Re: [FRIAM] Can empirical discoveries be mathematical?

[Roger Frye]

A completely different example of mathematical metaphor is representation
theory. The formula 3*3 + 4*4 = 5*5 can be represented as a right triangle
with the sides touching the right angle having lengths of 3 and 4, and the
hypotenuse having length 5. I like to think of one representation being a
metaphor for the other.

On Mon, Sep 13, 2021 at 11:52 AM  wrote:

> Roger,
>
>
>
> If I weren’t immured with my income tax, I would engage you on this.  I
> believe that metaphor --  aka “abduction”? – is the root of all evil *and*
> the root of all good.  And then I wonder about the connection to the naming
> fallacy.  The naming fallacy I take to be the idea that if two things have
> the same name, they have the same properties.  This assertion is absurd as
> a statement of fact but often useful as a source of hypotheses.  So, on
> this view, we humans take Adam’s Task very seriously.  We stumble around
> the world naming every new experience that confronts us and then
> frantically try to work out how much we can trust the implications of that
> name.  “My love is … a … rose!  How long are her thorns?”
>
>
>
> Ugh!  I now see that I have gone all anthropocentric, here.  What IS the
> relation between perception (cognition, what-have-you) and naming.  The
> Whorf hypothesis would have it that all perception is run though a
> dictionary, but I understand that the Whorf hypothesis is not wearing well,
> these days, and, more important, animals perceive quite well without
> dictionaries.  Classical conditioning (a la Pavlov) produces abductions.
> (This bell MEANS foodpowder)  Would a dog think, “This bell is … a
> ….foodpowder!”  Probably not.  It might think “Oh Goody Food Powder!”   So
> whatever the naming thing contributes, it is layered on to something else,
> something more fundamental.  (Two bird hunters are walking through the
> underbrush,  guns ready when, the leader calls out “Duck.”; his companion,
> stops, raises his gun,  and scans the sky, only to be struck full in the
> face by a bent hickory sapling.]
>
>
>
> These are the things I might have written to you about were I not doing my
> income tax.
>
>
>
> Nick
>
>
>
> Nick Thompson
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam  *On Behalf Of *Roger Frye
> *Sent:* Tuesday, September 7, 2021 9:28 AM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@redfish.com>
> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>
>
>
> Reuben had an article in Issue 65 of Eureka Magazine titled 'Solving
> Problems by "Cheating": Operational Calculi, Function Theory, and
> Differential Equations'. The article is a compilation of tricks that he ran
> across during his career that seemed to apply in a general way to solving
> problems. The theme is that you doodle with methods that you have no right
> to assume would work in this particular case, and if you get something
> worthwhile, then go back and prove it.
>
>
>
> Towards the end of his life he became more interested in the metaphors
> that are at the basis of mathematical thinking, the bodily actions that
> have been abstracted into mathematical concepts. Yuri I. Manin also spoke
> of Mathematics as Metaphor is a slightly different way in his essays.
>
>
>
> -Roger
>
>
>
>
>
> On Mon, Sep 6, 2021 at 8:34 PM Frank Wimberly  wrote:
>
> Our late friend Reuben Hersh was interested in these questions.
>
> ---
> Frank C. Wimberly
> 140 Calle Ojo Feliz,
> Santa Fe, NM 87505
>
> 505 670-9918
> Santa Fe, NM
>
>
>
> On Mon, Sep 6, 2021, 7:58 PM Eric Charles 
> wrote:
>
> As I said a few days ago: I think traditionally,  "mathematical" would
> have been synonymous with "rigorous deduction from a minimal number of
> axioms", but I doubt that approach is clear cut anymore.
>
>
>
> I am pretty confident that modern mathematics is WAY more open-field than
> that.  The Stanford Encyclopedia of Philosophy seems to agree with that
> intuition, though I think it is an even broader topic than implied by just
> this entry:  Non-Deductive Methods in Mathematics (Stanford Encyclopedia
> of Philosophy)
> <https://plato.stanford.edu/entries/mathematics-nondeductive/>
>
>
>
>
>
>
>
>
> On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan <
> barry.mackic...@mackichan.com> wrote:
>
> Briefly, and in my opinion, mathematics can only make claims like ‘if A is
> true then B is true’. To say B is true, you must also say A is true.
> Eventually you have to go back to the beginning of the deductive chain, and
> the truth of the initial statement is ind

Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

Roger, 

 

If I weren’t immured with my income tax, I would engage you on this.  I believe 
that metaphor --  aka “abduction”? – is the root of all evil and the root of 
all good.  And then I wonder about the connection to the naming fallacy.  The 
naming fallacy I take to be the idea that if two things have the same name, 
they have the same properties.  This assertion is absurd as a statement of fact 
but often useful as a source of hypotheses.  So, on this view, we humans take 
Adam’s Task very seriously.  We stumble around the world naming every new 
experience that confronts us and then frantically try to work out how much we 
can trust the implications of that name.  “My love is … a … rose!  How long are 
her thorns?”

 

Ugh!  I now see that I have gone all anthropocentric, here.  What IS the 
relation between perception (cognition, what-have-you) and naming.  The Whorf 
hypothesis would have it that all perception is run though a dictionary, but I 
understand that the Whorf hypothesis is not wearing well, these days, and, more 
important, animals perceive quite well without dictionaries.  Classical 
conditioning (a la Pavlov) produces abductions.  (This bell MEANS foodpowder)  
Would a dog think, “This bell is … a ….foodpowder!”  Probably not.  It might 
think “Oh Goody Food Powder!”   So whatever the naming thing contributes, it is 
layered on to something else, something more fundamental.  (Two bird hunters 
are walking through the underbrush,  guns ready when, the leader calls out 
“Duck.”; his companion, stops, raises his gun,  and scans the sky, only to be 
struck full in the face by a bent hickory sapling.]

