I was reading about the origin of fluctuations in the cosmic microwave background, about string theory, about how merging forces could have caused a fast expansion of the universe, and how we might fix the problem of that damn big bang, and for once I felt like it was something that I could actually dedicate myself to studying. My goal in life now is now to solve all outstanding mysteries about what the hell happened 13 or 14 billion years ago.

But as I was thinking this, I was flipping through a presentation overviewing some of the early evolution of the universe, when I hit a slide that presented, without any explanation, this parable:

The Emperor of the South Sea was Fast, The Emperor of the North Sea Furious, the Emperor of the center was Primordial Blob. Fast and Furious were discussing how to repay Primordial Blob’s bounty.

“All men have seven holes through which they look, listen, eat, breathe; he alone doesn’t have any. Let’s try boring them.”

Every day they bored one hole, and on the seventh day the Primordial Blob died.

- Chuang-tzu (c. 350 BC)

Would any Taoists in the audience care to enlighten us? I’m no expert in ancient Chinese philosophy, but suddenly I don’t feel so eager to poke my nose into the primordial plasma of the big bang anymore.

This year, daylight savings time is starting earlier, and as with any change, there are people out there who love it and people who are upset about it. They all seem to be forgetting one thing, which I’d like to take this opportunity to remind everybody of—changing the numbers on a clock does not actually change what time it is.

Take this guy, for example, who is happy to have more daylight savings time:

Jerry Smits, who runs his own painting company in Southern California, says that he can get more work done with the time change. Since exterior paint has to be applied by 3 p.m. to dry properly, Smits can squeeze in another job during daylight saving time.

– “The new daylight saving time: Will it really work?“, Columbia News Service

Listen, Jerry. Putting the clocks ahead does not actually make the sun set an hour later in the day. There are no more hours of sunlight than the day before. If you want to get more work done, just wake up when the sun wakes up. You can call it three in the afternoon if you want and work until midnight in bright sunshine, but the sun’s going to set at the same time regardless.

Same goes to you farmers. Cows do not observe daylight savings time. They do not set their clocks back or forward an hour and expect you out in the barn to do the milking when the big hand and the little hand are wherever they like the big hand and little hand to be when being milked. If anything they probably get confused when you start showing up an hour early in the spring.

The people who tend to think daylight savings matter are actually the ones to whom it matters the least. If you require daylight to do your work, you’re working with animals who know no time, or doing anything else that depends on the day/night cycle, then the arbitrary numbers on a little display don’t change anything about what you do. For the rest of us, all that changes is how bright it is when we happen to leave our classrooms and offices to venture into some other builing.

The only thing that actually changes the number of hours in the day is the tilt of the Earth’s axis and its orbit around the sun, and no act of the US Congress is going to change that.

Mother nature’s favourite number:

2 . 7 1 8 2 8 1 8 2 8 4 5 9 0 4 5 2 3 5 3 6 0 2 8 7 4 7 1 3 5 2 6 6 2 4 9 7 7 5 7 2 4 7 0 9 3 6 9 9 9 5 9 5 7 4 9 6 6 9 6 7 6 2 7 7 2 4 0 7 6 6 3 0 3 5 3 5 4 7 5 9 4 5 7 1 3 8 2 1 7 8 5 2 5 1 6 6 4 2 7 4 2 7 4 6 6 3 9 1 9 3 2 0 0 3 0 5 9 9 2 1 8 1 7 4 1 3 5 9 6 6 2 9 0 4 3 5 7 2 9 0 0 3 3 4 2 9 5 2 6 0 5 9 5 6 3 0 7 3 8 1 3 2 3 2 8 6 2 7 9 4 3 4 9 0 7 6 3 2 3 3 8 2 9 8 8 0 7 5 3 1 9 5 2 5 1 0 1 9 0 1 1 5 7 3 8 3 4 1 8 7 9 3 0 7 0 2 1 5 4 0 8 9 1 4 9 9 3 4 8 8 4 1 6 7 5 0 9 2 4 4 7 6 1 4 6 0 6 6 8 0 8 2 2 6 4 8 0 0 1 6 8 4 7 7 4 1 1 8 5 3 7 4 2 3 4 5 4 4 2 4 3 7 1 0 7 5 3 9 0 7 7 7 4 4 9 9 2 0 6 9 5 5 1 7 0 2 7 6 1 8 3 8 6 0 6 2 6 1 3 3 1 3 8 4 5 8 3 0 0 0 7 5 2 0 4 4 9 3 3 8 2 6 5 6 0 2 9 7 6 0 6 7 3 7 1 1 3 2 0 0 7 0 9 3 2 8 7 0 9 1 2 7 4 4 3 7 4 7 0 4 7 2 3 0 6 9 6 9 7 7 2 0 9 3 1 0 1 4 1 6 9 2 8 3 6 8 1 9 0 2 5 5 1 5 1 0 8 6 5 7 4 6 3 7 7 2 1 1 1 2 5 2 3 8 9 7 8 4 4 2 5 0 5 6 9 5 3 6 9 6 7 7 0 7 8 5 4 4 9 9 6 9 9 6 7 9 4 6 8 6 4 4 5 4 9 0 5 9 8 7 9 3 1 6 3 6 8 8 9 2 3 0 0 9 8 7 9 3 1 2 7 7 3 6 1 7 8 2 1 5 4 2 4 9 9 9 2 2 9 5 7 6 3 5 1 4 8 2 2 0 8 2 6 9 8 9 5 1 9 3 6 6 8 0 3 3 1 8 2 5 2 8 8 6 9 3 9 8 4 9 6 4 6 5 1 0 5 8 2 0 9 3 9 2 3 9 8 2 9 4 8 8 7 9 3 3 2 0 3 6 2 5 0 9 4 4 3 1 1 7 3 0 1 2 3 8 1 9 7 0 6 8 4 1 6 1 4 0 3 9 7 0 1 9 8 3 7 6 7 9 3 2 0 6 8 3 2 8 2 3 7 6 4 6 4 8 0 4 2 9 5 3 1 1 8 0 2 3 2 8 7 8 2 5 0 9 8 1 9 4 5 5 8 1 5 3 0 1 7 5 6 7 1 7 3 6 1 3 3 2 0 6 9 8 1 1 2 5 0 9 9 6 1 8 1 8 8 1 5 9 3 0 4 1 6 9 0 3 5 1 5 9 8 8 8 8 5 1 9 3 4 5 8 0 7 2 7 3 8 6 6 7 3 8 5 8 9 4 2 2 8 7 9 2 2 8 4 9 9 8 9 2 0 8 6 8 0 5 8 2 5 7 4 9 2 7 9 6 1 0 4 8 4 1 9 8 4 4 4 3 6 3 4 6 3 2 4 4 9 6 8 4 8 7 5 6 0 2 3 3 6 2 4 8 2 7 0 4 1 9 7 8 6 2 3 2 0 9 0 0 2 1 6 0 9 9 0 2 3 5 3 0 4 3 6 9 9 4 1 8 4 9 1 4 6 3 1 4 0 9 3 4 3 1 7 3 8 1 4 3 6 4 0 5 4 6 2 5 3 1 5 2 0 9 6 1 8 3 6 9 0 8 8 8 7 0 7 0 1 6 7 6 8 3 9 6 4 2 4 3 7 8 1 4 0 5 9 2 7 1 4 5 6 3 5 4 9 0 6 1 3 0 3 1 0 7 2 0 8 5 1 0 3 8 3 7 5 0 5 1 0 1 1 5 7 4 7 7 0 4 1 7 1 8 9 8 6 1 0 6 8 7 3 9 6 9 6 5 5 2 1 2 6 7 1 5 4 6 8 8 9 5 7 0 3 5 0 3 5 4 0 2 1 2 3 4 0 7 8 4 9 8 1 9 3 3 4 3 2 1 0 6 8 1 7 0 1 2 1 0 0 5 6 2 7 8 8 0 2 3 5 1 9 3 0 3 3 2 2 4 7 4 5 0 1 5 8 5 3 9 0 4 7 3 0 4 1 9 9 5 7 7 