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What the Next Generation Needs Is Math, Not Programming

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Re: What the Next Generation Needs Is Math, Not Programming

#81

Post by yellowapple »

veddox wrote: post #37

> Today, we can get away with ‘knowing’ how Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that. Part of the advancement of technology is that fewer and fewer people actually understand how stuff works. What percentage of the population has any notion of how a computer works under the hood? How many people understand how our national power grid works? Our se…

I'm suddenly reminded of the episode "When the Bough Breaks" from Start Trek: TNG. Long-lost hyperadvanced planet-society finds itself infertile and unable to sustain its own population, steals kids from Enterprise to teach them how to be a generation of little Mozards and Rembrandts; Enterprise rescues kids and in the process figures out that said hyperadvanced society - having focused entirely on arts and humanities - forgot even the most basic understanding of the technologies they relied upon and were now falling victim to radiation poisoning brought on by ozone depletion and the power plant they were using to power their tech. Scaling down the power plant's energy production and reseeding the ozone layer implicitly fixes the fertility issues, at the cost of the long-lost planet now no longer being long-lost and the additional cost of the planet's inhabitants pledging to learn more about their technologies instead of blindly depending on them.

Moral of the story: make sure understanding of relied-upon technologies is prioritized, lest they bite you in the rear later.

Re: What the Next Generation Needs Is Math, Not Programming

#82

Post by cousin_it »

strictnein wrote: post #68
cousin_it wrote: post #45

Earlier quoted context omitted.

What the next generation really needs is an economy where everyone can make a decent living with a modest effort, without having to desperately "outcompete" other job seekers. The US had that kind of economy at some point. Since we haven't lost any arcane secrets since then, it must be still achievable today.

What's a "modest effort"? And when did we have an economy based on a "modest effort"? Work has never been easier in the US than it currently is. Record number of office workers, minimal number of farmers, factory workers, and manual labor in general.

Take a look at the Beat Generation books. For these folks it was not just possible, but normal, to travel across the US and find a job in every town they stopped.

Re: What the Next Generation Needs Is Math, Not Programming

#83

Post by pavedwalden »

cynicalkane wrote: post #67
cousin_it wrote: post #45

Earlier quoted context omitted.

What the next generation really needs is an economy where everyone can make a decent living with a modest effort, without having to desperately "outcompete" other job seekers. The US had that kind of economy at some point. Since we haven't lost any arcane secrets since then, it must be still achievable today.

The "decent living" of past generations is still available today, but past generations were poorer than you think they were, particularly for those who don't come from white and privileged backgrounds.

Although almost everyone is better off in material terms than they were two generations ago, I fear that the level of wealth required to live a "comfortable" life may have outpaced that increase. How many hours does a blue collar worker have to put in to live close to a grocery store and good schools? How much time do the working poor spend commuting? If you break your arm, what percentage of your income will be consumed by medical costs?

I don't have any data on this, but it's my hunch about why there's so much economic resentment these days.

Re: What the Next Generation Needs Is Math, Not Programming

#84

Post by JoeAltmaier »

tzs wrote: post #80
veddox wrote: post #37

> Today, we can get away with ‘knowing’ how Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that. Part of the advancement of technology is that fewer and fewer people actually understand how stuff works. What percentage of the population has any notion of how a computer works under the hood? How many people understand how our national power grid works? Our se…

That reminds of some idle thoughts I had several years ago, when I lived in an apartment, during a storm. It was a dark and stormy night. The rain was coming down hard, and there was a good bit of wind. It was not a night you would want to be outside in. As I sat in my dry, warm, lighted apartment I got to thinking about how different life was compared to my distant cave dwelling ancestors. If they wanted a drink of…

Ok, but 'we' are gods compared to them. We've build a better society together. You can take some pride in your part in that!

Re: What the Next Generation Needs Is Math, Not Programming

#85

Post by graycat »

Here is some of why the OP is correct:

From 50,000 feet up, we take in data, maybe already have some other data, manipulate all that data, and get results we want to be powerful, valuable, etc.

This little process is more important now because computers let us do much more in the data manipulations.

That said, there is a remaining question: What manipulations should we have the computers do?

Shockingly often in the past, we understood the manipulations well enough to program them because we were largely just programming what we had done or in principle knew how to do just manually.

But, as we have programmed more of what we knew how to do manually, we will want more powerful, valuable manipulations.