 

These are the things I might have written to you about were I not doing my 
income tax. 

 

Nick   

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Roger Frye
Sent: Tuesday, September 7, 2021 9:28 AM
To: The Friday Morning Applied Complexity Coffee Group 
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

Reuben had an article in Issue 65 of Eureka Magazine titled 'Solving Problems 
by "Cheating": Operational Calculi, Function Theory, and Differential 
Equations'. The article is a compilation of tricks that he ran across during 
his career that seemed to apply in a general way to solving problems. The theme 
is that you doodle with methods that you have no right to assume would work in 
this particular case, and if you get something worthwhile, then go back and 
prove it.

 

Towards the end of his life he became more interested in the metaphors that are 
at the basis of mathematical thinking, the bodily actions that have been 
abstracted into mathematical concepts. Yuri I. Manin also spoke of Mathematics 
as Metaphor is a slightly different way in his essays. 

 

-Roger

 

 

On Mon, Sep 6, 2021 at 8:34 PM Frank Wimberly mailto:wimber...@gmail.com> > wrote:

Our late friend Reuben Hersh was interested in these questions.

---
Frank C. Wimberly
140 Calle Ojo Feliz, 
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

 

On Mon, Sep 6, 2021, 7:58 PM Eric Charles mailto:eric.phillip.char...@gmail.com> > wrote:

As I said a few days ago: I think traditionally,  "mathematical" would have 
been synonymous with "rigorous deduction from a minimal number of axioms", but 
I doubt that approach is clear cut anymore.

 

I am pretty confident that modern mathematics is WAY more open-field than that. 
 The Stanford Encyclopedia of Philosophy seems to agree with that intuition, 
though I think it is an even broader topic than implied by just this entry:  
Non-Deductive Methods in Mathematics (Stanford Encyclopedia of Philosophy) 
<https://plato.stanford.edu/entries/mathematics-nondeductive/>  




 

 

 

On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan mailto:barry.mackic...@mackichan.com> > wrote:

Briefly, and in my opinion, mathematics can only make claims like ‘if A is true 
then B is true’. To say B is true, you must also say A is true. Eventually you 
have to go back to the beginning of the deductive chain, and the truth of the 
initial statement is inductive, not deductive or mathematics. You can predict 
the time and place of an eclipse, and this prediction is based on mathematics 
and a mathematical model of reality — Newton’s laws in this case. But the truth 
of this prediction is inductive since the initial positions and velocities for 
the calculation are inductive, as is the applicability of Newton’s laws to 
reality, and even the ‘fact’ that mathematics can describe the universe is 
inductive.

And Einstein showed that the applicability of Newton’s laws was in fact wrong 
and offered a new model — which we inductively accept as true, if only 
provisionally.

Mathematics cannot prove any statement about the real world. Any such statement 
will depend at some

Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

Our late friend Reuben Hersh was interested in these questions.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Sep 6, 2021, 7:58 PM Eric Charles 
wrote:

> As I said a few days ago: I think traditionally,  "mathematical" would
> have been synonymous with "rigorous deduction from a minimal number of
> axioms", but I doubt that approach is clear cut anymore.
>
> I am pretty confident that modern mathematics is WAY more open-field than
> that.  The Stanford Encyclopedia of Philosophy seems to agree with that
> intuition, though I think it is an even broader topic than implied by just
> this entry:  Non-Deductive Methods in Mathematics (Stanford Encyclopedia
> of Philosophy)
> 
>
>
> 
>
>
> On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan <
> barry.mackic...@mackichan.com> wrote:
>
>> Briefly, and in my opinion, mathematics can only make claims like ‘if A
>> is true then B is true’. To say B is true, you must also say A is true.
>> Eventually you have to go back to the beginning of the deductive chain, and
>> the truth of the initial statement is inductive, not deductive or
>> mathematics. You can predict the time and place of an eclipse, and this
>> prediction is based on mathematics and a mathematical model of reality —
>> Newton’s laws in this case. But the truth of this prediction is inductive
>> since the initial positions and velocities for the calculation are
>> inductive, as is the applicability of Newton’s laws to reality, and even
>> the ‘fact’ that mathematics can describe the universe is inductive.
>>
>> And Einstein showed that the applicability of Newton’s laws was in fact
>> wrong and offered a new model — which we inductively accept as true, if
>> only provisionally.
>>
>> Mathematics cannot prove any statement about the real world. Any such
>> statement will depend at some point on an inductive truth or a definition.
>>
>> —Barry
>>
>> On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:
>>
>> Ok, is mathematics (logic, etc.) a way of arriving at true propositions
>> distinct from observation or are mathematical truths different from
>> empirical truths?
>>
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>>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Eric Charles]

As I said a few days ago: I think traditionally,  "mathematical" would have
been synonymous with "rigorous deduction from a minimal number of axioms",
but I doubt that approach is clear cut anymore.

I am pretty confident that modern mathematics is WAY more open-field than
that.  The Stanford Encyclopedia of Philosophy seems to agree with that
intuition, though I think it is an even broader topic than implied by just
this entry:  Non-Deductive Methods in Mathematics (Stanford Encyclopedia of
Philosophy) 





On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan <
barry.mackic...@mackichan.com> wrote:

> Briefly, and in my opinion, mathematics can only make claims like ‘if A is
> true then B is true’. To say B is true, you must also say A is true.
> Eventually you have to go back to the beginning of the deductive chain, and
> the truth of the initial statement is inductive, not deductive or
> mathematics. You can predict the time and place of an eclipse, and this
> prediction is based on mathematics and a mathematical model of reality —
> Newton’s laws in this case. But the truth of this prediction is inductive
> since the initial positions and velocities for the calculation are
> inductive, as is the applicability of Newton’s laws to reality, and even
> the ‘fact’ that mathematics can describe the universe is inductive.
>
> And Einstein showed that the applicability of Newton’s laws was in fact
> wrong and offered a new model — which we inductively accept as true, if
> only provisionally.
>
> Mathematics cannot prove any statement about the real world. Any such
> statement will depend at some point on an inductive truth or a definition.
>
> —Barry
>
> On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:
>
> Ok, is mathematics (logic, etc.) a way of arriving at true propositions
> distinct from observation or are mathematical truths different from
> empirical truths?
>
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>
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[FRIAM] Can empirical discoveries be mathematical?

