Category Archive: science and math

Blogging LaTeX

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Mon. July 18, 2011

Honestly, I just wanted to try piecing together a function using LaTeX notation. Let’s see…

\phi=\frac{1-\sqrt{5}}{2}\approx 1.618...

Yeah, that would be the Golden Ratio. Thing of beauty, that is. Get it? That was a math joke. Blah.

What’s the LaTeX notation like? Well:

\phi=\frac{1-\sqrt{5}}{2}\approx 1.618... &s=3

What does it look like as an infinite series? Hmm…

\phi=\frac{13}{8} + \sum_{n=0}^\infty \frac{(-1)^{(n + 1)}(2n + 1)!} {(n + 2)!n!4^{(2n + 3)} }

And the LaTeX code:

\phi=\frac{13}{8} + \sum_{n=0}^\infty \frac{(-1)^{(n + 1)}(2n + 1)!}
{(n + 2)!n!4^{(2n + 3)} } &s=3

Neat!

Back in the day, I was kind of fond of using Microsoft Word’s equation editor tool. I found it fun laying out equations. It wasn’t about the math (although that was interesting in itself) but more about typesetting and layout. So knowing that WordPress supports LaTeX is a sweet deal. Of course, I probably don’t really have any use for the tool these days. It’s not like high school or university where I had a need to print out equations like these in reports and what not. Still, the idea that I can do it if I wanted to is pretty cool.

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Purpose of a fever

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Tue. November 30, 2010

Last night when I said I was going to sweat things out I wasn’t kidding. My temperature has been pretty high all day today. That’s a good thing. I looked this up on Wikipedia. Having a fever is actually a defense mechanism. Apparently the raised temperature is inhospitable to bacteria and viruses. Also, white blood cells multiply faster in the raised heat, so it’s kind of like a jab followed by a right hook. BAM. Anyway, I didn’t go to work today. I spent the day in bed under two blankets trying to stay warm. I had to drink a lot of water just to keep my fluids up.

At this point, I’m not feeling as gross as I was last night. I think I still have a fever, but the hacking cough is present. Actually the cough isn’t producing anything, so it’s dry. It’s also kind of shallow. I still feel pressure in my sinuses, so I’m suspecting an infection there. I’ll continue taking the meds to combat everything. I’m still on the fence as to whether I can make it to work tomorrow, but of course my course of action will be clearer tomorrow morning. If I’m still coughing heavily, I’ll probably stay away. I don’t want to be that bastard coughing everywhere and infecting everyone else. Nope.

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Sunday’s probabilities

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Tue. September 21, 2010

As Sunday approaches I’ve been keeping a close eye on the weather forecasts. Ideally, I would love it if the whole race took place with temperatures at around 10°C, or even less. Overcast skies would be wonderful. My experience tells me that it’s not bloody likely: the past two times I’ve done this event have been warm and humid. As such, all I can do is hope and pray that things will be in my favour. I really want this race to go well.

The thing about forecasts, though, is that they’re never perfectly accurate. By nature, it’s just not possible. Instead, weather forecasts always deal with probabilities. The powers that be have heavy duty computers that do a lot of number crunching based on trends and empirical evidence to predict what’s likely to happen. In terms of short term forecasts, the scientific models are good enough to have a good grasp of likely temperature trends. Precipitation is a tricky matter. I mean, that’s why they always talk in terms of POP (probability of precipitation), right? If they could say with certainty whether it’s going to rain or not on a particular day, the forecasts would always give a POP of 0 or 100%. That’s often not the case, is it?

Anyway, for Sunday’s weather, the date is still outside of the short term, so I’m taking the forecast with a grain of salt so far. Still, as the date approaches I’m getting more and more anxious. We all could use a good forecast. No matter what though, I predict that the probability of awesomeness will indeed be 100%.

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Prime and perfect

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Mon. August 23, 2010

+10 points if you get the nerdy joke right away.

sweaty dragon says (2:50 PM): of the people coming…you will know [two people].
Jebus! says (2:51 PM): What’s your expected numbers?
sweaty dragon says (2:51 PM): currently…5 coming.
Jebus! says (2:51 PM): That’s a solid number…prime, in fact
sweaty dragon says (2:51 PM): 6 would be perfect.

