What hump?

Al Denelsbeck

Today marks the day we’ve all been waiting for, and by “we” I mean those of us in the northern hemisphere who don’t like the axial tilt of the planet. Yes, today is the day the days no longer day get shorter; from here on out the days will be getting longer. No, that’s not true at all, the days are the same length as always – it’s simply that the time period of the sunlit portions will be increasing over the non-sunlit portions. Dance in the streets, it’s the winter solstice!

It’s also the first day of winter, which shows that things just aren’t as orderly as a mathematician would have planned, since the solstice should fall in the middle of the season, shouldn’t it? Or there be no such thing in the first place. But anyway, this encroaching season is apparent right now by it being 20°c (70°f) outside as I type this. Brrr!

Green lynx spider on rosemaryAnyway, in days gone by I’ve recognized this barely-noticeable event by going back to see what I was photographing during the summer solstice, finding that I had no digital images (the only ones with dependable date stamps) from those particular days anyway – I don’t take photos every day, though some people I know have a hard time believing this. So this time around, I just decided to see what I could find today.

At left, one of the green lynx spider pups (Peucetia viridans) that I’ve been keeping an eye on, this one on the rosemary again, one of many. This is pretty much how they’re found every time, since this isn’t the season for huge amounts of activity; apparently they plod through the winter on little sustenance, perhaps whittling away at their stores of fly jerky.

But before long I discovered an old friend, if by friend you think of a species that has bitten both The Girlfriend and I for no good reason (you tend to make definitions work for you when you’re desperate.) Along a fencepost wandered an animated patch of lichen, and astute naturalist that I am, I can inform you that lichen is not particularly known for perambulation in the absence of gravitationally-animated stones. Therefore, something was up under the surface. With the skill of long experience, I captured it without harm to it or myself, though at times this was touch-and-go, and brought it in to photograph in a little more control on a sprig of cypress.

GathersNoStone
Having cats in the house, hairs frequently have to be removed from macro scenes, but in this case they’re part of the insect’s handiwork. Tarsiwork. Whatever. This is the larva of some species of green lacewing fly, family Chrysopidae, which camouflages itself with whatever debris it can find and forages as a ambulatory junkheap, much like some cars I have driven. The actual material used is not always moss – most times I’ve seen molted exoskeletons from other species, sometimes leaf litter, and in one case an artfully posed dead ant (this was probably a Viking subspecies.) Getting a good look at the insect itself takes particular angles and a bit of luck and/or patience. Below my model peeks out from under its mask, perhaps hoping for a kiss from Mary Jane (no, that’s not a drug reference, but a Spider-Man one… look, just… never mind.)

lacewing peering out
lacewing undersideThese insects were the subject of my first “Too cool” post, and I’ve encountered them many times since. If you look closely at the above image, against the bright green leaf to the right of the head, you’ll see a few threads poking out from under the toupee, and these are actually part of the anatomy, also vaguely visible in the image at right, sprouting from a stalk at its shoulder. Also visible is the high-contrast coloration, which has me puzzled, since the insect goes to great effort to completely cover this. Perhaps it is useful at some other point in the life cycle, or maybe it’s just vestigial remnants from previous species on the evolutionary tree; other current species of lacewing do not actively disguise themselves at all, and some have mottled patterns while others hide in sand traps as ant lion larva and remain unseen for most of their juvenile stage. Or maybe, and I wonder if this idea has been carefully considered by entomologists, the coloration is the reason why lacewing nymphs cover themselves with debris, like teenagers who wear a heavy coat to try and conceal the ugly sweater from grandma that they’re made to wear. It’s the right age, after all – this could be the insects’ Grunge Phase. I think I’m onto something here.

Some time back, both out of curiosity and for a presentation I was working on, I TSA’d another that I’d found and got some images in all its naked g[l]ory, showing off the elaborate structures it grows solely, I believe, to support this camouflage. You should appreciate this (money’s fine,) since these insects are perhaps 6mm long and the appendages are delicate, so removing the debris took careful work with some small tools. The things a nature photographer does…

lacewing without camouflage
The camouflage isn’t so much a mystery now at all, is it? I’d cover up too if I looked like that, instead of being the devastatingly handsome specimen that I am. A suspicion is growing, and I now want to go back and see if there’s any evidence of this species existing before we started nuclear testing. Though neither The Girlfriend or I have displayed any superpowers since being bitten, so maybe I’m barking up the wrong tree. Interesting, though, is considering this from an evolutionary standpoint, since these appendages are pretty specialized and need to be augmented by behavior as well, to actually place the camouflage, while it seems much easier to just evolve protective coloration like most species do. Then again, the teenager hypothesis gains another point in its favor, since they always have to do things the hard way…

And while this wasn’t the original intention, this image goes nicely with the post title as an additional meaning – I’m clever as well as stunning. It’s homage, of course, to Young Frankenstein. But you already knew that – people so lacking in class as to be unfamiliar with every line from that film surely wouldn’t be visiting this site…

Odd memories, part 12

Al Denelsbeck

christmas lights & wine bottleSpurred on by this post from The Bloggess, who is a delightfully warped person, I dredged up some memories of christmases past. Part of the reason I don’t put a lot of effort into holidays is not, as some clueless people seem to think, from being an atheist, but from growing up in my family. Holidays tended to be overly tense affairs from the belief that things should be traditional, or include certain dishes at mealtime, and should be perfect, and all that hoohah – no small number of people will recognize this, I’m sure. Think of the bride and her mother on the wedding day, then dial it back a bit.

It did not help that my mother, who carried approximately a kilogram of pure uncut coupons in her purse at all times, could not write down christmas lists and carry them with her when shopping, and her memory is of the ‘broad category’ type. My brother wanted a model kit of a Datsun 280Z one year (this was a while ago) and received a Porsche 924 instead – they both had numbers, and that was how she had remembered. I soon learned to take her around the stores and point to exactly what I wanted, which largely worked, but I still got unwanted Atari cartridges because, “I knew you wanted a racing game,” which was true, but a specific racing game. Ah well.