[Jon Zingale]

Nick writes:

"""
I think I am starting to know the answer just by being badgered by you
guys.  I can from relativity theory predict that during a solar eclipse a
distant star will pop out from behind the sun at T=  =/-  sec.  I
can observe empirically that, indeed, the star popped out within that time
range.  Thus I have arrived at the same proposition both by mathematical
and empirical means.  Is that oK?
"""

and in particular:
"Thus I have arrived at the *same* proposition"

In some cases, it is fine to speak about strict equivalence, though in
others it might be better to consider what is preserved between the two
models (one model with the privilege of being designated *real*). The
mathematical model agrees pretty well with the other on some things but not
others, and not necessarily in a pedantic or trivial way. It is the case
that one can apply a small force to the planet mercury as well as perform a
corresponding manipulation in the mathematical theory to arrive at
agreeable results between the two models. In this sense, the mathematical
model (Newton's laws, say) is *faithful* to the real. On the other hand,
the mathematical model may have no *full* relation to the real. That is,
there may be more to discover about the real that has no counterpart
(actually nor effectively) in the mathematical model. Granted a full and
faithful relation between models, I see no harm in pronouncing a functorial
equivalence, or what DaveW might call a *dead metaphor*.

"""
To be a bit more pedantic, you have discovered that t-shirts transform
under the SO(3) _representation_ of the rotation group.  If you were not a
mathematician or a physicist, you would say “I had “the” group of
rotations; what is there to represent?”  But a mathematician would tell you
that there are many representations of the rotation group, all having the
same algebra, yet different formal constructs...
"""

Changing the image slightly, consider a favorite melody[턞]. One *may*
crudely choose to represent this melody in any of 12 keys by translating
about a piano. These choices all give grounds for the melody. But if jazz
music taught us anything, ultimately not even the notes need be the same,
somehow the melody can be found to transcend pitch, mood, and rhythm to a
significant degree. For one such instance, we could instead look to
arpeggios, those collections of notes which illuminate an implied harmonic
moment. At each moment along the melody we can imagine substituting our
original for another in the class, and not only can we find the melody
preserved by often with pleasant results.

[턞] I woke up with "My Favorite Things" in my head this morning, and not
necessarily anyone's particular rendition. I considered playing John
Coltrane's version but then finally settled on Julie Andrew's version.
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Re: [FRIAM] Can empirical discoveries be mathematical?

[uǝlƃ ☤ $]

I feel left out. So I'll plop my 2 cents down, too. EricS' description of 
consistifying several models to target reality mirrors Nick's original question 
about the 2 transform requirement. Neither of these imply an overly simplified 
single point of reality-check/validation. They both imply, to me, an 
*iterative* (though perhaps not merely sequential) reality-checking method.

So it's not clear to me that we can cleanly separate induction (including 
abduction) from deduction. What's required are methods by which a little bit's 
induced, a little bit's deduced, a little bit's induced, etc. [⛤] And it may 
not need to be a *single* loop, there might be parallel loops, operating at 
different rates. E.g. the rate at which we learn the symmetries of (embedded) 
electrons is, I'd bet, slower than the rate at which we learn the symmetries of 
(embedded) t-shirts. [π]

This argues that our conceptual separation of induction from deduction is an 
artificial separation ... done to rationalize and model an actual, messy [⛧], 
learning process. And *that* might argue for a more rare answer to Nick's 
question. Math and reality are not necessarily the same thing. But they're 
probably not as distinct as we think they are.


[⛤] It's not quite right to say "Newton's laws are in fact wrong". They're not 
entirely wrong. But they're a little bit wrong. We can say the same about 
general relativity and QM ... They're both a little bit wrong. And their 
wrongness depends fundamentally on when, where, who, what, and why.

[π] Such rates might be a function of the logical depth of the models. Maybe 
deeper models imply longer cycles through the loop. And, even between deep 
models, there might be long loops like string theory or biological evolution, 
with fewer opportunities to error-correct against reality versus long loops 
like general relativity with more common opportunities to bang up against 
reality.

[⛧] By messy, including but not limited to para- or non-consistency, 
[in]completeness, multiple modes, etc.

On 9/6/21 8:13 AM, Barry MacKichan wrote:
> Briefly, and in my opinion, mathematics can only make claims like ‘if A is 
> true then B is true’. To say B is true, you must also say A is true. 
> Eventually you have to go back to the beginning of the deductive chain, and 
> the truth of the initial statement is inductive, not deductive or 
> mathematics. You can predict the time and place of an eclipse, and this 
> prediction is based on mathematics and a mathematical model of reality — 
> Newton’s laws in this case. But the truth of this prediction is inductive 
> since the initial positions and velocities for the calculation are inductive, 
> as is the applicability of Newton’s laws to reality, and even the ‘fact’ that 
> mathematics can describe the universe is inductive.
> 
> And Einstein showed that the applicability of Newton’s laws was in fact wrong 
> and offered a new model — which we inductively accept as true, if only 
> provisionally.
> 
> Mathematics cannot prove any statement about the real world. Any such 
> statement will depend at some point on an inductive truth or a definition.
> 
> —Barry
> 
> 
> On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:
> 
> Ok, is mathematics (logic, etc.) a way of arriving at true propositions 
> distinct from observation or are mathematical truths different from empirical 
> truths? 

