Deep Thoughts on Infinity

Formula for why the sum of all natural numbers is not -1/12
from the blog, "Data Bonanza" 

Are all infinities equal? Why? Why can't some infinities be larger than other infinities? Why do I ponder this?

Why? And who cares, right?

But … stay with me now — there are infinite numbers between 0 and 1 (e.g., 0.01, 0.0025, 0.00968, etc.), with at least the same numbers (perhaps double or triple or more?) between 0 and 2. Right? And so forth and so on, ad infinitum, each infinity with more numbers than the ones before. So doesn't it stand to reason that some infinities are larger than other infinities?

And yet, whenever you add to, subtract from, multiply, divide, or raise or lower any number to the infinite power, the answer is ALWAYS infinity.

How come I’m thinking about this? Well … because my 6-year-old grandson who’s in the first grade brought it up during a conversation. First grade. Imagine that. And he helped me formulate the “Larger Infinity Hypothesis.” Amazing kid.

Ponder that. My brain is too small for all of this.

~ Inspired by my grandson, and something

Hazel Grace Lancaster said in the

film, The Fault in Our Stars

The Double Bubble Passenger Jet

According to the designers at the Massachusetts Institute of Technology, who took advantage of a multi-million dollar NASA grant, this is what you may be flying in 2035:

That's a mere 20 years from now, and the "Double Bubble," as it's been labeled, is expected to use 70% less fuel than a Boeing 737. Plus, it will emit much less nitrogen-oxide, the culprit that causes acid rain. Good thing too, because air travel is expected to double over the next two decades.

The Double Bubble will carry 180 passengers at an airspeed of 433 mph, about 10% slower than a 737. Slower, yes, but not by much. And ooooh, the fuel savings!

Double Bubble ... It ain't no chewing gum.

I read this in Popular Science in the doctor's office waiting room. Sometimes it pays to have a long wait to see the doc.

Coqui Frogs vs Little Fire Ants

First, it was the coqui (Eleutherodactylus coqui Thomas), those little frogs that found their way here from Puerto Rico about 35 years ago.

Those blasted toadies were blamed for wreaking havoc on Hawaii’s insect population, on which Hawaii’s own insects and spiders subsist.

It started on the Big Island, then spread to Oahu, and most recently, to Kauai. The State of Hawaii is attempting to control them with citric acid (y’know, vitamin C).

Although the State of Hawaii has categorized them as an “injurious species,” there’s actually a website in support of the coqui – KillerCulture.com – that advocates leaving the frogs alone. Did you know there was an International Save the Frog Day (April 29, 2011)? Well, try recruiting the Hawaii residents who are kept up all night with their incessant and loud “co-kwee” chirping during mating season.

So that’s one pest that’s back in the news lately. Why?

Because the news media needs to augment its stories about another invasive species, the Little Fire Ant (Wasmannia autopunctata). They’re called “little” for a reason – they are about half the size of a sesame seed (1.5 mm in length).

The second part of their name, “fire,” comes from the pain of their sting, with welts often lasting for weeks. As infesters of agricultural fields and farms, damage crops (chew chew) and they sting agricultural workers.

They are under control on Kauai, but not on the Big Island. And now, they have been found on Oahu, inadvertently spread by the shipment of nursery plants. The Hawaii Ant Lab (www.littlefireants.com) has a bunch of “how-to” guides that tell you all about these little buggers and how to deal with them.

Okay … so there are frogs and ants. Frogs eat insects. Ants are insects. Ants sting frogs.

I have an idea: Let’s get the Coqui and the Little Fire Ants to make war on each other. It would be interesting to see which will prevail. Will the frogs eat up all the ants? Or will the ants sting the frogs to hell and back? The numbers of whichever emerges the winner will be decimated and easier for us to control.

The enemy of our enemy is our friend.

A second thought: Maybe they already are at war. Maybe that’s why the frogs have lumpy skin from their encounters … o O ( Okay, that’s enough. Stop it, Craig.)

Popcorn Rock: Day 21 (The End)

Well, I think this is the end. This is what the Popcorn Rock project looked like yesterday on Day 21. Not too much different from Day 17, so I’ve decided to end the experiment.

All in all, it was okay. A bit of a disappointment, though, I must say, because I expected something a little more spectacular. Was I doing something wrong? Or did I just get ahold of a wimp Dolomite?

No matter. It was interesting to watch the Aragonite crystals form, and indeed the big mass on the tip of the rock does look like popcorn. In my opinion, it was a success. Not the best I’d expected, but good enough, and that’s pretty rare for me to say that.

Normally, “good enough” is not good enough. But what the hell, huh?

Popcorn Rock: Day 17

There’s not much different since I showed you the popcorn rock project three days ago, but there is some additional crystallization starting to appear. That “bathroom ring” is getting much thicker; hey maybe it’ll expand so much it’ll join up with the aragonite crystals coming out of the dolomite rock?

Whatcha think?

Actually, I think it’s pretty much as developed as it’s going to be. I’ll keep an eye on it and if anything exciting happens further, I’ll let you know.

Popcorn Rock: Day 14

Well, it’s now been two weeks since I began the Popcorn Rock project, and there’s quite a bit of popcorn (albeit yellow) atop the dolomite rock that I soaked in vinegar.

