Continuous as the stars

Continuous as the stars

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No computer stuff today.

Martin Gardner - writer, skeptic, recreational mathematician - died recently. As a teenager I would scour the back room of Casablanca Books looking for back issues of Scientific American for interesting Mathematical Recreation columns. Martin Gardner was one of the people whose work got me interested in mathematics, science and computing, so I'd like to dedicate today's blog to his memory.

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I was driving home late from dinner at a friend’s house the other day. It wasn’t raining, so the top was down, in keeping with my policy. As I merged onto the highway I glanced up and saw Vega, which made me happy. Of course. Who isn’t happy when they see part of the Summer Triangle? It makes me think of long moonless nights on the beach in my youth, watching for shooting stars and polar orbit satellites with my physicist friend John and our respective cousins.

Vega is only 25 light years away, hardly any distance at all astronomically speaking. And yet it appears as just a point of light in the sky. No matter what binoculars or telescopes you aim at it, Vega will not resolve into a disk. It’s just too small.

Or is it?

As I was driving home I started to think about the big picture of Vega; what is it really like? I want to consider not just Vega the highly localized, rapidly rotating mass of incandescent gas, but everything Vega was, is, and will be.

Vega is a young star, only 455 million years old, give or take a dozen million years. There were vertebrate fishes swimming in the oceans of the planet Earth when a sizeable ball of gas and dust falling towards its center attained sufficient mass and pressure to start thermonuclear fusion of its hydrogen. At that moment of ignition massless photons of many wavelengths started streaming symmetrically away from the center of the new star, along with charged particles like electrons, neutral neutrinos and so on.

The set of photons and other particles originating from the ignition of Vega forms a sphere. At the moment of ignition that sphere was relatively small, but of course immediately behind those first photons were more and more photons. We have an ever-expanding, (and increasingly tenuous) sphere of particles.  

A scant twenty-five years later a new star lit up in the Paleozoic night sky; the sphere of photons had reached 25 light years in radius, forming a volume of about 4 * 10^50 cubic meters. Of course, some of those photons were intercepted by collisions with atoms in the interstellar medium, and each Vega photon is getting farther and farther apart from its nearest neighbor as it gets farther away from its creation.

That sphere's diameter has grown inexorably by 36 billion metres every minute for the last 455 million years. The original sphere of ignition photons is now 910 million light years in diameter, encompassing not only our entire galaxy and its local group, but the entire supercluster. That outermost sphere has got to be exceedingly low density by now, but surely some of those photons and neutrinos and whatnot have survived. We can easily see visible light from galaxies billions of light years away through the Hubble Space Telescope; those photons are light from stars just like Vega, light that has travelled through the interstellar medium for billions of years only to fall onto the primary mirror of the Hubble.

The Earth is practically at the center of that sphere now, only 25 light years away from the center of a sphere almost a billion light years in diameter. Vega is not small; the entire object that is the light emitted by Vega is huge. The angular size of the surface of the star right now is tiny, but the angular size of the whole thing since its ignition is enormous. The reason it looks so small to me is a function of my limited perspective; I can deduce what some of the characteristics of the whole billion-light-year wide sphere of photons is like, but I can only see an infinitesimally tiny fraction of it. If I had sensors all over the galaxy and some ability to integrate their data into a coherent whole over a large time scale, my perspective of Vega would be quite different.

In short, Vega doesn’t look like a point because it is a point with respect to me; Vega looks like a point because I am a point with respect to it.

  • Beautiful. :-)

  • It is a part of human freedom to chose our point of reference. Since the 16th century, humans were their own points of reference. Antic and middle-age physics reflected this point of view. Galileo learned us to change our point of view, teaching that the center of the universe is the Sun and not the earth. Physics changed accordingly.

    Yet, choosing a point of reference is an ideological, not a physical question. Physics teach that all referenctal systems are equivalent. Since the choice is not imposed by physics, it is a matter of choice. And a matter of freedom. Why us humans should not choose the humanity as the center of our own world? Why should we take a referential system that makes less sense for us?

    For most engineers, Newton's physics and classic chemistry make sense. Only a fraction of scientists need a model of the reality that is more distanced from the human experience, such as quantic and relativist mechanics.

    For most humans, it is still meaningfull to think that the sun raises in the morning and sleeps during the night, and to consider Vega as a small point in the sky.

