Physics, Math & Chemistry – Relatively Interesting
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Sun, 21 Oct 2018 00:39:13 +0000en-UShourly139163838Understanding Scale: The Universe, Atoms, and Homeopathy
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http://www.relativelyinteresting.com/understanding-scale-the-universe-atoms-and-homeopathy/#commentsFri, 24 Aug 2018 14:03:24 +0000http://www.relativelyinteresting.com/?p=3719Numbers, especially the very large and very small, can be deceiving. It’s almost impossible for our brains to compute the immense scale in the fields of astronomy or microbiology. Nevertheless, understanding and being able to visualize the incredibly large scale of our universe is valuable. Let’s take a look at time and distance, and translate […]

Numbers, especially the very large and very small, can be deceiving. It’s almost impossible for our brains to compute the immense scale in the fields of astronomy or microbiology. Nevertheless, understanding and being able to visualize the incredibly large scale of our universe is valuable.

Let’s take a look at time and distance, and translate smaller units of time into understandably larger units:

1 second equals 1 second 1 million seconds equals 12 days 1 billion seconds equals 30 years 1 trillion seconds equals 30,000 years!

1 millimeter equals 1 mm 1 million mm equals 1 km 1 billion mm equals 1000 km 1 trillion mm equals 1,000,000 km! (this is like going around the world 25 times)

Here’s what $10k, $1 million, and $1 billion looks like:

And here’s $1 Trillion:

Understanding these large scales can help us visualize numbers that we might read or hear about.

For example, when you hear that something is “99.999% reliable”, it means there is an error rate of 10 out of a million. Using our references from above, that’s like being offline for only 10 seconds out of 12 days. Or, looking at it from the perspective of “distance”, you can have a tolerance of 10mm (about the width of your pinky finger) for every kilometer.

The phrase “One part per million” is often used by chemists to measure concentrations of substances. One ppm is like having a presence of 1 second in 12 days. And a part per trillion? Only 1 second every 30,000 years!

To help humanity visualize the large scale of our universe, the American Museum of Natural History has produced a movie that begins with a view of the Earth’s Himalayan Mountains and then zooms out: showing the orbits of Earth’s satellites, the Sun, the Solar System, the extent of humanity’s first radio signals, the Milky Way Galaxy, galaxies nearby, distant galaxies, and quasars. Every object in the video has been rendered to scale using the best scientific research available in 2009. The film has similarities to the famous Powers of Ten video, which you can also see below:

And here is the famous Powers of Ten video:

So how does estimating scale and magnitude apply to skepticism and critical thought?

The pseudoscience of Homeopathy is a great example.

The “law of infinitesimals” in homeopathy states that dilution increases the curative power of homeopathy medications. This means that a part-per-million solution of a substance is more medicinally powerful than a part-per-thousand solution, which has in turn more curative power than a part-per-hundred solution. In contrast, many of our modern drugs are ineffective in small quantities and the efficacy increases with dosage.

Let us put modern medicine aside and consider the dosages involved in homeopathy.

Homeopathic medicines often come in 12x, 24x, 28x dilutions (“28x” means the solution has been diluted 28 times) . If a substance were to be diluted 30 times, this means that there would be one part medicine to one trillion quadrillion parts water (or other inert ingredient). That’s a 1 with 27 zeros, or 1,000,000,000,000,000,000,000,000,000. Going back to our “time” example, that the equivalent of being offline 1 second in 10,000,000,000,000,000,000 years!

What does this mean? It means that a homeopathic solution is effectively water. Nothing more. Yet, it is sold, and people buy it. Homeopathy defies the laws of physics and chemistry, but due to effective marketing and a proper lack of FDA involvement, homeopathic “remedies” continue to be sold alongside legitimate medications.

One more reason to think twice before you consider purchasing Snake Oil.

]]>http://www.relativelyinteresting.com/understanding-scale-the-universe-atoms-and-homeopathy/feed/2371920 Mind Boggling Facts About Plastic
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http://www.relativelyinteresting.com/20-mind-boggling-facts-plastic/#commentsMon, 23 Jul 2018 11:00:45 +0000http://www.relativelyinteresting.com/?p=4729Plastic is everywhere. In fact, you’re probably never more than a metre away from something made with the material. Super flexible, resilient and waterproof, plastic is in your phone, your keyboard, your bag, your mobile phone, your nearest wall sign, all the sockets in your home and your bathroom fittings etc., etc., etc. Essentially, it’s […]

]]>Plastic is everywhere. In fact, you’re probably never more than a metre away from something made with the material. Super flexible, resilient and waterproof, plastic is in your phone, your keyboard, your bag, your mobile phone, your nearest wall sign, all the sockets in your home and your bathroom fittings etc., etc., etc. Essentially, it’s one of the most widely produced materials across the globe and it isn’t going away anytime soon.

If you’re not already sure that plastic is a megastar in the material world then read on to find out 20 interesting things about the versatile hero. Be warned, they aren’t all positive…

Let’s kick things off with something a little scary…

Our food companies don’t know 100% of what makes up the plastic they use for packaging. That means that neither do consumers. As plastic is made from oil or gas, the basic constituents are always the same. Yet, dozens of chemicals are added at manufacturing plants to give different types of plastic its required properties and these mixtures remain trade secrets. Pretty scary that we don’t really know what chemicals have been in contact with the food we’re about to eat right?

Oh, and there’s this…

Plastic isn’t necessarily vegetarian-friendly. Amongst the masses of chemicals which are added to plastics, some are pretty gross. Chicken fat has been found in some plastic bags to give them their slippery texture and other animal fats have been used to prevent plastic sticking to machinery. I doubt any vegetarian would consider munching on their latest grocery bag but this gives them all the more reason to find another way of carrying stuff home from the supermarket.

But I wouldn’t mess with tough-man plastic…

Plastic is very resistant to bacteria and fungi. The material’s closely interconnected molecules are too large for microbes to get their biters around, never mind digest.

And yet, plastic’s super strength is why…

It takes 450 years for plastic to begin decomposing and then up to another 80 for it to disappear completely.

And this means…

Every piece of plastic ever made, ever, has still not even begun to decompose. Wow, that hammers home the world’s landfill problems right?

But still…

The world churns out more than 600 billion pounds of plastic every year. That means more than one plastic bag is made per minute.

Which is mostly…

Polyethylene – the most common type of plastic on the earth. The material consists of gigantic, strong hydrocarbon chains which make it ideal for shopping bags and bottles.

And the second most common type of plastic is…

Polypropylene – typically used for bottle caps, straws and food containers. The material’s high heat resistance means it microwave and dishwasher safe and super strong for reusable bags.

But what’s with ‘poly’ in the name of these plastics?

The word ‘Polymer’ is Greek. ‘Poly’ translates to ‘many’ and ‘mer’ translates to ‘unit’. Hence a polymer is a ‘many-unit’ material.

I think this needs a little more explanation…

Polymers are giant molecules which contain thousands of smaller molecules called monomers. Plastic is produced through a process called polymerisation which links these monomers into long-chains.

Who discovered this could happen?

Alexander Parkes invented the first plastic substance in the 1850s. The material was called ‘Parkesine’ but was a bit of a let down as it cracked easily and was highly flammable. He hadn’t cracked it yet.

Then we got a step closer…

In 1907, Chemist Leo Hendrik discovered Bakelite, a plastic made from heated wood alcohol and tar. The material was strong and fire-resistant and soon became the ‘Material of a Thousand Uses’. It was used to build telephones, appliances, cameras, fittings and multiple other items across the planet.

And although it looks and feels the same…

Cellophane is not a plastic. Swiss chemist Jacques E. Brandenberger discovered the material in 1908 from mixing viscose with acid. It got its name from a mix of the French word for transparent: ‘diaphane’ and its ingredient, ‘cellulose’.

Anyway, plastic really made its entrance when…

Polyethylene was invented by German Chemist Karl Ziegler in 1953. This was shortly followed by the invention of Polypropylene by Giulio Natta.

And just to reinforce how much the world relies on plastic…

More than 13 billion plastic bags are produced every year. This is equal to 300 per adult, per year in the USA.

And this isn’t good news for the future of our planet…

24 million gallons of oil are needed to manufacture 1 billion plastic bottles. Oil is a finite resource.

And neither is plastic any fun for the environment…

150,000 tons of plastic is disposed into our oceans every year. Besides visual pollution, this plastic thrash has caused the death of more than one million animals which mistook the material for food. In fact, plastic pollution isn’t just a problem underwater. There have been reports of cows, sheep and desert animals dying due to the ingestion of garbage plastic.

But if not thrown away, plastic CAN be recycled…

Recycling plastic can save up to two thirds of the energy required for producing plastic from raw materials. And besides less energy, fewer resources are used up and less non-biodegradable plastic is released into our planet.

To put this energy saving into perspective…

One recycled plastic bottle can save enough energy to light a 60W light-bulb for 6 hours.

Plastic isn’t all bad. Let’s go out on a high…

Plastic is footing innovation in medical science. In 2011, Swiss chemists produced the largest ever synthetic molecule called PG5. In the future, this polymer could be ingested to deliver an appropriate does of medicine to the specific areas of the body.

