I How do you answer "So what's the practical application....?"

[lavinia]

That point of view always makes me wonder, specially when mathematicians themselves state it.(You're a mathematician, right?)

I am not a mathematician.

I threw the language viewpoint out there because it is widely said on the Physics Forums and IMO needs to be corrected. It underlies a disdain for mathematics. It also implies the attitude that if something doesn't solve an empirical problem then it is meaningless.

I think that culture engenders the creativity that makes understanding how the world works possible and much of art and music and philosophy are part of that. I would argue that mathematics is also part of that in part because it travels into places where only the mind can go and the empirical world can only stand by and watch. These wanderings of the mind are just as important as figuring out how to fix a faucet or light a wood burning stove or how to make money on a new organic compound. They allow us to see truth and beauty and for some inexplicable reason to penetrate the mysteries of the world.

 

[Nugatory]

It underlies a disdain for mathematics.

I think you're hearing something that isn't there. The people who are saying that are expressing neither disdain for nor endorsement of mathematics in its own right. They're asserting a basic rule for intelligent discussion of their own discipline, physics, and the comment is directed at people who are flouting that rule.

I can claim that mathematical fluency is a requirement for understanding physics without claiming that understanding physics is the justification for mathematics.

 

[dkotschessaa]

I think you're hearing something that isn't there. The people who are saying that are expressing neither disdain for nor endorsement of mathematics in its own right. They're asserting a basic rule for intelligent discussion of their own discipline, physics, and the comment is directed at people who are flouting that rule.

I can claim that mathematical fluency is a requirement for understanding physics without claiming that understanding physics is the justification for mathematics.

It might be a mild disdain, actually. It accompanies a funny territorial sort of behavior I've found in some academics, which goes along with some jocular behavior and a bit of stereotyping. You can even read it into people like Feynman. You can find it in "An engineer a physicist and a mathematician walk into a bar" type jokes. I've been gleefully told this not-really-family-friendly quote by a physicist. It goes both ways. The mathematical retort is Gauss's "mathematics is the queen of scientists" quote, noted in an earlier post.

I once toured Fermilab and asked if they employed mathematicians. They told me that a mathematician would probably get lost in there. I have to admit that at least in my case he would be correct. (Actually, it was on that same trip that I looked at that particle accelerator and thought "hmm, it is really just a big old mess of wires and metal, isn't it?" and decided to pursue math instead of physics.)

Anyway, it is as they say, all good. You are in your discipline because you like it, so naturally you find something less appealing about the other. If that didn't exist then we wouldn't be able to come at scientific discovery from a true diversity of backgrounds.

-Dave K

 

[Bandersnatch]

 

[houlahound]

A friend taught in the poorest parts of asia...there was no need ever to justify math or education. Science and math in particular were seen as a pathway to freedom, liberty, dignity and a better standard of living. Hard math/STEM is the tool they use to escape abject poverty for themselves and their nation...and they are thankful for it and respectful of it.

As kids in the west slip further behind in international testing, in step with our declining economy, all the while demanding/extorting educators to make everything easier and expecting a full justification of why they should make any effort at all.

Affluenza and sense of entitlement...things go in cycles. Deny your math base and expect an economic and cultural whooping.

 

[zinq]

Math is of course many things — it is a language for expressing certain kinds of concepts, it is a tool for solving practical problems, and it is a universe unto itself.

As a mathematician I have been mainly concerned with pure mathematics, which in 1971 I defined as the science of patterns — and I still think that's a good description.

All theorems discovered in pure math, as we currently know it, can be described as deductions made from a specified set of axioms. In that sense, pure math is one facet of absolute truth. It's an interesting question, what exactly constitutes absolute truth. But theorems of pure mathematics are certainly aspects of it.

In other areas of science, earlier discoveries are later adjusted to take new developments into account. In mathematics, early discoveries are never adjusted. But they are often put into a larger context. (For example, the plane geometry of ancient Greece was put into the context of being just one case of a 2-dimensional geometry with constant curvature; the others — elliptical and hyperbolic geometry — now shed new light on the geometry of Euclid. But Euclid's theorems have not needed adjustment.)

The way that mathematicians make progress in pure math is of course not just proving arbitrary theorems from arbitrary axioms. (If that were the case, we could just add up random columns of numbers that had never been added before, and publish that in leading journals.)

For me, the universe of mathematical truth is like a landscape that is just there, waiting to be discovered. We are mainly concerned with finding the most beautiful portions of that landscape, portions that help us to better understand the parts of the landscape that we are already familiar with.

