A new blog member asked “Why do you use Mathcad?” in response to my most recent post about using some of the funds donated by visitors to the blog to help fund my research.
It’s a very good technical question, and one that deserves more than just a reply to the comment. So I’ll try to explain why here.
I build dynamic models of the economy using systems of ordinary differential equations. There are many programs that support this these days, from public domain programs like Scilab to commercial giants like Mathematica and Mathcad. I’ve tried most of them, and I’ve stuck with Mathcad for two reasons:
Its interface is very natural; and
Its error messages are easy to interpret.
I’ll try to illustrate this with simulations of the same system in both Mathcad and Mathematica. Firstly, here’s a successful output from Mathematica of my simplest endogenous money model with growth and a credit crunch:
And here’s the same model in Mathcad:
Though there’s much more that you can do with Mathematica graphs, I find the Mathcad display more intuitive–more like what a mathematician would write on a sheet of paper, which is precisely Mathcad’s design philosophy.
But the main difference comes with the next feature: the error messages the two programs generate when, as so often happens, you make a mistake in your early attempts to simulate a model. In this instance, I have typed “ss” where I meant to type “s” in a particular function. Here’s Mathematica’s reaction to that:
Huh? What does “NDSolve::ndinnt: Initial condition 400. ss is not a number or a rectangular array of numbers” mean? That’s a trivial example, and of course I already know, but when you’re crafting a complex model and make an accidental mistake, it can be non-trivial exercise to locate the error–even if it is in fact a trivial one like this.
Now here’s the same error in Mathcad, and the first stage of its reaction:
Ahah! I have an (as yet unidentified) undefined variable! I click on “trace error”, and get the next window. If there was a cascade of errors, the “Previous” button would be highlighted, but since there’s only one, when I shut this window down Mathcad puts the cursor right on the offending “ss” variable.
This makes developing and debugging a model in Mathcad an order of magnitude easier than in Mathematica. I know that Mathematica is the more powerful system, but that power comes at a cost of a much more opaque error correction interface.
If these errors were parsed by the program, so that it did what Mathcad did in identifying the source of the problem, then I could quite easily consider developing initially in Mathematica. There would be advantages here–notably the ability to export equations directly to TeX for journals that require that format, but many many others.
But until that happens, I make an engineer’s choice to choose the most effective tool rather than the most powerful or elegant one.
September 26th, 2009 at 9:44 pm
OK, so my next question is: how do I understand these equations?
One thing which following this blog has done is to make me interested in how these models are, um, modeled. I vaguely remember differential equations from school, and I know I understood them at the time (though it seems like a long time ago now).
Can anyone point to any good resources – books, ebooks or websites – which would act as a good refresher but give enough detail to understand the intricacies of these formulas? Or am I being a bit hopeful, thinking A level maths can cut the mustard?
September 27th, 2009 at 2:04 am
Steve – Walras would be very proud of you. Menger wouldn’t.
cja – One book I have used in the past for that purpose is FORGOTTEN CALCULUS by Barbara Lee. I am not sure of any resources that serve that purpose specifically for linear algebra, but I’d be curious to hear about them as well–especially with respect to online resources.
September 27th, 2009 at 2:32 am
Hi Steve, iam a uni student in the health field but would like to learn the basics of economics If i was a first year first semester economics student what text books would you recommend?? or lecture slides
September 27th, 2009 at 7:14 am
Hi cja,
That same dilemma for an audience at the Post Keynesian conference in 2006 was the reason I developed the manner of setting out the financial flow equations that I now use to great effect to not only explain the models, but develop them.
So if you want to understand the equations used in the financial side of those simulations, the first stop is my lectures 9-11 on Behavioural Finance, which are posted on the Lectures tab here (read the 8th too to understand the empirical basis to the endogenous money case).
As noted earlier, I dreampt up the method when Scott Fullwiler challenged me after my presentation at the 2006 conference that the raw differential equation model I presented then “must have had an error in double entry book-keeping terms” to get its results. Since I was confident the model was correct, it occurred to me that maybe it could be presented in double entry book-keeping terms–and that method has become a seriously important tool in my modelling arsenal ever since.