7 7 0 9 3 5 0 3 6 6 0 4 1 6 9 9 7 3 2 9 7 2 5 0 8 8 6 8 7 6 9 6 6 4 0 3 5 5 5 7 0 7 1 6 2 2 6 8 4 4 7 1 6 2 5 6 0 7 9 8 8 2 6 5 1 7 8 7 1 3 4 1 9 5 1 2 4 6 6 5 2 0 1 0 3 0 5 9 2 1 2 3 6 6 7 7 1 9 4 3 2 5 2 7 8 6 7 5 3 9 8 5 5 8 9 4 4 8 9 6 9 7 0 9 6 4 0 9 7 5 4 5 9 1 8 5 6 9 5 6 3 8 0 2 3 6 3 7 0 1 6 2 1 1 2 0 4 7 7 4 2 7 2 2 8 3 6 4 8 9 6 1 3 4 2 2 5 1 6 4 4 5 0 7 8 1 8 2 4 4 2 3 5 2 9 4 8 6 3 6 3 7 2 1 4 1 7 4 0 2 3 8 8 9 3 4 4 1 2 4 7 9 6 3 5 7 4 3 7 0 2 6 3 7 5 5 2 9 4 4 4 8 3 3 7 9 9 8 0 1 6 1 2 5 4 9 2 2 7 8 5 0 9 2 5 7 7 8 2 5 6 2 0 9 2 6 2 2 6 4 8 3 2 6 2 7 7 9 3 3 3 8 6 5 6 6 4 8 1 6 2 7 7 2 5 1 6 4 0 1 9 1 0 5 9 0 0 4 9 1 6 4 4 9 9 8 2 8 9 3 1 5 0 5 6 6 0 4 7 2 5 8 0 2 7 7 8 6 3 1 8 6 4 1 5 5 1 9 5 6 5 3 2 4 4 2 5 8 6 9 8 2 9 4 6 9 5 9 3 0 8 0 1 9 1 5 2 9 8 7 2 1 1 7 2 5 5 6 3 4 7 5 4 6 3 9 6 4 4 7 9 1 0 1 4 5 9 0 4 0 9 0 5 8 6 2 9 8 4 9 6 7 9 1 2 8 7 4 0 6 8 7 0 5 0 4 8 9 5 8 5 8 6 7 1 7 4 7 9 8 5 4 6 6 7 7 5 7 5 7 3 2 0 5 6 8 1 2 8 8 4 5 9 2 0 5 4 1 3 3 4 0 5 3 9 2 2 0 0 0 1 1 3 7 8 6 3 0 0 9 4 5 5 6 0 6 8 8 1 6 6 7 4 0 0 1 6 9 8 4 2 0 5 5 8 0 4 0 3 3 6 3 7 9 5 3 7 6 4 5 2 0 3 0 4 0 2 4 3 2 2 5 6 6 1 3 5 2 7 8 3 6 9 5 1 1 7 7 8 8 3 8 6 3 8 7 4 4 3 9 6 6 2 5 3 2 2 4 9 8 5 0 6 5 4 9 9 5 8 8 6 2 3 4 2 8 1 8 9 9 7 0 7 7 3 3 2 7 6 1 7 1 7 8 3 9 2 8 0 3 4 9 4 6 5 0 1 4 3 4 5 5 8 8 9 7 0 7 1 9 4 2 5 8 6 3 9 8 7 7 2 7 5 4 7 1 0 9 6 2 9 5 3 7 4 1 5 2 1 1 1 5 1 3 6 8 3 5 0 6 2 7 5 2 6 0 2 3 2 6 4 8 4 7 2 8 7 0 3 9 2 0 7 6 4 3 1 0 0 5 9 5 8 4 1 1 6 6 1 2 0 5 4 5 2 9 7 0 3 0 2 3 6 4 7 2 5 4 9 2 9 6 6 6 9 3 8 1 1 5 1 3 7 3 2 2 7 5 3 6 4 5 0 9 8 8 8 9 0 3 1 3 6 0 2 0 5 7 2 4 8 1 7 6 5 8 5 1 1 8 0 6 3 0 3 6 4 4 2 8 1 2 3 1 4 9 6 5 5 0 7 0 4 7 5 1 0 2 5 4 4 6 5 0 1 1 7 2 7 2 1 1 5 5 5 1 9 4 8 6 6 8 5 0 8 0 0 3 6 8 5 3 2 2 8 1 8 3 1 5 2 1 9 6 0 0 3 7 3 5 6 2 5 2 7 9 4 4 9 5 1 5 8 2 8 4 1 8 8 2 9 4 7 8 7 6 1 0 8 5 2 6 3 9 8 1 3 9 5 5 9 9 0 0 6 7 3 7 6 4 8 2 9 2 2 4 4 3 7 5 2 8 7 1 8 4 6 2 4 5 7 8 0 3 6 1 9 2 9 8 1 9 7 1 3 9 9 1 4 7 5 6 4 4 8 8 2 6 2 6 0 3 9 0 3 3 8 1 4 4 1 8 2 3 2 6 2 5 1 5 0 9 7 4 8 2 7 9 8 7 7 7 9 9 6 4 3 7 3 0 8 9 9 7 0 3 8 8 8 6 7 7 8 2 2 7 1 3 8 3 6 0 5 7 7 2 9 7 8 8 2 4 1 2 5 6 1 1 9 0 7 1 …

