Trivia question - Laplace transform

[OpticsEngineer]

Something I remember from a pre-lecture chat from one of my EE professors many years ago.

Who discovered the Laplace Transform? And why was it named after Laplace instead of its discoverer?

 

[alanr0]

Something I remember from a pre-lecture chat from one of my EE professors many years ago.

Who discovered the Laplace Transform? And why was it named after Laplace instead of its discoverer?

Some plausible, but mildly conflicting answers culled from the web:

Thomas Ulrich on Quora refers to M A B Deakin's historical articles [2 ] [3] in which Laplace himself attributes the technique to earlier works by Leonhard Euler published in 1753 and 1768.

Laplace used this approach to solve differential equations in 1782, and 30 years later returned to the subject in a treatise on probability.

Brittanica attributes Pierre-Simon Laplace as the inventor, but points out that the method was more systematically developed by Oliver Heaviside.

Wikipedia is broadly consistent with the above, and references both the work of Euler, and later developments by Joseph-Luis Lagrange. However, they claim Laplace actually invented what we now call the z-transform, and for good measure, throw in a mention of the Mellin transform (which I had never heard of).

Not exactly a clear and unambiguous answer, but some interesting snippets. I have no idea which version gets top marks in a pub quiz.

Cheers.

--
Alan Robinson

 

[JimKasson]

Something I remember from a pre-lecture chat from one of my EE professors many years ago.

Who discovered the Laplace Transform? And why was it named after Laplace instead of its discoverer?

Some plausible, but mildly conflicting answers culled from the web:

Thomas Ulrich on Quora refers to M A B Deakin's historical articles [2 ] [3] in which Laplace himself attributes the technique to earlier works by Leonhard Euler published in 1753 and 1768.

Laplace used this approach to solve differential equations in 1782, and 30 years later returned to the subject in a treatise on probability.

Brittanica attributes Pierre-Simon Laplace as the inventor, but points out that the method was more systematically developed by Oliver Heaviside.

Wikipedia is broadly consistent with the above, and references both the work of Euler, and later developments by Joseph-Luis Lagrange. However, they claim Laplace actually invented what we now call the z-transform, and for good measure, throw in a mention of the Mellin transform (which I had never heard of).

Not exactly a clear and unambiguous answer, but some interesting snippets. I have no idea which version gets top marks in a pub quiz.

I am reading a biography of Claude Shannon, written by Soni and Goodman. In it, the authors talk about Vannevar Bush and his idea that engineers should learn math on a gut level by constructing and using machines that perform mathematical operations. I credit Laplace transforms for getting me to the understanding of electrical filter design on the right side of my brain. I never stretched a rubber sheet over dowels and nailed down parts of it, but the image was always in my mind.

As to the origins of some arbitrary math concept? Euler is not a bad first guess.

Jim

 

[Mark S Abeln]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

 

[JimKasson]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

I agree. I have long argued that secondary education would be better served by far less emphasis on geometric axioms, proofs, and theorems. I think that approach to math should be taught as part of the calculus. As it is, that topic is usually (or used to be, anyway) taught as something called Real Variables, and taught mainly to math majors. I don't think any real purpose is served by dragging all high school students through the whole axiom-proof-theorem thing.

BTW, I recommend the Shannon bio:

Loading…

www.amazon.com

Jim

 

[jonas ar]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

I agree. I have long argued that secondary education would be better served by far less emphasis on geometric axioms, proofs, and theorems. I think that approach to math should be taught as part of the calculus. As it is, that topic is usually (or used to be, anyway) taught as something called Real Variables, and taught mainly to math majors. I don't think any real purpose is served by dragging all high school students through the whole axiom-proof-theorem thing.

BTW, I recommend the Shannon bio:

https://www.amazon.com/Mind-Play-Shannon-Invented-Information/dp/1476766681

Jim

 

[slstr]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

I agree. I have long argued that secondary education would be better served by far less emphasis on geometric axioms, proofs, and theorems. I think that approach to math should be taught as part of the calculus. As it is, that topic is usually (or used to be, anyway) taught as something called Real Variables, and taught mainly to math majors. I don't think any real purpose is served by dragging all high school students through the whole axiom-proof-theorem thing.

