Thursday, October 22, 2020

Arduino Science Journal

I've commented on both Arduino and Science Journal on this blog. Now they're the same. Google has transferred Science Journal to Arduino, so, if you use Science Journal, it's time to upgrade.

I'm expecting good things in the future. Although Google has had a strong focus on education, it's sorta spread out and I've felt that the Journal hasn't grown nearly as much as it could. Arduino expresses a commitment to Science Journal and Arduino boards as an ongoing tool for learning. Hopefully we'll see exciting change in the future.

Tuesday, October 20, 2020

LabBooks

My dream job is "tutor". I enjoy seeing "the light go on" when someone grasps a difficult concept, such as differentiation. 

I've heard people say that calculus is hard because, unlike arithmetic, it's not intuitive. I've even heard people grudgingly say that algebra and trigonometry are intuitive. But not calculus.

Things are intuitive when we are exposed to them so much that they become second nature. We aren't exposed to fractions - we are exposed to parts of objects and fractions are the way we are taught to think about parts. Why are fractions intuitive and derivatives aren't? Derivatives are the way we learn to mathematically handle change and we are surrounded by change.

Why is, say, multiplication, intuitive? You probably know how to multiply two big numbers using long, or partial product, multiplication. You multiply one long number by each digit of the other long number and then you add the products together, but you have to position each of them just right before you add them. Why do you do that and why should you be confident that such a complicated procedure will work every time?

Is that intuitive?

Did you know that all the arithmetic you use is based on a handful of assumptions that nobody tries to prove. One is: a=a. Everything is equal to itself. That might be true in a single case, but how do we know that it's always true? I'm not at all equal to the me of five years ago, but then, I wasn't the same person five years ago that I am today. This instant, I am equal to myself.

Can you divide and always come up with whole number answers. There's a perfectly legitimate and useful way to do that and you might not remember it, but I can just about guarantee that you did it in elementary school! 

How do you know that 2+2=4, and why would you think that it is always the case? Can you prove it? We take an awful lot for granted.

Isaac Asimov was a great popularizer. Through most of his publication history, word processors didn't exist. Have you ever used a typewriter? Typewriters were what we used to create documents when I was in college. Word processors came out while I was in college. The typewriter word processors let you look at sentences you typed before you committed them to paper, but the computer programs were really cool. You could type an entire book, then go back and make corrections, change formats, and even add pictures (!!) before you printed it out. And then there were desktop publisher applications that made it all much easier and added a lot of options.

But the end result was still what I call "flat copy". The page just sat there while you read it. I still use word processors, for instance, I am typing this blog on a word processors app, Google Docs, on my cellphone. While you are reading it, it just sits there. I have embedded videos into some of the blogs, but they're still not anything you could call "interactive".

What I really enjoy using for educational materials is a spreadsheet application.

There's a link up there to the right that will take you to the download page of my other website. The page is called "Excursions". Most of the free downloads there are programs (like the statistics spreadsheet DANSYS) and their user guides, and LabBooks.

LabBooks are textbooks that are spreadsheet documents. Since they are spreadsheets, they're not flat copy. While you're reading them you can be doing other things, too.

LabBooks are lifelong projects for me. I might not live long enough to finish one, but I place them on my Excursions page when I update them. I just reposted the Mathematics LabBook. I waited until I had completed the first part of the first section. It's about the natural numbers (AKA the whole numbers) and the basis of arithmetic. All those questions I asked above? Read the Mathematics LabBook and you will understand the answers.

It has exercises you can do on the page and some buttons you can push to generate problems and get the answers. And you can do your own calculations in it.

I like to open up a concept and show how the insides work.

There are a few loose ends I need to tie up in the rest of the first section. For instance, I've been saying that I will show you how to memorize long numbers in mental calculations, and I will do that on the next sheet.

Talking about interactive documents, I would think the next wave of educational software might be virtual reality. A housemate is into VR. It makes me dizzy but I can imagine "Mister Wizard in a can." 