She does everything with exponentials.

More fun holidays:
March 14th - Pi day
October 23rd - Mole day (we even got a cake once)

This past Thursday evening I attended the Lorne Trottier Public Science Symposium. It’s a highfalutin name for either a very important or completely useless question, depending on who you ask. The audience in the package Leacock 132 lecture theatre, I would guess, consider it to be the former.

The topic was this: Why is the universe just right for life? There are various approaches one can take in an attempt to answer it. One speaker broke it down into three possibilities:

1. The universe must be the way it is, and it’s just lucky that it supports life at all.
2. There are an infinite number of universes, so one suitable for humans was bound to show up eventually.
3. God did it.

The discussion largely ignored the third option, which was fine by me. As for the first two, though, there were some interesting points made. As many people see this question as being highly controversial, especially with you involve intelligent design, I found the most significant statement of the night to be “There is no controversy, only questions,” from Leonard Susskind.

Fine tuning of the universe is a significant part to the problem, and is often used as proof of intelligent design. One of the scientists on the panel (I forget which) made a good analogy to water. We often talk about how if ice were heavier than water (as is the case with most other substances) all the oceans and lakes would be frozen solid and life wouldn’t be able to survive here. Whether that’s true or not, it’s based on the idea that the densities are parameters we could have arbitrarily set. However, now that we have more knowledge of atomic physics than a hundred years ago, we can see that water and ice density is not an arbitrary parameter at all but a consequence of something more fudamental. Thus, it’s quite likely that the many arbitrary parameters people point to to claim fine tuning are just manifestations of something deeper that may yet be explained and nothing special at all.

Similarly, one panelist (either Susskind or David Gross) provided an example that two years before the discovery of DNA, someone published a paper proving that there was no way enough information could be coded in a cell to be passed on to create new generations. With a little more understanding this biological miracle isn’t so miraculous afterall. I wouldn’t be at all surprised if the water molecule analogy is apt here as well, to explain the supposed irreducable complexity of biological systems. Yes, proteins and their functions are incredibly complicated, but it’s all just atoms and fundamental forces scrammbled together in chemical reactions. As Douglas Adams said of evolution, “We may never know precisely what steps life took in the very early stages of this planet, but it’s not a mystery.” No controversy, only questions.

However, I noticed a complete lack of addressing the question of (in the case of number two) where the infinite number of universe came from in the first place, or why, if there is a single unified theory (as implied by number one), it’s that particular unified theory and not some other. Well, Paul Davies did address it for a moment, but only to acknowledge the problem — that no matter which position you took there still seemed to be a appeal to something outside the universe.

It actually boils down to the question of why there’s something here at all and not nothing. A few weeks ago my dad posited at the dinner table that the most important question people ask themselves is “who am I?” or something of that ilk. My reply to that wasn’t a well formed philosophical question and nothing interesting could come from asking it. I still believe that. Interestingly, the response David Gross gave to the question “why is there something and not nothing?” was that it wasn’t a well formed physical question and nothing could come from asking it. “What is nothing?” he asked.

