So this is issue 747, and besides the obvious affiliation with the big passenger jet, I was poking around the web looking for any other numerical fun about the number.

That’s when I saw a weird thing. 747, it turns out, is equal to this: 

 What is that?

I wasn’t familiar with the symbol that’s like a bracket with the top bar erased. The number — 4²³ / 3²³ — is equal to about 747.47, which is not exactly 747, but pretty close, just with a little bit of a decimal left over.

That’s when I realized what the symbol is. It means “floor”.

You’re probably familiar with rounding: You round up to the nearest integer, say, if a number has a decimal (technically called the mantissa) value of .5 or more, and you round down if it’s less than that. But there are times you want to force the number to be rounded up, or rounded down. Those functions are called ceiling and floor, for obvious enough reasons.

The floor symbol looks like that bracket with the top bar missing, and ceiling has the bottom one missing. I actually like these symbols; once you see them they make sense visually for what they represent. 

So anyway, welcome to the floor(4²³ / 3²³) issue of the BAN!

P.S. The next issue like this will be #996 (in early-ish 2026), which is floor(4²⁴ / 3²⁴).

On July 12, 2022, NASA and ESA released the very first official images from JWST. It’s been two years since, with a lot of extremely cool stuff from the infrared observatory — both pretty images and amazing science — during that time.

On the second anniversary of this event, the space agencies have released a new image, and it’s very cool: the interacting galaxies Arp 142.

The object is informally named the Penguin Galaxy, although to me it looks more like a hummingbird (and you just don’t see the wings because they’re beating too rapidly). Perfect for the theme, too, is the smaller elliptical galaxy to the lower left, called the Egg, because of course it is. The official names of the individual galaxies are NGC 2936 and 2937, and they’re about 300 million light years from Earth.

To the experienced astrofan the Penguin is clearly the result of a galactic collision (in this case, with the Egg). As two galaxies pass each other, the gravity of each can draw out the other like taffy. They swing by each other in a curve, flinging that material away in great, graceful arcs. This particular collision is a little different, though. The Penguin was a large spiral galaxy, its old core making the eye and the rest of it from the spiral arms. The Egg, though, is a compact elliptical galaxy, and was able to retain its shape better.

The image combines near-infrared observations from JWST’s NIRCAM with far-infrared ones from MIRI, its two cameras. Several filters were used to create this multi-hued shot. Most of the light you see here is emitted by cold molecular hydrogen gas (two atoms bound together) and dust (sooty, carbon-based molecules). The clumps in the body and beak are likely where stars are actively forming due to gas clouds were compressed by the collision and collapsed.

I like all the other galaxies in the background; that string of several along the bottom of the Penguin may very well be related, though much farther away (I’m guessing here, but they do all appear roughly the same size). The galaxy to the upper right is a nearly edge-on disk galaxy possibly similar to the Milky Way. The two stars next to it are very likely in our own galaxy; if they were in that other far more distant galaxy they’d be impossibly luminous; not even a supernova could get that bright.

The name of these collective galaxies, Arp 142, is interesting too. Halton Arp was an astronomer who was among the first to catalog interacting galaxies that could be spotted in sky surveys due to their weird shapes. Quite a few bear his name.

Arp was an iconoclast. In the 1960s the first quasars were discovered, galaxies that were point-like in images but relatively bright, and blasting out radio waves, too. Spectroscopic data showed them to have very high redshifts (well, for the time), which indicated they were at great distance, up to a couple of billion light-years away. That in turn meant they must be incredibly luminous, far more than normal galaxies.

Some astronomers, though, didn’t agree that redshifts indicated distance, but may be indicative of something else. Mind you, the basis of our understanding that the Universe is expanding is that redshift corresponds to distance, and the greater the redshift the more distant a galaxy. In essence and in fact, astronomers arguing against that were arguing against the Big Bang.

Arp was one of them. He studied images of quasars and believed that they always turned up near galaxies we knew were much closer to us. He thought that implied a relationship between them, which in turn meant those quasars were close to us as well. One idea he had was that they were objects ejected from the cores of galaxies, and that some other physical phenomenon was going on to mimic redshift. He even thought he saw that their redshifts were quantized, meaning they were all multiples of a number instead of a smooth distribution.

Despite a lot — a lot — of evidence against this idea, he clung to it and his denial of the Big Bang model until he died. In my opinion (and that of essentially all astronomers) he was wrong. Before his death he even wrote a book on his beliefs, called Seeing Red, and his tone throughout is aggrievement, upset about what he felt was unfair treatment by other astronomers.

I think it’s a cautionary tale of what happens when you love your own ideas so much you can’t fairly weigh the evidence against them; you just argue against that evidence and have to come up with more complicated and Rube Goldbergesque machinery to support your conclusion. For some people — a lot of people, really — it’s not easy to look back and realize just how twisted up they’ve gotten. I’ve seen it happen to a lot of scientists, and of course we see it a lot in pseudoscience as well. And politics, and religion, and pretty much any personal belief system where self-identity is tied in.

So, as with so many people, Arp’s legacy is a mixed bag. His earlier work with interacting galaxies was a big step forward in our understanding of how galaxies behave, and his later work, well, maybe the lesson there is different than what he intended, but an important one nevertheless. 

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