]]>http://www.relativelyinteresting.com/20-mind-boggling-facts-plastic/feed/24729Does 0.99999… really equal 1?
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http://www.relativelyinteresting.com/does-0-99999-really-equal-1/#commentsFri, 20 Jul 2018 16:53:00 +0000http://relativelyinteresting.com/?p=103Does 0.999 (repeated) equal “one”? You might be surprised by the answer… which is “yes“. I heard this on a couple of podcasts over the last few months, and I still find it hard to accept at face value. However, I am now convinced and here’s several simple proofs that .99999 does indeed equal 1… […]

]]>Does 0.999 (repeated) equal “one”? You might be surprised by the answer… which is “yes“. I heard this on a couple of podcasts over the last few months, and I still find it hard to accept at face value. However, I am now convinced and here’s several simple proofs that .99999 does indeed equal 1…

Method 1:

Let x = 0.9999…

Then 10x = 9.9999…

If we then subtract x from both sides of the equation, then:

10x – x = 9.9999… – 0.9999…

So, 9x = 9

Divide both sides of the equation by 9, and…

x = 1 … which, when we started, we said = 0.9999…

Method 2:

1/9 = 0.11111…

Multiply both sides of the equation by 9:

9 X 1/9 = 9 X 0.11111…

1 = 0.99999…

Method 3:

We know that 0.9 is not equal to 1; neither is 0.999, nor 0.99999. If you stop the expansion of 9s at any finite point, the fraction you have (like .99999 = 99999/100000) is never equal to 1. But each time you add a 9, the margin error is smaller (with each 9, the error is actually ten times smaller).

You can show (using calculus or other summations) that with a large enough number of 9s in the expansion, you can get arbitrarily close to 1. There is no other number that the sequence gets arbitrarily close to – it is always 1. Another way of saying this is that “the limit is 1?.

Thus, if you are going to assign a value to 0.9999…, the only sensible value is “1?.

]]>http://www.relativelyinteresting.com/does-0-99999-really-equal-1/feed/3103How Many Times Can You Really Fold a Piece of Paper in Half?
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http://www.relativelyinteresting.com/how-many-times-can-you-really-fold-a-piece-of-paper-in-half/#respondTue, 17 Jul 2018 13:16:39 +0000http://www.relativelyinteresting.com/?p=6723A popular myth exists that one can only fold a single piece of paper in half, seven, maybe eight times at most. To squelch this popular myth, the folks over at Mythbusters did what any “rational” person might attempt; they produced an enormous sheet of paper, something roughly the size of a football field. Together […]

]]>A popular myth exists that one can only fold a single piece of paper in half, seven, maybe eight times at most. To squelch this popular myth, the folks over at Mythbusters did what any “rational” person might attempt; they produced an enormous sheet of paper, something roughly the size of a football field. Together with a team of their accomplices, a steam roller and a forklift, they successfully folded this enormous sheet eleven times.

Following this feat, their explanation of being unable to accomplish a twelfth fold, was that it would have produced something resembling a semi-circle and not an actual fold. But what if they obtained a piece of paper the size of two football fields or even three for that matter? Would they still be able to fold it even more?

A student named Brittany Gallivan was able to successfully fold an extremely long piece of toilet paper in half twelve times. Later, students at the St. Marks school in Southborough, together with their teacher, James Tanton, stated they were able to fold an even longer piece of toilet paper a total of thirteen times, breaking the previous record set by Gallivan.

But according to Gallavan, she claimed that both the Mythbusters and Southborough students had “broken the rules.” Brittany explained in a press release that Mythbusters and the students from St. Marks had both admittedly used paper that needed to be taped together, rather than the single sheet that was required by this paper folding challenge.

When Gallavan made her record-breaking twelve folds, she supported it with a book entitled “How to Fold Paper in Half Twelve Times: An Impossible Challenge Solved and Explained,” which is what inspired the Southborough students to break her record. In her book, she noted exactly how she was able to perform this stunt and also backed it up with some mathematical equations that precisely explained her victory and the limitations that this challenge presented.

Oh boy – Here Comes The Math!

When she was originally presented with this problem by one of her high school math teachers, to reach a dozen creases, she came up with an equation that addressed folding the paper in half the traditional way, top to bottom and side to side. Where the width (W) results from the thickness (t) of the material and number (n) of folds.

She then came up with a second equation where she believed she could conquer this challenge by folding the paper in half lengthwise instead and continue to fold it in this way. Here length (L) was derived from the thickness (t) of the paper and number (n) of folds.

Her conclusion was that with each lengthwise fold, it would require roughly four times more paper to arrive at a dozen. In order to reach her goal of twelve, her computations showed that she would need a piece of very thin paper that was 1.2 kilometers in length, or almost 4,000 feet long.

What this mathematician was ultimately able to prove with her equations is that the smaller and thicker the piece of paper, the fewer of times you can fold it and vice versa. As we continue to fold, the smaller square footage of the paper doesn’t allow for the thickness of the folds to continue, which makes logical sense. The bottom line is that as the height of the folds continue to rise, as the amount of paper also increases, the thickness will grow exponentially.

More simply put, for ‘n’ number of folds, you will end up with 2^n pieces of paper in thickness. This adds up quick. 3 folds is easy: 2 x 2 x 2 = 8 pieces of paper thick. When you get to 7 (my personal record and seen below), you’re at 2^7 or 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 pieces thick. I could not make the 8th fold because 256 pieces of paper this is like trying to fold a piece of lumber, and I am weak from sitting at a computer all day.

It gets exponentially thick…

The thickness grows soexponentially quickly, in fact, according to another mathematician, these amounts can be staggering, stretching the limits of the known universe. His figures show that as the folded pile grows…

At 23 folds, you’ll reach one kilometer or 3,280 feet

30 folds will get you into outer space at 100 kilometers or just over 62 miles

Over 40 will land you on the moon

A little over 50 gets you to the sun

More than 80 folds is near the thickness of the Andromeda galaxy, estimated to be 141,000 light years wide

Near 90 folds and it will be bigger than Virgo supercluster at around 130 million light years in length

Finally, at 103 folds, you’re now outside of the observable universe which is estimated to be 92 billion light years in diameter.

While these mathematicians and students can clearly see through Brittany’s numbers to accomplish even more folds, to the ends of the universe and back, but at what price? To what lengths, literally, are we willing to go to be the paper folding champion? How much time are we willing to spend? How many trees must die to accomplish our paper folding dreams? Who will rise as our next Paper Folding Hero?

In Brittany’s case, the cost for her extra-long roll of toilet paper was $85 and the length was almost 4,000 feet as mentioned previously and 13,000 feet for the students at Southborough. It took Brittany over seven hours to get to the eleventh fold and snap her record breaking picture and subsequently make the twelfth and final fold. All of this was to simply get some extra credit in her high school math class.

These paper-folding pros keep talking about “breaking a record,” but is it really a world record if it isn’t even recognized by Guinness? According to Mr. Tanton, the teacher from St. Marks, the people from The Guinness Book of World Records don’t even have a category for paper folder and doesn’t keep track of these kinds of records, which is a damn shame.

And as for Gallivan’s claim that both the Mythbusters team and the students didn’t follow the rules of it being one continuous piece of paper, who made up those rules in the first place? Was it her teacher? Guess you’ll have to buy her book to find out.

As far as notoriety goes, obviously Ms. Gallivan has gotten plenty of online recognition for her achievement and is still selling copies of her book. Her equation was also mentioned on the CBS prime time series “Numb3rs,” where a young mathematician helps his older brother solve crimes for the FBI by using various equations.

… And In Conclusion

Today, we dispelled the myth that paper can only be folded in half 7 or 8 times. We tried ourselves, but failed in our attempt. Others have succeeded however – Mythbusters, Brittany, and the students from Southborough – all the way up to 13 folds. We also learned a new way to get famous: fold a single piece of paper in half 14 times… But good luck on the final fold, it’s 16,384 sheets of paper thick.

]]>http://www.relativelyinteresting.com/how-many-times-can-you-really-fold-a-piece-of-paper-in-half/feed/06723Pyramid Schemes Explained (And Why They Are A Scam)
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http://www.relativelyinteresting.com/pyramid-schemes-explained-and-why-they-are-a-scam/#commentsWed, 04 Jul 2018 23:02:00 +0000http://relativelyinteresting.com/?p=58Pyramid Schemes: An Impossible Way to Make Money At some point in your life, you were probably approached by a friend or acquaintance who just discovered an incredible investment or business opportunity, and said that you, yes you, could join him and reap the benefits. All you have to do is pay your buddy $100, […]

]]>Pyramid Schemes: An Impossible Way to Make Money

At some point in your life, you were probably approached by a friend or acquaintance who just discovered an incredible investment or business opportunity, and said that you, yes you, could join him and reap the benefits. All you have to do is pay your buddy $100, and then get 6 other people to do the same for you – for a cool $500 return on your investment! You would tell your recruits to do the same thing – to each recruit 6 more people. And on and on it would go. At this point, your skeptical senses should be tingling and you should ask yourself, “This sounds too good to be true. Could it be a pyramid scheme?”

I’m often asked for a “practical” use of skepticism and critical thought. Well, here’s a great example where skepticism can save you money and time. Pyramid schemes are a scam, plain and simple. Worried that your investment opportunity is a pyramid scheme? Read on, my friend.

What is a pyramid scheme?

There are two kinds of pyramid schemes: naked, and product based. A pyramid scheme works well for only a very small number of people at the top of the pyramid. The main characteristic of a pyramid scheme is that is that people only make money by recruiting other members. The number of people involved in the scheme grows geometrically, so that the base of the pyramid becomes very wide, very quickly.

