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The scientific method and jigsaws.


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59 minutes ago, studiot said:

So can you apply the scientific method to jigsaws and if so, how ?

It got lost in translation, may I ask for a clarification? Are we discussing a picture cut into various pieces or a saw with a fine blade enabling it to cut curved lines?

I guess both can be approached scientifically. Unsupervised Learning within machine learning is one area where solving jigsaw puzzles is scientifically analyzed as far as I know.

Edited by Ghideon
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Thank's for the replies.

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Joigus' link

The algorithm ends when all points have been classified.

 

The method appears to be try every combination until correct fit is achieved.

Can brute force and ignorance be called 'scientific'  ?

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46 minutes ago, studiot said:

Can brute force and ignorance be called 'scientific'  ?

Brute force yes* Ignorance no. Brute force + ignorance probably no.

Here is one paper not based on brute force or ignorance:

Quote

In this paper we study the problem of image representation learning without human annotation. By following the principles of self- supervision, we build a convolutional neural network (CNN) that can be trained to solve Jigsaw puzzles as a pretext task, which requires no manual labeling, and then later repurposed to solve object classification and detection. 

https://arxiv.org/abs/1603.09246 (I have not had time to read the paper in detail)

There are several properties of jigsaw puzzles that have interesting connections to machine learning in case you wish to discuss that aspect of your question. 

 

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10 minutes ago, Ghideon said:

There are several properties of jigsaw puzzles that have interesting connections to machine learning in case you wish to discuss that aspect of your question.

 

Thank you both again for your contributions.

I agree there are interesting connections to computing.

 

This was in part prompted by my family having a large jigsaw map of the world to work on at lockdown Christmas time.

Another part of the family had a personalised jigsaw made from a closeup photograph of their family dogs on a grey sofa.

Darth Vader black has nothing on fine hair/fur on a grey featureless sofa background.

 

But in invoking the scientific method I was also considering human ingenuity as compared to something a monkey could do, given time.

 

Since neither of you are english, you may not be familiar with the english expression "Brute force and ignorance" as some method   'any fool (or monkey) could employ'.

 

 


 

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1 hour ago, studiot said:

Since neither of you are english, you may not be familiar with the english expression "Brute force and ignorance" as some method   'any fool (or monkey) could employ'.

I'm familiar with a shorter version of it, "brute force", as synonym of a not-very-refined method of solving a problem. As in,

"instead of trying to find a clever change of variables, we may try to solve the equation by brute force."

All I remember from neural networks is that it was about implementing an algorithm for "machine learning". The machine is involved in a repeated process of trial and error and the statistical weight are optimised. Something like that. @Ghideon --and other users too-- is the expert. Solving a jigsaw puzzle is kind of a paradigmatic problem for machine learning, as well as many other processes in which recognition of shapes and colours plays a part (texts in different fonts, etc.)

I consider the thread very interesting, and I'm here to learn really.

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3 hours ago, studiot said:

Since neither of you are english, you may not be familiar with the english expression "Brute force and ignorance" as some method   'any fool (or monkey) could employ'.

Think makes more sense to evaluate based on the time and the resources each method takes.

You don't want to spend forever on something the computer can brute-force for you. Password cracking for example.

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4 hours ago, studiot said:

But in invoking the scientific method I was also considering human ingenuity as compared to something a monkey could do, given time.

Are you looking for heuristics that could be developed and supported by science (models and observations) as comparison to reasonable methods that may be not scientifically tested? Example: sorting out all edge pieces that makes up the other boundary of a jigsaw is a reasonable starting point, but is it more efficient* than first sorting pieces by color?

Your question also trigger many interesting thoughts regarding a human's approach vs what the outcome would be from a computer model. I'm thinking different that heuristics may be applied; for instance if there is only one way pieces fit due to their shape then the jigsaw could (theoretically) be solved even if pieces are upside down, by only looking at shapes. But for a tessellated jigsaw puzzle the shape is not giving away information where a piece should be placed. If two pieces of a tessellated jigsaw would have an identical printed motive then there are more than one possible solution.

To me it looks like various types of jigsaws and hence the methods used to find the solution belongs to different "classes". Can these types be approached by formal mathematics**, analyzed and compared? If so that is another scientific aspect of jigsaw I guess.

I'll postpone adding more machine learning aspects until/unless you wish to dig deeper into that area, I would risk turning this post into a blog at this time. 

 

2 hours ago, joigus said:

I consider the thread very interesting, and I'm here to learn really.

I totalt agree. This triggers some healthy out of the box thinking, a good way to spend some of the time this first day on the new year***.

 

*) as measured by some agreed upon scientific way, I have no suggestion at this time.
**) I do not know what branch of mathematics that would be. 
***) according to local time zone and calendar. standards here

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