Will it rot my students' brains if they use Mathematica? (2002)(theodoregray.com)
theodoregray.com
Will it rot my students' brains if they use Mathematica? (2002)
https://theodoregray.com/BrainRot/
168 comments
I wholeheartedly agree, I used to tutor calculus in college and getting students to focus on the fact that the derivative was the slope of the curve or the rate of change and the integral was the area under the curve and the significance of that made calculus so much easy. Drawing the unit circle to explain the cos, sin, and tan was also so enlightening to students. Most students just see a list of characters when the see math problem, but "math people" understand what is going on underneath and become excited to solve a problem and see multiple paths of potentially solving it. If you can unleash that excitement the problem solves itself.
Once you understand the why, the how becomes so much easier.
Once you understand the why, the how becomes so much easier.
> Once you understand the why, the how becomes so much easier.
The interesting thing is how each student has a different path to understand the "how". It sounds like you have particularly vivid mental imagery, and gravitate towards visualizations for solving problems. This isn't true for everyone; it's not necessarily aphantasia but a unit circle or slope/area curve just isn't as useful for some as it is for you, others might prefer to think in terms of limits or series or patterns or a myriad of other techniques. You can repeat "The derivative is the slope of the curve" until you're blue in the face but some people just won't 'get it', finding the means by which they can get it is the fun part.
The interesting thing is how each student has a different path to understand the "how". It sounds like you have particularly vivid mental imagery, and gravitate towards visualizations for solving problems. This isn't true for everyone; it's not necessarily aphantasia but a unit circle or slope/area curve just isn't as useful for some as it is for you, others might prefer to think in terms of limits or series or patterns or a myriad of other techniques. You can repeat "The derivative is the slope of the curve" until you're blue in the face but some people just won't 'get it', finding the means by which they can get it is the fun part.
What’s the TL;DR?
I watched it a while ago, but the TLDR is more or less that the learning styles (ex: visual learners, or auditory, reading/writing, by doing etc...) are a myth. People do not learn better when we use their preferred learning style. But overall, people do learn better with multi-modal (mixed support / style).
Yep - multiple representations, and interactivity, for the win. It is incumbent on the instructional designers and teachers to construct a process where the learner actually learns the concepts rather than learning processes and using computational resources to cover a lack of understanding.
>>You can repeat "The derivative is the slope of the curve" until you're blue in the face but some people just won't 'get it'.
Then you have to explain why the slope of a line is significant. For example if you have the position of something in the form of an equation you can take the derivative and get the velocity. Anybody who understands why the slope of the line is interesting will fair far better.beyond that the area under the curve of a velocity graph will give you the distance traveled.
Then you have to explain why the slope of a line is significant. For example if you have the position of something in the form of an equation you can take the derivative and get the velocity. Anybody who understands why the slope of the line is interesting will fair far better.beyond that the area under the curve of a velocity graph will give you the distance traveled.
> Something that occurs to me is that most of us have a poor grasp of why we even teach school math
One of my favorite math courses was a college class that focused on concepts - technically not an education class but intended for those in education majors. It covered 5th-8th grade math and showed me the why of so many things I had just taken for granted previously, and I'm sure if math was taught that way it would be much better remembered.
Of course, it could still be argued over whether math should be intended for practical use or not, but I think it's important that math be taught from (at least one of) a conceptual basis, or a historical basis (eg. [0] on the creation/discovery of imaginary numbers - it explains why they were needed, as well as interesting historical background).
(This was typed in a hurry, sorry if it's not entirely cohesive.)
[0] https://www.youtube.com/watch?v=cUzklzVXJwo
One of my favorite math courses was a college class that focused on concepts - technically not an education class but intended for those in education majors. It covered 5th-8th grade math and showed me the why of so many things I had just taken for granted previously, and I'm sure if math was taught that way it would be much better remembered.
Of course, it could still be argued over whether math should be intended for practical use or not, but I think it's important that math be taught from (at least one of) a conceptual basis, or a historical basis (eg. [0] on the creation/discovery of imaginary numbers - it explains why they were needed, as well as interesting historical background).
(This was typed in a hurry, sorry if it's not entirely cohesive.)
[0] https://www.youtube.com/watch?v=cUzklzVXJwo
> I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel.
Doing mathematics on a computer is pretty darn tricky. It's not impossible but tools like Mathematica tend to lack the flexibility that pen and paper grant you.
Of course computers are better at computation, but I don't think that counts as 'doing math'. That would be like saying a loudspeaker composes music.
Doing mathematics on a computer is pretty darn tricky. It's not impossible but tools like Mathematica tend to lack the flexibility that pen and paper grant you.
Of course computers are better at computation, but I don't think that counts as 'doing math'. That would be like saying a loudspeaker composes music.
> Doing mathematics on a computer is pretty darn tricky.
Sounds like a case of:
"The math that is "real" to them is just what they happened to learn, the way they learned it"
Programming is doing mathematics, and computers do a great job of enabling one to program.
Sounds like a case of:
"The math that is "real" to them is just what they happened to learn, the way they learned it"
Programming is doing mathematics, and computers do a great job of enabling one to program.
As a counterpoint I'd like to claim that pen and paper is a massively underrated tool for programming, and furthermore that the parts that you can do on pen and paper are more mathematically interesting than the parts that can't be done without a computer.
Math is a broad field. Of the many branches of math, the one that programmers engage in, is programming. But I've observed that programmers tend to have the same proficiency in general math as anybody else, i.e., most people forget the math that they learned in school.
At the places where I've worked, general math or quantitative problems that go beyond the capabilities of Excel are brought to the "math person."
At the places where I've worked, general math or quantitative problems that go beyond the capabilities of Excel are brought to the "math person."
Programming is <<shudder>> _applied_ mathematics.
Nah. Programming is its own thing. Math is lovely and all, but programming isn't applied mathematics any more than playing the cello is applied physics.
Sadly as a good physicist and terrible cellist I have to agree.
The execution of the code is applied mathematics. The creation of the code is doing mathematics.
I 100% agree with you that math is real and that there is real benefit from learning it. With that out of the way,
> It's treated as some kind of tournament to get into college
and
> But most people admit that they forgot all of their math immediately upon finishing school.
in those 2 quotes, you summarize the current issues with school mathematics. There is no real benefit in learning school math as most people will just use up to 6th/7th grade math in their daily work. Even professions that "do math" daily (like carpenters) have, most of the time, figured out ways to do it "quickly" without really doing math (see, for example, the diamonds on a measuring tape and how they are used to solve the Pythagorean theorem).
That leaves school math as "the great sorter" of students. Students that "can" take advanced math classes and use those as leverage in college admissions. To see this process in motion, look up parents' concerns with California's new math sequence and how those usually involve college readiness (as in, college admission advantage) over career readiness (as in, calculus II is needed for whatever profession my kid will do after high school).
> It's treated as some kind of tournament to get into college
and
> But most people admit that they forgot all of their math immediately upon finishing school.
in those 2 quotes, you summarize the current issues with school mathematics. There is no real benefit in learning school math as most people will just use up to 6th/7th grade math in their daily work. Even professions that "do math" daily (like carpenters) have, most of the time, figured out ways to do it "quickly" without really doing math (see, for example, the diamonds on a measuring tape and how they are used to solve the Pythagorean theorem).
That leaves school math as "the great sorter" of students. Students that "can" take advanced math classes and use those as leverage in college admissions. To see this process in motion, look up parents' concerns with California's new math sequence and how those usually involve college readiness (as in, college admission advantage) over career readiness (as in, calculus II is needed for whatever profession my kid will do after high school).
I thought those diamonds were placed at common stud/joist intervals for construction, and some searching doesn't find any connection to the Pythagorean theorem. What did you mean?
I'm not sure what the OP is getting at, because you're right, they indicate stud centers for 16" on-center.
He might be talking about the 3-4-5 trick (pythagorean triples). But the only place I can think of where that is really useful (roofing) has other, better, tricks for figuring out lengths of hypotenuses.
He might be talking about the 3-4-5 trick (pythagorean triples). But the only place I can think of where that is really useful (roofing) has other, better, tricks for figuring out lengths of hypotenuses.
