[seqfan] Re: Miis France and OEIS
M. F. Hasler
oeis at hasler.fr
Mon Feb 7 16:39:05 CET 2022
Well, the 1 + 3 considered "reasonings" are already outlined in the article
:
0 - Obviously "equal" does not mean "identical / same" but a different
binary relation.
1 - If the relation is reflexive, the answer is 5
2 - If the relation is symmetric, the answer is 1
3 - The relation is not an ("acceptable") function, because OEIS does not
contain the subsequence (5, 25, 605, 10855)
Obviously, the last reasoning is more than flawed, so Olivier's suggestion
of polynomial extrapolation is understandable although explicitly ruled out
in the article with the OEIS "argument". (Also, it sounds misleading when
Olivier writes "not exclusive",
because (1) and (2) obviously *are* (mutually) exclusive! Which actually
appears to be a main "reason" (although invalid) why (2) should be
preferred to (1): "given that 1 is equal to 5, 5 *must* be equal to 1 and
can't be equal to 5...".)
I find it intriguing that the "popular verdict" (and author of the quiz)
considers symmetry more fundamental than reflexivity.
Usually we always teach that "the properties defining equivalence relations
are (r), (s), (t)"
in that order, probably the most easy to memorize, since r,s,t are
consecutive letters in the alphabet,
and the respective properties are unary, binary and ternary, i.e., using 1,
2 resp. 3 variables
(and you will often prove the properties in that order in view of the
increasing complexity).
So I think in any possible regard, reflexivity should be considered before
symmetry.
It might be interesting for experts to study why non-mathematicians
consider "1 equals 5, so 5 equals 1" more natural than "5 equals 5"...
I reply to this threat also because I also frequently encounter a similar
"weirdness" on instagram:
One of the most popular "series" of math "tiktok's / shorts / reals" (to
reuse r,s,t reversed),
besides the infamous "2 / 1 (1+1) = 1 or 4 ?" with the disputable argument
that the multiplication must be made after the division
(while again most mathematicians would read 1/2x as 1/(2x) and not
(1/2)x for which we can unambiguously write x/2...
and it totally makes sense to consider "multiplication denoted by absence
of symbol" to be stronger binding that multiplication and division denoted
with a symbol -- among other "esthetical" considerations, that also makes
more useful to have this choice between the two.
And so far I've never seen a textbook explicitly stating the contrary - but
yes, YMMV...)
it is also very popular to see posts of the form
2 + 2 = X
3 + 3 = Y
4 + 4 = Z
5 + 5 = ?
(or sometimes also : "1+2 = X, 2+3 = Y, 3+4 = Z, 4+5 = ?" and variants,
see, e.g., http://instagr.am/reel/CXmAvR0Pa_4 or
http://instagr.am/reel/CXpH4Dxjtp9 etc.)
where "2+2, 3+3" etc. "obviously" (according to the authors) means f(2),
f(3), ...
Every other time I see this, I can't resist suggesting to "use at least a
symbol different from + if you don't mean the usual addition,
about any other choice like & or * or T or # or even x would be better,
IMHO."
But I think we must get used to seeing such nonsensical "popularized math"
-- fortunately there are also many publications of much higher quality!
- Maximilian
On Mon, Feb 7, 2022 at 9:22 AM Olivier Gerard <olivier.gerard at gmail.com>
wrote:
> I cannot see the point in asking this to anyone, in a beauty pageant or
> anywhere,
> especially in this biased form.
>
> In fact this was asked to the twenty-something final contestants
> in the middle of a General Knowledge Quizz they had to take before the show
> exactly like this :
>
> 36. Si 1 est égal à 5, 2 est égal à 25, 3 à 605, 4 à 10855, 5 est égal à
> quoi?
> a. 5 est égal à 1
> b. 5 est égal à 2
> c. 5 est égal à 5
> d. 5 est égal à 25
>
> And in this form the only (barely defensible but not exclusive) answers are
> a) and c)
> and a) is the accepted answer. What a mockery of the meaning of
> *equal* and of the meaning of *is* !
>
> A more mathematical interpretation would have been :
> f(1) = 5, f(2) = 25, f(3)= 605, f(4)= 10855
> What is f(5) ?
>
> Polynomial interpolation gives : 39885
>
> But I would not attempt the computation without paper and there is nothing
> particular or exceptional to this polynomial or series of values which
> starts
as a geometric series then oscillates.
>
> Question 37 is more of the OEIS kind:
>
> 37. Compléter cette suite logique : 89-87-83-77-69
> a. 59
> b. 47
> c. 53
> d. 62
>
> Most will have counted differences : 2, 4, 6, 8, ... so out of simplicity
> one could guess the answer is a) 59 that was the accepted answer
> but as all seqfan members know, any numeric answer is "logical".
>
> At least, last year's quizz asked to know the definition for bissector
> (which is required knowledge by the end of middle-school in France).
> Olivier
>
>
>
>
>
> On Sun, Feb 6, 2022 at 8:30 PM jean-paul allouche <
> jean-paul.allouche at imj-prg.fr> wrote:
>
> > No joke (and possibly no interest).
> > I have seen this yesterday and unsucessfully
> > tried to find a smart answer. Finally I seem to
> > have read that *the* answer was just about
> > symmetry of equality: if 1=5, then 5=1.
> > Totally dull (the link given by Michel Marcus
> > even claims symmetry being intuitively stronger
> > than reflexivity, hence 5=1 being a more natural
> > answer than 5=5...! At least that link cites
> > the OEIS)
> >
> > jp
> >
> >
>
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