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Everyone is capable of, and can benefit from, mathematical thinking

quantamagazine.org

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Re: Everyone is capable of, and can benefit from, mathematical thinking

#261
post #206

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

Come on, get real. If people had all of their needs covered a lot more of them would sit around getting high and playing video games than perfecting their art.

[deleted]

Re: Everyone is capable of, and can benefit from, mathematical thinking

#262

Great to see so many reactions to my interview, thanks! I see that many people are confused by the interview's title, and also by my take that math talent isn't primarily a matter of genes. It may sound like naive egalitarianism, but it's not. It's a statement about the nature of math as a cognitive activity. For the sake of clarity, let me repost my reply to someone who had objected that my take was "clickbait". Thi…

> I see that many people are confused [...] by my take that math talent isn't primarily a matter of genes

Speaking only for myself, I'm not confused at all. Rather I vigorously disagree with this statement, and think that stumping for this counterfactual premise leads to cruel behavior towards children (in particular) who plainly do not have what it takes to learn, for example and in particular, algebra.

> In other words: the people who run the mathematical 100m in under a second don't think it's because of their genes.

This is not their subject of expertise, and they are simply wrong. Why? Simpson's Paradox, ironically.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#263
post #259

Earlier quoted context omitted.

I don't think UBI is feasible, it is anathema to the human condition to be content with the bare minimum. if not for our own selves, we would want the best life possible for our loved ones (present or future). my "UBI" would be a couple of million dollars. I want to learn those subjects because I enjoy learning and understanding. Life should be lived with knowledge applied through wisdom. > Could you volunteer me how…

> my "UBI" would be a couple of million dollars. There's a difference between what your human brain would become accustomed to (which you'd be right, it'd scale up and up forever) versus what would allow the base level of health and opportunity. As in, not having to worry about eating the next day. And because you're right that human brains strive for more wealth, UBI should grant you the opportunity to pursue it wit…

UBI can be used as a replacement for existing welfare programs, but you're not pursuing arts or starting a business on it. My point was, people will still prioritize earning more money when on UBI instead of pursue their passions because it won't be enough. UBI is not a safety net, if a middle class salary person fails, they would have to work hourly lower wage work, that's why they keep working their middle class job, it isn't because they fear starvation or losing their shelter.

UBI would relieve stress for the lowest earning people, but it won't result in pursuit of passion for most people. economically speaking, because most people can afford certain things (like rent) the price of those things will go up, things are priced based on what potential consumers are willing to pay. If rent costs $1000 for a specific type of unit, but suddenly everyone on UBI can afford that easily, the landlord would raise the rent, the cost of things won't remain static when wages rise for a large portion of the population. Increased demand without increased cost is loss of potential revenue. The quality of life for people on UBI would be barely surviving, and UBI would need to increase constantly to keep people from becoming homeless or starving.

This is the "Cobra effect" embodied. It provides a perverse incentive. healthcare in the US is out of control for this reason. health care providers keep increasing cost, because the patient is not the client, the insurance company is, so long as everyone is getting insurance, the cost of care is the maximum reliably predictable pay out by the insurance company. Not increasing cost is just bad business. You will have to also force all kinds of businesses from raising prices if it can work, and even when it works UBI will result in subsidizing low-wager workers for businesses, because they'll still have to work some job to afford anything outside of food,shelter and the basics.

A practical alternative to UBI is a local tax on businesses, kind of like a property tax but this tax is based on an inverse of an assessment of wages, rent, welfare pay out and other social conditions in the area. the higher wages are, lower rent is,etc.. the lower the tax is, it might even result in a credit. An inverse of a perverse incentive like UBI. Unemployment would also be partially funded through this, the unemployed would forever get a UBI like pay out so long as they are pursuing education or work of some kind based on what is in demand in their area. Businesses get a healthy talent pool to choose from and cost of living is balanced.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#264
post #252

Earlier quoted context omitted.

You get a huge variability if you consider the absolute extreme outliers. Most people should be able to reach a level of competence where they can understand mathematical concepts abstractly and apply that same reasoning to other areas, and not feel a visceral rejection at the mere idea. I think that's a modest enough standard that a good portion of any given population should be able to reach, and yet education is f…

Your statement is not backed up by data and simply wishing it should happen isn’t a strong argument. You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student) and too loose with what it means to “understand mathematical concepts abstractly”. Take an analogy: imagine professional musicians saying that most people should be able to take a piece of music and un…

Where's the data backing up what you said?

>You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student)

I was thinking "3-4 out of 5 people you pick on the street at random".

>too loose with what it means to “understand mathematical concepts abstractly”.

Enough that they could recognize whether a mathematical concept is applied correctly (e.g. if I have a 2% monthly interest, should I multiply it by 12 to get the annual interest? Why, or why not?) and conversely to correctly apply concepts they already understand to new situations, as well as to leverage those concepts to potentially learn new ones that depend on them.

