What’s The Biggest Number?

My son’s in first grade now, which I still don’t quite believe. But it’s true. And, thanks to first grade, he’s really starting to get a handle on this ususual technology we call “math”. It’s just adding and subtracting right now, but he’s really getting excited about it. He’ll ask me random math questions, and ask me what my favorite number is, and so on and so forth. Then, one day, he asks me this: “What’s the biggest number?”

Well. I’m ready for this. One of the classes I took for my woefully under-used BS in Computer Science and History was on logic and number theory. “There isn’t one.”

“Yes there is!” he declares.

“No,” I tell him. “Because, no matter what, you can always add one to the number.”

“No you can’t!” he insists, shocked by his first glimpse of the concept of infinity.

“Well,” I ask him, “what’s the biggest number you can think of?”

“A googol!” he announces with some confidence.

“Do you know what that is?” I respond. His puzzled expression tells me he doesn’t, so I fill him in. “You know how one hundred is one followed by two zeros, right?” He nods. “Well, a googol is one followed by a hundred zeros.”

His eyes go wide. “What’s a googol take away one?” he asks.

“That would be…” I think for a moment. “Ninety-nine nines.”

“Wow,” he says. “What’s that called?”

“Uhm… I don’t know.”

What is the biggest number?

Like I said, there really isn’t one. You can always add one to any arbitrarily large number. A googol, for example, is one followed by a hundred zeros. It looks like this (adjust your browsers, please):

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Pretty big, right? Well, a googol plus one is:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,001

Clearly, all of these zeros get unwieldy in an absurdly short period of time. That’s why exponential notation is used. This, if you’re not familiar with it, is written in the format xy and means that x is multiplied by itself y times. 32 is 3*3 (equaling 9), while 23 is 2*2*2 (equaling 8). For convenience, since we count by 10s, most numbers are presented in a 10y format – sometimes called “scientific notation”. In this format, a googol is 10100, which you’ll have to admit is a whole lot easier to write than all those zeros I typed out above.

We do have names for a lot of really big numbers, though. Oddly enough, the names you use depend on whether or not you are using the “long scale” of numbering, the “short scale” of numbering, or Metric prefixes.

Hang on. I know what Metric is, but what’s short scale and long scale?

Brace yourself. The rabbit hole goes deep, here.

Short and long scale is just different ways of naming really big numbers, depending on where you live. According to Wikipedia, most English-speaking and Arabic-speaking countries use short scale, while most other countries in continental Europe and most countries that speak Romance languages use long scale. The difference sounds simple, and is all based on what you call numbers bigger than a million (106). Here goes:

  • When using short count for numbers larger than a million, you get a new name every time you get 1,000 times larger. So you count 1 million, 10 million, 100 million, 1 billion.
  • When using long count for numbers larger than a million, you get a new name every time you get 1,000,000 times larger. So you count 1 million, 10 million, 100, million, 1,000 million, 10,000 million, 100,000 million, 1 billion.

Simple, right?

No.

Yeah, it kind of confused me too. I grew up using short count, so it looks intuitive and long count looks really wierd. I’m sure that if I grew up counting long count instead, than I’d flip those attitudes. Maybe a table would help?

Probably

All right. Here goes. Brace yourself.

Number Short Count Long Count Metric Prefix
1 One One N/A
10 Ten Ten deca-
102 Hundred Hundred hecto-
103 Thousand Thousand kilo-
106 Million Million mega-
109 Billion Thousand Million (or Milliard) giga-
1012 Trillion Billion tera-
1015 Quadrillion Thousand Billion (or Billiard) peta-
1018 Quintillion Trillion exa-
1021 Sextillion Thousand Trillion (or Trilliard) zetta-
1024 Septillion Quadrillion yotta-
1027 Octillion Thousand quadrillion (or Quadrilliard) N/A
1030 Nonillion Quintillion N/A
1033 Decillion Thousand quintillion N/A
1036 Undecillion Sextillion N/A
1039 Duodecillion Thousand sextillion N/A
1042 Tredecillion Septillion N/A
1045 Quattudorcellion Thousand septillion N/A
1048 Quindecillion Octillion N/A
1051 Sexdecillion Thousand octillion N/A
1054 Septendecillion Nonillion N/A
1057 Octodecillion Thousand nonillion N/A
1060 Novomdecillion Decillion N/A
1063 Vigintillion Thousand decillion N/A
1066 N/A Undecillion N/A
1069 N/A Thousand undecillion N/A
1072 N/A Duodecillion N/A
1075 N/A Thousand duodecillion N/A
1078 N/A Tredecillion N/A
1081 N/A Thousand tredecillion N/A
1084 N/A Quattuordecillion N/A
1087 N/A Thousand quattuordecillion N/A
1090 N/A Quindecillion N/A
1093 N/A Thousand quindecillion N/A
1096 N/A Sexdecillion N/A
1099 N/A Thousand sexdecillion N/A
10100 Googol Googol N/A
10102 N/A Septendecillion N/A
10108 N/A Octodecillion N/A
10114 N/A Novemdecillion N/A
10120 N/A Vigintillion N/A
10303 Centillion N/A N/A
10600 N/A Centillion N/A
1010100 Googolplex Googolplex N/A

There are, of course, proposals for names for larger numbers. I won’t go into too many details here, beyond saying that the proposed name for the number 103003 is “millinillion” for short count naming conventions and “thousand quingentillion” for long count naming conventions. And now you know.