-- 
☤>$ uǝlƃ

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Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

What Barry said.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Sep 6, 2021, 9:19 AM Barry MacKichan 
wrote:

> Briefly, and in my opinion, mathematics can only make claims like ‘if A is
> true then B is true’. To say B is true, you must also say A is true.
> Eventually you have to go back to the beginning of the deductive chain, and
> the truth of the initial statement is inductive, not deductive or
> mathematics. You can predict the time and place of an eclipse, and this
> prediction is based on mathematics and a mathematical model of reality —
> Newton’s laws in this case. But the truth of this prediction is inductive
> since the initial positions and velocities for the calculation are
> inductive, as is the applicability of Newton’s laws to reality, and even
> the ‘fact’ that mathematics can describe the universe is inductive.
>
> And Einstein showed that the applicability of Newton’s laws was in fact
> wrong and offered a new model — which we inductively accept as true, if
> only provisionally.
>
> Mathematics cannot prove any statement about the real world. Any such
> statement will depend at some point on an inductive truth or a definition.
>
> —Barry
>
> On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:
>
> Ok, is mathematics (logic, etc.) a way of arriving at true propositions
> distinct from observation or are mathematical truths different from
> empirical truths?
>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Barry MacKichan]

Briefly, and in my opinion, mathematics can only make claims like ‘if 
A is true then B is true’. To say B is true, you must also say A is 
true. Eventually you have to go back to the beginning of the deductive 
chain, and the truth of the initial statement is inductive, not 
deductive or mathematics. You can predict the time and place of an 
eclipse, and this prediction is based on mathematics and a mathematical 
model of reality — Newton’s laws in this case. But the truth of this 
prediction is inductive since the initial positions and velocities for 
the calculation are inductive, as is the applicability of Newton’s 
laws to reality, and even the ‘fact’ that mathematics can describe 
the universe is inductive.


And Einstein showed that the applicability of Newton’s laws was in 
fact wrong and offered a new model — which we inductively accept as 
true, if only provisionally.


Mathematics cannot prove any statement about the real world. Any such 
statement will depend at some point on an inductive truth or a 
definition.


—Barry


On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:

Ok, is mathematics (logic, etc.) a way of arriving at true 
propositions distinct from observation or are mathematical truths 
different from empirical truths? 
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Barry MacKichan]

That’s good — it means you didn’t put your legs through the sleeves.

Sent from my iPad

> On Sep 3, 2021, at 8:39 PM, thompnicks...@gmail.com wrote:
> 
> No.  I never managed upside down

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Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

Hi, Frank, 

 

Perhaps when I get back.  Mid Oct, it’s looking like.  

 

I just spent a whole day unable to reach the net because my vpn was in need of 
repair.  

 

Ugh!

 

N

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Frank Wimberly
Sent: Saturday, September 4, 2021 1:01 PM
To: The Friday Morning Applied Complexity Coffee Group 
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

Nick,

 

Reuben Hersh gave me a small book on Lie groups.  I would be happy to help you 
read it.  Alternatively, John Baez has a chapter on the topic in his book Gauge 
Fields, Knots and Gravity.  The latter is a much briefer presentation.  Same 
offer.

 

Frank

 

---
Frank C. Wimberly
140 Calle Ojo Feliz, 
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

 

On Sat, Sep 4, 2021, 10:29 AM mailto:thompnicks...@gmail.com> > wrote:

EricS,

 

I have read this through once and dare only to say what a remarkable bit of 
work it is and how grateful I am to you for it.   I will study on it. 

 

I suggest you put it in a file some where where it will be handy. 

 

I hope others more qualified than I will comment.   

 

Nick 

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam mailto:friam-boun...@redfish.com> > On 
Behalf Of David Eric Smith
Sent: Friday, September 3, 2021 11:04 PM
To: The Friday Morning Applied Complexity Coffee Group mailto:friam@redfish.com> >
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

Please allow me to try to make things worse, if I can.

 

I worry that I may be partly responsible for the origin of this thread, in my 
jabs at the analytical philosophers, who I think are responsible for…. No, 
wait; I won’t start that again.

 

In any case, I read Nick’s post as a good-faith effort to ask the question 
productively, rather than scholastically or rabbinically.  (Or philosophically 
… No, no,…)

 

Nick, do stay with the t-shirts.  It is a better example for the question you 
started with.  When you go off on bachelors you are off in a narrow corner of 
language and designation, which is a different question.

 

You have made several discoveries, certainly empirical.  I will use math to say 
what they are, just because I have the language and it is shorter that way.  
Mostly you have not yet “built” any math, and you probably can only make a 
mathematical discovery once you are in some way operating within a domain that 
is math.  Here are some things I think you can say:

 

1. Whatever we mean by “space, as a place in which one can put things and 
orient them” has a local coordinatization and geometry that is characterized by 
the rotation group.  Now you don’t yet know what “the rotation group” is — to 
use that as a whole concept you would have to build some math and show that it 
hangs together as a descriptive (meaning, formal) system.  But if you or 
anybody else builds that system, you can claim the empirical discovery that 
whatever “space as a place to put things” is, it has the rotation group as a 
symmetry of the orientations for things.  That discovery isn’t empty: lots of 
phenomena describable with systematic language don’t have the rotation group as 
symmetries.  The set of all phylogenetic trees, or all strings of letters, 
don’t need any description in terms of the rotation group.

 

2. If you had said a bit more, you might have observed that t-shirts have 
orientations (in the topologist’s, rather than the direction-pointing, sense).  
You can imagine putting the t-shirt into a mirror-image configuration, since 
you can look at it in the mirror and clearly imagine what such a t-shirt would 
look like, occupying space.  But you can notice that there is no way that by 
rotating or otherwise deforming it, that you can produce the t-shirt in the 
mirror-image form.  I would borderline give you credit for a mathematical 
discovery here.  You may not have the language to express it, but you have the 
seeds of building such a language, which is that there is a group of 
transformations that include the reflections and the rotations, and the 
reflections are not reducible to the rotations.  