Thursday, October 15, 2020

Autumn trees




People are talking about going to the mountains for fall colors. I don't understand that. Back East, most of the mountains were covered by deciduous forest which blaze into color during the fall but even there, at the higher altitudes in the Blue Ridge, they turn into alpine forests of assorted evergreens. 

Here, the Rockies gain altitude quickly from east to west and become evergreens and aspen. The aspen provides patches of bright yellow and there are some colorful low shrubs, but most of the color are in the towns where many of the trees are from other parts of the world. 

The photos above are from Centennial, where the residential areas have colored up nicely. The plains host some nice fall colors where there are trees. Willows, cottonwoods, and sumacs grow along streams and produce bright yellows and reds.

The color pigments in tree leaves are associated with sugars that have been stored up in the plants. They're always there but chlorophyll, the pigment that converts sunlight, carbon dioxide and water into stored energy in the form of sugars, is more important to the tree so the green drowns out the other colors. When the Earth tilts away from the sun and trees get ready for less light and colder temperatures, the deciduous trees stop producing as much green chlorophyll before dropping the leaves altogether. Assuming that a landowner doesn't rake up the leaves for a landfill, they rot and add nutrients to the soil for future use.

Last year, I wanted to photograph the Highline Canal Trail in each season. Unfortunately, we didn't have a fall as far as the trees were concerned. To produce sugars and pigments, trees need rain and last year was a rather dry year. It suddenly became cold, the trees went brown, and the leaves came down in a matter of days. 

This year, we're getting colors, so, if you want fall colors, check out the aspens, but also visit the overlooks and view the towns like Kitteridge, Vale, Golden, and Boulder, and don't miss the cities of the plains.

How are the fall colors in your area? Do they seem to be related to the weather, and how? There are many ways to study leaf colors and, for that, I will recommend that you visit the Science Buddies website (https://www.sciencebuddies.org) and search for projects concerning leaf colors.

Wednesday, September 30, 2020

Get closer: cell phone proximity detector

I like my pocket computer - I'm not crazy about my cellphone (they're the same thing.)

For one thing, I'm old and it still bothers me to overhear people's intimate conversations. It's not like tv that I can turn off. And often there's no telephone in sight. They're wearing a tiny headset. Who are they talking to? Are they talking to me? - an imaginary friend (I hear they're never unkind) - a voice in their head?

But the designers of cell phones have improved some irritating issues. When you are using your cell phone as a phone, it puts all the other apps to sleep so you aren't punching buttons on the desktop while you're talking. It senses when your face is near the faceplate.

The problem with my last phone is that, when I took my face away, it didn't wake up, so I couldn't enter numbers from the keyboard or use other apps to get information. I downloaded an app to disable the sleep mode while I talked on the phone. It was quite unreliable.

My new phone doesn't have that problem. When I get close, the apps go to sleep, and when I take my face away from the phone, the apps wake up.

But how does a cell phone know that your face is close? The answer is "proximeter". All cellphones have them. Usually the proximeter is an infrared LED and detector under the faceplate. You can find it if you have a sensor app like Physics Toolbox or Examobile's Sensors. Both access the proximeter so that you can see when it toggles on and off. Just waggle your finger around in front of the phone until you see the proximeter flip.

I can see the IR LED under the faceplate at the upper left of my phone. The LED constantly shines infrared light out and when an object moves close enough, it reflects the invisible light back to the detector which triggers the proximeter on.

I'll be using my proximeter later to measure periodic events like pendulum swings, so I wanted a more precise idea what to expect from it. It was pretty easy with an optical bench. Home Science Tools (https://www.homesciencetools.com) has an inexpensive one - basically a stand for a ruler and sliders that will carry lenses, a candle, screens, etc. It also has a sliding object, a metal pointer that can be used to form images with lenses and mirrors, or, in my case, a target that I could move toward and away from my phone. With the optical bench, I could measure the distance between the object and the proximeter. I also stuck a plastic pill bottle on the object for a larger target.

Here's my setup.




I used a gooseneck camera stand to position the phone over the ruler.

