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+WEBVTT
+
+
+00:00:03.620 --> 00:02:36.639
+Introduction
+
+00:02:36.640 --> 00:04:54.279
+What is Calc?
+
+00:04:54.280 --> 00:06:37.398
+calc-algebraic-entry
+
+00:06:37.399 --> 00:08:07.759
+calc-roll-down
+
+00:08:07.760 --> 00:08:58.179
+Advanced functions
+
+00:08:58.180 --> 00:09:54.719
+Solving equations with calc-solve-for
+
+00:09:54.720 --> 00:12:00.079
+Systems of equations
+
+00:12:00.080 --> 00:12:39.959
+calc-find-root
+
+00:12:39.960 --> 00:14:17.539
+Derivatives and integrals
+
+00:14:17.540 --> 00:18:12.159
+Programmable functions
+
+00:18:12.160 --> 00:20:08.799
+Plotting
+
+00:20:08.800 --> 00:22:38.599
+Wish list
+
+00:22:38.600 --> 00:23:35.920
+Wrapping up
diff --git a/2025/captions/emacsconf-2025-calc--basic-calc-functionality-for-engineering-or-electronics--christopher-howard--main.vtt b/2025/captions/emacsconf-2025-calc--basic-calc-functionality-for-engineering-or-electronics--christopher-howard--main.vtt
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+WEBVTT captioned by sachac
+
+NOTE Introduction
+
+00:00:03.620 --> 00:00:08.799
+Hello, my name is Christopher Howard and welcome to my talk.
+
+00:00:08.800 --> 00:00:11.319
+This is basically an introduction
+
+00:00:11.320 --> 00:00:15.119
+to the built-in Emacs calculator,
+
+00:00:15.120 --> 00:00:18.319
+properly known as Emacs Calc,
+
+00:00:18.320 --> 00:00:21.439
+particularly from the perspective of someone
+
+00:00:21.440 --> 00:00:27.559
+with a technical background such as engineering or electronics.
+
+00:00:27.560 --> 00:00:32.879
+I will say, though, my personal interest is not really
+
+00:00:32.880 --> 00:00:37.839
+in digital computing or digital calculators,
+
+00:00:37.840 --> 00:00:42.519
+but lately has been focused more on analog computing.
+
+00:00:42.520 --> 00:00:46.799
+I have, for example, been working to master
+
+00:00:46.800 --> 00:00:50.839
+the venerable slide rule, a mechanical computer
+
+00:00:50.840 --> 00:00:57.319
+that calculates multiplication powers and logarithms.
+
+00:00:57.320 --> 00:01:02.199
+Here's a picture of one.
+
+00:01:02.200 --> 00:01:06.799
+It's a physical tool that was used for hundreds of years
+
+00:01:06.800 --> 00:01:08.999
+for this sort of thing
+
+00:01:09.000 --> 00:01:16.679
+before the handheld calculator was made popular.
+
+00:01:16.680 --> 00:01:18.639
+And I also had a project that I did
+
+00:01:18.640 --> 00:01:21.119
+for a while to several months
+
+00:01:21.120 --> 00:01:33.119
+to build an electronic analog computer.
+
+00:01:33.120 --> 00:01:38.679
+A rudimentary attempt of mine, but it's functional,
+
+00:01:38.680 --> 00:01:43.399
+and it's basically a 1960s or 1970s style
+
+00:01:43.400 --> 00:01:48.839
+electronic analog computer built very much on a budget,
+
+00:01:48.840 --> 00:01:52.559
+but the box in the middle is the computer proper
+
+00:01:52.560 --> 00:01:55.719
+which has most of the components inside of it
+
+00:01:55.720 --> 00:02:00.199
+as well as the potentiometers for setting values,
+
+00:02:00.200 --> 00:02:02.039
+and an operation switch.
+
+00:02:02.040 --> 00:02:04.399
+There's a patch panel on the left
+
+00:02:04.400 --> 00:02:07.119
+for connecting the different integrators,
+
+00:02:07.120 --> 00:02:11.319
+amplifiers, multipliers, and so forth together.
