A minimally configured Windows laptop

November 22, 2020 Windows , , , , , ,

I’ve now installed enough that my new Windows machine is minimally functional (LaTex, Linux, and Mathematica), with enough installed that I can compile any of my latex based books, or standalone content for blog posts.  My list of installed extras includes:

  • Brother HL-2170W (printer driver)
  • Windows Terminal
  • GPL Ghostscript (for MaTeX, latex labels in Mathematica figures.)
  • Wolfram Mathematica
  • Firefox
  • Chrome
  • Visual Studio
  • Python
  • Julia
  • Adobe Acrobat Reader
  • Discord
  • OBS Studio
  • MikTeX
  • SumatraPDF
  • GVim
  • Git
  • PowerShell (7)
  • Ubuntu
  • Dropbox

Some notes:

  • On Windows, for my LaTeX work, I used to use MikTex + cygwin.  The cygwin dependency was for my makefile dependencies (gnu-make+perl).  With this new machine, I tried WSL2.  I’m running my bash shells within the new Windows Terminal, which is far superior to the old cmd.
  • Putty is no longer required.  Windows Terminal does the job very nicely.  It does terminal emulation well enough that I can even ssh into a Linux machine and use screen within my Linux session, and my .screenrc just works.  Very nice.
  • SumatraPDF is for latex reverse tex lookup.  i.e. I can double click on pdf content, and up pops the editor with the latex file.  Last time I used Sumatra, I had to configure it to use GVim (notepad used to be the default I think.)  Now it seems to be the default (to my suprise.)
  • I will probably uninstall Git, as it seems superfluous given all the repos I want to access are cloned within my bash file system.
  • I used to use GVim extensively on Windows, but most of my editing has been in vim in the bash shell.  I expect I’ll now only use it for reverse tex (–synctex) lookup editing.

WSL2 has very impressive integration.  A really nice demo of that was access of synctex lookup.  Here’s a screenshot that shows it in action:

I invoked the windows pdf viewer within a bash shell in the Ubuntu VM, using the following:

pjoot@DESKTOP-6J7L1NS:~/project/blogit$ alias pdfview
alias pdfview='/mnt/c/Users/peete/AppData/Local/SumatraPDF/SumatraPDF.exe'
pjoot@DESKTOP-6J7L1NS:~/project/blogit$ pdfview fibonacci.pdf

The Ubuntu filesystem directory has the fibonacci.synctex.gz reverse lookup index that Summatra is able to read. Note that this file, after unzipping, has only Linux paths (/home/pjoot/…), but Summatra is able to use those without any trouble, and pops up the (Windows executable) editor on the files after I double click on the file. This sequence is pretty convoluted:

  • Linux bash ->
  • invoke Windows pdf viewer ->
  • that program reading Linux files ->
  • it invokes a windows editor (presumably using the Linux path), and that editor magically knows the path to the Linux file that it has to edit.

Check out the very upper corner of that GVim window, where it shows the \\wsl$\Ubuntu\home\pjoot\project\blogit\fibonacci.tex path

As well as full Linux access to the Windows filesystem, we have full Windows access to the Linux filesystem.

Not all applications know how to access files with UNC paths (for example, the old crappy cmd.exe cannot), but so far all the ones I have cared about have been able to do so.

A new computer for me this time.

November 5, 2020 Incoherent ramblings , , , , , , , , , ,

It’s been a long long time, since I bought myself a computer.  My old laptop is a DELL XPS, was purchased around 2009:

Since purchasing the XPS lapcrusher, I think that I’ve bought my wife and all the kids a couple machines each, but I’ve always had a work computer that was new enough that I was able to let my personal machine slide.

Old system specs

Specs on the old lapcrusher:

  • 19″ screen
  • stands over 2″ tall at the back
  • Intel Core I3, 64-bit, 4 cores
  • 6G Ram
  • 500G hard drive, no SSD.

My current work machine is a 4yr old mac (16Mb RAM) and works great, especially since I mainly use it for email and as a dumb terminal to access my Linux NUC consoles using ssh.  I have some personal software on the mac that I’d like to uninstall, leaving the work machine for work, and the other for play (Mathematica, LaTex, Julia, …).

