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Most of the new users since perhaps around 2012 came for the data analytics side.

IPython, NumPy, SciPy had been around for a while, but with maturing Jupyter, Pandas and TensorFlow/Keras, it really caught on. Other NLP and Machine Learning libraries probably helped too.

My use of Python today is completely different from how I used it earlier, nearly two decades ago, when it was mainly seen as a better Perl, back when Perl was THE scripting language. Now it is seen as a better MATLAB or a better R, even though the base language isn't itself vectorized as the others. The language and the standard library didn't improve much towards this. It was mainly the third party libraries that emerged and matured.

Speaking purely from a language standpoint, Julia has all right features for the analytics side, but the scientific community is right now with Python.

SageMath is free and is easily accessible from Python. It runs on Linux, and other O/S's including those from Microsoft.

SageMath is very powerful and is a good alternative to MatLab and Mathematica.

http://www.sagemath.org/
[...]
SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.

Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
[...]

http://www.sagemath.org/ should be visited by anyone interested in helping promote (including R) open source software that is numerical in nature. I agree that programming is important if you need answers to tough (realistic) math questions, and SageMath will allow you to explore a number of open-source packages ( NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R, etc.). Really, SageMath needs more users . . . please help!

Clicking "Try Sage Online" doesn't require downloading or installing Sage on your computer. But more importantly:

More importantly, can we agree that in equilibrium, power in = power out?

No. I am not aware of any "conservation of power" law. [Jane Q. Public]

Energy is conserved, which means that if you draw a boundary around some system (like the heated plate), power going in minus power going out equals the rate at which energy inside that boundary changes. At equilibrium, that rate is zero because the system doesn't change. So at equilibrium, power in = power out.

That's the basis of all these calculations, which is why I've repeatedly asked if we could agree on it.

Once again, can we agree that in equilibrium, power in = power out?

For the moment, I'll assume we can. If not, please explain why you don't agree that in equilibrium, power in = power out.

I'm sorry that I didn't realize earlier that we have such a fundamental disagreement. I should've been building a common understanding of equilibrium and conservation of energy rather than solving increasingly complicated thought experiments. So let's take this step by step and see if we can agree on anything.

Let's start with conservation of energy just inside the chamber walls at equilibrium: power in = power out.

A blackbody plate is heated by constant electrical power flowing in. Blackbody cold walls at 0F (T_c = 255K) also radiate power in. The heated plate at 150F (T_h = 339K) radiates power out. Using irradiance (power/m^2) simplifies the equation:

electricity + sigma*T_c^4 = sigma*T_h^4 (Eq. 1)

(Eq. 1 looks better in LaTeX, but hopefully this version is legible.)

Yes/No: can we agree that Eq. 1 is based on the Stefan-Boltzmann law and correctly describes conservation of energy just inside the chamber walls at equilibrium?

If yes, the next step is to solve Eq. 1 for the constant electrical input using a calculator or the Sage worksheet I provided.

If no, could you please write down the equation you think correctly describes conservation of energy just inside the chamber walls at equilibrium?

Earlier I made an offhand remark that enclosing the heated plate is like suddenly warming the chamber walls. This simpler scenario might be more helpful. Suppose the chamber walls are suddenly warmed from 0F to 149F. What will happen to the heated plate if the electrical power heating the plate remains constant? If you claim it would remain at 150F, think carefully about energy conservation at equilibrium. When the walls were at 0F, the plate was in equilibrium because power in = power out. But now the net power radiating out is much smaller, which means power in > power out. So what happens to the heated plate?

