[FRIAM] Can empirical discoveries be mathematical?

[Pieter Steenekamp]

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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