Category Archives: History

A neat geometry lesson! And a rant…

13 Thursday Feb 2020

Posted by in education, flat, History, Math, Optics, teaching, Telescope Making, Uncategorized

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Here is some information that teachers at quite a few different levels could use* for a really interesting geometry lesson involving reflections involving two or more mirrors, placed at various angles!

Certain specific angles have very special effects, including 90, 72, 60, 45 degrees … But WHY?

This could be done with actual mirrors and a protractor, or with geometry software like Geometer’s Sketchpad or Desmos. Students could also end up making their own kaleidoscopes – either with little bits of colored plastic at the end or else with some sort of a wide-angle lens. (You can find many easy directions online for doing just that; some kits are a lot more optically perfect than others, but I don’t think I’ve even seen a kaleidoscope that had its mirrors set at any angle other than 60 degrees!)

I am reproducing a couple of the images and text that Angel Gilding provides on their website (which they set up to sell silvering kits (about which I’ve posted before, and which I am going to attempt using pretty soon)).

At 72º you see 4 complete reflections.

When two mirrors are parallel to each other, the number of reflections is infinite. Placing one mirror at a slight angle causes the reflections to curve.

 

https://angelgilding.com/multiple-reflections/

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Rant, in the form of a long footnote:

* assuming that the teacher are still allowed to initiate and carry out interesting projects for their students to use, and aren’t forced to follow a scripted curriculum. It would be a lot better use of computers than forcing kids to painfully walk through (and cheat, and goof off a lot) when an entire class is forced to use one of those very expensive but basically worthless highly-centralized, district-purchased computer-managed-instruction apps. God, what a waste of time – from personal experience attempting to be a volunteer community math tutor at such a school, and also from my experience as a paid or volunteer tutor in helping many many students who have had to use such programs as homework. Also when I was required to use them in my own classes, over a decade ago, I and most of my colleagues found them a waste of time. (Not all – I got officially reprimanded for telling my department chair that ‘Renaissance Math’ was either a ‘pile of crap’ or a ‘pile of shit’ to my then-department head, in the hearing of one of the APs, on a teacher-only day.

Keep in mind: I’m no Luddite! I realized early on that in math, science, and art, computers would be very, very useful. I learned how to write programs in BASIC on one of the very first time-share networks, 45 years ago. For the first ten years that my school system there was almost no decent useful software for math teachers to use with their classes unless you had AppleII computers. We had Commodore-64’s which were totally incompatible and there were very few companies (Sunburst was one) putting out any decent software for the latter. So when I saw some great ideas that would be ideal for kids to use on computers to make thinking about numbers, graphs, and equations actually fun and mentally engaging, often I would have to write them my self during whatever free time I could catch, at nights and weekends. Of course, doing this while being a daddy to 2 kids, and still trying to teach JHS math to a full load of students (100 to 150 different kids a day at Francis Junior High School) and running a school math club and later coaching soccer. (I won’t say I was a perfect person or a perfect teacher. I believe I learned to give better math explanations than most, didn’t believe that you either have a ‘m,ath gene’ or you don’t, at times had some interesting projects, and at times was very patient and clear, but had a terrible temper and often not good at defusing things. Ask my kids or my former students!) Later on, I collaborated with some French math teachers and a computer programmer to try to make an app/program called Geometrix for American geometry classes that was supposed to help kids figure out how to make all sorts of geometric constructions and then develop a proof of some property of that situation. It was a failure. I was the one writing the American version, including constructions and tasks from the text I was currently using. There was no way I could anticipate what sorts of obstacles students would find when using this program, until I had actual guinea pig students to use them with. Turns out the final crunch of writing however many hundreds of exercises took place over the summer, and no students to try them on. Figuring out hints and clues would require watching a whole bunch of kids and seeing what they were getting right or wrong. In other words, a lot of people’s full time job for a long time, maybe paying the kids as well to try it out so as to get good feedback, and so on. Maybe it could work, but it would require a lot more investment of resources that the tiny French and American companies involved could afford. We would have really needed a team of people, not just me and a single checker.

I find that none of these computer-dominated online learning programs (much less the one I worked on) can take the place of a good teacher. Being in class, listening to and communicating logically or emotionally with a number of other students and a knowledgeable adult or two, is in itself an extremely important skill  to learn. It’s also the best way to absorb new material in a way that will make sense and be added to one’s store of knowledge. That sort of group interaction is simply IMPOSSIBLE in a class where everybody is completely atomized and is on their own electronic device, engaged or not.