In a naked pyramid scheme, there isn’t even a product. The formula for “success” is as follows:

One person recruits 6 other people to participate in the “wonderful opportunity”

The 6 new recruits each pay the recruiter $100

The recruiter now tells them to recruit 6 more people and do the same

So if each recruit gets someone new, they will each end up with $500 from a very cool $100 investment.

So what’s the problem? Pyramid schemes become unsustainable very quickly.

For example, assume the 6 new recruits each find 6 more people to make their $500. Now these newer recruits will need to find 216 people so they can each make their $500. Assume again, for the sake of argument, that these 216 newest recruits are successful. They have to find 1,296 people just so they can each make their $500. At this point, you’re at the size of a small town, and at the next level, 7,776 people are needed. Pretty quickly, you run out of people to find as new recruits, and the pyramid collapses since everyone at the bottom has lost their investment… By level 11, you require just about every person in the United States to become a recruit, and by level 13, you’ve exceeded the Earth’s population! The larger the initial group of people, the less levels needed until the pyramid collapses.

In a product based pyramid scheme, it’s the same idea, except that it’s masked as a “sales” opportunity, usually of a bogus product:

A distributor recruits 6 salespeople who each pay $100 for a starter kit of products to sell.

The distributor gets 10 percent of each starter kit that’s sold.

The distributor also gets a cut of 10 percent of each product that any of the recruits sell (including additional starter kits).

The recruits are told that the fastest way to make money isn’t by selling products, but by recruiting more people to buy starter kits (sound familiar yet?)

The people at the top of the pyramid get commissions from everyone in their downline (the people below them in the pyramid).

Usually, the products have such a low margin, that it’s nearly impossible to make a profit without getting more recruits… and we we know what happens then. By the time you’re at the 12^{th} level of the pyramid, you need to recruit 2 billion people so that everyone can make back their money. At the ninth level, you’d need 13 billion people… which is almost twice the population of the Earth.

Now, take a light break before we get into the mathematical proof…

Michael Scott from The Office gets himself into a pyramid scheme, and, as usual, hilarity ensues:

Mathematical Proof that Pyramid Schemes Are A Scam

For simplicity, assume there is one person on top of the pyramid and this person asks for a fixed amount of money, say $1, to a second person, with the promise that if he convinces two more people to join and pay the entrance fee of $1, he will get $2 which would double up the initial investment.

At this point the first two people have made $1 dollar each. The other two people have to recruit two people each in order to double up their money. Now, we’re at the fourth level of the pyramid, where 1+1+2+4=8 people are involved in the scheme.

As the pyramid grows and more levels are added, the number of people involved increases geometrically, so that at level n there will be 1+1+2+…+2^{n-2} persons in the scheme, and the bottom 2^{n-2} have to recruit 2^{n-1} new people in order to receive money. For example, when n = 34 (ie, there are 34 levels in the pyramid), the number of people invovled is 2^{34-1 }or 8,589,934,592 people, which again, is larger than the population on Earth (I chose n = 34 levels to illustrate that point).

This is what makes the scheme fraudulent: since the amount of people involved increases geometrically, the pyramid collapses because there are no more people to recruit and the people at the bottom of the pyramid all lose their initial “investment”.

This table shows how many new paying members must be recruited at each level for programs (schemes) that require each new member to recruit 4, 5, 6, 7, or 8 new members. (data courtesy http://www.consumerfraudreporting.org/MLM_pyramid.php ). Red cells indicate the times when it’s literally impossible for the scheme to work, as too many people are involved. Orange indicates the instances where it’s theoretically possible, but realistically impossible (since no organizations exist with that kind of magnitude. Yellow cells indicate that it’s possible, but you’d have to be an incredible salesperson to succeed… and be part of a large international organization…

Level

Number of new members each level must recruit to be profitable. (columns indicate the numbers for requirements of recruiting 4, 5, 6, 7, or 8 new members)

4

5

6

7

8

1

4

5

6

7

64

2

16

25

36

49

512

3

64

125

216

343

4096

4

256

625

1,296

2401

32,768

5

1,024

3125

7,776

16,807

262,144

6

4,096

15,625

46,656

117,649

2,097,152

7

16,384

78,125

279,936

823,543

16,777,216

8

65,536

390,625

1,679,616

5,764,801

134,217,728

9

262,144

1,953,125

10,077,696

40,353,607

1,073,741,824

10

1,048,576

9,765,625

60,466,176

282,475,249

8,589,934,592

11

4,194,304

48,828,125

362,797,056

1,977,326,743

68,719,476,736

12

16,777,216

244,140,625

2,176,782,336

13,841,287,201

13

67,108,864

1,220,703,125

13,060,694,016

Pyramid Scheme Statistics:

88 percent of the members will be on the bottom level of most pyramid schemes will lose their investment.

In a naked (productless) pyramid scheme, 90.4 percent of people lose their investment.

In product-based pyramid schemes, 99.88 percent lose their investment.

What About Multi-Level Marketing Schemes?

Multi-level marketing (MLM) is similar to pyramid schemes in that, to be successful, you have to recruit new members from your network and form a downline. In MLMs, you earn money in two ways: by selling a product, and/or by receiving commissions from the sales of your downline. MLMs, although subject to constant debate, are legal, however, pyramid schemes are not. An example of a popular MLM is Amway Corp.

Even though MLMs are legal, they still provide a terribly low income for most people. Several sources have commented on the income level of specific MLMs or MLMs in general:

The Times: “The Government investigation claims to have revealed that just 10 per cent of Amway’s agents in Britain make any profit, with less than one in ten selling a single item of the group’s products.

Scheibeler, a high level “Emerald” Amway member: “UK Justice Norris found in 2008 that out of an IBO [Independent Business Owners] population of 33,000, ‘only about 90 made sufficient incomes to cover the costs of actively building their business.’ That’s a 99.7 percent loss rate for investors.”

Newsweek: based on Mona Vie’s own 2007 income disclosure statement “fewer than 1 percent qualified for commissions and of those, only 10 percent made more than $100 a week.”

Business Students Focus on Ethics: “In the USA, the average annual income from MLM for 90% MLM members is no more than US $5,000, which is far from being a sufficient means of making a living (San Lian Life Weekly 1998)”

USA Today: “While earning potential varies by company and sales ability, DSA says the median annual income for those in direct sales is $2,400.”In an October 15, 2010 article, it was stated that documents of a MLM called Fortune reveal that 30 percent of its representatives make no money and that 54 percent of the remaining 70 percent only make $93 a month.

How To Avoid Being Sucked Into A Pyramid Scheme:

Be skeptical, be careful, don’t let a sales pitch get you so excited that you can’t even think straight.

Get an unbiased opinion from a family member or friend before jumping in.

Research the “investment opportunity”, make sure the company is legitimate. Verify the claims – check the organizations track record.

Make sure you fully understand the business strategy. Don’t jump in because it sounds too good to be true, because it probably is too good to be true.

The Ironic Conclusion

Pyramid schemes are a scam, plain and simple. Multi-level marketing schemes are barely legal, and offer very little return for their required investment of cash and time.

So, did you find this article helped to improve your understanding of pyramid schemes? If so, do your friends and family a favor by sharing this information with at least ten of them. Then ask each of them to share it with ten more people, and suggest they tell each of them to share it with ten more, and . . . .

]]>http://www.relativelyinteresting.com/pyramid-schemes-explained-and-why-they-are-a-scam/feed/15810 Math Tricks You Can Use To Impress Your Friends
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http://www.relativelyinteresting.com/10-math-tricks-you-can-use-to-impress-your-friends/#commentsWed, 27 Jun 2018 17:44:00 +0000http://relativelyinteresting.com/?p=37Want to impress your friends with your arithmetic skills? Here’s a list of simple math tricks you can use on a daily basis. Some are even practical – who said you’d never use what you learned in school? For most of these math tricks, the idea is to get manageable numbers to work with in […]

]]>Want to impress your friends with your arithmetic skills? Here’s a list of simple math tricks you can use on a daily basis. Some are even practical – who said you’d never use what you learned in school?

For most of these math tricks, the idea is to get manageable numbers to work with in your head, and stick with operations that you are most familiar with.

Math Trick #1:

How to multiply a two digit number by 11:

For example, 43×11. Take the original number and imagine a space between the two digits:

4_3

Now add the two numbers together and put them in the middle:

4_(4+3)_3 which is the same as 4_7_3

The answer… 473

If the numbers in the middle add up to a two digit number, insert the second number and add 1 to the first:

For example, 67×11

6_(6+7)_7

(6+1)_3_7 which is the same as 7_3_7

The answer… 737

Math Trick #2:

How to square a two digit number ending in 5

If you need to square a two digit number ending in 5, multiply the first digit by itself + 1, and put 25 on the end.

For example, 65^2 (which can be written as 65×65)

6x(6+1) or 6×7 = 42

Put a 25 on the end of it…

The answer… 4225

Math Trick #3:

How to multiply big numbers by 5

Take any number, then divide it by 2. Then…

If the result is whole (that is, theres’s no remainder), add a 0 at the end.

If it is not whole, ignore the remainder and add a 5 at the end of the number.

For example, 4252×5 = (4252/2) and add a 5 or 0 to the end of the number

4252/2 = 2126 (it’s a whole number so add a 0 to the end)

The answer… 21260

Here’s another example: 8667×5

Divide the number by two: 4333.5 (there’s a remainder so add 5 to the end)

The answer… 43335

Math Trick #4:

How to multiply by 4

The trick here is to simply multiply by two, then multiply by two again. Ultimately, you want to work with smaller numbers that are easier to work with in your head.

