Maths

            I’ve done some math during my life. It was always my favorite subject in school and I eventually ended up studying engineering in college, which was practically all math. My job doesn’t go to quite the same level, but I’m still using a calculator regularly. What I’m setting up is the possibly unexpected idea that I don’t believe math applies directly to the real world. Let me explain.

            Math to me is a conceptual tool that is useful for modeling, predicting, and simplifying real life phenomena, but only after the phenomena has been reduced to an idealized form. Generally the more math you use the less idealization, but even the most basic parts of math are based on idealizations of the real world. Take pi as an example. Pi is the ratio between a circle’s diameter and its circumference, and already we’re dealing with idealization because perfect circles don’t exist in nature. Already one step removed from the real world, pi still doesn’t fit into our math. Pi gets a lot of attention for being an irrational number, meaning that it consists of a never ending and never repeating string of digits. This might seem mysterious and unpredictable, sort of a loose cannon of the number world, but to me this is a glaring example of how our math is flawed (I keep saying “our math” because I don’t believing the math that humans use is the only possible math, but that is a whole other discussion that I don’t want to get into at the moment). Since it’s impossible to write down all the digits of pi, it can only ever be used as an approximation. The true value of pi completely escapes our grasp. Just a heads up, this fact is also true of every single measurement ever taken. That’s a pretty devastating blow to math’s ability to represent the truth of the real world, and it’s also a reason why pi isn’t all that special. Technically, there are a few measurements that define units. When you weigh the International Prototype Kilogram it’s exactly one kilogram, but that’s more a(nother) reason why the IPK is stupendous and less a triumph for mathematics.

The IPK is so great

            Leaving out all that irrational number bullshit, we’re still left with adding, subtracting, multiplying, and dividing, aka doing arithmetic to, discreet objects. For example, take four apples. Add two apples to get six. Double the number of apples to have twelve. Divide out a fourth of the apples to have three. Then subtract two apples and one apple is left. Repeated an infinite number of times, this process should always result in one apple. It’s too bad that the apples have to be completely idealized first. The reason this apple arithmetic works is that it assumes that one apple equals one apple equals one apple, just like how the number one equals the number one equals the number one. In the real world, every single apple is unique, so they can’t be used like numbers. One apple plus another apple is not equal to a different apple plus another different apple, but one plus one always equals one plus one. Numbers are also homogenous in a way the worldly objects aren’t. It is impossible to cut an apple in half and have two identical pieces the same way that the halves left after dividing one in half are identical. The only example of arithmetic that might work in the real world is if you subtract out everything to get zero, because if you have three apples and then take all three away it doesn’t really matter what kind of apples you had to begin with. Only math has to go and ruin this situation too, since if you ask any math major they’ll tell you that subtraction doesn’t exist, it’s only addition of an inverse. Inverse apples definitely aren’t a real thing, so there goes that.

An inverse apple?

            Now it might be possible to do this kind of arithmetic with quantum particles, because as far as physicists can tell all electrons are identical (as far as values for mass, charge, and spin go anyway). Assuming this isn’t just due to a lack of measurement precision; electrons start to look a lot like numbers. An electron can’t be divided into fractions and subtraction is still right out (an anti-electron is kind of like an inverse electron, but an electron plus an anti-electron results in energy, not zero) so it’s not perfect. This leaves addition and multiplication as a sort of fancy way to count. There’s also the fact that the quantum mechanics that describe the behavior of electrons are far removed from experiences of the macroscopic universe and can only be expressed using math, so I’m not ready to except quantum particles as an example of how math existing in the physical world.

            I’m not trying to say that math is bad or doesn’t have value. The measurements, predictions, and models that math can create are absolutely amazing and incredibly useful. Almost none of the aspects of modern civilization would be possible without math. Sure, the Romans build some pretty great stuff without using math as we understand it, but I think we’re doing things better now (the road I help build beat Roman roads any day). I just think it should be acknowledged that math is using abstractions and idealizations, and isn’t some great truth at the heart of the universe. Also pi really isn’t that cool.

Wildlife Pictures

            I also took some pictures while I wasn’t working or underwater. They’re all wildlife photos. I think my fallback career should be a National Geographic photographer. That, or a foot model.