Nice link. Do you really expect me to read that .sws file? How about something human-readable? [Jane Q. Public]

These open source Sage worksheets show my work for these thought experiments. Clicking "Try Sage Online" would let you upload my third worksheet, and hitting shift-enter a few times would recalculate all its answers. But in case you don't want to do that, here's a formatted copy of that worksheet and its answers:

#Calculate constant electrical power/area heating 1st plate.
var('sigma T_c T_h electricity epsilon_h epsilon_c')
eq1 = electricity == sigma*(T_h^4 - T_c^4)/(1/epsilon_h + 1/epsilon_c - 1)
soln1 = solve(eq1.subs(T_c=255.372,T_h=338.706,sigma=5.670373E-8,epsilon_h=0.11,epsilon_c=0.11),electricity)
soln1[0].rhs().n()

ANSWER = 29.3986743761843

6379^2/6371^2.n()

ANSWER = 1.00251295644620

338.706*1.00251295644620^(-.25).n()

ANSWER = 338.493545219805

#Completely surrounded by 2nd plate
soln2 = solve(eq1.subs(T_c=338.493545219805,electricity=29.3986743761843,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11),T_h)
soln2[0].rhs().n()

ANSWER = 385.286813818721*I

This could also be done on a calculator, which is why I explained how to derive the equations using the principle that at equilibium, power in = power out.

... its outer temperature is 149.6F ... pretend the enclosing shell is a thermal superconductor, so its inner temperature is also 149.6F ... [Dumb Scientist]

So, first you postulate a thermal superconductor, and then assert that it has a far higher temperature on one side than on the other? What a magical world you must live in. [Jane Q. Public]

No, I said both sides of a thermal superconductor enclosing shell are at 149.6F. Accounting for aluminum's finite conductivity would mean its inner temperature would be higher than its outer temperature. If you'd like, we could see how an aluminum plate warms the inner plate higher than the 233.8F it would be at with a superconducting plate. Just let me know, and I'll do the calculations.

But I don't think that would be helpful yet, because I didn't realize we have a fundamental disagreement:

More importantly, can we agree that in equilibrium, power in = power out?

No. I am not aware of any "conservation of power" law. [Jane Q. Public]

Energy is conserved, which means that if you draw a boundary around some system (like the heated plate), power going in minus power going out equals the rate at which energy inside that boundary changes. At equilibrium, that rate is zero because the system doesn't change. So at equilibrium, power in = power out.

That's the basis of all these calculations, which is why I've repeatedly asked if we could agree on it.

Once again, can we agree that in equilibrium, power in = power out?

For the moment, I'll assume we can. If no

We've determined equilibrium temperatures in a simple example, so let's solve a more general example.

Jane's concerned that the enclosing plate is bigger than the heated plate. But Earth's mean radius is 6371 km, and the effective radiating level is ~7 km higher, so these surface areas are only ~0.2% different. Of course, in a thought experiment this difference can be made arbitrarily smaller. Despite Jane's protests, this doesn't change the fact that enclosing the heated plate makes it warmer.

More importantly, I treated the plates as blackbodies where absorptivity alpha = 1 and emissivity epsilon = 1. This is a reasonable approximation for plates made of carbon nanotube arrays (PDF) which have alpha = ~0.99955. But more conventional plates have alpha and epsilon considerably less than 1.

The next step is to treat the plates as graybodies where absorptivity and emissivity are independent of wavelength, so they appear gray. Kirchoff's Law states that absorptivity = emissivity for graybodies.

MIT calculates heat transfer between graybody plates using an infinite sum of emission, reflection and absorption. Using my variable names, their final expression is:

net heat flow = sigma*(T_h^4 - T_c^4)/(1/epsilon_h + 1/epsilon_c - 1) (Eq. 2)

(Again, Eq. 2 looks better in LaTeX, but hopefully this version is legible.)

At equilibrium, net heat flow equals the electrical input. Note that MIT's Eq. 2 reduces to my Eq. 1 for blackbodies where epsilon_h = epsilon_c = 1.

Suppose the plates and chamber walls are made of oxidized aluminum with emissivity = 0.11. In this case, Sage solves Eq. 2 for a constant electric input of 29.6 W/m^2, which is lower than before because aluminum doesn't radiate as well as a blackbody.