I made ten measurements with each target moving it toward the phone until the proximeter toggled on, and then away until it toggled off.

I could take the average of ten distances as the "true" distance and the differences between the measured distances and the averages as the amount of error in the measurements.

I found that, for the small target, I could rely on the proximeter to toggle at 5.5 cm ± 0.8 cm. To get it to toggle off, I had to back off to 6.49 cm ± 1 cm. For the large target, the proximeter would toggle on at 4.63 cm ± 1 cm and would toggle off at 6.62 cm ± 1.6 cm.

I was a little surprised that I had to bring the large target closer to get the proximeter to toggle. I assume that the smaller, metal target reflected the infrared light better than the large, white, plastic target.

The errors in the readings behaved. If I added them up, the sum was 0 which means that they were random and followed a normal (or, at least, symmetrical) distribution. So, I can reduce errors in measurements with the proximeter by taking multiple readings and averaging them.

Notice that I had to back off further than I had to approach to make the proximeter toggle. Many control systems show that kind of behavior; it's called hysteresis. If the heat in your house goes above a certain level, your air conditioner will come on, but to make it stop, the temperature has to fall considerably below that level. If the cutoff and cut-on temperatures were the same, the air conditioner would just flip off and on all day.

You can roughly determine how near and far away from your phone you have to move to trigger the proximeter by just moving your hand in front of it, but if you want to use it as a precise instrument, you need to use a set up similar to mine that allows you to make actual distance measurements.





Sunday, September 27, 2020

play, learning, and risk

I've told a lot of tales here and they're all true (I swear by my tattoo - movie reference there.) I've talked about being in storms, falling off mountains, and walking until I'm near collapse. I'm a lifelong learner and an adventurer and I've put myself at risk to experience new things. 

In my defense, I will say that I thoroughly educate myself about things I do before I do them. I don't take risks just to take risks. And I prepare for accidents.

Learning involves risks - risk of failure, risk that someone will make fun of you, sometimes actual physical risks. When handling chemicals, fire, or electricity, there's dangers. That's why school labs come with lots of safety instructions. Unfortunately at home, people often don't bother to learn safety tips.

I have often lamented the disappearance of "real" chemistry sets and other science kits. But they seem to be coming back. It's true that there were many things in those old kits that would not even be allowed in children's toys today - including mercury and asbestos. I played with arsenic and explosives. But I'm pleased to see that modern kits like the ones produced by Thames and Cosmos, and Elenco provide lots of safety information.

Still, it's up to folks at home to safeguard their homes if they are going to allow risky play and studies...and there is plenty of research that indicates that we can easily err to one side or the other - challenges or safety (Norton, C., J. Nixon, and J. R. Sibert. 2004. Playground Injuries to Children. Archives of Disease in Childhood. http://adc.bmj.com/pages) (Bond, Michael (2020) From Here to There: The Art and Science of Finding and Losing Our Way. The Belknap Press. Cambridge, MA. Esp. Chapter 2: Right to Roam) (Tierney, John (July 18, 2011) Can a Playground Be Too Safe? New York Times Reports.) Many studies seek a happy medium...safe playgrounds that are also challenging.

I want to thank Me. Colleen Stewart for the following safety resources.

https://www.safehome.org/resources/childproofing-guide/

https://www.mortgagecalculator.org/helpful-advice/fire-safety.php

https://www.firstalert.com/community/safety-corner/escape-plan/

https://www.highsecurityhome.org/home-security-measures-that-will-help-people-with-disabilities-stay-safe-at-home/

https://bighappybackyard.com/how-to-make-your-backyard-safe-for-kids/

https://www.verywellfamily.com/what-to-put-on-a-babysitter-checklist-620333

https://www.gspcic.com/learning-center/hurricane-safety/

https://www.belfor.com/en/us/water/staying-safe-during-flood

https://crisisequipped.com/how-to-prepare-for-a-tornado/

https://www.savethechildren.org/us/what-we-do/us-programs/disaster-relief-in-america/earthquake-tips

https://www.ferguson.com/content/emergency-preparedness/wildfire

https://www.almanac.com/news/almanac/musings/power-outages-what-do-when-power-goes-out

And Ms. Stewart's website is:

https://playdatefitness.com/

Part of learning is learning to learn. Learn to be safe in learning. Here is your home safety library.