Without a human being trying to make sense out of the material, what I found quite consistently, in all the computerized settings, that most students absorbed nothing at all or else the wrong lessons altogether (such as, ‘if you randomly try all the multiple choice answers, you’ll eventually pick the right one and you can move on to some other stupid screen’; it doesn’t matter that all your prior choices were wrong; sometimes you get lucky and pick the right one first or second! Whee! It’s like a slot machine at a casino!).

By contrast, I found that with programs/apps/languages like Logo, Darts, Green Globs, or Geometer’s Sketchpad, with teacher guidance, students actually got engaged in the process, had fun, and learned something.

I find the canned computer “explanations” are almost always ignored by the students, and are sometimes flat-out wrong. Other times, although they may be mathematically correct, they assume either way too much or way too little, or else are just plain confusing. I have yet to detect much of any learning going on because of those programs.

Trying to Figure Out Problems With a Century-Old Refractor

22 Sunday Sep 2019

Posted by in astronomy, History, Optics, Telescope Making, Uncategorized

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I am disassembling the lens cell of the >100 year old 6” f/14 Kiess refractor that produces horrible results on star tests.

There is absolutely no information inscribed anywhere inside the cell, inside the tube or outside it, nor on the edges of the lens elements. I can only guess as to what type of glass they used, and figuring it out won’t be easy. The least destructive method I can think of beginning to do this is by weighing them and calculating out their precise volumes, and from that calculating their densities. A graduate gemologist could probably calculate their indices of refraction, but not me.

Tomorrow I plan to measure the curvatures of the lens elements; perhaps someone familiar with old telescopes will then have clues as to who might have made this particular type of optical prescription.

The shims seem to me to be intact, so I think I can rule out astigmatism from lens elements put in crooked. [OTOH, someone on the Antique Telescopes Facebook group says that the large number of small black spacers in between the lenses may itself be causing the massive astigmatism problem that we found in the star test. I don’t have enough experience to be able to tell whether that’s correct or not.]

The small chips on the edge of the second (meniscus? Flint?) lens element were already there when I got it. I was also surprised to find that the first (biconvex, crown?) lens element has a small bubble very close to the center. It’s probably not significant, but I will check for strain as well.

 

Gently tapping off the lens cell from the tube
Note that the retaining ring holding the front of the first lens merely slides into the cell; it’s held in place by four screws. The threading is on the inside of the ring, and the outside is smooth
You can see the black tape and tan cardboard spacers
Me looking puzzled
The cardboard spacers around the edges
The two lenses together; note the multiple, small black tape spacers between the pieces of glass
The original chips on the second lens element
The empty lens cell. Note that they didn’t make it black

Cleaning Up a Century-Old Refractor

18 Sunday Aug 2019

Posted by in astronomy, History, Hopewell Observatorry, Optics, Telescope Making

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Last week, I was helping staff and students at the University of Maryland’s Observatory to clean out a storage trailer.

We noticed a seven-foot-long, 6-inch diameter telescope that had been sitting in a corner there, unused, ever since it was donated to the National Capital Astronomers (NCA) club nearly ten years earlier by the son of the original owner, Carl Kiess,  who had worked at the Lick Observatory in California and the National Bureau of Standards in or near DC, but who had passed away nearly fifty years earlier. I figured I could put it on a motorized telescope mount at Hopewell Observatory and at a minimum test the optics to see if they were any good. The current officers and trustees of NCA all said they thought this was a good idea.

One thing that caught my eye was how filthy and flaky the coating was on the tube itself, although the lens appeared to be in good shape.

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The drive, while impressive, does not have a motor, requires a pier, and is extremely heavy. I decided not to mess with the drive and to put it temporarily on our existing, venerable, sturdy, motorized, electronic drive we have at Hopewell Observatory.

So I experimented with various abrasives and solvents to clean off the nasty green coating; a fine wire wheel inserted in an electric drill did the best job. Here it is partly cleaned off:

I then used Brasso for a final polish, followed by a final cleaning with acetone, and then applied several coats of polyurethane to keep it looking shiny for a number of years. (The lenses stayed covered for all of this!) So this is how it looks now:

The next task is to make a temporary holder and then put it on the mount, and then test the optics.

