For Power Mathematics, Retire the Spreadsheet

The transcript below has been edited for clarity.

Jim Anderton: Hello everyone and welcome to Designing the Future. You know mathematics is the mother of all science and engineering, whether you're designing a bridge or a fusion reactor, the ability to set up and solve problems in a coherent way, well, it's fundamental to the design process. Now software to do this has been around for decades, but there's a new generation of platforms that promise to do more complex work faster and with better integration with other software. Now joining me to discuss this today is Brian Thompson, division general manager for PTC, CAD and general engineering calculations businesses. In his current role, Brian responsibilities include market analysis, solution defining and strategy solution, marketing, strategic business and customer development activities.

Brian, welcome to the show.

Brian Thompson: Hey Jim, thanks for having me. It's great to be here.

Jim Anderton: Brian, it is so fundamental, what we're talking about here. It is core to the entire engineering process, even the process of scientific discovery these days. So, it's really good that we're having this conversation.

You know we're talking in this case about Mathcad. Now Mathcad has been around a long time. It's ubiquitous. I've used it. Almost everyone I know in the industry has used it and considered by many to be the gold standard. It's certainly regarded like the “Kleenex”, if you will, the brand name for this kind of software. You know in its earlier form its original forms as I remember it, the key attribute about it was that you could actually lay out an equation in the same way that you could with a pencil and paper. So conceptually, the way you could lay the problem out, made it much more intuitive, so it wasn't a matter of learning how to program. So, chi squared wasn't two asterisks. Is that still a major factor today? Is that level of usability that the driving force?

Brian Thompson: It really is. And of course, since that time we've continued to expand it. The natural math aspect of Mathcad is at the very core of why engineers, research scientists, anybody who wants to lay out calculations in a way that they learn them when they were going to university is of the most importance. But secondarily, maybe even 1A and 1B, is the fact that it honors the unit systems that you are using with the calculations, and so it's units aware and makes sure that you can't make a mistake in the units in Mathcad without Mathcad telling you, this doesn't work. That these units are not consistent with one another.

And I'd say those two things have stayed at the very center of why engineers and scientists have loved to use Mathcad for many, many years. Of course, there's other aspects that I'm sure we'll talk about today, but you’re right on the money, there that those two things together are really at the center of why engineers and research scientists and really anybody involved in in any kind of significant engineering calculations loves Mathcad

Jim Anderton: You know scientists and engineers, they usually joke with us down the trenches about how we lop a couple of decimal points off every calculation, like math-lite. But I've noticed that in some industries, and one that comes to mind is like RF electronics: Fast Fourier transforms are a big thing for those types of folk. You're talking about Bessel functions, some very, very sophisticated math. Now is the market going that way? Basically, are we demanding more and more out of math and out of the software to handle it?

Brian Thompson: It's interesting you asked the question that way because we've seen a couple really crazy trends in the use of Mathcad. The symbolics of Mathcad have always been really powerful, and I think that's why Mathcad got maybe some of its initial attention. The strengthened symbolics that it has handling equations at the symbolic level, but we see more and more of a trend towards heavy duty, hardcore mathematics calculations where the answer is not some, you know, equation or some expression. The answer is actually a number. Or a series of numbers, a vector or matrix.

That has been a trend and we've seen a lot more of that, and it's really driven from this world where companies are trying to do more and more simulation overall as part of whatever their process is, for whatever it is they happen to be bringing to market and either as a front-end system, a back-end system, or even right in the middle of the development process, Mathcad can be automated. It can be integrated with extensive API's and so you can use it as part of the overall digital continuity of your calculations throughout the entire process, irrespective of what market you're in.

Jim Anderton: Well, it's interesting you brought up simulations. In the engineering design world of simulation, that's where it's at today. And the idea now is simply you take that digital twin essentially and iterate your way to success, with multiple attempts at something that you couldn't do if you had to physically make a prototype and it then actually test it.