For example 82 x 4 = (82 x 2) x 2 = (164) * 2 = 328

To multiply by 8, just multiply by 2 one more time (656).

Math Trick # 5

How to multiply by 9, or 99, or 999

Multiplying by 9 is really like multiplying by 10-1.

9×9 is the same as 9x(10-1) which is (9×10)-9 which is 90-9 or 81.

There are cases when you’re multiplying two numbers together and one of the numbers is even. In this case you can divide that number by two and multiply the other number by 2. You can do keep doing this until you get numbers that are easy to work with in your head.

Let’s say you want to multiply 14 by 16. You can double and halve the numbers till you get your answer:

14×16 = 28×8 = 56×4 = 112×2 = 224

Another example: 12×15 = 6×30 = 6×3×10 = 180

Here’s another example:

48×17 = 24×34 = 12×68 = 6×136 = 3×272… this may seem large, but you can break it down further into:

3×270 + 3×2 = 810 + 6 = 816

Math Trick # 7

Working with Percentages

Remember that “per cent” is like saying “parts of one hundred”.

So, it follows that 8 percent of 100, is 8. As another example 23.89% is the same as saying “23.89 parts of 100”.

Find 8% of 200.

8% of the first hundred is 8. 8% of the second hundred is also 8. So it follows that 8% of of 200 is 8 + 8 = 16. Therefore 8% of 200 is 16%.

Another bonus trick: you can flip percents. For example 35% of 8 is the same as 8% of 35.

Using percents has a very practical application when you’re at a restaurant. Let’s say you want to leave a tip of 15% on a $50 dinner. You can quickly calculate it in your head:

15% of $100 is $15, so then 15% of 50 is half of that, or $7.50.

Let’s try one more example: Calculate a 15% tip on a $60 dinner.

Using the same approach, 15% of $100 is $15, so then 15% of 50 is half of that, or $7.50. Also, you know that 15% of $10 is $1.50.

So then 15% of 60 is the same as 15% of 50 + 15% of 10… which equals $7.50 + $1.50, or $9.00.

Math Trick # 8

Quick Addition using the left-to-right approach (instead of the familiar right-to-left):

Instead of using a right to left approach, we can start from the left and move to the right. Take the following example:

45
+ 34

Usually, you would first sum up 4 to 45, and then add 30 to the result. But by using the left to right approach, you first sum up 30 to 45, and then you add 4 to the result. Although this example is very simple, you’ll see the advantages of this method as you start to use it.

If you’re working with three digit numbers, the process is the same.

459
+ 637

This example is a bit more complicated than the previous one, yet it’s very easy to solve using the left to right approach. You first start by adding 600 to 459, which results in 1059. Now the problem is simplified to 1059 + 37. You simplify it even further by adding 30 to 1059, and then adding 7 to the result… which is 1096.

Math Trick # 9

Subtracting a large number from 1000.

To subtract a large number from 1000 you can use this basic rule: subtract all but the last number from 9 (taking the absolute value… that is, ignoring if the number is negative), then subtract the last number from 10:

1000
– 736

Step 1: subtract 7 from 9 = 2 Step 2: subtract 3 from 9 = 6 Step 3: subtract 6 from 10 = 4

Your answer: 264

Math Trick # 10

Multiplication rules… Multiply by 5: Multiply by 10 and divide by 2 Multiply by 6: Multiplying by 3 and then 2 is easy Multiply by 9: Multiply by 10 and subtract the original number Multiply by 12: Multiply by 10 and add twice the original number Multiply by 13: Multiply by 3 and add 10 times original number Multiply by 14: Multiply by 7 and then multiply by 2 Multiply by 15: Multiply by 10 and add 5 times the original number Multiply by 16: You can double four times or multiply by 8 and then by 2 Multiply by 17: Multiply by 7 and add 10 times original number Multiply by 18: Multiply by 20 and subtract twice the original number Multiply by 19: Multiply by 20 and subtract the original number Multiply by 24: Multiply by 8 and then multiply by 3 Multiply by 27: Multiply by 30 and subtract 3 times the original number Multiply by 45: Multiply by 50 and subtract 5 times the original number Multiply by 90: Multiply by 9 and put a zero on the right Multiply by 98: Multiply by 100 and subtract twice the original number Multiply by 99: Multiply by 100 and subtract the original number

]]>http://www.relativelyinteresting.com/10-math-tricks-you-can-use-to-impress-your-friends/feed/937The Bat and A Ball Problem
http://www.relativelyinteresting.com/the-bat-and-a-ball-problem/
http://www.relativelyinteresting.com/the-bat-and-a-ball-problem/#commentsSun, 24 Jun 2018 15:45:48 +0000http://www.relativelyinteresting.com/?p=3414If a baseball and a bat cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost? Was your answer that the ball cost 10 cents? If so, you’d be wrong. Here’s the solution: Although $1.00 + $0.10 does equal $1.10, if you take $1.00 – $0.10 you […]

]]>If a baseball and a bat cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost?

Was your answer that the ball cost 10 cents?

If so, you’d be wrong.

Here’s the solution:

Although $1.00 + $0.10 does equal $1.10, if you take $1.00 – $0.10 you get $0.90, but the problem requires that the bat costs $1 more than the ball.

So, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10

[divider style=”hr-dotted”]

Still not convinced? You can use algebra to solve the problem:

First, let’s set up the equation:

x + ($1.00 + x) = $1.10

$1.00 + 2x = $1.10

2x = $1.10 – $1.00

2x = $0.10

Finally, solve for x:

x = $0.05

Check your work:

x + ($1.00 + x) = $1.10, so

$0.05 + ($1.00 + $0.05) = $1.10

Why does the bat-and-a-ball problem have any significance?

If you answered 10 cents you are inclined to believe in religion. If you answered 5 cents you are inclined to disbelieve. Why? Because, according to research reported in the journal Science, the 10 cent answer indicates that you are an intuitive thinker, and the 5 cent answer indicates that you solve problems analytically, rather than following your instincts.

Their study of 179 Canadian undergraduate students showed that people who tend to solve problems more analytically also tended to be religious disbelievers. This was demonstrated by giving the students a series of questions like the one above and then scoring them on the basis of whether they used intuition or analytic logic to reach the answers. Afterward, the researchers surveyed the students on whether or not they held religious beliefs. The results showed that the intuitive thinkers were much more likely to believe in religion.

… Professor and Chairman Terrence Reynolds of the Department of Theology at Georgetown University finds it plausible that analytic thinking could make religious belief more difficult. “If one assumes that all rationality is tied to what we know directly through the five senses, that limits our understanding of meaning questions. Religion tends to focus on questions of meaning and value, which may not be available through analytic verification processes… by definition God is a being that transcends the senses.”

Quick Poll – What was your answer, and do you believe/disbelieve in religion?

Another interesting puzzle, which you may or may not consider tricky:

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

]]>http://www.relativelyinteresting.com/the-bat-and-a-ball-problem/feed/723414Why does multiplying two negatives give you a positive?
http://www.relativelyinteresting.com/why-does-multiplying-two-negatives-give-you-a-positive/
http://www.relativelyinteresting.com/why-does-multiplying-two-negatives-give-you-a-positive/#respondMon, 05 Feb 2018 14:27:51 +0000http://www.relativelyinteresting.com/?p=7753I found myself in a difficult situation the other day: explaining the multiplication of two negative numbers to my 8 year old. Negative numbers are rather simple to illustrate when using temperature because there is a clearly visible “zero” Celsius and numbers on either side of it. Living in Canada, we can see dramatic fluctuations […]

]]>I found myself in a difficult situation the other day: explaining the multiplication of two negative numbers to my 8 year old.

Negative numbers are rather simple to illustrate when using temperature because there is a clearly visible “zero” Celsius and numbers on either side of it. Living in Canada, we can see dramatic fluctuations in temperature in a single day.

But then I had to explain why temperature even needs to go below zero in the first place… why not start at a lower number? I told her about the concept of absolute zero and the Kelvin scale and quickly got in over my head. And I struggled to provide a very simple explanation to her initial question: why does multiplying two negative numbers give a positive number?

So I looked to the information superhighway, where I was met with a much better analogy: money.

Found on reddit in the ELI5 (Explain Like I’m 5) subreddit, this question had many responses. But the one voted to the top was provided by reddit user Zerotan.

Here’s the explanation that was provided:

I give you three $20 notes: +3 * +20 = +60 for you

I give you three $20 debts: +3 * -20 = -60 for you

I take three $20 notes from you: -3 * +20 = -60 for you

I take three $20 debts from you: –3 * -20 = +60 for you

The result is the gain or loss from where you started.

This response was quickly rebuked by another user, who had a good point: the answer describes the abstraction but not the underlying roots. It’s like saying Greenland is further north than Italy because it’s higher up on the map. It doesn’t actually explain anything.

If we reduce math to counting physical things, like say, bottle caps, then a negative number can be seen as a bottle cap debt. So, 5 + 5 is 10, 5 – 5 is 0, this is obvious. 5 + -5 is 0, 5 – -5 is 10.

-5 means take away 5, so 5 – -5 means take away a 5 unit takeaway.

Multiplying is simply saying add a number to itself some number of times. 5 times 6 means add 5 to itself 6 times, or 0 + 5 + 5 + 5 + 5 + 5 + 5 = 30.

