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Catch-22: Hobson’s Choice, Buridan’s Ass, or Morton’s Fork?

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You caught me, that is not exactly a catch-22. The definition of each:

Hobson’s Choice: a situation where you have a free choice, but only one option is offered. You can either take it or leave it. This is named after a stable owner in the 1500’s by the name of Thomas Hobson wanted to make sure that all 40 of his horses were being worked equally. Instead of letting his customers pick their horse to ride, he offered them the horse in the stall nearest the door or no horse at all.

Buridan’s Ass: Buridan’s ass is when you find yourself in a difficult decision between two equally appealing options – the decision making process is so slow you would be better off just picking one. Let’s assume an ass will always go eat the hay closest to him. In our fictional scenario an ass walks into a barn and finds himself equidistant between two identical bales of hay. Unable to make a decision which hay to eat, the ass remains in the same spot and starves to death. This one is named after 14th century philosopher Jean Buridan (although Aristotle wrote about it first) and is often quoted to exhibit the folly of politicians.

Morton’s Fork: the opposite of Buridan’s ass is Morton’s fork (obviously right? no duh). This is when you are forced to decide between two equally unpleasant options. Between a rock and a hard place. Wikipedia’s history lesson: the expression originates from a policy of tax collection devised by John Morton, Lord Chancellor of England in 1487, under the rule of Henry VII. His approach was that if the subject lived in luxury and had clearly spent a lot of money on himself, he obviously had sufficient income to spare for the king. Alternatively, if the subject lived frugally, and showed no sign of being wealthy, he must have substantial savings and could therefore afford to give it to the king. These arguments were the two prongs of the fork and regardless of whether the subject was rich or poor, he did not have a favorable choice.

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What Are the Odds Two People in the Room Have the Same Birthday?

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Photo: surlygirl

Situations arise from time to time where you are in a room with a whole bunch of strangers. They key to making friends and the opposite sex swoon? Probability.

What are the odds that two people in the room have the same birthday? Memorize some of these numbers so that you can spout them off, I guarantee you will be the coolest guy in the room – 9 people = 10%, 13 = 20%, 15 = 25%, 18 = 35%, 23 = 51%, 57 = 99%, 366 = 100%.

It’s important that you mention the assumptions before your new worshipers start poking holes in you numbers – random distribution of birthdays, no leap years, no twins, etc. Then you can go into what is interesting – with only 23 people in the room, odds are two people share a birthday. It only takes 57 people to jump to 99% probability, but to get to 100% you need to have 366 people.

Now to really make their mouths drop. How many people would it take for the odds to be in your favor for someone having the same birthday as you? 253. They may question you because this is much higher than 365/2, but stick to your guns and point out that two of the other people could have the same birthday. How many people would it take for two to likely have a birthday within a week of each other? Only 7. Ya, but a random distribution is a hell of an assumption. Oh really? Actually the odds are slightly more in your favor because birthdays tend to clump – summer babies, C-sections aren’t on weekends, and so on.

Here’s one to set up on a tee for them: what are the odds that two people have the same half birthday? If they can figure this out, you may just have found your soulmate.

One or Two Spaces After the Period – How Wikipedia Handled the Ultimate Question

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Photo: Kevin Spencer

While typing, how many spaces do you put after a period? I was taught to hit the spacebar twice after the end of a sentence. Turns out not everyone does this. I knew there were single spacers out there, but I thought they were heretical troglodytes. Then I saw this poll result: with a huge sample of 44,000 people, 47% use a single space!

How does this happen? I go for soooo long thinking almost everyone was on the same page, but in reality it is split down the middle.

Once I got over my ignorance as to how the rest of the world operates, I needed to know – how did Wikipedia standardize on which one to use? Obviously if you are going to embark on an monumental distributed encyclopedia, all authors should agree to either use single or double space. I could see this holding up the entire project and just turning into a huge debate to settle it once and for all. Propitiously, the HTML of web pages renders on the screen the same way whether you do a single space or ten spaces. Problem averted.