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Story of the heart

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Sat. November 14, 2009

Earlier today I went with a friend over to the Ontario Science Centre to take in the Body Worlds exhibit. If you recall, we tried to go there over three years ago but were pretty much rejected because we tried going on one of the last days of the exhibit and it was already sold out. This time though we planned ahead and got tickets earlier on. We made it in at 4:45 and started wandering around taking in the sights. Let me tell you, it’s really a fascinating exhibit. There were several prevalent feelings throughout my time there. The first was just an amazement about the whole exhibit. It wasn’t so much about seeing all of the internal components, but more about how the how the bodies were processed. The process of plastination just seems so difficult. When you see some of the items, it just makes you wonder how the heck they managed to produce it. For example, there were a couple of displays that showed off the networks of blood vessels in parts of the body. I can understand how they injected plastic into the system to get the shaped and all, but how the heck did they clear out all of the surrounding flesh afterwards without affecting the molded parts? Crazy! Having a sliced giraffe is just so odd that it’s fun.

Another feeling I had was one of wondering just how desensitized I seemed to be regarding the whole thing. I mean, there I am, surrounded by corpses of actual people. There were once living people with dreams and aspirations, and now there they were on display all flayed and dissected in the name of education. It’s pretty macabre. There were a couple of moments where I seemed to have been surrounded by med students. They were all talking about different visible structures and musculature. I can’t say I understood everything, but I was struck by how much more they seemed to have gotten from the whole thing. I mean, sure, there were displays in there that would have spoken to anyone without any real medical background. For example, there was something that had a healthy lung side by side with a smoker’s lung. The stark contrast between the healthy colour and the tar soaked lung is rather astonishing. For other things, I might not have been able to tell if there was any special significance to the way something was done. For the full models, the first few were jaw dropping, but after a while I admit that I started thinking that they were all pretty much similar. I mean, I know they aren’t, and that each tells a different story, but in the end it all kind of became a blur of flesh.

All in all, I found it great, but not something I really need to see again. When the exhibit shows something great, it’s really amazing. Otherwise, it’s…just all right. The shock value of it all really wears off quickly if that’s what you’re interested in. No matter what though, it really is informative. Would I recommend going to see it? Why not? I think anyone can benefit from having a look. Still, try not to make the exhibit something that it isn’t. It’s not a Halloween gore show; everything is rather tastefully done. This is a case where I can truly say, “it is what it is.” It’s up to you to decide exactly what “it” is.

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One to Nine

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Fri. July 17, 2009

I mentioned a little bit yesterday regarding posts that I’ve recently put up that have had something to do with numbers, either in the title, or perhaps due to some ordinal list. Like I said, it’s probably not a coincidence. That’s because on my rides on the subway I’ve been trying to take in a book on numbers that I picked up at Chapters about two weekends ago. The title is One To Nine: The Inner Life Of Numbers. This book has nine chapters exploring aspects of each digit, one through nine. I tend to really like quirky non-fiction that has something of a cultural bend to it. That’s why I kind of enjoyed books like Malcolm Gladwell’s things (I still have to read The Outliers), Freakonomics, and Eats, Shoots & Leaves. I don’t think any of the books have been perfect by any means. Even so, the writing in them had enough pull to make me want to finish the books. And then there are books like One to Nine. Jesus, I was preparing myself to like the book. I mean, the blurb that the publisher had on the book made it look like something that I would be into:

Have you ever thought about the uniqueness and simplicity of One, or what it means to be Two? Is Four really so square and why are there Seven days of the week, Seven deadly sins, or even Seven wonders of the world?

Wow. To me that sounded like it had enough content to not seem like some dry, purely theoretical tome. I’ve always enjoyed numbers a little more than the average person. In my mind there’s something very cool about how something seemingly black and white like mathematics has a lot of beauty in terms of patterns found in unexpected places. I was interested in seeing how all of that applied to everyday life situations. So, that’s why I thought such a book would be a good idea for subway reading. As I made my way through though…I quickly became more and more disappointed. Really, the book depends on the reader having a really good grasp of deep mathematical concepts. For example, maybe if I knew more about Twistor theory I’d be able to appreciate that part of the book better.

I will admit that there were some interesting things. For example the author touched on patterns that appear when you take the Fibonacci pattern modulo some number. That was kind of cool. Still, there wasn’t enough there to make me feel like I could get enough out of the things discussed. Way too much of it either went over my head, or was just presented so abstractly that my mind just didn’t want to bother trying to understand. See, that kind of bothers me. I took a lot of math long ago during engineering undergrad. I actually did learn about topics covered in the book like RSA encryption, Taylor series, etc. I don’t think any of that helped me absorb what was being said. I’m sure there were many points where my eyes must have been scanning over the page but not taking anything in. I’ve actually fallen asleep on the train a couple of times while holding the book. How sad.

I’ll take a guess and say that people that are doing some deep mathematics studies in university will probably enjoy this thing. For the casual reader, it’s not that great. Even if you have some mathematical background, the heavy parts are just too much to deal with. The blurb is inviting, but the text just talks over your head and doesn’t care if you don’t understand.

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“Have you tried epsom salts yet?”