+
+00:02:11.320 --> 00:02:16.919
+Then the output of the simulation is displayed
+
+00:02:16.920 --> 00:02:19.799
+on the oscilloscope on the right side,
+
+00:02:19.800 --> 00:02:25.479
+which is a digital oscilloscope.
+
+00:02:25.480 --> 00:02:28.439
+To be honest, I think that a talk about analog computing
+
+00:02:28.440 --> 00:02:30.199
+would be much more interesting
+
+00:02:30.200 --> 00:02:32.039
+than the talk that I'm about to give,
+
+00:02:32.040 --> 00:02:36.639
+but unfortunately that would be out of scope for EmacsConf.
+
+NOTE What is Calc?
+
+00:02:36.640 --> 00:02:39.919
+So instead I will talk about Emacs Calc,
+
+00:02:39.920 --> 00:02:43.359
+the digital calculator built into Emacs.
+
+00:02:43.360 --> 00:02:47.519
+Emacs Calc, while not being a replacement for software
+
+00:02:47.520 --> 00:02:51.479
+like GNU Octave, does have advanced calculator functionality
+
+00:02:51.480 --> 00:02:55.039
+that can be useful in engineering, electronics,
+
+00:02:55.040 --> 00:03:00.759
+or other technical applications. So I don't want to oversell it,
+
+00:03:00.760 --> 00:03:06.479
+but I think functionality-wise, Calc is somewhere in between
+
+00:03:06.480 --> 00:03:12.239
+what you'd expect of a decent scientific calculator
+
+00:03:12.240 --> 00:03:23.939
+and an advanced graphics calculator.
+
+00:03:23.940 --> 00:03:28.839
+So this talk I'll mention is not intended to be a tutorial
+
+00:03:28.840 --> 00:03:33.839
+but only a brief introduction to Calc.
+
+00:03:33.840 --> 00:03:37.439
+Please refer to the built-in Calc info manual
+
+00:03:37.440 --> 00:03:46.739
+for detailed instructions on how to complete operations.
+
+00:03:46.740 --> 00:04:01.479
+Turn off my volume here.
+
+00:04:01.480 --> 00:04:05.719
+The documentation for Emacs Calc is built-in,
+
+00:04:05.720 --> 00:04:10.439
+although on some distributions you may have to install
+
+00:04:10.440 --> 00:04:24.479
+the Emacs documentation separately for licensing reasons.
+
+00:04:24.480 --> 00:04:28.599
+Calc presents itself as a stack-based calculator
+
+00:04:28.600 --> 00:04:31.599
+where entries are dropped onto a stack
+
+00:04:31.600 --> 00:04:36.739
+and then an operation is performed on the stack entries.
+
+00:04:36.740 --> 00:04:42.899
+For example, I can drop 1.23 onto the stack,
+
+00:04:42.900 --> 00:04:54.279
+and then 8.56, and then multiply them together.
+
+NOTE calc-algebraic-entry
+
+00:04:54.280 --> 00:05:01.559
+It may present itself as a stack-based calculator,
+
+00:05:01.560 --> 00:05:05.399
+but indeed, Calc is also capable of accepting input
+
+00:05:05.400 --> 00:05:07.739
+in the more well-known algebraic format
+
+00:05:07.740 --> 00:05:10.759
+by using the calc-algebraic-entry command,
+
+00:05:10.760 --> 00:05:14.999
+which by default is bound to the apostrophe (') key.
+
+00:05:15.000 --> 00:05:19.759
+So you type the apostrophe key, enter the algebraic input,
+
+00:05:19.760 --> 00:05:22.759
+including parentheses as needed.
+
+00:05:22.760 --> 00:05:28.199
+For example, here's a calculation of the resonance frequency
+
+00:05:28.200 --> 00:05:35.039
+of a coil which has an inductance of 250 microhenries
+
+00:05:35.040 --> 00:05:41.059
+and 160 picofarads, taken from one of my electronics handbooks.