Scott is our own Stf–I don’t often spell these out here, respecting privacy, but Scott is an important member of the Post Keynesian community, and I like to publicly acknowledge my intellectual debts. I owe Scott bigtime for helping develop that insight.
So read those lectures cja, and the financial equations in this post should be understandable.
The next problem however is the general methodology of ordinary differential equations (ODEs), which are the basis of dynamic modelling. There the best book I have found on the subject is Martin Braun’s Ordinary Differential Equations and their Applications (Springer). Braun breaks every rule for textbooks, and the book is fantastic as a result: he uses humour, writes six-page histories of important historical events explained using ODEs–including the Battle of Iwo Jima and the Vietnam War–and has everything you need to know in one volume, including the necessary linear algebra.
He writes so well that it virtually qualified as bedtime reading when I first read it (I had already done courses in advanced ODEs by that stage however and was merely looking for a good textbook–but I think you’ll still find it a superb way to be introduced to the area).
September 27th, 2009 at 7:16 am
We used Paul Samuelson. Not long after I gained a pass on that subject, a debate broke out at the Economics Faculty in Sydney U which eventually gave birth to a new school of thoughts. I don’t know a lot about the debate, but my impression was that Paul Samuelson was no longer worshipped in some quarters. The only thing I learned from his text book was the 4 elements in economics viz. capital, land, labour and resources; and of course the supply and demand curve. To put Paul Samuelson’s theory to practice, you first save your capital by selling your labour, and then you use your savings to buy land and some resources stocks. People nowadays use other people’s savings to buy land and own resources stocks. Apparently these people discovered a fifth element called debt. This is a good site to learn something debt. But to those who are burdened with Paul Samuelson, it’s going to be a steep learning curve.
September 27th, 2009 at 7:25 am
Precisely westlch! I’ll describe the multi-sectoral modelling as GD for “General Dynamics” or–for economists–”General Disequilibrium”. That should really piss some neoclassicals off, and some Austrians too!
Just a quick note: ODEs are not merely calculus, though you need to understand it to do ODEs. A lot of economists think they know ODEs because they can differentiate, but differentiating to ODEs is rather like a monkey working an organ grinder to Beethoven.
The reason is one of the paradoxes of mathematics: almost any function can be differentiated, while almost no ODE can be analytically solved. Neoclassical economists who are obsessed with calculus and differentiation think that all problems in mathematics have analytic solutions, when any engineer knows after 3 weeks of a course in ODEs that the vast majority of them are analytically insoluble. This is just another reason why I describe neoclassical economists as having extremely limited knowledge of mathematics, despite their pretensions to being mathematical social scientists.
Back to Walras. He approached the leading mathematician of his day (and virtually of all days) Henri Poincare, to ask for backing for his tatonnement model–specifically to confirm Walras’s hunch that tatonnement would converge to a stable equilibrium. Poincare declined to provide that backing–which is just as well because the development of a later theorem on the properties of matrix with all non-negative entries indirectly showed that tatonnement would be unstable.
September 27th, 2009 at 7:27 am
Check my lectures on Managerial Economics michael1982, on the Lectures tab on this site. Then for a textbook, the best would be Nova Goodwin’s, combined with Debunking Economics.
September 27th, 2009 at 7:39 am
Absolutely. We would have been contemporaries–I was one of the activists in that debate. And I regard Samuelson’s Foundations of Economic Analysis as one of the key steps in demolishing what Keynes had attempted to do in the General Theory.
Paul Samuelson has had an ambivalent relationship with economic scholarship. He’s a fiercely intelligent individual, and he readily engaged with Piero Sraffa when Sraffa’s Production of Commodities by Means of Commodities–a Prelude to a Critique of Economic Theory challenged the foundations of neoclassical economics, in what became known as the Cambridge Controversies. This puts him above run of the mill neoclassical, who simply assumed the neoclassical theory had to be correct.
However his textbook has played a major role in inculcating and developing the neoclassical model, which the Cambridge Controversies showed to be provable false–at least in the single sectoral abstraction that remains the basis of that theory today. It’s worth quoting the end of the Wikipedia entry on this point:
September 27th, 2009 at 7:42 am
I should have added a link to Braun: here’s the Amazon link:
http://www.amazon.com/Differential-Equations-Their-Applications-Introduction/dp/0387978941/ref=sr_1_1?ie=UTF8&s=books&qid=1253997649&sr=8-1
US$60 and worth every cent.
