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#26 2014-04-02 09:35:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,138

Re: How to solve this?

Hi;

When we began programming computers to be intelligent we started with things that were even dumber than Justin Bieber, dumber than Rihanna. Expert systems were developed by condensing the rules of many disciplines and programmed in. The result in 90% of the cases the expert system out performed the human expert. This was all known by the late 70's. It turned out that the things humans think require intelligence such as medical diagnosis, chemistry, mathematics and chess to name a few required little! Computers could do all of those things equal to or superior to man. In other words things that "experts" do can be reduced to an algorithm. Reduced to a flowchart or a recipe.You would find it hard to believe if you do not already know, what computers find hard!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#27 2014-04-02 11:22:45

eigenguy
Member
Registered: 2014-03-18
Posts: 78

Re: How to solve this?

ShivamS wrote:

Tell that lady to first know what she is talking about. Now, if she had said "high school math is just knowing which formulas to use", I would agree with her.

I wouldn't agree with her even then.

Considering the problem, I note that it is 17(b). Further the solution makes use of something not indicated anywhere in the problem itself, namely this "7.5" term. These two bits of information, and some peculiarity in the wording points to problem 17(a) providing additional information we did not have for solving this problem.

bobbym is correct that the problem we saw has many other solutions. but I strongly suspect that had we been given the information in problem 17(a), it no longer would, and the solution there would make sense.


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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#28 2014-04-02 11:23:39

PatternMan
Member
Registered: 2014-03-08
Posts: 171

Re: How to solve this?

bobbym wrote:

Hi;

When we began programming computers to be intelligent we started with things that were even dumber than Justin Bieber, dumber than Rihanna. Expert systems were developed by condensing the rules of many disciplines and programmed in. The result in 90% of the cases the expert system out performed the human expert. This was all known by the late 70's. It turned out that the things humans think require intelligence such as medical diagnosis, chemistry, mathematics and chess to name a few required little! Computers could do all of those things equal to or superior to man. In other words things that "experts" do can be reduced to an algorithm. Reduced to a flowchart or a recipe.You would find it hard to believe if you do not already know, what computers find hard!

The computer had the rules and algorithms preprogrammed into it. If you give a computer a rigid well defined task it can out perform humans. Even those tasks that seem complicated are just computers following lots of simple rules. Virtually everything peice of human knowledge should be easy to learn because they're based on lots of simple concepts stacked on top of each other.

Now the computer can follow a lot of simple rules alone but it needs those programmed into it. The computer doesn't reason itself. It wont come up with mathematical proofs based on the algorithms in it. Unless we define how to find proofs and give the computer that code then it wont do it. If we could define what consciousness is and come up with an alorithm for it then maybe computers would become better than us at everything. Maybe we are but biological machines executing code ourselves.

I watched a video on youtube where someone made a computer do something that kinda mimicked intelligence. If they figure out a way to make AI the same as human consciousness then they'll be doing all the work from now on.

Last edited by PatternMan (2014-04-02 11:40:24)


"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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#29 2014-04-02 11:30:01

PatternMan
Member
Registered: 2014-03-08
Posts: 171

Re: How to solve this?

eigenguy wrote:
ShivamS wrote:

Tell that lady to first know what she is talking about. Now, if she had said "high school math is just knowing which formulas to use", I would agree with her.

I wouldn't agree with her even then.

Considering the problem, I note that it is 17(b). Further the solution makes use of something not indicated anywhere in the problem itself, namely this "7.5" term. These two bits of information, and some peculiarity in the wording points to problem 17(a) providing additional information we did not have for solving this problem.

bobbym is correct that the problem we saw has many other solutions. but I strongly suspect that had we been given the information in problem 17(a), it no longer would, and the solution there would make sense.

You we're right. I need to read more carefully before I start acting like two part questions are standalone ones.

tqmy.png

Last edited by PatternMan (2014-04-02 11:30:13)


"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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#30 2014-04-02 11:45:12

ShivamS
Member
Registered: 2011-02-07
Posts: 3,465

Re: How to solve this?

eigenguy, why? The math taught in high schools here in US and Canada (where I was before) is practically all memorization.

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#31 2014-04-02 12:27:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,138

Re: How to solve this?

We cannot really get very far without a memory. Just imagine forgetting everything everyday. Some amount of memorization is mandatory. I was not aware that math was taught in the US anymore.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#32 2014-04-02 12:59:52

ShivamS
Member
Registered: 2011-02-07
Posts: 3,465

Re: How to solve this?

That's harsh, but true for high schools.

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#33 2014-04-02 14:10:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,138

Re: How to solve this?

Hmmm, post #29 is not the same problem as post #1. Has a whole lot less solutions too!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#34 2014-04-02 15:29:31

eigenguy
Member
Registered: 2014-03-18
Posts: 78

Re: How to solve this?

ShivamS wrote:

eigenguy, why? The math taught in high schools here in US and Canada (where I was before) is practically all memorization.

That is the problem. It shouldn't be, andi it is because of attitudes such as this lady's that it is this way. I was fortunate enough to have a particularly good teacher in high school. He taught math as it needs be taught. Math should be understood, not memorized.

I never worry about remembering a formula, and I seldom look one up. If I cannot remember how it goes, I back off to what I do remember and re-derive it. I do this because I understand the math behind it, so deriving the formula is seldom hard to do. In fact, it is often takes me less time to rederive than it does to search it out on Google. I usually only look up formulas for areas of mathematics I haven't mastered yet. And when I do look them up, I generally search for a derivation so I can improve my understanding. (Okay - when the calculation is unusually nasty, I am happy to let someone else slog through it, and just look up the result. But such nasty calculations generally means I (or they) have not found the right approach.)


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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