My school had mandatory art class till 5th grade, and I imagine more schools had some mandatory art class. Yet, I have not really practiced any sort of coloring or painting since my last art class.
I am not sure what this similarity with mathematics means for either mandatory art or math classes, but perhaps there is something to consider in our arguments.
I am not sure what this similarity with mathematics means for either mandatory art or math classes, but perhaps there is something to consider in our arguments.
This reminds me of Lockhart's Lament[0], an essay about if art or music were taught how we teach math now.
[0] https://www.maa.org/external_archive/devlin/LockhartsLament....
[0] https://www.maa.org/external_archive/devlin/LockhartsLament....
Can we at least use statistics as the great sorter? The mindset gained from doing advanced statistics is more likely to be useful than the mindset gained from doing integration by hand.
Indeed, I'd like to see more statistics. In fact, stats play right into the strengths of computers. Thanks to computers doing the drudge work, people can be introduced to stats by directly manipulating sets of numbers, rather than learning theorems about the properties of those sets. While I loved college stats, and especially the proofs, most people don't love math in that way. And if they memorize theorems without proofs, then I'd say they'd be better off without them.
> Something that occurs to me is that most of us have a poor grasp of why we even teach school math
I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.
I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.
Some of it comes down to insufficient grounding in math education preparation. In Illinois at least, K5 teachers are required to take a class that's effectively high school algebra, but at least where I got my credential, the class was taught as if it were just a remedial math class (which, to be honest, it was for more than a few of these would-be K5 teachers), rather than making it clear that the math that they would be teaching would be preparatory for the later class. Similar situations occur with 6-12 mathematics education preparation.
This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why.
In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.
This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why.
In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.
> Like with programming, if you learn one language, you can usually learn another in a jiffy.
I actually agree with you in general but, this isn't a guarantee.
I've known plenty of people who "only" know how to "program" in Visual Studio. They don't understand how to use git outside of a helper GUI, they didn't understand the distinction between a compiler and a linker, or build options, or pathing issues--at least not down to the bare wires of what's actually going on.
I'm not saying "everyone" is like that, but when you give exhaustive encapsulating tools, oftentimes people will only learn what they have to, to get running and never delve deeper. Of course, never delving deeper is the key issue but some frameworks/systems make delving deeper much easier than others, and better yet, encourage it.
For an example, it was way easier for me to learn deep aspects of "what is really going on" when I started learning Linux--even immediately when I had to decide how to partition my hard drive correctly just to install it. I "could" just hit auto format but... what are all these buttons? Why is there different types of partitions? Is there a benefit? Not hiding me the inherent complexity allowed me information to better my understanding.
Perhaps this applies more to programming than math, as, the core is to do math... right? The rest is just implementation details of "how do I tell this [math thing] to do [thing I want]". So as long as you know what you're asking "I need a line integral" that's a general enough term. You're learning the _techniques_ not only the framework itself.
I actually agree with you in general but, this isn't a guarantee.
I've known plenty of people who "only" know how to "program" in Visual Studio. They don't understand how to use git outside of a helper GUI, they didn't understand the distinction between a compiler and a linker, or build options, or pathing issues--at least not down to the bare wires of what's actually going on.
I'm not saying "everyone" is like that, but when you give exhaustive encapsulating tools, oftentimes people will only learn what they have to, to get running and never delve deeper. Of course, never delving deeper is the key issue but some frameworks/systems make delving deeper much easier than others, and better yet, encourage it.
For an example, it was way easier for me to learn deep aspects of "what is really going on" when I started learning Linux--even immediately when I had to decide how to partition my hard drive correctly just to install it. I "could" just hit auto format but... what are all these buttons? Why is there different types of partitions? Is there a benefit? Not hiding me the inherent complexity allowed me information to better my understanding.
Perhaps this applies more to programming than math, as, the core is to do math... right? The rest is just implementation details of "how do I tell this [math thing] to do [thing I want]". So as long as you know what you're asking "I need a line integral" that's a general enough term. You're learning the _techniques_ not only the framework itself.
Also not worried about proprietary since I got started learning programming through a pirated version of Mathematica and solving ProjectEuler problems.
It is impossible to “build IQ”, you have the IQ you were born with minus whatever brain damage you might have endured.
"New Evidence for a Way to Raise Your IQ":
https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/...
https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/...
I doubt this will replicate
Making people get used to (and be somewhat dependent on) Mathematica, a very expensive proprietary program, is doing people a large disservice. But it is very profitable for Wolfram.
Also, the “video games make people violent” argument rears its ugly head.
Also, the “video games make people violent” argument rears its ugly head.
If violent video games make people violent, then surely Mathematica makes people want to do more math.
Violent video games make me want to do math. Some of the most enjoyable projects seem to stem from theorycrafting questions.
I think Monster Hunter World was the first time I worked out a dynamic programming algorithm in anger.
I think Monster Hunter World was the first time I worked out a dynamic programming algorithm in anger.
> I think Monster Hunter World was the first time I worked out a dynamic programming algorithm in anger.
Care to elaborate?
Care to elaborate?
Why can’t both be true?
There is an argument to be made that gangsta rap made a generation of impressionable kids much more rough around the edges, as it defined the new “cool” for them. Even though it wasn’t “supposed to be for them”, they knew all the words, which are loaded with expletives and misogynistic lyrics, and sowing distrust of the police etc.
Maybe I am just a social conservative but I agree with this lady who tried, in vain, to fight against the capitalist machine that is ths music industry: https://m.youtube.com/watch?v=Pr6gb1w72xA
Kids are impressionable — the Merchants of Cool documentary clearly shows how capitalist industries exploit that to sell more stuff: https://www.pbs.org/wgbh/frontline/film/showscool/
It also helped shape a rift, in my opinion, between the Black and the White youth that grew up now, which had been closing thanks to Liberalism and efforts to move past it.
There is an argument to be made that gangsta rap made a generation of impressionable kids much more rough around the edges, as it defined the new “cool” for them. Even though it wasn’t “supposed to be for them”, they knew all the words, which are loaded with expletives and misogynistic lyrics, and sowing distrust of the police etc.
Maybe I am just a social conservative but I agree with this lady who tried, in vain, to fight against the capitalist machine that is ths music industry: https://m.youtube.com/watch?v=Pr6gb1w72xA
Kids are impressionable — the Merchants of Cool documentary clearly shows how capitalist industries exploit that to sell more stuff: https://www.pbs.org/wgbh/frontline/film/showscool/
It also helped shape a rift, in my opinion, between the Black and the White youth that grew up now, which had been closing thanks to Liberalism and efforts to move past it.
Please let's not point fingers at hip hop as if there are not lots of examples of violence in rock, pop, and country. If you suggested "Janie's Got A Gun", "Pumped Up Kicks", and "Goodbye Earl" were making kids more violent, you would be laughed out of the room, Karen.
Music is a reflection of culture, and when there is violence in culture, artists make art out of it to cope. If black music seems more violent to you than white music, please meditate on how much more violence black people experience than white people, and why someone would presume one genre is reactive and another genre is causative.
Music is a reflection of culture, and when there is violence in culture, artists make art out of it to cope. If black music seems more violent to you than white music, please meditate on how much more violence black people experience than white people, and why someone would presume one genre is reactive and another genre is causative.
Or the countless songs in the Punk genera about burning down buildings and causing general havoc (like giving someone the wrong time). The set of people who actually commit domestic terrorism (or say no to tea) is much smaller than the set of people who listen to the Sex Pistols for instance. If anything, there's no compelling reason to think they it's the music causing the violence, rather than people who are into that lifestyle selecting an art form that reflects what they already believe.
Punk didn't have nearly the distribution, but yes punk rock is the closest I can think of to an analogue for exporting violence to non-Black youth. The other being Italian mafioso movies, creating a stereotype for some to "look up to". If you grew up around Bay Ridge in Brooklyn around those times, you'd see the effect. It isn't a race thing, it's a culture thing where the worst elements are being purposely amplified and distributed to everyone by a movie/music industry.
Why has Blaxploitation became not ok but gangsta rap is still considered “just art” with misogynistic and violent lyrics portraying Blacks self describing themselves as materialistic thugs, they were role models “poppin bottles”? Are women not 50% of the population, why is it OK? Why is it OK to have lyrics about mistreatinf Black women etc. as “just art” and Ice Cube who uses B’s and H words about women in his music comes on to Bill Maher’s show to lecture him about how using the N word even about yourself in a joking way is “not cool”? Yet it is cool to be a non-woman and using slurs against women? I think both are uncool.