+
+00:05:41.060 --> 00:05:50.019
+The formula for that is 1 over 2 pi
+
+00:05:50.020 --> 00:05:57.439
+and then the square root of our inductance
+
+00:05:57.440 --> 00:06:06.279
+which is in this case 250 microfarads - excuse me, microhenries
+
+00:06:06.280 --> 00:06:19.399
+and then the capacitance is 160 picofarads.
+
+00:06:19.400 --> 00:06:24.399
+Small typo here.
+
+00:06:24.400 --> 00:06:26.639
+Now I need to evaluate that one more time,
+
+00:06:26.640 --> 00:06:30.919
+because pi is a symbol.
+
+00:06:30.920 --> 00:06:37.398
+I get about 800 kHz resonant frequency.
+
+NOTE calc-roll-down
+
+00:06:37.399 --> 00:06:41.679
+The command calc-roll-down,
+
+00:06:41.680 --> 00:06:44.199
+which by default is bound to the TAB key,
+
+00:06:44.200 --> 00:06:47.919
+will swap the top two stack entries,
+
+00:06:47.920 --> 00:06:51.559
+which is sometimes useful if you need to manipulate something
+
+00:06:51.560 --> 00:06:56.999
+that's further down the stack.
+
+00:06:57.000 --> 00:07:02.039
+So I can swap this around and say multiply by two
+
+00:07:02.040 --> 00:07:05.479
+and then put it back where it was.
+
+00:07:05.480 --> 00:07:14.039
+This command is also capable of rolling the entire stack.
+
+00:07:14.040 --> 00:07:18.899
+Say I want to shift them all around.
+
+00:07:18.900 --> 00:07:21.399
+This can be done by passing extra arguments
+
+00:07:21.400 --> 00:07:23.559
+to the calc-roll-down function.
+
+00:07:23.560 --> 00:07:28.279
+That's a little bit inconvenient to do manually,
+
+00:07:28.280 --> 00:07:40.079
+so in my init file, I defined here a key definition
+
+00:07:40.080 --> 00:07:45.759
+that passes in those arguments correctly.
+
+00:07:45.760 --> 00:07:49.179
+I attached this to shift-tab,
+
+00:07:49.180 --> 00:07:52.319
+so this way, I can roll the entire stack.
+
+00:07:52.320 --> 00:07:56.159
+Then I could change one entry here
+
+00:07:56.160 --> 00:08:03.459
+and then put it back where it was.
+
+00:08:03.460 --> 00:08:07.759
+So Calc does algebraic input.
+
+NOTE Advanced functions
+
+00:08:07.760 --> 00:08:10.159
+It also does advanced functions
+
+00:08:10.160 --> 00:08:15.599
+that you would expect any handheld scientific calculator,
+
+00:08:15.600 --> 00:08:19.159
+including trigonometric functions.
+
+00:08:19.160 --> 00:08:25.319
+For example, we can get the sine of a number.
+
+00:08:25.320 --> 00:08:30.719
+Now I'll mention here that Calc has multiple modes.
+
+00:08:30.720 --> 00:08:32.319
+Right now it's in degree mode.
+
+00:08:32.320 --> 00:08:38.159
+You can switch over to radian mode if you want.
+
+00:08:38.160 --> 00:08:42.799
+I'm going to put it back in degrees.
+
+00:08:42.800 --> 00:08:49.799
+Drop 12 degrees on the stack, and then get the sine of that.
+
+00:08:49.800 --> 00:08:58.179
+And then with the inverse sine function, I can put it back.
+
+NOTE Solving equations with calc-solve-for
+
+00:08:58.180 --> 00:09:07.519
+Calc also has the nifty ability to solve equations for you
+
+00:09:07.520 --> 00:09:13.919
+so long as the equation is not too complicated.
+
+00:09:13.920 --> 00:09:19.959
+This is using the calc-solve-for function.
+
+00:09:19.960 --> 00:09:31.699
+For example, we could enter in an equation algebraically,
+
+00:09:31.700 --> 00:09:36.679
+then run calc-solve-for, and we just have to tell it
+
+00:09:36.680 --> 00:09:40.999
+what variable we want to solve for. And there we go.