Yeah. It’s big.

But, what about infinity? Isn’t that the largest number?

Nope.

What? But, I’ve always heard…

“Infinity” isn’t the largest number, because infinity isn’t a number. Infinity is a concept, and in numbers it refers to either an arbitrarily large or undefined number (such as how the value of X/0 goes to infinity in calculus), or it represents sets of numbers. When using infinity as a set, you get two basic types of infinity: countable, and uncountable. Countable infinity is an infinite set whose “elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.” Basically, it’s a clearly defined set. All natural numbers (1, 2, 3, 4, … infinity) is a countable infinity. So is all even numbers, all odd numbers, all prime numbers, and so forth.

Uncountable infinities, on the other hand, aren’t quite so neat. An uncountable set “contains so many elements that they cannot be put in one-to-one correspondence with the set of natural numbers. In other words, there is no way that one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.” For example, the set of all real numbers between 0 and 1 is uncountable. Why? Because there will always be an infinite number of fractions between any two members of that set you care to name.

Could you try and make all that a little clearer?

Sure. A countable infinity has a finite (although possibly large) number of points between any two elements of the set. An uncountable infinity has an infinite number of points between any two elements of the set. As an example, take the countable set of all natural numbers. If you pick a starting point (let’s say the number 12) and an ending point (let’s say the number 17), then it you have to count only 5 steps to get from 12 to 17. If your starting and ending points were 2 and a googol, then you’d have to count 9,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,998 steps – that’s a whole lot of counting, but you could do it in a finite (but large) amount of time. It can be counted.

Now, consider the set of all real numbers between 3 and 5. It looks shorter at first glance, but remember that real numbers include fractions and decimals. So, let’s pick our starting point as 3.0001 and 3.0001001. 3.00010001 is between them. So is 3.00010002, and 3.00100000000007, and every other amount of extra decimal places that could conceivably be tacked on. And since there is no limit to the number of extra decimal places, you would never be able to count every single possible number that lie between 3.0001 and 3.0001001. Ever. It cannot be counted, so it is uncountable.

My head hurts.

Mine, too. Now, let me make it hurt worse. Uncountable infinities are larger than countable infinities, even though both infinities are infinite in size.

What?

Yes, and it’s all down to that the countable versus uncountable aspects of the sets. Let’s look at the set of all natural numbers versus all real numbers, and then count the “steps” between 2 and 3. The countable infinite has a finite distance between those two numbers, while the uncountable infinity has an infinite distance between the two numbers. So the uncountable infinity is larger because, between any two arbitrary points, it is larger than the countable infinity for the same segment of the set.

So, in summary, there is no “largest number”. You can always add one to any number you choose (a millinillion and one, a millinillion and two, a millinillion and three,…), and infinity doesn’t count because it’s not a number. Even when it’s countable.  And a googol take away one would be called, in short count, “a googol minus one” because I couldn’t find a short count name for numbers that big.

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Why Don’t We All Get A Balloon, And Then We Can Fly Into The Sky?

A couple of weeks ago, I was at a birthday party for one of my son’s friends. It was a great day, at a little park a half hour drive north and east of where I live, situated on a tributary of the Ohio River. The kids all had squirt guns and the like, and got each other soaked down while the adults sat back and watched and took pictures and were grateful that they brought extra clothes and towels. There were balloons as well, because there were kids.

One child was super excited about the balloons. They were your ordinary latex kind, that you blow up with your own lungs, but he was bouncing them around and laughing. “Why don’t we all get a balloon?” he asked excitedly. “And then we can fly into the sky!”

So, yeah. It wasn’t my son that asked it. But it’s the kind of question he could have asked, so I’ll answer it.

How does a balloon float?

The same way a boat does.

Care to elaborate?

Of course.

It’s tempting to say that things float because they’re light, but that’s not quite accurate. For example, an oil tanker floats but it is not light – they can carry anywhere from 1,500 to 550,000 deadweight tons, depending on size. No. Floating has everything to do with the mass of the object, and the fluid that surrounds it. See, all objects placed into a fluid displace some of the fluid (put a rock in a cup of water to see for yourself). If the mass of the fluid you displace is greater than your mass, you float. And air, for these purposes, can be considered a fluid.

But let’s look at some math, since the University of Chicago was kind enough to put together a document (Lighter Than Air: Why Do Balloons Float?) that explains all of this in some detail. There are two forces in play, the downward force (which is the pull of gravity) and the upward force (which is how much the fluid resists the downward force). The downward force (Fg) is the mass of the object (M) x gravitational strength (g), which is also how you calculate “weight” in physics. Weight, after all, is mass times gravity (which is why you weigh less on the moon, even though you retain the same mass). Upward force (Fb) is the mass of the fluid displaced (m) x gravitational strength (g).

Once you have Fg and Fb, you can calculate life=t. All that is is Fb – Fg. If the result is positive (meaning Fb is larger than Fg), you are sinking. If the result is negative (meaning Fb is larger than Fg), you are rising. And if the result is 0 (meaning the two forces are equal), you are floating immobile in midfluid.

Uhm. Okay.

Let’s do an actual example, shall we?

Yeah. Lets.

After consulting Google, I found an estimate that the average-sized party balloon masses 1.7 grams, and several notes that they can weigh more depending on the actual size, thickness, etc, etc. This will be important, momentarily.

