16 ms·

Learning algebra in my 60s

171 points by trocado 4y ago

collimator 4y ago
No, but once you have learnt some algebra you'll be in a position to learn other things - electrical physics for example, or audio engineering. These subjects, and many others, use the language of algebra, because algebraic explanations are very compact and easy to follow.
- deleted 4y ago
  [deleted]
inetsee 4y ago
In my opinion, nothing can make you smarter. Learning rationalist techniques may make you better at thinking through problems, learning memory techniques like Memory Palace may improve your memory, using learning techniques like Spaced Repetition may help you learn and retain large amounts of information with the minimum necessary effort, but nothing can make you smarter.
- water8 4y ago
  What about adderall? /s
  - inetsee 4y ago
    Adderall doesn't make you smarter; it just makes you more alert. It helps you focus longer on whatever intellectual task you're working on, be it problem solving or studying. (Not /s)
    - water8 4y ago
      So being able to work longer and focus harder than what would normally be physically possible is not the definition of “smarter” even if it’s temporary?
- haskellandchill 4y ago
  I agree you are about as smart as you will ever be. However that does not apply to me thank you very much.
- jonathanstrange 4y ago
  I'm pretty sure this is wrong. The brain adapts to whatever activity you do and, as far as I know, is way more plastic than researchers thought decades ago. If you're doing dumb things all the time you're making yourself dumber over time and when you're performing difficult tasks repeatedly and daily your brain adapts to them to be able to solve them easier. I realized that a long time ago in a completely different area, in martial arts. When you start it's extremely hard to follow complex movements shown by other people. Beginners struggle with this a lot. Over the years it's getting easier and easier and you can often grasp complicated movements after seeing them once. I suppose it's the same in dancing and ballet. The brain adapts to sports, painting, writing poems, or solving complex math puzzles. It just happens that some of these activities are considered smart and also (partly) measured with traditional IQ tests. You can even train to become better at IQ tests if you desire to acquire a completely useless skill set.
- magpi3 4y ago
  I think you have to define what "smart" means. I mean if you dropped me into some of my undergrad courses today, especially my CS courses, I would dominate like Wilt Chamberlain and people would think I am a genius. But what does it even mean to be smart anyway? I think in school a lot of the people we deem to be smart simply have more prior experience in the subject or just work very hard.
fargle 4y ago
Probably not. Knowing more stuff doesn't make you "smarter". Nor would mastering kinds of math that many people find challenging prove you are more intelligent. Clearly many intelligent people are not great at math or don't know algebra. But exercising your curiosity and practicing the art of learning will always increase your mental fitness and the ability to apply your intelligence better. It's always good to keep in shape - mentally too. I don't think it matters much what the subject is. It doesn't have to be algebra, as long as it captures your interest. Algebra is very challenging because it requires thinking in abstract concepts, so it's a great subject. It will indirectly lead to deeper understanding in many other fields too, including computer science. Intelligent people are often curious and desire to learn new things, so No I don't think learning algebra makes you smarter - but I think the desire to is a possible symptom of this kind of curiousity.
trocado 4y ago
Despite the title, I don't think the article is about algebra "making you smarter", but more whether you can learn it successfully and if by pursuing such an endeavor you can hamper age-induced cognitive decline.
mattwilsonn888 4y ago
It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the ability to understand math as anything other than a human attempting to be a computer. The author expresses his misintuition of variables - there are plenty of simple examples and thought exercises which can inform the intuition. Later he expresses getting mixed up dealing with fractions - this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions. Modern math education is spectacularly guilty of going too far too fast. Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. If the fundamentals are well understood, the applications feel trivial, intuitive, beautiful, clever - when the fundamentals are taken for granted, one word describes the relationship to the rest of the material: arbitrary.
- deleted 4y ago
  [deleted]
- As_You_Wish 4y ago