Using Eq. 2 and the same reasoning as before, fully enclosing the heated plate warms it to the same equilibrium temperature of 235F (386K). Fully exposing the plate to the cosmic microwave background radiation cools it to 13F (263K), which is lower than before because the CMBR is a blackbody and aluminum chamber walls aren't.

So even for graybody plates, MIT's mainstream physics refutes Dr. Latour's nonsensical claim that the enclosed heated plate remains at 150F. They also use this equation to explain how thermos bottles insulate drinks, and describe the same radiation shields used since at least

His actual argument is that "k is the fraction of re-radiation from the second bar absorbed by the first hotter bar... k must be identically zero, so no cold back-radiation is absorbed and T remains 150. Quod Erat Demonstrandum, QED."

Again, he's completely wrong. The hotter bar absorbs cold back-radiation, and T does not remain 150F. That's why I refuted Dr. Latour by showing that a completely enclosed heated plate reaches an equilibrium temperature of 235F (386K), which is less than the infinite temperature he claimed.

Maybe it would help if we checked my calculations step by step. Start with conservation of energy just inside the chamber walls at equilibrium: power in = power out.

The plate is heated by constant electrical power flowing in. The cold walls at 0F (T_c = 255K) also radiate power in. The heated plate at 150F (T_h = 339K) radiates power out. Using irradiance (power/m^2) simplifies the equation:

electricity + sigma*T_c^4 = sigma*T_h^4 (Eq. 1)

(Eq. 1 looks better in LaTeX, but hopefully this version is legible.)

Yes/No: can we agree that Eq. 1 is based on the Stefan-Boltzmann law and correctly describes conservation of energy just inside the chamber walls at equilibrium?

If yes, the next step is to solve Eq. 1 for the constant electrical input using a calculator or the Sage worksheet I provided.

If no, could you please write down the equation you think correctly describes conservation of energy just inside the chamber walls at equilibrium?

Maybe it would help if we checked my calculations step by step. Start with conservation of energy just inside the chamber walls at equilibrium: power in = power out.

The plate is heated by constant electrical power flowing in. The cold walls at 0F (T_c = 255K) also radiate power in. The heated plate at 150F (T_h = 339K) radiates power out. Using irradiance (power/m^2) simplifies the equation:

electricity + sigma*T_c^4 = sigma*T_h^4 (Eq. 1)

(Eq. 1 looks better in LaTeX, but hopefully this version is legible.)

Yes/No: can we agree that Eq. 1 is based on the Stefan-Boltzmann law and correctly describes conservation of energy just inside the chamber walls at equilibrium?

If yes, the next step is to solve Eq. 1 for the constant electrical input using a calculator or the Sage worksheet I provided.

If no, could you please write down the equation you think correctly describes conservation of energy just inside the chamber walls at equilibrium?

I hope the Foundation folks say "Thank you, much appreciated", and let the kids decide.

That was pretty much what I spent the day saying.

Educators the world over have often decided to insulate and protect children from the gamut of choices available to them in the Real World(tm). I don't always agree with the extent to which we "protect" children, especially as they grow older and feel very limited by society's restrictions, but I believe some amount of guidance can be helpful.

Letting the children decide between Mathematica and alternatives sounds amazing to me, and I'm very appreciative that you proposed the idea.

Atmosphere among the educators in the room when Conrad announced it this morning was pretty electric.

What do these educators think about Sage and other alternatives to Mathematica? Do you think these educators are famiilar enough with the Pi system, Mathematica, and mathematics software alternatives such that they can explain the differences and pros/cons to their young charges?

If people don't like the fact that it's only free as in beer, there's always Sage.

Yes, there is Sage, but while Mathematica's efforts got a big boost with front page billing, I see nary an article about Sage Math on the RaspberryPi blog. Whereas you just "announced a partnership with Wolfram Research to bundle a free copy of Mathematica and the Wolfram Language into future Raspbian images" (the officially-built/recommended OS), I believe that Sage has never been included in these images.