But if you, if you can simulate something using a digital twin and do hundreds, thousands, maybe hundreds of thousands of trial runs to get to a design, in theory you could also create an exponential number of differential equations, a matrix of exponential size as you increase the complexity, not in in how complex the problems are, but a number of problems you've got to solve.

Brian Thompson: Definitely, and we see Mathcad being used kind of as a calculation engine in support of a process like that. That's part of a broader cycle of calculations that are done over and over. We see Mathcad as an input engine. More and more simulation is being done as part of delivering, say, discrete manufactured products to their market, which is kind of PTC core market, but certainly not the only market for Mathcad and the more simulation is done as part of the develop process.

Well, the most thought has to go into one of the right boundary conditions. What are the right loads? What are the preconditions? What other post processing do I need to do of simulation results? And that’s what Mathcad is being used more and more for that kind of thing as well, somewhat driven by, really the entire market's desire to know more about what the design options that they're considering might do if we actually built those prototypes through simulation.

Jim Anderton: And what markets we are talking about here intuitively, we know that the electronics industry, I mean those guys do with imaginary numbers. They've got interesting problems that those in the mechanical world don't have to worry about. And there's often a sense, that those of us who cut metal, we have a relatively simple set of approximations to work with. And we're pressed later to be dragged down this road. So, we think of things like the electronics industry, perhaps the nuclear industry, the aerospace industry, as early adopters, and everybody else in the wake of them. Is that still true today? Are they the leaders?

Brian Thompson: I would say that what we've seen is an awakening of the use of technologies like Mathcad in other industries. More than you might think. It’s funny you mentioned those of us that cut metal. There are some pretty good closed form solutions for things we do, all true. But we have seen remarkably complex civil engineering Mathcad notebooks.

Because a lot of the rules that are used to govern the basic foundational calculations you do to build a bridge, what have you right? They're all governed by closed form equations or equations that are iteratively solvable, and then can be solved in Mathcad. And so, we see it really all over the map. I mean, it's certainly very complex and some of these electrical engineering, RF engineering as you describe, but we're seeing it in places like civil engineering, and even more as upfront research in biotech and pharma.

In fact, it's interesting. Even though PTC's market is primarily discrete manufacturers, about 75% of our Mathcad customers, they're not customers with PTC in any other way, because they don't manufacture something that you can touch or feel, they do something else right? But they're using Mathcad in some of these domains that we're talking about.

Jim Anderton: Yeah, it's funny. You mentioned in back in college - which is eons ago in my case - I was a using a very early, probably original iteration of Mathcad now that I come to think of it. I was kind of a lone wolf who did that independently, and I remember working on a problem set and then getting hammered by a teaching assistant because I told in no uncertain terms that you're expected to use SnapCalc for this.

The use of spreadsheet software in general, Excel comes to mind, because Excel of course, that Microsoft done a good job of putting some functionality into something that's probably better suited for the accountancy or the financial industry. But it's ubiquitous even in engineering, because it’s accessible in that case, do you still see that there's some pull there? That’s where there are still some people who have the tendency to say “Geez, you know I'm simple. My problems are not that complex. I'm going to stick with a spreadsheet type solution.”

Brian Thompson: We do see it and it's unfortunate, all of us that have worked in engineering have felt the pain of learning that lesson. I myself have felt the pain of learning that lesson. Before coming to PTC, I worked in engineering for 16 years and did a lot of thermal calculations. And I remember very, very distinctly building a very sophisticated spreadsheet calculation. I didn't know about Mathcad. I’m going to be honest. I didn't know about it.

As soon as I tried to reuse that calculation for something else that looks similar but had enough differences that I started questioning whether or not the formulas I had entered, you know that were this long inside the cell, I started questioning whether they were right, and I couldn’t be sure anymore. And that is the beauty of Mathcad because the equation is there in the same form that I had it written in my notebook before I transposed it into the cell in Excel, you know?

And do I have all the parentheses in the right places? Are the symbols what they should be? Are they coming from the right cells? I mean, it's really hard to use Excel and to frankly reuse excel over and over again for engineering calculations, as you want to vary them. That's what one of the key strengths of Mathcad is. It's very clear what the calculations are doing. They look like they did in your heat transfer book. They certainly look like they do in my heat transfer book.