She compounded this as well, in never making a list for herself and almost always claiming she didn’t need anything, making shopping for her a monumental chore (she still does this, by the way.) I was, however, responsible for contributing to her own bitterness over the holidays once. That year, there was a particular perfume she wanted, a rarity, since she generally did not like perfumes. It was called “Lily of the Valley,” and she told me exactly where it could be found – just inside the door of a particular drugstore, with white lilies all over the box. Thus armed, I set out and got her present. Come christmas morning, however, it was revealed that I had gotten the wrong one, disappointing her greatly, especially since she’d been so specific.

Now, in my defense, I had (and have) no idea what a lily looks like, and the display featured not a word or name of the perfume at all – but it sat covered with white flowers just inside the door of the goddamn drugstore. Between her sighting and my shopping, perhaps about a week, the staff had switched displays, I can only assume on purpose. It also must be said that when my mother returned, the perfume was nowhere to be found in the store anyway.

Various places that I’ve worked since then have done the Secret Santa thing, generally an ill-advised system anywhere. Depending on the size and how busy the workplace is, one often has no opportunity to find out what anyone might want for christmas, and rarely ever socializes with coworkers outside of the workplace; if you have it differently, lucky you – don’t believe it’s like that everywhere. On occasion I would have an idea what someone might want, but did not ever draw their name, so that never worked out. I have always been in administration, so my coworkers tended to think I wanted office supplies, despite the fact that I frequently had my camera with me…

One year, when I drew one woman’s name, I recruited another worker to find out what she actually wanted. This worked well; I was told about a particular little blown glass elephant, with a blown glass mouse inside, and exactly where it could be found locally. The other bit of info I received was helpful too: It seems each year my giftee had received a candle during the Secret Santa fol-de-rol (see what I mean?) and had remarked on this curious trait.

At the same time, another coworker, who had briefly been an actress, had let it slip that she’d been in a movie with Chuck Norris, but refused to reveal which one – this tidbit had come about because my giftee had house-sat recently for the actress and had seen an autographed photo of Norris with the actress. Naturally, such secrets are fed on ravenously in most workplaces, and a quest began to determine which movie she’d been in.

“I know it was a western-style movie,” said my giftee while trying to pump the actress for more info, “because he was wearing a cowboy hat.”

I snorted. “I don’t think that means much, since he wears a cowboy hat in every movie,” I said. “I think he was wearing one in Invasion USA, which took place in Florida.” It was one of the few Chuck Norris movies I’d seen, and mostly regretted.

Credit to the actress and her skills, because she didn’t bat an eye at this, and I’d been watching. Once she was gone, several workers announced their intention to find out which movie, plotting delightedly. This was in the very early days of the internet, and few people had access, or indeed a computer. I just picked up the phone and called my cousin in his comp sci graduate office. In less than a minute, the Internet Movie Database had confirmed that our coworker had indeed been in Invasion USA. With christmas rolling around, it was imperative that we locate a copy of the VHS tape to rent.

This proved to be harder than imagined – most video stores had discarded the cassette long ago. Finally, through a confederacy of conspirators, we located the movie, and I sat down with it the day of the christmas party to find her appearance in the film. Fast-forwarding through Invasion USA doesn’t make it any better, and I went through the movie twice before finding her fifteen seconds – there was a horrifying moment when I suspected she was one of the topless dancers in a bar, but then found her part, cued up the tape, and took it with me to the party.

In the meantime, I’d been busy on my Secret Santa thing as well. Going to a cheap drugstore, I located the cheesiest damn christmas candle I could find, this ugly little spherical thing badly made up to look like Santa Claus. I dutifully wrapped and tagged this, but also placed the blown-glass elephant in a plain box simply marked “Mystery Box” – I had given up cursive decades before, but used it (slowly and ineptly) to mark the box so my handwriting would not be recognized. Once at the party, I sneaked this onto the gift table so no one would see who brought it.

When the exchange came around, my giftee had the greatest “I told you so” look on her face when she unwrapped the candle, showing it to my informant wryly. Then she saw the attached tag, which said that she could exchange the candle for the Mystery Box. What was completely unexpected was how bad she dithered over this decision, trying to find out who had done this so she could quiz them over the box. Someone eventually clued her in that it was me, and she pleaded with me to know what was there – she was reluctant to give up that ugly candle. I refused to bargain, telling her I was going to have to take one of them back either way (the candle had cost me a dollar, and was way overpriced at that.) She eventually convinced herself to go for the box, and was exceptionally pleased with the elephant, showing it off to everyone. And then turned to me: “But can I still keep the candle?”

After the exchange, the boss (who I’d let in on the plot) announced that we had a special holiday video to watch, and with everyone’s attention, started the tape. People were a little confused, since it started in mid-movie during a car chase, but in literally two seconds our coworker actress recognized the scene and shrieked, covering her face in her hands. This produced a bare second of further confusion before she appeared onscreen to pummel the villain ineffectually, and the place erupted in laughter. You gotta love it when a plot comes to fruition.