If you do want to give schoolchildren a choice between the two of them, why not start by writing an article about Sage and putting it in the default install as well? Unlike Mathematica, children will be able to download and run Sage easily and for no fee on any Win/Mac/Linux computer accessible to them, which will allow them to start projects on the Pi and move to beefier hardware later, or start a project on a school computer and bring it home to their Pi.

If children are able to make an informed choice between Mathematica and Sage (or other alternatives), then I support their opportunity to do so. Computers and the software that lives upon them should be given to children to explore, investigate, break, and repair. To truly give our future generations an opportunity to see the beauty of hardware and code I believe we should allow them to tweak and fiddle with the frobs inside these complex systems. A closed-source package like Mathematica curtails the possibility of investigation and dampens the fires of curiosity and innovation that can be seen in children everywhere.

Give children a choice? Certainly. But make sure that our educators can provide our students with exploration limited only by one's own imagination.

sage

There are far more feature rich notebooks systems that include more than just TeX: http://www.sagemath.org/tour.html
But if you want primarily TeX plus computer algebra (Maple) it exists but it is commercial. http://www.mackichan.com/

I suggest sage, it outperforms Matlab & is free!

http://www.sagemath.org/
[...]
Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
[...]

You should check out SAGE: http://www.sagemath.org/ It is based on Python. It is a free open source alternative to Magma, Maple, Mathematica and Matlab, created at the University of Washington. It has a CAS that is on par with Mathematica, but it has a lot of capabilities that no other package has (especially in Algebra). SAGE is the most scientific package I know of, since everything is open source, so you can actually prove how accurate its results are by analyzing the code. You don't just enter a formula and get a magical result.

Mathics for a great free Mathematica-compatible CAS system with decent 2D plotting.
Sage is another great CAS system but the plotting is less flexible.

Mathics is a great CAS system with Mathematica-compatible syntax and great 2D plotting.
Sage is another great CAS system but it's plotting facilities seem less flexible.

The best part? Completely open source (so you *know* how the result is being calculated, no Mathematica/Matlab-like black magic) and free - both as in beer and freedom (Mathematica/Matlab cost ~5k USD normal, per-seat license ...).

If you don't mind doing coding, try Sage or Python + IPython + NumPy + SciPy. For a quick calculator I like to just use bc in a terminal.

Many implementations can be found here: http://sagemath.org/ It's essentially a big mathematics library written in python

Well, the issue then is that testing and unstable aren't quite stable enough for me. I want something which I can learn and set up, then leave running for years. Debian stable could do that, but neither testing nor unstable could.

However, at times I also want to play with the newest goodie from Debian Sid. I don't want to reboot, I don't want to use a VM, I just want to run a program from Sid. With Bedrock Linux, I can do that: I can have a system which is almost entirely Debian Stable, except for the packages I want from Sid when I want them. Any library compatibility issues one would normally have trying to get a .deb from Sid into Stable are non-issues with Bedrock Linux.

Add on to that that I can use Gentoo's portage to relatively easily keep a specific package customized to my specific tastes. Say I don't like dbus, but I want firefox - Debian's iceweasel is dependent on dbus. I could just get it from Gentoo with the flag set to exclude dbus. Yet everything else would be Debian.

At the same time, I am 100% library-compatible with Ubuntu, so for projects like sage mathematics, which I know provides packages for Ubuntu, I can use those with absolutely no worry that they won't work. Debian Testing cannot do that.

I use Sage quite a bit. It's basically a wrapper for almost all the mathematics software available. http://www.sagemath.org/ While you still need to drop down to C for great performance, it solves a lot of the interoperability issues discussed. In other words, take the example from the summary: from Sage, you can call Matlab commands and then immediately use the results with R commands. Sage works through a web browser, and it's based on Python, which is a plus.

I strongly recommend Python.

The reason I like Python so much is that it has the least syntactic silliness of any language I've used: Python code often reads like psuedocode, but it actually works.