  • It turns out the double space is a holdover from the typewriter days when fonts were monospaced. Utterly useless now and really dating me beyond my years.

  • With my lofty aspiration to be the most efficient human alive, I must cut out the extraneous second space. I’ll keep you updated on the progress.

  • Here is something else I found even more eye opening (although I will not discuss my personal proclivity): Sitters vs. Standers – The Great Wipe Hope

The New Bay Bridge

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Engineers love bridges. I think it is because they appear so simple, but engineers appreciate how much thought and calculation are required.

Living in the Bay Area, we have two of the most impressive bridges in the country. It’s a great time to be here because they are currently rebuilding the Bay Bridge, designed to last 150 years and withstand a whopping 8.5 earthquake. Check out this short video showing how awesome it will be:

And for those of you that haven’t seen this famous video of how not to build a bridge:

Nerd note: In engineering classes we were taught that the reason the Tacoma Narrows Bridge collapsed was because the wind provided a periodic frequency that matched the natural frequency of the bridge. (Non-nerd note: think of a parent pushing a child on a swing – the parent (the wind) is providing a periodic push of the child (the bridge), who is moving back and forth at a frequency. If those frequencies match the kid will swing higher and higher.) The real cause was aeroelastic flutter – aerodynamic forces, not periodic wind gusts, that matched the natural frequency of the bridge. There is a startup that created a tiny wind powered generator using this principle.

Why Merle Haggard Out Travels Lady Gaga – What You Should Know About Radio Waves

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Photo: Peter Megyeri

The radio is a perfect example of an old technology that we completely take for granted – do you know how it works or are you just cluelessly upset when all you hear is static? These older technologies are much easier to wrap my head around – if a some guy in the 19th century could figure it out, I should be able to understand the basic idea. I’m not going to focus on how a radio transmitter physically creates the signal or receiver is able to turn it into sound, but rather the basic theory and some interesting things to know.

What is the major difference between AM and FM?
AM stands for amplitude modulation. This means the sound determines the amplitude of the radio wave. FM stands for frequency modulation – the sound alters the frequency of the radio wave. The transmitter is able to turn the sound being created into the appropriate wave. Here is an example of a sound and how it would look as an AM and FM wave:

Source: Berserkerus

Another major difference is that AM radio waves are a much lower frequency than FM. Think of AM having the wavelength of a football field and FM the ball. In reality you can broadcast amplitude modulation or frequency modulation at any frequency, but high quality FM audio must be a high frequency to allow for the differences (or modulation) in frequency.

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Is .9 Repeating Less Than 1? – Not So Fast …

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Image: Melchoir

.99999 repeating is the representation of an endless string of 9s. Just when you think it should end, add another 9. Then do it again. Intuition tells us that without rounding this number is less than 1. We know it must end in a 9, and any decimal that starts 0.999… regardless of how many 9s you write, has to be less than 1. Well here is proof that you are wrong!

x = .999…
10x = 9.999…
10x – x = 9.999… – .999…
9x = 9
x = 1

How is this even possible? Why wouldn’t you just right 1 instead of .9 repeating? Now you can – if anyone questions you show this proof to blow their mind! You also now have the right to tell the joke “How many mathematicians does it take to change a lightbulb? Point nine repeating!”

Things You Didn’t Even Know Had a Name

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Photo: White Gold Wielder

Just about every obscure item you can imagine has a proper name. Someone before you previously attempted describing the item, discovered that “blue thingy” was not descriptive enough and took the liberty to making up a name that everyone can use. But of course not everyone knows the official name and the item is inevitably still referred to as adjective + “thingy”. I am not advocating adding thousands of nouns to your vocabulary in the off chance that you may one day want to refer to the flap of skin on your hand between your thumb and index finger (purlicue). But there are a few that I would like to pass on to my readers in hopes that they will be widely used one day. Try dropping these into conversations:

  • Aglet – the hard plastic part at the end of a shoelace
  • Cairn – a pile of stones made by hikers
  • Ferrule – the metal piece at the end of the pencil that holds the eraser on
  • Muselet – the wire thing on the top of a bottle of champagne to keep the cork from flying off under the pressure
  • Zarf – the cardboard coffee sleeve you receive at Starbucks to keep you from burning yourself through the thin cup

Photos: Tom Wefald, Ian W. Fieggen, Steve Webel, Fredrik Thommesen

When you do in fact use one of these words in conversation, you will undoubtedly have to explain the meaning. This is a perfect opportunity to share all five of these words, which will make you look like a genius and promote the use of adding of these words into common use!

Famous Supreme Court Cases and Interesting Tidbits

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Photo: Ken McCown

One day my friend was cutting a piece of delicious cheesecake when it was proposed to do a “you cut, I choose” method to split it evenly. I took it a step further and told him to “Plessy v. Fergurson it” – meaning I wanted the pieces separate but equal. Of course no one understood what I was talking about, no one laughed, and I myself was not even sure I quoted the correct Supreme Court case.

So I went online to verify my dorky joke and found the Supreme Court information available to be quite underwhelming. You can find articles dozens of pages long about each particular case, but no concise summaries. Here are some of the famous cases ruled upon by the Supreme Court and a short description of why it was so significant to the United States.

Famous Supreme Court Cases

1st tier

  • Roe v. Wade (1973) — Outright abortion bans are unconstitutional
  • Marbury v. Madison (1803) — Judicial review (for Supreme Court)
  • Plessy v. Fergurson (1896) — Separate but equal (segregation)

2nd tier

  • Miranda v. Arizona (1966) — Rights to counsel and to remain silent
  • Regents of CA v. Bakke (1978) — Affirmative action
  • Tinker v. Des Moine (1969) — Freedom of speech of students in public schools
  • Brown v. Board of Education (1954) — Segregated schools is unconstitutional
  • McCulloch v. Maryland (1819) — Constituation is supreme law of the land
  • Dred Scott v. Sandford (1857) — Slave is not a citizen but property of his owner

3rd tier

  • Slaughter-House Cases (1873) — Limits privileges and immunities of state citizens
  • Gideon v. Wainwright (1963) — Right to court appointed attorney if unable to afford one
  • Griswold v. Conneticut (1965) — Individual’s right to privacy
  • Mapp v. Ohio (1961) — Evidence procured by illegal search or seizure is not permissible in court
  • Greg v. Georgia (1976) — Death penalty in not unconstitutional

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The Smart Mathematics of Credit Cards

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Photo: Andres Rueda

You most likely use credit cards daily, but have you taken the time to consider how they work? Let’s examine one of the most obvious aspects of the credit card: the number. Credit card numbers are 14 to 16 digits long and link your purchase back to your account at the bank. But what do they mean?

The first digit is reserved for specifying what type of card it is. 3 = Travel and Entertainment card (34/37 = AMEX, 38 = Diner’s Club), 4 = Visa, 5 = MasterCard, and 6 = Discover. Each type handles the next 12 to 14 digits differently. They are used to identify the account number, bank number, whether it is a business or personal account, and/or the currency. Check out these sites for a more in depth coverage of how each credit card provider uses these digits.

One thing all credit cards have in common is a check digit at the end which is used to verify that it is a valid credit card. The check digit uses the Luhn algorithm, also known as the modulus 10 algorithm, to “check” the rest of the numbers. It’s goal is to not prevent counterfeit, but rather to protect against the accidental mistyping or mistransmission of the number.

The algorithm:

  1. Double the value of every second digit moving from right to left.
  2. Sum the value of every individual digit.
  3. If the total ends in zero it is valid, any other number it is invalid.

Let’s take a simple example: 47142

  1. 2×4 = 8, 2×7 = 14. Therefore we have 4(14)1(8)2
  2. 4+1+4+1+8+2 = 20
  3. 20 ends in zero so the number is valid.

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