September 27th, 2009 at 8:00 am
Are you really one of the activists in that debate? Hey Steve you are one of my heroes! Thanks for putting me back in historical perspectives. I hope I can keep posting comments here. You know what aged baby boomers are like when they try to catch up with the Joneses.
September 27th, 2009 at 8:25 am
Yep. The dispute began long before I got to Sydney Uni–in at least 1968 I think when Professors Hogan and Simkin were appointed, and replaced the then rather generalist-Keynesian program with a strongly neoclassical one. Bill Waters and David Hill surveyed students reactions to the new course–which were strongly negative–and a year later they were sacked.
All that was still going on when I arrived as a generally conservative first year student in 1971. I reacted more to the theory than the surrounding politics, and by 1972 I found myself organising a Conference on Radical Economics with an anarchist by the name of Richard Fields. The conference was dreadful (save an excellent paper by Bruce McFarlane), but its momentum spilled into 1973 when the Philosophy Strike erupted, and a strike also started in economics.
There were over 50 people actively involved in that, with me as one of the two lead figures in it–the other being a Government student named Richard Osborne. By the end of the year we’d helped precipitate an enquiry by the Economics Faculty into the Department of Economics, which a year later recommended the establishment of the Department of Political Economy.
The history is well told in Frank Stilwell’s recent book Political Economy Now!.
September 28th, 2009 at 6:54 am
Another free software worth looking at is Sage:
http://en.wikipedia.org/wiki/Sage_%28mathematics_software%29
Its oriented to mathematicians rather than engineers and hence closer to Mathematica than Mathcad, with the disadvantages mentioned by Steve.
But its free, its comparable to Mathematica and a glance through just the contents page of the reference manual is a useful reminder of just how pointless the claims of mathematical sophistication by neoclassical economists are compared with what mathematicians actually do on with computers.
(I haven’t actually tried it yet – just received a recommendation and checked out the docs and wikipedia description).
BTW Is there any way to export from Mathcad to Mathematica (ie import to Mathematica from Mathcad files). There is between Sage and Mathematica so that might provide a means for making Mathcad worksheets freely accessible via a two step process. Also enables LaTex mathematical typesetting for direct inclusion in papers.
October 3rd, 2009 at 5:03 pm
Hi Steve
Re comment #4, your explanation of the origin of your presentation of your differential equations (DEs) in double-entry book-keeping terms. You commented on this as a way to make your modelling understandable to people who haven’t been trained to solve DEs.
There was also the passing reference, “that method has become a seriously important tool in my modelling arsenal ever since”. So if I understand you correctly, thinking in terms of double-entry book-keeping actually helps you, as well as readers.
In much the same vein, I would like to suggest that this approach would be a very important component of any effective undergraduate unit in DEs for maths students. A few months ago, when you introduced this approach to this blog in your posts on Ponzi maths, I was really excited. I wished that you could have introduced me to DEs, but this was a few years before you started as a student at the same university.
My DE unit started, not with readily understandable ordinary differential equations (ODEs), but with second-order partial differential equations (PDEs). I was really struggling with the related abstractions, having no assistance (in the 1960s) from practical computers to get my hands dirty with solving such equations for intelligible cases. We moved quickly to the further abstraction of Laplace transforms, to do reams of algebra to obtain formulas to solve a few special cases. I was freaked out, and gave up university and took a technical assistant’s job with CSIRO. Fortunately I worked there with some inspiring mathematicians, and even came to love working with nonlinear PDEs!
One of my clearest memories from university maths is of a proof of the divergence theorem of vector calculus. For a PDE describing the dynamics of movement of materials, the theorem means that if we add up rates of flow into the region studied, this total inflow rate matches the aggregate rate of increase of content within the region. With 20/20 hindsight, this means that an important aspect of understanding these PDEs is to think in terms analogous to double-entry book-keeping to track the flow of money between accounts.
