Date: Sep 13, 2012 7:54 PM
Subject: Re: Non-Euclidean Arithmetic
On Thu, Sep 13, 2012 at 12:39 PM, Paul Tanner <firstname.lastname@example.org> wrote:
<< snip >>
> I avoided the term "God" - a being as we all know according to many
> who believe in various types of scholastic theologies knows our
> futures and any and all futures of any and all universes, but maybe it
> seems I should have not to make my point.
> My point is that the idea that a thing does not exist unless and until
> it exists in the mind of some human being is clearly and unavoidably a
> rejection of that philosophy of mathematics called mathematical
> realism as well as a rejection of major forms of theism.
So? What's wrong with clearly and unavoidably rejecting some specific
philosophy such as "mathematical realism", an infantile philosophy of
little repute, believed in by lesser minds through the ages? I think
it my civic duty to cast aspersions on these inferior memes trafficked
in by the purveyors of ignorance.
> If you wish to dump on the belief that mathematical objects can have
> some sort of existence outside of the human mind and promote that they
> cannot have some sort of existence outside of the human mind, then OK,
> but note that in doing so you are dumping on many people's belief in
> God, since many people's notion of God is that anything we could
> possibly "invent" or "discover" (or even our futures or any future of
> any universe in any multiverse) is already known to this God. Perhaps
> then you could be more respectful of the beliefs of those who believe
> differently than you.
I'm sure if they need to bolster their beliefs, they can do so on
their own without my assistance. The mangled "philosophy" you present
is so unbelievable on the face of it that I wouldn't no where to
I do speak of "math objects" though and agree that institutionalized
ways of thinking transcend any one individual's thinking. There's a
"zeitgeists" aspect to ideas, which is another way of saying "the
whole is more than the sum of the parts".
Some people use "God" for "ultimate sum" whereas others use "Theo"
(might as well give Him a name, and a character -- a redeeming feature
of ancient Greek polytheism was their deities had many hooks into the
human psyche, seemed personable, whereas without those human
qualities, you really don't have most of the benefits of any kind of
theism (fortunately, monotheists tend to be polytheists in practice,
which contributes to their mental health)).
> No, mathematical realism does not imply the existence of such a God,
> but the existence of such a God does imply mathematical realism, and
> so negating mathematical realism yields negating the existence of such
> a God. (Notice I said "such a God" since I'm allowing for the
> possibility that some might believe in an ignorant God.)
It's very possible to believe in God and yet to think human beings and
their pathetic "real numbers" are not godly in any way.
In humans, you're dealing with an inferior life form of less than
average intelligence (as ETs go) who have indulged in a kind of brain
rot we today call "mathematics". It's nothing to be proud of, and if
we were more faithful, better people, we would have a much more
adequate mathematics than we do today.
I'd say that's closer to my thinking than mindless obeisance to one
particular lineage of human ancestor and their one particular "cruft
wagon" (aka "dogma cart" aka "belief system").
> Specifically on reals: If you or anyone else wishes to reject the
> existence of any being outside of humanity in whose mind real numbers
> are an object of thought, then be my guest, but claiming that it's not
> possible that some such being exists really and clearly is a form of
> that human hubris that says, "Not only am I the center of all that is,
> not only am I the measure of all things, I am all that could know of
> real numbers."
There are no "pawns" outside of the game of chess, with the meaning
that "pawns" have in chess. Sure, you can find a pawn in the garbage
and pawn it in a pawn shop, but without the game of chess to keep the
meaning alive, the chess meaning of "pawn" will fade. Chess itself
will become a memory, then be gone.
When the world is consumed by the sun going nova, there will be no
more "chess" after that, though "chess" may well have ceased, as a
cultural practice, long before then.
In that sense, "pawn" has meaning only within a game and that game in
turn gets its meaning from a broader context, wherein people play
chess in championships.
Learning chess is not compulsory. We don't test kids in chess or have
a "chess SAT" for getting into college.
But in the complete genome that is pi, there's probably a DNA encoding
that would make it so. <sarcasm />
Of browbeating people into believing just the right stuff to make
advances in that stuff, is par for the course. It's what we do.
Mostly, that's what we call "education" (a brainwashing in the local
And I'm not saying humans shouldn't continue to propagate their very
human inventions, of chess, of real numbers, of postage stamps, of bus
systems. Keep those wheels turning, why not? I'm not an
obstructionist in that sense.