Originally, I posed that question as being much more important than simply “who am I?” and it probably is the biggest question there is, in a sense, but I realise that Professor Gross is right in his suggestion that there’s no point in thinking about it yet since it is so far outside the realm of what science can say. Perhaps sometime it will be within reach, but not today, and probably not for a long time.

I learned a lot of things from Professor Hanna in my Astrophysics class, this being one of them. I’ve already given away the punch line, but for those who aren’t familiar with it:

A farmer is having trouble with a cow whose milk has gone sour. He asks three scientists—a biologist, a chemist, and a physicist—to help him. The biologist figures the cow must be sick or have some kind of infection, but none of the antibiotics he gives the cow work. Then, the chemist supposes that there must be a chemical imbalance affecting the production of milk, but none of the solutions he proposes do any good either. Finally, the physicist comes in and says, “First, we assume a spherical cow…”

Physicists use the phrase to poke fun at themselves for all the simplifications we tend to make. Another McGill prof, Cliff Burgess, was heard to say, “Life is either a free particle or a harmonic oscillator,” and I think most physics students would believe it, even though most things in everyday life are neither free particles nor harmonic oscillators. What does everyday life have to do with physics, anyway?

But it’s not all crazy talk, for I did see a spherical cow yesterday. Metaphorically at least. I’ve heard it said a couple times that many things, even non-fluidic things, can be modelled as fluids. In particular, people, physically speaking, behave like fluids. Not an obvious jump, sure, but it works.

I was coming down to the Milton gates just past 17h, when the majority of people are walking home through the ghetto. The light changed from red to green and a massive hoard of people surged ahead to cross Rue University, each one darting around obstacles and jostling for a position among the other pedestrians. On one side of the corner a stream of people splashed onto a car turning right, some people being diverted away from Milton and up University, others flowing down the middle of Milton. As people spread down the street they spread out, the pressure that had built up at the stop light releasing. Faster people passed others on the inside by skipping along the curb or going into the street, while the average paced people were buffered from the buildings by the occasional group of people who had stopped at the side to talk, mimicking the way water moves down a pipe. We were all just molecules in the same fluid.

There’s something about this book that looks very inviting. It’s got a nice velvety matte burgandy cover, simple text layout, and a artistic phographic inset right in the middle. I see this book and I think it will be filled with similar artistic renderings, bright and colourful, illustrating all the wonders of the universe, like an art history of cosmology. But alas, upon opening it, we see the same old stuff from every one of my plain cover physics and math textbooks:

I suppose I just built myself up for disappointment. But there’s something deeper doing on here. I think everybody, at some point or another, gets a semester or at least one class in their university careers where everything starts being woven together. For me I suddenly saw complex variables being applied in signal processing, differential equations solving mechanics problems, mechanics in quantum physics, quantum physics explaining particle behavior, and looking at particles in special relativity. Suddenly it was obvious that all these classes were talking about the same thing. Here it happens again, except this time the connection is of a much different nature.

It is this: The page above, in my General Relativity textbook, covers the same material as a textbook in one of my philosophy classes, even with the same terminology. I always said there was a connection between physics and philosophy.

Such thoughts always bring me to think about where I want to take my studies after undergrad. I still can’t decide if I like philosophy because it’s just one step higher in abstraction than cosmology (one step too far, say some), or if I like cosmology because it’s one of the areas of physics that has the most philosophical implications. I tell people that I want to study “Philosophy and Physics” but not “Philosophy of Physics”. Unfortunately there are many graduate programs in the latter but only a couple of the former.

But what would a program in “Philosophy and Physics” be, anyway? Today I realised what was lacking about the phrase, and refined it. What I’m really interested in, what’s been my motivation all along is this: The Philosophical Consequences of Physics. In particular, the philosophical consequences of cosmology. Now all I have to do is find a graduate program for it.

Well, I gave it a try.

The wonders of the universe awaited me! How can I turn that down, even if the wind chill was -24 degrees? Half an hour past sunset I put on my winter gear and headed up the mountain, camera in hand. But as I wandered my way up the winding road to the summit (unable to find the direct route of the staircase, hiding in the snow as it was) the cold made its way into my socks and gloves. Good enough though they may be to get me to and from campus on paved sidewalks, they weren’t quite up to the windy mountain snow covered paths.

