, the world’s most venemous snake. Don’t touch! Photo via Wikipedia.

4. Australia has an enormous population of emigrants from all over the world.

According to The Australian Bureau of Statistics, more than one-quarter of the entire Australian population of 24 million was born abroad.

Australia has a net migration rate of 5.65/1000; in comparison, during 2015, the United States had a net migration rate of 3.86 per thousand and the United Kingdom a rate of 2.54 per thousand.

5. Australia has one of the lowest population densities in the world.

Australia has one of the lowest population densities in the world: only 3.13 persons per square kilometer ( 8.11 per square mile.) In the United States, it is 33 persons per square kilometer (85 person per square mile). In the United Kingdom it is 262/km² (679/m²).

Over 60% of the Australia’s population lives in only five cities: Adelaide, Brisbane, Sydney, Melbourne, and Perth.

If you ever decide to go on a road trip throughout this continent, you might not see a human face for weeks.

6. Despite the fact that Australia is usually associated with the constant sun and heat, this is not entirely the truth.

In fact, at the Australian Alps, you can find much more snow than in the whole of Switzerland combined!

Australia beachesPhoto via Shutterstock

The Australian coastline is 25,760 kilometers (16006.522 miles) long, sporting some of the best beaches in the world. But the Australian Alps is just as enticing, comprising an area of 1,232,981 hectares (3,046,760 acres).

7. The 90 Mile Straight

Throughout the entire Australia’s Nullarbor Plain runs the second longest straight road in the world, the “90 mile straight.” It’s actually 91 miles (146.6 km) long, without any, not even the tiniest, turn.

8. The world’s longest fence is in Australia.

The world’s longest fence or border wall, as it turns out, is not the Great Wall of China.

In fact, Australia is the one who can be proud of their so-called “Dog fence,” the Dingo Fence. This border divides the Australian continent into two parts, roughly along 29th parallel of latitude. This protective fence was built in the 1880s primarily to protect South Queensland’s pastures and farms which were occasionally attacked by hungry wild animals.

The Dingo Fence is an incredible 5 614 km (3,488 miles) long. To put it in perspective, that is almost 500 kilometers (more than 3oo miles) longer than the longest distance from the East Coast to the West Coast in the United States.

Regarding the Great Wall of China, only 725 km (450 miles) of the original 21 196 km (13,171 mi) survived the ravages of time.

9. Weather in Tasmania, it is believed, it is the cleanest throughout our planet.

Tasmania can be the best place to escape from buzzy cities. Tasmania is usually overshadowed by Australia but, with its natural beauty and clean air, in recent years has attracted more tourists. In fact, of the more than 7 million people who visit Australia each year, more than 1 million make the effort to visit Tasmania. So, soon you might need to fight for a seat on a plane flying there!


One of the cutest animals in the world, the Koala. Found only in Australia.

Australia population trivia factoids

74 million sheep, 50 million kangaroos, 26 million cattle, 24 million people.

Article by Michelle Ross.

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How time actually tricks us http://didyouknow.org/how-time-actually-tricks-us/ http://didyouknow.org/how-time-actually-tricks-us/#comments Tue, 12 Apr 2016 12:30:05 +0000 http://didyouknow.org/?p=4277 Time is truly a complicated matter. Remember how as a child you were waiting for your birthday and how it seemed to take forever to arrive? And now as an adult, the time from Monday to Sunday passes all too briefly.

How does time do that? How does time trick us?

Looking from a scientific, psychological and biological perspective, the greatest influence on how we perceive time is made by our internal rhythms, gained experiences, and memories.

Everyone perceives time differently

Five minutes seems to be a definite time limit. However, after five minutes, ask ten people how it passed for them – did it go quick or did it seem long? We can bet that each of them would have a different opinion.

Hours - Shutterstock Image Shutterstock

Emotions and time are connected

How do you feel? Happy, depressed, horrified, fascinated, angry, sad? When you look at the full scale of emotions you will soon realize that time is perceived differently during each of those sensations. However, one study suggests that pleasant emotions theoretically last longer.

Researchers say that negative emotions can be adopted in different ways, especially then it comes to anxiety or tension. Meanwhile, boredom is usually distinguished by the sense that time slows or stops.

The older we become, the faster time seem to pass

Why does time appear to pass more quickly the older we get?