Silvering Mirrors, and More, at Stellafane

05 Monday Aug 2019

Posted by in astronomy, flat, History, Math, monochromatic, optical flat, Optics, science, teaching, Telescope Making, Uncategorized

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For me, these were the two most significant demos at the 2019 Stellafane Convention in Springfield, Vermont:

(1) Silvering large mirrors, no vacuum needed

We had a demonstration by Peter Pekurar on how to apply a layer of Silver (metallic Ag, not aluminum) onto a telescope mirror, accurately, with a protective, non-tarnishing overcoat, that works well. I looked through such a scope; the view was quite good, and I was told that interferograms are great also.

What’s more, the process involves overcoating a mirror with spray bottles of the reagents, without any vacuum apparatus needed at all. Note: Silver coated, not aluminum coated. This is big for me because the upper limit at our club’s aluminizer is 12.5″, but some of us are working on larger mirrors than that; commercial coaters currently charge many hundreds of dollars to coat them.

You can find information on some of these materials at Angel Gilding. Peter P said he will have an article out in not too long. Here are a few photos and videos of the process:

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Finished mirror; notice it’s a little blotchy

 

 

IMG_4985IMG_4987

(2) Demo and links for Bath Interferometer (see http://gr5.org/bath )

How to set up and use a Bath interferometer to produce highly accurate interferograms of any mirror for many orders of magnitude less cash than a Zygo interferometer. As I wrote earlier, Alan Tarica had taken the lead on fabricating one at the CCCC – NCA ATM workshop, and we eventually got it to work, but found it rather frustrating and fiddly to use.

The presenter is a HS teacher, and it shows: he explains things very clearly! On his website ( http://gr5.org/bath ) you can get plans for 3-D printing the parts for the Bath device, if you have any access to a 3-D printer, so you can print the parts out for yourself. He also has links to vendors that are selling parts for it, such as certain small lenses, mirrors and beam splitters. He shows you where you can get them for very little money from Surplus Shed and such places. Or you can purchase his really inexpensive kits that he’s already 3-D printed for you. Plus parts for an XYZ stage, which you will need for fine focus. The whole setup (not counting mirror stand and two tripods, which he assumes you have access to already) is under $130.

I will need to look carefully at our setup as built almost completely by Alan, and see how it differs and what we would need to do to make it better. The problem is that there are lots of little, tiny parts, and many of them need to be adjustable. We saw him doing LOTS of little adjustments!

Before his talk, I had absolutely no idea how this (or similar interformeters) really worked. Now I understand: the interference fringes that we see are really contour lines – like we see on on a USGS topo map, only with the mirror tilted in one direction or the other. A big difference with the USGS topo map is that there, the contour lines (isohypses – a new word for me today) are often 10 feet to 100 meters apart. In interferometry, the contour intervals are either one or one-half lambda (wavelength of light) apart – a really tiny amount! We need that level of accuracy because the surface we are studying is sooooooo flat that no other measuring system can work. His explanation of this whole thing now makes perfect sense to me. And the purpose of the software (free!) is to un-slant the mirror and re-draw it using the countour-line information.

Beautifully clear explanation!

Caution: a friend who works professionally in optics told me his team had made three Bath interferometers, using cheap but good quality ebay xyz stages, and found that they were just too much trouble; so they borrowed a very expensive commercial interferometer (costing many tens of kilobucks) from another department and are using that instead. I’m not selling my house to get a Zygo interferometer!!! But I will try the Bath interferometer instead.

 

 

Math – How Come We Forget So Much of What We Learned in School?

27 Monday Aug 2018

Posted by in astrophysics, education, History, Math, science, teaching, Telescope Making, Uncategorized

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This was a question on  Quora. Here is an answer I wrote:

In the US, judging strictly on what I’ve seen from my time in the classroom as both a student, a teacher, and a visiting mentor of other math teachers, I find that math and science was very often taught as sort of cookbook recipes without any real depth of understanding. The recent National Council of Teachers of Mathematics prescriptions have attempted to correct that, but results have been mixed, and the Common Core has ironically fostered a weird mix of conceptual math marred by teachers being *OBLIGATED* to follow a script, word-for-word, if they want to remain employed. Obviously, if students are really trying to understand WHY a certain mathematical or scientific thing/fact/theorem/theory/law is true, they are going to have questions, and it’s obviously the teacher’s job to figure out how best to answer said questions — which are not likely to have pre-formulated scripts to follow in case they come up — and which are going to take time.

