What Would Happen If The Sun Blew Up?

“Daddy,” my son asked, “what would happen if the sun blew up?”

This was one of those questions he decided to ask out of nowhere. Maybe it was inspired by Star Wars, maybe not. “Well, we’d all die,” I said. Because it’s, you know, the truth.

“Well, what if the Earth had a force field that protected it? Then people could live on and on!”

I shrugged my shoulders at that. “I don’t know.”

Grim.

Maybe. It’s an interesting question, though.

Sure. So, what would happen if the sun blew up?

A whole lot of astrophysicists would be really confused before they died.

I’ll bite. Why?

Because our sun is, according to everything we know, really, really unlikely to explode. It’s too small.

Really?

Yes. See, all stars begin their lives molecular clouds of (mostly) hydrogen that collapse under the influence of gravity to form a protostar. I discussed this in detail way back on 2016 in How Do They Build A Planet?, if you want more details. But, in brief, the molecular cloud becomes denser and denser until gravity causes the hydrogen to begin fusing together. This generates a lot of energy and helium. According to NASA the sun fuses about 600 million tons of hydrogen per second or, put differently, about the Earth’s mass in hydrogen every 70,000 years. Our sun has been doing this for about 5 billion years (meaning it’s fused about 71,000 Earths worth of hydrogen), and will keep doing it for about 5 billion more years.

In about 5 billion years, once the hydrogen has all fused into helium, the sun’s core will contract until pressure and temperature grows great enough to start fusing helium into carbon. This will cause the sun to expand into a red dwarf, becoming large enough to potentially swallow the Earth (and even if it doesn’t, drag from the solar atmosphere will slow our planet down until it no longer can maintain orbital velocity, at which point it will fall into the swollen red star that once gave it life. Unless the expansion sends us sailing off into deep space, that is).

All right. So why can’t our Sun explode?

Again, it’s not big enough. Stars massing eight times the mass of the sun and smaller, as their core collapses after all of the helium has fused into carbon, can’t generate enough temperature and pressure to start fusing carbon. These stars, which obviously include our Sun, end their lives as white dwarf stars.

Bigger stars continue fusing the heavier elements with the residual helium in the core to form other elements. Over about 100,000 years, the carbon fuses with helium to make oxygen. Then, over the course of about 10,000 years, the oxygen fuses with helium to make neon, which fuses with helium to make magnesium, which then fuses with helium to make silicon. From there, over the course of about 24 hours, the silicon fuses with helium to make sulfur, which fuses with helium to make argon, which fuses with helium to make calcium, which fuses with helium to make titanium, which fuses with helium to make chromium, which fuses with helium to make iron, which does not fuse  – not at any temperature or pressure a star can generate, at least.

At this point, the rapid (remember, all of this took 24 hours) core collapse stops cold. This causes a shockwave that blasts out through the core of iron and the shells of silicon, oxygen, neon, carbon, helium and hydrogen in a massive explosion called a supernova.

And what happens during a supernova?

There are roughly five stages to a supernova, and we’ve already seen stage one: the 24 hour core collapse as the star races towards making iron. Stage two is the shockwave I mentioned. Over the next few hours the shockwave rebounds outwards through the various shells, compressing and heating them and generating light (which moves faster than the physical shockwave). At stage three the star actually explodes, blasting the surface material out at abut 50 million kilometers per hour. Stage four is the superheated expanding surface of the star, glowing bright enough that (for a short period of time at least) it may actually be brighter in the sky than the galaxy that contains it. And then, at stage five, you have molecular cloud expanding away from the surviving core, which may be a neutron star or even a black hole.

Just for fun, what would happen to us if our sun did supernova? Right now?

That’s an… interesting definition of fun. Still, let’s go with it.

Let’s assume that this all starts at 7:22 am Eastern time on June 11, 2018, and that we’re accelerating the process at a rate of 1,000,000 years equals a day. The Sun would rapidly expand into a red giant, and stay that way until 7:22 am Eastern time on October 9, 2018. Then the core would begin to collapse. At 9:46 am Eastern time, all of the helium would have burned into carbon. Then, 24 seconds after 10:00 am Eastern time, the carbon would have burned into oxygen. At 25.64 esconds after 10 am Estern time, the supernova would begin.