So, it's a lesson that engineers learn once, and once they start using Mathcad that I really feel like they never go back unless, they're a project engineer and they're doing financial calculations to support their product develop process. Great, you know Excel is very well suited for that, but it has a lot of engineering calculation functions built in and they lure engineers in. At least I regretted it, because I couldn’t reuse that really sophisticated radiation calculation spreadsheet I had developed over again. Because too much had changed, and I was no longer confident even my original calculations of it. It really is problematic for engineers, .

Jim Anderton: Well, I feel your pain because you know, I've been down that heat flow, heat flux, route too and the horrors having to simultaneously cope with conduction, convection and radiation, scaling to the 4th power of temperature.

Brian Thompson: Exactly, it's like come on. And you know, like a little carrot with a four next to it. In Excel, it's like yeah OK, I get that's what that means. But when you have a calculation that takes many steps, and you're trying to do a good job of documenting that right in Excel. Every step of the way you're trying to make sure each term in the equation is calculated properly, because you're not 100% sure your answer looks right. And all of that debugging that you do is completely immaterial when you're seeing the calculations right there in front of you in natural math notation, you know the calculation is correct because you've written it exactly as it looks in the book.

So now you’re really worried about the real problems, which is as an engineer, it's really thinking about figuring out what the inputs are to the calculation, like really trying to make sure you understand the boundary conditions of the analysis you're trying to do. That's where engineers really have to think and apply their knowledge and learning, the actual calculation itself should be secondary, and it should be something that you understand and it's really about understanding the whole aspect of the problem. And I personally spent way too much time deciding whether or not I had to continue debugging my spreadsheet, when I used spreadsheets to do radiation calculations. So, I stopped, I learned my lesson and started using Mathcad.

Jim Anderton: At some point your job is about making heat exchangers, not creating code.

Brian Thompson: That's exactly right. The funny thing is, this is the kind of project that the company I was at, at the time did over and over again, and never mind me trying to share that spreadsheet with another engineer.

We had four or five of us that were project engineers supported by 20 or 30 design engineers who did the detailed design work. I couldn't even share that spreadsheet with my future self, never mind with the design engineer down the hall. It's a true story and that's how Mathcad came into my life as an engineer.

Jim Anderton: One thing I've noticed and when visiting a lot of operations. Wherever they may be in the world. And especially you see this in medium sized operations, some larger operations as well, and that is where solving a problem, of the type we're describing, is sometimes best handled by someone who's most experienced in the shop in that specific technology.

So, in our case, the heat exchanger expert or the heat guy, he might be someone who's 58 years old, but the engineer that can make the spreadsheet in the earlier iterations we we're talking about, the one who could make it sing is 28 years old, so he's not the subject matter expert, but he's the one basically that can structure the problem in a way that the software can best handle. So, the tendency for engineering managers I’ve noticed is to sometimes assign the problem to the less optimal engineer, because the one who's less optimal for the problem is the one who can actually make the software work. A problem?

Brian Thompson: Yeah, but isn't that missing the point, right? It's like boy, wouldn't it be great if the software worked the way the engineering worked? So that way you could get to the engineering, and not worry about making the software work. And given that I manage other software at PTC, it's something we think about all the time, right? We're trying to make the engineer focus on the engineering, and not focus on making the engineer try to have the software work correctly, right?

It's definitely a challenge for any of us that are in the software business, but the problem you're describing, it's a real problem for sure, we see it.

Jim Anderton: One thing that all software, and this is not this is not unique to software that handles mathematics, is that as it gets more and more complex, it’s there is a tendency to produce outputs for which we are not sure whether they're good or bad, but it's an output. Because it's like a black box. We throw inputs on one end, we get an answer. And if intuitively that answer doesn't feel right. The question is that how do we know whether or not in fact, it is right?

Again, back in college, they always hammer the desk and say show your work. You got to be able to show your work so we can backstep our way through a process. Talk to any CNC machinists and they'll say it's essential to be able to step through code as it executes to actually watch to debug the thing down there. Is the same thing true if you're working up a solution to say, complex matrix or differential equations?