BTW, I recommend the Shannon bio:

https://www.amazon.com/Mind-Play-Shannon-Invented-Information/dp/1476766681

Jim

 

[J A C S]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

I agree. I have long argued that secondary education would be better served by far less emphasis on geometric axioms, proofs, and theorems. I think that approach to math should be taught as part of the calculus. As it is, that topic is usually (or used to be, anyway) taught as something called Real Variables, and taught mainly to math majors. I don't think any real purpose is served by dragging all high school students through the whole axiom-proof-theorem thing.

Please, math is dumbed down enough in the US, do not try to make it worse.

I have not really seen the axiom-theorem approach in the US high schools, and I do have some experience with it. Of course, US is a huge country and the education is not centralized as in many small countries.

The "formal" way to teach math teaches logical thinking in the first place. Having spent several years on dpreview, my opinion is that the vast majority of the posters here (I am not talking about the PST forum) have problems with basic logic like that A=>B does not imply B=>A, they have trouble forming negations of statements, etc. It does not matter what theorem you prove - the most important benefit is to learn how to think logically.

About the intuition - it is the other side of the math literacy, they cannot be separated. Einstein has said that intuition is more important than knowledge. I can believe that but without logical skills, you would never know when your intuition failed you.

 

[ZilverHaylide]

@JimKasson, @Mark Scott Abeln.

"The Pleasures of Counting", by Thomas W. Korner, though more than two decades old, remains excellent in its motivation for the study of mathematics (at the beginning college student or intelligent high-schooler level), achieved by a fine blend of pragmatism, intuition, and logic.

 

[Joe Pineapples II]

Euclid's method of teaching geometry has two sides: construction with compass and straightedge, and axioms, proofs, and theorems. In my experience, too much emphasis is given to the theoretical side and not enough on the constrictive side; perhaps that's because it is seen as too childish. But that's a shame.

I see far too many people who seem to lack an intuitive understanding of what's going on. I've had peers who could crank out pages of equations, without error, yet failed to see the bigger picture. Just taking one step up or down the conceptual ladder can often simplify problems dramatically.

I agree. I have long argued that secondary education would be better served by far less emphasis on geometric axioms, proofs, and theorems. I think that approach to math should be taught as part of the calculus. As it is, that topic is usually (or used to be, anyway) taught as something called Real Variables, and taught mainly to math majors. I don't think any real purpose is served by dragging all high school students through the whole axiom-proof-theorem thing.

In my high school education we studied calculus in maths and around the same time we studied mechanics and RLC circuits in physics. The two approaches were complementary, and I found that very helpful. Where I live, maths seems about the same, but the physics curriculum has had a lot of the mathematical content stripped out, which is a great shame.

On discoveries being attributed to the "wrong" person, there are so many examples. The story of the Poisson Spot in optics was one that always made me smile; or the fact that while the "square root" of the Laplacian operator is usually attributed to Dirac and associated with QM, you can find it in Maxwell's Treatise, where he acknowledges his friend Taite for the discovery.

J.

 

[OpticsEngineer]

It is pretty quiet on this thread now, so I guess it is time to share the answer our professor told us

1. Things aren't simply named after the "discoverer." They are named after the person who develops it into something useful and publishes on it.

2. Joseph Petzval was the first person to realize the immense usefulness of this transform and how it could be used to solve differential equations. He wrote a couple of books on it. So it really should have been called the Petzval transform.

3. But Petzval had a difficult, argumentative, sarcastic nature. He was constantly involved in disputes. Anyone who worked with him didn't care to see anything named after him. Especially his students who steered attention toward Laplace later.

The Wikipedia article on Petzval has more detail.

I suppose our professor was taking a little time off the lesson plan to share with us a life lesson.

 

[Mark S Abeln]

Joseph Petzval

The same Petzval of lens fame, who used human Austrian Army ballistics "computers" to calculate the design of the eponymous lens, making the first suitable portrait lens.