Spurred by The Bloggess’ post, I’ve been trying to figure out my best and worst christmas presents, without a lot of luck. But while I’m at it, I have to give credit to my brothers, who had their own fun one christmas eve. I was to receive a GI Joe ‘Secret of the Mummy’s Tomb’ adventure set, featuring the same ATV that would carry Joe facefirst into the couch, and they set the whole thing up on the edge of the couch (foreshadowing or something) in full action pose, winching the mummy up over the edge. It was, in fact, this set:

There was also one christmas, at the time when I was no longer waking up in excitement at that hour, that Santa himself, jollier than anyone should be at 2 AM, woke us all up and herded us downstairs to receive our presents. Almost all of us, anyway – my brother couldn’t be convinced, but he was likely hungover (I was probably 16, my brother 23 at this point, and mind you I was the youngest.) Also, curiously, my dad didn’t come down either until, with dismal timing, a few minutes after Santa left (some of us did indeed wonder why Santa departed upstairs instead of through the door or, you know, up the chimney of the fireplace that was right there.) This is what you get when your dad is asked to play Santa for the office party, and is permitted to borrow the costume afterward…

Many years later, having moved out-of-state and finding myself with a significant amount of money come christmastime, I deigned to a) fly home during the holiday season, and b) go north in the winter – I said I had money, not sense. While shopping for gifts with my mom, I selected a particular board game for my two young nieces, one that my mother argued would be too young for them. It was called Splat!, and was your typical game where you roll dice, draw cards, race your Play-Doh insect playing pieces to the finish line, and occasionally stomp the hell out of the pieces with a giant plastic hand (that left them squished out broadly with the game’s logo impressed upon them.) When this happened to you, you scraped up your Play-Doh from the playing board, reincarnated your bug in the mold while uttering a little hindu prayer, and started again from the beginning. As might already be apparent from other posts, I have never fully grown up, and I suspected this would be an interesting game.

Now, those of you who have played Uno among family members are well aware of what I’m talking about, when I say that there are games that provoke a lot of ire without anyone really getting upset – that plastic hand was the same as a well-timed ‘Draw Four’ card. Almost frightening was my then-brother-in-law, the girls’ father, who demonstrated his conscientious role-model attitude by wielding that hand with unholy glee every time the game play selected him – this was later to reappear in his daughters’ therapy. He had also, in his delicate youth, learned how to roll dice, something I’d discovered earlier during AD&D sessions. So when it finally came time for us to raise plastic hand over his own playing piece, the Play-Doh smears went across most of the board and occasionally a good stretch of table. If my mother still has that table, I’m willing to bet a close inspection will reveal evidence of that christmas afternoon tournament 20 years ago…

I’m guessing that the worst present I received was a book from my parents, What Color is Your Parachute?, about finding a career. Gifts from unobservant coworkers are at least somewhat expected, but messages of that nature should probably be left for some other time, you know? Meanwhile, one of the unintentionally funniest gifts was from The Girlfriend, who had located a speaking South Park stein for me – press the button and hear a bit of wisdom from Eric Cartman. She’s never been good at interpreting Cartman’s speech, especially from the early days, and even when she gave it to me still didn’t know the gift was emitting, “I’m not fat – I’m big-boned!”
Sound clip courtesy of Hark.com 
The stein, it must be said, was stuffed with Almond Joy candy bars…

Best gift? I have to admit christmas almost always makes me think of the Millennium Falcon model kit I got one year – it’s the kind of thing you hope for, big and cool, coming at an age when you can appreciate it most because you’ll never be able to buy it for yourself. It was the original issue that came with lights, and I did that bad boy justice, not just painting it in detail but adding battle damage and a plethora of fiber-optics (scrounged from one of those color-changing hippie lamps that had just fallen from popularity) to add running lights in various locations as well.

Yet, The Girlfriend is someone who gift shops at least half of the year, and is very good about noting when someone wants/needs something; at the same time, she can spot clever, interesting, or novelty gifts. So item for item, she’s got everyone beat by a mile. I try, but I don’t have the same knack. We’ll see, however, how well I did this year.

Anyway, kick back, go mellow, let the rants from neurotic relatives wash over you if you have to, and remember what the holidays are, truly, all about:

Weird stories.

Stupid atheists

Al Denelsbeck

Jon Rosenberg at Scenes From A Multiverse is picking at scabs (click for complete version):
SFAMThe-Good-Pope
This… is totes uncalled for! Atheists are level-headed, fair, well-adjusted individuals, and none of them would ever get cranky because a favorite whipping boy turned respectable.

Good thing he hasn’t, then…

Actually, and it’s stupid that I even have to say this yet it’ll be news to some, but atheists are as varied as any other group (except Apple users,) and while I haven’t actually seen an example of this behavior myself, I’m sure it exists. Others, meanwhile, are pleased that the new pope is much more mellow than the previous one, and still others (ahem) shrug and don’t really care, since the whole edifice is one huge joke. But I’d love to hear some of the e-mails of protest Rosenberg receives anyway.

If you’re not going to Scenes From A Multiverse regularly, I am most disappointed in you, because I’ve directed you there before and now I know you’re mocking me like a rebellious teen (which is redundant, true.) It’s like Family Circus Without Family Circus, which is to say nothing at all like Family Circus – Rosenberg is actually clever and original, and puts a lot of effort into his drawing. Even when he stoops to cheap shots…

Too cool, part 21

Al Denelsbeck

Unicorn Reentry
So, what is it?

I’ve had this experiment in the back of my head for a while now, and tried it last night. What you’re seeing here is Sirius, otherwise known as the Dog Star or the Dog’s Nose, and the brightest star in the sky. As a quick aside, for some reason many people think Polaris, or the North Star, is supposed to be the brightest, which would be handy but is far from the case. Also, there are brighter things in the sky at night, but they’re not stars. This distinction sometimes annoys people, but it’s worth noting, because planets are much closer and move separately from the starfield, so are in different positions each night – in fact, they change position throughout.

Part of the reason Sirius looks like this is because I panned the camera on the tripod during the one-second exposure – you can see where it began on the right side, and also that the panning was not Hollywood smooth. But the other reason is much cooler, because you’re looking at ‘twinkling.’ It really is this distinct and this fast.