By the same token then, -5 times 6 (0 + -5 + -5 + -5 + -5 + -5 + -5) is -30.

So what about 5 times -6. What do we mean when we multiply by a negative number? Well, we subtract instead, so 0 – 5 – 5 – 5 – 5 – 5 – 5 = -30, and -5 times – 6 : 0 – -5 – -5 – -5 – -5 – -5 – -5 = 30

In short, it’s like, “How come -(-X) = X?” It’s the same reason the opposite of “the opposite of up” is up.

]]>http://www.relativelyinteresting.com/why-does-multiplying-two-negatives-give-you-a-positive/feed/07753A Brief History of Atomic Theory
http://www.relativelyinteresting.com/brief-history-atomic-theory/
http://www.relativelyinteresting.com/brief-history-atomic-theory/#respondMon, 15 Jan 2018 21:30:42 +0000http://www.relativelyinteresting.com/?p=9808All matter is made up of atoms, the basic unit of a chemical element. This is something we now take as a given, and one of the things you learn at the beginning of high school or secondary school chemistry classes. Despite this, our ideas about what an atom is are surprisingly recent: as little as one […]

]]>All matter is made up of atoms, the basic unit of a chemical element. This is something we now take as a given, and one of the things you learn at the beginning of high school or secondary school chemistry classes.

Despite this, our ideas about what an atom is are surprisingly recent: as little as one hundred years ago, scientists were still debating what exactly an atom looked like.

This infographic takes a look at the key models proposed for the atom and how they changed over time: from Democritus, to Bohr, and through till the quantum mechanical models.

]]>http://www.relativelyinteresting.com/brief-history-atomic-theory/feed/09808Just the Facts: Radiation, Cell Phones, Wi-Fi, and Cancer.
http://www.relativelyinteresting.com/just-facts-radiation-cell-phones-wi-fi-cancer/
http://www.relativelyinteresting.com/just-facts-radiation-cell-phones-wi-fi-cancer/#respondTue, 11 Oct 2016 15:56:32 +0000http://www.relativelyinteresting.com/?p=8467Electromagnetic fields (EMF) are just about everywhere as our society becomes more and more technological. Sources of EMF include WiFi, lighting, microwaves, radio, television, cell phones, among many. Increasingly, there are a number of individuals and activist groups who believe that these electromagnetic fields pose a health risk. Perhaps the two most controversial sources are WiFi […]

]]>Electromagnetic fields (EMF) are just about everywhere as our society becomes more and more technological. Sources of EMF include WiFi, lighting, microwaves, radio, television, cell phones, among many. Increasingly, there are a number of individuals and activist groups who believe that these electromagnetic fields pose a health risk. Perhaps the two most controversial sources are WiFi and cell phones. Some schools have gone so far as to ban WiFi. Websites like Natural News highlight the supposed link between cell phone usage and brain cancer.

Why is ionizing radiation dangerous?

Ionizing radiation is any type of particle or electromagnetic wave that carries enough energy to “ionize” or remove electrons from an atom. When atoms in living cells become ionized, one of three things usually happen – the cell dies, the cell repairs itself, or the cell mutates incorrectly and can become cancerous. Not all cells are affected by ionizing radiation in the same way. The cells that reproduce the most and are the least specialized are the most likely to be affected by ionizing radiation, for example those in a forming fetus.

This is a chart of the ionizing radiation dose a person can absorb from various sources both naturally and artificially. The unit for absorbed does is the “sievert” (Sv), and measures the effect a dose of radiation will have on the cells of the body. One sievert (all at once) will make you sick, and too many more will kill you, but we safely absorb small amounts of natural radiation daily. Note that that same number of sieverts absorbed in a shorter time will generally cause more damage, but your cumulative long-term dose plays a role in things like cancer risk.

Click the Radiation Dose Chart to see a legible version.

The chart was created by Randall Munroe, with help from Ellen, Senior Reactor Operator at the Reed Research Reactor, who suggested the idea and provided many of the sources. This is in the public domain, so share, share away.

The Canadian Nuclear Safety Commission provides a similar, yet simpler and more graphical chart to visualize the radiation doses from various sources.

Notice what’s not on the list.

Cell phones. Wi-Fi.

Why not?

Because they emit non-ionizing radiation.

Radiation is energy that is transmitted in the form of waves or streams of particles. It is present everywhere in our environment and can be described based on the effect it has on things. Usually, it is divided into two types of radiation: ionizingand non-ionizing.

Ionizing radiation includes the radiation that comes from both natural and human-made radioactive materials such as cosmic rays, nuclear power plants, and X-ray machines. The stuff you see in the charts above.

Non-ionizing radiation is a lower energy radiation such as radio waves, ultraviolet rays, microwaves, and sunlight.

Cell phones work by sending signals to (and receiving them from) nearby cell towers (base stations) using RF waves. This is a form of electromagnetic energy that falls between FM radio waves and microwaves. Like FM radio waves, microwaves, visible light, and heat, RF waves are a form of non–ionizing radiation.

Do cell phones cause cancer?

The American Cancer Society has collected the results many studies. Here are the results from a few:

According to the Food and Drug Administration (FDA), which regulates the safety of radiation-emitting devices such as cell phones in the United States:

“The majority of studies published have failed to show an association between exposure to radiofrequency from a cell phone and health problems.”

According to the Federal Communications Commission (FCC):

“There is no scientific evidence that proves that wireless phone usage can lead to cancer or a variety of other problems, including headaches, dizziness or memory loss. However, organizations in the United States and overseas are sponsoring research and investigating claims of possible health effects related to the use of wireless telephones.”

According to the Centers for Disease Control and Prevention (CDC):

“At this time we do not have the science to link health problems to cell phone use. Scientific studies are underway to determine whether cell phone use may cause health effects.”

According to the National Institute of Environmental Health Sciences (NIEHS), which is conducting studies of the possible health effects of cell phones:

“Current scientific evidence has not conclusively linked cell phone use with any adverse health problems, but more research is needed.”

According to the National Cancer Institute (NCI):

“Studies thus far have not shown a consistent link between cell phone use and cancers of the brain, nerves, or other tissues of the head or neck. More research is needed because cell phone technology and how people use cell phones have been changing rapidly.”

The short answer is… there’s no real evidence to suggest that cell phones cause cancer… but more studies are required to be even more sure.

Does WI-FI cause cancer?

Wifi signals, which are in the 2.4 to 5.x GHz range are also non-ionizing. The folks over at IFLS summarize as follows:

Is there any evidence to suggest that the radiation used in Wi-Fi networks – known as radiofrequency radiation – also causes these types of harm? The International Agency for Research on Cancer (IARC) decided that radiofrequency radiation could possibly be harmful, perhaps inducing cancer. It is classified as a Class 2B possible human carcinogen, but this is by no means evidence of actual danger.

Wi-Fi actually shares this category with coffee, carpentry, Styrofoam cups and pickled vegetables – all “possible” human carcinogens. Inclusion in this category means that the possibility that they cause cancer hasn’t been ruled out, but the link hasn’t been demonstrated.

As discussed above, cell phones use radiofrequency radiation. This radiation is similarly energetic to that used by Wi-Fi. There have been a plethora of studies investigating links between mobile phone usage and health problems, including brain tumors. Although some have suggested that the most frequent users are more likely to develop tumors, this could be explained by problems with the way the study was carried out.

In fact, the studies that seem to show a link between brain cancer and radiofrequency radiation exposure are often found to be poor or flawed studies. The evidence is, at the very least, massively inconsistent, and far larger studies that have analyzed the results of multiple smaller ones have concluded there is no such link between cell phoneor Wi-Fi exposure and the disease in adults, children and even animals.

The radiation emitted is simply not energetic enough to be dangerous. A small number of medical researchers may be wary of this “sea of radiation” produced by cell phone and Wi-Fi networks, but even they admit that there is literally no evidence to suggest that they are harmful.

Some people may claim to be hypersensitive to Wi-Fi, in that being exposed to these networks induces headaches, nausea, and fatigue. The WHO, as does every other major health collective around the world, concludes that this hypersensitivity isn’t a real phenomenon.

It’s not just the dose, it’s the dollar.

At this time, the evidence is clear. Bad Science Watch, a consumer protection watchdog and science advocacy organization investigated the issue in depth. Here’s their conclusion, based on their report:

Bad Science Watch was unable to locate any compelling evidence of legitimate scientific debate about WiFi induced illness, or the safety of low-level EMF exposure in general. While fringe groups continue to present flawed arguments and promote poorly designed experiments, the preponderance of research on the matter robustly dispels the connection between WiFi and IEI-EMF. For those tasked with making decisions about the inclusion of WiFi technology in their organization, school, or home, we can find no reason to ignore the advice of health organizations worldwide. The benefits of WiFi are numerous and varied, and there is no compelling evidence that any health effects arise as a result of this technology.

Evidence aside, one should always ask what the ultimate goal of activist organizations and individuals might be. Is it to make the world a safer, better place? Or is it about money and fame?

Bad Science Watch’s report also discovered several damning conflicts of interest (five, actually). For example, activist/entrepreneur Kevin Byrne, who not only runs the activist website DirtyElectricity.ca is also the president of EMF Solutions Canada, the largest Canadian distributor of EMF home inspections and abatement equipment.

Ah – so in this case, it’s money.