Now, the density of air at sea level is about 0.0012 grams per cubic centimeter. So, if you inflate your hypothetical average-sized party balloon to a diameter of 1 foot (0.3048 meters, which means 30.48 centimeters), you get a sphere (for the sake of not making me crazy) containing 14,826.7 cubic centimeters of air. The inflated balloon weighs a total of (14,826.7 x 0.0012) + 1.7 = roughly 19.5 grams, and displaces 17.8 grams of air. So, it sinks. If you inflate the balloon to 2 feet in diameter (60.96 centimeters), you get a balloon containing 116,613 cubic centimeters of air. It weighs 141.6 grams, and displaces 139.9 grams of air.

Clearly, both balloons sink. And, in a vacuum, both would sink at the same rate because they have the same lift (-1.7).

But they don’t fall at the same speed. Not the ones I’ve played with, anyway.

Nope. Because we live in an atmosphere. And atmospheres create air resistance. I won’t go into the math there, because it made my head hurt a little, but it works like this: an object produces drag (a resistance to acceleration) based on the cross-section of the object perpendicular to the direction of movement. As the cross-section gets larger, the power needed to overcome the drag increases. How much? Well, it’s based on the cube of the cross-section. If you double it, you need 8 times as much power. If you triple it, you need 27 times as much power. And so on.

For the balloon, acceleration is down towards the ground and the cross-section is the diameter of the balloon. Doubling the diameter of the balloon means you would need 8 times the power to make it fall at the same speed as the smaller balloon. Since gravity (roughly) stays the same, that means you would expect to see it fall 8 times as slowly.

So, getting back to the wish to “fly into the sky”…

Sure. See, to make a balloon fly, you need something less dense than room-temperature air. That’s why hydrogen and helium are so popular. They’re gaseous at “room temperature”, and they weigh far, far less. Hydrogen weighs 0.000089 grams per cubic centimeter, and helium weighs 0.00018 grams per cubic centimeter. So, looking at the two balloons from the earlier example, we get the following information:

  • The 1 foot balloon weighs 3 grams if you fill it with hydrogen, and 4.4 grams if you fill it with helium. It displaces 17.8 grams of air.
  • The 2 foot balloon weighs 12 grams if you fill it with hydrogen, and 23 grams if you fill it with helium. It displaces 139.9 grams of air.

Regardless of which gas you fill the balloon with, it weighs less than the gas it displaces. So it has positive lift and it goes up. In fact, it could even lift additional weight – the 2 foot balloon filled with hydrogen would have neutral buoyancy with a 127.9 gram weight attached to it, so you could attach two Hershey’s chocolate bars (1.55 oz, or 44 grams each) to the balloon and still watch it go skyward.

Heating the air will also work, as gasses become less dense with heat. Sadly, I don’t have a good equation (that I understand) to show how much you’d have to heat the air to make it lift.

How many balloons would I need to fly to the sky, then?

Well, that’s more or less easy. How much do you weigh, and what gas are you using? I’ll illustrate with my son. He weighs around 60 pounds right now. That’s 27.2155 kilograms, or 27,215.5 grams. Looking at the two foot balloons, the lift for the hydrogen balloon is 127.9 grams per balloon and the lift for the helium balloon is 116.9 grams. So, it would take 27,215.5/127.9 = 213 2 foot hydrogen balloons to give him neutral buoyancy. 233 2 foot helium balloons would be required to achieve the same effect. You’d need another 18 hydrogen (20 helium) balloons to offset the weight of his clothes (maybe more if he’s planning on flying high). And I have no idea how many balloons would be required to offset the weight of the lines he’s holding on to or the harnesses to keep the balloons attached to him. And, of course, he’d need more to actually go up.

By contrast, I weight 316 pounds. So I’d need 1,121 hydrogen balloons or 1,227 helium balloons to achieve the same effect. That’s 37,553.5 cubic feet of hydrogen balloons, or a sphere roughly 42 feet in diameter. Oh, and it could explode.

Don’t do this at home.

No kidding.

You’d think so, but at least one person did.  Larry Waters used 45 8-foot weather balloons filled with helium to lift himself, his lawn chair, his parachute, his pellet gun (so he could pop balloons and descend), his CB radio, his camera, and sandwiches and beer to a height of 16,000 feet.  He flew for 45 minutes, and got fined $1,500 by the FAA after an appeal.  But, because he was a trained pilot and lucky, he didn’t die.

How Long Would It Take To Get To The Moon?

“Dad?” my son asked while we were playing with his Legos. “How long would it take to get to the moon?”

“I think that depends on how fast you’re going,” I replied.

“No,” he says, sounding exasperated as only a 6-year-old can, “I mean, if you were going as fast as the Death Star!” Because that was entirely clear from the context, right?

“I don’t know,” I tell him. “I don’t know how fast the Death Star is.”

“It’s really fast,” he assures me.

Where to start?

There are a couple of things we need to know here, in order to answer the question. How far away is the moon? How fast do we have to go at minimum to make it? Oh, and how fast is the Death Star? So, let’s dig in.

How far is it to the moon?

The distance from the Earth to the Moon varies based on the time of the month, because the Moon orbits us in an ellipse – so it gets closer and then moves further away. At apogee (the farthest it gets from us), it’s 405,400 km away, while it gets as close as 362,600 km at perigee. So, clearly, how long it takes will really depend on how fast we’re going – just like any other trip we can take.

How fast do we need to go?