Astronomers refer to this as seeing – no, this doesn’t mean just looking at something, but the atmospheric conditions that may degrade the ability to, um, see a stellar object; “the seeing is particular bad tonight.” Seriously, astronomers, get another word, it’ll save confusion – I’ll make up a few for you if you like. Because you did this, every time someone wants to talk about astronomy they have to switch to words like “view” and “observe” to avoid confusion with the technical term. Sheesh.

Now, if you (the rest of my readers, all two of them) used the term scintillation, I can’t blame you – I did too, initially, but technically, this only refers to changes in luminance (which is indeed visible here) but not to the diffraction effect that produces all the colors. Or so some sources say; it appears numerous astronomers use it to mean the color change as well, so chances are you’re not going to look like a boob if you use it this way.

What’s fun is, there’s a lot of disagreement on what’s actually happening. They all agree that it’s the air, specifically different densities and the turbulence between layers. However, some sources, including Wikipedia, state that the atmosphere splits the light into separate wavelengths from diffraction, like a prism does, but the brightness change comes from just one rod in our eyes (it should be cone anyway) receiving the light, but it wanders across different rods/cones, shifting position slightly in our eyes. That’s nonsense too, because a camera lens is much wider than a human eye and receives light from its entire front surface, focusing (recombining) it all back down to the single point on the sensor/film – the effect would be averaged out and the twinkle would vanish. We can’t even suppose that this comes from single color pixels in the sensor receiving light and no others, since a) the image is wider than a single pixel, and b) there are a lot more colors than the three in the sensor.

So the diffraction seen here is very real, and falls in a broader area – wider, at least, that the camera front element, which is roughly 73mm. But one effect very likely is due to the camera, and that’s the places where the light simply vanishes. There are two possibilities that come to mind: 1) that the light was simply dimmed or diffused enough to prevent adequate exposure in the tiny fraction of time that area of the sensor was exposed while the camera was panning, or 2) that the diffraction actually passed into the infra-red or ultra-violet which the sensor could not detect. Possibly both, though I lean towards the former because Sirius never seemed to blink out when observing it by eye, and we can’t see IR or UV either. That reasoning, however, is still in question because of the image below.

DontBlinkThis is an LED christmas light, also taken by panning during a one-second exposure. Alternating current causes all lights to blink, and since LEDs don’t use a filament, they go out immediately rather than fading – you cannot detect this visually, but it’s revealed with a simple camera trick. If you try it with a phone camera you’ll probably get something even weirder, but that’s because phone cameras are goofy. Anyway, Sirius really could go completely black to our eyes, if it does it fast enough (see those gaps in the top image again,) and we might never know it.

More than a few UFO reports involve things that change color rapidly, which supposedly are not stars because “they don’t change color that much.” Uh huh. Or, “It was bigger than that.” But go out on a clear night and take a good look – Sirius, Vega, Spica, and others all look larger because they’re significantly brighter – this isn’t something I’m able to demonstrate easily because, in the camera, they will be larger, but that’s due to flare from the lens. And yes, it’s possible that the eye’s lens produces flare too, though this is a little hard to prove (let me remove yours for a few hours and we’ll run some tests.) At some point, I’ll shoot both Venus and Sirius at the same magnification and demonstrate how much larger Venus actually is, even though many observers would say Sirius is at least the same size.

Anyway, it’s a cool effect, and maybe later on I’ll try it with a cluster like Pleiades. In the meantime, I’ll refer you back to a previous ‘Too Cool’ post on the Horsehead Nebula, and a recent Astronomy Picture of the Day which places it in reference to Orion’s Belt and Cellphone – it would have been nice if this was available when I was composing that post.

I could just tell you…

Al Denelsbeck

Stego
… but it’s better if you find it on your own.

North Carolina doesn’t really see ‘winter’ as many people imagine it – honestly, it’s pretty boring – but we do get cold spells from time to time, and went through one a few days back, after some heavy rains. Things that had collected water were frozen over, and in some cases nearly solid, so I took the opportunity to play around a little.

Above, what you’re seeing is… well, it’s hard to explain. On the underside of the thick surface ice in an old bucket were several thin blades of ice extending down into the water in these curious shapes. This particular image is of the removed ice, inverted and backlit by the sun at an angle that accentuated the contrast (and likely includes a certain level of polarization, if I’m interpreting it correctly.) Usually, I can look at some natural phenomenon like this and reason out what physics were at work, but these have eluded me. I wondered about different layers of water, with varying contamination or salinity perhaps, and these blades marked the levels between them, but that made no sense because they should have been parallel to the top surface. Ice had started down the inner sides of the bucket, close to freezing completely solid, but these blades weren’t parallel to the sides either. Worse, a couple of nice straight lines of them converged, laying over at different angles, completely trashing any ideas that they were dictated by the shape of the bucket or different qualities of the water.

IDontGetItEither
The biggest clue, perhaps, is the bubble tracks nearby also follow the same angle, so my current guess is it had something to do with the ice expanding as it thickened, but that’s as far as I’ve gotten.

Conformity
Bubble trails in ice aren’t too hard to comprehend. Gases (primarily oxygen and nitrogen) that release their bonds with water as the temperature and pressure change rise to the surface, but may be trapped under the ice. As they ice extends downwards, it forms around the bubble and eventually encapsulates it – the vertical expansion is what draws it out into elongated tubes as seen here. But it’s not always vertical, and some bubble trails form at odd angles to others, presumably due to differential expansion rates, though why this takes place I couldn’t say. In most of the cases I’ve photographed, leaves were present in the water and may have contributed to temperature differences; there’s also the possibility of residual heat from the sun having warmed one side of the vessels, or the wind causing greater cooling.

IceShapes
But then there’s this. This is a broken section of ice seen from the edge, a cross-section. The air bubbles are self-evident, but the shapes surrounding them? The appearance is of liquid water surrounding the gas bubbles and enclosed by ice, and my inclination is to see this as greenhouse heating, sunlight that penetrates the ice and warms the gases faster than the ice, but some of this heat is shed into the surrounding water and melts it. This doesn’t explain the flattened tops and bottoms of those channels (the tops I could see, since the air bubble might press against the flat underside of the initial ice layer,) so I’ll just leave it as, “damn if I know.”