Brian Thompson: You know that's exactly one of the key strengths of using a technology like Mathcad, because every step of the way as you go through the development of the solution of the problem, you're seeing the interim steps in exactly the same notation that you've been used to seeing throughout your entire time in education. And so, you can build the confidence you touched on an important point that was a subplot of my story about my pain and the radiation calculations in Excel.

You get an output that doesn't quite match your instinct. Your instinct said, you know, I really thought the heat flux would have been higher there, but it's not. And so now you start unwinding the calculation in your mind, and you're wondering which of these Excel cells has the error in it. And then you start you have the horrifying realization that you had used this same spreadsheet on a previous project. And you’re not sure if there was an error that goes all the way back to that project, but anyway with the black box problem that you described is far less of an issue when you're seeing every step symbolically of the calculations one at a time, and at any point in time you can periodically interject and have Mathcad tell you what it is. This symbol is at what value at this stage in the calculation, so you can easily check it as you go, but always see the calculations in a form that you as an engineer are aware of and a much, more feeling of comfortable “is it right?” because it's in the same notation that you would have written it in your notebook by hand. But it’s there in front of you.

Jim Anderton: Yeah, I mean the emissivity of aluminum is a lot different from mild steel, but man, you plug that wrong constant in there and it's easy to do if you're transcribing it from a handbook.

Brian Thompson: It's a good point. And not to mention the fact that if you're looking up other types of properties that have units associated with them, and you can only find the property in one set of units. And OK, you put that in, but then you realize, OK, in order to use it in this Excel calculation, I have to change the units.

Well, that's already a challenge for you, but you know, in Mathcad it's really not a problem. Mathcad is units aware and will do the units transfer for you. You're all set. That's a built-in set of opportunity for mistakes that’s not really there, right? So those kind of look ups you can always double check them, but Mathcad will make all the units sing and make sure everything is all aligned. Then it'll come out with the right units when you're done as well. It's a real opportunity to make sure you spend your time on the engineering problem and not on the debugging of making the software produce the result you're trying to make it use.

Jim Anderton: Brian, we all want the right answer. We want solutions would be confident in solutions, basically that that allow us to go to the next step and not second guess ourselves. We've all been there.

But I'd like to ask about a human factor issue here: I come from the automotive industry and one of the best ways to see great ideas die is in the conference room. It's in the engineering meeting and many of the time I've seen people who have who are truly, truly brilliant minds who have difficulty taking that equation or that cyst with differential equations. And presenting it in a PowerPoint presentation in a way that is coherent enough that they can get buy in from senior managers in that room down there. Can we talk about that? I mean it's great to get the right answer, and it's great to show your work, but you got to show other people. And maybe other people who are not necessarily experts in thermal conductivity.

Brian Thompson: Yeah, and there are a couple interesting dynamics there because it's on the one hand Mathcad being a natural math notation engine that allows you to do a set of fundamental calculations with the same fundamental math that you will find in the Roark’s handbook. The fact that it's there for you can help you do that. That's already a starting point. The fact you can share that in natural math in a computation is one thing. But what we're also seeing is Mathcad used in concert with other, say, more finite element, brute force type of calculation methods.

And what we see engineers doing a lot of is they're now preparing, say, an initial approximation in Mathcad to a problem using what they know about the structure. Let’s say it's a structural problem using what they know about the structure to see am I in the ballpark, then doing a finite element analysis to double check they got the boundary conditions and loads right, then doing another finite element analysis to make sure that their finite element analysis matches the result. Then because Mathcad gives you a way of integrating photos or doing 3D plots of some of your results, it has API so you can integrate the results from other systems.

What we find is that engineers that are using Mathcad, and also supplementing that with other calculation methods, are actually a lot more successful in being able to communicate. Whether or not they really do have a good handle on the problem at hand. So, it's not about the math that Mathcad can do. It's about the way Mathcad can be used as part of an overall process to do simulation and how the integrations can work, so that the engineer, can really get his or her Ideas across as effectively as possible for those that are not as familiar with how the core calculation should be done, but when they see a bunch of different methods that all seem to align within a reasonable error, now you've got building confidence that the engineer has a good handle on the dynamics of the problem at hand.

