The Cascades Raptor Center

The Cascades Raptor Center, Eugene, Oregon (image credit)

I am currently travelling in the US, and recently dropped in at the Cascades Raptor Center in Eugene, Oregon (see the Raptor Center website and Raptor Center instagram). This is primarily a hospital and rehabilitation centre for injured raptors (eagles, hawks, falcons, ospreys, owls, vultures, etc.). By my count, 37 birds are on public display in wire mesh aviaries (mostly birds too seriously injured to be released).

Admission is US$10 per adult, and there is a small gift shop. Viewing the birds takes about an hour, and I really enjoyed my visit (the Center would also appeal to children of all ages). Tripadvisor gives the Center 4½ stars, which is probably a little more than I would give, given the Center’s size (but the money supports the Center’s work). There are also more interactive night-time viewing events, which I did not experience.

Ferruginous hawk (Buteo regalis) and Gyrfalcon (Falco rusticolus) at the Raptor Center (photographs by Anthony Dekker)

---

Australia Day Honours, 2021

It’s Australia Day again, which means the annual Australia Day honours. Some recipients of note this year in the field of the sciences include:

• Emeritus Professor Cheryl Elisabeth Praeger, now a Companion of the Order of Australia (top left in photo: credit John Henstridge). Professor Praeger has published extensively in group theory and other areas of mathematics, and was the Inaugural Director of the Centre for the Mathematics of Symmetry and Computation at the University of Western Australia.
• Professor Mark Randolph, now an Officer of the Order of Australia (top right in photo: credit UWA). Professor Randolph is a geotechnical engineer specialising in foundation systems for offshore structures such as oil rigs, and has published extensively in that field, as well as holding important academic and other posts. He is a Fellow of The Royal Society.
• The Honourable Patricia Lynne (Trish) White, now a Member of the Order of Australia (bottom left in photo: credit @trishwhiteeng). Trish White has been an engineer, academic, government scientist, politician, cabinet minister, board member, company director, and National President of Engineers Australia.
• Dr Carden Crea Wallace, now a Member of the Order of Australia (bottom right in photo: credit Carden Wallace). Dr Wallace is an expert on corals, and has published extensively in that field, including her book Staghorn Corals of the World. She is also Emeritus Principal Scientist at the Queensland Museum.

Congratulations to all four of these outstanding Australians, and to the many others on the list.

---

For another perspective:

• Top left: the Petersen graph is the smallest vertex-transitive graph which is not a Cayley graph. One of the many publications of Professor Cheryl Praeger AC constructs other such graphs.
• Top right: an oil rig (photo credit Ken Hodge). Professor Mark Randolph AO is an expert in their engineering, and a Fellow of The Royal Society.
• Bottom left: the headquarters of Engineers Australia (photo credit Bidgee). The Honourable Trish White AM is a past National President.
• Bottom right: a staghorn coral (photo credit Albert Kok). Dr Carden Wallace AM has written a definitive book on Staghorn Corals of the World.

---

Spot the difference

I have been playing around with “spot the difference” puzzles. This one is based on a photograph by Daderot, with a few edits of my own. More of these on my Instagram.

---

The Sydney Observatory

Observatory exterior (photo by Greg O’Beirne, 2006)

An unusual free science museum in Sydney, Australia is the Sydney Observatory. This opened in 1858 as a working observatory. The time ball, which dropped each day to mark the exact time, is still operating at 1:00 PM each afternoon. The observatory now operates as a small museum, having been refurbished during 1997–2008. The telescopes can also be used on paid night tours.

The observatory is a stiff climb up Observatory Hill. The exhibits are limited in number, but include some excellent orreries. Unless you have some astronomical expertise, the paid guided tours will be helpful. My brief visit was an enjoyable one.