I’ll close with another frost pic. This looks largely the same as previous images because that’s really all I’ve seen here so far; the conditions haven’t been right for much more than this, and almost every leaf in the immediate area is exactly the same, thanks to the oak tree that dominates the back yard. I admit to not dragging myself out at dawn to go down to the river for more variety – if someone wants better frost photos enough to pay for them, I can be motivated, but not for my own stock ;-). So I just go for the occasional attempt at an interesting approach, where I can go back inside to warm up easily.

HoarShards

Perpetually confusing

Al Denelsbeck

Infinity is this curious concept, wide open for misinterpretation, but even in its refined sense, it often suffers from one of the biggest problems of philosophy: we believe that since we’ve put a lot of effort into it, it must be important.

To explain the most misunderstood aspect of it, I’m going to steal brazenly from an article in Science ’82, a now-defunct magazine that I cannot refer back to and may have even mistitled (since the title relied on the year of the issue’s publication.) The article included a simple illustration: a cloud of dots disappearing over the horizon labeled, “Infinite number of dots.” Next to it, a long box disappearing over the horizon labeled, “Box the dots came in.” And next to that, a semi-truck also disappearing labeled, “Truck the box came in.” This is a graphic illustration (okay, it’s a text description of a graphic illustration) of Georg Cantor’s Set Theory.

Isn’t that simple? Infinite does not mean, “everything,” it simply means “without end.” It can be constrained in other manners, such as height and width, yet still be infinite depth. And because of this, the box and the truck both have infinite volume even though one can fit inside the other.

Another example is to think of a line. It passes in front of you, but extends to infinity in both directions. Fine. Now imagine removing a one-centimeter segment from the line, right in front of you. What you have done is create two lines, both infinite. The one-centimeter gap between the latter two lines is not, despite our instincts with finite lengths, “infinity minus one centimeter.” Initially, I had said here that, “You cannot subtract from infinity,” but as Set Theory and the non-illustration above implies, yes, you can. Just reduce the height of the box. Will it still hold all the dots? Sure, just put the overflow down at the other end…

Now, let’s have some fun. I propose a number: 0.[infinite number of zeros]1, or if that’s confusing, perhaps we’ll use the ~ symbol to fill in for an unending string, rendered 0.000~1. Is this even possible? How can you put a 1 on the end of a string of zeros that never reaches an end? It’s a nonsense number!

But not quite. It’s what you’d add to 0.999~ to get the sum of 1. Wasn’t that easy?

Since, of course, you cannot add a number onto the end when there’s no end, this is supposed to be the mathematical ‘proof’ that 0.999~ is equal to 1. It is also expressed by the idea that 1 divided by 3 produces 0.333~, multiplied times 3 again gives 0.999~. I simply find it mathematical proof that mathematics is an abstract, and trying to make it define logic is stupid. The issue is not with 0.999~ actually equaling 1, making an infinite series actually end, it’s with trying to use a Base 10 numbering system to represent certain discrete concepts, like division by 3. If we use other numbering systems, like Base 3 or Base 9, we have no issues with it at all, though it may introduce other interesting examples of infinite fractions.

As another example of the flaw, we can refer to a basic logic/math puzzle, where one travels half the distance to a goal, then half the remaining distance, and so on – the goal is never reached because one never travels the entire distance to it. However, if you travel 90% of the distance, then 90% of that, and so on, you’re supposed to reach the goal, according to the 0.999~=1 crowd. Yeah, right.

Want a fun mind bender? Take those lines we messed with above, with the centimeter gap in between. Those lines do have an end, but just one each. So we place the 1 on that end, and extend the infinite line of zeros backwards towards the decimal point: 0.~0001 instead of 0.000~1. I’m willing to bet someone would call that cheating in some way, but it’s the same as taking a piece of super elastic just a meter long and grasping both ends close together, leaving a half-loop of elastic drooping between. Now, take that loop, which represents all the zeros between the decimal and the 1 on either end, and stretch it away from you infinitely.

We haven’t pissed off the mathematicians enough yet, because we haven’t gotten to the real heart of the matter, which is that all of it is just word games. Regardless of how specific you want to make a number, or properties you want to apply to a concept, we reach a very real limit in attempting to use this in any application at all, for instance to measure the smallest object or distance. Even if we ignore the difficulties with clumsy rulers made of a real substance, eventually we reach the sub-atomic level where everything becomes a haze of energy anyway, without distinct boundaries and hard enough to simply pin down a position. At this level, it has become clear that ‘solid’ (and perhaps even ‘matter’) is a term we can only use within a specific set of circumstances – coincidentally, the one we inhabit every day.

Infinity is, in fact, a meaningless abstract. We have no actual examples of it, anywhere, and no real use for it. It’s easy to say that numbers are infinite – we can keep counting forever. But, we actually can’t. Ignoring for the moment that we’re going to die before reaching 11,352,960,000, or that the sun is going to fry the planet at some point in the future, there’s also the very simple fact that we start repeating once we pass a mere ten digits. It’s not infinite; it’s just a pattern. The pattern even gets so unwieldy and boring that we start using shortcuts, like 3×1018.

From time to time, someone says, “It’s an infinite universe; anything is possible.” I’ve even said such things myself (probably elsewhere in this blog.) But it’s not necessarily true. Any of the infinite lines, above, will never cross themselves, even in a curved universe – though in such a case they may form a circle. And if the universe really does run by the laws of physics we know, neither infinity nor eternity will allow certain things to happen, such as heat transferring from a colder (less active) to a hotter (more active) atom, increasing their difference in reverse entropy.