How fast you need to go to get to the moon will depend on the method you’re using to get there, and the amount of time you want to take. So, let’s start with the concept of escape velocity. This is the minimum speed required to “out-pull” gravity and leave an object behind. If you launch at that speed or greater, you fly away. If you don’t, you fall back to the surface. Eventually. Escape velocity varies with the gravity of the object and is approximately 11.2 km/s, or 40,320 kph on Earth. Assuming there is no friction, which is a popular physics assumption to keep equations simple. If you launch at that speed, you fly away from the earth – you slow down over time, as Earth’s gravity pulls on you, but you never actually stop moving. Ever.

There’s a down side to trying to get to the moon by launching at escape velocity (say, by using a variant of Project HARP’s big gun): Earth’s force of gravity is 9.807 m/s2, so you’re pulling around 1,142 gravities at the instant of launch. You would be a thin, wide smear on your pilot’s chair well before you reached the moon.

Clearly, we didn’t send a gelatinized melange of Neil Armstrong, Michael Collins and Edwin Aldrin to the moon on Apollo 11 – those three men made it to the moon and back with bones and organs intact, after all. So, how did they do it? Well, the important thing to remember is that escape velocity is only needed if you have an initial push and then add no additional thrust after that. This isn’t how the Saturn V – or any other rocket for that matter – works. They lift themselves at a slower pace, but apply a constant (or near-constant) thrust by carrying fuel. There’s a point of diminishing returns on this, because you have to lift your fuel as well as the ship (something described in the Tsiolkosky rocket equation, which I discussed when I tried to describe how to make a house fly).

The Saturn V was a multi-stage rocket, with the first stage burning for 2 minutes 41 seconds and pushing the rocket about 68 km into the air (hitting a velocity of 2,756 meters per second). Then it ditched the first stage and started the second stage burn. This pushed it another 107 km (for a total of 175 km) into the air over the course of 6 minutes, reaching a velocity of 6,995 meters per second). Stage 3 burned for about 2 minutes 30 seconds, reaching a velocity of 7,793 meters per second and putting it in orbit at an altitude of 191.1 km. Stage 4 burned for six minutes, pushing the ship to a velocity of 10,800 meters per second once it was time to head for the moon.

So, how long would it take?

How fast are you going?

Let’s say you just boosted off Earth with a canon, firing you straight up at escape velocity. Let’s also say you timed things so that you’d intersect with the moon at perigee. That’s 362,600 km, or 362,600,000 meters. At 11.2 meters per second, that’s 32,375,000 seconds to reach the moon. This translates into 8,993 days, or 24 years, 7 and one half months. Approximately. Your gelatanized corpse has a long trip ahead.

Apollo 11 was moving at 10.8 kilometers per second, which (mathematically) means you’d expect the trip to the moon to take 33,574.07 seconds. In theory, this means 9.326 hours. It actually took three days. Why? Well, there’s two reasons and they’re both gravity. See, the Apollo 11 wasn’t maintaining constant thrust. It had fuel that it used for course corrections and orbital insertions and the like, but it coasted most of the way. Earth’s gravity pulled on the ship the whole time, slowing it down. In addition, the ship didn’t fly in a straight line. It was in a long, figure-eight-shaped orbit with the Earth and the Moon – like so:

But what about the Death Star?

Ah, yes. That. Well, it still depends on the speed the ship can manage.

How fast is the Death star?

This is… questionable. According to the DS-1 Orbital Battle Station entry on Wookieepedia, the Death star had a speed of 10 megalight (MGLT).

So, what’s a megalight? Well, also according to Wookeepedia, a megalight “was a standard unit of distance in space”. Which is entirely unhelpful, although it does indicate that when it was used in the Star Wars: X-Wing Alliance instruction manual, it appeared to be a unit of distance and that when used as speed it should imply “megalights per hour”.

In all likelihood, “megalight” is a word that got made up because it sounded cool and had no actual meaning attached to it. But if we try to break it down, “mega” as a metric prefix means million. So, one megalight could be a million light seconds. However, this would mean that the Death star flies at 10 million light seconds per hour, or 2,777.7 times the speed of light – meaning that it could reach Alpha Centauri from earth in less than 14 hours of cruising on its “sublight” drives.  So I’m going to assume that this is not what was intended.

The Star Wars Technical Commentaries on TheForce.net speculate in “Standard Units” on what MGLT means in terms of real world [i]anything[/i]. The author of the article comes to the conclusion that 1 MGLT is “at least 400 m/s2” acceleration, which is roughly 40 gravities of acceleration.

One thing we also know about ships in Star Wars is that constant acceleration isn’t an issue – they have something close to the “massless, infinite fuel” I mentioned above. The Death Star isn’t fast, compared to the other ships in Star Wars, but it can accellerate at a constant 4 kilometers per second. Now Dummies.dom provides us with a simple formula for determining the distance (s) covered for a given time (t) at a particular acceleration (a), and that formula is s = 0.5at2. Which means we can reverse engineer, because all we need is the time. The equation looks like this:

362,600 = 0.5(4)t2
362,600 = 2t2
181,300 = t2
t = square root of 181,300 = 425.7933771208754 seconds

So, assuming that the Death Star didn’t engage it’s hyperdrive, it would take a little over 7 minutes to reach the Moon at a velocity of approximately 1,703.17 kilometers per second. And it would keep going, because it can only slow down at 4 kilometers per second. So, if the Death Star wanted to stop at the Moon, it would need to slow down about halfway there (yes, I know that orbital mechanics are a little more complex than this, but we’re talking about a 160 kilometer diameter ship that can accelerate at 4 kilometers per second. So cut me some slack, would you?). That it would have to accelerate to halfway to the moon, and then decelerate the rest of the way. So, that would look something like this:

2(181,300 = 0.5(4)t2)
2(181,300 = 2t2)
2(90,650 = t2)
2(t = square root of 90,650 = 301.0813843464919)
t = 602.1627686929838 seconds, or slightly over 10 minutes.