Why has Blaxploitation became not ok but gangsta rap is still considered “just art” with misogynistic and violent lyrics portraying Blacks self describing themselves as materialistic thugs, they were role models “poppin bottles”? Are women not 50% of the population, why is it OK? Why is it OK to have lyrics about mistreatinf Black women etc. as “just art” and Ice Cube who uses B’s and H words about women in his music comes on to Bill Maher’s show to lecture him about how using the N word even about yourself in a joking way is “not cool”? Yet it is cool to be a non-woman and using slurs against women? I think both are uncool.
You make a good point that hiphop has a misogyny problem, (it also suffers from misogyny's sibling disease, homophobia,) but why keep that issue focused on black music when all music has a misogyny problem[1]. Is Kanye worse than Robin Thicke or The Nails?
[1]https://www.flavorwire.com/489278/25-of-musics-most-obnoxiou...
Edit: Thanks for your Soundcloud link. I like your flow. You make fair points, but I see no evidence that any of the issues you raise are worse in hiphop than any other genre. (Or that hiphop's issues are internally generated, and not amplified by an exploitative industry that makes bank off stereotypes.)
[1]https://www.flavorwire.com/489278/25-of-musics-most-obnoxiou...
Edit: Thanks for your Soundcloud link. I like your flow. You make fair points, but I see no evidence that any of the issues you raise are worse in hiphop than any other genre. (Or that hiphop's issues are internally generated, and not amplified by an exploitative industry that makes bank off stereotypes.)
Yes but the violence was only in select pockets of inner city culture. The gangsta culture was exported to kids living in perfectly fine neighborhoods. Their parents were away working for corporations (more corporatism) while the kids who were raised by public schools and the street were most susceptible.
If you want to hear the arguments against gangsta rap and the exploitative music industry (exploiting externalities just like any capitalist industry)
Listen to me do it in rap form, from 2015 … and please comment
https://m.soundcloud.com/gregory-magarshak/gangsta-rap
If you want to hear the arguments against gangsta rap and the exploitative music industry (exploiting externalities just like any capitalist industry)
Listen to me do it in rap form, from 2015 … and please comment
https://m.soundcloud.com/gregory-magarshak/gangsta-rap
I can believe gangsta rap culture may (nevertheless I would require evidence to believe it does) affect kids characters an undesirable way but I can't believe violent computer games can make mentally healthy kids enjoying them to want doing violence in real life. I and many people I knew were such a kids enjoying violent computer games and preferring as much virtual blood and dismembering as possible but doing violence in the real world never ever came into my mind and apparently nobody of the classmates did any either. I also enjoyed crazy and violent driving in Carmageddon and GTA2 but in real life I don't even drive as I believe driving is dangerous.
Why is it obvious fictional music crime inspires more real crime than fictional game crime? Just like games, one could come up with random examples of fans doing real world violence, but the vast majority of the suburban kids that prop up the industry are just looking for escapist thrills.
I rarely see games significantly affecting the way how do people look and behave in the real world beyond cosplay events. At the same time it is very common for fans of particular music style to dress and behave a specific way so it in fact does affect their behavior at least in some extent, it may also affect what kind of people do they hang out with. Music also usually has a huge degree of influence on the listener's mood and attitude. Games probably have too but apparently in a much less degree. I don't insist any music style is inherently harmful (let alone for everybody) nevertheless I believe music has more potential to be dangerous than games.
I think you have cause and effect inverted. Gangsta Rap was a response to racial tension and distrust of police.
Or maybe I’m wrong, maybe NWA caused the LAPD to brutalize Rodney King.
Or maybe I’m wrong, maybe NWA caused the LAPD to brutalize Rodney King.
> There is an argument to be made
Ok, then make the argument. There must be a mountain of evidence if this is true.
Ok, then make the argument. There must be a mountain of evidence if this is true.
How do you feel about cowboy movies?
There’s an argument to be made that political austerity causes social segregation and people to die in poverty of preventable problems.
Why don’t we set aside the rap battle and Mathematica concerns and focus on well known human society features failing people.
Cut the crap with the pearl clutching “there’s an argument to made other peoples behavior did…” and consider yours as a member of an implicitly caste based society.
Treat yourself like the subject of study instead of abstractly focusing on the flock, dad.
Western psychotherapy role play is the worst personality trait.
Why don’t we set aside the rap battle and Mathematica concerns and focus on well known human society features failing people.
Cut the crap with the pearl clutching “there’s an argument to made other peoples behavior did…” and consider yours as a member of an implicitly caste based society.
Treat yourself like the subject of study instead of abstractly focusing on the flock, dad.
Western psychotherapy role play is the worst personality trait.
I don't use Mathematica or similar software, so it's an honest question: is there an open source alternative that would be that good?
If there is, then it's a genuine grievance.
But if there's not — what's wrong with paying for a good product? I have yet to see an equally good alternative to other software products, like Excel, Photoshop or Logic Pro. There are alternatives that have the same functions, but none that have the same level of quality.
After all, most of us here on HN are being paid to write code. It's really weird that we would expect to use someone else's software with thousands of years of developers, designers, testers and other professionals without having to pay for it.
If there is, then it's a genuine grievance.
But if there's not — what's wrong with paying for a good product? I have yet to see an equally good alternative to other software products, like Excel, Photoshop or Logic Pro. There are alternatives that have the same functions, but none that have the same level of quality.
After all, most of us here on HN are being paid to write code. It's really weird that we would expect to use someone else's software with thousands of years of developers, designers, testers and other professionals without having to pay for it.
is there an open source alternative that would be that good?
Between SageMath, Numpy, scikit-learn, Pandas, Folium etc. Python can probably match Mathematica feature for feature and even beat it in some cutting edge research areas.
However Mathematica makes it a lot easier to get started if you don't know how to program. Just start Mathematica, enter the equation like it looks on the page in your math book using the equation editor GUI, click solve and you're done. Also since everything is built in you don't have to worry about working out which package implements Moving Median or Facial Recognition.
Mathematica also comes with a bunch of real time data sources which are really fun to play with. Want to plot Germany's GDP vs Natual Gas prices or Gold prices vs global average temperatures? The datasets are there and ready to be explored.
Between SageMath, Numpy, scikit-learn, Pandas, Folium etc. Python can probably match Mathematica feature for feature and even beat it in some cutting edge research areas.
However Mathematica makes it a lot easier to get started if you don't know how to program. Just start Mathematica, enter the equation like it looks on the page in your math book using the equation editor GUI, click solve and you're done. Also since everything is built in you don't have to worry about working out which package implements Moving Median or Facial Recognition.
Mathematica also comes with a bunch of real time data sources which are really fun to play with. Want to plot Germany's GDP vs Natual Gas prices or Gold prices vs global average temperatures? The datasets are there and ready to be explored.
In principle, the Python scientific ecosystem allows you to do everything, but the notation is atrocious and not in line at all with how Mathematics is written on paper. So, people familiar with mathematics can bear the pain, but it's terrible for actually teaching mathematics.
For instance in SageMath, to get the eigenvalues of a matrix M, you have to do A.eigenvalues(). What is that supposed to mean? To a programmer, that means A is an object (in the sense of OOP), and you are calling an internal method on it.
But that's not how you think about mathematics. Mathematics is functional. A mathematician knows that eigenvalues(A) means, to choose an appropriate eigenvalue-finding algorithm and apply it to the matrix A.
The mathematics program should conform to how one should think about mathematics, rather than forcing mathematics students to think like programmers. Mathematica does that.
For instance in SageMath, to get the eigenvalues of a matrix M, you have to do A.eigenvalues(). What is that supposed to mean? To a programmer, that means A is an object (in the sense of OOP), and you are calling an internal method on it.
But that's not how you think about mathematics. Mathematics is functional. A mathematician knows that eigenvalues(A) means, to choose an appropriate eigenvalue-finding algorithm and apply it to the matrix A.
The mathematics program should conform to how one should think about mathematics, rather than forcing mathematics students to think like programmers. Mathematica does that.
