Resonant Constellation

I was reading an article recently (on how best to use a press pot for making coffee, if it matters) in order to improve my coffee brewing method (so far, my coffee presses have been of hit or miss quality, with about one out of every three pots turning out amazing and the rest so-so), and a single phrase the author used stood out to me. Here’s the quote from the article:

…many people see the leap from instant to press pot coffee as one in the quantum variety – it’s almost too much to go for.

Now, this author is not alone in this mistake; plenty of people make it. I’m just left wondering why? If you understand the science, even at a very basic level, you would know that the word quantum implies something extremely, unimaginably small–so small, even, that it is not observable in the normal course of human existence. So how has the phrase, “Quantum Leap” entered the common lexicon meaning “Something Extremely Large”? This is entirely mystifying to me. Almost assuredly, no physicist nor indeed anybody with any direct experience with the subject would claim that quantum mechanics is anything but extremely tiny. This is similar to, though less understandable than the common usage of the term ‘Lightyear,’ to mean a large measure of time or progress.

I think some small amount (perhaps a quanta) of insight can be gained from this entry at Answers.com:

Q:
How big is a quantum leap?

A:
Extreamly big. The true fans would wish that a quantum leap movie will come out.

Yes, it is Extreamly big, as is my annoyance.

Here’s two unrelated, but cool things.

First, from Phil Plait’s website, LRO has gotten a picture of the Apollo 17 landing area on the moon including the flag! Here’s a link to Phil’s post with the actual pictures. This is extra cool, because I have a friend who is a grad student in lunar geology who works with LRO data, and she knows a hell of a lot about the moon. Once, when a bunch of us physics/astro people had gathered around to imbibe some beer and partake of good company, we saw her skype status message was a physics problem about diffusion of gas from a thruster rocket hitting a certain object a certain distance away. We, being the huge nerds we are, immediately began working this problem out and arrived at a sensible answer, which we sent to her. Her reply? “Oh, God, please tell me you didn’t really do that, it was supposed to be a joke!” A few minutes later, our solution was sent to NASA. Keep in mind, by this point none of us was exactly 100% sober. If you hear about some moon satellite disaster, you may know who to blame…

Anyway, the other, unrelated cool thing I wanted to share was this, a periodic table table. That’s pretty neat.

P.Z. Meyers, a biologist, professor, and an excellent blogger who runs the blog Pharyngula, has located what I can only classify as a perfect example of the word wharrgarbl. View it here. It is a lecture by a homeopathic “doctor” on physics. Let’s critique.

She begins by asking about the background of her audience, which is a good move, there’s usually no way to tell if your lecture will go right over the audience’s heads if you don’t ask. Next, she proceeds to proclaim that light is energy. This is a bit of an oversimplification, as light is oscillating electric and magnetic fields, but it’s not wrong enough that I’ll make any special deal out of it. She then tells us that energy is mass times the speed of light, which is almost correct (it is really the speed of light squared), but then gets the equation correct, so I’ll also let that one go. The next bit is where we go down the rabbit hole:

If you collapsed all the mass down into the universe so there was no space between the mass…do you know how much mass there is in the entire universe? You think you’re a lot of mass, right? I’m a lot of mass, right? This building is a lot of mass. Well, the whole universal mass can be consolidated down into the size of a bowling ball. That’s all there is in the whole world. In the universe.

This is wrong. Assuming that the entire universe is made of protons and that the mass of the entire observable universe is grams (give or take), if we condensed that mass into a sphere with no space between the protons it would have a radius of a bit more than the earth’s orbit. This is more than just a little bigger than your average bowling ball. I can also guarantee you that this would immediately collapse into a black hole, which means that it would all be in a single, geometrical point. This is much smaller than a bowling ball (% smaller, to be exact).

But even my all proton universe is not a great model. The vast majority of the matter in the universe is dark matter-close to 95%, and we have no idea how it behaves, nor how dense it really is. I have no idea where the bowling ball figure comes from, but it is clearly untrue. Let’s see how this continues:

So, how much mass are you? That’s right, an infantesimal [sic] amount. So if you take that formula, , you can almost cross out mass! So the formula ends up being energy equals the speed of light!

This is the point where I feel like going to bang my head against a very hard brick wall. The fact that she has completely misunderstood the mass-energy equivalence theorem is not uncommon, but the fact that she tries to make believe that she does understand it is just…mind boggling. You may now consider my mind fully boggled.