+
+00:09:41.000 --> 00:09:43.199
+We can do this manually as well
+
+00:09:43.200 --> 00:09:54.719
+just so you can see that we get the same result.
+
+NOTE Systems of equations
+
+00:09:54.720 --> 00:09:57.959
+Calc is also able to solve systems of equations.
+
+00:09:57.960 --> 00:10:03.439
+We can put more than one equation on the stack,
+
+00:10:03.440 --> 00:10:08.959
+and then solve for several variables.
+
+00:10:08.960 --> 00:10:13.319
+To give a technical example for this,
+
+00:10:13.320 --> 00:10:30.659
+I'll show you a resistor network scribble that I did recently.
+
+00:10:30.660 --> 00:10:32.819
+Hopefully you can see that. Basically,
+
+00:10:32.820 --> 00:10:38.719
+it's fairly simple, a pretty simple resistor network
+
+00:10:38.720 --> 00:10:42.159
+with 1 kilo ohm and 10 kilo ohm resistors,
+
+00:10:42.160 --> 00:10:48.959
+and using the loop methods, we are calculating the currents,
+
+00:10:48.960 --> 00:10:52.759
+the current in each loop, and then that current can be used
+
+00:10:52.760 --> 00:10:58.839
+to solve for the voltage of each individual resistor
+
+00:10:58.840 --> 00:11:06.199
+if we want to. So at the bottom there we have the equations
+
+00:11:06.200 --> 00:11:11.519
+that we come up with as we work through each loop.
+
+00:11:11.520 --> 00:11:19.579
+And I'm going to paste that into Calc.
+
+00:11:19.580 --> 00:11:22.719
+To save some time, I'm going to copy and paste that
+
+00:11:22.720 --> 00:11:34.259
+from my notes instead of typing it out.
+
+00:11:34.260 --> 00:11:38.259
+So we have two equations there on the stack
+
+00:11:38.260 --> 00:11:44.719
+in one stack entry. We run that calc-solve-for function again,
+
+00:11:44.720 --> 00:11:49.899
+and we tell it which variables we want to solve for.
+
+00:11:49.900 --> 00:11:51.959
+And voila! Those are our currents,
+
+00:11:51.960 --> 00:11:55.719
+which we can then use to get the voltages
+
+00:11:55.720 --> 00:12:00.079
+for the individual resistors.
+
+NOTE calc-find-root
+
+00:12:00.080 --> 00:12:01.999
+I'll just briefly mention
+
+00:12:02.000 --> 00:12:05.839
+that if Calc is not able to solve an equation
+
+00:12:05.840 --> 00:12:07.779
+with calc-solve-for,
+
+00:12:07.780 --> 00:12:10.279
+then you might be helped by another calc function
+
+00:12:10.280 --> 00:12:11.559
+called calc-find-root.
+
+00:12:11.560 --> 00:12:14.439
+This function basically does a manual search
+
+00:12:14.440 --> 00:12:30.199
+for a numerical solution to the equation.
+
+00:12:30.200 --> 00:12:39.959
+And there's the documentation page on that.
+
+NOTE Derivatives and integrals
+
+00:12:39.960 --> 00:12:44.039
+Calc can also solve or find derivatives of functions,
+
+00:12:44.040 --> 00:12:47.579
+at least the more straightforward functions.
+
+00:12:47.580 --> 00:12:49.839
+For a simple example,
+
+00:12:49.840 --> 00:13:00.559
+we can get the derivative of that
+
+00:13:00.560 --> 00:13:11.979
+with the derivative function.
+
+00:13:11.980 --> 00:13:17.159
+On the other hand, Calc is also capable of figuring out
+
+00:13:17.160 --> 00:13:22.099
+indefinite integrals.
+
+00:13:22.100 --> 00:13:26.859
+Say we put that function back on the stack,
+
+00:13:26.860 --> 00:13:32.559
+and this time, we call the integral function.
+
+00:13:32.560 --> 00:13:35.079
+There you go. Of course, you have to add
+
+00:13:35.080 --> 00:13:39.819
+your own constant of integration.