There's open source functional options too. The handful of times I've needed a CAS for something I've used Maxima, it's not quite as full featured as Mathematica or Maple but it costs $0 and is open source. There doing "eigenvalues(A)" will do exactly as you describe. You can even get nice front ends that will pretty print the equations in LaTeX.
I am using a lot of Numpy and Pandas at work and hate them. When I come home I open Mathematica and enjoy every minute of it. It is much more polished, consistent and faster than anything in Python land.
The only place where Python is better if you need to share your code - not everyone has Mathematica license.
The only place where Python is better if you need to share your code - not everyone has Mathematica license.
> Between SageMath, Numpy, scikit-learn, Pandas, Folium etc. Python can probably match Mathematica feature for feature and even beat it in some cutting edge research areas.
Haven't tried Folium, but from people who are familiar with both: The number of ways Mathematica has an edge over Sage (in terms of math capabilities, not interface), significantly outnumbers the reverse comparison.
Sage is better in a few ways. Mathematica is better in many ways.
Still, for the typical undergrad curriculum, Sage is probably good enough.
Haven't tried Folium, but from people who are familiar with both: The number of ways Mathematica has an edge over Sage (in terms of math capabilities, not interface), significantly outnumbers the reverse comparison.
Sage is better in a few ways. Mathematica is better in many ways.
Still, for the typical undergrad curriculum, Sage is probably good enough.
mathematica just works, I spend 0 time chasing down software dependencies or version conflicts - that alone is worth the license fees.
> what's wrong with paying for a good product?
Nothing in principle.
But if we teach people to do math with Mathematica, and they graduate and don't have access to Mathematica any more, how are they going to do math?
Nothing in principle.
But if we teach people to do math with Mathematica, and they graduate and don't have access to Mathematica any more, how are they going to do math?
I think it's fairly common, in different professional fields, to teach skills that would require expensive equipment.
Most of the practical lab skills you're taught for doing "wet" biology require quite an expensive lab, and doing computational biology often requires a much more expensive supercomputers.
Most of the practical lab skills you're taught for doing "wet" biology require quite an expensive lab, and doing computational biology often requires a much more expensive supercomputers.
To an extent.
But the MATLAB skills I honed in university have seen little direct use after graduating - because it's faster to teach myself to do whatever it is in Python than to get an employer to adopt MATLAB.
But the MATLAB skills I honed in university have seen little direct use after graduating - because it's faster to teach myself to do whatever it is in Python than to get an employer to adopt MATLAB.
> what's wrong with paying for a good product?
You can pay to get access to Mathematica, but you can’t pay to get the freedom you would get from open source. No matter how much you pay, Mathematica is still proprietary. There is, indeed, no price for freedom.
You can pay to get access to Mathematica, but you can’t pay to get the freedom you would get from open source. No matter how much you pay, Mathematica is still proprietary. There is, indeed, no price for freedom.
> what's wrong with paying for a good product?
Here is an editorial from an American Math Society journal that expresses very well one aspect of Mathematica that lots of us find troubling: http://www.ams.org/notices/200710/tx071001279p.pdf
Here is an editorial from an American Math Society journal that expresses very well one aspect of Mathematica that lots of us find troubling: http://www.ams.org/notices/200710/tx071001279p.pdf
Full disclosure: The second author started a new math-
ematics software system in 2005 called SAGE
Yes, one that is fully Free. So he walks the walk.
I think that software like mathematica is a great tool, and anyone genuinely doing research that would benefit from it should be happy to pay for it as a matter of course. But I can also see many of the downsides to using closed-source software for research (I myself use some, not mathematica but related) - you don’t know what algorithms are being used, and can’t check yourself that they do what you expect, or fix them if they go wrong. For truly research-level questions, checking that an algorithm produces the correct output may be as hard as writing the algorithm itself…
Checkout maxima, sympy, and sagemath. I have used maxima and sympy and both are decent. sagrmath is a collection of open source math tools glued by python: it uses both maxima and sympy as backend.
It's a fantastic math education tool. Manipulate[] itself is worth the fee for the home/hobby price. The student price is half of that.
But sure! Take the limited motivation and effort the student's got and make them go through 16th century tech to learn it all.
But sure! Take the limited motivation and effort the student's got and make them go through 16th century tech to learn it all.
And hobbyists don't even have to pay the student price since Wolfram has made the full version of Mathematica free (as in beer, not as in libre) for Raspberry Pi users.
It's such a nice, accessible environment for learning. My daughter is still too young to begin exploring SageMath, NumPy, SciPy, etc., but we've had fun together plotting things in Mathematica.
It's such a nice, accessible environment for learning. My daughter is still too young to begin exploring SageMath, NumPy, SciPy, etc., but we've had fun together plotting things in Mathematica.
Uni students get a student license (free), and then can go on to pirate it until they are making good money. At that point they can either pirate it forever or pay a small fee to use it (relative to their income). They could also take the programming skills they picked up and switch to another platform (Python or Julia). Having said that though, I haven’t used anything like Mathematica, which makes symbolic maths very simple. I’ve tried some libraries in python that didn’t cut the mustard (Sympy) and haven’t experimented in Julia yet.
I don’t know if you know but Mathematica inspired a lot of people.
> Also, the “video games make people violent” argument rears its ugly head.
Can't stand this kind of rhetoric. Arguments aren't scary monsters.
Can't stand this kind of rhetoric. Arguments aren't scary monsters.
If you want to use it and not pay a ton for it, buy a Raspberry Pi and it's a free install. (Used to be included with the OS but now you have to go get it).
Obviously you might want to get a nice recent version of the Pi and splurge on getting the max memory, but...it's the cheapest way into Mathematica (and the Wolfram language) other than winning a copy.
Obviously you might want to get a nice recent version of the Pi and splurge on getting the max memory, but...it's the cheapest way into Mathematica (and the Wolfram language) other than winning a copy.
even easier to just use the free online version - standard freemium model
I don’t think a couple hundred bucks a year is that expensive, people spend way more on their smart phone data plans.
The first time I had a problem and received a technical fix via support email, I was sold on being a subscriber. Whether I could justify the commercial license to an employer is another matter…
The first time I had a problem and received a technical fix via support email, I was sold on being a subscriber. Whether I could justify the commercial license to an employer is another matter…
These days fortunately we have Python and SymPy eating Mathematica cake.
Yes! SymPy is a beautiful thing. Between using it on the command line, or in jupyter notebooks, or the live shell online at https://live.sympy.org, students have the best-in-class computer algebra system easily accessible.
For anyone not familiar with SymPy, check out this short tutorial I wrote: https://minireference.com/static/tutorials/sympy_tutorial.pd... ; also available as notebooks https://github.com/minireference/sympytut_notebooks#play .
For anyone not familiar with SymPy, check out this short tutorial I wrote: https://minireference.com/static/tutorials/sympy_tutorial.pd... ; also available as notebooks https://github.com/minireference/sympytut_notebooks#play .
>a very expensive proprietary program, is doing people a large disservice.
You can use it for free if you use a Raspberry Pi (non commercially)
You can use it for free if you use a Raspberry Pi (non commercially)
Some people might be able to use it for free, but nobody can use it non-proprietarily.
This dialog isn't really about Mathematica.
The second “chapter” of this post is pretty disappointing. It seems like one of the authors doesn’t like violent video games (and thinks that they’re the cause of school shootings!) and because of that thinks (or at least implies) that educational software is bad because it’s on a spectrum with violent video games.
Also, while even some of the best educational software (like Duolingo) have problems, they’re generally not the problems that the authors expected.
Also, while even some of the best educational software (like Duolingo) have problems, they’re generally not the problems that the authors expected.
There should probably be a [2002] date in the title.
The discourse around Mathematica, educational software, and video games has changed a lot in 20 years. I've the whole thing, not much is particularly relevent. Wolfram asks simply too much per license to be widely used in primary and secondary education.
The discourse around Mathematica, educational software, and video games has changed a lot in 20 years. I've the whole thing, not much is particularly relevent. Wolfram asks simply too much per license to be widely used in primary and secondary education.
Yes, he also uses "On Killing" to support his argument for video games. It is a very fascinating (and disturbing) book. But most of the book is focused on the changes in military training that led to the increase in "shoot to kill" between WWII and Vietnam.