I’ll still install the vpn software for work on the new personal machine so that I can use it as a back up system just in case.  Last time I needed a backup system (when the mac was in the shop for battery replacement), I used my wife’s computer.  Since Sofia is now mostly working from home (soon to be always working from home), that wouldn’t be an option. Here’s the new system:

New system specs

This splurge is a pretty nicely configured, not top of the line, but it should do nicely for quite a while:

  • Display: 15.6″ Full HD IPS | 144HZ | 16:9 | Operating System: Win 10
  • Processor: Intel Core i7-9750H Processor (6 core)
  • RAM Memory: XPG 32GB 2666MHz DDR4 SO-DIMM (64GB Max)
  • Storage: XPG SX8200 1TB NVMe SSD
  • Graphics: NVIDIA GeForce GTX 1660Ti 6GB
  • USB3.2 Gen 2 x 1 | USB3.2 Gen 2 x 2 | Thunderbolt 3.0 x 1 (REAR)| HDMI x 1 (REAR)
  • 4.08lbs

The new machine has a smaller screen size than my old laptop, but the 19″ screen on the old machine was really too big, and with modern screens going so close to the edge, this new one is pretty nice (and has much higher resolution.)  If I want a bigger screen, then I’ll hook it up to an external monitor.

On lots of RAM

It doesn’t seem that long ago when I’d just started porting DB2 LUW to 64bit, and most of the “big iron” machines that we got for the testing work barely had more than 4G of ram each.  The Solaris kernel guys we worked with at the time told me about the NUMA contortions that they had to use to build machines with large amounts of RAM, because they couldn’t get it close enough together because of heat dissipation issues.  Now you can get a personal machine for $1800 CAD with 32G of ram, and 6G of video ram to boot, all tossed into a tiny little form factor!  This new machine, not even counting the video ram, has 524288x the memory of my first computer, my old lowly C64 (I’m not counting the little Radio Shack computer that was really my first, as I don’t know how much memory it had — although I am sure it was a whole lot less than 64K.)

C64 Nostalgia.

Incidentally, does anybody else still have their 6402 assembly programming references?  I’ve kept mine all these years, moving them around house to house, and taking a peek in them every few years, but I really ought to toss them!  I’m sure I couldn’t even give them away.

Remember the zero page addressing of the C64?  It was faster to access because it only needed single byte addressing, whereas memory in any other “page” (256 bytes) required two whole bytes to address.  That was actually a system where little-endian addressing made a whole lot of sense.  If you wanted to change assembler code that did zero page access to “high memory”, then you just added the second byte of additional addressing and could leave your page layout as is.

Windows vs. MacOS

It’s been 4 years since I’ve actively used a Windows machine, and will have to relearn enough to get comfortable with it again (after suffering with the transition to MacOS and finally getting comfortable with it).  However, there are some new developments that I’m gung-ho to try, in particular, the new:

With WSL, I wonder if cygwin is even still a must have?  With windows terminal, I’m guessing that putty is a thing of the past (good riddance to cmd, that piece of crap.)

Crashing Mathematica with HatchShading + Opacity

May 31, 2020 math and physics play , , ,

I attempted to modify a plot for an electric field solution that I had in my old Antenna-Theory notes:
j \omega
\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}
\lr{ 1 + \cos\theta }
-\cos\phi \thetacap
+ \sin\phi \phicap
and discovered that you can crash Mathematica ( by combining PlotStyle with Opacity and HatchShading (new in 12.1).  Here’s a stripped down version of the plot code that demonstrates the crash:

ClearAll[ rcap]
rcap = {Sin[#1] Cos[#2], Sin[#1] Sin[#2], Cos[#1]} & ;

rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> { HatchShading[0.5, Black]}
, ParametricPlot3D[
rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> {Directive[Opacity[0.5`]]}
], ParametricPlot3D[
,{p,0,2 π}
,PlotStyle\[Rule]{Directive[Opacity[0.5`]], HatchShading[0.5, \

The first two plots, using one, but not both of, Opacity or HatchShading work fine:

In this reproducer, the little dimple at the base has been removed, which was the reason for the Opacity.

I’ve reported the bug to Wolfram, but wonder if they are going to come back to me saying, “Well, don’t do that!”


EDIT: Fixed in Mathematica 12.1.1

Exploring 0^0, x^x, and z^z.

May 10, 2020 math and physics play , , , , , , ,

My Youtube home page knows that I’m geeky enough to watch math videos.  Today it suggested Eddie Woo’s video about \(0^0\).

Mr Woo, who has great enthusiasm, and must be an awesome teacher to have in person.  He reminds his class about the exponent laws, which allow for an interpretation that \(0^0\) would be equal to 1.  He points out that \(0^n = 0\) for any positive integer, which admits a second contradictory value for \( 0^0 \), if this was true for \(n=0\) too.