Before long I had to admit to myself that it was getting darker much faster than I was climbing the hill. I knew Comet McNaught, if it had been visible at all, was quickly setting beyond the hill. I should have brought my compass, but it would have been fairly useless anyway. “Montreal West”, I guessed, was probably too close to being south, meaning the sun had gone down on the other side of the buildings on Redpath Cresent, which I stilll hadn’t overcome, and maybe even on the other side of the mountain entirely. My comet, which had gone down with it, was not going to show herself to me tonight.

At least the view was nice. The more astute of you might notice that this photo was taken facing east, entirely in the wrong direction for chasing a setting sun, but I wasn’t about to go home empty handed.

My childhood is punctuated with memories of my dad waking me up in the middle of the night, driving me to unknown locations, and then pointing something out in the sky. The earliest I can remember was driving over an hour, thermos of hot chocolate in hand, to Fundy National Park, where I saw the rings of Saturn through a telescope for the very first time. Once, while camping in that same park, he brought me out into the woods away from other campers and pointed out the diffuse glow spanning the sky that is our own galaxy, the Milky Way. Perhaps less visually impressive but equally memorable was when we went out into the back woods of French Village to see a small seemingly insignificant fuzzy dot—a comet.

Naked eye comets are rare enough as it is, but this month Comet McNaught has been making headlines around the world. In this picture, from Nasa’s Astronomy Pic of the Day, it can be clearly seen above the city of Krakow, Poland, just after sunset. Now there’s word (eg. from Phil Plait and Astroprof) that the comet is so bright that it’s visible in broad daylight.

Unfortunately, not only has the brightness probably piqued this past weekend, so with each successive day it’ll get harder to see, but Mother Nature chose today to finally start winter, so the Montreal sky is full of snow and clouds. Otherwise I’d be tempted to trek up Mount Royal and try to get a look at it. Hopefully it’ll be nice and clear tomorrow, so I’ll finally be able to get a look at this, the brightest comet in 30 years, far surpassing that fuzzy blob of my youth, if only in aesthetics and not significance.

… that I’ll mention this negative one twelfth business. From my string theory final exam this afternoon:

1. (g) What is the physical significance of the sum 1+2+3+…, and how can it be evaluated? What does it evaluate to?

I must have known it was coming somehow. Who ever said blogging isn’t good for my studies? I totally nailed that exam today. Where by “totally nailed” I mean “at least passed”, but that’s pretty good for this class.

I was worried I was going to sleep in today, or be really tired all afternoon, after having some trouble getting to sleep last night. I just lay in bed for at least a couple hours. Eventually my craving for a big glass of milk grew too great and I had to get out of bed. And of course once I was in the kitchen I had to have a cookie, and then make some tea as well.

Before long I was settled onto the couch watching i heart huckabees. There was a strange connection between that and my string theory studies, so I like to think the movie ended up putting things in a nice perspective and helped me pass. It’s all about the blanket. It’s all about space-filling D25-branes and their excitation modes. One and the same, oh baby yeah.

Well, the sum of all positive numbers is equal to negative one twelfth afterall. Or at least I found the part in the textbook that explains it. The downside is that it’s not explained so much as there’s a problem telling the reader to figure it out for themselves. Problem 12.4. It was assigned as a homework problem a few weeks ago and everything, so in theory I should understand it.

It has something to do with the zeta function, defined as:

The argument can be complex, but there is a finite answer for any where the real part is greater than one. But what we want to know is what happens if .

Apparently you do some fancy calculus trickery (analytic continuation), which I won’t try to explain because frankly it’s mostly lost on me, to get an equation for which is valid down to . Then you can find not only

but also

.

For the record, that has nothing to do with string theory. It’s just mathematics. Crazy complex variable calculus, to be sure, but still just mathematics.

In english, not only is the sum of all positive numbers (1+2+3+…) equal to negative one twelfth, but if you add one to itself an infinite number of times (1+1+1+1…) you get negative one half.

Bet you didn’t see that coming.