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On Oct 12, 2022, at 2:55 PM, Prof. Keith S. Taber via Phys-l <phys-l@mail.phys-l.org> wrote:
On 12/10/2022 17:36, Philip Keller via Phys-l wrote:
Well it is a kind of game! I am eager to hear the interpretations that
give 1,5,12... or 1,5,14.... I just see 1,513.
I thought the point being made was it can be seen to represent the basic nature of inductive sciences, in that there are always multiple ways to explain any data set (although we might prefer those which we think show simplicity, elegance, etc.) A theory or law is always underdetermined by the data available. (Any number of points on a graph can be connected y multiple curves - even if the points all lie on a straight line that does not prove anything. Consider a graph of a sine function where you have only the points representing the maximum amplitude, or any set of points that are multiples of the wavelength apart - the best guess would be a straight line.) Or perhaps I misread the intention.
So the problem setter may have been thinking of a rule (e.g., count all triangles) that led to 1, 5, 13, but it could be something less straightforward.
One of my twelves was simply the sum of the number of small triangles plus the number 'diamonds' formed by two triangles: 1; 4+1=5; 9+3=12
Also the number of small triangles pointing up plus double the number of those pointing down gives 1; (3+2x1=) 5; (6 +2x3 =) 12
If you have the number of small triangles plus the number horizontal lines minus 1 you get (1+1–1=) 1; (4+2–1=) 5; (9+3-1=) 11
If you give a value of 1 to triangles in the the bottom row, 2 to those in the second row, 3 to those n the third: 1; 3+2 = 5; 5 + 6 + 3 = 14
I am sure there many other rules that could be created… but ars longa vita brevis as Emerlist Davjack reminded us.
Best
Keith
--
“there is no ‘scientific worldview’ just as there is no uniform enterprise ‘science’ - except in the minds of metaphysicians, schoolmasters, and scientists blinded by the achievements of their own particular niche” <https://science-education-research.com/commonplace/>
Dr. Keith S. Taber
Emeritus Professor of Science Education
University of Cambridge
http://www.educ.cam.ac.uk/staff/taber.html
Senior Member
Homerton College, Cambridge
https://science-education-research.com
Some recent postings include
Falsifying research conclusions. You do not need to falsify your results if you are prepared to draw conclusions contrary to the outcome of your data analysis. <https://science-education-research.com/falsifying-research-conclusions/>
Delusions of educational impact. A 'peer-reviewed' study claims to improve academic performance by purifying the souls of students suffering from hallucinations <https://science-education-research.com/delusions-of-educational-impact/>
Can deforestation stop indigenous groups starving? <https://science-education-research.com/can-deforestation-stop-indigenous-groups-starving/>
How much damage can a couple of molecules do? Just how dangerous is Novichok? <https://science-education-research.com/how-much-damage-can-a-couple-of-molecules-do/>
Of mostly natural origin. Is your shampoo of natural, unnatural, or supernatural origin? <“https://science-education-research.com/of-mostly-natural-origin/”;>
Bats are [almost certainly] not closely related to viruses. <“https://science-education-research.com/bats-are-almost-certainly-not-closely-related-to-viruses/”;>
Recently published scholarship:
*Taber, K. S. (2019). Experimental research into teaching innovations: responding to methodological and ethical challenges. *
/Studies in Science Education./ doi:10.1080/03057267.2019.1658058
*/The Nature of the Chemical Concept/*/: Re-constructing Chemical Knowledge in Teaching and Learning/
Royal Society of Chemistry, https://pubs.rsc.org/en/content/ebook/978-1-78262-460-8
*Taber, K. S. (2021). The Challenge to Educational Reforms during a Global Emergency: The Case of Progressive Science Education./C.E.P.S. Journal/, 11 (Special issue), 1-21. doi:doi: 10.26529/cepsj.1109*
Recent publications primarily for teachers:
*/Foundations for Teaching Chemistry/*/: Chemical knowledge for teaching/
Routledge, ISBN: 9780815377740
*/MasterClass in Science Education/*/: Transforming Teaching and Learning/
Bloomsbury Academic, ISBN: 9781474289412
Editor-in-Chief: */RSC Advances in Chemistry Education Series/*
Royal Society of Chemistry Book Series
Proposals for Advances in Chemistry Education volumes (edited or monograph) are invited. Scholarly books on all aspects of chemistry education are being considered for publication in the series ( https://science-education-research.com/advances-in-chemistry-education/ )
*ECLIPSE - /Exploring Conceptual Learning, Integration and Progression in Science Education/*
https://science-education-research.com/projects/eclipse/
*Reject publisher contracts that ask you to waive your legal rights*
Authors are granted the 'moral' right to protect the integrity of their works in law.
There is no reason for reputable academic publishers to ask authors to allow them to be able to make changes of any kind, at any time, to authors' works, without the author's approval.
Scholars should not be prepared to abandon their legal right to object to changes that undermine the integrity of their scholarly works.
Academics should refuse to sign publishers' contracts that include clauses that require authors to waive their legal moral rights.
Sign a petition to ask publishers to respect authors' legal rights: *https://science-education-research.com/academic-standards/defend-the-moral-right-to-the-integrity-of-your-scholarly-work/*
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