The TLDR;

So here’s the TLDR; Cell phones and WIFI use non-ionizing radiation. This form of radiation does not carry enough energy to harm cells. When we look at the results from large studies, the general consensus is that there insufficient evidence to suggest that the radiation emitted from these devices cause cancer.

]]>http://www.relativelyinteresting.com/just-facts-radiation-cell-phones-wi-fi-cancer/feed/0846715 Science DIY Ideas and Experiments for Kids and Parents
http://www.relativelyinteresting.com/15-science-diy-ideas-and-experiments-for-kids-and-parents/
http://www.relativelyinteresting.com/15-science-diy-ideas-and-experiments-for-kids-and-parents/#respondTue, 05 Jul 2016 12:22:49 +0000http://www.relativelyinteresting.com/?p=8290School may be out for summer, but the learning doesn’t have to stop there. Looking for an activity that’s both fun and educational? Look no further. Quench your kid’s curiosity and their appetite for wonder by performing these great DIY science experiments. All you need are a few common household items. As you perform the experiments, ask […]

]]>School may be out for summer, but the learning doesn’t have to stop there. Looking for an activity that’s both fun and educational? Look no further. Quench your kid’s curiosity and their appetite for wonder by performing these great DIY science experiments. All you need are a few common household items.

As you perform the experiments, ask your child what’s happening and why they think it’s happening. Then, take the opportunity to explain a little bit about physics, chemistry, and how stuff works.

This is a visually beautiful way to introduce kids to the chemistry of liquid density – some liquids don’t mix because they are more or less dense than others. By coloring them with dye, you can create a rainbow!

You’ll need the following: A large, clear jar or container that can hold at least 2 1/2 cups of liquid, rubbing alcohol, corn syrup, olive oil, blue liquid dish soap, water and a pack of food dye that contains red, blue, green and yellow.

Start to fill the container with purple, which will be your densest liquid. In a smaller container, mix one-half cup of corn syrup with one drop of blue and one drop of red food dye, then have your child pour it into the jar.

Rinse the small container after mixing and slowly pour each colored layer into the jar, and use the following ingredients to create the next four layers:

Blue– one-half cup of blue dish soap – pour slowly

Green– one-half cup of water with two drops of green food dye – pour slowly

Yellow– one-half cup of olive oil – pour slowly

Red– one-half cup of rubbing alcohol with two drops of red food coloring – pour slowly

You’ll need white glue, borax powder – located in most laundry detergent aisles – food coloring, corn starch, warm water, two plastic cups and two wooden craft sticks.

First, pour a tablespoon of glue into one of the cups. Add a few drops of food dye and stir with one of the craft sticks until mixed.

In the other cup, combine one-half teaspoon of borax with 2 tablespoons of warm water, then stir until dissolved. This is now your borax solution. Take one teaspoon of borax solution and one tablespoon of cornstarch and add both to the glue mixture.

Let this mixture stand for 15 seconds, then stir until it becomes too thick to keep stirring. You can now remove the mixture from the cup and roll it into a ball. It will be sticky at first, but keep rolling and it will smooth out into a solid.

Now it will bounce! See how high it will go. For a larger ball, simply double each ingredient.

Bouncy balls bounce so high because they have great elasticity. When a rubber ball hits the ground it gets compressed, or squished, and because it is very elastic, it quickly returns to its original shape.

Here’s a really cool way to not just grow a plant, but see the whole process in action.

You’ll need a clear CD case, potting soil, a small bowl, lima beans or pinto beans, an eyedropper, water, clear tape and a permanent marker.

To create the greenhouse, begin by opening the CD case and removing the tray that holds the CD. Place a handful of soil into the bowl and use the dropper to add water until it is wet – but don’t let it become muddy.

Fill the empty case halfway with soil, leaving space for the plant to grow. Place your bean in the middle of the soil with the concave side facing toward the bottom – so it looks like a frown.

Add a few more drops of water to the bean and then close the case so it stands upright with the hinge at the top. Tape up any gaps and let it grow. It should take roughly 10 days to germinate. To illustrate your plant’s growth for your child, mark its progress on the outside of the case with a permanent marker.

Summer brings every imaginable type of cloud, from fluffy white stratus clouds to the dark cumulonimbus clouds that accompany a summer storm. A great way to introduce kids to the concept of rain is this fun experiment that can be done outdoors or even at bath time.

All you need is a clear glass or jar, water, blue food dye, a dropper for the food dye and shaving cream.

Have your child pour water into the glass slowly, filling it almost to the rim. Then carefully add a layer of shaving cream to the surface of the water – not too thick. Explain that the shaving cream is a cloud and the water is the atmosphere.

Add a few drops of dye to the shaving cream. Its weight will slowly push through the shaving cream and fall down through the water. This represents rain building up in clouds and then falling.

Teach your kids about chemical reactions while adding a silly spin. You won’t need much, just a plastic bottle, warm water, yeast, hydrogen peroxide, dish soap and food dye.

Place the bottle in a pan or sink so the reaction overflow is contained (Tip: there will be overflow!). In a separate container, mix 2 tablespoons of warm water with 1 tablespoon of yeast.

In the bottle, mix a half-cup of hydrogen peroxide, four to five drops of food dye and a squirt of dish soap.

Pour the yeast mixture into the bottle, and voila! Have your child touch the bottle and feel the warmth of the reaction releasing energy as heat.

The hydrogen peroxide is composed of two hydrogen atoms and two oxygen atoms, and when exposed to light and yeast, it rapidly breaks down into separate water and oxygen. The dish soap then catches the oxygen and bubbles, and the food dye creates a colorful reaction.

To preface, the answer is yes. Did you ever wonder why?

A lot of kids hate sunscreen, as it can feel like a hassle and a barrier between them and getting outside to play. Use this experiment to get them thinking a little differently about skin protection.

All you need is a bottle of sunscreen and some dark construction paper. You can go even further by testing different SPFs or the lens from a UV-resistant pair of sunglasses.

Have your child apply sunscreen to one half of the paper. He or she can leave a handprint or draw a design. Make sure that the other half of the paper remains untouched. Draw a line and label each side if need be.

Leave the paper out in the sun for a couple hours at most and you will see results. Definitely a teachable moment.

Oobleck, if you haven’t heard of it, is a fascinating material – sometimes a solid, sometimes a liquid, but always fascinating.

To make your own, it’s two parts cornstarch to one part water. Have fun playing!

What’s even more fun is to make the oobleck dance. If you have the materials, let your kids play and experiment with the oobleck while you set up.

You’ll need a subwoofer, a thin metal baking sheet, optional food dye and an audio file to feed through the subwoofer – preferably something with a substantial amount of bass.

Simply place the oobleck on the sheet, and then the sheet onto the subwoofer. From here, it’s just a matter of watching as the material responds to the beat and intensity of the audio.

So why does it act so weird? Applying pressure to the mixture increases its viscosity (thickness). A quick tap on the surface of Oobleck will make it feel hard, because it forces the cornstarch particles together. But dip your hand slowly into the mix, and see what happens—your fingers slide in as easily as through water. Moving slowly gives the cornstarch particles time to move out of the way.

Oobleck and other pressure-dependent substances (such as Silly Putty and quicksand) are not liquids such as water or oil. They are known as non-Newtonian fluids. The silly name comes from a Dr. Seuss book called Bartholomew and the Oobleck.

Geodes are a beautiful, natural geological phenomenon. Geodes start their lives as a hollow bubble inside a layer of rock. The bubble could be from air inside explosive volcanic rock or it could come from the hollow remains of animal burrows or tree roots. Imagine one of those bubbles completely surrounded by black or red volcanic rock. As rain pelts down on the hot bubble, the chemicals in the rock are slowly released into the water. Some of the water soaks through the hard, rocky outside of the bubble and is trapped for a moment on the inside. As the mineral-rich water moves on through the bubble, tiny crystals are left behind, clinging to the sides of the bubble. Millions of years pass while this in-and-out flow of water gradually builds crystals inside the empty space.

Now you can make them with the relative ease of dying eggs.

The ingredients are a little less orthodox, but worth the hunt. You’ll need potassium aluminum sulfate, better known as alum powder, which you can find on the internet. You’ll also need plastic eggshells, glue, a paintbrush, an empty egg carton, a large bowl, a whisk and a measuring cup. Food dye is optional.

The day before the experiment, paint the eggshells – inside and out – with a thin layer of glue. Sprinkle them with a thin layer of alum powder and let them sit in the egg carton overnight to dry.

The next day, if you’re using food dye, mix it into 2 cups of water in the bowl. Heat the water to nearly boiling – about five minutes in the microwave should do.

Add 3 cups of alum powder and stir until there are nearly no crystals left. Make sure the crystals are saturated, but not overly wet. Pour the mixture into the eggshells – which should be in the egg carton at this point – and wait.

How long? That’s up to you – the longer you wait, the better the crystals will turn out!

This one is incredibly easy, and another fun chemical reaction that will have your kids ooh-ing and ahh-ing.

Simply fill a clear glass vase or other clear bottle about two-thirds of the way full with vegetable oil. Then add water until there are only a couple inches of air space left at the top.

Add five drops of food coloring. Then the fun begins – you’ll need Alka Seltzer tablets – or a generic brand. Separate the tablets into quarters, and have your child drop a quarter tablet in.

The sodium bicarbonate – also known as baking soda – and citric acid contained within the tablets dissolves and releases carbon dioxide bubbles, which then mix the oil and colored water into a hypnotic display.