Here’s another example that often sparks confusion and debate. Quantum mechanics tells us subatomic particles can occasionally play silly games and thumb their noses at standard physics, jumping to a position far from their original location, even through other objects. And if one can do it, then there’s a tiny chance that every particle of the billions upon billions in your bobblehead of Quentin Tarantino [I know that’s redundant] will all leap in exactly the same direction at the same time and teleport instantly from your desk into Madonna’s hope chest. The chances of this are, of course, somewhat small, but in an infinite universe, there is an infinite number of chances for reiteration, right? So not only is it guaranteed to happen, it already has, someplace. That’s how the reasoning goes, anyway.

But this ignores numerous factors. For one, the probabilities that we determine for quantum foolishness are based only on our observations, which even if wholly accurate, does not mean such events are typical, or unrestricted by other factors we have not yet discovered. As the universe expands, energy becomes more dissipated, so probabilities on what it is capable of doing constantly change. And then there’s the possibility that any given event is a singular thing, never to repeat again – it’s impossible to calculate a probability for that, and even impossible for us to know that it was singular.

And, how do we know that the universe is infinite? We don’t. We simply haven’t found any edges or constraints, but have found lots of space, a truly staggering amount really (by law, I am obligated to include the word “vast” here.) In every direction we point our telescopes, we find much the same conditions, indicating no border or limitation – we do not, for instance, see stars no further than 100 million light years if we look off in that direction (no, not there; there,) which might indicate the edge of the expanding matter from the Big Bang. But since the universe has been expanding, according to our best estimates, for 13.8 billion years, this is enough time to develop quite a waistline.

What might we expect an ‘edge’ to be like? Well, it could be one of three things. It could reflect back any energy that reaches it, like a mirror. It could absorb and collect any energy that reaches it, like a wall. Or it could simply absorb such energy and vanish it, like, um… we don’t know of anything that can do that, actually. The first would mean that the energy from the earliest stars would bounce back once it reached the edge, probably provoking more star formation at the outer rim and certainly reflecting a lot of light. The second would mean much the same, since the ‘matter’ thereof would gain so much energy it glowed, if not actually producing a collapsing force in itself – an explosion turned inside-out. The third is, really, identical to empty space anyway, so the point is academic. No matter what, however, any potential edge is so far away from us that there’s no chance we could possibly reach it, nor even that any effect that it had could reach us. It could even be made of pepperoni pizza, but if it’s expanding faster than light there’s no way we could even see it.

And that is really what defines infinity for us puny humans: so big we can’t fathom it and have no use for it. It’s fun to speculate about how it works and whether it can actually exist, but there’s really nothing more to it than semantics.

Listen to that voice

Al Denelsbeck

GibbousMoons
For some unknown reason, I have a desire to capture sunrise on Tycho, the prominent rayed crater on the moon. Since it’s unlikely I’ll be able to afford a trip there anytime soon, I’ve been pursuing this remotely, but what it means is capturing a particular phase of the moon at just the right time. Shown above, we have the moon from yesterday evening and tonight, showing the advancement of the phase in about 30 hours. I’ve remarked before, moon observations are usually much more interesting in any phase but full, since the oblique angle of the sunlight makes the rough terrain stand out better, throwing shadows that define details starkly. Note how different things look along the terminator, the shadow line, between the two images.

Now here’s the same image with some guide marks:
GibbousMoonsINdexed
‘A’ is Tycho, though in the blue-sky image all you can see is the barest edge of the crater; a day later it’s fully defined. Don’t confuse it with ‘B,’ which is Maginus; well-defined in the earlier shot, it has reduced to a subtle outline in a day. Below that, invisible the day before, sits Clavius, where the moon base is.

Tycho has a large central peak, a strange artifact of large impacts, and my goal is to photograph it just as the sun is illuminating this peak, a bright spot in the darkness of the surrounding crater floor still in shadow. In the first image, the sun is only shining on the edge of the crater, but 30 hours later, it has advanced far enough that the peak is no longer throwing a shadow that I can discern with my longest lens.

Lunar days are 29.5 Earth days long, so sunrise takes a while but, obviously, the gap between my two photos was too much. Yesterday as I looked at the images I’d taken, I told myself I should go out a few hours later, not long before the moon set, and see what I captured then. Yet I ignored that voice, when it now seems likely that I could have captured just that image. One part of my brain is currently gloating “I told you so,” while the other part is muttering petty insults in return.

Anyway, there are still a few details that show nicely between the two. The small but deep crater that appears on the terminator of the latter image is Copernicus, sitting near the end of the curved mountain range known as the Lunar Appenines, much better defined in the earlier image. Towards the top, visible in both, is the crater Plato.

The sharply defined dark region at upper center, the one bisected by a brighter line, is Mare Serenitatis, or the Sea of Serenity. The brighter line is a ray from the crater right at the lower edge of the Mare, Menelaus. While the ray appears to continue out of sight towards the top of the moon, it actually intersects a ray from Thale crater at the upper edge, which cannot quite be made out in these images – it is, however, responsible for that bright region at top.

A quick bit of trivia while I’m on the subject. There is an account from 1178 of five monks that observed a peculiar effect on the crescent moon, the tip splitting into two and giving off “sparks.” For a while, it was suspected that the monks had witnessed the creation of the Giordano Bruno crater (not visible from earth – it was found by orbiters.) But recently it was determined that this was very unlikely; not only is the crater much older than that, the effect would likely have looked entirely different from what they described, and it would have resulted in a week-long meteor shower on earth. Any of those craters showing rays would have produced enough ejecta to escape the moon’s gravity and be captured by our own. I would dearly love for this to happen sometime in my lifetime.