    So I think this statement about the size of a human is nor true nor false, but is simply the result of you exercising your free choice of referential system.

    It probably makes more sense to most humans to see Vega as a point.

    * * *

    Some computer stuff related to that.

    Choosing a referential system, or an ideology, is like making a choice of language. Languages are a semantic network; nodes of the network (ideas, believes) make sense because of their connections to other nodes (not unlike Google PR algorithm). There are different ideological system: christian, marxists, or liberals explain the world and the history differently; all explanations make sense inside their own system but don't make in another system.

    A language may be appropriate to a set of problems and not to another. For instance, the christian system is appropriate to give sense to human action and relationships, but does not make sense to explain physic processes. Darwinism is great to explain the evolution of spieces. Does it make sense to give sense to human action? Today's rate of people thinking life is meaningless gives a clue that many people are probably evaluating their own life with the wrong language.

    So just as in programming, humans must choose their thought framework according to the problem they are addressing. I could use C# for everything, but some maths I would prefer Matlab, for logical programming Prolog, for massively parallel computing Erlang, and so on. C# would make it, but it would be much more painful (even with the help of PostSharp :).

    The same for humans. I do not choose the same framework of thoughts if I am solving an engineering problem as if I am considering how I should behave with my neightboors. I could use a scientific framework of though for everything, but it would make my life much more painful.

    (Of course, this choice is so important that the mighty try to push the framework that will direct the action in their advantage -- as catholicism in past centuries or liberalism more recently).

    So for my everyday's life, I still prefer seeing Vega as a point.

  • I remember reading Martin Gardner's articles in SA with fondness. I recall particularly enjoying the puzzles on polyominoes.

  • Interesting take on "the big picture of Vega", inverting the usual perspective on, um, perspective.  

    Thinking about Vega since first ignition is interesting for the effects of relativity, too.  That expanding sphere of photons is not just the first light from Vega--it's the first information of any kind, which of course includes the fact of Vega's existence.  (Setting aside faster-than-light communication).  In that sense, the sphere is the border between a universe in which Vega exists, and a universe in which it doesn't.  We can imagine an array of sensors surrounding Vega, but if they're not turned on before Vega exists, there's no way we could flip the switch in time to get the picture of the first light.  

    In order to be sufficiently far from Vega to perceive the geometric entirety of it, you'd have to be where Vega doesn't, for practical purposes, exist.  

    I think Gardner would approve.

  • Excellent !!!!!!!

    Especially the last line.

  • I initially thought the topic of your article was related to OLAP and not stellar astrophysics.  I was pleasantly surprised you chose the later as a topic.  What’s interesting to me is that one observes a point of light but is able to perceive in the mind’s eye an expanding sphere.  It’s a beautiful yet counter-intuitive metaphor of how abstraction reveals truth more succinctly than cursory observation.  ...Which relates back to OLAP in a way--at least from my perspective. :-)

    Now try to visualize it not as an expanding sphere, but as a four-dimensional cone. What angle do the surfaces of spheres that make up cross sections of the hypercone make with each other?  45 degrees of course; it only makes sense to calibrate the time dimension such that one year of time is equivalent to one light-year of distance, and therefore the hypercone is twice as broad as it is tall! The part of the 4-cone you can directly see is the intersection of the surface of a particular spherical cross section with the locus that is your retina, (at those points in space/time when the retina is oriented correctly, of course.) - Eric

  • Fantastic post.  I was recently watching some of Carl Sagan's Cosmos and your post reminds me a lot of some of his amazing narrative.  I always experience a profound (as profound as I can be anyway) sense of awe when considering, well, the Cosmos.

    If you haven't come across it already, there's a great set of videos someone put together from pieces of different scientific films and shows called Symphony of Science.  The jewel of the set is A Glorious Dawn: www.youtube.com/watch  (it starts a little odd, give it a minute).

  • Very nice tribute to a great communicator - reading back issues of SciAm was a childhood passion of mine, and Mathematical Games was the best part.

    If Vega's "true" size is the size of the sphere of light it has emitted, because it is an emitter, then I assert that my true size - given that I am predominately a consumer of light - is the size of the sphere of light that I can consume. Why should be emission be favoured over consumption?

    "I" am as large as the totality of my perception - which must include ancient features of the primordial universe perceptible as ripples in the cosmic background radiation. And so compared to "me", Vega is indeed merely a point. :)

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