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Dr Stephen MᶜAteer

The guilty 12

(My reaction to Why did Essendon alone take the fall? by Tracy Holmes).

Rusty's Beard for P.M.

Vote 1 P.U.P.

Caged

Buckle Up

The Curious Case of Dustin Fletcher

The original images are here and here.

On The Scale of Things, you're pretty huge:

-40       -30       -20       -10        0         10        20         30
 |----o----|---------|---------|---------X---------|---------|-----o----|
      |                                  |                         |
      Plank length                       you are here              observable universe

(the numbers are log base 10 of length/human height)

The Star-Triangle Relation

A pattern I noticed (while reading a book on the planets to my son)

This is probably something which is well known, but not being in the field I don't know where to find info about this (I did check on Wikipedia and did a bit of Googling to no avail). If it is well known, or there is some sort of explanation then please let me know.

Here is the observation: the planets are arranged so that the orbital radius of the planets increases exponentially with each successive planet (I included Ceres/the asteroid belt because the fit was better).

I was a bit surprised by this because I always thought of the orbits as being uniformly spaced. On second thought it seems to make more sense -- think of the shape of an accretion disk. But on third thought it stops making sense -- the mass is not distributed in an exponentially decaying fashion, it's clumped up around Jupiter. My feeling is that it must have something to do with orbital resonances ... but I don't really know what that means. By the way, for the statistically minded out there, the linear regression came in with a Pearson's correlation of 0.993 -- 1 being a perfect correlation, 0 being no correlation. The python code I used to generate the plot and correlation can be found here.

Pythagoras (slide the point at the bottom to adjust):

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(Created in Geogebra)

xkcd failure:

(Link, xkcd: Money.)

There's a problem with an item in xkcd's Money Chart. The problem is in 'Value of an investment of \$1000/year' in the thousands box. The claim is basically that if you invest \$1000 per year in a savings account with 5% interest starting today for the next 30 years, at the end of the 30 years your gains due to interest will be wiped out in totality by 3% inflation: in terms of today's money, you end up with just \$27,370. This simply does not make sense.

I recreated the figures that were quoted in the chart and here's some Python code that does the job:

01 #!/use/bin/python
02 
03 savings = 0
04 
05 for i in range(30):
06     savings *= 1.05 # annual interest
07     savings += 1000 # annual contribution
08     print 'Year {0:2d}: ${1:5.2f}'.format(i+1, savings)
09
10 for i in range(30):
11     savings /= 1.03 # depreciation on all savings
12
13 print 'After depreciation: ${0:5.2f}'.format(savings)

The problem here is that you are depreciating the total amount across the full 30 years (i.e. the contribution you made last month gets depreciated like as if you put that money in 30 years ago). Here is an altered version that does three things: 1) interest is calculated monthly, 2) the depreciation due to inflation is calculated on the fly at the end of each year and 3) adjusts the monthly contribution to maintain it at $1000 in today's money (an unnatural thing to). Here is is in Python:

01#!/use/bin/python
02 
03 savings = 1000/12
04 total_contribution = savings
05 
06 for i in range(12*30):
07     savings *= 1 + 0.05/12 # monthly compound interest
08     contribution = 1000/12/(1.03)**((i+1)/12) # monthly contribution - depreciating
09     savings += contribution
10     total_contribution += contribution
11     if (i+1) % 12 == 0:
12         savings /= 1.03 # annual depreciation of current balance
13         print 'Year {0:2d}: ${1:5.2f}'.format((i+1)/12, savings)
14 
15 print 'Total contribution: ${0:5.2f}'.format(total_contribution)

In this case you end up with \$28,540 in today's money, but it is important to note that you have only invested \$20,140 in today's money (due to the depreciation in the amount you have been investing). Here is the code for the same scenario except that you increase your contribution with inflation (this is natural as you would expect to see your salary and other living expenses to increase in this way). The code:

01  #!/use/bin/python
02 
03 savings = 1000/12
04 
05 for i in range(12*30):
06     savings *= 1 + 0.05/12 # monthly compound interest
07     savings += 1000/12 # monthly contribution
08     if (i+1) % 12 == 0:
09         savings /= 1.03 # annual depreciation of current balance
10         print 'Year {0:2d}: ${1:5.2f}'.format((i+1)/12, savings)

The result is that at the end of the 30 years you have \$40,640 in today's money (after an investment of \$30,000 in today's money). The lesson is that if your analysis is producing some strange counter-intuitive result, it's not necessarily a mind-expanding victory. For shame xkcd, for shame.

(The syntax highlighting in this post was generated by tohtml.com.)

Noise in temperature data:

A group at Berkeley have released a series of reports which address criticisms of the climate change orthodoxy. A stated goal of the group is transparency and openness to criticism. The reports can be found here: www.berkeleyearth.org. Below is an observation I made while reading one of the papers.

The paper presents a convincing argument that the UHI effect does not affect the existing conclusions of climate change orthodoxy -- my observation is probably a bit off topic.

Figure 3 in Wickham et al. (Influence of Urban Heating on the Global Temperature Land Average) contains two histograms representing the distributions of temperature changes per 100 years based on their entire dataset (which comes from various sources). While there is a clear bias towards temperature increase - the mean is about 1 degree C - the thing that strikes me is the width of the distributions. On the 30+ year datasets the deviation seems to be about 3 degrees (just from eyeballing the histogram) which means the middle 95% of the sample lies between -5 and 7 degrees C. The widths of the distributions for the shorter duration datasets is even greater. In other words it's about an even chance that any given weather station will observe temperature increase or decrease.


Part of Figure 3 from Influence of Urban Heating on the Global Temperature Land Average.

This point is driven home by Figure 4 which shows the spacial distribution of weather stations in North America which observed increasing and decreasing temperatures.


Part of Figure 4 from Influence of Urban Heating on the Global Temperature Land Average.

Reference: C. Wickham, J. Curry, D. Groom, R. Jacobsen, R. Muller, S. Perlmutter, R. Rohde, A. Rosenfeld and J. Wurtele, Influence of Urban Heating on the Global Temperature Land Average Using Rural Sites Identified from MODIS Classifications, 2011, (in press) , preprint: http://www.berkeleyearth.org/Resources/Berkeley_Earth_UHI.

ED-IS-ON:

A mate of mine, Luke Morrison, is raising some money for a (semi-para-historical) film "ED-IS-ON".

VY Canis Majoris:

This is an image I made to illustrate the difference in size between VY Canis Majoris (the largest known star) and the earth (via the Sun).

No paper policy at work:

Paralell postulate pwnd! ... play with me:

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