The speed of light is 299,792,458 meters per second, so we’d see the supernova at approximately 44.6 seconds after 10:08 am Eastern time, and it is the very last thing we’d ever see. The neutrinos accompanying the flash of light would kill every human being on earth. Then, at 56.6 seconds after 12:59 am Eastern time, the expanding outer shells of the exploding Sun would smash into our planet. Nobody would be around to see it.

Uhm…

But cheer up! The question assumed we could build a force field to protect ourselves! Next time, we’ll see what would happen if we live!

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How does your brain freeze?

Last summer, my son and I went out for ice cream. It’s something I probably shouldn’t do, since I’m trying to lose weight, but I really love the stuff. So I justified it to myself as an exercise in teaching the concept of “moderation in all things” (really! It was!) and we had ice cream cones. And being 6 (at the time), he ate it really fast. “Brain freeze!” he declared shortly thereafter.

“Press your tongue against the roof of your mouth,” I tell him. Why? Uhm… mostly because my mom told me to do that when you was his age. So I passed it on, even though it really never seems to help. I mean, my mom taught it to me so it must help. Right?

I don’t know if he actually tried. But a minute later, he asks a question: “How does your brain freeze?”

“It doesn’t, really,” I tell him, feeling confident in my answer.

“Then why is it called a brain freeze?” he replied.

Say it with me, everyone: “I… don’t know.”

What is “brain freeze”?

I did a little reading on the subject, and most sources I found were in agreement with the information from the article “Brain freeze: The science behind ice cream headache” on Medical News Today. “Brain freeze” is also known colloquially as “ice cream headache” (the name I always used as a kid) and more formally as “cold stimulus headache” or “sphenopalatine ganglioneuralgia”.

That’s great, but what is it?

Interestingly, up until 2012, nobody really knew. That’s when one Dr. Jorge Serrador did some research trying to deliberately cause ice cream headaches in volunteers. The results were published in “Cerebral Vascular Blood Flow Changes During ‘Brain Freeze’”, and here’s what the abstract says about it:

Using transcranial Doppler, we evaluated cerebral blood flow velocity (CBFV) in the middle (MCA) and anterior (ACA) cerebral arteries in 13 healthy adults while consuming ice and ambient water. Subjects drank ice water through a straw against the palate until pain developed. CBFV, heart rate, and blood pressure were analyzed, before pain, during pain and after pain.

Consumption of ice water produced a tendency towards increased cerebral flow velocity in the ACA (P=0.078) but not the MCA (P=0.24). Ice water also resulted in greater cerebrovascular resistance during the experimentally induced “brain freeze” when compared to following ambient water consumption.

Our results support a vascular mechanism for brain freeze. Ice water consumption resulted in a significantly greater cerebrovascular resistance as compared to that during ambient water consumption. However, the fact that cerebral flow increased during pain along with increases in blood pressure may suggest autoregulation was not as effective. Supported by NASA and NIH.

Which means?

I couldn’t find the full article to check my interpretation, but Medical News Today and Wikipedia agree that it’s something along the lines of how sinus pressure can cause tooth pain. See, your mouth is full of nerves, and signals can ‘leak’ from one nerve to another (citation: my orthodontist when I was 14 and wearing braces). So the cold liquid or solid you consume causes the blood vessels in the roof of your mouth to construct rapidly. Since this happens rapidly, it causes something called “referred pain“, as the signals telling your brain that your mouth is freezing are carried by the trigeminal nerve, which also happens to sense facial pain. As a result, you feel like you have a headache.

And does that tongue thing your mother recommended actually work?

That’s a definite “maybe”. Most articles recommend gently warming the mouth as a way to deal with the headache, so pressing the underside of your tongue to the roof of your mouth might work – it’ll be based on how much ice cream you ate. Other suggestions include breathing in warm air and placing your hands over your nose and mouth and breathing through your mouth.

Personally, the only cure I’ve ever really found is waiting it out. Or more ice cream, and accepting that you’re just delaying onset.

Interestingly, Wikipedia also states that “Cats and other animals have been observed experiencing a similar reaction when presented with a similar stimulus.” So don’t let your cat gobble down his ice cream too fast.

What’s A Whippersnapper?