When reviewing the exponent laws Woo points out that the exponent law for subtraction \( a^{n-n} \) requires \(a\) to be non-zero.  Given that restriction, we really ought to have no expectation that \(0^{n-n} = 1\).

To attempt to determine a reasonable value for this question, resolving the two contradictory possibilities, neither of which we actually have any reason to assume are valid possibilities, he asks the class to perform a proof by calculator, computing a limit table for \( x \rightarrow 0+ \). I stopped at that point and tried it by myself, constructing such a table in Mathematica. Here is what I used

griddisp[labelc1_, labelc2_, f_, values_] := Grid[({
({{labelc1}, values}) // Flatten,
({ {labelc2}, f[#] & /@ values} ) // Flatten
}) // Transpose,
Frame -> All]
decimalFractions[n_] := ((10^(-#)) & /@ Range[n])
With[{m = 10}, griddisp[x, x^x, #^# &, N[decimalFractions[m], 10]]]
With[{m = 10}, griddisp[x, x^x, #^# &, -N[decimalFractions[m], 10]]]

Observe that I calculated the limits from both above and below. The results are

and for the negative limit

Sure enough, from both below and above, we see numerically that \(\lim_{\epsilon\rightarrow 0} \epsilon^\epsilon = 1\), as if the exponent law argument for \( 0^0 = 1 \) was actually valid.  We see that this limit appears to be valid despite the fact that \( x^x \) can be complex valued — that is ignoring the fact that a rigorous limit argument should be valid for any path neighbourhood of \( x = 0 \) and not just along two specific (real valued) paths.

Let’s get a better idea where the imaginary component of \((-x)^{-x}\) comes from.  To do so, consider \( f(z) = z^z \) for complex values of \( z \) where \( z = r e^{i \theta} \). The logarithm of such a beast is

\ln z^z
&= z \ln \lr{ r e^{i\theta} } \\
&= z \ln r + i \theta z \\
&= e^{i\theta} \ln r^r + i \theta z \\
&= \lr{ \cos\theta + i \sin\theta } \ln r^r + i r \theta \lr{ \cos\theta + i \sin\theta } \\
&= \cos\theta \ln r^r – r \theta \sin\theta
+ i r \lr{ \sin\theta \ln r + \theta \cos\theta },
z^z =
e^{ r \lr{ \cos\theta \ln r – \theta \sin\theta}} \times
e^{i r \lr{ \sin\theta \ln r + \theta \cos\theta }}.
In particular, picking the \( \theta = \pi \) branch, we have, for any \( x > 0 \)
(-x)^{-x} = e^{-x \ln x – i x \pi } = \frac{e^{ – i x \pi }}{x^x}.

Let’s get some visual appreciation for this interesting \(z^z\) beastie, first plotting it for real values of \(z\)

Plot[ {Re[x^x], Im[x^x]}, {x, -r, r}
, PlotRange -> {{-r, r}, {-r^r, r^r}}
, PlotLegends -> {Re[x^x], Im[x^x]}
], {{r, 2.25}, 0.0000001, 10}]

From this display, we see that the imaginary part of \( x^x \) is zero for integer values of \( x \).  That’s easy enough to verify explicitly: \( (-1)^{-1} = -1, (-2)^{-2} = 1/4, (-3)^{-3} = -1/27, \cdots \).

The newest version of Mathematica has a few nice new complex number visualization options.  Here’s two that I found illuminating, an absolute value plot that highlights the poles and zeros, also showing some of the phase action:

ComplexPlot[ x^x, {x, s (-1 – I), s (1 + I)},
PlotLegends -> Automatic, ColorFunction -> "GlobalAbs"], {{s, 4},
0.00001, 10}]

We see the branch cut nicely, the tendency to zero in the left half plane, as well as some of the phase periodicity in the regions that are in the intermediate regions between the zeros and the poles.  We can also plot just the phase, which shows its interesting periodic nature

ComplexPlot[ x^x, {x, s (-1 – I), s (1 + I)},
PlotLegends -> Automatic, ColorFunction -> "CyclicArg"], {{s, 6},
0.00001, 10}]

I’d like to take the time to play with some of the other ComplexPlot ColorFunction options, which appears to be a powerful and flexible visualization tool.

Condensed matter physics notes

February 16, 2019 math and physics play , , ,

Here’s an update of my old Condensed Matter Physics notes.

Condensed Matter

Along with a link to the notes, are instructions on building the PDF from the latex and the github clone commands required to make a copy of those sources.  Mathematica notebooks are also available for some of the calculations and plots.

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