Thread: Ansatz

From wiki:

In physics and mathematics, an ansatz (/ˈænsæts/; German: [ˈʔanzats], meaning: "initial placement of a tool at a work piece", plural Ansätze /ˈænsɛtsə/; German: [ˈʔanzɛtsə]) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.^[1]

Until yesterday I’d never heard this term but math not something I can be comfortable with. Ansatz appears to me like a form of cheating, like scientists who ignore experimental evidence that’s contrary to their opinions. Always thought mathematicians dealt in absolute truths. I don’t qualify to critique mathematician methods, so perhaps someone could clue us in on how commonplace an Ansatz is in their work.

I don't think this is "cheating". Sometimes you don't have all the info you need to move ahead with a problem so you start playing "what ifs". Sort of "if I make this assumption that may help me do I advance our understanding and what are the implications". It is always understood that this assumption will ultimately have to be either justified or discarded later. A good example is Planck's hypothesis to explain black body radiation. At the time no one believed this was true but if it was assumed theory fit experiment whereas before they disagreed badly. Exploring the implications of this hypothesis led to Einstein's Nobel Prize and quantum mechanics.

Originally Posted by zinjanthropos

From wiki:

In physics and mathematics, an ansatz (/ˈænsæts/; German: [ˈʔanzats], meaning: "initial placement of a tool at a work piece", plural Ansätze /ˈænsɛtsə/; German: [ˈʔanzɛtsə]) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.^[1]

Until yesterday I’d never heard this term but math not something I can be comfortable with. Ansatz appears to me like a form of cheating, like scientists who ignore experimental evidence that’s contrary to their opinions. Always thought mathematicians dealt in absolute truths. I don’t qualify to critique mathematician methods, so perhaps someone could clue us in on how commonplace an Ansatz is in their work.

I don't see this as cheating at all. The goal is to figure things out. How is it cheating to figure things out more quickly? There are lots of commonalities in nature, so it would be foolish not to recognize that truth and make use of it as a creative spark. As with other things in science, you then check the result. Who cares how one gets an inspiration? You make a guess, then check it. If you make a guess that is based on something with some common elements, I'd call that a potentially much smarter guess than a totally random one.

Originally Posted by tk421

I don't see this as cheating at all. The goal is to figure things out. How is it cheating to figure things out more quickly? There are lots of commonalities in nature, so it would be foolish not to recognize that truth and make use of it as a creative spark. As with other things in science, you then check the result. Who cares how one gets an inspiration? You make a guess, then check it. If you make a guess that is based on something with some common elements, I'd call that a potentially much smarter guess than a totally random one.

‘Cheating’ was a poor choice of words I admit. It’s just that I don’t associate guessing, albeit educated, with mathematics. I realize now that it does. Surely some calculations don’t require any guesswork. IOW I don’t need to assume 1+1=2. I just hope the assumed answers aren’t made by guys building a bridge or sending a craft to Mars but that may be how they do it, IDK. Maybe it’s just my lack of mathematical prowess that makes me think math has one exact answer and perhaps some that are reasonably close. Is this educated guesswork related in a way to the Uncertainty Principle?

Generally speaking, it is much easier to prove that a solution to a given maths problem is correct than to derive that solution in the first place. Thus, if one can obtain the solution by some form of shortcut, guess, oracle, or whatever, then by proving that the solution is correct, we do indeed have the correct solution without the difficulty of properly deriving that solution. If the correct solution is all we need, then a proof will suffice.

Is this educated guesswork related in a way to the Uncertainty Principle?

No.

Originally Posted by zinjanthropos

Originally Posted by tk421

I don't see this as cheating at all. The goal is to figure things out. How is it cheating to figure things out more quickly? There are lots of commonalities in nature, so it would be foolish not to recognize that truth and make use of it as a creative spark. As with other things in science, you then check the result. Who cares how one gets an inspiration? You make a guess, then check it. If you make a guess that is based on something with some common elements, I'd call that a potentially much smarter guess than a totally random one.

‘Cheating’ was a poor choice of words I admit. It’s just that I don’t associate guessing, albeit educated, with mathematics. I realize now that it does. Surely some calculations don’t require any guesswork. IOW I don’t need to assume 1+1=2. I just hope the assumed answers aren’t made by guys building a bridge or sending a craft to Mars but that may be how they do it, IDK. Maybe it’s just my lack of mathematical prowess that makes me think math has one exact answer and perhaps some that are reasonably close. Is this educated guesswork related in a way to the Uncertainty Principle?

You're still misunderstanding this idea at quite a fundamental level. KJW expressed it very well, so I would recommend looking more closely at what he wrote. But your basic misunderstanding is that you seem to think that the guessing part is the end. It's not. It's the beginning. Then we check it. If it's found to be false, we discard it and try something else. If it's found to be correct, then great!