Now for an aside, to clarify to some readers the issue of tracking the money or materials. Double entry means that if I pay you $1,000, this amount is subtracted from the balance in my account, and exactly the same amount is added to the balance in your account. If we consider an aggregate account, being yours plus mine, the balance in the aggregate account has zero change due to our transaction. Now suppose that a modeller simulates the results of managing a set of accounts with a set of ODEs. There will be one ODE for each account, with the left side of the equation being the rate of increase in the balance in the account, and the right side of the equation being the sum of rates of adding (alas often negative numbers) money according to a set of rules, e.g. interest rates, salary etc. For each transaction on the right side of an equation, there is a potential problem, if the modeller independently estimates the amount of the transaction with some error. Thus there may be different errors for each component of what should be an exact double entry. It is not practical for the modeller to eliminate all errors by using an infinitely dense grid of points for the calculations. However, if the modeller can think like an accountant, and choose a technique for solving the finite difference equations with exact double entries, this will provide an important constraint on errors.
Now back to the above proof of the divergence theorem. Alas, the last line of the proof of the theorem was disastrously misleading. It implied that the theorem would hold only for the continuous differential equation, whereas it holds also when the PDE is approximated in finite difference form on a grid of points. I didn’t discover this latter fact, until over 20 years later, when Peter Ross of CSIRO explained his application of this principle to solutions of the highly nonlinear PDE used to model the dynamics of water movement in soils. I set out the algebra for the set of finite difference equations for modelling the response of a vertical column of soil to rain. I was stunned to see wholesale cancellation of the double entries, so that solving the set of finite difference equations exactly must yield increased soil water content exactly equal to cumulative rainfall. In practice, Peter had water conservation errors less than 1 part in 10 to the 10th! Also, errors in distribution of this water were remarkably low, in spite of using a coarser grids of points than most of his colleagues. His computational speeds were about 100,000 times as fast as those of some of the well known people in the field.
In short, I do hope that mathematics students will come to enjoy the benefits of applying double-entry accounting thinking to solving differential equations, thanks to the efforts of people like you and Peter.
OK the good news is that I think that your approach can potentially improve the education of students majoring in maths, not just economics students needing some maths. But I am concerned, because I have encountered generic ODE solvers that exclude the possibility of exact accounting for double entries. Exact accounting appears to require properly formulated “finite difference” techniques, rather than the widely used high-order Runge-Kutta techniques.
This leads to my preliminary questions about Mathcad, as I can only find limited information in the Mathcad web site.
1. Do Mathcad’s solution technique options include “finite difference”, or are they limited to Runge-Kutta?
2. If the latter, does Mathcad include 1st-order Runge-Kutta, which corresponds to a simple explicit “finite difference” technique that permits exact accounting?
3. Does Mathcad routinely provide outputs to facilitate assessing accounting errors?
4. I note that Mathcad can be asked to provide eigenvalues of the Jacobian matrix. Do you use eigenvalues to guide choice of time steps for your computations?
5. With this matrix being used in the package, there seems to be the potential to use this matrix routinely in a Newton-Raphson scheme for implicit finite difference techniques. Does Mathcad provide this option, and if not, do you believe that this would be possible? My reason for this last question is that in my experience, implicit solution techniques have comparable importance to exact accounting, in constraining numerical error. In fact a lot of “chaotic” behaviour is numerical stuffup, due to failure to assess eigenvalues with explicit techniques, or lack of implicit techniques.
October 3rd, 2009 at 10:18 pm
Re #13 David Short,
I haven’t used Mathcad but recently scanned the documentation available online as well as an example of Steve’s model in Mathcad. My impression is its intended to provide comprehensive and sophisticated use of ODE solvers with everything you might want (except for not being free software and now having a bad reputation for selling cheap student copies with known bugs for which fixes only available with expensive maintenance contract according to wikipedia).
Also provides for Delay Differential Equations with handling of essential “lags” more intuitively and flexibly than the trick Steve uses as a workaround. (But of course this requires an initialization interval rather than a single initial point).
As well as Sage mentioned above, some other relevant software I’ve been googling includes pyDSTool and XPP-XPPAUTO.
SBML provides a data interchange format for large numbers of both FOSS and proprietary packages used by molecular biologists with kinematic laws more sophisticated than simple “reaction rates” plus model changes based on thresholds. These strike me as closely resembling requirements for economic modeling.