Jim Anderton: Integrated packages, this is the buzzword we hear around the industry. Everybody wants to create a global solution for everything, we want the purchasing agent using the same package as a design engineer in a perfect world. In the real world it's a lot of operations. They're a patchwork quilt of different applications doing different things at this point.

In your case Mathcad Prime 7. A new product. I understand your end sailing some of the older product. It's taking a notebook from a different platform bringing it over. Still an issue? Should that be a concern anymore or is it a matter of we can go ahead and dive in, it'll be fine.

Brian Thompson: For the vast, vast majority of customers it's a complete nonissue. We have a way of moving your old Mathcad worksheet into Prime 7. Not a problem at all. There are an increasing array of automation capabilities in Prime 7, which is frankly what a lot of Mathcad 15 customers really loved. And we're doing a great job at and making those automation capabilities, really sing in Prime 7.

Not only that, we're taking the symbolic capabilities of Prime even further the hardcore calculations abilities of prime are going even further than Mathcad 15 could have ever gone with the new Symbolics engine that we have in in prime. I’m going to be completely honest with the audience. There are still a few areas where we're still working on making prime as good or better then 15 was, that's still a thing. And we're working with customers to make sure that they're all set there where,

But what we've seen is a huge change in awareness, perception, acceptance of the prime family of Mathcad products now, particularly with the last few releases of prime customers, they are really starting to like it, and I really appreciate some of the enhanced capabilities that we're putting in the product.

Jim Anderton: Brian last question. Project the future for me. Think 15, 20, 30 years in the future. And I know in this world it's impossible to predict five, let alone to really, really go that far. Are we looking at a future where we're going to stop thinking about what platform we're using and have devices that are somehow connected with AR/VR? Are we going to think of a problem and then have a solution emerge from the from the gloom? Are we still going to need basic understanding of the mathematics to be good engineers?

Brian Thompson: I have been astounded at what I've seen with generative algorithms lately, and their ability to produce potential solutions to problems that engineers of today, especially particularly experienced engineers of today, would not think of. But that is an artifact, frankly, of the way you and I were taught to think about design, because I remember very distinctly my very first mentor coming out of college. I did a design in Pro Engineer at the time and showed it to him and he said that's great. That's great, Brian. Tell me how are we going to machine that?

Are we going to see a lot more of “think it and you can have it type” solutions? And I think it is going to happen but what we are seeing are these engines, these generative engines. PTC has one as well that we acquired a couple years ago. These generative engines need a lot of teaching. They need a lot of teaching and nobody is ready to use the results of an engine like this in production like that. You still have to validate it. You still can do closed form or finite element calculations to make sure it looks right. I am actually really optimistic about where generative optimization algorithms are going in the future, particularly because when you talk about augmented reality and virtual reality, they think about connectivity and the types of inputs that some of these generative algorithms. Imagine a generative algorithm that takes the lifespan of thousands or 10s of thousands of products into account. As it calculates what the next generation design could be, that's actually not that far away, right? You couple that with a few inputs into the design that the engineer has to think about, but in the end, somebody, a person still has to say yes this is ready for production.

I don't think we're going to be far away from that, and that person better have good fundamental engineering understanding of the problem that the design is supposed to solve. I don't think we'll ever get away from that, but I think we'll get candidate solutions to problems a lot faster going forward. I do think that is coming and it's going to come in niche areas first in large amounts, but slowly but surely those types of algorithms and engines are going to get better and better and better.

Jim Anderton: Great future.

Brian Thompson: It's going to be amazing.

Jim Anderton: Brian Thompson, thanks for joining me on the show.

Brian Thompson: It was great being here and I look forward to talking to you sometime again in the future.

Jim Anderton (to audience): And thank you for joining us on Designing the Future. See you next time.