Tuesday, August 18, 2020

Rocks, smoke, and chipmunks

It's good to be back on some serious trails again. Badger and I hiked up Independence Peak, in Pence Park, South of Bear Creek and Kitteridge, last week. It was more demanding than Panorama Point being a little further, about a hundred feet more elevation gain, and fewer switchbacks. Still, there were a lot of people out and, if you've been reading this blog, you know that I consider that a plus.

If you're on the Eastern Slope of the Rocky Mountains, you might have noticed a more-golden-than-usual sun lately. When I wrote about sky colors, I neglected to mention that some of the most beautiful (and weird) displays are caused by things you don't want in your lungs. If you've ever seen any of the images from Mars, that sky is the opposite of ours - red during the day and bluish at sunrise and sunset. NASA thinks it has to do with Mars dust, which has magnetite (basically rust) in it.

I sorta felt like I was back in the Great Smoky Mountains.



The forest fires causing this is almost 400 kilometers (over 240 miles) away, but the prevailing winds are from west to east here. I've read that much of the topsoil in Brazil is blown across the Atlantic from the Sahara Desert in northern Africa.

I remember a fire in the Okefenokee Swamp in Georgia that made Selma, Alabama look like the woods just outside town were burning.

The Smokies in the Appalachian Mountains were known to be smokey long before Europeans moved in. The valleys and hollows created natural channels that captured and held aerosols from campfires and natural forest fires all over the East. With industrialization, acid rain from nearby Copperhill, Tennessee became a serious problem.

The stars of this trip are these fellas.





Chipmunks were all over the rocks and they seem to have no fear of humans.

How does the wildlife in your area behave around humans? Do wind patterns there collect smoke, dust, or pollution, or do they clear them out? How?

Sunday, August 16, 2020

The Rainbow Connection

I guess I've seen a handful of rainbows since I moved to Colorado in 2013. They're not a common occurrence here like they were in the much rainier South. The rain, the sun, and you have to be lined up in a certain way to get a rainbow.

My favorite rainbow memory is from my days as a welder's assistant on a pipeline barge in the Gulf of Mexico. We were installing a riser (the part of the pipeline that connects it to an oil well platform) and it was late on an overcast day. The sky was dark but the horizon was clear and where the sun was setting it was blood red, casting a deep red light across the underside of the clouds. Against that backdrop was a brilliant triple rainbow.

I had to get out our lawn sprinkler to get this one.




Here's how rainbows work. A rainbow is actually a cone. The part you see is where a sheet of rain intersects the cone - it's actually a circle. It looks like a bow because part of it is below the horizon or underground.

The apex of the cone, it's point, is at your anti-solar point. If you draw a line from the sun (don't try this) through your head (right between your eyes) and continue it down into the Earth, that's your solar axis. The anti-solar point is somewhere on the solar axis below you. Now, imagine a cone extending back toward you from that point.

The cone has an angle of 40 (the blue part) to 42 (the red part) degrees - that's the angle at which the light leaves the raindrops). That means that the sun has to have an angle of inclination of 42 degrees or less to see the rainbow. For my rainbow (the sun's angle of inclination is the same as the top of my shadow's angle of declination - only positive.



49.1° ... wait... that's more than 42°.

Hey, okay, notice that my rainbow was formed by a lawn sprinkler and it's below the horizon.

I mentioned that my favorite rainbow was a triple rainbow. If you ever see one of these, pay attention to the order of the colors. In a secondary rainbow, the order is reversed with the blue on top. That's because the light is reflected twice inside the drops. The drops that cause a secondary rainbow are completely different drops and the cone is at 51° to 54° of the anti-solar point.