Sometimes I just don’t know where these things come from. Case in point. Recently, my son has been using the word “whippersnapper”. I don’t know why. I don’t recall running into it in a book (whether we’ve read it to him or he’s read it to himself), and I don’t remember hearing it on any of the shows he watches. But, there it is. Whippersnapper. And one day, as we were piling out of the car and he’s been using the word in a song he’s been making up, he asks the fateful question. “What’s a whippersnapper?”

“It’s an old word some people used to use to refer to children,” my wife says. Or maybe I said it. Honestly, it’s been just long enough that I don’t remember.

“Oh,” he says. “Why?”

Go on. Why?

Yeah. I got nothing.

Pretty short article, then.

Well, let’s start with the actual definition of a whippersnapper. Maybe that will help. Merriam-Webster defines it as “a diminutive, insignificant, or presumptuous person”, and then indicate that the first known use was CE 1700. So I can see why it was used in an insulting fashion in all the books I’ve seen it in. It is an insult.

Then again, maybe it would be more correct to describe it as condescending than insulting. The Oxford Dictionaries define it as “a young and inexperienced person considered to be presumptuous or overconfident”. Meanwhile, Vocabulary.com defines it as “someone who is younger than you are but also irritatingly overconfident and impertinent, like your little smart aleck  cousin”. Based on that definition, I’d describe it as a versatile word that can be insulting, condescending, or both. Vocal tone is a magnificent thing, after all.

Still, that’s a weird word. Where did it come from?

Good question. The Online Etymology Dictionary tells us the following about the word:

whipper-snapper (n.)

also whippersnapper, 1670s, apparently a “jingling extension” [OED] of *whip-snapper “a cracker of whips,” or perhaps an alteration of snipper-snapper (1580s). Compare also late 16c. whipperginnie, a term of abuse for a woman.

So that’s clear as mud. Right? Although that “jingling extension” suggests an origin as a dismissive way of describing an annoying little thing that makes a lot of noise and isn’t particularly necessary. That’s entirely my speculation, but I feel good about it.

Whipper… ginnie?

That one’s really obscure. The various online dictionaries I normally use failed me entirely, because when they referenced it at all they just mentioned it as a feminine variant of whippersnapper. the only real clue I found was a Quora article titled Maritime Piracy: What does the phrase “Crack the Jenny’s daughter” mean in Caribbean pirate lingo? Near the end of the article, we get this paragraph:

Nor do the definitions of jenny that I have seen. It may be a reference to the itching or spinning jenny, which coarse slang meant a vagina in the 19th century and if so crack means, among other things, to deflower. At various times jenny has also meant a donkey, a young woman, a hot-water bottle and a housebreaker’s tool (a variant on the more commonly used jemmy). There is also whipperginnie, which was an old word for a woman (apparently based on a card-game known as ‘whip her jenny’). Jenny can also be an abbreviation of standard English engine (thus the mechanical spinning jenny, invented by James Hargreaves in 1764, which helped revolutionize weaving in factories), and specifically a generator (but neither were exactly central to pirate world). And none of them naturally have a ‘daughter’, of whatever the variety.

It’s tempting to try to relate “whipperginnie” to the spinning jenny, in the same way that wooden shoes (sabots) became associated with people who broke industrial equipment as a form of protest. But the relationship with the card game “whip her jenny” makes more sense.  Sadly, I couldn’t find the rules for that game anywhere, so I have no idea what the context is.  I suspect though, based on the slang meaning of “jenny” described in the quote, that whipperginnie had a fairly obscene meaning – much like a certain modern four-letter word, starting with c, that is used to refer to ‘uppity’ women today.

So let’s not go and use it now.  All right?

Why Don’t The Girls Have Antlers?

Two days ago, on Christmas Eve, I was watching Rudolph the Red-Nosed Reindeer with my son. He loves the song and the movie. Me, I love the song. But as a movie it’s kind of a genuine nightmare when you watch it as an adult. But I’ll digress a lot if I pursue that train of thought, so I’ll get back on track now.

We’re watching Rudolph, and we’re eating popcorn, and we’ve just gotten to the part where Rudolph goes to the Reindeer Games but not quite to the point where Santa tells Donner he should be ashamed of himself for siring a freak. My son looks at the screen for a moment, then looks at me quizzically. “Why don’ tthe girls have antlers?”

“Huh?” I ask.

