Jim Simons

YouTube video by Jim Simons How Far Away is the Sun? Part 3

Here's the third of my videos on "How Far Away is the Sun?". We look at how the transits of Venus in 1761 and 1796 were predicted 50 years earlier and then observed from all around the world to find out how far away Venus is. Starring intrepid Yorkshireman James Cook. youtu.be/QazkPvqo_cw

YouTube video by Jim Simons How Far Away is the Sun? Part 2

Here's the second part of my video series "How Far Away is the Sun?" This covers the amazingly brilliant work that got us from the terrible ancient Greek estimate to being able to make an accurate measurement. Particularly Kepler's astonishing work on elliptical orbits.
youtu.be/-Fe0am6M-Uk

This is interesting. I'm not going to look at any of reponses, because I want to give this serious thought. I might be back in a day or two.

YouTube video by Jim Simons How Far Away is the Sun? Part 1

How far away is the Sun? The story of how we answered this question includes lots of fascinating mathematics and science. Here's the first part: how the ancient Greeks got a pretty good estimate of how far away the Moon is, and a terrible estimate of how far away the Sun is.
youtu.be/xCqPZ7o0ad4

Then the 𝜔'th mathematician says "Hang on, what about my order".

Of course Euclid thought about this as being about areas. The area of the square on the side R being the sum of the areas of the squares on the other two sides minus twice the area of a certain rectangle.

I think it is Euclid's proposition 13 from book II. Often quoted as the origin of the cosine rule. It is sort of saying the same thing as the cosine rule, but without any trigonometry, indeed without any angles being measured.

I'm getting warm. I haven't found an image yet, but it look like it was Kepler's Astronomia Nova. Google says he used ', '', ''' and a IV superscript. It also says Mathematicians of that era (ie mediaeval) used Roman numeral superscripts to teach the rules of sexagesimal multiplication.

I have a mental images of an ancient book that ses thus notation. It mighr take me a while to find it.

Did you know that the similar looking symbols for minutes and seconds really are meant to be roman numerals as they are the first and second digits of a sexagesimal fraction. A sixtieth of a second is a third etc.

Babylonian table of squares, starting with 43 21 is the squqre of 51, in decimal 2601=51^2

Here's a copy of a copy of a copy of a copy of a copy of a copy

Did you know that the Babylonians, nearly 4000 years ago, had big tables of squares so that they could multiply fairly large numbers using precisely the method you describe in the first section of your blog post?

That seems right to me too.

Or even negative!

A demo for your delight.

Go backwards in time. We start with equal numbers of boys and girls. Add 15 boys and the ratio B:G goes up to 3:2, so there must have been 30 boys (and girls) to start with. Then add 25 girls, ending up with 55 girls and 45 boys.

I should have added "I'm never going to accept H0, that would be accepting defeat".

I think "not enough evidence to reject H0" comes from real applications, where experimenters are desparate to reject H0. You really want your new drug to work, or your fancy new particle to exist. So the subtext is "... can't honestly reject H0 yet, but I going to keep trying."

Fred Hoyle's "The Black Cloud" is another exception. In fact I have always imagined that he invented an extraterrestrial intelligence as far from humanoid as he could.

This is like the way the Babylonian scribes thought about algorithms, such as solving quadratics. They did not have algebra, so they demonstrated the method with generic examples. I'd love to have been able to listen in to a lesson to hear what the scribe said whilst working through an example.

That is a well established rule for interviews, and an interview is an aural exam.

Go to work on an egg! Ad campaign from the 50s and 60s.
www.egginfo.co.uk/go-to-work-o...

Yes, I've always thought of "more or less" as meaning "or maybe a bit more or a bit less". I suppose "plus minus" means "plus or minus a little bit" except that the "plus minus" comes before the number, as in "plus minus 1000".

Maybe there is a South African on the team. In South African English, "plus minus" means "approximately". See dsae.co.za/entry/plusmi...

Indeed, some scholars have argued that some early Homo species should be reclassified as Australopithecus.

Ah I see.

Excellent! I find that St Kentigern has no wikipedia page, though there are several churches named after him, and one college in New Zealand. So your mission, should you choose to accept it, is now clear.

And the HMRC website is brilliant. It's not the web developers' fault that the tax system is complicated, and they have made it about as simple as it is possible to imagine.

I'm self-employed, so I have to fill in a tax form every year, and I have a guilty secret - because it is all numbers and spreadsheets, I rather enjoy doing it.

Meanwhile what you almost always really want is an estimate of 𝞼. The square root of neither is as unbiassed estimator. There isn't a simple unbiassed estimator but using n-1.5 isn't bad.