[FRIAM] Can empirical discoveries be mathematical?

Fri Sep 3 14:38:34 EDT 2021

I would guess that most mathematical discoveries are first encountered
empirically. Then the mathematician who encounters it attempts to prove the
observed phenomenon mathematically. Your bachelor example illustrates. Once
you discovered the apparent phenomenon that all unmarried men are bachelors
-- and as you also noticed that all bachelors are unmarried -- you proved
that the two collections are identical by determining that that's how
bachelor is defined, a mathematical relationship. Will you be writing up
and submitting this result to a mathematics journal -- rather than, for
example, to a journal of sociology?

-- Russ Abbott
Professor Emeritus, Computer Science
California State University, Los Angeles

On Fri, Sep 3, 2021 at 11:09 AM Pieter Steenekamp <
pieters at randcontrols.co.za> wrote:

> Eric,
>
> Nick's question and the parsing of discoveries into two types intrigue me.
> I'm an engineer, so maybe I have a deep seeded philosophy of science envy?
>
> Pieter
>
> On Fri, 3 Sept 2021 at 19:58, Eric Charles <eric.phillip.charles at gmail.com>
> wrote:
>
>> Why are we parsing discoveries into those two types?
>>
>> I think traditionally,  "mathematical" would have been synonymous with
>> "rigorous deduction groin a minimal number of axioms", but I doubt that
>> approach is clear cut anymore.
>>
>> Given that you claim to have sussed out your insight via systematic
>> *empirical* observation,  and you claim it regarding a particular class
>> of *empirical* objects... I'd go with "empirical"... if I had to choose
>> one for you... but I'm also not sure why we would play this game to begin
>> with.
>>
>> Unless you confessed to me that it was insecurities tied to a deep seeded
>> physics envy... in which case I'd at least understand why you asked.
>>
>> On Fri, Sep 3, 2021, 1:25 PM <thompnickson2 at gmail.com> wrote:
>>
>>> By discovery, I mean only happening on a regularity that was unexpected.
>>>
>>>
>>>
>>> I guess I didn’t need all the razzle-dazzle about the t-shirts.  Let’s
>>> say that I, being totally naïve of logic, announced to friam that I had
>>> made a survey of all my never-married male friends and each and every one
>>> claimed to be a bachelor.  I offered to you-all, as an insight, that all
>>> unmarried men are bachelors.   I think I have made that “discovery”
>>> empirically; you might have arrived at the same insight logically.  Perhaps
>>> the empirical vs mathematical thing is methodological.  Of course, I now
>>> realize that inorder to arrive at my empirical conclusion, I had to invoke
>>> the logical form, induction: this man is un-married, this man is a
>>> batchelor, all batchelors are unmarried.  You might have arrived at the
>>> same conclusion deductively (i.e., mathematically).
>>>
>>>
>>>
>>> Nick Thompson
>>>
>>> ThompNickSon2 at gmail.com
>>>
>>> https://wordpress.clarku.edu/nthompson/
>>>
>>>
>>>
>>> *From:* Friam <friam-bounces at redfish.com> *On Behalf Of *Pieter
>>> Steenekamp
>>> *Sent:* Friday, September 3, 2021 12:48 PM
>>> *To:* The Friday Morning Applied Complexity Coffee Group <
>>> friam at redfish.com>
>>> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>>>
>>>
>>>
>>> Nick,
>>>
>>> I quote from https://www.britannica.com/science/scientific-theory
>>>
>>> "In attempting to explain objects and events, the scientist employs (1)
>>> careful observation or experiments, (2) reports of regularities, and (3)
>>> systematic explanatory schemes (theories). The statements of regularities,
>>> if accurate, may be taken as empirical laws expressing continuing
>>> relationships among the objects or characteristics observed."
>>>
>>> Based on this, I reckon, because you have reported the regularities, you
>>> have discovered an empirical scientific law. Congratulations!
>>>
>>> Next is to systematically explain it, then you have a scientific theory!
>>>
>>> Maybe I did not answer your question? You asked if this is an empirical
>>> discovery or a mathematical one.
>>>
>>>
>>> IMO you have done only the first part, the empirical discovery. This
>>> could now be taken further and if you can prove it using formal
>>> mathematics, then only can you claim you have made a mathematical
>>> discovery. So, it is (not yet) a mathematical discovery. Sorry to blow your
>>> bubble.
>>>
>>> P
>>>
>>>
>>>
>>> On Fri, 3 Sept 2021 at 17:24, <thompnickson2 at gmail.com> wrote:
>>>
>>> Colleagues,
>>>
>>>
>>>
>>> Years ago, my daughter, who knows I hate to shop, bought me a bunch of
>>> plain T-shirts.  The label’s on the shirts were printed, rather than
>>> attached, and so have faded.  Each morning, this leaves me with the problem
>>> of decerning which is the front and which the back of the shirt, and even,
>>> which the inside and which the out-.  After years of fussing with these
>>> shirts I decerned a pattern.  Up/down, inside-in/inside-out, left/right,
>>> front/back, crossed arms/uncrossed arms, you can’t do one transformation
>>> without doing at least one other.
>>>
>>>
>>>
>>> Is this an empirical discovery or a mathematical one?
>>>
>>>
>>>
>>> I guess it boils down to whether “front/back” entails in its meaning
>>> another transformation.   Should we call empirical discoveries
>>> “discoveries” and mathematical discoveries “revelations”?
>>>
>>>
>>>
>>> Nick
>>>
>>>
>>>
>>> Nick Thompson
>>>
>>> ThompNickSon2 at gmail.com
>>>
>>> https://wordpress.clarku.edu/nthompson/
>>>
>>>
>>>
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