Triple rainbow? Well, there are a lot of different kinds of rainbows. Some can be formed by light from the sun bouncing off the surface of a lake or the ocean and then hitting rain. If a rainbow is caused by sea mist, salt water has a different index of refraction than fresh water, so the angle of the cone will be different. Also look for rainbows in waterfalls and geysers. And if you're in a plane and see a rainbow in the clouds below you, you may be able to see the whole circle!

Rainbows are special, and rare. If you see one, see if it looks different than the one I described and see if you can figure out what makes it different.

Monday, August 10, 2020

Sunsets and mountains

Suddenly, I'm hiking again. The bug has bitten one of my housemates. We have been to the Lair O'the Bear, between Morrison and Kitteridge, Colorado the last two weekends. At the western end of Bear Creek Canyon, it's a short drive from home and it's near a new favorite restaurant, the Switchback Smokehouse, in Kitteridge (they have an ice cream shop next door!), so it's a great destination for me.

I didn't get many photo-ops the first time. Everything's so big it's hard to get a good picture, but Panorama Point provides some workable views. Here are some of the pictures.


Maidenhair ferns

Penstemon. The main wildflower season is done, but there are still some nice surprises out there. We also saw a lot of anemones but they looked pretty tired.


I don't know why there are things in this tree but it makes an interesting subject. There may have been people rappelling off the Point.


View to the southwest

Kitteridge and, in the distance, Mount Evans


I've also picked up some nice shots from home.

An airplane. We're near Centennial Airport and get a lot of air traffic over our house.

The sunsets have been nice recently.

I'm still working on physics and astronomy excursions and should have something to show for it soon. In the meantime, keep exercising that camera.

Saturday, July 25, 2020

Clouds

"I've looked at clouds from both sides now"
Joni Mitchell


Lenticular clouds in Centennial, Colorado.

People have looked for images in clouds for at least as long as humanity has been recording it's activities.

I lived most of my life in the Southeast United States leaving only for a construction job in Montana, four trips to or through Denver (and the states I passed through on the way), and two seasons on a laybarge in the Gulf of Mexico. But I've seen some weather.

Every area has its distinctive weather. The reason we could predict our weather with any certainty in Alabama was that it was coming from where I live now, Colorado, and we had plenty of time to see it coming.

As each area has its characteristic weather, each has its characteristic clouds.

The massive high-topped thunderheads with anvil shaped tops are rare here. We get a lot more hail; they get a lot more tornadoes. They also get hurricanes.

We get these weird lenticular clouds like the ones in the picture above.

As air flows across the Rockies and out over the plains, it can set off standing waves, like those that form when a person blows across the top of a soda bottle. At the bottom of the waves, the air is warm and can hold moisture as invisible vapor, but when the air is carried to the top of the waves, it cools off and releases the water as cloud droplets. A person from the east might think "rain coming," but these are actually stable weather clouds, like the big fluffy cumulus clouds of the Southern summer.

Those Southern cumulus clouds could build up into far from stable cumulonimbus clouds. I had one drop a tornado into a farmer's field next to where I was driving once. I didn't usually speed. I did that time. Clouds can cause you to get excited.

I was driving near Tuskegee, Alabama on I 75 and there was this huge thunderhead over me. The bottom was flat and it looked like I could reach up and touch it. It was electric blue. There was so much water in the cloud that it piped the color of the sky above it right down to the bottom. That's the kind of cloud that can drop a tornado down right on top of you without any warning.

The funny thing is that I saw so much storm activity before I became a storm watcher about five years before my retirement and never saw sign of another tornado, not even during the disastrous outbreak of 2011.

One of the weirdest cloud formations I have ever seen were the hole-punch clouds one summer in Selma. An even sheet of clouds had big circular holes in it, all the way up to clear blue. We didn't know what caused them back then. It turns out that planes flying through clouds can cause droplets to coalesce, like when you put a drop of detergent in a bowl of greasy water.

The most beautiful display of weather I have seen was a very darkly overcast afternoon on a laybarge. There was a clear band on the horizon where the sun was setting blood red. It cast a red glow over the bottom of the clouds and there was a brilliant triple rainbow.

