Accomplishing the same task through a different set of rules

[Unity+]

I was thinking about the quote "Nothing is impossible" and it brought up the idea of carrying out a specific task the same, but with a different set of restrictions or rules applied to that task needed to be done.

 

Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how we find a way to accomplish that task another way. I find it interesting how this can be done even within a different set of rules and restrictions. So, it got me thinking that these tasks being done in a different set of restrictions can be generalized by a function that if you have found the process of completing a task within one set of restrictions then you can find the process of completing a task with any set of restrictions.

 

What does anyone think about this idea? Is it something to think about? I put this in the mathematics section because it is taking an algorithm and defining it for all set of rules.

Edited May 3, 2014 by Unity+

[Acme]

I think it is mistaken. You can't do brain surgery with a hammer and an anvil.

[Unity+]

I think it is mistaken. You can't do brain surgery with a hammer and an anvil.

It is a hypothetical. You theoretically COULD, but the likelihood of succeeding with such tools would be 1/10^n.

 

EDIT: In someways, I think this may be related to the P vs. NP problem because that problem is dealing with the question of whether a problem that currently lies in the NP spectrum of complexity can also exist in the P part of the spectrum.

 

One speculative idea that could be presented is the idea of the reflective property of distribution dealing with algorithms. An algorithm that lies in the complex part of the spectrum also lies in the reflective side of the simplicity spectrum. Though, this is merely speculative.

Edited May 3, 2014 by Unity+

[Acme]

It is a hypothetical. You theoretically COULD, but the likelihood of succeeding with such tools would be 1/10^n.

Then describe your hypothesis for hammer/anvil brain surgery. Simply saying anything is possible is baseless. Yes, many problems have multiple solutions, but it does not follow that all problems have multiple solutions or that all problems have even one solution.

[Unity+]

Then describe your hypothesis for hammer/anvil brain surgery.

I looked up the surgery process, and one way it can be done with a hammer and anvil is using the anvil to break open the upper part of the skull and then use the sharp end of the hammer cut open the tissue that remains above the brain. Then, using the hammer, complete the surgery needed to be done.

 

Remember, those solutions assume a set of particular axioms.

Edited May 3, 2014 by Unity+

[Acme]

I looked up the surgery process, and one way it can be done with a hammer and anvil is using the anvil to break open the upper part of the skull and then use the sharp end of the hammer cut open the tissue that remains above the brain. Then, using the hammer, complete the surgery needed to be done.

 

Remember, those solutions assume a set of particular axioms.

Yeah I guess that would work...if killing the patient is OK.

[Unity+]

Yeah I guess that would work...if killing the patient is OK.

You didn't say the patient had to be alive. But, all jokes aside, I my point is all of this is merely hypothetical. Same applies to the paper clip idea when finding what can be done with a paper clip.

 

I think there would have to be some set of circumstances the idea would have to apply to this.

 

EDIT: Had to fix some grammatical errors.

Edited May 3, 2014 by Unity+

[Acme]

You didn't say the patient had to be alive. But, all jokes aside, I my point is all of this is merely hypothetical. Same applies to the paper clip idea when finding what can be done with a paper clip.

 

I think there would have to be some set of circumstances the idea would have to apply to.

You mean the paper clip weight problem from that other thread?

 

Anyway, I agree this is all speculative, but not hypothetical. If you give/specify a set of circumstances then we could examine them, but the no-holds-barred layout you present just gets us nowhere fast. If by no other basis, Gödel's incompleteness theorem does not allow a generalized function as you prescribe.

 

Maybe if you give me some concrete examples that you have in mind I can apply the hammer & anvil to them.

[Unity+]

You mean the paper clip weight problem from that other thread?

I refer to the common IQ test(I think IQ?) where the task is to name as many things that a paper clip can be and do.

 

 

 

Anyway, I agree this is all speculative, but not hypothetical. If you give/specify a set of circumstances then we could examine them, but the no-holds-barred layout you present just gets us nowhere fast. If by no other basis, Gödel's incompleteness theorem does not allow a generalized function as you prescribe.