“All your tides are belong to us, now.”

Why Do Sharks Eat So Many People?

“Dad?” my son asked as we got out of the car. “Why do sharks eat so many people?”

I assume he’d seen something about sharks at school, but the question still came out of nowhere. Thirty seconds before, he’d been telling me about his school’s Mardi Gras party and asking me if I felt better (because I’ve been sick, which is why this article still isn’t looking at the fossils he found). So, I put my mind to it. “I don’t think they do,” I answer.

“They don’t eat people?” he responds, sounding skeptical.

“Well, they can,” I concede. “But they don’t eat people all that often.”

“Why not?” he asks, and I swear he sounds disappointed.

“Well, a lot of them are kind of small. And we aren’t the kind of things they normally hunt.” I’m trying to remember shark facts, now. “Most of them are probably just wondering what we are, and people get scared of them and think they’re attacking.”

“Why do people get scared?” he asks.

I shrug. “Why did you get scared of them, when we went to the aquariam?”

“Because they look mean!” Then he grabs my hand. “Since you’re not feeling good, can we take a break and play Star Wars?”

Do sharks eat a lot of people?

This is one of those questions where I really hope I told my son the right thing, because I was working from half-remembered articles I’d read years ago, and memory is a fickle, tricky thing. Fortunately, it turns out that the University of Florida maintains the International Shark Attack File (ISAF), which they describe as “the longest running database on shark attacks, has a long-term scientifically documented database containing information on all known shark attacks, and is the only globally-comprehensive, scientific shark attack database in the world”.

Before we dive into the numbers, though, it’ll be important to define two terms the ISAF uses: provoked attacks and unprovoked attacks.

  • An unprovoked attack is edfined as “incidents where an attack on a live human occurs in the shark’s natural habitat with no human provocation of the shark.”
  • A provoked attack, on the other hand, usually occurs “when a human initiates physical contact with a shark, e.g. a diver bitten after grabbing a shark, attacks on spearfishers and those feeding sharks, bites occurring while unhooking or removing a shark from a fishing net, etc.”

The ISAF reports that 2016 was a pretty typical year, with a total of 150 alleged shark attacks. Out of those 150 attacks, here’s how the results broke out:

  • 81 were classified as unprovoked attacks (53 total in the United States, 43 of which were in Hawaii).
  • 37 were classified as provoked attacks.
  • 12 were sharks biting boats (aka “boat attacks”).
  • 1 was a shark eating part of an already dead human cadaver.
  • 12 had insufficient evidence to prove a shark attack.
  • 7 were determined to be attacks by other marine animals (including a barracuda and an eel).
  • 5 were determined to be abiotic injuries (that is, an environmental injury – scraping coral or rock, for instance).

So, in the fairly typical year of 2016, there were 118 total shark attacks on humans (131 if you count the boat attacks and the scavenging). 2015, by contract, hit 98 unprovoked shark attacks- the highest yearly total on record. On average, shark attacks result in 6 to 8 fatalities per year (depending on what period of time you average out), but 2016 only had 4 shark attack fatalities. Statistically, surfers are most likely to be attacked 958% of the total), followed by recreational swimmers and waders (32.1% of the attacks).

That’s not a lot of attacks, is it?

No, not really. In fact, there’s a whole lot of animals that are much more likely to kill you. According to the BBC, venomous snakes kill an estimated 50,000 people each year, rabid dogs kill an average 25,000 people each year, crocodiles kill an estimated 1,000 humans per year, and hippos kills an estimated 500 people per year. All of which makes the paltry 6-8 shark kills each year pretty tame.

friendly-shark

Still, it’s probably best not to do this unless you know what you’re doing.

The ISAF provides some other interesting comparisons. The odds of dying from a shark attack are 1 in 3,748,067. Fireworks are about 11 times more lethal (odds of death: 1 in 340,733), sun and heat exposure are 273 times more lethal (odds of death: 1 in 13,729), and the flu is 59,664 times more likely to kill you (odds of death: 1 in 63).

Why do shark attacks get so much attention, then?

Rarity, in my opinion. Rarity and shock/

See, we notice things that appear out of the ordinary. According to the CDC, heart disease is the leading cause of death in the United States (614,348 deaths in 2014), followed by chronic lower respiratory diseases (147,101 deaths), accidents (136,053 deaths), stroke (133,103 deaths), Alzheimer’s disease (93,541 deaths), diabetes (76,488 deaths), and influenza and pneumonia (55,227 deaths). Most of those get no attention at all, unless they’re really spectacular or they happen to someone famous. But death by animal attack? That’s unusual, particularly in the United States. And particularly because we like to think we’re outside the food chain. Homo sapiens sapiens is, realistically, the ultimate alpha predator and one of the dominant environmental forces on the planet. It’s unsettling to be reminded that we’re still animals, and that we can still become prey.