It is argued that as a younger person gets acquainted with the world all that new information raises a lot of intrigue and thus, according to Scientific American, a lot of “firsts” but as we get older we generally lack new experiences.

Psychologist William James, in his 1890 text Principles of Psychology, wrote that as we age, time seems to speed up because adulthood is accompanied by fewer and fewer memorable events.

One study states that 20-year-olds felt time quite accurately while the persons in their 70s significantly overestimated the time (they said, that the time has passed much faster). The mentioned Scientific American article points out –

“How fast did the last 10 years pass for you?” yielded a tendency for the perception of the speed of time (in the last decade, anyway) to increase with age; this pattern peaked at age 50, however, and remained steady until the mid-90s.

Time flies - Shutterproof Image Shutterstock

Latest technologies changing the concept of time

A few recently done studies state that social networks and smart devices are “stealing” our time more than we think about it. We are always checking the latest news or messages, often wasting time, and we become new technologies’ hostages. In fact, a 2013 Internet Trends report by Kleiner Perkins Caufield & Byers shows that people check their phones up to 150 times a day. According to RawHide, “Every year, teens spend almost 7 full work days taking selfies.”

Stanford University psychologist Dr. Phillip Zimbardo believes that social networking is actually changing the concept of time, and how we take it.

So maybe if you are constantly online but can’t understand where the time passed, log off and enjoy your life without the blue screens.

Joan Rivers said it perfectly: “Yesterday is history, tomorrow is a mystery, today is God’s gift, that’s why we call it the present.”

Past, present, future

However, if you don’t want tomorrow to be a mystery, you should realize that every moment is now, because the past and future concepts become one. The essence lies in the fact that every event in the past and the future is and will be affected by what we do now.

As G.I. Gurdjieff explained:

“In order to know the future it is necessary first to know the present in all its details, as well as to know the past. Today is what it is because yesterday was what it was. And if today is like yesterday, tomorrow will be like today. If you want tomorrow to be different you must make today different.”

Original article by Michelle Ross.

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Beware the ‘awestruck effect’ – How charismatic leaders influence followers http://didyouknow.org/beware-the-awestruck-effect-how-charismatic-leaders-influence-followers/ http://didyouknow.org/beware-the-awestruck-effect-how-charismatic-leaders-influence-followers/#respond Wed, 17 Feb 2016 14:26:19 +0000 http://didyouknow.org/?p=4251 Charismatic business leaders can cause their followers to suppress emotions, which can harm companies over the long term, according to new research.

While charismatic leaders may be magnetic, they can cause their followers to suppress emotions, which can harm companies through increased strain, lower job satisfaction and reduced information exchange among employees, according to new research from the University of Cambridge.

How charismatic leaders influence followers

The study, published in The Leadership Quarterly, found that while charismatic leaders may put their followers in awe, reinforcing the leader’s standing in the group, ‘awestruck’ followers are unlikely to benefit the group in the long-term.

The study also finds that leaders who show individual consideration tend to encourage followers’ emotional expression. While this may circumvent the negative implications of emotion suppression, at “rampant” levels such expressiveness can be detrimental because it violates workplace norms and can cause conflict and harm employee coordination.

The study is based on responses to various leadership scenarios by several hundred research participants at universities and companies in Germany and Switzerland.

Although previous studies had looked at how charismatic leaders influence followers’ emotional experience, the new study focuses instead on how followers regulate their emotional expressiveness in response to charismatic leaders – and does so by examining separately the effect of both a leader’s charisma and individualised consideration on followers.

Keeping emotions in check

“Emotion suppression is associated with a wide range of negative outcomes,” said Dr Jochen Menges of Cambridge Judge Business School, one of the study’s authors. “The problem is that for emotions to be suppressed, our brain needs to allocate resources to self-regulation processes that allow us to appear calm and collected on the outside when on the inside we are emotionally stimulated.”

While our brain is busy keeping emotions in check, it cannot allocate resources to other mental tasks – such as memorising or scrutinising messages or coming up with new ideas. “So while we are awestruck – overwhelmed with the emotions that charismatic leaders stir and yet too intimidated to express these emotions – we are impaired in our mental abilities,” said Menges. “That makes us vulnerable to the influence of charismatic leaders, and likely impairs our own effectiveness in dealing with work challenges.”

crowd in awe Such inhibition of expressiveness can deploy mental resources and impair the cognitive processing capacity of followers – which may make them less able to evaluate the actual messages of charismatic leaders, and therefore make them more likely to endorse such leaders with little scrutiny.