 

[Planobilly]

It is pretty difficult to do anything "practical" until some mathematician waste his time and money developing the math behind the "practical"...lol

If "practical", and making money from this practical mindset is one's only interest then there is little point to much of life. Just paint the whole world olive drab and dye all the clothes the same while you are at it.

This speaks to a wider issue of polprised views that are so prevalent in today's world. The type of thinking that discounts the endeavors by others is arrogant at best.

Cheers,

Billy

 

[lavinia]

All theorems discovered in pure math, as we currently know it, can be described as deductions made from a specified set of axioms.

My cursory experience of Physics is that it is made from a specified set of axioms. For instance one postulates that the speed of light is constant in every inertial reference frame and then logically deduces the physical consequences for instance the relativity of simultaneity.

While mathematics certainly uses axioms I see it more as an exploration of a world of ideas, identifying structures and general properties, unifying principles, clarifying intuitions,examining mathematical objects. Axioms are often an afterthought or a tool to understand when multiple approaches to something actually are equivalent.

 

[zinq]

I agee with lavinia's last paragraph. (My comment about deductions from axioms was intended only to show that theorems in math are part of what I call absolute truth.)

 

[rcgldr]

Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.

I recall one of my old bosses mentioning this issue when he was learning this stuff decades ago, only to end up using it for Reed Solomon error correction code, and later AES encryption. So in his case, the practical (commercial) application for what he had learned came years later. Once this stuff went into hardware, some clever math was used to reduce gate counts. While I was at that company, I met E J Weldon Jr (author of Error Correcting Code from the 1960's), and Jack Wolf (professor at UC San Diego's Center for Magnetic Recording Research, also active in the field in the 1960's or 1970's). I was a programmer, but assisted the hardware guys with error code correction implementation.

Still maybe this case is an exception to the rule. My analogy for general research is you send students off to climb mountains and return with what they find, but maybe only 1 in 10 or less discoveries ever leads to something practical. Similar to climbing mountains, when asked why do they do it, the answer is "because it is there". The other issue, is how do you maintain such specialized knowledge over generations of students and professors in the cases where there aren't practical applications (or at least not yet)?

 

[Demystifier]

Feynman said: "Physics is like sex: sure, it may give some practical results, but that's not why we do it."

The same can be said about mathematics.

 

[Demystifier]

People do what they do because it has some value. Sometimes the value is practical, sometimes it's not (music, movies, theoretical physics, pure mathematics, etc.). Just because some value is not practical doesn't mean it's less important.

Sometimes the value is understandable to many (pop music, blockbuster movies, popular science/math books), sometimes only to a smaller population (classical music, art movies, academic science/math papers). Just because majority of people cannot see some value doesn't mean that there is no value at all.

Pure mathematics, theoretical physics etc. are human activities which have non-practical value that cannot be understood by majority. But that's still a value.

 

[dkotschessaa]

I see lots of great ideas here, but still, what I am looking for is not how we consider this question amongst ourselves, but how we respond to others.

-Dave K

 

[Cool4Kat]

I suppose you recognize, by title, the situation I am referring to. I don't know if physics people get it as often as math people.

The situation of course is that I tell somebody that I am studying math, and if I mention some specifics, like mention Topology or Algebra, (which I have to sort of explain is not "college algebra"), or whatever. Then comes the question "So what's this used for in..you know, real life?"

As I see it there are two extremes to answer this question:

a) A speech or possible tirade about how this question is not really relevant. Possible comparison of science to art, i.e. "Well, what's the practical application of music?" Trying, perhaps in vain to explain how mathematics doesn't always seek applications but that they often find their uses later, then tell a story about number theory and cryptography. Another variant is that for me, I've studied mathematics for the joy of it and because I think the thinking skills I learned can be applied to anything.

b) Just say some stuff I heard about what people might be using this for. "Topological data analysis!" "Cryptography" (again). "Something in physics!"

So, I don't know if this is helpful but a quote from Ben Franklin might do the trick (Faraday liked this one):

someone says, "What's this used for in real life?"
Answer: "As Ben Franklin used to say, "What is the use of a newborn baby?"" Or basically I don't really know yet but I bet it will be amazing.

 

[micromass]

I suppose you recognize, by title, the situation I am referring to. I don't know if physics people get it as often as math people.

The situation of course is that I tell somebody that I am studying math, and if I mention some specifics, like mention Topology or Algebra, (which I have to sort of explain is not "college algebra"), or whatever. Then comes the question "So what's this used for in..you know, real life?"