Also SysUML profile of UML provides boxes and arrows modeling used for Model Based Systems Engineering. Free tools include TopCase with the Eclipse papyrus framework. This won’t do the actual solving but could be useful for designing easier to comprehend diagrams of models of the sort used in Vissim, Scicoslab and Netlogo (and should end up being able to talk to separate backend solvers).
Another thought while I’m at it. LyX TeX editor has add-on Sweave for weaving in access to “R” statistics package. Since R interfaces with many things including Sage, and Sage interfaces with many things and provides adequate solvers there might be some neat ways to combine things.
Re “double entry” my understanding of the way Steve’s models work is simply that the derivatives of each stock (balance sheet account) are equated to the corresponding flows. So each component of a flow has to appear with opposite signs in two separate equations. This simply means “treating flows as from somewhere to somewhere else”. That could be enforced in a SysUML profile but I dont believe Mathcad or anything else would provide that intrinsically. Steve’s separate table of flows is for keeping track of that. Then, having entered a letter for each flow with + and – in separate columns of the table, the “double entry” is obtained when simply adding up the behavioural equations for each flows in each column to create the equation for the derivative of the stock corresponding to that column. This is both clear and foolproof and displays fine when done (manually) in Mathcad. (ie easy to see what it’s about from inspection of an uncommented Mathcad model produced by Steve).
PS Thanks for the interesting insight on conservative vector field flows conserving “double entry” book-keeping. BTW I suspect that fuller models will require such PDEs (eg for paramaterized production functions allowing choice of technique). Also needed for stochastic DEs – essential to at least represent distributions of wealth that can change with concentration and centralization.
October 4th, 2009 at 12:28 am
I think it’s a problem that being critical of neoclassical theory (that name by now in fact is an empty phrase and describes very little, but that’s a different topic) and being math-averse is higly correlated.
Many people a) know no maths AND b) they see neoclassical theory building on maths AND c) they don’t like neoclassical theory. If only a) and b) was right, they would just do neoclassical politics and when being questioned refer to the proofs of neoclassical theory that they don’t understand.
But when a person unites the characteristics a) and b) and c), he or she will often blame mathematics for the theory they don’t like and dropping the maths in fact many will drop any scientifc approach. It’s hard understanding proofs and counter-proofs, but there’s no way around it (except for ideology, faith or ignorance). Of course not every individual is a talented mathematician (I am none), but the least should be accepting that mathematics is important.
So Steve, thanks for doing so much more than the blah-blah that I often read that was written by critical minds.
October 4th, 2009 at 8:26 am
Thanks for that AD,
Only time lags–if that’s what you mean as the trick–aren’t a trick but an established and natural component of the systems engineering approach. It’s simply a formalised way of handling exponential decay or growth. The systems engineering community refers to delay differential equations as time delays rather than time lags.
I agree also with the comment you refer to about PTC’s upgrade policy, which annoys most established Mathcad users. Things like this–and an impenetrable PTC website if you’re an individual user–are encouraging many people to look for alternatives. There are good odds that I’ll move to Mathematica again when I need to produce production-quality output.
October 4th, 2009 at 9:02 am
Hi David,
You’ve reminded me of how much mathematics I’ve forgotten! One of the problems of being an academic in Australia’s overworked and under-resourced tertiary sector is that you don’t get the free time to practice techniques you learnt as a student–even when you’re not as active in other fields as I am–and therefore you forget them. I’d have to grab a textbook to re-teach myself how to solve PDEs these days.
Thanks also for the observations on the teaching benefits of the double entry approach–at least for financial flows. I’m hoping to have time to work out whether I can extend the tabular method to cover other systems. It could be a rival for the systems engineering approach, which I think is great for combining many isolated systems (as in the combination of subsystems in a car) but not so great when dependencies between systems are widespread.
I just gave my first lecture on this to my 3rd year economics class last week, and there appeared to be complete comprehension of the models across the class. Since economics students are poorly educated in maths, I was very pleased with this. I’ve also found that I can use the table with a public audience and get a fair degree of comprehension from them.