If there is such an impairment of cognitive functioning, then charismatic leadership may carry costs for followers that have so far been overlooked. Charismatic leadership may have a dark side for followers irrespective of whether leaders’ goals are moral or immoral.

“Charisma has effects that can be harmful, but these effects can be counterbalanced by other leadership behaviours, such as individualised consideration and support as well as mentoring and coaching,” said Menges.

Charisma and influence

The two styles of leadership that the researchers looked at are quite different, but they are not mutually exclusive. It is the combination of both styles that will serve the leader best, so they can bring together people for a common mission with charismatic messages from the podium, but then also solicit their advice and input when stepping down from the podium.

“While charisma can help leaders establish power and exert influence, it may be intimidating to those who look up to them for guidance and inspiration,” said Menges. “To leverage the full potential of their followers, leaders need to balance charismatic appeal with the consideration of each follower’s individual needs. And for those who find themselves awestruck by the charisma of their leader, remember that even the most charismatic person is only human.”

Reference: Menges, Jochen et. al. “The awestruck effect: Followers suppress emotion expression in response to charismatic but not individually considerate leadership.” The Leadership Quarterly (2015). DOI: 10.1016/j.leaqua.2015.06.002

Article by University of Cambridge Research under a Creative Commons Attribution 4.0 International license. See the original article.

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The 22 million digit number … and the amazing maths behind primes http://didyouknow.org/the-22-million-digit-number-and-the-amazing-maths-behind-primes/ http://didyouknow.org/the-22-million-digit-number-and-the-amazing-maths-behind-primes/#respond Thu, 21 Jan 2016 09:21:46 +0000 http://didyouknow.org/?p=4216 It is a quite extraordinary figure. Dr Curtis Cooper from the University of Central Missouri has found the largest-known prime number – written (274207281)-1. It is around 22m digits long and, if printed in full, would take you days to read. Its discovery comes thanks to a collaborative project of volunteers who use freely available software called GIMPS (Great Internet Mersenne Prime Search) to search for primes.

A number which can only be divided by itself and 1 without a remainder is called a prime number. Here is a list of the primes less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Unlucky 13

Numbers appear everywhere in our lives – and good and bad superstitions have developed out of them. Remarkably, most of these superstitious numbers are prime. The superstition that 13 is unlucky results in some hotels and office buildings not having rooms or floors labelled 13. And we all fear Friday 13th, especially sufferers of paraskevidekatriaphobia. [See more Phobias.]

Unlucky for some. Dave Bleasdale/flickr, CC BY

The most popular explanation for 13 being unlucky is that at the last supper there was Jesus and the Twelve Apostles, with the 13th guest being Judas Iscariot who went on to betray Jesus.

The number 3 also has religious significance and references to it can be found not only in the Holy Trinity of Father, Son and Holy Ghost, but also the Three Wise Men and in the architectural structures of churches. There is also a superstitious fear of walking under a ladder, which seems to have its origins in the number 3. Propped against a wall, a ladder forms the longest side of a triangle, with the ground and the wall forming the other two sides. A person passing under the ladder is symbolically breaking the Trinity and thus brings bad luck on themselves.

Don’t do it! Shutterstock

Big rewards

Mathematicians have been searching for patterns in prime numbers for more than 3,000 years and have made only a small amount of progress, believing that there are still many patterns to find. This recent discovery continues that pursuit of understanding.

But why? Well, you could be doing it for money. The Clay Mathematics Institute is offering a million dollars to anyone who can solve the “Riemann problem”. This is a complex mathematics puzzle that emerged from the attempts by mathematicians to understand the intricacies of prime numbers. And so finding larger primes, some believe, may help in this quest.

Or maybe you are just looking for “the truth”, something mathematicians have been doing for a very long time. Eratosthenes was a Greek mathematician who was working at the library in Alexandra around 200BC when he discovered the first method of listing primes.

He was very keen on all types of learning (his nickname was Philogus, or “the one who loves learning”). He called his method “the sieve”, as primes just fall out when you apply it – and it offers a flavour of prime searching.

First – and this begins to get technical – note that if a number is a composite, such as n=ab, then a and b cannot both exceed √n. For example, with the composite “21” – 21=3×7 – only 7 is bigger than √21 = 4.58. Therefore, he determined that any composite integer n is divisible by a prime p that does not exceed √n.