 

3. It could then be another empirical discovery to say that our physical 
space-as-a-place-to-put-things is has that group as a symmetry group.  

 

4. To be a bit more pedantic, you have discovered that t-shirts transform under 
the SO(3) _representation_ of the rotation group.  If you were not a 
mathematician or a physicist, you would say “I had “the” group of rotations; 
what is there to represent?”  But a mathematician would tell you that there are 
many representations of the rotation group, all having the same algebra, yet 
different formal 

Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

Nick,

Reuben Hersh gave me a small book on Lie groups.  I would be happy to help
you read it.  Alternatively, John Baez has a chapter on the topic in his
book Gauge Fields, Knots and Gravity.  The latter is a much briefer
presentation.  Same offer.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Sep 4, 2021, 10:29 AM  wrote:

> EricS,
>
>
>
> I have read this through once and dare only to say what a remarkable bit
> of work it is and how grateful I am to you for it.   I will study on it.
>
>
>
> I suggest you put it in a file some where where it will be handy.
>
>
>
> I hope others more qualified than I will comment.
>
>
>
> Nick
>
>
>
> Nick Thompson
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam  *On Behalf Of *David Eric Smith
> *Sent:* Friday, September 3, 2021 11:04 PM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@redfish.com>
> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>
>
>
> Please allow me to try to make things worse, if I can.
>
>
>
> I worry that I may be partly responsible for the origin of this thread, in
> my jabs at the analytical philosophers, who I think are responsible for….
> No, wait; I won’t start that again.
>
>
>
> In any case, I read Nick’s post as a good-faith effort to ask the question
> productively, rather than scholastically or rabbinically.  (Or
> philosophically … No, no,…)
>
>
>
> Nick, do stay with the t-shirts.  It is a better example for the question
> you started with.  When you go off on bachelors you are off in a narrow
> corner of language and designation, which is a different question.
>
>
>
> You have made several discoveries, certainly empirical.  I will use math
> to say what they are, just because I have the language and it is shorter
> that way.  Mostly you have not yet “built” any math, and you probably can
> only make a mathematical discovery once you are in some way operating
> within a domain that is math.  Here are some things I think you can say:
>
>
>
> 1. Whatever we mean by “space, as a place in which one can put things and
> orient them” has a local coordinatization and geometry that is
> characterized by the rotation group.  Now you don’t yet know what “the
> rotation group” is — to use that as a whole concept you would have to build
> some math and show that it hangs together as a descriptive (meaning,
> formal) system.  But if you or anybody else builds that system, you can
> claim the empirical discovery that whatever “space as a place to put
> things” is, it has the rotation group as a symmetry of the orientations for
> things.  That discovery isn’t empty: lots of phenomena describable with
> systematic language don’t have the rotation group as symmetries.  The set
> of all phylogenetic trees, or all strings of letters, don’t need any
> description in terms of the rotation group.
>
>
>
> 2. If you had said a bit more, you might have observed that t-shirts have
> orientations (in the topologist’s, rather than the direction-pointing,
> sense).  You can imagine putting the t-shirt into a mirror-image
> configuration, since you can look at it in the mirror and clearly imagine
> what such a t-shirt would look like, occupying space.  But you can notice
> that there is no way that by rotating or otherwise deforming it, that you
> can produce the t-shirt in the mirror-image form.  I would borderline give
> you credit for a mathematical discovery here.  You may not have the
> language to express it, but you have the seeds of building such a language,
> which is that there is a group of transformations that include the
> reflections and the rotations, and the reflections are not reducible to the
> rotations.
>
>
>
> 3. It could then be another empirical discovery to say that our physical
> space-as-a-place-to-put-things is has that group as a symmetry group.
>
>
>
> 4. To be a bit more pedantic, you have discovered that t-shirts transform
> under the SO(3) _representation_ of the rotation group.  If you were not a
> mathematician or a physicist, you would say “I had “the” group of
> rotations; what is there to represent?”  But a mathematician would tell you
> that there are many representations of the rotation group, all having the
> same algebra, yet different formal constructs, and a physicist would tell
> you that electrons do not transform under the same representation as
> t-shirts do.  If you turn your t-shirt around in one full turn of a
> pirouette (any axis is fine), it will be back the way it started.  If you
> do that for an electron, it will not be.  You 

Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

EricS,

 

I have read this through once and dare only to say what a remarkable bit of 
work it is and how grateful I am to you for it.   I will study on it. 

 

I suggest you put it in a file some where where it will be handy. 

 

I hope others more qualified than I will comment.   

 

Nick 

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of David Eric Smith
Sent: Friday, September 3, 2021 11:04 PM
To: The Friday Morning Applied Complexity Coffee Group 
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

Please allow me to try to make things worse, if I can.

 

I worry that I may be partly responsible for the origin of this thread, in my 
jabs at the analytical philosophers, who I think are responsible for…. No, 
wait; I won’t start that again.

 

In any case, I read Nick’s post as a good-faith effort to ask the question 
productively, rather than scholastically or rabbinically.  (Or philosophically 
… No, no,…)

 

Nick, do stay with the t-shirts.  It is a better example for the question you 
started with.  When you go off on bachelors you are off in a narrow corner of 
language and designation, which is a different question.

 

You have made several discoveries, certainly empirical.  I will use math to say 
what they are, just because I have the language and it is shorter that way.  
Mostly you have not yet “built” any math, and you probably can only make a 
mathematical discovery once you are in some way operating within a domain that 
is math.  Here are some things I think you can say:

 

1. Whatever we mean by “space, as a place in which one can put things and 
orient them” has a local coordinatization and geometry that is characterized by 
the rotation group.  Now you don’t yet know what “the rotation group” is — to 
use that as a whole concept you would have to build some math and show that it 
hangs together as a descriptive (meaning, formal) system.  But if you or 
anybody else builds that system, you can claim the empirical discovery that 
whatever “space as a place to put things” is, it has the rotation group as a 
symmetry of the orientations for things.  That discovery isn’t empty: lots of 
phenomena describable with systematic language don’t have the rotation group as 
symmetries.  The set of all phylogenetic trees, or all strings of letters, 
don’t need any description in terms of the rotation group.

