What, in your opinion, is the most recent great advance in applied mathematics?
eg.
Genetic algorithm, 1985.
Wavelets, 1993.
Fractal mountains, 1982.
Accurate computer graphics of sea surface, 2003.
mollwollfumble said:
What, in your opinion, is the most recent great advance in applied mathematics?eg.
Genetic algorithm, 1985.
Wavelets, 1993.
Fractal mountains, 1982.
Accurate computer graphics of sea surface, 2003.
VisiCalc, and subsequent developments.
No, I’m serious.
Also dynamic analysis of complex structures.
mollwollfumble said:
What, in your opinion, is the most recent great advance in applied mathematics?eg.
Genetic algorithm, 1985.
Wavelets, 1993.
Fractal mountains, 1982.
Accurate computer graphics of sea surface, 2003.
Genetic algorithms started in 1985? Are you sure?
Internet says:
Genetic algorithms came from the research of John Holland, in the University of Michigan, in 1960 but won’t become popular until the 90’s.
Just read the actual question.
The most recent advance that could be considered great?
Not sure.
If they ever get quantum computers to do anything useful, I guess that will be it.
For maths that I apply myself, I tempted to say Euler’s theory of beam bending, but I’ll go with solution techniques for sparse systems of linear equations.
Not sure what the date would be, but probably 2000’s, at least for people using small computers.
Are computer algorithms considered applied mathematics
Cymek said:
Are computer algorithms considered applied mathematics
I don’t see why they wouldn’t be.
Ones that do maths anyway.
The Rev Dodgson said:
Cymek said:
Are computer algorithms considered applied mathematicsI don’t see why they wouldn’t be.
Ones that do maths anyway.
wouldn’t all computer algorithms be doing maths?
The Rev Dodgson said:
Cymek said:
Are computer algorithms considered applied mathematicsI don’t see why they wouldn’t be.
Ones that do maths anyway.
What about Wolfram Alpha
JudgeMental said:
The Rev Dodgson said:
Cymek said:
Are computer algorithms considered applied mathematicsI don’t see why they wouldn’t be.
Ones that do maths anyway.
wouldn’t all computer algorithms be doing maths?
I guess they do at some level.
But if you apply that to the computers in our head, it makes everything we do maths.
The Rev Dodgson said:
JudgeMental said:
The Rev Dodgson said:I don’t see why they wouldn’t be.
Ones that do maths anyway.
wouldn’t all computer algorithms be doing maths?
I guess they do at some level.
But if you apply that to the computers in our head, it makes everything we do maths.
You can have algorithms that directly relate to mathematics powered by mathematics, computational engines,etc
In fact I suppose physics engines for computer games are another example
Cymek said:
The Rev Dodgson said:
Cymek said:
Are computer algorithms considered applied mathematicsI don’t see why they wouldn’t be.
Ones that do maths anyway.
What about Wolfram Alpha
Are you asking if Wolfram Alpha does maths? (I’d say yes)
Or suggesting it as the most recent great advance?
Or both?
I’m not sure how great it is.
I asked the Internet, but that wasn’t sure either.
The Rev Dodgson said:
Cymek said:
The Rev Dodgson said:I don’t see why they wouldn’t be.
Ones that do maths anyway.
What about Wolfram Alpha
Are you asking if Wolfram Alpha does maths? (I’d say yes)
Or suggesting it as the most recent great advance?
Or both?I’m not sure how great it is.
I asked the Internet, but that wasn’t sure either.
Not great but just an example, applied mathematics in areas you might not thing about.
Cymek said:
The Rev Dodgson said:
Cymek said:What about Wolfram Alpha
Are you asking if Wolfram Alpha does maths? (I’d say yes)
Or suggesting it as the most recent great advance?
Or both?I’m not sure how great it is.
I asked the Internet, but that wasn’t sure either.
Not great but just an example, applied mathematics in areas you might not thing about.
As an engineer, I’d say that applied maths is woven into almost everything that we do.
What is unapplied maths then or what maths in not applied?
The Rev Dodgson said:
Cymek said:
The Rev Dodgson said:Are you asking if Wolfram Alpha does maths? (I’d say yes)
Or suggesting it as the most recent great advance?
Or both?I’m not sure how great it is.
I asked the Internet, but that wasn’t sure either.
Not great but just an example, applied mathematics in areas you might not thing about.
As an engineer, I’d say that applied maths is woven into almost everything that we do.
That is true
Peak Warming Man said:
What is unapplied maths then or what maths in not applied?
I’m pretty sure there is plenty of maths that has no direct application at the moment, but even for maths that does have practical applications, if you are studying the maths, I’d say that counts as pure maths, and if you are studying how it is applied in practice, or are actually applying it, that counts as applied maths.
According to my applied philosophy anyway.
“They gone, comes Rayner, the boatmaker, about some business, and brings a piece of plate with him, which I refused to take of him, thinking indeed that the poor man hath no reason nor encouragement from our dealings with him to give any of us any presents. He gone, there comes Luellin, about Mr. Deering’s business of planke, to have the contract perfected, and offers me twenty pieces in gold, as Deering had done some time since himself, but I both then and now refused it, resolving not to be bribed to dispatch business, but will have it done however out of hand forthwith.