  Right. >Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. This is so true. I was exactly like the author. I could not understand any math beyond algebra. Trigonometry was way beyond my ability. But one day, I found an old trig book lying around when I went to visit my parents - it was one of my sibling's books when she took it. I picked it up and had a thought - all those people who DID understand trig and higher math were not that much smarter than me. I mean, yeah, the super smart ones were, but I'm just talking about the regular students. So I got a bug to show myself that if they could do it, then I could do it. My approach that I would do is to read the first section of the first chapter until I understood it completely and not move on until I did. I would not even move on from a sentence, or indeed a word or term, until I understood exactly what was happening. I would look all over the internet, watch youtube videos on that one single concept, or that one single word, until I understood, and I was absolutely adament about not moving on until I understood. Word by word, sentence by sentence, section by section, I rolled on. I wanted to completely completely completely understand the very very basics of trig. It was slow going, as you might imagine. Super slow. Well........all of a sudden, about 4 or 5 chapters into the trig text, my mind exploded. It was blown apart by a blinding light. In one single instant, I swear, one instant, I knew all of trigonometry. I got it. All of trig. One single instant. It was probably one of the most singular moments in my life. So I then started paging through the entire rest of the trig book, and I knew it all. I swear. I would just glance over the pages and know what everything was about. Now, I was NOT an expert, by any stretch of the imagination, I'm not claiming I became a savant. No. I'm just saying I "got" it. As you said, I has the exponential results. So exponential, it was instantaneous. >If the fundamentals are well understood, the applications feel trivial, intuitive, beautiful, clever - when the fundamentals are taken for granted, one word describes the relationship to the rest of the material: arbitrary. This is it exactly. You describe it perfectly. I did not continue on, because I actually had other things in my life that I had to move on to. But it was great because I knew then that math was easy. No doubt I could do the exact same with any math class, no doubt in my mind whatsoever. For whomever wants to do great in almost any area of study, study HARD on those first 3-5 chapters. They set the tone for the rest of the course. If you study hard on them, they remainder of the course is trivial, with some things here and there that you need help with, but for the most part it is simple.
librarianscott 4y ago
Brain games do little for the older mind. You are much better off lowering blood pressure and walking. But, if you insist, read [1]. [1]: https://www.nia.nih.gov/health/cognitive-health-and-older-adults https://www.nia.nih.gov/health/cognitive-health-and-older-ad...
- bitshiftfaced 4y ago
  That link did mention the "Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE)" study. Apparently it found that training can affect quality of life and reduced car accidents in driving seniors.
- bamboozled 4y ago
  Not sure why but this just seems so useless and defeatist. Why is learning new things “brain games”?
BirAdam 4y ago
I personally found that learning math was far easier as an adult. Like the author, I sucked in grade school. I learned multiple foreign languages. I did well in the sciences. History and geography were simple. Math? It was the one thing that escaped me. As an adult, after various misadventures, entering into college everything was different. My mind was more disciplined, my teacher was far better, and I was more humble. It was easy then.
k_sze 4y ago
The title sounds like a non-question. I posit that learning anything (even fengshui or astrology), at any age, will make you smarter, as long as you bring a pair of critical eyes with you. Besides learning about the actual “thing” (which you can still fail at the end of the day), you can always introspect to figure out why/how you failed and what your limits are, and then you’ll maybe find closure in saying “I’ve tried. It didn’t work out. There was no 'wasted potential' - the potential was never there to begin with. And I’m a wiser person now.”
- dangus 4y ago
  The title is there to get you to click, there's not much need to analyze it. The article has little to do with it. This reminds me of On Cinema At the Cinema when Gregg Turkington, as a parody of the film critic persona, often bases his critical opinion of the films based on what he thinks of the title and runtime.
zxcvbn4038 4y ago
I have to sit on my hands and not help my son with his math homework. The way they have taught him to do math is great - he can solve just about anything in his head - but I can’t help him without introducing him to the old slow way I learned of doing everything.
- stinkytaco 4y ago
  I really liked the Common Core early math curriculum. My daughter was taught to do calculations the way I had to come to them myself later on: break the problem apart into easier pieces. A simple example: If you are adding 73 and 29 break it to 70+20 and 3+9. Quick calculations takes the burden off on harder problems later on. Also, she learned to round and estimate and they did lots of practical math applications -- especially in probability -- so she's learned to think of math in a "common sense" way, for lack of a better word. It's easier for her to look at an answer and say "wait, that doesn't make any sense considering the givens".
victor106 4y ago
My friends dad in his late 60's wanted to learn math and used the No Bullshit math and physics from https://minireference.com/ https://minireference.com/ and loved it. Their Linear Algebra is quite good too.
- guidorice 4y ago
  I highly recommend the Ivan Savof books as well. A Statistics title is upcoming.
- ivansavz 4y ago