“Only the boys have antlers,” he says, pointing at the screen. Sure enough, the young male reindeer have antler nubs and the adult males have antlers, but there aren’t any on the females of any age. “Why don’t the girls have them?”

“I… don’t know,” I tell him. “I’m pretty sure that girl reindeer have antlers in real life.”

“That’s not fair,” he tells me. “They should have them in the show as well.”

Do female reindeer have antlers?

This, it turns out, is one of those questions that is really simple to answer. Yes. They do.

Care to elaborate?

Sure. A Google search took me to the website of the San Diego Zoo – specifically to their page on Reindeer, or Rangifer tarandus. Both male and female reindeer, according to the zoo, grow antlers.

Males begin to grow antlers in February and females in May. They both finish growing their antlers at the same time but shed their antlers at different times of the year. A male drops his in November, leaving him without antlers until the following spring, while female reindeer keep their antlers through the winter until their calves are born in May. This fact has led many to believe that, based on the presence of antlers, Rudolph the red-nosed reindeer must have been a female to have those antlers on Christmas Eve!

Wait. Rudolph is a girl?

A woman actually, if you want to use a term like that.  Now, based on the script of the Rankin/Bass movie from 1964, Rudolph was born “a couple of years before the big snow”, and went to the Reindeer Games when she (he, as the script misgenders her) was a year old.  Female reindeer reach the age of maturity at four years old, and you’d probably need an adult or near-adult reindeer to help pull a sleigh, so Rudolph would have been three to four years old by the time she returned to find her parents missing, and probably about 6 months older when the “big snow” hit (since Rudolph was born in the springtime, according to the narrator). And since it’s rude to refer to an adult female as a “girl”, let’s go with “woman” if you want to anthropomorphize her or “female” if you don’t.

Here’s where things get a little confusing.  See, the Reindeer Games take place in the spring, which starts around March 20.  As a result, it appears that Rudolph is a boy – like the other boys he’s growing his antlers, the adult males have their antlers, and none of the females have begun to grow them at all.  And these antlers are probably her (his?) second set, since the Reindeer Owners and Breeders Association states that young reindeer “have already grown their first set of ‘Rudolph’ antlers” by the age of 4 months, by which age they weigh around 90 pounds.

[b]That’s not what I meant. Rudolph is female?[/b]

Well, yeah.  The majority of the evidence still points towards Rudolph being female, along with the rest of Santa’s sled team.  See, as described above, “a male drops his [antlers] in November, leaving him without antlers until the following spring…”. Now, here’s Santa’s sled team from the show:

It’s the night of December 24 in that picture, and the reindeer have antlers. Only female reindeer have antlers in December. Therefore, Santa’s sled team are all female – including Rudolph.  Unless the same genetic alterations that caused Rudolph’s nose to glow also caused him to retain his antlers longer than ordinary male reindeer.  In that case he’d still be male and the only male on Santa’s sled team.  But I find that unlikely – given how Santa and the other reindeer shunned and mocked her for having the glowing nose, they’d probably have mocked and shamed her out for having “girl antlers” as well, if she was actually male.

So, why don’t the female reindeer have antlers in the show?

I’m going to go with a mix of 1960s sexism, and the fact that you probably shouldn’t draw your lessons about anatomy from a stop-motion animation program.

Will President Trump Be On Money?

My son earns his allowance by doing chores. Each night he checks them off on a magnetic board, and then each Saturday we tally up how many chores he’s done, and he gets his cash. At this point he has to divide it up into three categories – “give”, “spend”, and “save”. “Give” is money he gives to charity (such as when he bought canned food for a food drive), “save” is money he is saving to buy a large toy, and ‘spend” is money he can just take when we go shopping and use to buy anything he wants. The idea is, obviously, to get him used to the idea of savings and giving to charity now while he’s young.

This time, he’s looking at the faces on the money (coins and dollar bills), and for the first time he’s asking quesitons about who the people on the money are. I’m explaining that, for the most part, they’re presidents. he thinks about that, and thinks about some things he heard at dinner last night, and considers the money he’s holding carefully. “Dad,” he finally asks, “will President Trump be on money?”

“Son,” I say, “I have no idea.”

Will he?

That’s an interesting question. The short answer, of course, is “not right now.”

Why not?

It’s against the law.