As I see it there are two extremes to answer this question:

a) A speech or possible tirade about how this question is not really relevant. Possible comparison of science to art, i.e. "Well, what's the practical application of music?" Trying, perhaps in vain to explain how mathematics doesn't always seek applications but that they often find their uses later, then tell a story about number theory and cryptography. Another variant is that for me, I've studied mathematics for the joy of it and because I think the thinking skills I learned can be applied to anything.

b) Just say some stuff I heard about what people might be using this for. "Topological data analysis!" "Cryptography" (again). "Something in physics!"

That is the problem with mathematicians and mathematics education. It teaches students a lot of abstract mathematics, but no applications to go with it. Nowadays it is possible to learn topology without knowing its background, its history or its huge importance in physics! Imagine that. The mathematics education has ripped out its own soul by neglecting the important links to physics, and the results have been detrimental.

Back in the day, a mathematics question was studied because of a link with physics, and both physics and mathematics kind of interacted with each other. Nowadays, you can do both in isolation, which I think is a very bad thing.

Come on, the OP has almost a master in mathematics and has no clue how important topology is to physics! That's a shame. And I don't blame the OP, I was like him for a long time. I even hated applications. But I realized it is wrong and how knowing applications is so very important if you want to be a good mathematician.

Sure, mathematics finds their applications only later, but all of mathematics has always been tied to nature in some way or another. Maybe that way was very much something abstract, but the link is there. Nobody just writes down an arbitrary structure and studies it.

 

[ZapperZ]

People do what they do because it has some value. Sometimes the value is practical, sometimes it's not (music, movies, theoretical physics, pure mathematics, etc.). Just because some value is not practical doesn't mean it's less important.

Sometimes the value is understandable to many (pop music, blockbuster movies, popular science/math books), sometimes only to a smaller population (classical music, art movies, academic science/math papers). Just because majority of people cannot see some value doesn't mean that there is no value at all.

Pure mathematics, theoretical physics etc. are human activities which have non-practical value that cannot be understood by majority. But that's still a value.

But this doesn't quite answer the question, does it?

One can argue about the value or worthiness of something. But if the question is "What is the application of such-and-such?", then your response here avoids answering it.

Zz.

 

[ShayanJ]

One can argue about the value or worthiness of something. But if the question is "What is the application of such-and-such?", then your response here avoids answering it.

To be honest, it seems a useless question to me. Some parts of physics and mathematics currently have applications and some don't. Some may never be applied anywhere. So what?

 

[ZapperZ]

To be honest, it seems a useless question to me. Some parts of physics and mathematics currently have applications and some don't. Some may never be applied anywhere. So what?

But that in itself can be the answer. We can be honest and say that as of now, we don't know of any practical application. And we can elaborate that this does not diminish its importance, especially if we are aware of the history of physics on how seemingly-useless ideas found huge relevance later on.

There is no need to get defensive in our answers, and we should never have such dismissive attitude towards people, and the public, for asking that type of a question. I deal with the public a lot and such questions pop up often.

Zz.

 

[ShayanJ]

But that in itself can be the answer. We can be honest and say that as of now, we don't know of any practical application. And we can elaborate that this does not diminish its importance, especially if we are aware of the history of physics on how seemingly-useless ideas found huge relevance later on.

There is no need to get defensive in our answers, and we should never have such dismissive attitude towards people, and the public, for asking that type of a question. I deal with the public a lot and such questions pop up often.

Zz.

Well that is the answer. And Demystifier wasn't defensive in his post at all. He was just saying exactly what you said here, that having no application doesn't diminish its importance.
In fact that should be everyone's answer to this question in front of a laymen audience because just running around looking for applications and throwing any application that comes to mind at the audience, gives the impression that some of physicists are just fooling around and receiving money for nothing. Its even a responsibility of scientists to give that answer because physics and mathematics as parts of the engine that leads mankind's intellect forward should be appreciated at some level by laymen so that they can actually have that effect among people.

 

[dkotschessaa]

That is the problem with mathematicians and mathematics education. It teaches students a lot of abstract mathematics, but no applications to go with it. Nowadays it is possible to learn topology without knowing its background, its history or its huge importance in physics! Imagine that. The mathematics education has ripped out its own soul by neglecting the important links to physics, and the results have been detrimental.

Perhaps, but I take responsibility for my own knowledge of the history and background of the subjects I am studying. And I've read on the history of topology, and the emphasis is usually on "pure" mathematics. (It is typically traced back to Euler's polyhedron formula.)

