Starry Eyed Dimensions

By The Metric Maven

Bulldog Edition

My friend Dr Sunshine is very good at expressing and interpreting numbers. He has a favorite example from Star Trek IV: The Voyage Home (1986) that he uses to illustrate numerical importance:

Spock: [in response to Kirk pawning his antique spectacles from Wrath of Khan] Excuse me, Admiral. But weren’t those a birthday gift from Dr. McCoy?

Kirk: And they will be again, that’s the beauty of it.

[to Antique Store Owner]

Kirk: How much?

Antique Store Owner: Well, they’d be worth more if the lenses were intact. I’ll give you one hundred dollars for them.

Kirk: …Is that a lot?

Recently the farthest star ever viewed by a telescope was sighted. Phil Plait, Bad Astronomer, and worse metric user, attempted to impress his audience by saying:

This is incredible: Due to a quirk of cosmic geometry, astronomers have detected the light from the farthest individual star ever seen. How far away is it?

Over nine billion light-years away.

Yes, you read that right. Nine. Billion. Light-years.

A single star, from that distance. Holy yikes. Seriously, when I read about this the hairs on the back of my neck stood up. This is seriously amazing, so much so that for a moment I couldn’t believe it was real. Then I read the paper, played with the math a little, and, sure enough, this appears legit.

I was immediately uncertain just how far away this star is. A billion light years?—is that a lot? In my essay Long Distance Voyager, I use metric prefixes to categorize different astronomical items:

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I define nearby stars as those measured in Petameters (1015), and far away when measured with Exameters (1018). Long ago it stuck in my brain that the observable universe has a dimension that is in Yottameters (1024). So just how big is 9 billion light years? Well, knowing that a light-year is 9.4607 Petameters we multiply this by 9 billion (Giga-) and obtain 85 Yottameters! Wow, that is big. The farthest detected galaxy is about 126 Yottameters, and the diameter of the observable universe is about 880 Yottameters! This is one serious Yottasurprise. We can see two metric triads farther than the metric definition of far away stars! How on Earth, or actually how in the universe, did this happen?

Well, it is an interesting coincidence that allowed it. The star would normally be too faint to see, but a cluster of galaxies between the star and ourselves acts as a gravitational lens, which concentrates the light from that star enough for us to see it. Not only can we see it, the star has been identified as a blue supergiant, which is one of the brightest type of stars known. Rigel in the Orion constellation (lower right star) is a blue supergiant, but is at a distance of only about 8 Exameters from us. Deneb is 24 Exameters from us. One of the farthest stars ever seen is UDF 2457, which is 558 Exameters away; whereas the just discovered Lensed Star 1 (LS1) is 85 000 000 Exameters distant. The human eye can only detect a minute number of stars which are only about 10 Exameters from us, beyond that, individual stars fade into the blackness, hidden from our unaided gaze. Galileo was amazed at the number of normally invisible stars that his telescope allowed him to suddenly see. Keep in mind that our Galaxy is only about 1000 Exameters across, all the stars you see with your eyes are essentially local.

Einstein asserted that a large mass literally warps space. The closer one is to the large mass, the larger the amount of warping. On May 29, 1919, a group led by Arthur Eddington (1882-1944) and Frank Dyson (1868-1939) took a photograph during a total solar eclipse. Stars near the Sun changed their position with respect to stars further away. When images of the stars, taken when the Sun was absent, was placed over one taken by Eddington’s group during the eclipse, stars near the Sun were seen to be in a different position than those radially further away, and therefore less influenced by the Sun’s gravity. This bending of light has important uses in astronomy. When searching for planets that might have been ejected from their home solar systems into space, astronomers watch for a light-warped signature that a planet produces when passing in front of a star. In the case of LS1, lensing distortion occurs as it orbits around the center of the galaxy where it resides. The location of the individual galaxies that make up the “lensing cluster” are not homogeneous which also introduce undesired aberration.

The cluster of galaxies happen to be located in positions that add together (most of the time) in a way to capture and concentrate the light from this single star, and allow us to see an extra two metric triads (1 000 000) further in distance than is normally possible. Is that alot?—YES!

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Postscript: On 2017-08-24 Bad Astronomy posted an essay titled: A 500 TRILLION KM LONG STREAMER OF AMMONIA IN ORION. Is that a lot? Well, 500 Trillion Km is 500 Petameters, or a length that encompasses a distance to nearby stars in our own galaxy. When one uses Ye Olde English Prefixes with metric, it’s not even pigfish, it’s just fishy.

The Design of a Marking Rule

By The Metric Maven


I’ve discussed the design of rulers a few times before. I’ve always been amazed at the number of options which have been used to define their divisions, and label their values. The website BoingBoing introduced me to another option for ruler design-–stenciled holes. The Incra website has a  millimeter metric-only ruler with stenciled holes that allow a person to mark distances with great precision. I could not help but purchase a 300 mm version to see how well it works. To the left is the label which boasts that this rule is a new 300 mm long metric, albeit 300 MM on the label.

click to enlarge

The first thing one notices is that the numerical labels for the holes and slots bounce up and down. I suspect this was done with the intention that separating the numbers spatially, would make it easier to distinguish them. In my view, it tends to be a bit of a distraction, but this type of separation has been used on other rulers and seems workable. This is a minor concern as Incra offers millimeter-only rules of this type in the US, which is of great utility when other options are limited.

The rules are flexible enough to conform to many objects and allow for accurate marking.They are also essentially stencils, and without pressure, do not return to a flat planar state under their own weight when placed on a flat surface. They are not really designed for use as an everyday ruler, but are for woodworking projects and other designs which might need a conforming rule with precision measure.

Below is a close-up of the left end of the rule:

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Incra has a lot of marking options on these rules. They have openings that will just accommodate a 0.5 mm Pentel mechanical pencil lead. One must extend the pencil lead far enough out to protrude through the hole or slot as the outer lead guide is too large to fit. The zero marking spot on the left hand side of the rule for both the line and single dot markings is cut in half to maintain the best accuracy possible. In the case of the dots at the center they start with half and are stepped in case you want even more accuracy and option.

A video shows how certain versions of their rulers allow you to mark dots and lines with ease, but they tout their inch-length versions and only casually mention that metric versions are available. If a person misguidedly insists they must have both a US inch and millimeter scale, the best version in my view is the 10″ decimal/mm marking ruler. The top scale is millimeters which is a clue that metric is the preferred scale for measure. Below is the inch scale which is marked in tenths of an inch with 1/20″ openings between. Recall that a millimeter is about 1/25″ and is the most precise measurement increment on the scale.

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Related essays:

The Design of Everyday Rulers

Stickin’ it to Yardsticks

The American “Metric Ruler”

America’s Fractional Mind