An orrery at Sydney Observatory (photo by Anthony Dekker)

---

The Plimpton 322 tablet re-examined

Several years back I blogged about the Plimpton 322 tablet – a Babylonian clay tablet from around 1,800 BC. It contains four columns of numbers, written in base 60 (with a small number of errors, as well as some numbers missing through damage – these are corrected below). For example, 1.59:00:15 = 1 + 59/60 + 0/3600 + 15/216000 = 1.983402777777778.

Column B of the tablet (with a label on the tablet containing the word “width”) is one of the sides of a Pythagorean triangle, and column C (with a label on the tablet containing the word “diagonal”) is the hypotenuse, such that C² − B² is always a perfect square (yellow in the diagram). Column A is exactly equal to C² / (C² − B²), the ratio of blue to yellow.

A	B (“width”)	C (“diagonal”)	D
1.59:00:15 = 1.983402777777778	1:59 = 119	2:49 = 169	#1
1.56:56:58:14:50:06:15 = 1.949158552088692	56:07 = 3367	1:20:25 = 4825	#2
1.55:07:41:15:33:45 = 1.918802126736111	1:16:41 = 4601	1:50:49 = 6649	#3
1.53:10:29:32:52:16 = 1.886247906721536	3:31:49 = 12709	5:09:01 = 18541	#4
1.48:54:01:40 = 1.815007716049383	1:05 = 65	1:37 = 97	#5
1.47:06:41:40 = 1.785192901234568	5:19 = 319	8:01 = 481	#6
1.43:11:56:28:26:40 = 1.719983676268861	38:11 = 2291	59:01 = 3541	#7
1.41:33:45:14:03:45 = 1.692709418402778	13:19 = 799	20:49 = 1249	#8
1.38:33:36:36 = 1.642669444444444	8:01 = 481	12:49 = 769	#9
1.35:10:02:28:27:24:26:40 = 1.586122566110349	1:22:41 = 4961	2:16:01 = 8161	#10
1.33:45 = 1.5625	45	1:15 = 75	#11
1.29:21:54:02:15 = 1.489416840277778	27:59 = 1679	48:49 = 2929	#12
1.27:00:03:45 = 1.450017361111111	2:41 = 161	4:49 = 289	#13
1.25:48:51:35:06:40 = 1.430238820301783	29:31 = 1771	53:49 = 3229	#14
1.23:13:46:40 = 1.38716049382716	28	53	#15

What is this table all about? A good discussion is by Eleanor Robson [“Words and pictures: new light on Plimpton 322,” American Mathematical Monthly, 109 (2): 105–120]. Robson sees Plimpton 322 as fitting into standard Babylonian mathematics, and interprets it as a teacher’s effort to produce a list of class problems.

Specifically, Robson believes that the table was generated by taking values of x (in descending order of x) from standard Babylonian reciprocal tables (specifically the values 2:24, 2:22:13:20, 2:20:37:30, 2:18:53:20, 2:15, 2:13:20, 2:09:36, 2:08, 2:05, 2:01:30, 2, 1:55:12, 1:52:30, 1:51:06:40, and 1:48) and then using the relationship (x − 1 / x)² + 2² = (x + 1 / x)² to generate Pythagorean triples. If we let y = (x − 1 / x) / 2 and z = (x + 1 / x) / 2, then B and C are multiples of y and z, and A = z² / (z² − y²).

Just recently, Daniel F. Mansfield and N. J. Wildberger [“Plimpton 322 is Babylonian exact sexagesimal trigonometry,” Historia Mathematica, online 24 August 2017] interpret the table as proto-trigonometry. I find their explanation of the first column (“a related squared ratio which can be used as an index”) unconvincing, though. Why such a complex index? Robson calls such trigonometric interpretations “conceptually anachronistic,” and points out that there is no other evidence of the Babylonians doing trigonometry.