Mathcad doesn’t appear to offer first order Runge-Kutta; this is the complete list from the help file:
October 4th, 2009 at 9:20 am
Too true Patch!
I even had a journal reject a paper unrefereed because it depended on “one narrow mathematical result” when that result disproved the basic marshallian theory of the firm! I’ve now managed to get that journal to reconsider, but it was a classic instance of maths-phobia leading to a totally silly result.
I am also going to have to spend ages explaining to my fellow Circuit-oriented economists (most of whom are great mates of mine–hi Louis-Philippe!) why their beliefs about the limitations of the Circuit are wrong, and yet when someone who doesn’t start with those maths-phobic precepts sees my arguments, they wonder why I spend so much time proving the obvious.
October 4th, 2009 at 12:07 pm
Correction to #14
Not sure why I thought I had scanned the Mathcad docs. I haven’t (still waiting for bit torrent
. Must have been one of the others (I have been getting eye-glazed trying to get up to speed with this stuff). I would however assume that Mathcad includes the solvers available in other packages (and adds a much nicer WYSIWG interface etc). The underlying solver “codes” are common.
Also re SBML for “model changes with thresholds” I should have included the term “events” for clarity. See:
Hybrid Systems and SloppyCell
Re #16 Steve,
Yes, we’re both referring to time lags. Don’t take my word for it as I’m definately NOT up to speed on this stuff. But although the “trick” you use for delays is widely used in systems engineering and handles exponential growth I’m pretty sure economic models will need more than that (eg for vintages of fixed capital which have a lot to do with business cycles). Do check for yourself re the additional complexities of Delay Differential Equations. I’m also pretty sure this is important for your work (and might be relevant to selection of software). See also above links re available solvers.
October 4th, 2009 at 12:09 pm
Thanks AD, yes Delay DEs will be important in the future–especially in modelling government policy responses, which are in reaction to data that is often 1 to 8 quarters out of date by the time the policy is implemented.
October 4th, 2009 at 1:24 pm
Not just government responses. All business “rules of thumb” (and more sophisticated optimizations) respond to currently available information and businesses closely guard their strategic plans. Hence delay dynamics are inherent to a “market economy”. Only way to “control” the resulting instabilities is by phase change of the system (aka revolution) to ex-ante planned allocation instead of ex-post exchange.
Key example is the one I mentioned in passing – vintages of fixed capital investment. The “anti-cyclic” stimulus to investment during depressed periods turns up later as “pro-cyclic” overcapacity.
A well known proposition connected with theory of value, that the unity of exchange value and use value is only established by realization in actual exchange and systemically enforced only through fluctuations and crises. Sadly foreign to Keynesians etc who apparantly believe that a dynamic system can be controlled when it cannot even be observed and predicted, contrary to long established results in control theory etc.
If governments could respond instantly, the inherent dynamics would still be there. “Perfect foresight” beloved in the propaganda is provably equivalent to “perfect planning” and inherently contradicts the essential nature of a “market” economy.
“Perfect planning” is of course equally illusory but unavoidable uncertainties, including things we don’t know that we don’t know, would only result in “inefficiencies” and “mistakes” when the mechanism for disproportions is not crisis but simply reallocation.
Am stressing this because the models need far more attention to the disproportions in the “real” economy that are the underlying cause, not merely the consequence of financial disproportions.
eg Seems obvious that sub-prime mortages not merely a financial mistake, but a consequence of overcapacity in housing production and inability to house people who cannot afford because their incomes have nothing to do with the glut of investment funds available from exploiting them.
“Solutions” like tighter regulation so people don’t borrow for homes they cannot afford simply mean earlier outbreak of the underlying problem – ie massive layoffs in construction and poor housing.
October 10th, 2009 at 11:16 am
Ok, it was a long, slow (460MB) download, but I am now certain that Sage is the way to go.
Here’s an excellent overview (5pp) article for SIAM Review by reviewer with a 20 year investment in Mathematica (will use only Sage from now on).
Here’s a live online calculus “notebook” showing it can display nicely formatted equations like Mathcad. Use firefox browser, not Internet Explorer in case of problems. You can use these notebooks as a working environment through your browser locally (automatically installed on private webserver) or remotely via free account at above public server or to your own server – eg can use while travelling with iPhone.