It follows from this that to test for primes it is only necessary to divide a number by numbers less than or equal to its square root. To find primes from 2 to 30, then, we need only use the fact that √30 is less than 7, and work with the primes 2, 3 and 5.

So if you write out the list of numbers from 2 to 30 on a piece of paper, we can “sieve” out any numbers that are divisible by 2, 3 and 5 to leave us with the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Mysterious numbers

Primes are strange and curious numbers. There are, for example, no primes between 370,261 and 370,373, or between 20,831,323 and 20,831,533. And the primes 13,331, 15,551, 16,661, 19,991 and 72,227 and 1,777,771 are all examples of palindromic numbers. These are numbers that remain the same when the digits are reversed.

Magic number 7. Niklas Morberg/flickr, CC BY-SA

In 1956, psychologist George A Miller published a paper in The Psychological Review called The Magical Number Seven, Plus or Minus Two. In the paper, he talks about the prime number 7 “following him around”. Religion, for example, is filled with sevens, from the Seven Deadly Sins to the Seven Sacraments. And salesman believe in the “rule of seven”, which suggests people need to hear a marketing message seven times before they take action. Miller, however, claims that this is more than just coincidence. [Also see The Beautiful Number 7.]

Our immediate memory has been shown to perform well when remembering up to, but no more than, seven things. We can distinguish and make a judgement about seven different categories. Our span of attention will also remember around seven different objects at a glance. Miller also looked into other areas of how we record and store information and found to his surprise that seven appeared over and over. In conclusion, Miller makes no claim that this is something deep and profound, but says maybe, just maybe, seven could be more special than we had imagined and needs a closer look.

Prime numbers are interesting, don’t you think?

By Steve Humble MBE, Researcher in International Development and Education, and Head of PGCE Maths teacher training for Primary and Secondary Education, Newcastle University.

This article was originally published on The Conversation. Read the original article. The Conversation

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How to vet nonprofits before you give http://didyouknow.org/how-to-vet-nonprofits-before-you-give/ http://didyouknow.org/how-to-vet-nonprofits-before-you-give/#respond Wed, 02 Dec 2015 08:56:05 +0000 http://didyouknow.org/?p=4182 Charity solicitations are as much a part of the holiday season as decorations. If you give, it’s a good idea to know what the nonprofit organization does with your money. Here’s one way: use ProPublica’s Nonprofit Explorer, a tool for researching the financial details of nonprofits.

Organizations that receive a tax exemption from the Internal Revenue Service and take in at least $50,000 a year have to file an annual report, called a Form 990, which can serve as a guide to how they operate and what their programs are.

Nonprofit Explorer summarizes the financial data in 990 forms and also provides links to the documents. While not a complete picture of an organization’s activities, the form does provide insight on how a nonprofit operates. Here are a few things to look for when deciding whether to make that contribution:

Program Spending

detectiveCharities often tell donors that a certain amount of every dollar goes directly to “programs,” which usually mean direct services provided to the recipients of their assistance (the homeless, for example, or children). But read the fine print, says CharityWatch: sometimes these statements say “of every dollar spent” and sometimes they say “of every dollar donated.” Those are two different numbers, as ProPublica’s reporting on the Red Cross demonstrates. The Form 990 not only lists the totals for money coming in and going out, but in Part III (often the second page of the completed form, as with the 2013 form for the New York-based Coalition for the Homeless), the group also describes the program services that it performed, how much they cost and indicates whether there were any significant changes to existing programs. If you’re unsure about exactly what a charity does, Part III can help clear up that uncertainty, but it is also the place where charities promote their accomplishments.

Amount Spent on Professional Fundraisers

Charities rely on volunteers to ask for donations, but many also pay for-profit companies to help them raise money via telephone and mail solicitations. In its investigation of “America’s Worst Charities,” the Tampa Bay Times and the Center for Investigative Reporting identified nonprofits that raise millions via professional fundraisers and “regularly give their solicitors at least two-thirds of the take.” One organization, the Committee for Missing Children in Lawrenceville, Ga., paid its fundraisers nearly 90 percent of the $27 million it raised during the decade the report examined. The more that charities spend on fundraisers, the less money they have for direct program spending – the reason the organizations exist. On a 990 form, look for this amount on line 16a of the first page, labeled “Professional fundraising fees.”

