Two scientists obtained independently the same result theoretically. One used sophisticated mathematics, another simple algebra. They started with different assumption, but came to the same result.
If you need to quickly solve the problem, it is natural to apply a simple method.
If you need to develop tools for solving the problem, it is necessary to use all methods.
Both approaches are acceptable. Because both approaches enable us to develop a theory of the investigated subject. Furthermore, confirmation of a different theory methods amplify such a theory.
I´m not sure how to vote. If you use identical assumptions but different methods, I want to agree with Vyacheslavs statement. If you use different basic assumptions but end in the same result I have doubts that either method is correct. In such cases I tend to examine the assumptions very thoroughly.
Always the simplest ! COST (TIME) VS. BENEFITS
Why to do things more complex if they could be simpler?
SOME OTHER think:
Why to do things simpler if thet could be done more complex?
THE ANSWER IS EVIDENT: : Simple Algebra
Alexander
A very interesting observation. My experience is utilizing complicated mathematical analysis looks elegant and at the same time generally provides a solution in far fewer steps. However to understand people need to have extra skills. That may often be a difficult proposition so that many may not be able to appreciate.
On the other hand simple algebraic procedures require many more steps to arrive at the solution. The main advantage is that many people will be able to understand the procedure because everyone is conversant with basic algebra, and will be able to appreciate more.
If you need to quickly solve the problem, it is natural to apply a simple method.
If you need to develop tools for solving the problem, it is necessary to use all methods.
..perhaps the point is not simplicity but rigurosity...sometimes simpler methods are more clear and easy to follow or correct...fancy methods can hide mistakes easier and only an "elite of experts" can test them and "replicate"...so they can be abused.
If you want is certanty in the results, simpler methods can be better; if you look new avenues for math, the complex methods can be more interesting.
I should prefer the simple algebra approach.
The most sophisticated could be desirable if it could show us a new route to search for new experiments and new theoretical results. Otherwise it is just a mental gymnastic.
@Alexander, simple solutions are more elegant! I prefer simple algebra solutions whenever is possible. Unfortunately, it is very rare in my scientific field!
Dear Alexander, could you comment please, what you mean with different assumptions, I´d like to see an example.
It depends of the purpose, if the need is theoretical approach, the complex formalism is better as it is more related to general philosophy.. If the need is related to a specific problem, algebraical solution is better, simple to implement and more accurate...However the 2 methods must result to same data when used for the same problem.
Could you propose a simple example illustrating all this, either hypothetical or from history of science?
The simple algebra, if only if, the assumptions ensure the structure of the mathematical object (s) under consideration are correct.
If we want that the information is understood by as many people as possible, the simpler the better
In my opnion you should use the simplest mathematical solution.
However the solution must be appropriate to the problem that is being treated.
Thank you.
"Alexander et all, here is something that speaks itself that simple is better in the area of programming!
http://www.simple-is-better.org/
Concerning Ljubomir's answer. Programming is different from mathematical (analytical) solution! I would prefer simple and clear code - for debugging purposes. At the same time, there are different criteria: robustness, time, etc., where simple code is not always the best.
In mathematics. First of all, algebra is philosophy of mathematics. It could be quite complicated :-)....
There are different levels of proofs. I would prefer generalized proofs, when you see the problem in general, as a part of a bigger problem.
Another important criterion is beauty. Ingenious solution is simple, beautiful and short.... And correct:-)...
Just a note. Using "complicated" math is like using building blocks in construction building. Somebody else has done main job for you. You just put blocks together. It's easy! It does not necessarily mean that you understand the problem though. It might seam simple, but it is not...
An example. It speaks fot itself. I had to find an optimal solution for a distribution problem. The problem was simple, it would take me at most a day to solve the problem analytically, to write a simple code and to implement it. It was simple and easy and not costly at all: they did not pay me to much:-) ... My officials decided differently. They bought quite expensive software, very expensive. It was for much more complicated problem. In order to use it, I had to enlarge my problem, to add useless artificial data, which did not exist in reality, just to adjust my problem to given software. It took me about a week to do all necessary adjustments. They explained:
- Lucy, we need approach, which would not require thinking. If you decided to leave our company, we would not know, what to do with your solution...
The original problem was really very simple...
Usually, the broader the assumptions, the more complicated mathematics is required. But then, the researcher can see that he can not obtain an analitical sulutions on these premises, so, he/she start to narrow assumption, which allow him mathematical simplifications.
Another researcher starts his consideration with these reduced assumptions, so, he has simple mathematics from the beginning. As a result, both researchers obtain identical results.
- Badges
- Science topic
- Similar topics
- Mathematics