United States Code, Title 31, Section 5114(b) states that:

United States currency has the inscription “In God We Trust” in a place the Secretary decides is appropriate. Only the portrait of a deceased individual may appear on United States currency and securities. The name of the individual shall be inscribed below the portrait.

So, unless the law is changed, as of the date this article is published he doesn’t meet the legal requirements. President Trump is, after all, still very much alive.

How about after he dies?

In that case, it’s up to either the Congress or the Secretary of the Treasury. Under the question “Why were certain individuals chose to be pictured on our paper currency?” in the US Department of the Treasury Resource Center, we learn that:

As with our nation’s coinage, the Secretary of the Treasury usually selects the designs shown on United States currency. Unless specified by an Act of Congress, the Secretary generally has the final approval. This is done with the advice of Bureau of Engraving and Printing (BEP) officials.

The law prohibits portraits of living persons from appearing on Government Securities. Therefore, the portraits on our currency notes are of deceased persons whose places in history the American people know well.

The basic face and back designs of all denominations of our paper currency in circulation today were selected in 1928, although they were modified to improve security against counterfeiting starting in 1996. A committee appointed to study such matters made those choices. The only exception is the reverse design of the one-dollar bill. Unfortunately, however, our records do not suggest why certain Presidents and statesmen were chosen for specific denominations.

This is expanded on in the Second Legal Tender Act, also sometimes referred to as the “July 11, 1862 Act of Congress”  Section 2 of that act states:

And be it further enacted, That the Secretary of the Treasury be, and is hereby, authorized, in case he shall think it inexpedient to procure said notes, or any part thereof, to be engraved and printed by contract, to cause the said notes, or any part thereof, to be engraved, printed, and executed, in such form as he shall prescribe, at the Treasury Department in Washington, and under his direction; and he is hereby empowered to purchase and provide all the machinery and materials, and to employ such persons and appoint such officers as may be necessary for this purpose.

The line “in such form as he shall prescribe” is what gives the Secretary of the Treasury his (or her, although so far a woman has not served as Secretary of the Treasury) the power to decide who goes on US currency. This is a power granted to the Secretary by the US Congress, however, as Section 8 of the Constitution of the United States specifically grants the Congress the power “To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures”. They don’t tend to get involved with who is on money very frequently, but they have passed legislation specifying the design of coins. Nothing’s stopping them from doing it with paper money, as well.

With all that in mind,will Trump be on our money?

Possibly.

The portraits that currently appear on US paper currency were determined in 1929 and, despite an attempt to put Harriet Tubman on the $20 bill, they haven’t changed since that time. The youngest president to appear on US paper currency is Woodrow Wilson, and he died in 1924. I’m not expecting to see any changes any time soon. But paper currency isn’t the only form of currency out there. There’s also coins.

31 U.S. Code § 5112 governs “Denominations, specifications, and design of coins”. It covers quite a bit of territory and includes subsection (n) “Redesign and Issuance of Circulating $1 Coins Honoring Each of the Presidents of the United States”. Starting in 2007, $1 coins have been issued with the likeness of presidents – four each year, in order of presidential service. The law specifies that only dead presidents may be on the coins and that, once all of the dead presidents have been represented on the law will terminate and the coin design will revert to the “Sacajawea” dollar coin. The last president to appear on one of these coins was Ronald Reagan, on a coin issued in 2016.

That section of 31 U.S. Code § 5112 is now null and void, having served it’s purpose. But a similar law could be passed again and, if President Trump is dead by that time, he would qualify.

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.

Why Was The United States Underwater?

Several months ago, I wrote about the fossil my son found and what it most likely was. What I didn’t talk about in either article was the trip we took to the Trammel Fossil Park here on the north side of Cincinnati. It’s really just the exposed rocky side of a hill, with signs posting the various stratigraphic layers so you know where you’re looking and other signs showing you the fossils you’re likely to find at each level. There’s no cost to go, and you’re allowed to keep any fossil-bearing stones you find that you care to haul down the hill and back to your car. I found some brachiopods.

My son was extremely disappointed with the trip, at least for the first ten or fifteen minutes we were there. We’d told him we were going fossil hunting, after all, and he wanted to find a Tyrannosaurus rex skeleton. Which, lets be honest, would have been extremely unlikely even if the park had exposed strata from the Albian. But he was six at the time, and he wanted a dinosaur. So I reminded him that the layers we were looking at were from an ocean, because Ohio was underwater at the time.