+
+00:13:39.820 --> 00:13:43.399
+For integrals that Calc cannot figure out symbolically,
+
+00:13:43.400 --> 00:13:46.079
+a numerical integration method is available
+
+00:13:46.080 --> 00:13:59.998
+through the calc-num-integral command, which is documented...
+
+00:13:59.999 --> 00:14:17.539
+The function  documentation is available here, more or less.
+
+NOTE Programmable functions
+
+00:14:17.540 --> 00:14:20.399
+I definitely need to mention
+
+00:14:20.400 --> 00:14:24.759
+that Calc is capable of doing programmable functions.
+
+00:14:24.760 --> 00:14:29.619
+That is to say, you can program your own functions into Calc.
+
+00:14:29.620 --> 00:14:32.239
+There are three separate ways to do this.
+
+00:14:32.240 --> 00:14:36.279
+One is through a macro method
+
+00:14:36.280 --> 00:14:41.539
+similar to Emacs's usual keyboard macros.
+
+00:14:41.540 --> 00:14:46.519
+The second method is to transform an algebraic function
+
+00:14:46.520 --> 00:14:50.859
+into a stored function definition.
+
+00:14:50.860 --> 00:14:54.059
+And the third is to use Elisp directly.
+
+00:14:54.060 --> 00:14:56.599
+Personally, I find that the second method
+
+00:14:56.600 --> 00:15:01.799
+is the most practical, the most convenient and practical
+
+00:15:01.800 --> 00:15:08.059
+in my opinion. So I'll give a quick example of that.
+
+00:15:08.060 --> 00:15:14.159
+So I could... Let's say I wanted to have a function
+
+00:15:14.160 --> 00:15:20.699
+for calculating capacitive reactance.
+
+00:15:20.700 --> 00:15:28.899
+I'll define that in algebraic mode first.
+
+00:15:28.900 --> 00:15:33.639
+The function for that is 1 over 2 pi
+
+00:15:33.640 --> 00:15:41.599
+the frequency and the capacitance.
+
+00:15:41.600 --> 00:15:44.959
+Drop that on the stack. You see, it does automatically
+
+00:15:44.960 --> 00:15:52.079
+get simplified a little bit, but it's the same function.
+
+00:15:52.080 --> 00:15:58.839
+And then I press letters Z and F. Do that again.
+
+00:15:58.840 --> 00:16:06.239
+Z and F to start transforming that into a stored function.
+
+00:16:06.240 --> 00:16:11.039
+It asks me to select a user key, a single key press.
+
+00:16:11.040 --> 00:16:15.479
+I'll use the letter c.
+
+00:16:15.480 --> 00:16:19.079
+Then it's going to ask for a longer command name.
+
+00:16:19.080 --> 00:16:24.639
+I've actually defined this once before, so it prefilled in
+
+00:16:24.640 --> 00:16:38.339
+that command name.
+
+00:16:38.340 --> 00:16:42.999
+Then I need to enter which variables in the formula
+
+00:16:43.000 --> 00:16:46.559
+are actual arguments, rather than just symbols
+
+00:16:46.560 --> 00:16:52.559
+to be evaluated later. I prefer to put this in with frequency
+
+00:16:52.560 --> 00:16:54.279
+and the capacitance after that,
+
+00:16:54.280 --> 00:16:57.799
+but actually in this particular case,
+
+00:16:57.800 --> 00:17:07.339
+it doesn't matter at all to the mathematics.
+
+00:17:07.340 --> 00:17:11.399
+So, now all I have to do, that this is defined,
+
+00:17:11.400 --> 00:17:15.199
+is I can drop the frequency on the stack,
+
+00:17:15.200 --> 00:17:24.399
+which we'll say, for this example, will be 4.5 MHz,
+
+00:17:24.400 --> 00:17:32.279
+and then drop on the capacitance, which in this example
+
+00:17:32.280 --> 00:17:40.319
+will be 22 pF.
+
+00:17:40.320 --> 00:17:42.439
+Then I'll call the function that I just defined.
+
+00:17:42.440 --> 00:17:45.239
+I don't really like having to try to remember
+
+00:17:45.240 --> 00:17:48.679
+the short letters that I've come up with,
+
+00:17:48.680 --> 00:17:57.839
+so I'll just use the longer name.