In addition to the military training the book also talks about dis-association of killing through different methods and how that increased the "shoot to kill". The basic argument is that it is easier to kill someone when seeing them at a distance through the scope of a rifle than being right next to them and stabbing them. The other part of the dis-association is campaigns to dehumanize the enemy in war and not refer to them or acknowledge that they are individual humans.
The video games argument in "On Killing" isn't part of the main thesis of the book, it is more tacked on the end. Whereas the rest of the book is looking at the past and evidence of what has happened. The video game part of it was (at the time) more focused on current feelings and attitudes towards it and was not substantiated.
In addition to the military training the book also talks about dis-association of killing through different methods and how that increased the "shoot to kill". The basic argument is that it is easier to kill someone when seeing them at a distance through the scope of a rifle than being right next to them and stabbing them. The other part of the dis-association is campaigns to dehumanize the enemy in war and not refer to them or acknowledge that they are individual humans.
The video games argument in "On Killing" isn't part of the main thesis of the book, it is more tacked on the end. Whereas the rest of the book is looking at the past and evidence of what has happened. The video game part of it was (at the time) more focused on current feelings and attitudes towards it and was not substantiated.
When doing math at school I never quite enjoyed it because it didn't feel like it could "scale". You always had to do these clunky calculations which are so error prone, that the slightest mistake could mess up your whole work. Instead of focussing on the essence, my mind was occupied with not messing things up when applying the "instructions". I always wondered how the industry would actually use math to solve its problems.
With programming/mathematical software, it finally clicked and it gave me a powerful, practical tool to make mathematics work. Finally it was not so much about not messing up, but about actually building something. I enjoyed it a lot and in the end I obtained a PhD in theoretical particle physics and became a software developer.
With programming/mathematical software, it finally clicked and it gave me a powerful, practical tool to make mathematics work. Finally it was not so much about not messing up, but about actually building something. I enjoyed it a lot and in the end I obtained a PhD in theoretical particle physics and became a software developer.
Way back when I taught math, I remember having a student in one of my junior high mathematics for college students classes who pulled out her calculator to do 8+9 (that's the exact calculation, I remember it remarkably clearly). And yet, she was able to manage the symbolic manipulation around the rest of the algebra problem she was solving. The thing I took away from that is that while we tend to think of arithmetic as a prerequisite for algebra, the skill sets are largely orthogonal.
I kind of wonder if this was part of how the child of two math professors¹ was taking upper-division college level math classes at Harvey Mudd as a high school student. It's not so much that he learned K5 mathematics quickly and was on to pre-algebra and algebra as that he was likely introduced to algebraic concepts much sooner than his peers.
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1. I never met him, his time was a little before mine, but I recall someone who had met him saying that his parents taught him a lot of mathematics but not so much by way of social skills.
I kind of wonder if this was part of how the child of two math professors¹ was taking upper-division college level math classes at Harvey Mudd as a high school student. It's not so much that he learned K5 mathematics quickly and was on to pre-algebra and algebra as that he was likely introduced to algebraic concepts much sooner than his peers.
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1. I never met him, his time was a little before mine, but I recall someone who had met him saying that his parents taught him a lot of mathematics but not so much by way of social skills.
Quite interesting in that in the 20 years since that was written, the whole "socially unacceptable" to use a calculator to work out simple sums, is not (as far as I see) the norm. I would say that it is very normal to quickly pull out a phone, or ask on your watch, or as Alexa etc.
I don't know about that. Kids are still proud when they can do arithmetic in their head while society has been grumbling about adults who cannot do arithmetic without a calculator for generations.
Personally, I think that kids should learn simple mental arithmetic. It's not that I expect them to use it when they become engineers or cashiers, but it is useful for making quick approximations. It is useful to know when they have to pull out a calculator to check the price they are being charged at the store or to know when to check what they fed the computer (since they have the tools to figure out when an answer is wrong).
Personally, I think that kids should learn simple mental arithmetic. It's not that I expect them to use it when they become engineers or cashiers, but it is useful for making quick approximations. It is useful to know when they have to pull out a calculator to check the price they are being charged at the store or to know when to check what they fed the computer (since they have the tools to figure out when an answer is wrong).
Honestly, just my personal experience here, but amongst millennials, no one cares if you bust out the calculator app to add all your scores in a board game. It's actually superior to mental math because you can see the list of all the points you've added, if you add 20 numbers together it's nice to see them all after for verification purposes. There's no societal expectation placed on us whatsoever, it's all about getting the right answer.
Sorry, I meant children (rather than anyone younger than you are, which seems to be how some people use the word kids).
While I agree with being able to check the results with many modern calculators, my argument is that it is useful to know when the results have to be checked. For example: if you know that all of the points are less than 5 and you are adding 20 of them together, a result greater than 100 means you have to go back and check what was entered.
While I agree with being able to check the results with many modern calculators, my argument is that it is useful to know when the results have to be checked. For example: if you know that all of the points are less than 5 and you are adding 20 of them together, a result greater than 100 means you have to go back and check what was entered.
You don't group up the victory point chips in piles that each add up to 10 like I do? Heretic!
(I agree with you, btw).
(I agree with you, btw).
"You won't always have a calculator!" - Every teacher in school growing up
It's worth pointing out that virtually every math teacher I had growing up, in retrospect, had no knowledge or experience with any actual math.
I recall wondering out loud in hs geometry if one infinity could be bigger than another in typical early high school "big brain" thinking, and at the time my high school geometry teacher basically shrugged their shoulders.
Years later when I discovered cardinalities of infinite sets, which comes up pretty quickly when studying math in college, I was fairly disappointed that such a great potential teaching moment was passed over. I'm pretty sure early high school me would have been dramatically more engaged with math if a teacher has said "funny you should mention that, do you know about the difference between integers and real numbers..."
The tragedy of this is that most Americans, even the ones teaching math, believe mathematics is calculation, and even at the advanced levels will only rarely be exposed to real mathematical thinking.
I recall wondering out loud in hs geometry if one infinity could be bigger than another in typical early high school "big brain" thinking, and at the time my high school geometry teacher basically shrugged their shoulders.
Years later when I discovered cardinalities of infinite sets, which comes up pretty quickly when studying math in college, I was fairly disappointed that such a great potential teaching moment was passed over. I'm pretty sure early high school me would have been dramatically more engaged with math if a teacher has said "funny you should mention that, do you know about the difference between integers and real numbers..."
The tragedy of this is that most Americans, even the ones teaching math, believe mathematics is calculation, and even at the advanced levels will only rarely be exposed to real mathematical thinking.
It's interesting, because I was introduced to cardinal numbers and alef zero, plus Cantor proof, precisely during highschool mathematics class. In Poland though.
“Yeah well you won’t always have an encyclopaedia… you won’t always be able to ask your friends…” I think the single biggest and most overlooked change in the past 20 years has been the creeping ubiquity of knowledge. It may not be as sexy as Trinity downloading a helicopter piloting program but the ability to pull a datasheet for almost any piece of equipment literally out of thin air is damn near as useful.
> creeping ubiquity of knowledge.
I'd rather call it "information". Knowledge is one level above that, knowledge is information integrated in a coherent whole. Nowadays it's very easy to find information about anything, but most people still know very little about most things. Confusing information with knowledge and knowing nothing at the same time is why misinformation spreads so easily.
I'd rather call it "information". Knowledge is one level above that, knowledge is information integrated in a coherent whole. Nowadays it's very easy to find information about anything, but most people still know very little about most things. Confusing information with knowledge and knowing nothing at the same time is why misinformation spreads so easily.
I see it as information being the 1s and 0s, while knowledge is what you do with it.
I think it is relatable to the way that Archer has access to mission dossiers. "Yeah, but I never read them."
People have access to limitless information but have little interest in actually looking for and using it.
People have access to limitless information but have little interest in actually looking for and using it.
Yes, but how do you do some calculations when you are driving and thinking about some physics problem?
Don't solve systems of differential equations and drive.
You can't take D out of PID.
For most of the population, driving while thinking about a physics problem would be considered distracted driving, unless that problem involved avoiding hitting something in the road.