Also, sharks inhabit an alien environment that we can only meaningfully visit with the benefit of technology. A wolf or bear attack happens on dry land, so the surroundings aren’t inherently hostile to us. But sharks? A shark could kill us with their own environment, even if the bite isn’t fatal. So, they seem frightening.

Just in case I am one of the unlucky ones, any tips?

Actually, yes. Here’s what the ISAF says: “If one is attacked by a shark, we advise a proactive response. Hitting a shark on the nose, ideally with an inanimate object, usually results in the shark temporarily curtailing its attack. One should try to get out of the water at this time. If this is not possible, repeated blows to the snout may offer a temporary reprieve, but the result is likely to become increasingly less effective. If a shark actually bites, we suggest clawing at its eyes and gill openings, two sensitive areas. One should not act passively if under attack as sharks respect size and power. “

Can They Hear Me In China?

“BOO!” my son yells, leaping out from a shrub.  And then he dissolves into a fit of laughter.

This is a game he likes to play, whenever he gets the chance.  As soon as we’d parked and he got out of the car, he ran up the sidewalk towards the front door of our condo.  And then he ducked back behind the hedge, lurking.  The game, now, is for me to walk towards the door.  Then he’ll jump out and shout “boo” and try to make me jump.

“Did you know I was there, daddy?” he asks.

Of course I did, I think.  You hide in the same place every time.  “Kind of,” I tell him.  “I guessed where you were.”

He blows that off.  “I was loud, wasn’t I?”

“Yes, you were,” I answer, unlocking the door.

“Was I loud enough for them to hear me in China?”

How Do We Hear?

Obviously, we hear with our ears.

howdowehear

Sound waves, which are really just pressure waves in the atmosphere, strike the outer ear and are channeled into the ear canal.  These pressure waves vibrate the eardrum, which in turn vibrates the bones of the inner ear (the malleus, the incus, and the stapes), amplifying the vibrations and transmitting them into the inner ear (or cochlea).  Hairs in the cochlea are stimulated by these vibrations, creating an electrical signal that transmits along the auditory nerve to the brain.

Yes, this is terribly simplified.

How Loud Are You?

Strictly speaking, “loud” is a matter of perception – the same pressure wave can result in different experiences of “loudness”.  However, this perception is tied to the intensity of the pressure wave, just as the perceived pitch of a sound is tied to the frequency of the wave.

wavy33b

A wave

Using the above image of a wave, the intensity is how high the peaks and how low the valley is – the higher the peak, the more intense the wave.  Another way to think of intensity is how much energy the wave carries – the taller the wave, the more energy (just like how bigger ocean waves hit harder than small ones).  Frequency, on the other hand, is how fast the wave moves – the closer together the peaks, the faster the wave moves and the higher the frequency.  Generally speaking, we perceive intensity as loudness (because the pressure wave hits the ear harder) and we perceive frequency as pitch (because the pressure wave stimulates the bones in the ear faster).

“Loudness” is measured in decibels (dB), because one decibel is the “just noticeable difference” in sound intensity for the human ear – assuming the pressure wave generated is in the 1,000 Hertz (Hz) to 5,000 Hz range we are best at hearing.  Every 10 dB represents multiplying the intensity of the pressure wave by 10 – that is, a 10 dB sound is 10 times more intense than a 0 dB sound, a 40 dB sound is 10,000 times more intense than a 0 dB sound, and a 100 dB sound is 10,000,000,000 times more intense than a 0 dB sound.

We generally can’t hear anything below 0 dB, and normally speak in the 60 to 65 dB range.  A jackhammer 50 feet away is about 95 dB, a power mower 3 feet away is around 107 dB, and loudness causes pain starting around 125 dB.  Sounds at 140 dB and greater can cause permanent damage with even short exposure.

How Far Away Can We Hear?

This gets tricky, because the answer is “no further than when the perceived volume falls to 0 dB”.  Tricky, because sound obeys the inverse square law which states that for any source power P generated at the center of a sphere, the intensity of at the surface of that sphere is P/4πr2 (although a good approximation is P/r2, since the math gets easier).  According to Hyperphysics, r is pretty much always measured in meters for these purposes (because sound intensity is actually measured in watts per meter squared, so it keeps the units the same).

Since sound intensity can be transformed into decibels, it’s really not a stretch to directly apply the inverse square law to decibel measurements.  So, a 60 decibel conversation would be perceived as 60 decibels at 1 meter away, 60/(2*2) = 15 decibels at 2 meters, 60/(3*3) = 6.6 decibels at 3 meters, 60/(4-4) = 3.75 decibels at 4 meters, less than 1 decibel at 8 meters, and so on.  Realistically, at this point, it’s probably safe to call it “inaudible” (even though you could technically detect it).

How Loud Would You Have To Be For Someone To Hear You In China?

All right, here’s where the math gets… entertaining.  I live in Cincinnati, Ohio, which is (according to Google) 10,969 kilometers from Beijing.  Measuring along the curved surface of the Earth, that is.  But, to keep things simple, we’ll ignore that.  So, 10,909 kilometers is 10,909,000 meters.  To be heard in Beijing, we’d have to generate enough decibels to result in a greater than 0 dB sound 10,909,000 meters away.