So he gone, I to supper and to bed.”
Sam can not be bought by gold but a pretty buxom wench is another story.
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.
“VisiCalc” is a great suggestion.
mollwollfumble said:
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.“VisiCalc” is a great suggestion.
I think I might agree with the cryptography one.
I’ll have to look up Black-Scholes (I’m sure I knew all about it once).
What is unapplied maths then or what maths in not applied?
I imagine unapplied maths just needs a pep talk to get motivated, I mean pie used to just lie around waiting to be eaten then got a talk from its parents about applying itself and now pi is king of the circles
mollwollfumble said:
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.“VisiCalc” is a great suggestion.
I thought about nominating crypto, but it fails the OP criterion of recency. It’s been around since at least 1971, and possibly as long ago as 1951.
The Rev Dodgson said:
mollwollfumble said:
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.“VisiCalc” is a great suggestion.
I think I might agree with the cryptography one.
I’ll have to look up Black-Scholes (I’m sure I knew all about it once).
That’s the one when budgets don’t balance and they blame it on the Black Hole
btm said:
mollwollfumble said:
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.“VisiCalc” is a great suggestion.
I thought about nominating crypto, but it fails the OP criterion of recency. It’s been around since at least 1971, and possibly as long ago as 1951.
I’m the same with the Fast Fourier transform algorithm, it’s been around since the mid 60s.
btm said:
mollwollfumble said:
Had some thoughts about other possibilities yesterday.
The cryptography method using the product of two prime numbers.
The Black-Scholes equation in finance.“VisiCalc” is a great suggestion.
I thought about nominating crypto, but it fails the OP criterion of recency. It’s been around since at least 1971, and possibly as long ago as 1951.
I’ll have you know that things that got started in 1951 are still capable of great originality young man.
> Accurate computer graphics of sea surface, 2003.
I based that date of 2003 on the appearance of the movie “Sinbad”. It looks though I was right, though. The technical paper is:
http://graphicon.ru/html/2003/Proceedings/Technical/paper316.pdf
by Vladimir Belyaev Applied Math. Department, St. Petersburg State Polytechnical University, St. Petersburg, Russia
Given the waves’ spectrum, the height is immediately calculable from the fast fourier transform. The coefficients are Gaussian distributed random numbers with zero mean value and standard deviation depending on the wavenumber (ie. wavelength and direction). The algorithm can be easily adapted for shallow water waves and deep water waves. Surface normals come from the finite difference method.
The waves’ spectrum comes from sea surface observations together with elimination of too long and too short waves and control over “oblongness” whatever that is.
> Since the resulting surface is the sum of the number of sine waves, which tops can not be sharp as it is in a real life, we need to modify the grid to sharpen them. Every grid point is displaced and the surface normal recalculated.
I wish I’d thought of that!
For reflections, “the camera is reflected. Rendering into this camera produces a ‘reflection’ texture. Then using projection mapping, the textures are mapped onto the water surface and mixed. The result is a fake reflection which is placed on a plane above and parallel to the water surface. Then ray-tracing maps that reflection back onto the water surface. Refraction is handled in the exact same way, the refraction for a plane water surface is placed on a plane below and parallel to the water surface. To mix ‘reflection’ and ‘refraction’ textures we need to calculate a simple approximation to the Fresnel coefficient at every grid point. We increase the field of view for reflection and refraction cameras.”
To save calculation, “everything looks fine enough with the texture resolution 1.5 times less then output one”. Another saving is possible if the reflection is only of the sky and the bottom is invisible.
2-D vs 3-D grid.
Lovely piece of applied mathematics.
The Rev Dodgson said:
mollwollfumble said:
What, in your opinion, is the most recent great advance in applied mathematics?eg.
Genetic algorithm, 1985.
Wavelets, 1993.
Fractal mountains, 1982.
Accurate computer graphics of sea surface, 2003.VisiCalc, and subsequent developments.
No, I’m serious.
Equations are zero dimensional.
Lines on graphs are one dimensional.
Spreadsheets are intrinsically two dimensional.
We live in a space with three dimensions. I want to see a spreadsheet-like program that is intrinsically 3-D, not all numbers seen at once but visible using a slider and 3-D graphics with rotation.
> Wolfram alpha
Does anyone actually use that?
Mathematica was a huge advance in Applied Math in 1988. A look through the modules ought to reveal some important new maths.
mollwollfumble said:
Mathematica was a huge advance in Applied Math in 1988. A look through the modules ought to reveal some important new maths.
Mathcad came out in ’86 with WYSIWYG and checking for dimensional accuracy.
Check out https://demonstrations.wolfram.com/topics.php
The Wolfram Demonstration Project.
With a bit of luck they can be run on the free program CDF player on Mac, Windows or Linux. Not Android. https://www.wolfram.com/cdf-player/
I haven’t tried it yet, I’m typing this from Android, but more than a few of the demonstration examples look familiar from other contexts.
mollwollfumble said:
Check out https://demonstrations.wolfram.com/topics.phpThe Wolfram Demonstration Project.