  For anyone interested, here are preview PDFs of the two books: https://minireference.com/static/excerpts/noBSmathphys_v5_preview.pdf https://minireference.com/static/excerpts/noBSmathphys_v5_pr... https://minireference.com/static/excerpts/noBSLA_v2_preview.pdf https://minireference.com/static/excerpts/noBSLA_v2_preview.... and standalone concept maps that show the prerequisite graph (very useful when learning from any book): https://minireference.com/static/conceptmaps/math_and_physics_concepts.pdf https://minireference.com/static/conceptmaps/math_and_physic... and https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf https://minireference.com/static/conceptmaps/linear_algebra_... I recently released a new book with just high school materials, specifically targeted at adult learners. Check out the website here: https://nobsmath.com/ https://nobsmath.com/
  - victor106 4y ago
    Thank you. We can't wait for your stats book to be released.
rongenre 4y ago
One of my retirement goals is to redo my math degree - turns out it's really easy to get hooked up with online tutors, and I figure it's totally worth paying $20-$40 an hour to work through a textbook.
- wrycoder 4y ago
  If you have a math degree, you already know how to learn math. That hasn't changed. You're not going to try passing tests, so you don't really need a tutor. What you might want is a counselor to guide your "reading", as is done in places like Oxford. That can be worth the $40. All you need is updated texts, a plan of action, and maybe Wikipedia for an alternate take on sticking points. (Just using Wikipedia doesn't work well.) You could also look at the MIT or Harvard online curricula/syllabuses to get a feel for what the current subjects and texts are. Maybe take a couple of the free courses. Also, scan Kahn Academy first - that site is good for identifying holes in your background.
  - waynesonfire 4y ago
    interseting.. what are these counselors? what do they do?
- squeaky-clean 4y ago
  Where do you find an online tutor? My first guess would be fiver but there's probably some sites with a more academic focus?
miga 4y ago
Probably yes, since past research indicates that learning delays cognitive decay. Even more, there is research pointing that continuous learning will prolong your lifespan. Best indication is a study on how university professors tend to live longer.
JKCalhoun 4y ago
"Sometimes I dreamed that there were numbers falling from the sky into chasms I couldn’t see the bottom of." Reminds me of the night terrors I had when I was younger. I remember often having dreams that involve the unknowable, unseeable or in some other way were impossible for my finite mind to comprehend. In the worst of those nightmares I was left shaken with fear — feeling as though I had peered from just over the precipice of sanity itself.
- SketchySeaBeast 4y ago
  As a child I experienced sleep paralysis where I would hallucinate shapes of impossible dimensions, both simultaneously incredibly large and incredibly small, hanging over my bed and leaving me to question the nature of everything. Looking back on it I can't even begin to understand why I dreamed those dreams.
363849473754 4y ago
The author also wrote this excellent article: https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
wawjgreen 4y ago
My litmus test of someone being intelligent or not--among other such tests--is what they say about Shakespeare. This might anger the Brits, but Shakespeare is garbage--and the guy says: "I read .... most of Shakespeare." One famous guy lambasting Shakespeare (Tolstoy) was only marginally smarter, because according to his "Confessions", he read it many times over (incl. in English) and STILL could not find any artistic value in it. I could not have put up with that--for me, it was the first few pages that I knew this was a waste of time. You don't need to drink the whole festering junk of a decayed meal to know it is not edible. He also claims he wants to test the limits of his intelligence by tackling Mathematics once again--implying wrongly, as it were, that math education is fine and it is our brains that are incapable of learning. Not so fast: how am I less intelligent if the bozo teaching me does not know how to teach maths? Citing Carl Jung does not help either, though he namesdrops to mitigate the shame of not being able to do maths...Jung was not as bright as is commonly believed as well. He once claimed that UFO's were all imaginary-- a sweeping generalization by someone claiming to be scientist-- whereas I for sure know that UFO's are real for I have seen one and to prove that I wasn't seeing things, I had a camcorder ready which recorded the space-ship going vertically up very slowly. I have lost the video though but it certainly happened 20 years ago and I still remember it. EDIT: I see I have touched quite a few nerves.
- trebbble 4y ago
  > EDIT: I see I have touched quite a few nerves. It reads like a post you made for yourself, not for the benefit of any reader.
  - wawjgreen 4y ago
    Writing is always primarily of benefit to myself--and hence of any benefit to anyone else....would you cook a meal you wouldn't eat yourself but wish others did? Writing that is geared towards explicitly benefiting others (at the cost of not benefiting our own selves) is shallow, useless and fake.
    - trebbble 4y ago
Wistar 4y ago
