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Interesting Items...

EEPhil said:
First ever black hole image released (click)
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I have so much difficulty with the word "image"!

When this news broke, the reports were calling it a "picture" or "photo" or "image" - all of which give the general public an impression that (literally) a photograph has been taken. For "image" read "false-colour map of microwave emission intensity reconstructed by very-long-baseline radio interferometry".

I look at this as similar to deducing the structure of DNA from a few blobs on a photographic plate made by scattered X-rays. The "image" is a mathematical construct: it is one (of potentially many) solutions to the problem "given the data received from the radio antennas, what assumed map of emission would recreate that data", and is effectively a best guess. This is very different from what I believe Joe Public would think of as an image - an array of pixels directly sensing a field of view.

Nonetheless, it is an incredible achievement. It's like resolving detail out of a very fuzzy photo by deconvolution, when the fuzzy photo itself took an international collaboration years to achieve even before the processing, and the deconvolution relies on precise knowledge of the relative positions of the instruments within millimetres and millisecond by millisecond... when they are scattered over the whole Earth (which is not only rotating, but also subject to tidal distortions and tectonics). By my estimate (based on reports of the object being 40x10^9 km across and 500x10^18 km away), the scale of the map is of order 10 pico-degrees (pico = 10^-12)!!! :frantic:
 
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Black Hole said:
By my estimate (based on reports of the object being 40x10^9 km across and 500x10^18 km away), the scale of the map is of order 10 pico-degrees (pico = 10^-12)!!! :frantic:
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One of the lead scientists was being interviewed on the World Service and said that it's akin to photographing a standard size doughnut on the surface of the moon.
 
10cm / 400,000 km = 1/4,000,000,000 radians compared with 4/50,000,000,000 radians... I would say more like a 10p on the Moon, but if the doughnut is the glow and the 10p is the hole in the middle, I reckon we're in complete agreement!
 
Bath & North East Somerset are considering a planning application at the moment (ref 19/01265/AR). The application is retrospective for an advertising hoarding already put up by Kia Motors on the Lower Bristol Road in Bath.

Because of the restricted visibility caused by the hoarding when emerging from Midland Road, the council are minded to make the new bridge across the Avon northbound only, when it was originally promised to be two-way. The new bridge is a long-delayed replacement for a "temporary" Bailey bridge that had been there for 50 years, and was southbound only (the old bridge was known locally as the "destructor bridge" due to a nearby scrapyard).

This all seems disingenuous to me. The traffic planners are disregarding the original basis for the replacement bridge because of a structure than was erected without consent.

I am also strongly against retrospective planning approval on principle. Individual cases may have a strong argument, but the very existence of retrospective application as a mechanism encourages cheating: "we won't bother to apply for permission before going ahead; if we get challenged we can apply for retrospective approval and then there won't be any opportunity for the planners to impose conditions".

Maybe I am becoming more cynical in my old age.

(If anyone reading this lives in Bath, I suggest you go onto the BNES council web site and register an objection to the planning application.)
 
Why? For most practical purposes pi can be approximated as 22/7 or 355/113 or 3927/1250. I can remember it as 3.14159265358, which is more than adequate for use in electromagnetic simulations. Don't waste the computing power on calculating pi, use it to calculate the answer to the ultimate question of life, the universe, and everything. Alright, we know the answer (42), so calculate the question.
 
EEPhil said:
Why? For most practical purposes pi can be approximated as 22/7 or 355/113 or 3927/1250. I can remember it as 3.14159265358, which is more than adequate for use in electromagnetic simulations.
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That many decimal places is also enough to calculate the circumference of the earth to less than a hands width (assuming you can find an average radius in the ovoid shape we live on).
 
EEPhil said:
Why?
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Because they can. I make no comment on Google's motives, but if you want to test the raw speed/power of your supercomputer (to prove it's more powerful than the previous record-breaking supercomputer), it needs to be run on a problem you know the answer to (or at least can prove the answer is right afterwards).

Personally, I am fascinated by the algorithms use to compute an arbitrary number of digits of pi; I have implemented one but I have no idea how it works: an iteration which churns out another four (IIRC) significant digits per cycle - but you have to set up the size of the variables from the outset, so that would mean using 30 trillion digit variables in the calculations! Not sure how that gets to 170TB of storage though...
 
How do they actually do the calculation?
I mean, you could calculate 22/7 to umpteen places of decimals but the answer would still be wrong, as you are starting from an imprecise approximation.
 
Well, an inefficient method is the identity pi = 4(1 - 1/3 + 1/5 - 1/7...). 22/7 (and the other rule-of-thumb fractions) is only (and will only ever be) and approximation - you don't calculate pi that way!

There are series derived from other tangent formulae which converge much faster than that, but the method I referred to above uses an iteration formula which I have never got to the bottom of.
 
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