I would classify calculating how close you can drive to the vehicle ahead of you while being able to stop within 1.0 mm +/- 0.9 mm as reckless driving, not wreckless driving.
That calculation would probably be wrong anyway, unless you have a lot of practical experience with emergency braking. I constantly underestimate my reaction times.
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4.3 * 17 = 731 -- seemingly every kid who challenges that teacher and can't sanity check their calculator math.
Heh. I was a TA for a grad school engineering course. The professor accidentally assigned a problem he thought would be easy, but he had a typo and it led to very messy integrals. It wasn't hard, just tedious (think multiple pages of derivations, where at each step the expression was multiple lines long - repeated integration by parts).
He had a policy of no calculators/computer use, but he relaxed it for this assignment as he didn't want students to needlessly suffer.
All the kids that used software (Mathematica and similar ones) got it wrong. All of them. Each and every one made a typo somewhere.
Thing is, had any of these students done a very simple dimensional analysis, they would have known very quickly that their answer was incorrect. I'm sure they would have done that analysis had they attempted solving it by hand. However, people tend to forget sanity checks when working on a computer.
He had a policy of no calculators/computer use, but he relaxed it for this assignment as he didn't want students to needlessly suffer.
All the kids that used software (Mathematica and similar ones) got it wrong. All of them. Each and every one made a typo somewhere.
Thing is, had any of these students done a very simple dimensional analysis, they would have known very quickly that their answer was incorrect. I'm sure they would have done that analysis had they attempted solving it by hand. However, people tend to forget sanity checks when working on a computer.
To be fair I never got to use a calculator in university tests and I'm glad I learned mental math in years prior to prepare me for that. (Though admittedly that's of course a very artificially constrained school-imposed situation.)
In my college classes either calculators were permitted (physics and chemistry tests) or were irrelevant (upper division mathematics).
When I taught high school in the 00s, I had to impose rules about what sort of calculators were permitted to avoid cheating, especially as devices which could be used for communication like network-connected palm pilots were available.¹ I also wanted to have the kids avoid buying a $99 TI-89 when a much cheaper calculator was sufficient for the work they were doing.
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1. I remember one cheating technique that my friends in high school AP Chem used where a group of us were sharing a calculator. You would type in the question number you needed an answer for and someone else would type in the letter of the answer (we generally had multiple choice tests).
When I taught high school in the 00s, I had to impose rules about what sort of calculators were permitted to avoid cheating, especially as devices which could be used for communication like network-connected palm pilots were available.¹ I also wanted to have the kids avoid buying a $99 TI-89 when a much cheaper calculator was sufficient for the work they were doing.
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1. I remember one cheating technique that my friends in high school AP Chem used where a group of us were sharing a calculator. You would type in the question number you needed an answer for and someone else would type in the letter of the answer (we generally had multiple choice tests).
They probably meant electronic calculators. When I asked my prof about using a sliderule, they said that was fine.
(Granted, that was in physics where the graders usually use the final answer as a check and rarely deduct many marks if all of the work leading up to an incorrect numerical answer is correct.)
(Granted, that was in physics where the graders usually use the final answer as a check and rarely deduct many marks if all of the work leading up to an incorrect numerical answer is correct.)
"Noone will pay you for playing video games" - every parent growing up
That's still true. And before you say "streamers", they aren't exactly being paid to play video games - they're paid to perform in public. You don't even need to be great at video games to carve out a living as a streamer, but you do need a charismatic screen presence. If you wanted to get on the "streamer" career path as a kid, you'd have been much better off spending your time taking public speaking courses and getting involved in amateur dramatics than playing video games.
Note that esports are growing in popularity with paid gamers and real prize money for the top spots (e.g., 2.1 millions for the world champions in league of legends and 1.5 millions for counter strike).
But being good doesn't equate to being in a team. There are plenty of players who are the best in SoloQ who can't play on a team professionally because they lack the teamwork skills or have toxic personalities. Having leadership skills and game knowledge would let you coach a team or analyze without having to be the best in playing the game.
Do they pay you for playing video games?
No. They don't pay me for being a doctor either.
I still remember an IT director that I met @ Bank of Boston that said us: "To use google is for lazy people". 2003, I believe.
And now it's more about your "Google-Fu" and do you know how to search properly to find the result you need!
I wonder what things we consider "lazy" at the moment, will become the standard in 20 years
I wonder what things we consider "lazy" at the moment, will become the standard in 20 years
Now the Movie Wall-E[1] came to my mind, where humans couldn't even walk and all the job was done by robots.
[1]: https://en.wikipedia.org/wiki/WALL-E
[1]: https://en.wikipedia.org/wiki/WALL-E
Siri, what is a calculator?
In my trade school, we had this class devoted exclusively to calculating things fast in memory. The exam consisted of running a bunch of calculations as fast as possible without writing down anything other than answer.
It is interesting that you can learn to calculate a lot of useful stuff in memory and there is a lot of tricks and you can get quite proficient at it after one semester of classes and some training.
But once I left this school it was completely unusable skill. It sort of helps me estimate things, a little bit? I guess? But I also carry a phone with me at all times and I have a powerful calculator on my desk just within reach.
A skill that is not being used deteriorates, and now I can no longer multiply 5 digit numbers in memory and I use calculator for anything that involves more than 3 digits. And I don't feel like I lost anything.
There are so many useful skills to learn. If you want to spend time, learn something else that is more useful. And if you don't want to learn something useful learn something that gives you joy or impresses people.
It is interesting that you can learn to calculate a lot of useful stuff in memory and there is a lot of tricks and you can get quite proficient at it after one semester of classes and some training.
But once I left this school it was completely unusable skill. It sort of helps me estimate things, a little bit? I guess? But I also carry a phone with me at all times and I have a powerful calculator on my desk just within reach.
A skill that is not being used deteriorates, and now I can no longer multiply 5 digit numbers in memory and I use calculator for anything that involves more than 3 digits. And I don't feel like I lost anything.
There are so many useful skills to learn. If you want to spend time, learn something else that is more useful. And if you don't want to learn something useful learn something that gives you joy or impresses people.
TL;DR: using a calculator to add and multiply, or Mathematica to do integration is okay because as society advances there is no need for certain skills anymore, freeing you to obtain other skills.
I am not sure I agree. The argument only seems to work if you consider a very simplistic teleological model of skill learning: that the only benefit in learning a skill is mastering a very specific task, e.g. multiplication, or derivation. But you learn a lot of other skills on the way that may be useful for completely different tasks - or even tasks which aren't known yet and thus cannot yet be trained specifically.
As my university teacher in Latin once said: sure, you don't need Latin anymore, but learning it will unlock areas in your brain previously unknown to you.
I am not sure I agree. The argument only seems to work if you consider a very simplistic teleological model of skill learning: that the only benefit in learning a skill is mastering a very specific task, e.g. multiplication, or derivation. But you learn a lot of other skills on the way that may be useful for completely different tasks - or even tasks which aren't known yet and thus cannot yet be trained specifically.
As my university teacher in Latin once said: sure, you don't need Latin anymore, but learning it will unlock areas in your brain previously unknown to you.
Do you know “kill math”?
http://worrydream.com/KillMath/
http://worrydream.com/KillMath/
The idea that seemingly motivates this project -- that it is somehow impossible or undesirable or not ideal for people to learn enough symbolic manipulation to do basic algebra -- is depressing to me.
Now we're going to have people who know algebra programming apps to help people who don't know algebra solve extremely specific problems with no ability to generalize.
Now we're going to have people who know algebra programming apps to help people who don't know algebra solve extremely specific problems with no ability to generalize.
That is not the motivation. The motivation is to develop better interfaces for mathematical concepts. In the same way as Arabic numerals are better interfaces than Roman numerals.
"I want to do good things" isn't a substantial description of anyone's philosophy. The question is "what is good".
Web apps for visualizing math are nothing new, profs were doing it with Java 20 years ago. The manifesto on this page is the new and bad element being added.
Contrary to the manifesto, symbolic manipulation is not a freakish knack possessed only by an elite minority of humans. Barring severe and rare developmental issues, everyone can understand and manipulate written symbols. And in countries with effective educational cultures, people learn it.
Our problem is a damaged education culture, not a general human inability to do basic algebra.