Another thing that is true is that not everything in mathematics has real-world applications in every single person’s life. I taught a good bit of computer programming (aka ‘coding’ today), geometry, arithmetic, probability, algebra, statistics, and conic sections, and in fact I use a LOT of that every week fabricating telescope mirrors to amazing levels of precision, by hand, not for a living, but because I find telescope-making to be a lot of fun and good mental, aesthetic, manual, and physical exercise. But I’m a pretty rare exception!

Most people obviously don’t dabble in math and physics and optics like I do, nor should they!

In fact, I have made it a point to ask professional scientists and engineers that I meet if they actually use, on their jobs, all the calculus that they learned back in HS and college. So far, I think my count is several dozen “Noes” and only one definite “Yes” – and the latter was an actual rocket scientist / engineer and MIT grad and pro-am astronomer (and wonderful, funny, smart person) who deals/dealt with orbital rocket trajectories. (IIRC).

In France, when I went to school there 50 years ago and in my experience tutoring some kids at the fully-French Lycee Rochambeau near Washington, DC, is that they go very deeply into various topics in math, and the sequence of topics is very carefully thought out for each year for each kid in the entire nation (with varying levels of depth depending on what sort of track that the students elected to go into (say, languages/literature, pure math, or applied sciences, etc), but the kids were essentially obligated to accept certain ideas as factual givens and then work out more and more difficult problems that dealt with those particular givens. No questions allowed on where the givens came from, except to note the name of the long-dead classical Greek, French, Italian or German savant whose name is associated with it.

As an American kid who was mostly taught in American schools, but who also took 2 full years of the French system (half a year each of neuvieme, septieme, premiere, terminale, and then passed the baccalaureat in what they called at the time mathematiques elementaires, I found the choice of topics [eg ‘casting out nines’ and barycenters and non-orthogonal coordinate systems] in France rather strange. Interesting topics perhaps, but strange. And not necessarily any more related to the real world than what we teach here in the US.

Over in France, however, intellectuals are (mostly) respected, even revered, and of all the various academic strands, pure math has the highest level of respect. So people over there tend to be proud of however far they got in mathematics, and what they remember. Discourse in French tends to be extremely logical and clear in a way that I cannot imagine happening here in the public sphere.

So to sum up:

(a) most people never learned all that much math better than what was required to pass the test;

(b) only a very few geeky students like myself were motivated to ask ‘why’;

(c) most people don’t use all that much math in their real lives in the first place.

 

 

Safer Table Saws Should Be Mandatory

14 Monday Aug 2017

Posted by in History, Safety, science, Telescope Making

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Three parts to this little essay:

  • What happened to me about a month into my retirement, with an old, nearly-free table saw that lacked SawStop safety features (and which I was using totally improperly, because I didn’t know better)
  • Table saws are one of the most commonly-used power tools both commercially and at home, and are responsible for an AMAZING number of injuries and amputations every DAY.
  • A fix for this exists — the technology included in every single SawStop table saw. The inventor tried, but failed to convince table saw manufacturers to incorporate this essential, and not-terribly-expensive feature, and they ALL turned it down, essentially saying that ‘safety doesn’t sell’. Congress has the power to make this feature mandatory and to save many a hand, finger, or eye.

Part One

These are not trick shots. It’s just my left hand, imaged poorly just now with my smart phone. I was really ashamed, embarrassed, and sad when this injury occurred, roughly a month after I retired from teaching, for several reasons:

(1) It turned out that I was using the table saw totally improperly, holding a very small piece of wood as I fed it into the blade

(2) I literally did not know that was an improper way of feeding wood into a table saw; I was treating it like a band saw

(3) I should have read up on safety rules for table saws, even though I had used them without incident quite a few times earlier, and thought that I was safe enough (and I wasn’t)

(4) While I am right-handed, losing part of one’s left-hand index finger and having the adjacent finger be mauled so that it lacks feeling on one side, and doesn’t bend properly, and is crooked, means that there are many things one can never do again – for example typing quickly and efficiently. The letters e, r, t, d, f, g, c, v, and b (look at your keyboard and if you ever learned touch typing, you’ll see why) are all now much harder for me to type. And unfortunately for me, E and T are the two most common letters in the alphabet. (I’m not asking for sympathy! Just don’t do this to yourself!! Wear safety equipment and read the fri&&14& manuals!)

