What is the plan from here?¶
First of all, what is going on here?
It started as a place to draw tables with matplotlib. Or rather a home for a new version of the matplotlib.table module that I created way back in the day.
The table tries to be clever and pick the biggest font it can find that fits the data. I barely knew what I was doing creating this table, I was finding my way around matplotlib as I was writing the code. It quietly did the job for over ten years as I was busy elsewhere.
More recently I tried to fix up some of its problems and add some new features. It was difficult to do this in backward compatible ways.
Hence, blume is a new home for the table.
I decided it would be a good place to accumulate some examples of tables in use. Examples of ideas that take my interest.
I try to look for common themes across the examples and let that guide what happens next.
As things have progressed it has become clear that everybody already has a table: pandas, astropy, mathematica, every database query. So the scope of this project has expanded somewhat, to how to explore tables of data, with matplotlib generating all the pictures?
As far as python is concerned, I am leaning towards tables as lists of dictionaries as the lowest common denominator. With the same set of keys for each item in the list, there is a natural mapping to dictionaries with lists as values.
I am particularly interested in what I call, spherical data. Data where the observations lie on the surface of a sphere. Cosmological data and output from global climate reanalysis models.
Values that indicate a time or a place are of particular interest. I find myself repeatedly parsing and transforming such data to suit some, often implicit, choice of coordinates.
It feels that 99.99% of computing is trying to transform data from one coordinate system to another, one world view to another.
As an example, the astropy world is generally using the healpy software to store and manipulate data in the healpix format, where each pixel represents an equal area. It comes with tools to do spherical harmonic analysis, and was used to detect harmonics in the COBE, Cosmic Microwave Background data.
It also comes with some built in plotting, using matplotlib as the plotting engine.
Healpix does not have a table, as far as I know, but it is my current favourite for spherical data.
The meteorologists are using a grid based approach, dividing the planet into a rectangular grid of latitudes and longitudes. This has some benefits, in particular, it gives higher resolution at the poles. Computers like grid calculations.
The astroquery project provides tools to query data from a whole host of astronomical projects, using a common query language and returning results in common formats.
This may well reflect the extraordinary amount of international collaboration there is in the world of astronomy.
There is also no shortage of fascinating data sets to work with, and the set is growing too.
And gravitational waves are now a thing too.
Interactive magic¶
I find myself writing a number of short scripts, 100 lines or so, to display some data with matplotlib. As I explore the data the script acquires a number of variables that control what is displayed.
At this point I often resort to argparse to add a few command line options to control the key variables.
A typical blume module creates a blume.magic.Ball and adds it to a farm which ends up running the Ball.run co-routine in a loop.
It is possible to have keyboard events call co-routines which can in turn change the values.
This is a fairly quick way to build an interactive tool to explore data.
However, it soon gets tedious writing repetitive code for the co-routines. Then you have to decide what key to assign to each routine.
The latest enhancement, is to simply allow me to scroll through the attributes of the object, by pressing space, until I find the one I wish to change. Then a bunch of keys are matched to various co-routines that offer various changes.
It is a bit like running code in an interactive debugger.
This is all managed by a Shepherd, via which you can browse the values of the Ball objects, select one and change it.
Just run:
python -m blume.mb -r
This one generates images of the Mandelbrot set. It is a good one to experiment with the interactive mode.
Run things from a console. Type ‘h’ and you will see what keys do what. At this point it is a bit of an adventure game. All going well ‘q’ should quit. Failing that, ‘Control-c’ is your friend.
Pressing ‘i’ shows the attributes of the object that is currently selected. Spacebar lets you scroll through its attributes and then press ‘h’ to see the keys that will change the value.
You can do much of what I am trying to do with a Jupyter notebook and some ipython widgets.
I would really like to have dynamic key bindings that adapt to usage, but that will have to wait for the blume.magic.Roundabout to actually be magic.
Cosmology¶
A number of modules relate to astronomical data.
blume.gaia downloads and displays data from the Gaia survey of our galaxy. Over a billion observations and growing.
blume.cpr implements galactic rotation curves per [AP]. This module is a natural companion for Gaia data.
blume.gw plots waveforms for the waves generated by different mergers of black holes and neutron stars of specified sizes.
blume.dss visualise geodesics in de Sitter space, again per [AP].
At some point it will be productive to combine the ideas in the cpr module with the data in the gaia module. It would be good to try to get good estimates of both the mass, given the angular velocity of the black hole at the centre of our galaxy.
There are already a number of excellent projects processing this data. Many of these use some sort of Bayesian re-estimation to fit some sort of galactic model to the data set. It should be noted that prior assumptions can still impact such models.
I suspect some of these will be using the assumption that Sagittarius A* is at the centre of our galaxy and is just 26,000 light years away, but I have not followed that up.
There is a fair amount of work in understanding all the follow on processing that is being done on the dataset. The raw observations have a lot of sampling noise, multiple observations of each source.
For now, I think it is worth waiting for more data releases. I do not think it will be long before we have a much better picture of the structure of our galaxy and our place in it.
The de Sitter module is just a stub at this point. It has lead to the discovery of the einsteinpy project.
That was where, I learnt that there is a Gödel metric, a solution to Einstein’s general relativty equations.
The fascinating thing is that his solution implied that the universe should, in some sense be rotating. He would often ask if observations had yet confirmed this, only to be told, “not yet”.
I have been fascinated by Kurt Gödel since I learned of his wonderful incompleteness theorems, all mathematicians have cause to be greatful for these theores.
I am curious what Gödel would have made of the Cosmic Microwave Background.
Which reminds me, there is this delight to explore:
Legacy Archive for Microwave Background Data Analysis
https://lambda.gsfc.nasa.gov/
And the accelerating expansion of the universe.
Could this not be explained, in de Sitter space, by the probability that a distant galaxy is a new arrival increases as you get further away?
Some distant galaxies may be exibiting less red shift than would be expected given their distance.
Dwarf, blue galaxies, if you like.
It should be possible to calculate what we would expect to see based on [AP]
Putting it all together¶
Once the de Sitter module is a little further along, the goal is to develop a model that might explain the gravitational waves we are seeing, not as black hole mergers, but rather as waves arriving from giant black holes at the edge of our visible universe.
The puzzle is why we are not seeing gamma ray bursts at the same time as each gravitational wave.
The belief is that we should only see these when one component is a neutron star, and even then, not always.
Paradox¶
Simulataneously believing that rotating masses induce a rotation on space time and that it is not possible for black hole mergers to generate gravitational waves as they spiral into each other would appear to be some sort of paradox.
How to resolve this?
Multi-messenger astronomy may very well hold the key to resolving this mystery and many more.
The exciting part is that we already know some gravitational waves are followed up by a short gamma ray burst, and observations further down the spectrum too.
It would be surprising if these new observations do not change our current thinking in some significant way.