Web apps for visualizing math are nothing new, profs were doing it with Java 20 years ago. The manifesto on this page is the new and bad element being added.
Contrary to the manifesto, symbolic manipulation is not a freakish knack possessed only by an elite minority of humans. Barring severe and rare developmental issues, everyone can understand and manipulate written symbols. And in countries with effective educational cultures, people learn it.
Our problem is a damaged education culture, not a general human inability to do basic algebra.
> Barring severe and rare developmental issues, everyone can understand and manipulate written symbols.
Yes, but it doesn’t mean the symbols can’t evolve. Like Feynman Diagrams—they made the concepts way more accessible.
Yes, but it doesn’t mean the symbols can’t evolve. Like Feynman Diagrams—they made the concepts way more accessible.
I did not get that impression at all. The first example talked about visualizing differential equations.
I did not. Thank you for the link. I hope to explore the idea more. From a quick scan there seems to be a lot of value there.
> As my university teacher in Latin once said: sure, you don't need Latin anymore, but learning it will unlock areas in your brain previously unknown to you.
Couldn't you just learn some live language, that has those same grammar features as Latin (declensions for nouns, conjugation for verbs, whatever) that are new to English speakers?
Couldn't you just learn some live language, that has those same grammar features as Latin (declensions for nouns, conjugation for verbs, whatever) that are new to English speakers?
In my experience, about half of the benefit of learning a new language is in better understanding of grammatical structures (eg. cases - English has them too; and tangentially, (foreign) language classes taught me more about English from a grammatical perspective than public school English classes), and about half of it is seeing how languages relate to one another (eg. how so many words and phrases in English - and other languages - are derived from Latin). You could get the former, but I doubt you could get (the same level of) the latter from another language.
Now of course that's vastly simplified and I'm sure there are other mental affects (and numerous benefits to learning live languages), but those are the ones I've noticed, and the effects would definitely be different.
Now of course that's vastly simplified and I'm sure there are other mental affects (and numerous benefits to learning live languages), but those are the ones I've noticed, and the effects would definitely be different.
Is [a technology enhancing cognition] making us stupid?
In some sense - yes. Every cognitive prosthetics or enhancer means that we do not need to develop a particular set of skills. At the same time - it allows us to move further!
Thanks to writing, we don't need to remember everything. Thanks to the Internet, we can retrieve this information in seconds (not days or months, depending on if a book was in a nearby library).
Integrals are the art of the past. Sure, it is still worth doing some, but rather than memorizing hundreds of tricks, let's focus on something different than reinventing the wheel.
In some sense - yes. Every cognitive prosthetics or enhancer means that we do not need to develop a particular set of skills. At the same time - it allows us to move further!
Thanks to writing, we don't need to remember everything. Thanks to the Internet, we can retrieve this information in seconds (not days or months, depending on if a book was in a nearby library).
Integrals are the art of the past. Sure, it is still worth doing some, but rather than memorizing hundreds of tricks, let's focus on something different than reinventing the wheel.
You can get Mathematica for free on any Raspberry Pi (~$35), so that more or less renders the point about expense moot: https://www.wolfram.com/raspberry-pi/
There is also a pretty nice introductory book that is aimed at students: https://www.wolfram.com/language/elementary-introduction/2nd...
There is also a pretty nice introductory book that is aimed at students: https://www.wolfram.com/language/elementary-introduction/2nd...
Slight tangent - but back in the day while I was attending university I started turning in all my engineering assignments using MathCAD. MathCAD occupied this weird space of a living document for math with additional Mathematica like functionality for symbolic manipulation. I certainly don't feel to this day like I lost anything vs doing everything tediously by hand 100% of the time.
My professors liked it so much they standardized on it and licensed the student edition for the entire department.
My professors liked it so much they standardized on it and licensed the student edition for the entire department.
My professor had a variant of that discourse regarding the computation of Linear Programs : "Prefer Gurobi (or Mosek) over GLPK because GLPK is bugged". My (limited) test show that GLPK works just fine. (GLPK is free software, Gurobi is proprietary)
Now to be honest, the skills I learn over Gurobi, at the level I am, are super transferable to other software, so I'm not trapped into that proprietary stuff.
Now to be honest, the skills I learn over Gurobi, at the level I am, are super transferable to other software, so I'm not trapped into that proprietary stuff.
At least on integer linear programs, I have found the performance of GLPK to be very disappointing, but I didn't notice any bugs. When compared to GLPK, gurobi is usually orders of magnitude faster (I had programs which gurobi optimized in a few seconds, while GLPK couldn't even find a feasible solution in 24 hours).
If you need a free solver with reasonable performance, you should consider the COIN-OR project [0].
[0] https://www.coin-or.org/projects/
If you need a free solver with reasonable performance, you should consider the COIN-OR project [0].
[0] https://www.coin-or.org/projects/
> Misuse of computers is easy and a problem but no use is presently a bigger problem.
This argument seems to be from that techno-utopian era, when we thought that just having access to computers would elevate civilization, and that we'd always have access to computers, so things would keep getting better and better as long as we embraced technology.
What happened instead was a bit more complicated than that: when people got access to ubiquitous computing, it did teach them a new set of skills, and they did lose some old ones. But, we don't live in the world many people expected would come about as a result.
We live in a different world, with many tradeoffs we hadn't expected. Some good things, some bad things. But one thing I think it's safe to say is that the average person is not using computers as tools to think in more abstract and sophisticated ways than they were capable of in 2002.
So, the argument he's making is phrased as pragmatic, but I wonder to what extent that argument just assumes a certain, positive outcome. Would the author make the same argument, with the same level of confidence today?
This argument seems to be from that techno-utopian era, when we thought that just having access to computers would elevate civilization, and that we'd always have access to computers, so things would keep getting better and better as long as we embraced technology.
What happened instead was a bit more complicated than that: when people got access to ubiquitous computing, it did teach them a new set of skills, and they did lose some old ones. But, we don't live in the world many people expected would come about as a result.
We live in a different world, with many tradeoffs we hadn't expected. Some good things, some bad things. But one thing I think it's safe to say is that the average person is not using computers as tools to think in more abstract and sophisticated ways than they were capable of in 2002.
So, the argument he's making is phrased as pragmatic, but I wonder to what extent that argument just assumes a certain, positive outcome. Would the author make the same argument, with the same level of confidence today?
Issues of proprietary codes/services aside, tools like Mathematica and WolframAlpha are great for solving actual problems.
IMHO, a big problem with math education in general is that it focuses on formalisms and equations first while leaving the big picture as just an addendum. That's not so great for those having a hard time keeping motivated without seeing a real life application that is relevant to them.
IMHO, a big problem with math education in general is that it focuses on formalisms and equations first while leaving the big picture as just an addendum. That's not so great for those having a hard time keeping motivated without seeing a real life application that is relevant to them.
I have been thinking a lot lately about the point "such an attitude represents a tremendous degree of disrespect of our forepersons".
The other day I watched "Cargo" on Netflix, in which after a civilisational collapse, many indigenous Australians are depicted as going "back to the old ways". I found this quite problematic: it suggests that the pre-European way of life was so easy that a bunch of adults can just _start doing it again_. As if it's some natural animalistic habit you can just fall into, and not a set of skills and knowledge that evolved over millennia.
I guess it's possible we were supposed to read that these people's communities had passed down that knowledge and experience across the intervening centuries. Maybe they have.
The other day I watched "Cargo" on Netflix, in which after a civilisational collapse, many indigenous Australians are depicted as going "back to the old ways". I found this quite problematic: it suggests that the pre-European way of life was so easy that a bunch of adults can just _start doing it again_. As if it's some natural animalistic habit you can just fall into, and not a set of skills and knowledge that evolved over millennia.
I guess it's possible we were supposed to read that these people's communities had passed down that knowledge and experience across the intervening centuries. Maybe they have.
Mathematica is good. The language itself feels weird though. But for most students using Sage Math[1] would be a much more convenient option.
[1] https://www.sagemath.org/
[1] https://www.sagemath.org/
To be fair, this didn't exist in 2002 when the article was written.
It strongly depends on the problem set.
For teaching id broadly day either set it as a prerequisite to examine something it can't do or leave it until the last lecture to show the course material can be applied more efficiently.