>imagine professional musicians saying that most people should be able to take a piece of music and understand its harmonic structure, then apply it to a new setting to generate a new piece. Most people will reject this idea as absurd.

Okay, but we're arguing about what is the case, not about which idea has more popular support. Since most people don't understand thing 1 about composition, why should their opinion matter? A skilled composer's opinion on the matter should have more bearing than a million laymen's.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#265

Has anyone here self-taught themselves math in later life? I studied up to A level (aged 19) but honestly started hating math aged 16 after previously loving it. It’s a big regret of mine that I fell out of love with it. I self taught myself coding and Spanish and much enjoy self study if I can find the right material. Any suggestions?

Possibly making a small, focused game!

This is how I got back into learning maths... through necessity and immediate application.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#266

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

I'm an adult who's been programming computers professionally for 20 years, and went to school for it, and I've lost most mathematical skills past what I'd learned by 6th grade or so, from lack of use. People who aren't even working in a field that's STEM-adjacent have even less use for stuff past simple algebra and geometry (the latter mainly useful just for crafting hobbies and home-improvement projects) and a handf…

Do you play any games that require mathematical reasoning? You might realize you are using integration without calling it integration i.e. calculating expected values.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#267

A nice sentiment but clearly a large % of people never do learn even basic mathematical thinking and seem very confused by it. So is there some scientific study backing up the claim that all these people could easily learn it or are we just making it up because its a nice egalitarian thesis for a math popularization book?

That certain countries both now and in the past have had significantly higher mathematical ability among the general population and much higher proportions going on to further study suggests that ability isn’t innate but that people don’t choose it. In the Soviet Union more time was spent teaching mathematics and a whole culture developed around mathematics being fun.

> have had significantly higher mathematical ability among the general population

This is not really true is it? There were not that many standardized testing globally to measure such claims. Many people were in poverty and did not get tested, did not go to schools, or finished schools very early (5, 9 years). Many more kids go to school these days.

> In the Soviet Union more time was spent teaching mathematics and a whole culture developed around mathematics being fun

It is just wrong. It was the same as now, except it was critical for people to show results because otherwise you had grim perspectives in the life, there was little "fun". People wanted to get into universities to get better jobs and to get better apartments, to be able to leave their parents. You could not just buy places, but a good position in some public body would guarantee you a nice place. FYI engineers could earn more in comparison to other jobs, not to mention if you could get into defense industry.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#268

I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…

Sounds really cool. It reminds me of programming, that moment when new code starts to really sync up and code goes from being a bunch of text to more intuitive structures. When really in the zone it feels like each function has its own shape and vibe. Like a clean little box function or a big ugly angry urchin function or a useless little circle that doesn't do anything and you make a note to get rid of. I can kinda…

There's a lot of interesting discrete math that can supercharge programming at different levels of scale. What's pretty cool is that it reveals a layer of understanding when I watch my toddlers learn math from counting.

One of the interesting things is being able to exactly describe how something is an anti-pattern, because you have a precise language for describing constraints.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#269

I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…

Would you say the book ventures more into the practical side of learning this stuff or is it closer to the tone of this article? I found this article hard to gain anything from. A lot of just motivational cliche statements and nothing really groundbreaking or mind altering. If the book is better at that, I'd love to read it. If it's stories and a lot of fluff, I'd rather skip. So I'm curious what you are getting from it and how practical and applicable it feels to you?

Re: Everyone is capable of, and can benefit from, mathematical thinking

#270

Great to see so many reactions to my interview, thanks! I see that many people are confused by the interview's title, and also by my take that math talent isn't primarily a matter of genes. It may sound like naive egalitarianism, but it's not. It's a statement about the nature of math as a cognitive activity. For the sake of clarity, let me repost my reply to someone who had objected that my take was "clickbait". Thi…

> I see that many people are confused [...] by my take that math talent isn't primarily a matter of genes Speaking only for myself, I'm not confused at all. Rather I vigorously disagree with this statement, and think that stumping for this counterfactual premise leads to cruel behavior towards children (in particular) who plainly do not have what it takes to learn, for example and in particular, algebra. > In other w…

I think you really are confused. You are mistakenly equating "non-primarily genetic" with "easily teachable".

The story is much more complex than "if it's not genetic then everybody should get it". It's quite cruel to assume that if you don't get math today you'll never get it, and there are tons of documented counter-examples of kids who didn't get it at all who end up becoming way above average.

If you think that Descartes, Newton, Einstein, Feynman, Grothendieck (to just cite a few) are all equally misled on their own account because of Simpson's Paradox, which statistical result will to bring to the table to justify that YOU are right?

By the way, Stanislas Dehaene, one of the leading researchers on the neuroscience of mathematical cognition, is also on my side.

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