So then the function would only be generalized with limitation. Let us assume that B is a theory which contains an axiom A and we are trying to prove A using B. This is where this is contradictory because you are trying to prove something that is unprovable and therefore you assume an axiom to be a theorem within B. However, we assume that A will always be an axiom rather than a theorem because we would also assume that there is no simpler rule under alleged axiom A. Therefore, wouldn't that have to be taken into consideration?

 

 

 

Maybe if you give me some concrete examples that you have in mind I can apply the hammer & anvil to them.

You mean provide examples of tasks to complete with those tools?

Edited May 3, 2014 by Unity+

[Acme]

I refer to the common IQ test(I think IQ?) where the task is to name as many things that a paper clip can be and do.

Never heard of that one. If I took it they better have a time limit if they expect me to stop though.

 

So then the function would only be generalized with limitation. Let us assume that B is a theory which contains an axiom A and we are trying to prove A using B.

That would be a logical fallacy. (affirming the consequent?)

 

This is where this is contradictory because you are trying to prove something that is unprovable and therefore you assume an axiom to be a theorem within B. However, we assume that A will always be an axiom rather than a theorem because we would also assume that there is no simpler rule under alleged axiom A. Therefore, wouldn't that have to be taken into consideration?

"Alleged axiom" is not meaningful since an axiom is self-evident and does not require proof. While Gödel's theorem does restrict completeness in a [single] internally consistent system, it does not mean that some theorem so excluded from one system can't have a solution/proof/explanation is some other system with different axioms. This still does not mean everything is possible in some -as in at least one- system.

Edited May 3, 2014 by Acme

[Unity+]

Never heard of that one. If I took it they better have a time limit if they expect me to stop though.

 

That would be a logical fallacy. (affirming the consequent?)

 

"Alleged axiom" is not meaningful since an axiom is self-evident and does not require proof. While Gödel's theorem does restrict completeness in a [single] internally consistent system, it does not mean that some theorem so excluded from one system can't have a solution/proof/explanation is some other system with different axioms. This still does not mean everything is possible in some -as in at least one- system.

I see your points. Time to scrap this idea.

 

EDIT: Alleged wasn't a descriptor of me saying it isn't an axiom, but stating that there may be some lower system to prove the axiom that we don't know of(speculatively). However, this is already proven false.

Edited May 3, 2014 by Unity+

[Acme]

I see your points. Time to scrap this idea.

Ideas are like rabbits. You get a couple and learn how to handle them, and pretty soon you have a dozen. ~ John Steinbeck

source: >> http://www.brainyquote.com/quotes/keywords/ideas_3.html#wvqpjuPzHxgeJd1v.99

[Roamer]

I think the likelyhood of finding a solution to a problem decreases when the first solution to the problem is found;

very logical if only one solution is possible, but still applies when a hundred different solutions are possible.

(because we're much better in copying ideas instead of coming up with new ones)

[rktpro]

When I read the first post, my first reaction was of using different set of rules for problem solving. By "set of restriction" you could mean to solve a problem geometrically rather say algerically. But then, if you can do a problem one way, there might be more solutions but never infinite. What I mean is that 'any set of restrictions' can be created in infinite ways. It would be a question of ability to find another way.

[Unity+]

When I read the first post, my first reaction was of using different set of rules for problem solving. By "set of restriction" you could mean to solve a problem geometrically rather say algerically. But then, if you can do a problem one way, there might be more solutions but never infinite. What I mean is that 'any set of restrictions' can be created in infinite ways. It would be a question of ability to find another way.

Well, the idea also goes along the philosophy of "with such simple rules, there are complex results. With complex rules, there are simplistic results."

I think the likelyhood of finding a solution to a problem decreases when the first solution to the problem is found;

very logical if only one solution is possible, but still applies when a hundred different solutions are possible.

(because we're much better in copying ideas instead of coming up with new ones)

In fact, this idea has brought me to open this topic again to discussion. Though my original idea was flawed, I think there are some corrections that can be made to it. Though this is generally true, it is not always true.

 

EDIT: Adding onto this...

 

 

 

Gödel's incompleteness theorem does not allow a generalized function as you prescribe.

Could you give more detail onto why this is true? I want to have a list of ideas and restrictions that could lead to another idea I have.

 

One flaw that existed within the idea was assuming that we are dealing with an axiom rather than a theorem or set of processes. Instead, the focus should be on determining what set of axioms that process or algorithm rests in first, if that makes sense.