Back in the day, a mathematics question was studied because of a link with physics, and both physics and mathematics kind of interacted with each other. Nowadays, you can do both in isolation, which I think is a very bad thing.

It's a little more complicated than that. Mathematics and physics (or natural philosophy) have variously bifurcated and inter-meshed through history. Plenty of Greek mathematicians did not care much for physics. We had more polymaths in the past, but we are in the area of hyper specialization now. I actually don't think it's a bad thing at all. It allows people to focus on what excites and interests them.

Come on, the OP has almost a master in mathematics and has no clue how important topology is to physics! That's a shame. And I don't blame the OP, I was like him for a long time. I even hated applications. But I realized it is wrong and how knowing applications is so very important if you want to be a good mathematician.

Sure, mathematics finds their applications only later, but all of mathematics has always been tied to nature in some way or another. Maybe that way was very much something abstract, but the link is there. Nobody just writes down an arbitrary structure and studies it.

I know some category theorists and mathematical logicians who would debate that. :)

-Dave K

 

[dkotschessaa]

To be honest, it seems a useless question to me.

Well, me too. But nonetheless, I get asked it, and as I am not always ready with an answer, I started this thread.

-Dave K

 

[ShayanJ]

Well, me too. But nonetheless, I get asked it, and as I am not always ready with an answer, I started this thread.

-Dave K

I understand it. My point is that physicists and mathematicians shouldn't be obliged to apply their knowledge to some practical problems with some machine or whatever. So the answer to this question should at least partly be that even parts of mathematics and physics that have no applications are important too. So I think in addition to finding some applications of what you do, you should be able to explain the value of mathematics and physics besides their applications.

 

[Andreas C]

Hahaha that was hilarious! Only it's not really that accurate...

 

[Andreas C]

The issue is that most people don't see why you would ever enjoy something like math so much, similar to the way they would enjoy art, and go through all that trouble for something that doesn't really have a practical application. To which a valid reply could be "Ok then, I'm a weird person, I like math, shoot me".

 

[dkotschessaa]

So if I'm reading the replies to this correctly, not one person besides me has been asked this?

-Dave K

 

[symbolipoint]

So if I'm reading the replies to this correctly, not one person besides me has been asked this?

-Dave K

Many of us have been asked this, and not for what applications of topology or abstract algebra, or all that stuff that master's and PhD students study and research. Students ask what are the practical applications for high school Geometry and of Intermediate Algebra. Basic problem is their lack of experience, and in some cases, not yet having seen enough "applied" problem exercises. Let's think a little: Conic Sections? Optics, Lenses, Blasting Kidney Stones, Finding locations through observation stations, Satellite Orbits,..., and that is thinking JUST A LITTLE, and at a much less "advanced" mathematics study level.

One more:
Logarithms and Exponential Funtions ----
Are you kidding? Will the student ever take out a loan? What installments? How often to pay back each installment? How many months or years? What will be his total price for the loan?

 

[fresh_42]

Nobody just writes down an arbitrary structure and studies it.

I know some category theorists and mathematical logicians who would debate that. :)

Uhmm, not only them. I can tell you one. It is simple and has a couple of interesting properties which make me wonder why nobody ever studied it, but I still don't know, what it can actually accomplish, beside showing me I'm not smart enough to see.

 

[dkotschessaa]

Uhmm, not only them. I can tell you one. It is simple and has a couple of interesting properties which make me wonder why nobody ever studied it, but I still don't know, what it can actually accomplish, beside showing me I'm not smart enough to see.

If I were stuck on an island and only had to study one thing in math (now there's a thread) it would probably be large cardinals. I can categorically say they are of no practical value to anyone in physics, but man are they cool.

-Dave K

 

[fresh_42]

If I were stuck on an island and only had to study one thing in math (now there's a thread) it would probably be large cardinals. I can categorically say they are of no practical value to anyone in physics, but man are they cool.

-Dave K

And I thought we still struggle with the small ones ... The idea of an island is o.k., but difficult to write on ...

 

[Hypercube]

A friend taught in the poorest parts of asia...there was no need ever to justify math or education. Science and math in particular were seen as a pathway to freedom, liberty, dignity and a better standard of living. Hard math/STEM is the tool they use to escape abject poverty for themselves and their nation...and they are thankful for it and respectful of it.

As kids in the west slip further behind in international testing, in step with our declining economy, all the while demanding/extorting educators to make everything easier and expecting a full justification of why they should make any effort at all.

Affluenza and sense of entitlement...things go in cycles. Deny your math base and expect an economic and cultural whooping.

This. Absolutely. From personal experience.