I've been chased up Mount Carbon three times by thunderstorms. Walking east from Morrison on the Bear Creek Trail carries you through a broad, treeless area of Bear Creek Lakes Park. With no cover behind me and no cover and a lung busting switchback before me, I heard a rumble at my back and turned to see massive black clouds boiling up over Mount Falcon. There was green-ness in them, indicating hail, which I didn't want on me, so I walked fast.

All three times I reached the shelter at Mountain View before the storm hit.

What causes cloud colors. Well, I talked about sunrise and sunset clouds in the last blog. Why are clouds white and, of all colors, dark gray? Is water gray?

We talked about Rayleigh and Mei scattering last time. Mei scattering is caused by aerosols, particles that aren't molecules but they're still small enough to stay suspended in air. And remember that Mei scattering doesn't pick and choose specific wavelengths of light like Rayleigh scattering does, so it's not surprising when clouds are white, but gray?

A few years ago, I built a Joly Photometer. It's basically two chunks of paraffin separated by aluminum foil. Here it is.


If you put a standard light source on one side and a light source of unknown brightness on the other, then move the unknown source nearer or further away until both sides of the Photometer look the same, you can calculate from the difference in distances of the light sources from the photometer how bright the unknown source is.

But notice that the two halves, which are from the same slab of wax and, therefore, the same color, look different. The apparent color is from the white light illuminating the wax. The top slab is lit by more white light ..therefore, whiter.

Clouds are the same way. Less light makes its way down through the cloud so places with less light look less white and our eyes are rigged to emphasize contrasts so, next to the bright white of the tops of the cloud, the bottom sometimes looks positively black.

Notice that the gray parts of clouds are usually a cool gray until sunset. The blue of the sky also comes through misty clouds.

If you ever visit the Great Smoky Mountains, you will see that they, indeed, do look smokey. That area has always funneled aerosols in, hardwood tree pollen, smoke, and more recently, abundant industrial pollutants and they disperse white light efficiently. Add in the sky blue and there's smoky mountains.

Green clouds are a place where light has to pass through so much dispersion that all the blue is gone. Notice that it's a sorta dirty brown, meaning that light at the red end of the spectrum is there, too . Clouds with that much water and ice in them will often mean hail. I run from those! Mother Nature doesn't want me there.

Hail forms in clouds with strong updrafts. High up in cumulonimbus clouds, water freezes into tiny ice crystals until they are too heavy to remain suspended in the air and then they start to fall, but they get caught in the updraft and are blown back up. They pick up more moisture and freeze another layer. These little balls of ice will ride winds up and down until they're no longer little balls of ice. When they finally fall to the ground, they can be destructively big balls of ice!

Cloud watching is a great pastime. You can get a good idea of what to expect of the weather in your area and, occasionally, you'll see something rare and spectacular!


Thursday, July 23, 2020

What about that sky color?

There are a couple of hints as to why the sky is blue that are easy to obtain.

First, look straight up through a polarized sunglasses lens. Rotate the lens and see what happens. You'll see it lighten and darken. Second, note that the sky is not always blue. There's a definite sequence of colors as the day progresses: reds and oranges, yellows, blues, then the reverse.

What polarizes light? Reflection! When light bounces off something, it comes off organized. That's what causes glare and glare is why there are polarized sunglasses to start with.

Light is sorta complicated and maybe you don't want the excruciating details, but, at base, it's a wave (like ocean waves) made up of electric and magnetic fields. The fields move at right angles to each other. The waves can be oriented in any direction and they are when they leave the sun.

But when light hits a surface, whether it's a molecule or a lake, it's absorbed by the atoms in the surface. Some of the atoms send out light when they calm down, sometimes in a different color but often unchanged. Different materials are better at this than others. That's why metals reflect better than glass.

But the gas molecules in the atmosphere absorb and re-emit sunlight and the light they re-emit is polarized. Although molecules tend to be neutrally charged overall, most of them have different charges in different places. Remember that like charges repel so molecules next to each other tend to drive each other's electrons away from each other. So molecules tend to organize themselves. I say "tend to" because it's not a strong phenomenon and not all the molecules in air are lined up like a high school marching band. But light coming off these molecules also tends to be lined up. It's called Rayleigh scattering.