Despite that — or, maybe, because — my father was a math academic, I did poorly in school with math beyond basic arithmetic. When I was about 25 years old, a friend gave me three algebra textbooks written by an ex-military pilot, John Saxon. In a marathon session lasting about two weeks, I went through all three books from end-to-end and really learned algebra. For whatever reasons, the Saxon books worked really well for me — better than any other learning I have ever gotten from a textbook. Yes, I was really motivated but I attribute a lot of my success learning algebra to those books. Learning that opened a lot of doors since then, mostly because my confidence in taking on matters technical was so much improved.
racl101 4y ago
My grandpa used to enjoy doing Euclid's Elements compass and straightedge constructions and understanding proofs. He also enjoyed reproducing geometric proofs of certain equations. What's funny is he hated math as a student but for some reason or other got turned onto Euclid in old age. He then tried to get my dad to read Euclid but that didn't take. Then I came across the book as teen and took an interest so Grandpa and I bonded over that.
photochemsyn 4y ago
Scientists can't agree to what extent human intelligence is inherited vs. acquired, and so asking if doing some activity x will result in an increase in personal smartness y will result in a wide variety of answers. (sort of a differential equation isn't it? Change in intelligence over time as a function of doing algebraic manipulations every day). There are some plausible benefits - it's likely to help with internal mental organization, for example. However, some thought should be given to how to set to work, in particular avoiding bad habits that eventually thwart future progress (this can happen in say, learning to play a musical instrument). Learning algebra (or any other field) conceptually is like constructing a connected map of various islands, although from reading this article it isn't clear whether that was accomplished. There's no mention of concepts like associativity, distribution, commutation, how this applies to the order of operations when you start mixing up + * - /, and the rather strange but also fundamental notion of identity. For example: https://byjus.com/maths/commutative-property/ https://byjus.com/maths/commutative-property/ This is a bit sad because understanding these concepts opens the doors to fun higher math. Matrix multiplication is generally non-commutative, and this property makes it useful for quantum mechanics calculations. Symmetry operations - rotations and reflections and so on - are not generally commutative, but are associative. This is all very important in things like protein crystallography. A solid grasp of these ideas also allows for the introduction of the concept of groups as a way of looking at algebra. Here's a great series on that whole business: https://www.socratica.com/lesson/groups-motivation-for-definition https://www.socratica.com/lesson/groups-motivation-for-defin... A good rule is to spend at least as much time understanding fundamental concepts and abstractions as on working out the results of specific explicit examples.
newbie2020 4y ago
How did he get into college without knowing algebra?? The 70s were a wild time haha
synu 4y ago
This quote reminded me of learning chess as an adult as well: > In the paper Acquiring Skill at Mental Calculation in Adulthood, Neil Charness and Jamie Campbell say that middle-aged people perform as older ones do, but if they practise, they perform more as younger people do. If speed is valued more than accuracy, the decline in ability is obvious. If accuracy is valued more than speed, the decline is less obvious and maybe not even very pronounced.
dhosek 4y ago
I’ve been tempted to pick up an adjunct section of algebra at a local community college and invert the usual style of teaching and start with word problems. A lot of people have an intuitive sense of how to figure out, say, how to scale a recipe but when it gets turned into symbolic math it becomes a challenge for them. I’d kind of like to take advantage of that and start from the word problem and then move to how to turn that into symbols so that instead of thinking y = 1.4x-2.8 we'd say think in terms of you pay $1.40 for each donut but the first two are free. If all the x² and x³ have particular meanings, you’re less like to think that x²+x³ = x⁵ but recognize that you can’t simplify the expression until you know what x is.
y0ungarmanii 4y ago
Math is so much easier when your using it to model something that is real. I remember in Physics 1 in college when the professor was going over how a baseball hits a bat and how it is modeled with all of its nth order derivatives. Everything clicked! Not to say theoretical math isn't fun though!
mikewarot 4y ago
So that's how a packer thinks! I'm a mapper[1], and it's always been a mystery to me as to how packers got that way. When I was an IT Admin, I worked with woman who VERY competent at her job, but always needed help using the computer, for even basic tasks, even with a list instructions. It took time before it dawned on me she was a packer, and my instructions weren't specific enough. I started making exact instructions for her, accounting for any possible variance in each step. (As you would in a program) Once I did that, she was thrilled, and we got along very well after that. An example of things that can throw off a packer... in Windows Explorer, drag a file from one window to another... depending on context, there are 3 possible outcomes (move, copy, shortcut creation)... that confuses the heck out of people, especially packers. https://wiki.c2.com/?MappersVsPackers