 

On the good side, I am extremely grateful and amazed at the skill of Dr. Reisin, my hand surgeon. Without any warning that I could see, my hand got dragged into the blade by the tiny piece of wood. My two fingers looked like very fresh hamburger, and I thought I had lost them down to stumps. I was amazed that when I got my first view of the damage, I still had most of them! Yay Dr. Reisin! Really, amazing job!

In addition, we have Kaiser Permanente family high option insurance. It’s not cheap, something like $400 a month that I pay, plus I have a wonderful subsidy from the DC government, which pays something like $1000 a month. All of that adds up to just about 1/3 of my gross retirement pay, but at least I was never asked to liquidate my retirement savings or sell our house to pay for the astronomically huge bills for all of the doctors’ fees (think anaesthesiologist, primary care physician, ER physicians, surgeon, just to name a few) and the hospital stay and the several months of careful and skillful rehabilitation. It was tens of thousands of dollars, though I certainly don’t know the exact total. If we did not have medical insurance, it would have been very, very tough, but we had minimal co-pays for each visit and for the various antibiotics and painkillers. EVERYBODY SHOULD HAVE THAT!

Again, I was really embarrassed at my own stupidity. For the first few months, I labored under the misapprehension that the wood had been thrown INTO my hand by kickback. But a more knowledgeable friend (WHR) convinced me otherwise; plus I looked at the sawblade scars on the underside of the other pieces that I had fed through – in each case, the saw had started grabbing the wood and had left its marks on the pieces of plywood — and I was too stupid and ignorant to notice. This video shows how dangerous table saws can be – it’s pretty similar to what happened to me: the blade catches the wood, AND the author’s pushing block, AND just barely misses taking off his finger(s).

SECOND PART:

It took me a while to realize that I was far from the only person who had suffered this sort of injury. I was quite aware that the workers at my college (Dartmouth) were almost ALL missing a finger or two or five – but that was from industrial accidents in the textile mills that used to exist all over New England, but had moved on to other places, probably because the owners could get labor for even less and spend even less on safety than before… I wish now I had asked them more about those injuries… But I’m pretty sure that they were not operating table saws.

I did not know that anywhere from SCORES to HUNDREDS of Americans have some sort of an injury with a table saw not per year, not per month, not per week, but EVERY SINGLE DAY.

Let that sink in. Somewhere between 40 and 400 people in the USA have an accident with a table saw, EVERY SINGLE DAY. Some of these accidents were worse than mine, some were less so (two sources on numbers: here,  here and here, each with links pointing elsewhere. It seems to me reprehensible that Robert Lang, the author of the Popular Woodworking magazine (the second link), belittles the number of injuries, comparing them to the number of kids who are hurt by doors everyday.

‘Back in January 2005, the Consumer Product Safety Commission (CPSC) required that new tablesaw models include a riving knife and modular guard to prevent these injuries. Since that time injury rates have remained virtually unchanged, which begs the question: “Why are so many people hurt while using tablesaws, despite improvements in guards and splitters?”’ (source)

As soon as I could use my arm again, I supervised getting rid of that old table saw. I think we sold it for scrap iron. (It had been sold to us for a pittance by a friend — who passed away from a heart attack at a very early age, as it happened. I never had the chance to mention to him what happened to me.)

Fortunately, after this event, the same friend (WHB) got wind of someone who wanted to donate funds so that we at the NCA Amateur Telescope Making workshop could actually get a decent, SAFE table saw. We also used the monies to purchase a very nice H-Alpha solar telescope for the astronomy club under whose auspices we operate, as well as a nearly-unused Grizzly milling machine… And while it doesn’t have lots of fancy features, that SawStop table saw will immediately (in 0.003 seconds) if it senses anything like your finger touching the blade while in operation; if it does, it slams the blade down into an aluminum chunk and stops it immediately and OUT OF THE WAY. (Have you seen any of those hot-dog table-saw videos? or ) Sure, it kills the blade and the chunk of aluminum (roughly $60)  but that’s way better than cutting off your finger!

