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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

#71

Post by nateabele »

Here's a concrete example of what this is about:

"Conventional programming languages are growing ever more enormous, but not stronger. Inherent defects at the most basic level cause them to be both fat and weak [...] inability to effectively use powerful combining forms [...] lack of useful mathematical properties for reasoning about programs." [0]

It goes without saying that mathematics is at the root of computer science, but we've gotten so far away from those roots, which is why we're reaching the upper bounds of complexity that can be foisted upon our old, broken way of thinking. Time to go back to basics.

[0] https://web.stanford.edu/class/cs242/readings/backus.pdf

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

#72

Post by GuiA »

Retra wrote: post #62
jandrewrogers wrote: post #58

Earlier quoted context omitted.

All things that exist are mathematical objects and programs. Algorithmic information theory asserts that my cup of coffee is actually a program. While mathematics is important to computer programming, for most practical purposes it is of limited utility unless you are inventing new computer science. Knowing how to use a relational databases correctly requires no formal set theory. Understanding how to build a massive…

Mathematicians need to be more open to accepting computer programs as results. It's one of the reasons we need better programming languages.

The problem with accepting computer programs as results is that they require much more scrutiny, as computer programs typically incorporate structures that are irrelevant to the result and yet may affect it (think memory leaks, etc). Mathematical proofs are a "pure" program, unencumbered by the technicalities of the real world.

As far as better languages for math, you'll enjoy this article + HN discussion: https://news.ycombinator.com/item?id=9572426

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

#73

Post by yellowapple »

sanoli wrote: post #61

Teach kids basic arithmetic WELL, teach them logic in a fun way, find a way to get them to like reading and think critically about what they read. That's fine for me. I'd do away with all the rest of math (algebra, trig, etc) and have it as optional in high school. Really, if you got the stuff above right as a kid, you don't need to learn trigonometry if you don't want to at the time.

I'd personally throw in something like geometry, which (at least when I took it back in my middle school days; maybe my experience was atypical) had a heavy emphasis on mathematical proofs, how they worked, why they were important, the differences between postulates and theorems, how to prove theorems, etc. Whereas most of my prior and future math courses (particularly algebra) ended up feeling like an endless barrage of busywork, geometry forced me to actually think about what I'm doing.

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

#74

Post by thewarrior »

Every profession has a tendency to overstate it's own importance. In the eyes of programmers , we are misunderstood , under appreciated and people don't fully grasp our worth.

Management thinks that they're the real movers and shakers , having to take all the risk , make all the tough decisions , while having to deliver results while being saddled with sometimes recalcitrant and inefficient teams.

Mathematicians feel that they are the ones at the vanguard of progress and are angered by the fact that people have the temerity to say that they don't "get" math or have any use for it in real life.

Though Delmania's comment skirts dangerously close to what pg might call a "middlebrow dismissal" , he makes a very important point. Our increasingly unequal economy and limited opportunities are forcing us to increasingly push ourselves harder and into a fierce cycle of competition that is destroying us.

Some lessons in Humility , Resilience and Self acceptance would do us a world of good.

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

#75

Post by hsitz »

thewarrior wrote: post #69
Delmania wrote: post #16

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness/Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance Then we can focus on what area the person can best contribute in. Not everyone is going to suited for a job in programming…

Not exactly related , but my grandmother often tells my parents : Pray to god that you and your children have long lives. Whatever comes afterwards , we can endure.

What is this supposed to mean? I don't see it as anything wise or insightful. It just sounds strange. Am I missing something?

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

#76

Post by aaggarwal »

cousin_it wrote: post #45
Delmania wrote: post #16

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness/Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance Then we can focus on what area the person can best contribute in. Not everyone is going to suited for a job in programming…

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.

Due to the tremendous population growth, and higher standards of living of human population, I think it will be extremely difficult to achieve the kind of dream your talking about. Nevertheless, this dream would have to go through better education at all levels.

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

#77

Post by davidamarquis »

parasubvert wrote: post #6

Why place one body of knowledge in front of the other like this? Everything has to be a competition with some people. It's always been a mistake to believe math is somehow more noble than programming. Best explanation as to why comes from the preface of SICP by Abelson and Sussmann: "Underlying our approach to this subject is our conviction that ``computer science'' is not a science and that its significance has litt…

Where did you get nobility from. This isn't the author's point at all. Obviously knowledge about different areas of knowledge can be of more practical benefit at different times. The point is that in the next few years knowledge of math will become relatively more valuable and programming relatively less valuable.