171 points by trocado 4y ago

No, but once you have learnt some algebra you'll be in a position to learn other things - electrical physics for example, or audio engineering. These subjects, and many others, use the language of algebra, because algebraic explanations are very compact and easy to follow.

deleted 4y ago
[deleted]

inetsee 4y ago

In my opinion, nothing can make you smarter. Learning rationalist techniques may make you better at thinking through problems, learning memory techniques like Memory Palace may improve your memory, using learning techniques like Spaced Repetition may help you learn and retain large amounts of information with the minimum necessary effort, but nothing can make you smarter.

water8 4y ago
What about adderall? /s
- inetsee 4y ago
  Adderall doesn't make you smarter; it just makes you more alert. It helps you focus longer on whatever intellectual task you're working on, be it problem solving or studying. (Not /s)
  - water8 4y ago
    So being able to work longer and focus harder than what would normally be physically possible is not the definition of “smarter” even if it’s temporary?
haskellandchill 4y ago
I agree you are about as smart as you will ever be. However that does not apply to me thank you very much.
jonathanstrange 4y ago
I'm pretty sure this is wrong. The brain adapts to whatever activity you do and, as far as I know, is way more plastic than researchers thought decades ago. If you're doing dumb things all the time you're making yourself dumber over time and when you're performing difficult tasks repeatedly and daily your brain adapts to them to be able to solve them easier. I realized that a long time ago in a completely different area, in martial arts. When you start it's extremely hard to follow complex movements shown by other people. Beginners struggle with this a lot. Over the years it's getting easier and easier and you can often grasp complicated movements after seeing them once. I suppose it's the same in dancing and ballet. The brain adapts to sports, painting, writing poems, or solving complex math puzzles. It just happens that some of these activities are considered smart and also (partly) measured with traditional IQ tests. You can even train to become better at IQ tests if you desire to acquire a completely useless skill set.
magpi3 4y ago
I think you have to define what "smart" means. I mean if you dropped me into some of my undergrad courses today, especially my CS courses, I would dominate like Wilt Chamberlain and people would think I am a genius. But what does it even mean to be smart anyway? I think in school a lot of the people we deem to be smart simply have more prior experience in the subject or just work very hard.

fargle 4y ago

Probably not. Knowing more stuff doesn't make you "smarter". Nor would mastering kinds of math that many people find challenging prove you are more intelligent. Clearly many intelligent people are not great at math or don't know algebra. But exercising your curiosity and practicing the art of learning will always increase your mental fitness and the ability to apply your intelligence better. It's always good to keep in shape - mentally too. I don't think it matters much what the subject is. It doesn't have to be algebra, as long as it captures your interest. Algebra is very challenging because it requires thinking in abstract concepts, so it's a great subject. It will indirectly lead to deeper understanding in many other fields too, including computer science. Intelligent people are often curious and desire to learn new things, so No I don't think learning algebra makes you smarter - but I think the desire to is a possible symptom of this kind of curiousity.

trocado 4y ago

Despite the title, I don't think the article is about algebra "making you smarter", but more whether you can learn it successfully and if by pursuing such an endeavor you can hamper age-induced cognitive decline.

mattwilsonn888 4y ago

It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the ability to understand math as anything other than a human attempting to be a computer. The author expresses his misintuition of variables - there are plenty of simple examples and thought exercises which can inform the intuition. Later he expresses getting mixed up dealing with fractions - this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions. Modern math education is spectacularly guilty of going too far too fast. Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. If the fundamentals are well understood, the applications feel trivial, intuitive, beautiful, clever - when the fundamentals are taken for granted, one word describes the relationship to the rest of the material: arbitrary.