 

2. If you had said a bit more, you might have observed that t-shirts have 
orientations (in the topologist’s, rather than the direction-pointing, sense).  
You can imagine putting the t-shirt into a mirror-image configuration, since 
you can look at it in the mirror and clearly imagine what such a t-shirt would 
look like, occupying space.  But you can notice that there is no way that by 
rotating or otherwise deforming it, that you can produce the t-shirt in the 
mirror-image form.  I would borderline give you credit for a mathematical 
discovery here.  You may not have the language to express it, but you have the 
seeds of building such a language, which is that there is a group of 
transformations that include the reflections and the rotations, and the 
reflections are not reducible to the rotations.  

 

3. It could then be another empirical discovery to say that our physical 
space-as-a-place-to-put-things is has that group as a symmetry group.  

 

4. To be a bit more pedantic, you have discovered that t-shirts transform under 
the SO(3) _representation_ of the rotation group.  If you were not a 
mathematician or a physicist, you would say “I had “the” group of rotations; 
what is there to represent?”  But a mathematician would tell you that there are 
many representations of the rotation group, all having the same algebra, yet 
different formal constructs, and a physicist would tell you that electrons do 
not transform under the same representation as t-shirts do.  If you turn your 
t-shirt around in one full turn of a pirouette (any axis is fine), it will be 
back the way it started.  If you do that for an electron, it will not be.  You 
will have to do two full turns of the pirouette for the electron to be back the 
way it was.  Whether it is a discovery or a construction by the mathematicians 
that there is another concept (representation) beyond the concept (group) I 
won’t belabor.  I would say that mathematicians find that formal systems can be 
built up in which groups and representations are different constructs, and 
those formal systems can be made consistent, so whatever they instantiate as 
“concepts” has a definite referent.  But it is an empirical discovery that 
electrons and t-shirts don’t transform the same way under rotations, so however 
we package it in the math, we will need expressions that correspond to at least 
two representations of the one group.  (For reference, the one f

Re: [FRIAM] Can empirical discoveries be mathematical?

[David Eric Smith]

lors.   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
> thompnicks...@gmail.com <mailto:thompnicks...@gmail.com>
> https://wordpress.clarku.edu/nthompson/ 
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f=E,1,CxoV3-soQMap0aZ7-0ueqqGYjQKFXmEfLfybimqj7_3oKWdvM3OSq95UNkCQw22-kuoZ1z4snDbeGLXxf4kQ16gsp1RVHQERB_Lip55CaBk,=1>
>  
> From: Friam mailto:friam-boun...@redfish.com>> On 
> Behalf Of Pieter Steenekamp
> Sent: Friday, September 3, 2021 12:48 PM
> To: The Friday Morning Applied Complexity Coffee Group  <mailto:friam@redfish.com>>
> Subject: Re: [FRIAM] Can empirical discoveries be mathematical?
>  
> Nick,
> 
> I quote from https://www.britannica.com/science/scientific-theory 
> <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,  <mailto:thompnicks...@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
>> thompnicks...@gmail.com <mailto:thompnicks...@gmail.com>
>> https://wordpress.clarku.edu/nthompson/ 
>> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f=E,1,Gj0sAmr-90l8xsv85ZnwtVVEyp1HV_9DvDFSK5riP2nKQ9Iz50-jMjBz6azBtfMIKzbiDfEnPloTPHvtRjZACXZ1ENfnhj69C_aNxACYOJ7FvW8yRg,,=1>
>>  
>> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam 
>> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fbit.ly%2fvirtualfriam=E,1,QuUXl8-qUVPOPvjLDaTd9j4330SQWwM0CgH6_1Gvu7U81Neh4Cd15VNuWk8OfjpojIl6rh8SFzZ6ABIpqhQT0JIM_jtluw_U84kA1reLjuk,=1>
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com 
>> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com=E,1,9WjLP-Dka1BsXw_Ukd9fsgA4j8KxW2WRDFlAMtvspczJSCYqCJnFXtFICqSsveeIkTFaH-S8EcMWnQtwvqfXz4SvGQZjKYVuYvhpnCgPiwVJ7A,,=1>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ 
>> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f=E,1,dtNEwCKHVYp-6pGwZ8AbrYPavCxTLCZ37MvpdvhukdSA-6FctdE7VKT0L1oZNp8Wn6yVIoKzM4ZhQ59jzavRLE9ALL-z5K3364cG1L9UIQKjiA,,=1>
>> archives: http://friam.471366.n2.nabble.com/ 
>> <http://friam.471366.n2.nabble.com/>-  . -..-. . -. -.. -..-. .. ... 
>> 

Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

AM, thompnicks...@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
> thompnicks...@gmail.com
> https://wordpress.clarku.edu/nthompson/
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f=E,1,CxoV3-soQMap0aZ7-0ueqqGYjQKFXmEfLfybimqj7_3oKWdvM3OSq95UNkCQw22-kuoZ1z4snDbeGLXxf4kQ16gsp1RVHQERB_Lip55CaBk,=1>
>
> *From:* Friam  *On Behalf Of *Pieter Steenekamp
> *Sent:* Friday, September 3, 2021 12:48 PM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@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,  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
> thompnicks...@gmail.com
> https://wordpress.clarku.edu/nthompson/
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f=E,1,Gj0sAmr-90l8xsv85ZnwtVVEyp1HV_9DvDFSK5riP2nKQ9Iz50-jMjBz6azBtfMIKzbiDfEnPloTPHvtRjZACXZ1ENfnhj69C_aNxACYOJ7FvW8yRg,,=1>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fbit.ly%2fvirtualfriam=E,1,QuUXl8-qUVPOPvjLDaTd9j4330SQWwM0CgH6_1Gvu7U81Neh4Cd15VNuWk8OfjpojIl6rh8SFzZ6ABIpqhQT0JIM_jtluw_U84kA1reLjuk,=1>
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com=E,1,9WjLP-Dka1BsXw_Ukd9fsgA4j8KxW2WRDFlAMtvspczJSCYqCJnFXtFICqSsveeIkTFaH-S8EcMWnQtwvqfXz4SvGQZjKYVuYvhpnCgPiwVJ7A,,=1>
> FRIAM-COMIC http://friam-comic.blogspot.com/
> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f=E,1,dtNEwCKHVYp-6pGwZ8AbrYPavCxTLCZ37MvpdvhukdSA-6FctdE7VKT0L1oZNp8Wn6yVIoKzM4ZhQ59jzavRLE9ALL-z5K3364cG1L9UIQKjiA,,=1>
> archives: http://friam.471366.n2.nabble.com/
>
> -  . -

Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

No.  I never managed upside down.  Wait a minute!  Is upside down an exception 
to the rule?  Oh, no, it isn’t.  It reverses front to back.  

 

Barry, this is all coming from something I thought I heard EricS say about 
trying to get out of logic what only empirical observation will provide.  

 

N

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Barry MacKichan
Sent: Friday, September 3, 2021 3:51 PM
To: The Friday Morning Applied Complexity Coffee Group 
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

Well, your discovery was certainly empirical.

The explanation is mathematical, having to do what you can do with an oriented 
surface. BTW, did you take a picture when you put it on upside down? I can 
visualize a couple of ways you could have done that, but if you weren’t doing 
hand stands the pictures are not pretty.

—Barry

On 3 Sep 2021, at 11:23, thompnicks...@gmail.com 
<mailto:thompnicks...@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

thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> 

https://wordpress.clarku.edu/nthompson/

 

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Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

Proving once again that, no however deep Thompson tries to go, Zingale can go 
deeper, much deeper.  

 

Ok, is mathematics (logic, etc.) a way of arriving at true propositions 
distinct from observation or are mathematical truths different from empirical 
truths?  

 

I keep hearing Hywel in my ears:  Mathematics is all very well but sometimes 
you have to know what you are doing.  

 

I think I am starting to know the answer just by being badgered by you guys.  I 
can from relativity theory predict that during a solar eclipse a distant star 
will pop out from behind the sun at T=  =/-  sec.  I can observe 
empirically that, indeed, the star popped out within that time range.  Thus I 
have arrived at the same proposition both by mathematical and empirical means.  
Is that oK.  

 

Nick Thompson

thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> 

https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Jon Zingale
Sent: Friday, September 3, 2021 4:37 PM
To: friam@redfish.com
Subject: [FRIAM] Can empirical discoveries be mathematical?

 

Beginning with Oxford,

 

empirical: based on, concerned with, or verifiable by observation or experience 
rather than theory or pure logic.

 

Where then Nick goes on to argue, perhaps, that experience of logic is 
experience and so "experience rather than theory or pure logic" is meaningless. 
Then somewhere in hell's pub, far far away, Glen rolls his eyes and wonders 
whether he should write about scoping or simply berate Nick for navel-gazing.

 

But then, maybe this is the case for logic and not mathematics. Perhaps 
mathematics requires abstraction, representation, and objectification. It may 
be necessary to make bold claims like, "my love is like the integers". At some 
point during the process, one has to decide whether a thing has a front or a 
back or an inside to be out. Even the designation married comes with baggage, 
to be taken for granted in the objectification process.

 

Ah, but if I have it correct, Nick also believes that a day like no other is no 
day at all. Nothing can be known about such a day. The only days are those that 
are like the integers (type) or days like today (class).

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[FRIAM] Can empirical discoveries be mathematical?

[Jon Zingale]

Beginning with Oxford,


*empirical*: based on, concerned with, or verifiable by observation or
experience rather than theory or pure logic.

Where then Nick goes on to argue, perhaps, that *experience of logic* is
*experience* and so "experience *rather than* theory or pure logic" is
meaningless. Then somewhere in hell's pub, far far away, Glen rolls his
eyes and wonders whether he should write about *scoping* or simply berate
Nick for navel-gazing.

But then, maybe this is the case for *logic* and not *mathematics*. Perhaps
mathematics *requires* abstraction, representation, and objectification. It
may be necessary to make bold claims like, "my love is like the integers".
At some point during the process, one has to decide whether a thing *has* a
front or a back or an inside to be out. Even the designation *married* comes
with baggage, to be taken for granted in the objectification process.

Ah, but if I have it correct, Nick also believes that *a day like no other*
is *no day at all*. Nothing can be known about such a day. The only days
are those that are like the integers (type) or days like today (class).
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Barry MacKichan]

Well, your discovery was certainly empirical.

The explanation is mathematical, having to do what you can do with an 
oriented surface. BTW, did you take a picture when you put it on upside 
down? I can visualize a couple of ways you could have done that, but if 
you weren’t doing hand stands the pictures are not pretty.


—Barry

On 3 Sep 2021, at 11:23, thompnicks...@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

thompnicks...@gmail.com 

https://wordpress.clarku.edu/nthompson/




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Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

Well, speak for yourself, oh mathematician.  For me, it was first an empirical 
observation. 

 

n

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Frank Wimberly
Sent: Friday, September 3, 2021 3:16 PM
To: russ.abb...@gmail.com; The Friday Morning Applied Complexity Coffee Group 

Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

It doesn't take much observing to realize that rotations of an object in 3D are 
not commutative.