Regarding the quote, it is a best a great oversimplification. Mathematicians have been interested in computation for a long time. See the Euclidean algorithm for example. Interestingly its computational complexity was worked out a hundred years before computer science was even considered a subject. Many great mathematicians like Gauss also had a keen interest in computation. A description of the fast Fourier transform was found in his notes after he died.

It is true that mathematical theorems have historically not been written from a computational point of view. But many many theorems can easily be turned into an algorithm (anything based on induction for example). Mathematics has many different subfields and the number of such constructive theorems varies based on the area. However, constructive arguments in mathematics are so pervasive that I think it is silly to even try and separate computation and mathematics as separate ways of thinking.

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

#78

Post by crimsonalucard »

thewarrior wrote: post #74

Every profession has a tendency to overstate it's own importance. In the eyes of programmers , we are misunderstood , under appreciated and people don't fully grasp our worth. Management thinks that they're the real movers and shakers , having to take all the risk , make all the tough decisions , while having to deliver results while being saddled with sometimes recalcitrant and inefficient teams. Mathematicians feel…

>Management thinks that they're the real movers and shakers , having to take all the risk , make all the tough decisions , while having to deliver results while being saddled with sometimes recalcitrant and inefficient teams.

It is by far easier to imagine something than it is to make that imagination real.

It is by far easier to tell someone what to do then it is to do it.

Management is by far easier than engineering.

Management, however, is still a dramatically different skill than engineering, and it is a skill that is important.

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

#79

Post by Retra »

GuiA wrote: post #72
Retra wrote: post #62

Earlier quoted context omitted.

Mathematicians need to be more open to accepting computer programs as results. It's one of the reasons we need better programming languages.

The problem with accepting computer programs as results is that they require much more scrutiny, as computer programs typically incorporate structures that are irrelevant to the result and yet may affect it (think memory leaks, etc). Mathematical proofs are a "pure" program, unencumbered by the technicalities of the real world. As far as better languages for math, you'll enjoy this article + HN discussion: https://ne…

Those 'technicalities of the real world' are the things that lead to new and interesting mathematics. Maybe your 'whole number' concept doesn't properly model different kinds of measurement. Maybe you've got to iterate a couple time on the definition of 'smooth function' before you find one that's useful for modeling actual observations.

Mathematics is not unencumbered by the real world. It's just highly focused on specific classes of encumbrance. (If I put two marbles in an empty sack and poured out three, you can bet mathematicians would be interested in this new kind of arithmetical behavior, and try to model and explain it. Though talking to mathematicians, I get the impression they are so far up in the ivory tower, they think it isn't connected to the ground at the bottom!)

Our programs are not easily factorable. It is hard to separate different interactions across different problem domains. That's a problem of the language, not of the 'purity' of the program. Well, arguably. You could see it the other way, too, I guess.

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

#80

Post by tzs »

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 water, they had to leave their cave and go find running water. On a night like this, they would have to choose between thirst and going out in terrible weather.

In my apartment, I simply turn the handle on a faucet, and as much water as I want is instantly available. No need to leave the apartment when I get thirsty.

If I want to be in rain for some reason, such as to wash, I simply step into the shower and it will rain on my command, at whatever intensity I want, at whatever temperature I want. My ancestors would have to wait for rain, and accept whatever intensity and temperature that it happened to be.

If I get cold, I turn the thermostat up, and minutes later the temperature is to my liking. My ancestors would have to move around in their cave and hope to find a warmer spot, or build a fire and trade away clean air for some warmth.

If I want to do something that needs light and it is night out, I flip a switch and I have light. I can adjust the brightness to anything from just enough to get around to enough to do anything I can do in full sunlight. My cave dwelling ancestors would have to use fire for light at night, messing up the air of their cave and only partly lighting their home.

If I want to enjoy a gentle breeze, I turn on a fan. They had to go outside.

I then got to thinking about how if my ancestors could see me, they might think I was some kind of god as I summon running water, rain, wind, light at will, and control the temperature.

Then I realized that if they were put in my apartment and I in their cave, they would be able to do all that I can do after a couple minutes instruction...and I would have no idea how to actually make a fire.

I'm not a god compared to them. I just found a better cave.

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