> OK, but make that "repeated addition repeatedly redefined" while
> recalling that scaling has no problem and requires no redefinition
> from day one.
I never did any redefining. I came out with this interpretation from
the top, saying this is the full blown interpretation its champions
You kept saying, "oh, but that's a redefinition". But it's never
clear in these discussions how or why it is you have any authority to
tell me what's a definition and what's a redefinition. We don't
really get to that point. We just leave at this: I have a different
model of "repeated addition" than you, and always have by the looks of
things. We didn't go to the same schools. Stands to reason we don't
think the same way.
>> Thanks to my learning about multiplication as repeated
>> addition with whole numbers, and then with fractions, this
>> extending to real numbers is not conceptually a problem.
> With repeated redefinition of "repeated addition" you have gotten to
> the point of giving up what the function actually is, which is a,b ->
> f(a,b) - you have redefined things so much that we now just have a,b
> - -> *approximately* f(a,b).
Approximation is not a new idea. It was there from the beginning,
with estimation, which Devlin is not against.
>> When the teacher sides with Devlin and tries to censor my
>> thoughts, take away my repeated addition model, I fight
>> back, as it helps me and I see no reason to surrender this
> Keep it all you want. Just be up front about the fact that you have to
> redefine things every step of the way and then get to the point where
> you even have to replace what the function actually is, which is a,b
> - -> f(a,b), with a,b -> *approximately* f(a,b).
I have to redefine things *for you*. Me, I came in with this
definition and I'm leaving with it, happy as a clam as they say.
> [In reply to what some of the greatest mathematicians in history have
> done on the topics of the infinite and the continuum, Kirby writes:]
>> "They" -- you're sound so awed by authority.
Mathematicians are not universal in their assessment of one another's
work. The laity tends to be uniformly awed, but once you start
reading the history, you find that they squabble. Kronecker thought
Cantor was just silly, indulging in a kind of insanity and calling it
math. People jumped on that bandwagon though.
You may think of maths as monolithic, but I do not.
> Like I said before, you can ridicule what you do not understand and
> the accomplishments of all those who are way beyond your capabilities
> all you want. It speaks for itself.
I can also ridicule what I *do* understand. I consider that showing
one has taste when it comes to aesthetics.
When we talk about axiomatic systems, we're talking about aesthetics.
There's no proof here, and no necessity for things to "exist".
The proof God does not exist is that existence is precisely that
imperfection which makes one less than eternal. If God exists, then
He's not really God, as "existence" is a big step down from exalted.
Mere existence is too lowly for a true deity. If God exists, we
should pity Him as a poor slob.
You make the same mistake a lot of beginners make: they think for
something to have meaning, there must be some "existing object" that
is that meaning.
>> On the other hand, they shouldn't take away my games by
>> the same token.
> They are not trying to.
That's good, because they would fail if they tried. Their power is
not great enough, not by a long shot.
> It's just that you ought to be upfront with your repeated
> redefinitions of what "repeated addition" means all the way up to your
> replacing the actual binary operation a,b -> f(a,b), with something
> else entirely, a,b -> *approximately* f(a,b). Again, do this all you
> want, but just be up front about what I just said, that's all.
I think I was up front from the beginning but you've been slow to get
up to speed. Now that you're up to speed, perhaps we can tie this
> One final point based on your "you can have more angels on the head of
> a pin if not all of them are real": If you want to proceed along the
> line that, say, a positive integer is "real" but an irrational number
> is not, then be my guest, but do you realize how amateurish this
I'm just not a big fan of what I call "dark ages math" aka "scholastic
math" aka "angels on the head of a pin math" aka "pinhead math".
I'm free, as a citizen and a player, to denigrate the kinds of math I
consider undeserving of taxpayer funding and/or time on TV.
I don't like Abbott's 'Flatland' very much. I am liking 'Divided
Spheres' by Ed Popko, and not just because my name is in the
That Washington High School I write about, call our Ministry of
Education, just had a big math teaching event last night, where people
lined up around the block to look at domes and spheres 'n stuff. Live
music. Beer for those old enough. Adults. An art colony thing
(PICA / TBA).
The education district was not really involved, but the NW Film and
Video center was involved. It has a film school, so is also a school.
The idea that some subset of "schools" has a monopoly on math teaching
is becoming less and less true.
Those analog-math-only not-good-at-STEM schools may have trouble
filling those seats pretty soon, if they don't change their ways.
The younger generation is not necessarily going to be as patient with
all this inertia and foot dragging.
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