deleted 4y ago
[deleted]
As_You_Wish 4y ago
Right. >Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. This is so true. I was exactly like the author. I could not understand any math beyond algebra. Trigonometry was way beyond my ability. But one day, I found an old trig book lying around when I went to visit my parents - it was one of my sibling's books when she took it. I picked it up and had a thought - all those people who DID understand trig and higher math were not that much smarter than me. I mean, yeah, the super smart ones were, but I'm just talking about the regular students. So I got a bug to show myself that if they could do it, then I could do it. My approach that I would do is to read the first section of the first chapter until I understood it completely and not move on until I did. I would not even move on from a sentence, or indeed a word or term, until I understood exactly what was happening. I would look all over the internet, watch youtube videos on that one single concept, or that one single word, until I understood, and I was absolutely adament about not moving on until I understood. Word by word, sentence by sentence, section by section, I rolled on. I wanted to completely completely completely understand the very very basics of trig. It was slow going, as you might imagine. Super slow. Well........all of a sudden, about 4 or 5 chapters into the trig text, my mind exploded. It was blown apart by a blinding light. In one single instant, I swear, one instant, I knew all of trigonometry. I got it. All of trig. One single instant. It was probably one of the most singular moments in my life. So I then started paging through the entire rest of the trig book, and I knew it all. I swear. I would just glance over the pages and know what everything was about. Now, I was NOT an expert, by any stretch of the imagination, I'm not claiming I became a savant. No. I'm just saying I "got" it. As you said, I has the exponential results. So exponential, it was instantaneous. >If the fundamentals are well understood, the applications feel trivial, intuitive, beautiful, clever - when the fundamentals are taken for granted, one word describes the relationship to the rest of the material: arbitrary. This is it exactly. You describe it perfectly. I did not continue on, because I actually had other things in my life that I had to move on to. But it was great because I knew then that math was easy. No doubt I could do the exact same with any math class, no doubt in my mind whatsoever. For whomever wants to do great in almost any area of study, study HARD on those first 3-5 chapters. They set the tone for the rest of the course. If you study hard on them, they remainder of the course is trivial, with some things here and there that you need help with, but for the most part it is simple.

librarianscott 4y ago

Brain games do little for the older mind. You are much better off lowering blood pressure and walking. But, if you insist, read [1]. [1]: https://www.nia.nih.gov/health/cognitive-health-and-older-adults https://www.nia.nih.gov/health/cognitive-health-and-older-ad...

bitshiftfaced 4y ago
That link did mention the "Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE)" study. Apparently it found that training can affect quality of life and reduced car accidents in driving seniors.
bamboozled 4y ago
Not sure why but this just seems so useless and defeatist. Why is learning new things “brain games”?

BirAdam 4y ago

I personally found that learning math was far easier as an adult. Like the author, I sucked in grade school. I learned multiple foreign languages. I did well in the sciences. History and geography were simple. Math? It was the one thing that escaped me. As an adult, after various misadventures, entering into college everything was different. My mind was more disciplined, my teacher was far better, and I was more humble. It was easy then.

k_sze 4y ago

The title sounds like a non-question. I posit that learning anything (even fengshui or astrology), at any age, will make you smarter, as long as you bring a pair of critical eyes with you. Besides learning about the actual “thing” (which you can still fail at the end of the day), you can always introspect to figure out why/how you failed and what your limits are, and then you’ll maybe find closure in saying “I’ve tried. It didn’t work out. There was no 'wasted potential' - the potential was never there to begin with. And I’m a wiser person now.”

dangus 4y ago
The title is there to get you to click, there's not much need to analyze it. The article has little to do with it. This reminds me of On Cinema At the Cinema when Gregg Turkington, as a parody of the film critic persona, often bases his critical opinion of the films based on what he thinks of the title and runtime.

zxcvbn4038 4y ago

I have to sit on my hands and not help my son with his math homework. The way they have taught him to do math is great - he can solve just about anything in his head - but I can’t help him without introducing him to the old slow way I learned of doing everything.

stinkytaco 4y ago
I really liked the Common Core early math curriculum. My daughter was taught to do calculations the way I had to come to them myself later on: break the problem apart into easier pieces. A simple example: If you are adding 73 and 29 break it to 70+20 and 3+9. Quick calculations takes the burden off on harder problems later on. Also, she learned to round and estimate and they did lots of practical math applications -- especially in probability -- so she's learned to think of math in a "common sense" way, for lack of a better word. It's easier for her to look at an answer and say "wait, that doesn't make any sense considering the givens".

victor106 4y ago

My friends dad in his late 60's wanted to learn math and used the No Bullshit math and physics from https://minireference.com/ https://minireference.com/ and loved it. Their Linear Algebra is quite good too.