For laughs, let’s aim for a 60 dB sound.  That way, our sound can be clearly understood.  The radius is 10,969,000.  So, the equation looks like this:  x/10,969,0002 = 60.  Solving for x gives us x = 60(10,969,0002), or x = 7,219,137,660,000,000 dB.  This is a nonsensical level of perceived volume, and would render you deaf in ludicrously tiny fractions of a second.

What could generate that?  Well, we’d have to reverse engineer the decibels into watts of power, which converts to 721913765999988 watts per meter, or about 721.9 terawatts of power.  Now, you can roughly convert watts to Joules per second, so that’s roughly the explosion of a 200 kiloton nuclear weapon.

Assuming I did my math correctly, which I’m not guaranteeing.  What I can guarantee is that there is no way you’d want to be standing anywhere near something loud enough in Cincinnati that you can hear it in China.

Is It Medicine?

Recently, we were at our local “natural and health foods” store. While my wife shopped for a specific supplement she was advised to use, I got to ride herd on my energetic five year old as he roamed around the store looking at everything. He loved the posters over by the pet food section, one of which showed a lion with a lamb curled up against it. He thought that was amazing and cute. Nearby was an entire wall of homeopathic products, including an entire array of products for pets. My son stopped and looked at the boxes, then turned and looked at me.

“Is this all medicine?” he asked.

I didn’t really feel like tackling that subject right there in the store. Not in any detail, anyway. “No,” I said.

“Okay,” he answered, and then he was off to look at the selection of vegan, glutin free baked goods.

What is homeopathy?

According to the American Institute of Homeopathy:

Homeopathy, or Homeopathic Medicine, is the practice of medicine that embraces a holistic, natural approach to the treatment of the sick. Homeopathy is holistic because it treats the person as a whole, rather than focusing on a diseased part or a labeled sickness. Homeopathy is natural because its remedies are produced according to the U.S. FDA-recognized Homeopathic Pharmacopoeia of the United States from natural sources, whether vegetable, mineral, or animal in nature.

The website goes on to explain that there are three guiding principles of homeopathy:

  1. “Like cures like”. A principal that a symptom can be treated with a substance that causes a similar symptom.
  2. The minimum dose. From the AIH website, “Homeopathic medicines are prepared through a series of dilutions, at each step of which there is a vigorous agitation of the solution called succussion, until there is no detectible chemical substance left. As paradoxical as it may seem, the higher the dilution, when prepared in this dynamized way, the more potent the homeopathic remedy. Thereby is achieved the minimum dose which, none the less, has the maximum therapeutic effect with the fewest side effects.”
  3. The single remedy. Again, from the AIG website, “Most homeopathic practitioners prescribe one remedy at a time. The homeopathic remedy has been proved by itself, producing its own unique drug picture. That remedy is matched (prescribed) to the sick person having a similar picture. The results are observed, uncluttered by the confusion of effects that might be produced if more than one medicine were given at the same time.”

Is homeopathy medicine?

Merriam-Webster defines medicine as:

1 a: a substance or preparation used in treating disease
b: something that affects well-being

2 a: the science and art dealing with the maintenance of health and the prevention, alleviation, or cure of disease
b: the branch of medicine concerned with the nonsurgical treatment of disease

3: a substance (as a drug or potion) used to treat something other than disease

So. By some definitions of medicine it qualifies. Homeopaths are certainly involved in “the science and art dealing with the maintenance of health and the prevention, alleviation, or cure of disease” and homeopathic medicines are certainly “a substance or preparation used in treating disease”.

Does homeopathy work?

No.

Uhm… could you elaborate on that?

There’s no way it could work. Let’s take another look at that second principle of homeopathy, the minimum dose. The AIH states that “Homeopathic medicines are prepared through a series of dilutions, at each step of which there is a vigorous agitation of the solution called succussion, until there is no detectible chemical substance left.”

Here’s how the dilutions work, as explained by a FAQ from Boiron (described as a “world leader in homeopathic medicines”):

What does the “C” listed after the active ingredient stand for?

The most common type of dilutions is “C” dilutions (centesimal dilutions). The 1C is obtained by mixing 1 part of the Mother Tincture with 9 parts of ethanol in a new vial and then vigorously shaking the solution (succussion). The result is a 1/100 dilution of the plant (the Mother Tincture being a 1/10 dilution of the plant itself). The 2C is obtained by mixing 1 part of the 1C with 99 parts of ethanol in a new vial and succussing. Recurrently, the 3C is obtained by mixing 1 part of the 2C with 99 parts of ethanol in a new vial and succussing.

What does the “X” listed after the active ingredient stand for?
X dilutions are decimal dilutions prepared similarly to C dilutions, but the factor of dilution is only 1/10 from one dilution to the next.

What does the “K” listed after the active ingredient stand for?
The K refers to a method of manufacturing known as the Korsakovian method. The Korsakovian method dilutes the homeopathic preparation of the substance at the rate of 1 part of the previous dilution with 99 parts of solvent.

What does the “CK” listed after the active ingredient stand for?
Korsakovian dilutions are manufactured using a device specially designed to ensure that the dilution process is reproducible from one dilution to the next. Only one vial is used for the entire process. Using ultra-purified water as the solvent, the machine removes 99% of the Mother Tincture and replaces it with the same volume of solvent. The vial is succussed for 10.5 seconds. The result is called 1CK. The 2CK is prepared identically from the 1CK. The automatic process using only 1 vial allows higher dilutions to be reached. The most common Korsakovian dilutions are 200CK, 1,000CK (also called 1M), 10,000CK (10M), 50,000 CK (50M) and 100,000CK (100M or CM).