In fact, the inventor agrees to put HIS OWN finger into a SawStop table saw, under a high-speed camera and very bright lighting, here. He does so, and the sawblade stops instantly, you can see that no damage to his finger at all: no blood, no bruising, no nothing. The inventor says it felt a little like a buzzing insect or a tickle. Absolutely amazing!

Plus, the saws are really, really well made and easy to put together, and have a very good manual that comes with a spiral-bound notebook with laminated pages and very clear instuctions in English, that you can lay flat at any page you want.  In other words, not the incomprehensible hieroglyphics, printed on flimsy paper, that is so common with manuals today. (Think IKEA…) And the prices are well within range of the prices of other table saws with comparable features.

The original inventor has recently testified at the Consumer Product Safety Commission, and was interviewed by NPR. He could not get manufacturers to agree to put his device (or one just like it) into their saws, EVEN AS AN OPTION. So he set up his own company to make them.

It’s also reprehensible that something like the Power Tool Institute wants to prevent the government from making this electronic safety feature mandatory, as you can see here. 

It’s the usual crapload of hysterical propaganda: higher unemployment, making companies go bankrupt — the same lies that the Big Three carmakers said when they resisted putting in seat belts, antilock brakes, turn signals, doors that have hinges at the front and not the back, unleaded gas, airbags, and so on. But those inventions (and others) have saved untold millions of lives, despite the resistance of the rich and powerful. It’s disgraceful.

Yes, we ordinary humans do make mistakes, each and every single day. People are going to lose focus, or get distracted, or make stupid errors of judgement, like me. It doesn’t matter if you drive (or use a table saw) correctly 99.9% of the time: that still leaves that one time in a thousand where you don’t, AND IT CAN KILL YOU OR MAIM YOU FOR LIFE.

If the fix for that is simple — and even if it costs something — it should be done.

We are only human.

Religions based on … well … myths, or alternative facts. Or lies.

14 Friday Apr 2017

Posted by in History, nature, science

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Every single religion that I can think of seems to be based on totally unreliable witnesses and stories that are mis-remembered (at best) or deliberately distorted.

Judaism just celebrated one of its most important rituals, the Passover seder, in which I have participated about six times. If you’ve forgotten, the story is supposedly recorded in the Old Testament (or Tanakh) and the event celebrates the freeing of a large group of Hebrew people from Egypt. They then wandered the Sinai desert (a very, very hot and dry place – I lived next to it for about 9 months).

The problem is, there is absolutely nothing in the historical record that corroborates any of this story. The Egyptians kept a lot of records, and much of it is still readable — no mention of any such tribe fleeing, no first-borns murdered, no special heavenly plagues, yadda, yadda. No archaeological evidence whatsoever of any tribe of Hebrews wandering in the Sinai desert for any such expedition.

(Stuff like that gets preserved there! In fact, at the famous fort and palace known as Masada, near the Dead Sea, you can clearly see the streets and walls of the camp built by the legions of the Roman Army that besieged and eventually captured the fort, from roughly 2000 years ago! Now THAT incident and war is definitely mentioned — in Josephus, among other places…)

That story of Abraham getting ready to slit his son’s throat and god providing a lamb instead? Really? Inscribed tablets from Mount Sinai – really? How do we know any of this? We don’t. And in any case, if God tells you to commit genocide (it’s spelled out in Genesis / BeReshit), is that a wonderful thing? I don’t think so.

If we get to Jesus, well, again, the evidence that he produced any miracles or was somehow resurrected and became one with God (or didn’t) is pretty darned thin. Today is supposedly the day that he got crucified (the Romans were NOT nice people!!!), which was a shame. The Romans killed and tortured and enslaved a LOT of people. I’m not so sure that they should be held in such high esteem…

But I can think of many ways that a body can be taken out of a tomb, and none of them involve miracles or angels. Then, if you read all of the various Gospels, canonical or not, you realize that their outlooks and details are all profoundly at odds with each other.

If you come to Mohammed, I can think of many ways that somebody could appear to be possessed and to recite various lines of poetry (see Mormons, below) — although that would certainly explain why he would have prophecies that justified what he wanted to do (such as marry little girls) or needed to be amended (see Satanic Verses…)

Now both Jesus and Mohammed said some stuff about equality and supporting the poor, nonetheless the leaders of both religions (Popes, Kings, Emperors, Califs and so on) ended up being wealthy beyond anybody’s dreams, while the majority of people lived in pretty base poverty….