Continue to add quarter tablets as the bubbles run out.

Everyone loves sweets, but what’s even more fun is doing an experiment where you make your own. There are a few different ways to go about making rock candy, but this is the classic version.

Your only ingredients are 4 cups of sugar and 2 cups of water – food dye is optional if you want to color your candy. You’ll also need a small saucepan, a wooden spoon, a small, clean, clear glass jar, cotton string, a small weight to hang on the string, such as a washer or screw, wax paper, and a stick or pencil.

Heat the sugar and water in the saucepan, stirring until completely clear and dissolved. Add the food dye now if you plan to use it.

Remove the solution from the heat and pour it into the jar, covering the jar with wax paper.

Cut your string so it is about two-thirds as long as the jar is deep, and then tie one end to the weight and the other end to the pencil. Dip the string into the sugar solution.

Lay the string on another piece of wax paper, straighten it and let it dry overnight. Once dry, place the pencil on the lip of the jar so the string is dangling into the solution. Let it sit at room temperature for several days – you can keep checking back to see the progress of crystal growth.

You can explain to your kids that the crystal’s shapes are determined by the way individual sugar molecules stack and fit together.

If you want to take your rock candy a step further, you can try making edible geodes instead.

As mentioned earlier, geodes occur naturally – they look like rocks on the outside but contain beautiful crystals on the inside.

Candy geodes are a little less common in nature, but they’re a whole lot tastier. Check out the video for the extra steps that will turn your plain rock candy into a geode.

12. Cook Up Jurassic Park Amber Lollipops

Rating: adult supervision required

If you’re feeling more creative, you can try this fossil-themed recipe for amber lollipops for another candy treat. You can give kids a taste of how ancient bugs were trapped within tree sap by giving them a visual with candy bugs trapped inside the hardened sugar of the pops.

This awesome hands-on activity is great for kids to not only watch, but get a little messy with. Don’t worry, it involves soap.

You will need clear hand soap, warm water, food dye, baking soda, citric acid, several small plastic cups and a large plastic tub.

Mix one-quarter cup of clear hand soap, food dye and three-quarter cups of warm water in each small cup to create suds.

Have your kids scoop 2 tablespoons of baking soda into each cup and mix. Then have them add 2 tablespoons of citric acid, letting them know it’s the secret ingredient.

This will create a long-lasting eruption that grows the more you mix it. The reaction is endothermic, meaning all heat is absorbed during the reaction to create super cold foam. Best of all for parents, if you don’t use food coloring, you can use this mixture as a homemade, natural-ingredient cleaning solution for your household surfaces.

Possibly one of the easiest science experiments of all time is invisible ink. You need lemon juice, water, white paper and a cotton Q-tip or small paintbrush.

Just dilute lemon juice with water in a small dish, dip your writing utensil into the lemon juice and write your message.

Hold your message up to a heat source – such as a lamp – and reveal your message.

Because lemon juice is organic, it oxidizes when heated, causing it to turn brown. Diluting it makes it invisible on paper until heated. You can try this with other juices and natural liquids, too.

For kids who love animals, this experiment will help them better connect with the animal world by imitating the body of a polar bear using a rubber glove, plastic wrap and shortening.

Fill a bowl with icy water and have your kids put their hands in the bowl for as long as they can. You can use a stopwatch to show them their exact time. Stop them at around 30 seconds, however, so they don’t cause any harm to their hand. They will at least get a sense for the temperature of the water.

Next, have one child put on a rubber glove – don’t worry if their fingers aren’t long enough. Just have them make a fist instead. Cover the gloved hand with shortening. Be generous and make sure the whole fist is thoroughly covered. Then wrap the shortening-covered hand with plastic wrap.

Have your child dip their gloved hand into the water, and they won’t feel a thing. You can explain that the body of a polar bear has adapted so that they feel comfortable in icy water. You can easily slip the glove off of one child’s hand and onto another so everyone can try.

The work of an insulator (like a polar bears fat, or like the shortening in our experiment) is apparent when there is a constant source of heat. Since you are a warm-blooded mammal, your hand keeps sending out heat into the fat you’ve placed around it, and this heat stays close by because that fat is an insulator. When you place your hand directly into the water, the heat from your hand moves into the water because there is no insulator between you and the environment. It’s like heading outside without a sweater on a cold day: your body heat starts to go out into the environment around you. When you wear a sweater, your heat stays close.

There are tons of other science experiments out there to try with kids. They’ll be having so much fun, they won’t even realize they’re learning.

Which one was your favorite? Leave a comment below!

This article was a guest post by Megan Ray Nichols, who loves discussing the latest scientific discoveries with others on her blog Schooled By Science. You can follow her on twitter @nicholsrmegan

]]>http://www.relativelyinteresting.com/15-science-diy-ideas-and-experiments-for-kids-and-parents/feed/08290Our Friend the Atom: A Walt Disney Story Promoting Nuclear Energy
http://www.relativelyinteresting.com/our-friend-atom-walt-disney-propaganda-story/
http://www.relativelyinteresting.com/our-friend-atom-walt-disney-propaganda-story/#respondFri, 24 Jun 2016 18:54:49 +0000http://www.relativelyinteresting.com/?p=8186Roughly ten years after the atomic bombs were dropped on Hiroshima and Nagasaki and during the early part of the Cold War, the fear of nuclear war permeated the nation. At the same time, the promise of nuclear energy was beginning to take shape with the first nuclear power plant coming online in 1954. Being […]

]]>Roughly ten years after the atomic bombs were dropped on Hiroshima and Nagasaki and during the early part of the Cold War, the fear of nuclear war permeated the nation. At the same time, the promise of nuclear energy was beginning to take shape with the first nuclear power plant coming online in 1954. Being no stranger to propaganda, in 1956, Walt Disney produced The Walt Disney Story of “Our Friend the Atom“, in collaboration with Heinz Haber (a German physicist and professor at USC ) and illustrated by the Walt Disney Studio. The book’s intent, clearly, was to change the public’s perception of the atomic era and to embrace nuclear energy and atomic science.

I had the good fortune of discovering a copy at a used bookstore a few years back (hence the ripped cover in the images below). The book was considered to be the literary counterpart of the Walt Disney motion picture “Our Friend the Atom” which was first released on the Disneyland TV Program.

The story tells how the atomic age began and how knowledge of the atom’s energy finally emerged after much effort. The characters of the story are the great minds of the past who contributed to modern atomic science. The atom is explained and (hopefully) understood by the reader through [a]:

“simple and fascinating presentation and appealing illustrations… from the first speculations of Democritus to the beginnings of atomic power today. It gives close-up views of: Roentgen seeing his hand in the first X-ray picture… Rutherford bombarding the atom to find its nucleus… The Curies searching for radioactive elements… Einstein working out the equivalence of mass and energy… and in more recent years (the late 1940s and early 1950s), the scientists of many nations assembling atomic reactors for the world of the future.”

Explore pages from the book. Watch the slideshow:

The forward was written by Walt Disney himself:

Fiction often has a strange way of becoming fact. Not long ago we produced a motion picture based on the immortal tale 20,000 Leagues under the Sea, featuring the famous submarine ‘Nautilus.’ According to that story the craft was powered by a magic force.

Today the tale has come true. A modern namesake of the old fairy ship — the submarine ‘Nautilus’ of the United States Navy — has become the world’s first atom-powered ship. It is proof of the useful power of the atom that will drive the machines of our atomic age.

The atom is our future. It is a subject everyone wants to understand, and so we long had plans to tell the story of the atom. In fact, we considered it so important that we embarked on several atomic projects. … Of course, we don’t pretend to be scientists — we are story tellers. But we combine the tools of our trade with the knowledge of experts.

[…]

The story of the atom is a fascinating tale of human quest for knowledge, a story of scientific adventure and success. Atomic science has borne many fruits, and the harnessing of the atom’s power is only the spectacular end result. It came about through the work of many inspired men whose ideas formed a kind of chain reaction of thoughts. These men came from all civilized nations, and from centuries as far back as 400 B.C.

Atomic science began as positive, creative thought. It has created modern science with its many benefits for mankind. In this sense our book tries to make it clear to you that we can indeed look upon the atom as our friend.

The prologue hints at the story to come. The text is to the right of a mushroom cloud – the classic symbol of atomic destruction:

Deep in the tiny atom lies hidden a tremendous force. This force has entered the scene of our modern world as a most frightening power of destruction, more fearful and devastating than man ever thought possible.

We all know of the story of the military atom, and we all wish that it weren’t true. For many obvious reasons it would be better if it weren’t real, but just a rousing tale. It does have all the earmarks of a drama: a frightful terror, which everyone knows exists, a sinister threat, mystery and secrecy. It’s a perfect tale of horror!

But, fortunately, the story is not yet finished. So far, the atom is a superb villain. Its power of destruction is foremost in our minds. But the same power can be put to use for creation, for the welfare of all mankind.

While some of the pages are rather technical -demonstrating radioactive decay curves of elements or the periodic table (with only 101 elements) – the story is then presented in typical Disney fashion as a fable: The Fisherman and the Genie. All the while, it is delightfully illustrated in 1950’s fashion.

The story concludes with the a dire warning and the prospect for hope:

The Atomic Genie hold in his hands the powers of both creation and destruction. The world has reason to fear those powers over destruction. They could yet destroy civilization and much of mankind. So our last wish should simply be for the atomic Genie to remain forever our friend!