Energy does not equal the speed of light. Why? There are several reasons:

• The units are wrong. Energy is measured in mass times length squared per time squared, putting it in metric units would yield units of . The speed of light is measured in meters per second. A careful inspection will yield a shocking result: these quantities are not the same.
• Even in her equation, energy is still equal to the speed of light SQUARED. That is what the little 2 means above the c. The c is what stands for the speed of light.
• Her methodology for arriving at this result is wrong. You cannot, in fact, cross out mass. The equation tells us that mass and energy are equivalent with a certain scaling factor (that would be the afore mentioned speed of light…SQUARED). What it means is that energy and mass are basically the same thing, that they are interchangeable. Since you are a small bit of mass relative to the universal mass, you are also a small bit of energy relative to the universal energy. The equation tells us how to convert between the two media. By crossing out mass, you make the equation complete nonsense.

Okay, let’s continue:

Okay, and that’s why the vision system is so important, because we have lots of photoreceptors that receive light.

Okay, I know you think I’ve missed some words, and I thought so too at first, but I swear she goes straight from the last quote to this quote without a pause. Let’s see if she actually goes somewhere coherent with this (hint: she doesn’t):

But when Honnoman died, he, um, the scientists didn’t fall in his camp okay? The pieces of the puzzle didn’t fit well together. So God in his infinite wisdom sent another Einstein called Stephen Hawkings. Okay, Stephen Hawkings gave us the String Theory [emphasis in original].

I have to assume she’s talking about Stephen Hawking, the former Lucasian Professor of Mathematics at Cambridge. Hawking is a brilliant astrophysicist and a personal hero of mine in the field. As far as I know, he hasn’t really done too much work on string theory, his work concentrates more on general quantum gravity and black holes. Many people contributed to the formulation of string theory. Stephen Hawking was not one of them. Unless there really was a theoretical physicist working on the quantum gravity problem around the 1970s named Stephen Hawkings who worked in complete obscurity and came up with some primitive form of string theory, then I think we can call this myth busted.

I won’t even try to broach the subject of some sort of God sending us another Einstein. Oh, and who is Honnoman?

And what he discovered is that there are other “energetic particles” in the universe, and they’re shaped like little “U”ies, and what they do is they work by vibration.

She delivers this sentence while waving her hand around in a weird U shape. Let me take a moment to point out one thing: nobody has discovered any conclusive evidence that string theory is applicable to this universe. Nobody has discovered little “U”ies (whatever those are) that work by vibration. In fact, a lot of physicists think that string theory is totally bunk. On the other hand, a lot think that it, or a version of it, or perhaps another theory similar to it, may be found to be correct at some later date. None of them think that it has been proven.

As for the “little “U”ies that work by vibration” part, this gets confusing. The strings are not essential to the theory. They could be expressed as points, one dimensional objects, or even surfaces-they are not guitar strings or loops of yarn like many people seem to think. It is a very complicated idea, and few (if any) people really understand it. The reason it gets talked about so much is that the analogies that physicists use to talk about it are very pretty. The math behind them, however, is extremely ugly.

Anyway, let’s continue:

So our body is so wonderfully designed, we have light receivers, and we have ears. String, vibratory, they pick up vibration. So, if you added to that theory, Einstein’s theory of relativity, we have , but mass is crossed out, almost, and strings, vibration [begins to wave hand here to simulate vibration].

She is clearly confused. String theory does not postulate that the entire universe is made up of some sort of tiny string orchestra. The vibration of the strings in string theory is not something we could hear-don’t mistake me, I don’t mean that it would just be outside the human hearing range, I mean that it is not sound in any way, shape, or form.

But that still doesn’t tell us the whole picture!

Uh-oh.

Because, what is a cell?

Where is she going with this?

Right? Okay, so a cell has cell walls, cell membranes, cytoplasm. Is that mass?

No. It is matter, which has a property we call mass.

Not very much, really, right? So what are they? What is that? You can break down the cells into tiny pieces of energy…

I suppose you could if you used them in a nuclear bomb…

…called electrons, protons, neutrons, right? Okay, so the whole body has an infantesmial [sic] amount of mass, but what is the remainder? Energy. So I am energy, you are energy.

We are not energy as such. We are matter, which has mass, which is interchangeable with energy. They are not the same thing.

Okay, now if you go to study physics, energy cannot be created. We do not know how to create energy. But we don’t know how to destroy it either. That is not humanely possible. So what we do is we take energy and we transform it from one state to another. That’s all we do.

First off, I think going to study physics is a good idea for this woman, she clearly does not understand it. The real principle she is referring to here is conservation of energy, which she almost gets right. What it really says is that mass-energy cannot be created or destroyed. Mass-energy is simply the combination of mass and energy (you’ll recall that they are interchangeable-BUT NOT THE SAME). Oddly enough, she does get the transformation from one state to another correct-that is all that is physically possible (much less humanely). I’ll chalk that up to luck. So what’s next?