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Mon. June 8, 2009

One of the first Wednesdays of every month is massage day at the company. Every month, the massage lady that I sign up under (yes, the one that told me to use eHarmony) tends to ask the same questions. Her first question is usually: Is there anything you’d like me to focus on? I usually respond that there’s nothing in particular, and that’s only because I genuinely feel like I’m pretty much all right. Thing is, within moments she’ll find some place on my back that has me squirming even with some light pressure. Inevitably, the next thing she’ll ask is “so, have you tried epsom salts yet?” And my usual response is “no…not yet.” It’s starting to get embarrassing because it’s totally like I’m not paying attention to any of her advice. She’s recommended bath salts every single month and each time I say that I’ll give it a go only to have forgotten by the time the next month rolls around.

What’s so special about epsom salts? The more technical name for it is magnesium sulfate. Actually, epsom salt is magnesium sulphate with seven water molecules attached…err…so says Wikipedia. Anyway, when you put this into a bath and soak in it, the body tends to absorb this chemical and that helps to reduce inflammation. That’s the big reason the massage therapist wants me to soak in it. She warned me that I had to be careful doing so because I’d likely melt into a pile of goo after the bath: my muscles will be so very relaxed. Sounds great, right?

If you haven’t surmised it yet, I’ve finally gotten off my duff to get a bottle of bath salts. What spurred this? Why this month all of a sudden and not any previous ones? Eh, well a few days ago I must have done something like sleep in a really awkward position because my right neck and right shoulder have been aching like mad. It’s pretty bad. I knew that massage day is coming up, and I didn’t want to go in being in pain without even having tried something I know she’d recommend anyway. So yes, it looks like she finally guilted me into buying it.

Next step though, running a bath with the salts. We’ll see if I even get that far. Baby steps!

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Evening star, morning star

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Wed. March 4, 2009

Lately, I’ve been joined by a familiar sight every evening on my way home. The planet Venus sits there in the evening sky, shining like a distant beacon. Once you take notice of it, it’s hard to not see it there night after night. It’s really fascinating.

Earlier tonight, as I was walking to the station I paused to think: why does it seem like I’ve only noticed it as of late? For that matter, why is Venus given both “evening star” and “morning star” epithets? And what’s this about Venus going into retrograde motion? It’s actually all kind of related. There are, several concepts here that you might not consider together, but when you do you can’t help but get some greater appreciation between nature and geometry of it all.

(at least, that’s how I feel)

So, all right, let’s lay some foundation here. All of the stuff I’m explaining here is in my own words and might not be totally accurate, but I’ll try to be as correct as possible.

From Earth, all of the planets, and the sun and moon appear to move across a band of sky called the ecliptic. This band is where the constellations of the zodiac are located. Anyway, as the day goes the part of the ecliptic that we see keeps changing due to the rotation of the earth. Just like the sun, all of the bodies just rise and fall. They kind of look like they’re fixed against the same bit of the zodiac. However, if you look at them night after night you’ll actually notice that they’re moving slowly across the ecliptic–some faster than others. The moon, for example, is pretty darn zippy taking a little under a month to make one circuit. The sun takes a year to do a circuit of the zodiac. Makes sense, right? All of this is just a matter of perspective though. The sun isn’t really moving across the stars as much as the point of view from Earth is changing. This is happening such that it looks like the sun is moving across the ecliptic.

OK, so Venus is closer to the sun that Earth, right? Because of this, from Earth it looks like Venus is never more than around 45° away from where the sun is. Most of the time, Venus just moves forward along the ecliptic. If it’s located before the sun where it rises and sets before the sun rises and sets then it’s visible in the morning. From our perspective, Venus moves forward bit by bit until it overtakes the sun and starts coming after it, where it rises and sets after the sun rises and sets. That’s when it’s visible in the evening. These days, it’s visible in the evening.

Every 18 months or so, due to the Earth overtaking Venus in its orbit and the geometry of it all, Venus will appear to start backtracking. When it does it’s actually pretty speedy: it seems to take about 1.5 months for it to go from appearing far after the sun to appearing far before the sun. After that, it goes back into direct motion and starts plodding along to overtake the sun once again. We’re due for a Venus retrograde period in a few days.

So, we only notice Venus as a morning or evening star if only if it’s far enough away from the sun. Otherwise, the brightness of the sun kind of just drowns out the glimmer of the planet. I guess that’s why I haven’t noticed it as an evening star in lately up until recently. By mid-April it will have raced to appear before the sun such that it will be seen as a morning star.

Anyway, that’s my explanation. The movement of the planets is really quite a beautiful thing. Maybe over the next few evenings you’ll be able to look up and appreciate the evening star a little bit more.

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