It lies in our own hands to make wise use of the atomic treasures given to us. The magic power of atomic energy will soon begin to work for mankind throughout the world. It will grant the gifts of modern technology to even the most remote areas. It will give more food, better health – the many benefits of science – to everyone.

]]>http://www.relativelyinteresting.com/our-friend-atom-walt-disney-propaganda-story/feed/08186Computers, Probability, Logic: Blaise Pascal’s Impressive Legacy
http://www.relativelyinteresting.com/computers-probability-logic-blaise-pascals-impressive-legacy/
http://www.relativelyinteresting.com/computers-probability-logic-blaise-pascals-impressive-legacy/#respondTue, 16 Feb 2016 16:09:01 +0000http://www.relativelyinteresting.com/?p=7702You are probably reading this article online. In that case, you may not know it but you have a seventeenth-century Frenchman to thank for this experience. Blaise Pascal may not have known anything about the internet, but it is thanks, in no small part, to his precocious genius that we are able to do what we do […]

]]>You are probably reading this article online. In that case, you may not know it but you have a seventeenth-century Frenchman to thank for this experience. Blaise Pascal may not have known anything about the internet, but it is thanks, in no small part, to his precocious genius that we are able to do what we do online. Pascal’s experiments with practical mathematics underpin much of the coding that we take for granted today – that’s why Swiss computer pioneer Niklaus Wirth called his early coding language Pascal. And this mastermind’s contribution to coding is only the start of his incredible contribution to what we call modern life.

A Stubborn Genius

So just exactly who was Blaise Pascal? He may sound like a bad 1970s TV character, but he is someone who really ought to be more widely recognised outside his native land. Never mind twentieth century TV, Pascal deserves to be mentioned in the same breath as the likes of Leonardo da Vinci and the great 11^{th} century Chinese polymath Su Song. Mathematician, theologian, physicist, medical pioneer and author, the list of Pascal’s inventions and achievements is seriously impressive. And it is all the more impressive because at first his talents were actively suppressed by his father.

Pascal was born on June 19, 1623, in Clermont-Ferrand, provincial France. His mother died during his infancy and he was raised by his over-protective father. Pascal was, it seems, a sickly child and in order to protect his delicate health his father – a sometime judge and tax inspector – decided that his son should be home educated and, moreover, shielded from the rigors of mathematics until he was 15. Fortunately for mathematics, the young Pascal was having none of that.

Mathematical Prodigy

By the time he was 15 years old, Pascal had worked out the rudiments of geometry – actually inventing his own terms – as he quickly caught up with the insights of the likes of Euclid on the basis of nothing but his own natural genius. By the time he was 16, the young prodigy had completely overcome his father’s objections and was presenting his discoveries to the leading mathematicians of the day. Amongst his insights was the breakthrough calculation now recognized as the Mystic Hexagram. A year later, his ground-breaking Essay on Conic Sections was published. He was only 17.

A tangible legacy

Aside from the computer coding language that bears his name, perhaps the most glamorous and easily recognizable aspect of Pascal’s legacy is the roulette wheel. The wheel itself derived from Pascal’s attempts to design a perpetual motion machine. The frictionless mechanism of the wheel is the perfect testament of Pascal’s keenness to translate his mathematical theorizing into tangible, practical devices. He might have failed to create perpetual motion, but the roulette eventually became a great hit a couple of centuries later, first in Europe and then all over the world.

Had he been around today, Pascal would no doubt be running his own online casino or even playing poker professionally. The mathematical calculations of probability that operators of casino games of chance work to were – of course – in large part first established by-you-know-who.

The odds that determine the various bets that are available in roulette may now appear to be a straightforward matter of mathematic probability. But it is only thanks to the work of Pascal – along with the perhaps more famous Pierre de Fermat – that we have such a grasp of probability theory at all. In other words, it is not just the iconic roulette wheel that we owe to Pascal, it is the entire idea that within a fixed set of mathematical parameters, we can calculate the likelihood of future events. That is to say, Pascal and Fermat laid the foundations for all casino gambling, all bookmaking and a great deal of the predictive logic which underpins corporate planning – and especially the insurance industry.

An inveterate inventor, Pascal also developed a means of establishing atmospheric pressure in relation to altitude. It is on that basis that the unit measurement of atmospheric pressure is – you guessed it – the Pascal (Pa) – Cue barometers and altimeters and all that they enable. Along the way, he also came up with the surgical syringe and the hydraulic press.

An early computer

A fundamentally practical man, Pascal was always intent on breathing life into his theoretical calculations. The perpetual motion machine may never have been fully realized, but his experiments with calculating machines were genuinely groundbreaking. It is on the basis of his calculating machine – which he called the Pascaline – that Pascal’s name was still resonating in the 1960s, back when Niklaus Wirth was looking for a suitable name for his coding language.

The Pascaline was a precursor to Charles Babbage’s calculating machine by almost 200 years. Admittedly it was not entirely perfect, something which no doubt irked the fastidious Pascal to no end, but it was nonetheless a hugely significant as well as impressive engineering and mathematical feat. For example, unlike Babbage’s giant machinery, Pascal’s machine was readily portable by hand. Over the course of serial attempts to perfect his invention, Pascal produced around 50 different versions, a few of which survive to this day.

The most testing problem which the machine was designed to cope with – over and above the most basic mathematical functions of adding and subtracting decimals (base ten) – was the idiosyncratic arrangement of the French currency at the time which was made up of sols, livres and deniers: there were 20 sols in a livre and 12 deniers in a sol. Being able to reliably converts 20s into 12s, and 12s into 1s was itself a formidable mathematical challenge. For the son of a tax inspector, such problems were deeply significant.

More than Math

Pascal’s achievements were not confined to his mathematical accomplishments in any way. In 1646, following a near-death experience, he is said to have experienced a powerful religious awakening which led to him developing a typically insightful career as a religious theologian. One of his more lasting logical observations was what has become known as ‘Pascal’s wager’. The argument was that since it is impossible to prove whether or not God exists, that one should believe in him anyway, since if he does exist this is clearly the more sensible approach, and if he does not exist nothing has been lost. Seemingly impervious to cognitive bias of any sort, Pascal’s considerable body of religious thinking was published in the now famous Pensées (thoughts).

Computers (in more than 20 years of history), barometers, probability theory, casinos and an unshakable argument for believing in God: Pascal left us quite a legacy. Never a man of good health, Pascal died from stomach cancer in Paris on August 19, 1662. He was only 39 years old. There’s no way to even imagine what else this brilliant man could have come up with were he alive for longer.

]]>http://www.relativelyinteresting.com/computers-probability-logic-blaise-pascals-impressive-legacy/feed/07702Galton’s Paradox Explained
http://www.relativelyinteresting.com/galtons-paradox-explained/
http://www.relativelyinteresting.com/galtons-paradox-explained/#respondTue, 02 Feb 2016 15:13:02 +0000http://www.relativelyinteresting.com/?p=7605Galton’s Paradox supposes you have three fair coins. Necessarily, two sides will match (ie: two will be heads, or two will be tails). It’s an even probability that the third coin will be a head or tail. Therefore, the chance that all three will match is 1/2. Is our solution correct? Quite […]

]]>Galton’s Paradox supposes you have three fair coins. Necessarily, two sides will match (ie: two will be heads, or two will be tails). It’s an even probability that the third coin will be a head or tail. Therefore, the chance that all three will match is 1/2.

Is our solution correct?

Quite obviously not, or it wouldn’t be much of a paradox…

Francis Galton, in his book 1894 paper, noted that the fallacy lies in confusing a particular coin with any coin.

Here’s the fallacy in action:

At least 2 of the coins must turn up alike.

It is an 1/2 chance whether a third coin is heads or tails.

Therefore, it is a 1/2 chance whether the 3rd coin is heads or tails.

Wrong! “A third coin” is not the same as “the third coin“.

Let’s look at all the possible outcomes of flipping three coins to get the real answer. There are 2^3 possible outcomes:

H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T

The original claim said that the chance that all three outcomes would match was 1/2 (or 50%). But of the 8 possible outcomes, one of them is all heads (H H H) andone of them is all tails (T T T). Therefore, 2 of 8, or 25%, results in our desired outcome of all three coins getting the same side.

]]>http://www.relativelyinteresting.com/galtons-paradox-explained/feed/07605How common is your birthday?
http://www.relativelyinteresting.com/how-common-is-your-birthday/
http://www.relativelyinteresting.com/how-common-is-your-birthday/#respondThu, 08 Jan 2015 12:20:07 +0000http://www.relativelyinteresting.com/?p=5563Ever wondered how common your birthday is? What do you think is the most popular month to be born? What about the most popular day of the week? Why? Courtesy of the CDC: Vital Statistics of the United States – Volume 1, Natality (1994-2003), we can visualize it. By a slim margin, Tuesday is the […]

]]>Ever wondered how common your birthday is? What do you think is the most popular month to be born? What about the most popular day of the week? Why?

Courtesy of the CDC: Vital Statistics of the United States – Volume 1, Natality (1994-2003), we can visualize it.

By a slim margin, Tuesday is the most popular day of the week to be born (Saturday and Sunday are the least). Summer is the most common season to be born (we can imagine why, especially if there’s a colder winter forcing people to stay inside…).

It’s relatively interesting to see that along with weekends, December 24th and 25th, January 1st, and July 4th are the least common days to be born. After all, they are American holidays…

Click the image below to see a much larger, legible version of the infographic.