I don’t think he asked today’s question at that point, but it helped inspire it. Because, eventually, he asked me this: “Why was the United States underwater?”

Well? Why?

Uhm. Something to do with plate tectonics, I guess? And maybe changes in climate?

Can you do better than that?

Of course I can. This’d be a pretty lame blog post, otherwise.

What are plate tectonics?

That’s a great question, and to understand it we’ll need to cover the structure of the Earth itself. The Earth is comprised of multiple layers, rather like an onion. These layers are the:

  • Lithosphere: the outermost rocky shell of a rocky planet (our own, for instance).
  • Asthenosphere: the hot, viscous layer that the lithosphere floats on.
  • Mesosphere (or mantle). Geologists have an explanation for why this is distinct from the asthenosphere and the outer core, and it has something to do with temperature and pressure causing one type of mineral to decompose into another type of mineral. I didn’t quite follow the explanation, and I think I’ll save trying to understand it for the day when my son asks “what is the mesosphere?”
  • Outer Core, a sea of liquid iron and nickel.
  • Inner Core, an extremely hot ball of (mostly) iron and nickel kept solid by pressure.

The lithosphere is the layer we live on – the high parts are the continents and the lower parts are covered with water. And it isn’t a solid shell. It’s broken up into (depending on who you ask and the definitions they use) seven or eight major tectonic plates and a bunch of minor ones. And the plates move.

Why do they move?

The tectonic plates move because the Earth is hot.

Let’s start with an analogy. When you boil water, you get an uneven distribution of heat Heat rises, after all, but the source of the heat is at the bottom. So the hot water rises and the cool water sinks. But then the hot water at the surface cools and sinks, and the cool water at the bottom heats up and rises. This gives rise to something called convection currents. this effect isn’t limited to water, though. All liquids do it – our atmosphere, for instance (which functions a lot like a liquid).

The Earth, when you get below the lithosphere, is pretty much a liquid as well. The mesosphere has convection currents in it, and the tectonic plates can be thought of as the “cool water” part of the current in the boiling water analogy. Magma pushes up from the mesosphere into the lithosphere at the Ocean Ridge (a planet-circling chain of mid-ocean ridges), pushing and expanding the plates. The plates then sink back down towards the mesosphere at subduction zones. These currents also push around the solid chunks of the lithosphere, in much the same way that ice cubes floating in boiling water will be pushed and shoved around.

Now, even the “minor” tectonic plates are massive structures. So, when they get moving, there’s a lot of force built up. When they collide, something has to give. And frequently, what gives is the structure of the plate itself – it will buckle and crumple, throwing up mountain ranges and pushing parts of the plate below sea level. If water, in the form of the oceans, gets access to that portion of the plate below sea level, it will begin to fill the depression. That’s what happened in the theorized Zanclean Deluge, for instance. 5.33 million years ago, the Mediterranean was a depression in the Eurasian plate (bordered by the African and Arabian plates) that was below sea level. It had been a sea previously, until shifting plates cut off access to the Atlantic and the waters dried out. Then the plates shifted further, access to the Atlantic reopened, and the basin refilled in a period of approximately 2 years (with water gushing in at a flow rate 1,000 times greater than that of the Amazon River).

So. Plate tectonics is the answer?

Not completely.

Really? What else is there?

There’s changing climates. See, the Earth was – on average – a whole lot warmer back before the continents had moved into the form we’d recognize today. At present, our average global temperature is about 60 degrees Fahrenheit. During the Paleocene-Eocene Thermal Maximum (55-56 million years ago) the average got up to about 73 degrees F – there were no ice caps at the poles then, and there were palm trees and crocodiles above the attic circle.

Now, estimates are that if the ice caps melted then global sea levels would rise about 70 meters. So that’s not really enough to make an ocean out of (say) the Great Plains, although it would completely reshape the coast and drown Houston and New Orleans. But since the plates were buckled differently back then, the extra water would have increased the odds of flooding taking place.

But, ultimately, North America being underwater had far more to do with plate tectonics than changes in climate.

Oh, as a bonus, the Paleomap Project has a series of great maps of the Earth in different geologic epochs. Here’s what the Earth looked like during the age of the dinosaurs:

Yep.  It was a different world, back then.