guidorice 4y ago
I highly recommend the Ivan Savof books as well. A Statistics title is upcoming.
ivansavz 4y ago
For anyone interested, here are preview PDFs of the two books: https://minireference.com/static/excerpts/noBSmathphys_v5_preview.pdf https://minireference.com/static/excerpts/noBSmathphys_v5_pr... https://minireference.com/static/excerpts/noBSLA_v2_preview.pdf https://minireference.com/static/excerpts/noBSLA_v2_preview.... and standalone concept maps that show the prerequisite graph (very useful when learning from any book): https://minireference.com/static/conceptmaps/math_and_physics_concepts.pdf https://minireference.com/static/conceptmaps/math_and_physic... and https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf https://minireference.com/static/conceptmaps/linear_algebra_... I recently released a new book with just high school materials, specifically targeted at adult learners. Check out the website here: https://nobsmath.com/ https://nobsmath.com/
- victor106 4y ago
  Thank you. We can't wait for your stats book to be released.

rongenre 4y ago

One of my retirement goals is to redo my math degree - turns out it's really easy to get hooked up with online tutors, and I figure it's totally worth paying $20-$40 an hour to work through a textbook.

wrycoder 4y ago
If you have a math degree, you already know how to learn math. That hasn't changed. You're not going to try passing tests, so you don't really need a tutor. What you might want is a counselor to guide your "reading", as is done in places like Oxford. That can be worth the $40. All you need is updated texts, a plan of action, and maybe Wikipedia for an alternate take on sticking points. (Just using Wikipedia doesn't work well.) You could also look at the MIT or Harvard online curricula/syllabuses to get a feel for what the current subjects and texts are. Maybe take a couple of the free courses. Also, scan Kahn Academy first - that site is good for identifying holes in your background.
- waynesonfire 4y ago
  interseting.. what are these counselors? what do they do?
squeaky-clean 4y ago
Where do you find an online tutor? My first guess would be fiver but there's probably some sites with a more academic focus?

miga 4y ago

Probably yes, since past research indicates that learning delays cognitive decay. Even more, there is research pointing that continuous learning will prolong your lifespan. Best indication is a study on how university professors tend to live longer.

JKCalhoun 4y ago

"Sometimes I dreamed that there were numbers falling from the sky into chasms I couldn’t see the bottom of." Reminds me of the night terrors I had when I was younger. I remember often having dreams that involve the unknowable, unseeable or in some other way were impossible for my finite mind to comprehend. In the worst of those nightmares I was left shaken with fear — feeling as though I had peered from just over the precipice of sanity itself.

SketchySeaBeast 4y ago
As a child I experienced sleep paralysis where I would hallucinate shapes of impossible dimensions, both simultaneously incredibly large and incredibly small, hanging over my bed and leaving me to question the nature of everything. Looking back on it I can't even begin to understand why I dreamed those dreams.

363849473754 4y ago

The author also wrote this excellent article: https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

wawjgreen 4y ago

My litmus test of someone being intelligent or not--among other such tests--is what they say about Shakespeare. This might anger the Brits, but Shakespeare is garbage--and the guy says: "I read .... most of Shakespeare." One famous guy lambasting Shakespeare (Tolstoy) was only marginally smarter, because according to his "Confessions", he read it many times over (incl. in English) and STILL could not find any artistic value in it. I could not have put up with that--for me, it was the first few pages that I knew this was a waste of time. You don't need to drink the whole festering junk of a decayed meal to know it is not edible. He also claims he wants to test the limits of his intelligence by tackling Mathematics once again--implying wrongly, as it were, that math education is fine and it is our brains that are incapable of learning. Not so fast: how am I less intelligent if the bozo teaching me does not know how to teach maths? Citing Carl Jung does not help either, though he namesdrops to mitigate the shame of not being able to do maths...Jung was not as bright as is commonly believed as well. He once claimed that UFO's were all imaginary-- a sweeping generalization by someone claiming to be scientist-- whereas I for sure know that UFO's are real for I have seen one and to prove that I wasn't seeing things, I had a camcorder ready which recorded the space-ship going vertically up very slowly. I have lost the video though but it certainly happened 20 years ago and I still remember it. EDIT: I see I have touched quite a few nerves.

trebbble 4y ago
> EDIT: I see I have touched quite a few nerves. It reads like a post you made for yourself, not for the benefit of any reader.
- wawjgreen 4y ago
  Writing is always primarily of benefit to myself--and hence of any benefit to anyone else....would you cook a meal you wouldn't eat yourself but wish others did? Writing that is geared towards explicitly benefiting others (at the cost of not benefiting our own selves) is shallow, useless and fake.
  - trebbble 4y ago