You can use Google Earth to examine detailed images of the moon (look for the Saturn icon,) including some great videos from surveying satellites, but it’s also a little tricky. First off, all images are taken during ‘local noon’ which is a rotten way to define craters, making them hard to match up to images like this. Worse is the distortion that occurs as you zoom in, rolling details away and out of sight over the horizon quickly – the only time the proportions match what you see in my images is when the moon is zoomed as far away as possible. But check it out anyway.

Meanwhile, we’ll see what happens next month as daybreak on Tycho rolls around again…
GibbousMoonLarge

It’s a tad humid

Al Denelsbeck

DecemberDiamondback
I got out the camera to chase a particular subject, which disappeared on me, so while the strobe was still charged I decided not to waste that electricity and went looking for something else to photograph. Yeah, I really do think that way sometimes, though if I do find another subject, I’ll fire off a lot more frames (and flashes) than if I simply discharged the capacitor before putting the strobe away. However, the power didn’t go to waste, so calculate that any way that works for you.

Above, an angular spittlebug (Lepyronia angulifera) relies on its camouflage, in vain, while waiting out the recent saturating rains on the rosemary bush. You’re looking down on top of the head from the nose-end of the insect, and just behind the antennae you can make out the compound eyes breaking pattern, one of which sports a raindrop at its rear corner. The insect would look almost exactly like a new bud, except rosemary doesn’t grow that way.

I had initially identified this an a diamondback spittlebug (Lepyronia quadrangularis,) a variety of leafhopper, but now believe I was wrong, based on the slope of the head. Curiously, the images on BugGuide.net that convinced me of this were taken by my photographer friend back when he lived in this area – should have known he’d have images of the species. This was the only angle I could manage, and the specimen catapulted away when I tried to nudge it into a different position, so here are a couple of images of one from earlier this year, to give a better idea of the shape.

DiamondbackSpittlebug1

DiamondbackSpittlebug2
shortshooterDo you get the impression that their exoskeleton is good at repelling water? It’s actually incredibly good – they coat themselves with an internally-produced substance called brochosomes, microscopic soccer balls that exploit water’s surface tension to prevent adhesion. Definitely check out that article, because it also talks about why leafhoppers, alone among so many insect classes, should do this; it’s the lack of toilets.

Earlier this year I featured a post on sharpshooters, leafhoppers that fling their feces away without even the benefit of hands, making them the envy of most monkeys. But not every member of the Cicadoidea has a bowel-cannon, though most may have equally sticky excrement. To prevent coating themselves with their own copiously-produced ka-ka, they kryptonite themselves first with brochosomes – we have to wash our hands after communing with nature, but they have to wash their entire bodies before (you are welcome to use that to convince your kids they have it easy, if you think it’ll help.) Yes, this means they are one species which can brag that their shit doesn’t stick.

One could ask why wouldn’t they have feces that isn’t sticky? If they have to produce a completely separate substance that then has to be applied manually to their external surfaces, wouldn’t it have been more efficient to, perhaps, produce feces in the same manner as the brochosomes? But this is a perspective that almost assumes planning, which is entirely the wrong way of viewing it. Evolution often involves repurposing an existing trait or function. Numerous species exude one substance or another to protect their exoskeleton, skin, or feathers, often requiring it to be distributed by ‘instinct,’ and many insects already have habits to clean themselves of dirt, oils, or parasites; it’s not a huge jump to combining and/or changing these two traits for leafhoppers. The alternative is to change their digestive structure so the feces comes out in different form – for leafhoppers, their digestion is remarkably quick, since they pull very little from the sap as nutrition, expelling the rest. A system that changed the expelled sap so distinctly would not only slow down this process, it would take energy of its own, and likely require repurposing something else within the alimentary canal of the insect.

And then, there’s just the luck of the draw. Natural selection doesn’t produce any changes on its own – it simply works with changes that occur (more or less) randomly. If Gland A changed in a slightly more beneficial way before Organ B could, that’s what gets selected and incorporated into the species’ repertoire, though Organ B might have done it much better. Then, even if Organ B does later change, it would have to impart its own significant benefit over and above what Gland A does for selection to even act upon it. This is why ‘design’ is such a stupid concept to apply to nature, since what we see everywhere are actually examples of modified structures forced to do the job.

FennelTipI hadn’t originally intended to include most of that above – it came from suddenly recalling Ed Yong’s article while thinking about those water drops. What was intended was to include this other image from the same photography session, a lone raindrop hanging from the tip of the dog fennel flowers (see here for a shot of ‘typical’ perspective.) This was taken at night, freehand, the one frame I attempted, since there remained a slight breeze and the long arc of the stalk was drifting around under its direction. This is the exact same magnification as the top photo, so go back and look at that, paying attention this time to how short the range of sharp focus is – if it helps, the foreground stalk at bottom left is a rosemary leaf, and the whole insect is less than 4mm wide. Get the idea? Good. So when I tell you that this water drop was wandering several centimeters unpredictably right at eye-level, and I waited for it to come into focus range, you might realize just how precise the timing had to be. Luck had a lot to do with it, trust me – there’s a reason I only tried one frame before giving up the attempt for better conditions. I occasionally spend a lot of time trying to set up a particular shot and never achieve the result I was after, so getting this image so sharp on what was a casual, throwaway effort is a little ironic. But I’ll take it anyway.

The hurdle

Al Denelsbeck

With this entry I thee wed tie with 2011 for number of posts made in a year, and everything past this will be bonus content. Or something. It’s nonsense, really – I just vowed to try and do more posts, vaguely motivated by those who can apparently do seven a day (not looking in Jerry Coyne’s direction when I say this, no no.) But I’m comfortable with the current rate, and there really isn’t any point in trying to exceed this for the sake of numbers. As long as I don’t drop back to 2009’s stunning 30 posts*…

Anyway, in honor of this non-event, I provide a link to Headlines from a Mathematically Literate World, a post about interpreting statistics and figures in a critical, logical way. Simple, overriding rule, one of the few you can count on 99% of the time**: mainstream media articles are written to attract attention, and thus are overdramatic and, very often, completely wrong.