Mansfield and Wildberger also suggest that “the numbers on P322 are just too big to allow students to reasonably obtain the square roots of the quantities required.” However, I don’t think that’s true. The Babylonians loved to calculate. Using the standard square-root algorithm, even simplistic starting guesses for the square roots of the numbers in column A give convergence in 2 or 3 steps every time. For example, to get the square root of 1.59:00:15 (1.983402777777778), I start with 1.30:00:00 (1.5) as a guess. That gives 1.24:40:05 as the next iteration, then 1.24:30:01, and then 1.24:30:00 (1.408333333333333), which is the exact answer. That said, however, calculating those square roots was not actually necessary for the class problems envisaged by Robson.

Sadly, I do not think that Mansfield and Wildberger have made their case. Robson is, I believe, still correct on the meaning of this tablet.

---

Updated museum tag map

Since I have made even more museum-related posts, I have revised my earlier tag maps to give the clickable mosaic below. This tag map links to many (though not all) of my posts concerning museums (large and small) around the world. See the mouseover text, or click to jump to the relevant post:

The centre four rectangular photographs (and all six circular ones) here are mine; the others are public domain.

---

The Sci-Bono Discovery Centre, Johannesburg

Interior, Sci-Bono Discovery Centre (photo: Nick Gray)

On my recent South African trip, I visited the Sci-Bono Discovery Centre in Johannesburg. This science museum is a little like Questacon in Canberra. Sci-Bono’s strengths are the large number of well-built interactive exhibits and the large number of helpful staff. Exhibits concentrate mostly on physics and technology. All ages from toddlers to adults are catered for.

Interactive electrolysis exhibit (photo: Anthony Dekker)

The Sci-Bono Discovery Centre is not free, but is value for money. I enjoyed it, and Tripadvisor gives it 4.5 stars. Sci-Bono is active on Facebook and Twitter.

Atlas Cheetah E aircraft on display (photo: Alan Wilson)

---

Failure to collect type specimens of new species considered harmful

A September 2016 letter to Nature defended the naming of new species without the traditional type specimen. Some months earlier, Nature had an editorial on the same subject.

A group of 493 concerned taxonomists responded by saying that type specimens were essential for objectivity and replicability. Nature would not publish their letter, and so it appeared in Zootaxa in November. And they are right, of course – even with the ability to go back and check preserved specimens (especially their DNA), taxonomy can be a tricky business. Without that ability, it would be a nightmare.

---

The job’s not over yet, guys

The Bible (Genesis 2:19–20) describes the first man as beginning an inventory of the world’s animal species. Bob Dylan famously set the story to music in Man Gave Names to All the Animals (1979):

“Man gave names to all the animals
In the beginning, in the beginning
Man gave names to all the animals
In the beginning, long time ago

He saw an animal that liked to growl
Big furry paws and he liked to howl
Great big furry back and furry hair
‘Ah, think I’ll call it a bear’ …”

In spite of all the millenia that humanity has lived on our planet, this inventory has only just begun. An estimated 8.7 million eukaryotic species exist, with about 86% still awaiting description. At the current rate of progress, finishing the job will take centuries – and during that time, many species will become extinct without ever having been inventoried. Many species have already been lost forever.

Some of the older species descriptions will also need to be re-examined. There are specimens on museum shelves which represent unrecognised species. The job’s far from over yet, guys. We obviously need substantially more resources for the task.

---

The Museum of Osteology, Oklahoma City

Interior of the Museum of Osteology (my photo)

The Museum of Osteology in Oklahoma City is a small private museum devoted to bones and skeletons. Specimens in the museum (over 300 skeletons and 400 skulls) were collected by Jay Villemarette, a skeleton fanatic who appears to have found his niche in life during childhood. Villemarette also owns the company Skulls Unlimited, which is located next door to the museum, and which provides much of the material in the museum gift shop.

  
Left: human skull with bullet wound; right: Western Diamondback Rattlesnake – photos by Michael Alumbaugh (cropped)

Specimens in the Museum of Osteology are displayed well (see photos above and below), and I found the museum interesting. Tripadvisor also rates the museum highly. For admission prices and further information, see the museum website.

    
Left: Raccoon; centre: Northern Seahorse; right: Broad-footed mole – photos by Michael Alumbaugh

---