Wistar 4y ago

Despite that — or, maybe, because — my father was a math academic, I did poorly in school with math beyond basic arithmetic. When I was about 25 years old, a friend gave me three algebra textbooks written by an ex-military pilot, John Saxon. In a marathon session lasting about two weeks, I went through all three books from end-to-end and really learned algebra. For whatever reasons, the Saxon books worked really well for me — better than any other learning I have ever gotten from a textbook. Yes, I was really motivated but I attribute a lot of my success learning algebra to those books. Learning that opened a lot of doors since then, mostly because my confidence in taking on matters technical was so much improved.

racl101 4y ago

My grandpa used to enjoy doing Euclid's Elements compass and straightedge constructions and understanding proofs. He also enjoyed reproducing geometric proofs of certain equations. What's funny is he hated math as a student but for some reason or other got turned onto Euclid in old age. He then tried to get my dad to read Euclid but that didn't take. Then I came across the book as teen and took an interest so Grandpa and I bonded over that.

photochemsyn 4y ago

Scientists can't agree to what extent human intelligence is inherited vs. acquired, and so asking if doing some activity x will result in an increase in personal smartness y will result in a wide variety of answers. (sort of a differential equation isn't it? Change in intelligence over time as a function of doing algebraic manipulations every day). There are some plausible benefits - it's likely to help with internal mental organization, for example. However, some thought should be given to how to set to work, in particular avoiding bad habits that eventually thwart future progress (this can happen in say, learning to play a musical instrument). Learning algebra (or any other field) conceptually is like constructing a connected map of various islands, although from reading this article it isn't clear whether that was accomplished. There's no mention of concepts like associativity, distribution, commutation, how this applies to the order of operations when you start mixing up + * - /, and the rather strange but also fundamental notion of identity. For example: https://byjus.com/maths/commutative-property/ https://byjus.com/maths/commutative-property/ This is a bit sad because understanding these concepts opens the doors to fun higher math. Matrix multiplication is generally non-commutative, and this property makes it useful for quantum mechanics calculations. Symmetry operations - rotations and reflections and so on - are not generally commutative, but are associative. This is all very important in things like protein crystallography. A solid grasp of these ideas also allows for the introduction of the concept of groups as a way of looking at algebra. Here's a great series on that whole business: https://www.socratica.com/lesson/groups-motivation-for-definition https://www.socratica.com/lesson/groups-motivation-for-defin... A good rule is to spend at least as much time understanding fundamental concepts and abstractions as on working out the results of specific explicit examples.

newbie2020 4y ago

How did he get into college without knowing algebra?? The 70s were a wild time haha

synu 4y ago

This quote reminded me of learning chess as an adult as well: > In the paper Acquiring Skill at Mental Calculation in Adulthood, Neil Charness and Jamie Campbell say that middle-aged people perform as older ones do, but if they practise, they perform more as younger people do. If speed is valued more than accuracy, the decline in ability is obvious. If accuracy is valued more than speed, the decline is less obvious and maybe not even very pronounced.

dhosek 4y ago

I’ve been tempted to pick up an adjunct section of algebra at a local community college and invert the usual style of teaching and start with word problems. A lot of people have an intuitive sense of how to figure out, say, how to scale a recipe but when it gets turned into symbolic math it becomes a challenge for them. I’d kind of like to take advantage of that and start from the word problem and then move to how to turn that into symbols so that instead of thinking y = 1.4x-2.8 we'd say think in terms of you pay $1.40 for each donut but the first two are free. If all the x² and x³ have particular meanings, you’re less like to think that x²+x³ = x⁵ but recognize that you can’t simplify the expression until you know what x is.

y0ungarmanii 4y ago

Math is so much easier when your using it to model something that is real. I remember in Physics 1 in college when the professor was going over how a baseball hits a bat and how it is modeled with all of its nth order derivatives. Everything clicked! Not to say theoretical math isn't fun though!

mikewarot 4y ago

So that's how a packer thinks! I'm a mapper[1], and it's always been a mystery to me as to how packers got that way. When I was an IT Admin, I worked with woman who VERY competent at her job, but always needed help using the computer, for even basic tasks, even with a list instructions. It took time before it dawned on me she was a packer, and my instructions weren't specific enough. I started making exact instructions for her, accounting for any possible variance in each step. (As you would in a program) Once I did that, she was thrilled, and we got along very well after that. An example of things that can throw off a packer... in Windows Explorer, drag a file from one window to another... depending on context, there are 3 possible outcomes (move, copy, shortcut creation)... that confuses the heck out of people, especially packers. https://wiki.c2.com/?MappersVsPackers