Well, often the best approach to more powerful, valuable manipulations will be via mathematics. There, we can look at reality, see some situations or properties that appear to hold, let those be assumptions for some mathematics, that is, hypotheses for some theorems, proceed with theorems and proofs, get some mathematical results, and use those to say what manipulations to do.

E.g.: (1) Statistical hypothesis tests. (2) Systems of ordinary differential equations as growth models. E.g., what would happen if we released 1000 healthy US bobcats into the outback of Australia? (3) For real time local delivery, which vehicle takes the next order that comes in so that we can meet promises to customers and minimize expected delivery cost? (4) Pick a part of the ocean, drill a lot of oil wells; now, what should the sea floor oil pipeline network look like to carry the oil to where we want it meeting safety standards and minimizing cost, e.g., expected net present value over the life of the oil wells? There are many more such.

For such problems, data manipulations from theorems and proofs, sometimes new, can knock the socks off any other approach, e.g., intuitive heuristics.

That's some of the future of math, especially in what gets programmed.

Re: What the Next Generation Needs Is Math, Not Programming

#86

Post by Grue3 »

gizi wrote: post #44

According to the Curry-Howard correspondence, all mathematical proofs are actually programs. This is normal. A proof is a series of steps, and if you unambiguously describe these steps, a computer will obviously be able to execute them. Furthermore, since Alonso Church successfully proposed a Turing-complete axiomatization based on just functions (even numbers are just functions), a computer program is clearly a math…

>SQL is pretty much Zermelo-Fraenkel on steroids.

I didn't know SQL allows for infinite sets. In fact, most commonly used subset of SQL is non-Turing complete and decidable, while ZF is not decidable.

Re: What the Next Generation Needs Is Math, Not Programming

#87

Post by shmerl »

cynicalkane wrote: post #67
cousin_it wrote: post #45

Earlier quoted context omitted.

What the next generation really needs is an economy where everyone can make a decent living with a modest effort, without having to desperately "outcompete" other job seekers. The US had that kind of economy at some point. Since we haven't lost any arcane secrets since then, it must be still achievable today.

The "decent living" of past generations is still available today, but past generations were poorer than you think they were, particularly for those who don't come from white and privileged backgrounds.

> The "decent living" of past generations is still available today,

Not if all your resources are sucked by insane rent / housing prices.

Re: What the Next Generation Needs Is Math, Not Programming

#88

Post by enraged_camel »

strictnein wrote: post #68
cousin_it wrote: post #45

Earlier quoted context omitted.

What the next generation really needs is an economy where everyone can make a decent living with a modest effort, without having to desperately "outcompete" other job seekers. The US had that kind of economy at some point. Since we haven't lost any arcane secrets since then, it must be still achievable today.

What's a "modest effort"? And when did we have an economy based on a "modest effort"? Work has never been easier in the US than it currently is. Record number of office workers, minimal number of farmers, factory workers, and manual labor in general.

Easier in terms of lack of manual labor perhaps, but white collar work has its own unique challenges. I don't think it's fair to rate difficulty of work on a linear spectrum.

Several years ago I worked on a farm for a few months helping out a relative. It was exhausting work, but I found it much easier than some of the programming work I do as a living.

Re: What the Next Generation Needs Is Math, Not Programming

#89

Post by OvidNaso »

gizi wrote: post #44

According to the Curry-Howard correspondence, all mathematical proofs are actually programs. This is normal. A proof is a series of steps, and if you unambiguously describe these steps, a computer will obviously be able to execute them. Furthermore, since Alonso Church successfully proposed a Turing-complete axiomatization based on just functions (even numbers are just functions), a computer program is clearly a math…

If you want to extend even furthur into the metaphysics, it was Wolfram's "New Kind of Science" which (certainly not first) proposes that it's the computational universe that comes first given rise to the mathematical realism one.

Re: What the Next Generation Needs Is Math, Not Programming

#90

Post by vog »

haphazardeous wrote: post #7

This depends on how people learn and perceive information. If I hadn't learnt programming before I was taught Maths and Calculus, I probably wouldn't have understood some of the basics like Functions, Matrixes and Series etc or it would have taken me quite a while to grasp the idea. For me Maths is boring. It's abstract and you don't have any interaction whereas programming is more fun for me. I never truly understoo…

Indeed, programming something is a great trick to get a deeper understanding of it. It means writing everythin down to the details that even a dumb machine can understand it.

I guess this is like understanding something better by explaining it to others. Just that this "other person" is a machine. It is also well-known that it even helps to explain it to your own, by writing it down. For example, PG noted that in the introduction of http://paulgraham.com/writing44.html

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