What does “200CK” mean?
200CK means that the substance has been homeopathically diluted 200 times at the rate of 1 to 100.

The dilutions on the medicines I looked at (I didn’t look at all of them) appear to range between 3C and 12C, counting by threes (3C, 6C, 9C, 12C), with one hitting 30C. Here’s what that looks like:

  • 3C: 1 part active ingredient to 9,999 parts solvent (100 parts per million, or PPM).
  • 6C: 1 part active ingredient to 9,999,999 parts solvent (0.1 PPM).
  • 9C: 1 part active ingredient to 9,999,999,999 parts solvent (0.0001 PPM).
  • 12C: 1 part active ingredient to 9,999,999,999,999 parts solvent (0.0000001 PPM).
  • 30C: 1 part active ingredient to 9,999,999,999,999,999,999,999,999,999,999 parts solvent (0.0000000000000000000000001 PPM)

For comparison, let’s talk about the US Environmental Protection Agency’s Maximum Containment Level Goals (MCLG), Maximum Contaminant Levels (MCL), and Maximum Residual Disinfectant Level Goals (MRDLG):

  • Maximum Contaminant Level Goal (MCLG) – The level of a contaminant in drinking water below which there is no known or expected risk to health. MCLGs allow for a margin of safety and are non-enforceable public health goals.
  • Maximum Contaminant Level (MCL) – The highest level of a contaminant that is allowed in drinking water. MCLs are set as close to MCLGs as feasible using the best available treatment technology and taking cost into consideration. MCLs are enforceable standards.
  • Maximum Residual Disinfectant Level Goal (MRDLG) – The level of a drinking water disinfectant below which there is no known or expected risk to health. MRDLGs do not reflect the benefits of the use of disinfectants to control microbial contaminants.

With that in mind, let’s have a look at the EPA Table of Regulated Drinking Water Contaminants. If you go and look at it yourself, bear in mind that the units are in milligrams per liter (mg/L), which is equivalent to PPM:

  • Chlorine has a MCL of 4 PPM (effectively 4 5C dilutions).
  • Arsenic has a MCL of 0.01 PPM (meaning a 7C dilution)
  • Cyanide has a MCL of 0.2 PPM (two doses of a 6C dilution).
  • Lead has a MCL of 0.015 PPM (one and a half doses of a 7C dilution).
  • Mercury has a MCL of 0.002 PPM (two doses of an 8C dilution).

By sheer logic, if the “like cures like” principal was correct and the minimum dose worked, then we’d be immune to eye/nose irritation and stomach discomfort (caused by chlorine), circulatory system problems (arsenic), nerve damage and thyroid problems (cyanide), developmental development issues and kidney problems (lead), and kidney damage (mercury).

Moles and atoms and molecules

Let’s put it a different way, and talk about moles.

mole6

No, not these guys

A mole is the SI unit of that measures the amount of a chemical substance that contains as many elementary entities (atoms, molecules, whatever) as there are atoms in 12 grams of carbon-12. This odd calculation is used because the number of atoms in 12 grams of carbon-12 happens to be the same as the Avogadro constant: 602,214,085,774,000,000,000,000.

Why is this important? Watch, and see.

A homeopathic “mother tincture” is 10% ingredient and 90% solvent, by weight. So a mother tincture of peppermint would be, say, 1 gram of peppermint oil and 9 grams of water. The active ingredient of peppermint oil is menthol (C10H20O), and water is H2O. Consulting the Lenntech molecular weight calculator, menthol has a weight of 156.26 grams per mole and water weighs 18.02 grams per mole. So one gram of menthol has 3,853,923,497,849,737,616,792 molecules of menthol, and one gram of water has 33,419,205,647,835,738,068,812 molecules of water. So the mother tincture has a total of 304,626,774,328,371,380,236,100 molecules, and is only 1.2% menthol by quantity of atoms (despite being 10% menthol by weight).

A 1C dilution takes 1 gram of the mother solution and mixes that with 99 grams of water, giving us 100 grams of dilution with a total of 3,338,964,036,568,570,000,000,000 molecules, of which 385,392,349,784,973,000,000 are menthol.  That makes it 0.0115% menthol at this point.  Each dilution after that reduces the number of menthol atoms by a factor of 100, until at a 12C dilution you get 3.85 atoms (let’s be optimistic and call it 4).  So, at a 13C dilution, you quite literally have nothing but water.

Homeopathic-Dilutions_thumb18-621x210

Bear in mind that this is the case with a relatively simple molecule like menthol.  Most of the “active ingredients” in homeopathic dilutions are far more complex – according to Chemical composition, olfactory evaluation and antioxidant effects of essential oil from Mentha x piperita, for example, the components of peppermint essential oils were “menthol (40.7%) and menthone (23.4%). Further components were (+/-)-menthyl acetate, 1,8-cineole, limonene, beta-pinene and beta-caryophyllene”.  This reduces the number of atoms per gram of each ingredient, causing the atoms of each chemical that make up the ingredient to go away faster (although in the case of the peppermint essential oils, menthone’s molecular weight is 154.25 grams per mole, so you’d end up with about 2 atoms each of menthol and menthone at a 12C dilution).

So, is homeopathy medicine?  Only in a strict and narrow definition, because it is used to treat illnesses.  After all, the definition we looked at above doesn’t say the medicine has to work.  And it really doesn’t work.