So if that’s all we do, guess what the definition of disease is? It’s not mass! We have transformed our energy state into something different. That’s what the definition of disease is.

My Oxford English Dictionary, eleventh edition (2004), defines disease thusly:

Disease-Noun. 1: A disorder of structure or function in a human, animal, or plant, especially one that produces specific symptoms or that affects a specific part. 2: A quality or disposition that adversely affects a person or group: The British disease of self-deprivation.

I can’t really tell what she defines disease as, except that it’s not mass and there’s something having to do with transforming energy states. Perhaps my edition is out of date?

So we should be able to re-transform our energy into a previous, better state.

Is that like when I decide to wipe my computer’s hard disk and restore from a saved image?

What we do is we use light, we can use sound, we can use homeopathy. Okay, so what is homeopathy?

A bunch of crock?

Okay, if nothing is really mass, or an infantasimal [sic] amount of it, and everything is energy, that means everything has a vibration to it.

So why does everything have a vibration to it again? I don’t know, and I’m pretty sure she doesn’t either.

So what if I could encase some sort of energy for later use?

Congratulations! You have invented the battery! I expect you shall be hearing from Energizer and Duracell soon.

Alright, folks, this is the point at which she descends into pure nonsense and talks about blowing up her neighbor’s dog with chemicals because he crapped on her lawn. Or something. Suffice to say, nearly every word is complete wharrgarbl. She concludes with the line:

And that’s how it works.

I would like to consider myself a moderately intelligent guy: I’ve survived nearly four years of rigorous training in astrophysics and I haven’t gone entirely insane yet. At the very least, I understand the basic principles of logic. However, even after watching this video twice, I still have no idea how it works. All I can conclude is that she thinks that mass doesn’t exist and everything is energy, and that diseases are a change in energy.

She goes on for an encore to tell a short story:

Every single one of us vibrates with a certain vibration, and so we either vibrate with a plant, a mineral, or an animal.

What is this, 20 questions? Ted, are you a tank?

The way we talk, the way we interact with people, is that’s how we are.

Wisdom for the ages. She wraps up by telling a story about the time she had a patient with a squeaky knee. For a minute or two, it becomes a series of seemingly disconnected statements, then she says that he took a pill and his squeaky knee went away! My question: was that pill full of WD-40?

I simply don’t get it. Why do people believe this stuff? Why don’t people trust scientists and doctors who have spent decades intensely studying a single subject? I am simply baffled.

To begin the weirdness, let me direct you towards this link which I found on FARK.com, my favorite online not-news aggregator. It is ostensibly an image of a sculpture of Bernie Madoff being crushed against a wall by a farting bull. I told you it was going to be weird.

When I saw this, I noticed many odd details about the sculpture, not the least of which is the rather impressive…well, for lack of a better phrase, exhaust column. As a physics/astronomy major, my first thought was: Wow! I wonder how much energy that bull would have to produce and how much pressure that would cause on… you get the picture. So I worked it out using basic Newtonian mechanics and some (extremely shoddy) assumptions, and I figured out that the lower limit for the pressure on the…thrust nozzle (this time for lack of a more decent phrase)…would be approximately 2.88 million Pascals. To put that in other terms, that would be roughly 28.5 times atmospheric pressure or approximately 417 pounds per square inch. I did this quick calculation in Wolfram Alpha, which is great for giving alternate units and comparisons. My three favorites were that this pressure is roughly equivalent to the pressure under 300 meters of water, ~0.3 x atmospheric pressure on the surface of Venus (~9 MPa ), or (and this is the best one) ~100 x sound pressure of the Krakatoa explosion at 160 kilometers (~ 20000 Pa ). Remember, this is a lower limit to the pressure. In this case, I think the bull is to be pitied more than Bernie.

Recently several papers came out that indicate that magnetic monopoles (or magnetic monopole analogues) actually exist. If you don’t know what these are, look them up on wikipedia, and you’ll see that it’s a pretty exciting result. IF these results are true (note the big if), physics has some serious changing to do. For example:

no longer holds. WOAH! A change to Maxwell’s equations! HERESY!

Here’s some links to articles and papers about it:
Nature News
Science NOW
Observation of Magnetic Monopoles in Spin Ice, Kadowaki et al. 2009
Magnetic Charge Transport, Bramwell et al. 2009

Every once in a while, some technology from Star Trek becomes real. We already have communicators (cell phones), phasers and automatic doors, and we almost have cloaking and matter teleportation (yeah, really). Now, we almost have holodecks:

Link to video

That, my friends, is awesome. So, what’s next? Warp drive? Replicators? Androids? We can only hope.