+
+00:17:57.840 --> 00:17:59.799
+I need to evaluate one more time
+
+00:17:59.800 --> 00:18:05.619
+because the symbol pi is in there and not yet evaluated.
+
+00:18:05.620 --> 00:18:07.539
+And so if I've done that right,
+
+00:18:07.540 --> 00:18:12.159
+we have a capacitive reactance of about 1600 ohms.
+
+NOTE Plotting
+
+00:18:12.160 --> 00:18:16.839
+As the last feature that I'll mention here,
+
+00:18:16.840 --> 00:18:24.059
+Emacs Calc does have an interface with gnuplot,
+
+00:18:24.060 --> 00:18:30.799
+if you want to have Calc work as your graphing calculator.
+
+00:18:30.800 --> 00:18:33.159
+I do need to be honest and mention
+
+00:18:33.160 --> 00:18:35.579
+that I don't generally use it myself
+
+00:18:35.580 --> 00:18:39.719
+because there's another program in GNOME
+
+00:18:39.720 --> 00:18:43.499
+that I've found to be generally more convenient
+
+00:18:43.500 --> 00:18:47.399
+for the things that I want to graph quickly.
+
+00:18:47.400 --> 00:18:53.399
+But I think I can give you a simple example.
+
+00:18:53.400 --> 00:19:00.339
+So first, we need to drop a range on the stack.
+
+00:19:00.340 --> 00:19:06.619
+Let's say 0 to 10.
+
+00:19:06.620 --> 00:19:11.639
+And then we need to drop the function on the stack.
+
+00:19:11.640 --> 00:19:17.839
+And then I believe it's the letters g and f that graph this.
+
+00:19:17.840 --> 00:19:22.319
+Let's see. Yep, there we go.
+
+00:19:22.320 --> 00:19:25.059
+So there's our function and it looks nice.
+
+00:19:25.060 --> 00:19:26.659
+That was pretty easy.
+
+00:19:26.660 --> 00:19:29.019
+That's the fast way to do it.
+
+00:19:29.020 --> 00:19:32.839
+I will, as a disclaimer, mention that
+
+00:19:32.840 --> 00:19:34.159
+using this quick approach,
+
+00:19:34.160 --> 00:19:38.759
+that sometimes more complicated graphs
+
+00:19:38.760 --> 00:19:39.999
+will not turn out nicely,
+
+00:19:40.000 --> 00:19:44.339
+because by default, the resolution will be pretty low.
+
+00:19:44.340 --> 00:19:48.119
+That is to say it's... gnuplot is going to be
+
+00:19:48.120 --> 00:19:49.899
+skipping a lot of points
+
+00:19:49.900 --> 00:19:52.039
+and so you'll have to learn a bit more
+
+00:19:52.040 --> 00:19:55.319
+about how to use the interface,
+
+00:19:55.320 --> 00:19:59.519
+what parameters to pass if you want all your graphs
+
+00:19:59.520 --> 00:20:03.699
+to come out looking nice.
+
+00:20:03.700 --> 00:20:08.799
+So that covers all the features that I wanted to cover.
+
+NOTE Wish list
+
+00:20:08.800 --> 00:20:13.279
+I wanted to briefly mention a wish list of items
+
+00:20:13.280 --> 00:20:16.679
+that I'd like to see in Calc.
+
+00:20:16.680 --> 00:20:23.639
+One of them would be improper integrals.
+
+00:20:23.640 --> 00:20:25.159
+So that's like our definite integrals
+
+00:20:25.160 --> 00:20:32.859
+except for where a limit of integration is infinity.
+
+00:20:32.860 --> 00:20:38.559
+That's something that can be useful in a few applications.