This is where critical thinking really comes in useful. If we accept the headlines and inferences at face value, assuming that they wouldn’t be featured unless they were important, well, we’d be complete suckers. And if we consider the dramatic tones and inflections from virtually every newscaster or commentator to be indicative of something, that would be even worse. Unfortunately, this happens all the time.

One of the biggest mistakes I’ve seen is with misunderstanding percentages. By venturing into the crawlspace under the house, I increase the risk of death by black widow bite as much as several hundred percent! Some people would take that to mean it’s virtually guaranteed, but it all depends on what the base rate was in the first place – in reality, I might have driven it as high as 0.5%, but that’s probably overstating it. I’m far more likely to die of infection fostered by gouging myself on something sharp down there, and that’s still not high enough to warrant any fear response.

Anyway, more pics coming soon.

* If you look at the Archives list at right, you’ll see 31 posts – that’s because I started the blog with a post on December 28, 2008, but the old software crashed and I restored in WordPress in 2009, so earlier posts got counted in June.

** Yes, that was intentional humor. Stay with me.

Such efforts

Al Denelsbeck

WetBokeh
Just playing around the other evening while the holiday lights are up, trying a bunch of experiments. The raindrop on the lights was a subtle touch – while I’d like to do some shots against a nice layer of snow, that’s always an iffy thing at this latitude. I may annoy about half of the people in the country with this, but I was shooting in just a t-shirt (or is that tee-shirt?) Thursday night as I got this, and it was even warmer Friday. If it helps, The Girlfriend would have had at least a sweater on – it was 19°c (66°f) at 1 a.m.

The above shot required a little paying around; the soft globes are the neighbor’s lights across the road, rendered as round (and not hexagons) by using maximum aperture. They were significantly dimmer than the blue one of ours in the foreground, so this is a 1.3 second exposure, triggered with a long remote cord as I flipped the light switch so ours would be on for only part of the exposure. Any slight breeze would shake the wire and blur the closer blue one, and getting the right ratio of light levels was a timing thing, so I made several exposures. I even waited for a car to go past on the road, which would have painted some streaks across the bottom of the frame, but our road sees few cars at that time of night, and while I was waiting the neighbors shut their lights off for the evening.

WetIvyI also did lots of other night experiments, but none of them turned out quite the way I wanted; getting the light balanced for night exposures can be tricky, and the LCD on the camera is only partially useful in that regard – it doesn’t give a very good idea of exposure levels, especially not subtleties. During this I was trying to figure out why some of the images seemed to be coming up blurred, almost in a fog, while others were sharp without changing focus at all, until I realized my breath was sometimes fogging up the LCD ;-)

Some of my ideas required sitting down on the wet front steps, or shooting from ground level out in the yard, which meant I got more than a little damp, and still had nothing to show for it. I tried again on Friday evening, but by then the gentle breeze had become raging winds and nothing was going to hold still for a time exposure, plus we no longer had the wet conditions that provided raindrops and shiny surfaces. So, they’ll wait for another time.

Which brings us to these images from earlier in the day Thursday. When light is getting this dim from heavy overcast, it’s definitely recommended that you use a tripod. I’m sometimes as annoyed over fussing with them as anyone else, so I wasn’t using one here, and thus this is the only frame of five that was sharp enough. Had I wanted a little more depth-of-field I would have been out of luck, or forced to use the tripod, but even then it might have been difficult, since my position in among several trees was not exactly conducive to the wide leg spread. My primary tripod is a model that can mount the center column sideways as a horizontal arm, allowing a bit more flexibility, but this doesn’t fix every problem; the weight of the camera limits how far you can extend without some kind of counterbalance, and the arm works strictly horizontally. Often it’s easier to simply shoot a lot of frames and hope I was steady enough in at least one of them.

WetDogFennelA tripod would have been no real help with this one – it wasn’t the movement of the camera that was the biggest problem, but the gentle bobbing of the saturated plants in the breeze, so the “take lots of frames” technique was the only thing I could count on. In the foreground are the remains of the dog fennel plants, once towering over my head but now drooping from their age and burden of water, while in the lower background is one patch of pampas grass, still bright green but topped with their feathery gold fronds. The camera’s white balance for all of these was set for sunlight, which is essentially no compensation for the color of light. This keeps the blue-grey conditions accurate, which is what we expect to see with the rain; using Auto White Balance or the setting for overcast would have produced more neutral, warmer colors that reduced the atmosphere of the image.

When I selected the dripping tips as a subject, I shifted around a bit to see what background was going to work; I had the choice of open sky, bare tree branches, deep shade down below those branches, the lawn, and the pampas grass (not to mention a road and the neighbors’ houses, ruled out pretty quickly.) While I took a few different ones, this is the one that worked the best for me – there’s a hint of a hand reaching down, so the pampas grass had to represent an “object” as a target of the hand, which is another way of looking at the framing. Or you could just consider it as minimal interference between the dominant colors of the image, if that works. Any of these involved tiny shifts of position, and the belief that the background should work with the subject. The same holds true with both images above: the position of the lights at top required careful adjustments of the tripod, and the ivy leaves were specifically framed to extend across the corners, as well as giving a face-on aspect to the dominant leaf that used the short depth-of-field to advantage, preventing any part of it from going out of focus. The light angle also had to be a certain way to demonstrate the wetness of the ivy while not getting too much reflection that would wash out the colors and detail, something faintly visible in the third leaf. Even the dog fennel pic required finding a group of drops roughly in the same plane so the focus would be sharp for most of them, though one could also select a single drop to concentrate on, making it the focal point of the image by being the only sharp one.

But yes, hard work – exhausting, even ;-)

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