To learn C, you need to start by learning what a variable is, and that means learning what the different data types are, and when you use them. In Python, there really aren't variables: you just bind values to names.

And Python has lots of great libraries, so that he can easily write a non-toy program that does something interesting. In particular, there is the library, which would allow him to write a game.

And Python is useful for doing real work. It would be a poor choice to write an operating system or a word processing program, but it is useful for all sorts of actual problems in many fields. Particularly in science, Python is becoming a top language, thanks to SciPy.

Python is also the language used for SAGE, which he might enjoy using to plot graphs.

P.S. If he loves Python and wants to learn a second language, I would suggest C. Not C++, C.

steveha

Anyone interested in LastCalc is probably also interested in SAGE:

http://sagemath.org/

Basically this is every free math tool out there, glued together using Python, with a nice web "workbook" interface. It can make plots, do symbolic math, and all sorts of stuff.

Fun fact: someone ported TeX font rendering to JavaScript, and that is what SAGE uses to draw math equations in your browser.

steveha

I use SAGE, an AWESOME math engine. I use the browser "notebook()" mode.
And, it works beautifully in my Kubuntu 10.04 LTS. I don't have to run it in a virtual guest OS.

The math tool. Fantastic piece of software.

Well I just spent this weekend trying to find some neat physics to pep up my interest in amateur radio.
I am also angling to pep up my resume so I can wiggle into a job where there is a particle accelerator.

Here is an introduction to quantum physics with an emphasis on modern gadgets that use quantum phenomena.
http://www.colorado.edu/physics/2000/index.pl?Type=TOC

Here is a pretty reasonable home quantum physics project.
http://www.instructables.com/id/Homemade-Quantum-Laser-Micrometer-Nestors-Microm/?ALLSTEPS

An introduction to the Planck Constant and emission spectra.
http://www.radio-astronomy.org/educ/tutor2.htm

As I master the math, I plan to write my own tutorial and computation scripts using this tool.
http://sagemath.org/

Both the Sage notebook and codenode are similar projects that support development of Python programs via a web browser interface. They have been around for about 4 years, and full source code is available for both in case you want to setup your own server (there are dozens of Sage notebook servers used at universities around the world).

You personally had to buy three licenses to cover all your computers? And let me guess, you had to sign up three separate times to their annual charges to receive bug fixes for each of those licenses?

I was hit by a bug a couple of months after purchase, and when I asked for the point-point upgrade (x.y.(z+1)) that fixed the bug I was told to shell out annually for upgrades. Goodbye Wolfram, hello sage.

sage is where it's at.

Try working with Sage http://www.sagemath.org/ Useful math tools that cover your interest area.

Sage is an open source platform for mathematics and computation that ties together many C and C++ libraries with Python code. You could browse the project bug and enhancement tracker or the sage-devel google group for some ideas of where to contribute and the project culture. There are a very wide range of things to do. With Sage, and probably most other projects, a very good way to get started is to help improve the documentation. This is not glamorous, but it is effective. It involves you with other people in the project, and gets you familiar with their development practices. Its usually well appreciated since documentation quickly gets out of date on an active project. Writing documentation will suggest some coding projects naturally - to adequately describe a current bug to users, for example, you will have to understand it somewhat, and that might suggest a solution.

Sage is an open source platform for mathematics and computation that ties together many C and C++ libraries with Python code. You could browse the project bug and enhancement tracker or the sage-devel google group for some ideas of where to contribute and the project culture. There are a very wide range of things to do. With Sage, and probably most other projects, a very good way to get started is to help improve the documentation. This is not glamorous, but it is effective. It involves you with other people in the project, and gets you familiar with their development practices. Its usually well appreciated since documentation quickly gets out of date on an active project. Writing documentation will suggest some coding projects naturally - to adequately describe a current bug to users, for example, you will have to understand it somewhat, and that might suggest a solution.

Applied math student...knows C++...dude. Contribute to Sage.