+
+00:20:38.560 --> 00:20:41.079
+Something else that would be neat to have would be
+
+00:20:41.080 --> 00:20:45.679
+annotations for row entries. So for example
+
+00:20:45.680 --> 00:20:48.819
+if I was putting together a sum of numbers
+
+00:20:48.820 --> 00:20:53.279
+for, say, my monthly budget,
+
+00:20:53.280 --> 00:20:57.479
+let's say I was paying $2,000 for my rent
+
+00:20:57.480 --> 00:21:03.831
+and let's say $800 a month for my groceries,
+
+00:21:03.832 --> 00:21:07.931
+(a lot of kids to feed there)
+
+00:21:07.932 --> 00:21:14.565
+and then say another $60 for dining out, and so on,
+
+00:21:14.566 --> 00:21:18.259
+it would be nice if there was some way
+
+00:21:18.260 --> 00:21:21.319
+to put a little annotation next to each number
+
+00:21:21.320 --> 00:21:23.399
+so that you could remember
+
+00:21:23.400 --> 00:21:27.039
+what the meaning of that number was more easily.
+
+00:21:27.040 --> 00:21:31.199
+I actually looked into programming this into Calc myself,
+
+00:21:31.200 --> 00:21:35.919
+but discovered that it would require reprogramming
+
+00:21:35.920 --> 00:21:41.839
+quite a bit of Calc to make that work well
+
+00:21:41.840 --> 00:21:43.479
+across all calc functionality,
+
+00:21:43.480 --> 00:21:46.939
+and so, eventually, I gave up.
+
+00:21:46.940 --> 00:21:51.139
+But I'd still really like to have that feature.
+
+00:21:51.140 --> 00:21:52.039
+The final thing, though
+
+00:21:52.040 --> 00:21:54.579
+I think this would not necessarily belong in Calc,
+
+00:21:54.580 --> 00:21:57.919
+I think it would be cool if Emacs had some way
+
+00:21:57.920 --> 00:22:00.599
+to run numerical solutions
+
+00:22:00.600 --> 00:22:02.599
+for systems of differential equations,
+
+00:22:02.600 --> 00:22:06.019
+also known as a differential analyzer.
+
+00:22:06.020 --> 00:22:09.279
+So this would allow you to be able to set up simulation models
+
+00:22:09.280 --> 00:22:11.679
+involving systems of differential equations,
+
+00:22:11.680 --> 00:22:14.879
+for example, a spring mass system, or pressure temperature,
+
+00:22:14.880 --> 00:22:18.039
+or what have you, and then run the simulation
+
+00:22:18.040 --> 00:22:22.119
+using numerical approximation.
+
+00:22:22.120 --> 00:22:24.079
+Maybe it would be silly
+
+00:22:24.080 --> 00:22:25.999
+to actually put that in Calc itself,
+
+00:22:26.000 --> 00:22:30.339
+but a nice interface maybe to some other software,
+
+00:22:30.340 --> 00:22:33.299
+simple software that did that,
+
+00:22:33.300 --> 00:22:35.779
+an easy to use interface for that
+
+00:22:35.780 --> 00:22:38.599
+would be really great.
+
+NOTE Wrapping up
+
+00:22:38.600 --> 00:22:41.800
+So that's my entire talk.
+
+00:22:41.801 --> 00:22:44.534
+I'll just mention some information.
+
+00:22:44.535 --> 00:22:48.365
+If you want to learn more about me
+
+00:22:48.366 --> 00:22:50.119
+or things that I'm interested in,
+
+00:22:50.120 --> 00:22:57.779
+I do not any longer have a web presence.
+
+00:22:57.780 --> 00:22:59.659
+I don't have a website anymore,
+
+00:22:59.660 --> 00:23:03.359
+but I do have a Gemini capsule
+
+00:23:03.360 --> 00:23:07.139
+that I post to all the time.
+
+00:23:07.140 --> 00:23:13.879
+And if you can install, if you're willing to install the...
+
+00:23:13.880 --> 00:23:19.079
+Gemini browser known as Elpher
+
+00:23:19.080 --> 00:23:23.698
+into Emacs, which is available from ELPA,
+
+00:23:23.699 --> 00:23:27.359
+then you can browse directly to it
+
+00:23:27.360 --> 00:23:31.439
+and look around my Gemini capsule.
+
+00:23:31.440 --> 00:23:35.920
+Thank you very much.