Learning is as much getting used to using tools correctly as understanding what the tools do and how they do it.
I've worked with those who yes, have had their brain rot due to blindly trusting Mathematica or equivalent and they never spot first step errors from their blind spot. That being said I've worked with one person who used it really well and I think they were genuinely more efficient for it existing.
For teaching id broadly day either set it as a prerequisite to examine something it can't do or leave it until the last lecture to show the course material can be applied more efficiently.
Learning is as much getting used to using tools correctly as understanding what the tools do and how they do it.
I've worked with those who yes, have had their brain rot due to blindly trusting Mathematica or equivalent and they never spot first step errors from their blind spot. That being said I've worked with one person who used it really well and I think they were genuinely more efficient for it existing.
BC calc in high school, I probably leaned on Mathematica a little too much, but mostly to check my work. Once, I got stumped on an integral and what Mathematica churned out wasn't even close (this was '94). Got a nice little note about that in the margin from my teacher. 0 points. Might still be some Mathematica pitfalls for teachable moments.
The more I look at this topic, the more I'm thinking -- if the goal is "real world math" (which it perhaps shouldn't ALWAYS be, but let's go with it) it feels like the solution is probably "get the kids in front of Excel (or Calc/Sheets) as soon as possible."
A big wide open "environment" to get things done in the same way that people in the real world do. Incidentally, I'm also thinking that this might also apply to "programming?"
A big wide open "environment" to get things done in the same way that people in the real world do. Incidentally, I'm also thinking that this might also apply to "programming?"
Related, Alan Kay's views on this subject: https://www.quora.com/What-does-Alan-Kay-think-about-compute...
I knew a cryptographer who did their entire job in Mathematica for years and only rarely ever touched a common programming language. The output of their work informed a lot of other people's work. I don't know if their brain rotted, but they got a heck of a lot of work done with minimal effort and time.
I remember getting Mathematica because I thought it would help me solve hard integrals (a common pastime in my physics-oriented graduate career) but all it did was make more complicated integrals.
I actually wrote a whole python/mathematica interface that was very elegant, but most of what I learned was cool Python tricks.
I actually wrote a whole python/mathematica interface that was very elegant, but most of what I learned was cool Python tricks.
Are there any good textbooks that introduce applied math and engineering methods using software* (and not require solving problems by hand)?
*By software I mean both programming languages (Python) and software suites (MatLab, Mathematica, Sage, etc.),
*By software I mean both programming languages (Python) and software suites (MatLab, Mathematica, Sage, etc.),
Great read until they started suggesting that violent video games were leading to school shootings, which the science totally disagrees with.
As an science & engineering undergrad, I was taught some basic Mathematica usage in 2 subjects (Intro. Physics). The sentiment amongst engineering teachers was that ‘reliance on computer tools is dangerous’, since if you didn’t grasp the fundamentals, you couldn’t properly verify the answers produced. I found this to be one of the largest disappointments while earning my degree: this sentiment is holding people back from embracing the future and I mostly think that teachers just didn’t want to learn programming. As a result, engineers were phobic of doing any coding to solve problems (in my experience working in groups) and instead relied on primitive pen & paper or excel solutions, both of which are more time consuming to scale, re-use or even to verify! If you use Mathematica as a literate programming tool, like a Jupyter notebook, a solution is more readable and verifiable than hand-notes or excel. I had to mostly learn it on my own, and have built up a large library of tools to tackle engineering problems. As a result I can save time on forgetting/re-learning how to do things, as I have a searchable database of solutions at my fingertips. I check and test each of my ‘scripts’ against textbook answers, so I know I can trust them.
TL;DR: Teachers, please encourage computer usage for problem solving, but make students understand they need to grasp the fundamentals first!
TL;DR: Teachers, please encourage computer usage for problem solving, but make students understand they need to grasp the fundamentals first!
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I couldn't read past the first few analogies. Is there a TLDR?
Also, why must pages be without styles and so w i d e? What is this, a manpage? Long form text should not need to be so wide.
Basic CSS can be applied to a site to make it readable, don't even need to add classes to the HTML to do it.
https://watercss.kognise.dev/
Here is the page with readability turned on: https://imgur.com/a/0yzRY61
Also, why must pages be without styles and so w i d e? What is this, a manpage? Long form text should not need to be so wide.
Basic CSS can be applied to a site to make it readable, don't even need to add classes to the HTML to do it.
https://watercss.kognise.dev/
Here is the page with readability turned on: https://imgur.com/a/0yzRY61
I like pages like that. That's because they let me quickly "style" them to optimal size and shape using tools meant for this job - that is, browser zoom feature and/or window manager's facility to resize windows.
It's sad that we've forgotten why web rendering has fluid layout: the whole point was to enable the user to make a web document work for them. In contrast, the modern websites are essentially PDFs emulated with CSS and JS.
It's sad that we've forgotten why web rendering has fluid layout: the whole point was to enable the user to make a web document work for them. In contrast, the modern websites are essentially PDFs emulated with CSS and JS.
I think it's annoying that some pages do it one way on some the other; With 16:10 1920x1200 displays, I often run my windows (including the browser) in a vertical tile, but then about 1/3 of pages seem to think I'm on a mobile phone since the resolution is 960x1200 and they make everything giant and hide half of the controls.
At 400% zoom in Chrome in order to have a comfortable reading width about 2 sentences fit on the whole 1080p screen. I'm not sure zooming in and out is exactly a nice or helpful user experience.
Counterpoint: pages like this are awesome because they give the reader options! Rather than the website author forcing whatever they want on the reader, readers can read as they please.
- I see you know about Water.css: I've used the 'waterize' bookmarklet on pages like this. Similarly for Sakura. - Most browsers have a reader mode, and it works perfectly with this page, as you point out. - Pages like this work really well when printing, either to paper or PDF. Most websites just don't. - The total size of the page is...44k.
Overall, I actually prefer pages like this. Ironically, I wouldn't publish my own writing this way because so many people have the reaction you have; I guess I realize I'm in the minority on this one.
- I see you know about Water.css: I've used the 'waterize' bookmarklet on pages like this. Similarly for Sakura. - Most browsers have a reader mode, and it works perfectly with this page, as you point out. - Pages like this work really well when printing, either to paper or PDF. Most websites just don't. - The total size of the page is...44k.
Overall, I actually prefer pages like this. Ironically, I wouldn't publish my own writing this way because so many people have the reaction you have; I guess I realize I'm in the minority on this one.
A trick to using old web pages like these is to enable reader mode in your browser. In fact, I use that trick pretty much everywhere nowadays.
The footer provides a hint for the why:
> Converted by Mathematica May 30, 2002
> Converted by Mathematica May 30, 2002
And heres mathematica.com 2 years before that. https://web.archive.org/web/20000520004659/https://mathemati...
The trick to fixing wide pages is to
1) open devtools, 2) resize the page, 3) make devtools a popup, 4) then minimize the popup.
It works wonders on amazon cloud reader, read.amazon.com, although I am thinking about writing an dev-tools extension to make it even prettier. I believe text should be human scale, which means minimizing the amount of left-right muscle movement of the eyes, resembling as much as possible the format of paperback books.
1) open devtools, 2) resize the page, 3) make devtools a popup, 4) then minimize the popup.
It works wonders on amazon cloud reader, read.amazon.com, although I am thinking about writing an dev-tools extension to make it even prettier. I believe text should be human scale, which means minimizing the amount of left-right muscle movement of the eyes, resembling as much as possible the format of paperback books.
This user hostile and convoluted approach to making a page look readable must the the approach TeMPOraL mentioned above, lol.
How else to resize someone else's content hosted in an iFrame? I'm open to suggestions.
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Of course HN is upset someone is critical of manpage style no-formatting of HTML.
Something that occurs to me is that most of us have a poor grasp of why we even teach school math: It's treated as some kind of tournament to get into college, or a general IQ building exercise, or even a form of obedience training. The math that is "real" to them is just what they happened to learn, the way they learned it. But most people admit that they forgot all of their math immediately upon finishing school.
And school math isn't even how "math people" do math. I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel.
I'm not too worried about Mathematica being proprietary. Like with programming, if you learn one language, you can usually learn another in a jiffy.