It’s not a real pretty sight. Actually, the nicest crystals have always been the newest ones that pop out from the rock. Then they join up with each other and turn the color of coffee-stained teeth.

What’s really been interesting is the aragonite precipitate that’s clustering about the sides of the bowl. They’re actually starting to grow, like stalagmites.

I’m thinking that by the time this is all done, I might have bowl covered in the white stuff. That wouldn’t be half bad, would it?

Popcorn Rock: Day 11

Eleven days since the dawn of the Miyamoto Popcorn Rock experiment began, there’s some significant change under way.

The Vinegar Lake is fast disappearing; it seems the evaporation has picked up its pace. One result of this is the bowl’s inside surface has accumulated quite a bit of what looks like a bathtub soap ring. I presume it’s precipitate that was suspended in the liquid and after floating on the surface, found its way to the inside surface.

That nice formation that was forming at the tip of the rock has kind of morphed into a yellowish couple of globs of marshmallows. But the good news is that other aragonite crystals are emerging from the dolomite.

The lake itself is quite shallow now, maybe three-quarters of an inch deep. The bottom is full of sediment and rock crud, and the acrid vinegar smell seems to be intensifying.

Wonder how much longer I have to wait for it to become beautiful. I’m getting impatient.

Popcorn Rock: Day 7

My Popcorn Rock Adventure is now in its seventh day. This is where a dolomite rock immersed in a Vinegar Lake is slowly turning into aragonite crystals. Things are moving along nicely, albeit rather slowly:

 

The rock has been shedding some crud, so the vinegar lake is turning a bit brown at the bottom. The rock itself looks pretty neat (about an inch is exposed to air now) and the popcorn is growing.

The aroma/odor/smell is getting more and more overpowering by the day. Just standing there and taking a picture initiates coughing. I can only imagine it must be like working in a pickle or wasabi factory.

I’m thinking about investing in some clothespins for my nose.

Popcorn Rock: Day 4

The “Dolomite into Aragonite” geology science project (aka the “Popcorn Rock Adventure”) is now in its fourth day, and it’s beginning to show results. See?

 

There be crystals! They’re starting to form at the peak of the mountain, where about a half-inch of the rock has emerged from the Vinegar Lake. And it looks as though there are more just itching to burst forth when the lake evaporates even further.

Nobody pauses very long at the back door now. Hanging around there can be hazardous to one’s decorum. One whiff of the strong evaporating vinegar and the coughing and sneezing begin.

But hey! Nobody said discovery is painless, right?

Popcorn Rock: Day 2

My Popcorn Rock adventure is well underway as I try to form Aragonite crystals from a dolomite I drowned in white vinegar yesterday.

The first thing I noticed on Day 2 was that some tiny foam-like bubbles were coming out of the Popcorn Rock and amassing on the surface of Vinegar Lake, right smack dab in the center. And, the rock surface is beginning to sport white spots. See?

The second thing I noticed was that the Popcorn Rock Vinegar Lake bowl was directly in line with the warm air exhaust of our bedroom window air conditioner. Every time we stepped next to it and opened or closed the back screen door, you could smell vinegar.

It’s as though someone had left a plate of pickles there. Funny I didn’t notice it until afterwards, huh?

Still, there is some progress.

Pickle smell or not, it’s still the best place for Popcorn Rock to bathe in Vinegar Lake. So I ain’t moving it. Unless the rest of the family presents a signed petition threatening to kick me out of the house. Then, I’ll consider moving the project closer to my reading chair.

But then, I’d smell it when I’m lazing and messing with my iPad, so maybe that’s not an option either.

If anything exciting happens in the next 24 hours, I'll update again tomorrow. If not, we'll wait a couple of days. Okay?

Popcorn Rock: Day 1

I’m finally getting around to doing something I’d planned to do in February 2012. Hey, that’s almost a year and a half ago! Seventeen months!

I’d taken a two-day road trip to St. George, Utah, during Super Bowl weekend. My primary purpose was to see Zion National Park, which I would do on Day 2. On the day I arrived, after checking into my motel room and having lunch, I drove over to the Dinosaur Discovery Site and spent an hour or so wandering around the place.

As I usually do when I visit educational sites and museums, I stopped by the gift shop and spotted something I just had to have:

 

Yep. A “Popcorn Rock.” It’s actually a dolomite that produces Aragonite crystals when it’s immersed in white vinegar. Something that changes into something else? Heck, that’s for me!

Well, wouldn’t you know it, I didn’t have the appropriate bowl to begin my experiment, so for the next few weeks (whenever I remembered to do it), I shopped for a nice bowl that could not only help me sprout the popcorn crystals, but display it with some class as well.

Okay, so I found a good bowl a few months later. But you know how these things work … I kept the rock in its bag in the bowl in the kitchen and it promptly got buried under some stuff. Until recently. And that’s when I figured if I’m going to do this at all, I’d better get started.

What to do and how to do it? Here, you read for yourself:

 

I nestled the rock in the bowl, and covered it with white vinegar:

I'll post updates as the project progresses. Grow, popcorn, grow!