If you go back to the founding of Buddhism, what does that mean that someone is ‘enlightened’? How do we know if someone is in fact in that state? Is it even a good thing to attempt to achieve it? It seems to me that it’s more worth while to try to be good to other people (without endangering your own welfare unless absolutely necessary) and to try to leave the entire planet (and solar system) a better place for your descendants — by not driving species to extinction, not raising the global temperature if at all possible, and by helping so many billions of our kin to avoid lives of infernal poverty and oppression.

Hinduism seems to blame the poor and lowest classes for having been wicked people in a past life, and therefore should be not permitted equality with the upper castes. Sounds great if you are a Brahmin, but what an oppressive religion, really! And how can anybody with an ounce of skepticism believe any of those stories?

Going back to 2000+ years ago — All those stories that the Romans, the Greeksm the Babylonians, Persians and Egyptians made up about their gods — are you serious? They actually believed that? Well, you may as well believe in the Tooth Fairy or the Easter Bunny or the Flying Spaghetti Monster!

Oh, can’t leave out the Mormons. Golden plates buried in upstate New York but only viewable and translatable by someone talking through his hat, writing pseudo-king-James-English and talking about lots of animals and plants and metals that supposedly were used by warring tribes of American Indians — and nobody has ever found figs, wheat, camels, sheep, goats, or horses, or the use of iron or wheeled vehicles of any sort anywhere in the Americas for the entire period of say 500 BC to 1491. So that’s all a lie, too.

Sorry if I offend you, but while I know I’m not perfect (far from it) I don’t need fairy tales to try to be a better human being. I prefer to know things that are true and verifiable. And I really don’t like it when people try to kill each other to support ideas that are really just hoaxes.

 

How Britain Became an Island

06 Thursday Apr 2017

Posted by in History, science

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Interesting report with pretty geological maps indicate that the Island we call Britain got cut off from what we know as France and Belgium by a catastrophic waterfall and flood that broke through what we now call the Straits of Dover as the ice that covered Northern Europe was beginning to melt, and sea levels were much lower than today.

Gupta_NCOMMS-16-16909A_Fig2_rev2

Here is the link. 

By the way, if the weather is fairly clear, it’s easy to see the famous White Cliffs of Dover from the French side (for example, at Cap Gris-Nez).

The Mathematics of George Washington

24 Friday Feb 2017

Posted by in History, Math, Uncategorized

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I recently learned some things about how the young George Washington did math, including surveying. Mathematician and historian V. Frederick  Rickey gave a talk 2 nights ago at the Mathematical Association of America here in DC, based on his study of GW’s “cypher books”, and I’d like to share a few things I learned.

(1) The young George appears to have used no trigonometry at all when finding areas of plots of land that he surveyed. Instead, he would ‘plat’ it very carefully, on paper, making an accurate scale drawing with the correct angles and lengths, and then would divide it up into triangles on the paper. To find the areas of those triangles, he would use some sort of a right-angle device, found and drew the altitude, and then multiplied half the base times the height (or altitude). No law of cosines or sines as we teach students today.

(2) He was given formulas for the volumes of spheroids and barrels, apparently without any derivation or justification that they were correct, to hold so many gallons of wine or of beer. (You probably wouldn’t guess that you had to leave extra room for the ‘head’ on the beer.) Rickey has not found the original source for those formulas, but using calculus and the identity pi = 22/7, he showed that they were absolutely correct.

(3) GW was a very early adopter of decimals in America.

(4 ) This last one puzzled me quite a bit. It’s supposed to be a protractor, but it only gives approximations to those angles. The results are within 1 degree, which I guess might be OK for some uses. I used the law of cosines to convince myself that they were almost all a little off. Here’s an accurate diagram, with angle measurements, that I made with Geometer’s Sketchpad.

His method was to lay out on paper a segment 60 units long (OB) and then to construct a sixth-of-a-circle with center B, passing through O and G (in green). Then he drew five more arcs, each with its center at O, going through the poitns marked as 10, 20, 30, 40, and 50 units from O. The claim is then that angle ABO would be 10 degrees. It’s not. It’s only 9.56 degrees.