With a bit of luck they can be run on the free program CDF player on Mac, Windows or Linux. Not Android. https://www.wolfram.com/cdf-player/
I haven’t tried it yet, I’m typing this from Android, but more than a few of the demonstration examples look familiar from other contexts.
Thanks, downloaded.
Looks QI, but I suspect you’d have to buy Mathematica to do anything useful with it.
Some pretty pictures of algebraic surfaces here
mollwollfumble said:
Some pretty pictures of algebraic surfaces here
Nice.
No formula for “Möbius”.
Michael V said:
mollwollfumble said:
Some pretty pictures of algebraic surfaces hereNice.
No formula for “Möbius”.
And three others, too.
If, like me, the last thing your C: drive needs is another over-bloated program, see:
http://support.wolfram.com/kb/41414
for instructions on how to install somewhere else. It’s about 5 GB when installed.
The Rev Dodgson said:
If, like me, the last thing your C: drive needs is another over-bloated program, see:http://support.wolfram.com/kb/41414
for instructions on how to install somewhere else. It’s about 5 GB when installed.
Thanks for the warning. I’m OK because I have about 133 GB free.
I totally ran out of GB (on two computers) a couple of years ago when downloading the complete set of Kepler spacecraft data for analysis – but I’ve deleted all that since then.
The Rev Dodgson said:
mollwollfumble said:
Check out https://demonstrations.wolfram.com/topics.phpThe Wolfram Demonstration Project.
With a bit of luck they can be run on the free program CDF player on Mac, Windows or Linux. Not Android. https://www.wolfram.com/cdf-player/
I haven’t tried it yet, I’m typing this from Android, but more than a few of the demonstration examples look familiar from other contexts.
Thanks, downloaded.
Looks QI, but I suspect you’d have to buy Mathematica to do anything useful with it.
(Screams with laughter). The first CDF file I downloaded, actually gives as it’s source of information a paper that I wrote in 1988.
Wow. Some people actually read the technical stuff that I write.
mollwollfumble said:
The Rev Dodgson said:
mollwollfumble said:
Check out https://demonstrations.wolfram.com/topics.phpThe Wolfram Demonstration Project.
With a bit of luck they can be run on the free program CDF player on Mac, Windows or Linux. Not Android. https://www.wolfram.com/cdf-player/
I haven’t tried it yet, I’m typing this from Android, but more than a few of the demonstration examples look familiar from other contexts.
Thanks, downloaded.
Looks QI, but I suspect you’d have to buy Mathematica to do anything useful with it.
(Screams with laughter). The first CDF file I downloaded, actually gives as it’s source of information a paper that I wrote in 1988.
Wow. Some people actually read the technical stuff that I write.
That’s great.
mollwollfumble said:
The Rev Dodgson said:
mollwollfumble said:
Check out https://demonstrations.wolfram.com/topics.phpThe Wolfram Demonstration Project.
With a bit of luck they can be run on the free program CDF player on Mac, Windows or Linux. Not Android. https://www.wolfram.com/cdf-player/
I haven’t tried it yet, I’m typing this from Android, but more than a few of the demonstration examples look familiar from other contexts.
Thanks, downloaded.
Looks QI, but I suspect you’d have to buy Mathematica to do anything useful with it.
(Screams with laughter). The first CDF file I downloaded, actually gives as it’s source of information a paper that I wrote in 1988.
Wow. Some people actually read the technical stuff that I write.
Ref?
:)
mollwollfumble said:
The Rev Dodgson said:
If, like me, the last thing your C: drive needs is another over-bloated program, see:http://support.wolfram.com/kb/41414
for instructions on how to install somewhere else. It’s about 5 GB when installed.
Thanks for the warning. I’m OK because I have about 133 GB free.
I totally ran out of GB (on two computers) a couple of years ago when downloading the complete set of Kepler spacecraft data for analysis – but I’ve deleted all that since then.
My current computer I went with solid-state C drive, but I saved a few bucks by only getting 100 GB, which is about enough for Windows, and not much else.
The Rev Dodgson said:
My current computer I went with solid-state C drive, but I saved a few bucks by only getting 100 GB, which is about enough for Windows, and not much else.
I see. I was going to ask what your biggest programs are, but don’t need to now.
My desktop is 931 GB, and I keep the best of all the old stuff on a separate 1 Tera hard drive.
For decades I was running out of storage before anything else gave out, so have always gone for a big hard drive.
The desktop was dying on me so I got a fresh reinstall from scratch and disabled updates in 2016.
mollwollfumble said:
The Rev Dodgson said:My current computer I went with solid-state C drive, but I saved a few bucks by only getting 100 GB, which is about enough for Windows, and not much else.
I see. I was going to ask what your biggest programs are, but don’t need to now.
My desktop is 931 GB, and I keep the best of all the old stuff on a separate 1 Tera hard drive.
For decades I was running out of storage before anything else gave out, so have always gone for a big hard drive.
The desktop was dying on me so I got a fresh reinstall from scratch and disabled updates in 2016.
I have a 1TB hard disk as well, which has plenty of space. I just need to make sure big programs don’t install themselves on C without asking.