Here's a shot of the sky through a polarizing filter.


After turning the filter ninety degrees, it looks like this.


Notice the gradation of light toward the sun. There is another kind of scattering in the atmosphere. Mie scattering is from larger particles: dust and other aerosols like water droplets. A big difference between Mie and Rayleigh scattering is that Rayleigh scattering is affected by light wavelengths. The shorter wavelengths (violet, indigo, blue) are scattered more than the longer wavelengths (red, orange, yellow). Mie scattering disperses all the colors about the same. 

Space is black and the sun is almost white. As sunlight comes into our atmosphere, ultraviolet (eaten up largely by ozone in the upper atmosphere), violet, and indigo goes first. What reaches us is blue. As a spot on the Earth rotates away from the sun, light has to travel through more atmosphere to reach it. Green drops out, but you can't see much green since it's still mixed with a lot of blue. Yellow drops out, and then you get the oranges and reds of the sunset.

Keep in mind that the same sun creating beautiful sunsets over the Rockies is creating a blue California sky at the same time.
The sky closer to the sun looks whiter due to Mie scattering. So that's why the sky looks blue...and white and orange and red…

So, using color filters.

Filters have a coding system that looks rather arcane. I mentioned it in the last blog. The filter I used was a CTO ¼ 6500 to 4500 K ½ f/stop gel correction filter.

CTO stands for "color temperature orange". There are also CTB (color temperature blue) and "plus green" or "minus green" filters. CTB filters are specifically there to make tungsten light look like sunlight. They "cool down" yellowish light. CTB does the opposite. I wanted to take blue out of my picture so I needed a warmer filter. ¼ is just the strength of the color change. ¼ is a light colored filter.

The K number is color temperature. All bodies above absolute zero have molecules that vibrate - that's what heat is - vibrating molecules. And if molecules are vibrating, so are the charges within them. Moving charges are what causes magnetic fields. Moving magnetic fields create electric fields and when magnetic and electric fields start moving together, you get electromagnetic fields - light.

Relatively cool bodies like a summer sidewalk (see my blog for Friday, August 30, 2019, "Trail temperature vs. air temperature") might seem hot, but they're not hot enough to glow. But they are giving off light in the invisible, infrared range.  Infrared light is how heat is radiated because when infrared light hits matter, the matter heats up. 

As objects get hotter, they begin to glow a dull red, then orange, then yellow, then blue, and then they go white. The K number in filters stands for "Kelvin" as in "Lord Kelvin" after whom the Kelvin temperature scale, preferred by scientists, is named. The K number is the color that most closely resembles the color given off by a hot body around that temperature. A hot body from 6500 K to 4500 K will give off a yellow color. Larger numbers denote bluer colors, smaller numbers mean redder colors.

The f/stop is how much light the filter lets through. On a camera, the f-stop is the ratio of the lens' focal length to the diameter of the aperture. That might sound complicated but remember that the camera's focal length is related to its light gathering power and the larger the aperture, the more light can get in, so the smaller the f/stop number, the larger the aperture, and the more light is passed through.

An f/stop of ½ does not mean that half the light gets through. It's actually a very light filter that lets a lot of light through. An f/stop of, say, 8 would be much darker.

Correction or compensation filters tend to be pretty light. There are also color filters that are intended to really alter the color of photographs for special effects. They cut out a lot more light in specific colors. There are also neutral filters that just cut light in all wavelengths, polarizing filters, and special effects filters like diffraction gratings that give you rainbows.

Some photographic filters are made of glass or thick plastic. Gels are thin plastic films. I like them because they're inexpensive but they do the job and the thicker filters are harder to mount on my cell phone. I just slip the gel between my camera lens and the phone case and I'm ready to go.

The sky is what you have to look through to do astronomy so, if you're interested in sky watching, it behooves you to understand the weather.