I think the likelyhood of finding a solution to a problem decreases when the first solution to the problem is found;

That is more a human problem rather than a problem with the amount of ideas that exist for a solution. When a process has been found for finding an idea, we generally stick to processes that lie within the range of the original process found because we find that processes that lie in range of the original will work best.

Edited May 4, 2014 by Unity+

[Acme]

...

Gödel's incompleteness theorem does not allow a generalized function as you prescribe.Gödel's incompleteness theorem does not allow a generalized function as you prescribe.

Could you give more detail onto why this is true? I want to have a list of ideas and restrictions that could lead to another idea I have.

...

 

Uhmmmm ... I ... ehrrrrr ... the uhhh ... Sorry; brain fart day. I got nuthin'.

[Unity+]

Uhmmmm ... I ... ehrrrrr ... the uhhh ... Sorry; brain fart day. I got nuthin'.

Well, post when you have got something.

[Acme]

Well, post when you have got something.

OK. In the OP you said:

...

Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how [somehow] we find a way to accomplish that task another way. ...

Gödel aside, what task did you have in mind there?

[Unity+]

OK. In the OP you said:Gödel aside, what task did you have in mind there?

Well, one task I would have in mind would be finding the prime components of a number that is made up of two large prime numbers or other problems related to the P v NP problem.

[Acme]

Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how [somehow] we find a way to accomplish that task another way.

...

Well, one task I would have in mind would be finding the prime components of a number that is made up of two large prime numbers or other problems related to the P v NP problem.

That strikes me as a contradiction in terms. Can you give some example of a math problem solved without mathematics?

[Unity+]

That strikes me as a contradiction in terms. Can you give some example of a math problem solved without mathematics?

EDIT: Why would it be a contradiction in terms?

 

The whole point is to find a possible algorithms given a particular algorithm that solves a particular task.

Edited May 6, 2014 by Unity+

[Acme]

EDIT: Why would it be a contradiction in terms?

Because you said:

Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but somehow we find a way to accomplish that task another way. ...

So that is saying in effect we can find a way to do math or physics without math or physics rules. Whether you meant that or not, that is what your words communicate and it is contradictory.

 

The whole point is to find a possible algorithms given a particular algorithm that solves a particular task.

So since the general P vs NP problem remains unsolved* then you/we can only take each specific algorithm problem on its own merits. Even then, while a problem might be verified but not solved [yet] does not say anything about whether a solution is possible or impossible. Any approach however must still follow whatever rules the problem necessitates. No magic bullets.

 

There are numerous specific examples in the full article I quote from below.

 

*

The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. ...

source: >> http://en.wikipedia.org/wiki/P_versus_NP_problem

[Unity+]

The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. ...

But what I have been trying to get at is taking algorithms that are already possible to do and use the function at discussion to find another algorithm that is more efficient.

[Acme]

But what I have been trying to get at is taking algorithms that are already possible to do and use the function at discussion to find another algorithm that is more efficient.

Possibly. It just all depends on the specifics. Not only the specific what's but the specific who's. Take Fermat's last theorem for example. Wiles' proof drew on areas of math that are relatively recent and certainly not around in Fermat's time and even when those areas were extant, no one else but Wiles put them all together to form a proof. This does not mean other proofs aren't possible by other mathematical means or that Fermat had a proof or not.

[Unity+]

Possibly. It just all depends on the specifics. Not only the specific what's but the specific who's. Take Fermat's last theorem for example. Wiles' proof drew on areas of math that are relatively recent and certainly not around in Fermat's time and even when those areas were extant, no one else but Wiles put them all together to form a proof. This does not mean other proofs aren't possible by other mathematical means or that Fermat had a proof or not.

It also goes along to proving that .9999... is equal to 1.

 

We know that 1/3 equals .333.. and 3*1/3= 1

 

There is also other proofs of this, such as 1/9 = .1111... and 1/9 * 9 = 9/9 and .999.....

 

Therefore, a similarity between those two proofs is 1/3^n * 3^n = 1.

 

EDIT: Breaking this down, 1/n^s * n^s = 1.

Edited May 6, 2014 by Unity+