The goal of the Sage project is to creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. It is based on Python, but has many components written in C and C++. It has good capabilities for numerical computation, but more help is needed. It's pretty easy to dive in and start fixing bugs, and your work would immediately benefit thousands of mathematicians and mathematics students.

Sign up for the sage-devel list and start with Sage!

Microsoft has given significant funding to support the development of Sage and R. In the case of Sage the funding has always been "no strings attached". (I am director of the Sage project, and Sage is licenced under the GPL.)

Bingo. Much as I like R, the language leaves a lot to be desired compared to Python - it doesn't even have a built in dictionary type. For a fully integrated package including Python and R, SAGE is worth a look.

The HP 50G is definitely a top flight calculator in terms of key action, processor, and programming. I definitely prefer it over any TI I've used, which is pretty much their whole line except the Nspire. Most people I've heard that have used both prefer the 50G, but I tend to hang around engineering nerds.

To me the keyboard is the biggest win, though I do prefer RPN. The main advantage of a hardware calculator is the dedicated keyboard, which is why using TIs crappy keyboards is such a drag. Though to be fair, the HP 49 series also had crappy keyboards. The 48 and 50 series are golden though.

The downside is the place where stand alone evaluators make the most sense, education, your teacher probably will be showing you how to do things on a TI instead.

I love my 50G, but SAGE is more convenient and powerful for many tasks, so if I'm in front of a computer I'm probably using that. On my IBM model M, because input devices make a difference in input speed and correctness.

On a tangentally related note, if you're in the market for a non-graphing calculator, I was shocked at what you get for $15 these days with the Casio FX-115ES. Picked one up on a whim, and was fairly impressed.

Sage is free and rivals Matlab/Mathematica.

See http://www.sagemath.org/

There's also Sage Math. You could use the Sage Notebook to try it out. The programming interface is based on Python.

> I don't want to load 20 modules before I can begin coding. I just want to input my algorithm and get a result I expect (not 5/2=2). You might want to try Sage (sagemath.org and sagenb.org). It's Python, but it fixes the "5/2" issue and preloads numerous modules.

Sage has very fast 3d plotting capabilities! http://www.sagemath.org/

Have you tried using sage? http://www.sagemath.org/ [...] Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. [...]

You should really check out Sage: http://www.sagemath.org/ . Python based, includes pylab, ipython, scipy, numpy (everything you mentioned) plus much, much more.

With NumPy and SciPy, it is just as easy to do what MATLab does in a language that's actually fun to work with.

I just hope Sage succeeds and becomes more well-known. It's the best open alternative we have.

Flamebait? sage was a reference to http://www.sagemath.org/ .

You forgot the Python alternative to Mathematica

Erm, were you talking about this Sage? because my initial reaction to your post was "WTF is this guy talking about, Sage was made for Linux from the beginning", so I googled just in case.

Yes - it is called Sage http://www.sagemath.org/

I think a SAGE notebook is what you are looking for. It's basically multiple different open source mathematics software packages (such as Maxima) glued together with python. The notebook can typeset it automatically for you or you can output the LaTeX. Well you may like the custom system you have better, but SAGE is pretty slick since it goes into a wide range of math. I suppose any customizations you would like could be contributed to SAGE.

+1 to Sage http://www.sagemath.org/ from me, too. You are always limited by these tiny utilites and you are not able to program with them easily like with Sage - since it is based on Python.

What more could you need? (Acceptable answer: Sage?)

Have you had a look at

http://www.sagemath.org/
[...]
Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
[...]

I asked them before this came out, and they said they didn't want to post their code on the press release in order to avoid being slashdotted. Seriously. I think the code is certainly available upon request, and will be made available later when the hoopla dies down. Much of it is in FLINT, which is part of Sage.

This is a fantastic piece of work by some of the leading computational number theorists today. Most of the authors are involved in the Sage project in some form or another and their algorithms and code are driving the cutting edge of the field. Great work guys!!