It can also “weave” live displays of equations and plots of solutions directly into LaTeX papers (like “sweave” for “S” or “R” statistical calculations and plots).
For linux users, proceed to download as soon as you get intrigued by above.
For windows users the normal download is even larger and less convenient (as always). You may want to choose one of the two even bigger huge downloads (1.5GB) instead so you have LaTeX and lots of other stuff that you will end up needing on a virtual linux that runs under windows. Read the readme files for normal and 3 experimental variants carefully before choosing. Assuming you have 2GB RAM and modern CPU with hardware virtualization you may want the specific one that requires that.
Meanwhile windows users could play with it before choosing by working through the tutorial in .pdf docs via an online account as above.
October 10th, 2009 at 1:06 pm
Interesting Arthur; I’ll check it out. You might–if you have the time and the interest–see how well the single-sectoral model I detail in the latest post works in Sage.
October 10th, 2009 at 3:50 pm
I’m confused. Your “latest post” is titled Multi-sectoral…, not “single sectoral” as in #23 above. The linked mathcad filename starts with “3sectors…”, the .pdf filename is different. Neither of these files download.
(No error messages – consistent with site simply being overloaded – I have noticed it being very slow generally. You may need more bandwidth from hosting ISP generally due to increased traffic.)
Anyway, email them as well as fixing here if necessary and I’ll certainly be interested. Still no guarantee on how long it will take, so don’t wait to checkout Sage for yourself – but I was already thinking of using your earlier model for trying out Sage .
October 10th, 2009 at 4:07 pm
Now downloaded both files ok after refresh and seeing #3 in that post with implication that it must be working except for me.
(Still confused by filenames)
October 11th, 2009 at 7:12 am
I’ll put a PDF of the Mathcad file up too for easier access.
The model starts with a single sector and then expands to multiple, but looking at the paper I didn’t document all the steps to the latter as well as I might have (it’s more a book length thing in that case). So the PDF should help. I’ll amend the post and put a link on my research page.
October 19th, 2009 at 3:22 am
Meanwhile I strongly recommend you checkout TexMacs and start using it for WYSIWYG and WYSIWYM preparations of elegantly typeset papers with mathematical formulae – both direct to .pdf and via LaTex. For Windows version I recommend the option to install the full Cygwin first so you can easily add other unixish software that it interfaces to and automatically typesets maths and graphical plots for.
Here’s an example that includes TeXmacs display of “live” (algebraic) solutions of simple ODEs using Maxima (which is also available for Windows). It also interfaces direct to “R” which has comprehensive statistical stuff (free clone of “S”) highly relevant to economics and also to Matlab and Octave (free Matlab clone) with adequate numeric ODE solvers as well as to Sage (which itself interfaces to all 3 and SciPy numeric ODE solvers and matrix algebra etc and provides a superior combination environment).
The TeXmacs/Maxima example in 4th screenshot above is pretty similar to what you could get directly with TeXmacs/Sage numeric solutions of ODEs and looks to me pretty clearly superior to your Mathcad example.
Try TeXmacs first, simply as a general powerful scientific wordprocessor vastly superior to LyX et al and later add Sage. Even though Sage would be running on a virtual linux over windows it should still be just as easy and fast for it to communicate with Windows/Cygwin TexMacs as the interface is via network stack on “localhost” (and can also be made remotely accessible if you want).
BTW QtOctave GUI interface for Octave similar to the Matlab desktop is also available for Windows.
Likewise of course the normal “Notebook” browser interface to Sage is also via network to Firefox browser so despite the virtual linux for Sage itself you would be working entirely in your normal Windows environment apart from the initial hassles of setting it up.
October 19th, 2009 at 7:55 am
Thanks Arthur,
I’ve had a quick look, and what I might do is try simple TexMacs under Windows first of all simply as a LyX alternate to get a feel for it, and then if it seems workable, use that when I start writing Finance and Economic Breakdown properly next year and then do a full installation. I have a spare PC right now so I might make that a full Linux base machine (next year) and try with that.
For now I have to get this multi-sectoral stuff finished pronto, so working in what I know will be faster than learning a whole new system and restarting.