---
Frank C. Wimberly
140 Calle Ojo Feliz, 
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

 

On Fri, Sep 3, 2021, 12:41 PM Russ Abbott mailto:russ.abb...@gmail.com> > wrote:

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 mailto:piet...@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 mailto:eric.phillip.char...@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 mailto:thompnicks...@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

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam mailto:friam-boun...@redfish.com> > On 
Behalf Of Pieter Steenekamp
Sent: Friday, September 3, 2021 12:48 PM
To: The Friday Morning Applied Complexity Coffee Group mailto:friam@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 

Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

It doesn't take much observing to realize that rotations of an object in 3D
are not commutative.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Sep 3, 2021, 12:41 PM Russ Abbott  wrote:

> 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 <
> piet...@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.char...@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  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
>>>>
>>>> thompnicks...@gmail.com
>>>>
>>>> https://wordpress.clarku.edu/nthompson/
>>>>
>>>>
>>>>
>>>> *From:* Friam  *On Behalf Of *Pieter
>>>> Steenekamp
>>>> *Sent:* Friday, September 3, 2021 12:48 PM
>>>> *To:* The Friday Morning Applied Complexity Coffee Group <
>>>> friam@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!
>>&g

Re: [FRIAM] Can empirical discoveries be mathematical?

[Russ Abbott]

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 <
piet...@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 
> 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  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
>>>
>>> thompnicks...@gmail.com
>>>
>>> https://wordpress.clarku.edu/nthompson/
>>>
>>>
>>>
>>> *From:* Friam  *On Behalf Of *Pieter
>>> Steenekamp
>>> *Sent:* Friday, September 3, 2021 12:48 PM
>>> *To:* The Friday Morning Applied Complexity Coffee Group <
>>> friam@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
>>>
>>>
>>>
>>

Re: [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 
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  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
>>
>> thompnicks...@gmail.com
>>
>> https://wordpress.clarku.edu/nthompson/
>>
>>
>>
>> *From:* Friam  *On Behalf Of *Pieter
>> Steenekamp
>> *Sent:* Friday, September 3, 2021 12:48 PM
>> *To:* The Friday Morning Applied Complexity Coffee Group <
>> friam@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,  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
>>
>> thompnicks...@gmail.com
>>
&

Re: [FRIAM] Can empirical discoveries be mathematical?

[Eric Charles]

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  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam  *On Behalf Of *Pieter Steenekamp
> *Sent:* Friday, September 3, 2021 12:48 PM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@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,  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
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> archives: http://friam.471366.n2.nabble.com/
>
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>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

Group theory.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Sep 3, 2021, 11:25 AM  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam  *On Behalf Of *Pieter Steenekamp
> *Sent:* Friday, September 3, 2021 12:48 PM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@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,  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives: http://friam.471366.n2.nabble.com/
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
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> archives: http://friam.471366.n2.nabble.com/
>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Pieter Steenekamp]

It could be both.

If you just describe it in terms of t-shirts then it is an empirical
scientific law. You can claim to have discovered an empirical scientific law
If you now express it in mathematical terms, and the mathematical community
accepts it as true, then it is then a mathematical axiom. Now  (and nobody
else has previously discovered it)  you can claim to have discovered a
mathematical axiom.

Then, as I mentioned earlier, if you prove your mathematical axiom, using
formal mathematics, then only have you made a mathematical discovery.

Example
Bertram Russel started with the axiom 1+1=2 and then used 300 pages of
formal mathematics to prove it,


On Fri, 3 Sept 2021 at 19:07,  wrote:

> OK fine.  Is it an empirical thingamabob or a mathematical one.
>
>
>
> Nick Thompson
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam  *On Behalf Of *Eric Charles
> *Sent:* Friday, September 3, 2021 11:38 AM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam@redfish.com>
> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>
>
>
> I mean... I feel like "discovery" if the first challenge for your
> classification system to justify... ;- )
>
>
>
> On Fri, Sep 3, 2021, 11:24 AM  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives: http://friam.471366.n2.nabble.com/
>
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> archives: http://friam.471366.n2.nabble.com/
>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

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

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Pieter Steenekamp
Sent: Friday, September 3, 2021 12:48 PM
To: The Friday Morning Applied Complexity Coffee Group 
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, mailto:thompnicks...@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

thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> 

https://wordpress.clarku.edu/nthompson/

 

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Re: [FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

OK fine.  Is it an empirical thingamabob or a mathematical one. 

 

Nick Thompson

 <mailto:thompnicks...@gmail.com> thompnicks...@gmail.com

 <https://wordpress.clarku.edu/nthompson/> 
https://wordpress.clarku.edu/nthompson/

 

From: Friam  On Behalf Of Eric Charles
Sent: Friday, September 3, 2021 11:38 AM
To: The Friday Morning Applied Complexity Coffee Group 
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

 

I mean... I feel like "discovery" if the first challenge for your 
classification system to justify... ;- )

 

On Fri, Sep 3, 2021, 11:24 AM mailto:thompnicks...@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

thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> 

https://wordpress.clarku.edu/nthompson/

 

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Re: [FRIAM] Can empirical discoveries be mathematical?

[Pieter Steenekamp]

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,  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives: http://friam.471366.n2.nabble.com/
>
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Re: [FRIAM] Can empirical discoveries be mathematical?

[Eric Charles]

I mean... I feel like "discovery" if the first challenge for your
classification system to justify... ;- )

On Fri, Sep 3, 2021, 11:24 AM  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
>
> thompnicks...@gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
> -  . -..-. . -. -.. -..-. .. ... -..-.  . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives: http://friam.471366.n2.nabble.com/
>
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[FRIAM] Can empirical discoveries be mathematical?

[thompnickson2]

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

thompnicks...@gmail.com  

https://wordpress.clarku.edu/nthompson/

 

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