            Anyway, first off are some of St. John’s terrestrial and airborne wildlife:

A Ghost Crab on the beach

Some lazy Asses

Some angry anoles

A seagull that wanted my breakfast

  

Iguana

  

Here is the pelican that was diving into the school of minnows

            There were also Mongooses on the island, but they were too skittish to get a picture of. My only picture of the local deer was in low light so it didn’t turn out very well. I think the deer had island dwarfism because they were really small compared to the deer I’m used to. Speaking of deer, I also took some wildlife shots in South Dakota too.

This is what I think of when I hear the name Mule Deer

A nice sized mantis

  

And a fuzzy caterpillar

            The South Dakota animals may lack the novelty of those in the Caribbean, but I still like them. That does it for the picture dump. If you work for National Geographic feel free to give me a call.

Diving Pictures

            It was another good year for diving. As always, I was sure to keep my camera handy for any photogenic fishes. I found a couple, and a couple that weren’t fishes too.

            Working in North Dakota over the summer, I didn’t make it to the lake as much as I would like. I went out a few times, and took a few pictures:

A bass by some rocks

  

A catfish

            Much more exciting that any lake in South Dakota was my trip to St. John in the Virgin Islands. I spent a whole week snorkeling in the Caribbean, and it was stupendous. There were white sand beaches with coral and all sorts of exciting stuff just off shore. Plenty of good picture material:

This was one of the first things I saw

  

All the fish and coral!

Black fish

Blue fish

  

One fish

Two fish

Bold fish

Shy Fish

Fish with small fins

Fish with big fins

Lots of little of fish

One little fish

And these guys was probably my favorite

            All those were just the common stuff. There were some less common fish that I was able to spot too. These are the pictures I’m proudest of:

This one lived in a hole and was really good at swimming backwards

Most of the stuff that I had a hard time finding was nocturnal, so they would do stuff like hide in the rocks

This one could change color!

He looks mean, but he wasn’t very big

A sinister cephalopod

And the elusive Porcupinefish

            There were also a few things I found away from the coral. Things that weren't bony fish:

  

Rays were pretty common, but this was the biggest one I saw

A Cuttlefish and some Conchs

I really had to zoom for this one to catch it out of its shell

Another crab

And I can’t forget these dudes

            My only complaint about going to the Caribbean was that fresh water diving really doesn’t compare. Still totally worth it. I also have some pictures I took above the water, but this post was already long enough. Next time.

Work Pictures

So, I took a lot of pictures last year that I think are pretty alright. I want to share them, and the easiest way to do that would be to just have a few picture dump posts.

I’ll start off with some pictures I took while working. A camera is useful for documenting what is going on while surveying or observing construction, so I always carry one. It’s nice to have pictures that show where you were and what was going on. Plus, if the project makes it into the company newsletter you need some nice pictures to go with the article. I think I ended up with some decent project shots:

This is a Right of Way stake

A scoria pit that I helped survey

An old railroad tunnel

One of the more action packed moments of culvert installation

There are also plenty of non-work related pictures. I covered a good portion of western North Dakota over the summer, and I’d take landscape pictures whenever the scenery caught my eye:

  

Yeah, they’re just backlit trees in a cow pasture 

A canola field

  

Fields of flax

       

            No sunset pictures this trip. There are also the non-landscape features of North Dakota. Surprise, they're related to oil:

A common sight

You can generally see a couple of gas flares no matter where you’re at

The thing I always got the most excited about was wildlife photos. Maybe I just think that getting a picture of something that's alive takes more skill:

A dragonfly that landed on my passenger seat

An enormous fly

A Flickertail Gopher 

 

Cows!

Leopard Frog

A salamander I found hiking though the road ditch

Who would I be if I didn’t hunt down some waterfowl?

This is technically just a fresh water diving bird, but I’ll take it

And a bunch of lovely ducks

 

I even found some duck eggs

            I also took some picture to document the state of my life on the road. Pictures to capture the essence of what was important and what parts of life became inconsequential:

  

All I kept in my fridge was beef jerky and dill pickles

These are right of way peas, and they were a major part of my diet

Here is the other half of my diet

Here is my face after a day of surveying

 

Road Beard

My take of hotel toiletries for the summer

            I had a good time working over the summer, and not just because of all the pictures. There were boring or tedious moments, as with any job, but give me a camera and I’ll find something interesting (a book, and mp3 player full of podcasts also help). I also like to take pictures in my free time, especially while diving. Up next is shots I took while snorkeling.