Live long and prosper.

Every once in a while, I entertain myself by learning about random math stuff. A recent example is my foray into Fibonacci sequences which I mentioned in a previous post. This time, my friend Pete mentioned a peculiar number, called Graham’s number. As far as I can tell, this is the largest number to ever be used in a serious mathematical proof.

I know what you math-nerds out there are thinking: larger, even, than a Googol? (), or a Googolplex? (). Yes, my friends, Graham’s number is inconceivably big. It makes a Googolplex look like a mere handful. Interesting note: when I was little, no more than five, I remember writing out a Googol on an etch a sketch and trying to explain it to my grandparents. I was a weird kid.

Graham’s number is so absurdly large that there are not enough particles IN THE UNIVERSE to express it via any standard notation. Think about that-go outside to a high place and look around. Then think that everything you can see is made of inconceivably tiny particles which are so small, they cannot be seen by the human eye, nor any optical magnifier that has ever, or will ever, be made. Look at your hand-there must be millions, perhaps billions of particles in your hand alone. And yet including everything you can see, much less the entire friggin’ universe, there aren’t enough of these unfathomably tiny particles to write out this number, even using a series of exponents. Wow.

So how do you write it down? Well, mathematicians are relatively creative people (if not entirely practical), and they’ve come up with intriguing ways of expressing large numbers. One way is called “Up-arrow notation,” in which the number is expressed by a series of rows including numbers and arrows which signify computational steps to arrive at the number itself. Each higher row is predicated on how many arrows are in the last row. This is the only way to express Graham’s number. To show just how depressingly large this number is, you still can’t even express just the first row of up-arrow notation with all of the particles in the universe. There are 64 total rows.

What I can tell you about it is that it ends in the string “…262464195387″, where the … represents a whole lotta other numbers. So why would anybody in their right mind need such a comically large number? Were these mathematicians perhaps compensating for something (say, the budget differential between their department and a useful department like Astronomy)? From wikipedia:

Graham’s number is connected to the following problem in the branch of mathematics known as Ramsey theory:
Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?
Graham & Rothschild [1971] proved that this problem has a solution, N*, and gave as a bounding estimate 6 ≤ N* ≤ N, with N a particular, explicitly defined, very large number; however, Graham (in unpublished work) revised this upper bound to be a much larger number. Graham’s revised upper bound was later published — and dubbed “Graham’s number” — by Martin Gardner in [Scientific American, "Mathematical Games", November 1977].
The lower bound was later improved by Exoo[2003], who showed the solution to be at least 11, and provided experimental evidence suggesting that it is at least 12. Thus, the best known bounding estimate for the solution N* is 11 ≤ N* ≤ G, where G is Graham’s number.

Wow, that’s so useful (/sarcasm). It must have been a profoundly depressing result: “So, Ronald, how’s that proof you’re working on coming? Did you ever get a result?”
“Yeah, it’s somewhere between 11 and wharrgarbl.”

Even as an astronomer (a field which is known for large numbers, even coining the term ‘astronomical’), I’d probably just call it “effectively infinite for all foreseeable/sane purposes.” No wonder it was published in “Mathematical Games.”

In all honesty, stuff like this is probably good for the math departments-it will keep them at their desks during the inter-departmental war. I for one know that the physics department has long desired to vaporize the chemistry department with a large laser array. The mathematicians will likely be too busy coming up with crazy stuff like Graham’s number to be bothered by such events.

Last minute note:
I have just discovered that there is a larger named number, called TREE(3). It is part of a sequence of numbers: TREE(1)=1, TREE(2)=3, TREE(3)=Makes the word big seem hackneyed. Apparently, Graham’s number is “unnoticeable” next to a lower bound to TREE(3), which is itself unnoticeable next to TREE(3). I hear TREE(3), will anybody go to TREE(4)? Sold to the man in the straightjacket.

There are even bigger numbers yet, obviously, including “Totally Indescribable Cardinals,” (yes, that is the formal name), Transfinite numbers, and all sorts of made up names (Bajillion, Frumptillion, etcetera). For an incredibly humorous article on made up, unspecified numbers, look here.

Of course, infinity puts all of these so-called large numbers to shame. Compared to infinity, they might as well be 0. Maybe you should be careful next time you use the word “infinite” in casual conversation. You probably doesn’t mean that many.