Executive Compensation

Charity organizations are also required to list officers, directors, trustees, key employees and the five highest-paid employees of the organization 2014 and the amount each person was paid 2014 in Part VII of the 990 form. Because of this public disclosure, executive salaries are sometimes contentious, as recently highlighted during a congressional hearing on Planned Parenthood. (In 2013 the organization’s president, Cecile Richards, was paid $590,928 in salary, retirement contributions, bonuses and other pay.) But a high salary alone isn’t a red flag. The IRS requires only that compensation is “reasonable,” or what a similar position would be paid by a similar organization. A Charity Navigator study of charity CEO compensation noted that unsurprisingly, “as the size and to some degree the complexities of running a nonprofit increases, so does the salary of the institution’s top executive,” recommending that donors compare an organization’s executive salaries to other charities for a better assessment.

The study also points out that organizations that show $0 paid to executives may also warrant a closer look. “There are very few individuals that can afford to work full-time managing complex, multi-million dollar organizations without receiving any compensation.” There may be legitimate reasons for this, or the compensation figure may have been misreported to the IRS.

According to Ray Madoff, director of the Boston College Forum on Philanthropy and the Public Good, this could also be caused by a nonprofit outsourcing staff and management duties, essentially hiding the individual salaries of an organization by reporting it within an aggregate contractor payment. She points to Fidelity Charitable, the second-largest nonprofit in terms of donations: Although officers are listed in Part VII of the form 990, all salaries are listed as “$0*”, with the asterisk noting that “all services are provided to Fidelity Charitable” by FMR LLC, the parent company of the for-profit Fidelity Investments. A Fidelity spokesperson confirmed simply that “Fidelity Charitable does not report individual salaries because it does not itself pay any salaries” and that “it hires FMR LLC [2026] to provide a wide range of services.” They also point out that the charity “does, of course, report the fees paid to service providers, including FMR LLC.” According to Schedule O of the 990, FMR received over $32 million in “contractor compensation” from Fidelity Charitable.

Beyond the 990

While the 990 can help you root out scammers and gross underperformers, it does not tell you how effectively money spent on programs translates into results on the ground. In the words of the Foundation Center’s Luz Rodriguez, “some not-so-great charities are just really good at finances.” To examine a charity’s reputation in its target community, Rodriguez suggests looking through its social media for positive testimony or service complaints. Greatnonprofits.org aggregates crowd-sourced reviews of nonprofits. GuideStar has experts in the field weigh in on their favorite nonprofits on Philanthropedia.

In the absence of robust data on results, GuideStar CEO Jacob Harold said donors should look for groups that set out their work and measures of success with clarity and specificity. “Clarity is all too rare in the nonprofit sector,” he said. “Look for groups that clearly articulate the solution rather than just talking about the problem.” He recommends GiveWell, one of the more quantitatively rigorous nonprofit watchdogs, which weighs charities by lives improved per dollar spent. Its list is far from exhaustive, but incorporates the concept of scalability 2014 it selects groups that have “room for more funding,” and can do the most with your money

Giving Overseas 2014 One Thing To Remember

Sometimes your charity of choice’s mission could cause more harm than good by having unintended consequences for the recipients of its donations.

This is particularly relevant to “gift-in-kind” donations 2014 those old clothes, shoes, toys and food that well-intentioned Americans send in bulk to the developing world. These influxes of free, second-hand goods can undercut and destroy local industry. Indigenous manufacturers are priced out of the market, and the community is denied the growth benefits of textile and food processing industries that placed countries like Mexico and South Korea on the development ladder. Countries like Kenya and Haiti are having this first rung broken right under their feet by good intentions.

Charity evaluators like GiveWell prioritize health and infrastructure sectors instead, in which nonprofit interventions have an exponential impact on the local economy by attacking the problems of poverty at their core. They also recommend GiveDirectly, a direct cash transfer charity with a 90 percent program-to-overhead cost ratio that consistently ranks among GiveWell’s top performing nonprofits. GiveDirectly sends donor money straight to the poorest families in Uganda and Kenya through mobile banking. The mobile route ensures that the entire sum reaches the target family, and is even safer than in-kind donations, which can be siphoned off to the black market.

By Derek Willis and Mike Tigas, ProPublica, and Sahir Doshi, special to ProPublica. As a nonprofit, ProPublica also files Form 990; you can see the most recent one here.

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