]Michel Mayor and his exoplanet hunting team have done it again. Gliese 581e weighs in with a minimum mass of . For the technical details, followthis link to the pre-print paper. Of course, this is a pre-print (though accepted for publication in A&A), so it’s not in publication state yet, just out to show that this group discovered it first. The paper will likely be revised before it is finally published, but in my (admittedly short) experience, this is the only copy most people will read.

Most of the time, the inclination angle for these systems isn’t known (unless the planet transits the host star, in which case it can be derived from the impact parameter of the transit, b via a relatively simple formula), so the masses of most known extrasolar planets are listed as lower limits. In this case, however, the system has three other low mass planets, and since it is a stable system, it can be dynamically modeled and upper limits can be placed on the planet masses. In this case, the upper limits on all planet masses in the system is at 1.6 times the minimum, so the maximum mass for this newly discovered planet is only -still a significant discovery. The planet is, however, too close to the star to support life at 0.03 AU and has an orbital period of roughly days (3.14942 to be more exact).

The other planets in the system are worth mentioning as well. Gl581b, the first discovered is at least 15.62 earth masses with a semi-major axis of 0.04 AU, Gl581c is only 5.36 earth masses with a semi-major axis of 0.07 AU, and Gl581d is 7.09 earth masses and orbits at a distance of 0.22 AU. This last is particularly interesting because the planet lies in the habitable zone around the host star.

This remarkable system is only 20 lightyears distant from earth (it is actually the 87th closest known star system), and the host star is likely visible in relatively small (say, 6-7 inch) amateur telescopes. You can find it in the constellation approximately 2 degrees north of beta libra (’commonly’ called Zubeneschamali or Zuben el Chamali). For those of you who want to look for it yourselves, here’s a starchart centered on the location that should help you find it. Of course, libra isn’t up high in the sky until late these days, so you’ll have to stay up late to catch it.

It is now 6:30 PM. I have been in the physics building since 8:00 AM save two short (~10 minutes) breaks for food at around noon and 6 PM. I began today by studying for a test, and then I took it at 11. It was a horrific experience, none were left unscathed. Judging by the comments afterwards, it’s a good thing the exam was given by a proxy and that our teacher is out of town-there might have been…interesting dealings afterwards otherwise. Then I began work on the E&M homework due tomorrow. “There’s only four problems, how hard could it be?” I thought. Oh, past me, how naïve you are.

Here I am almost seven hours later having completed a grand total of half of the work. I wasn’t the only one working on this, either, there was a rotating group of about 6 people working on the same problems. The best part of it all was when we thought we had one problem finished, so almost everybody left, and then the remaining two of use figured out that it was wrong and spent three hours getting it right, which we eventually did before going to fetch dinner. Of course, when getting dinner, we realized that it still wasn’t right, so we got back to work.

I wonder what the outside is like, it’s been so long. Please, help us.

Today, 3/14, is a special day. That’s right, it’s Pi day! Today is the day to celebrate the gloriousness of the mathematical constant pi. Let’s consider:

3.14159265358979323846264338327950288419716939937510
5820974944592307816406286208998628034825342117067982
1480865132823066470938446095505822317253594081284811
1745028410270193852110555964462294895493038196442881
0975665933446128475648233786783165271201909145648566
9234603486104543266482133936072602491412737245870066
0631558817488152092096282925409171536436789259036001
1330530548820466521384146951941511609433057270365759
5919530921861173819326117931051185480744623799627495
6735188575272489122793818301194912983367336244065664
3086021394946395224737190702179860943702770539217176
2931767523846748184676694051320005681271452635608277
8577134275778960917363717872146844090122495343014654
9585371050792279689258923542019956112129021960864034
4181598136297747713099605187072114999999…and so on.

Ha ha! Pi is really irrational, it doesn’t continue with a string of nines forever (or does it? You’ll have to find out…). But anyway, pi day is a really special day for a lot of people. Today is Albert Einstien’s birthday for one, which is reason enough to celebrate, but on a more personal note, today is the anniversary of two very good friends of mine (one is a math teacher and the other is a physics student). For all these reasons, Pi day is one of my ever growing list of “Science Holidays,” (for example: Apple day or Gravmas, Issac Newton’s birthday. Which also happens to be Christmas.) I urge you to celebrate-bake a pie in the shape of pi, do some relativity, study brownian motion, there’s tons of things you could do!

Note: The point in pi at which I stopped (…999999…) is a very special sequence, known as the Feynman point. In a lecture once, Feynman said he wanted to memorize pi up until a point when he could say “Nine, nine, nine, nine, nine, nine, and so on,” implying that pi is rational and ends in a repeated sequence of nines. This is typical Feynman awesomeness. The fact that this sequence occurs so early in pi (starts at digit 762) is truly intriguing. Read more here.