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"no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

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"no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

"no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
on 8 August 1900, few of the assembled delegates seemed overly
impressed. According to one contemporary report, the discussion
following his address to the second International Congress of
Mathematicians was "rather desultory". Passions seem to have been more
inflamed by a subsequent debate on whether Esperanto should be adopted
as mathematics' working language.

Yet Hilbert's address set the mathematical agenda for the 20th
century. It crystallised into a list of 23 crucial unanswered
questions, including how to pack spheres to make best use of the
available space, and whether the Riemann hypothesis, which concerns
how the prime numbers are distributed, is true.

Today many of these problems have been resolved, sphere-packing among
them. Others, such as the Riemann hypothesis, have seen little or no
progress. But the first item on Hilbert's list stands out for the
sheer oddness of the answer supplied by generations of mathematicians
since: that mathematics is simply not equipped to provide an answer.

This curiously intractable riddle is known as the continuum
hypothesis, and it concerns that most enigmatic quantity, infinity.
Now, 140 years after the problem was formulated, a respected US
mathematician believes he has cracked it. What's more, he claims to
have arrived at the solution not by using mathematics as we know it,
but by building a new, radically stronger logical structure: a
structure he dubs "ultimate L".

The journey to this point began in the early 1870s, when the German
Georg Cantor was laying the foundations of set theory. Set theory
deals with the counting and manipulation of collections of objects,
and provides the crucial logical underpinnings of mathematics: because
numbers can be associated with the size of sets, the rules for
manipulating sets also determine the logic of arithmetic and
everything that builds on it.

These dry, slightly insipid logical considerations gained a new tang
when Cantor asked a critical question: how big can sets get? The
obvious answer - infinitely big - turned out to have a shocking twist:
infinity is not one entity, but comes in many levels.

How so? You can get a flavour of why by counting up the set of whole
numbers: 1, 2, 3, 4, 5... How far can you go? Why, infinitely far, of
course - there is no biggest whole number. This is one sort of
infinity, the smallest, "countable" level, where the action of
arithmetic takes place.

Now consider the question "how many points are there on a line?" A
line is perfectly straight and smooth, with no holes or gaps; it
contains infinitely many points. But this is not the countable
infinity of the whole numbers, where you bound upwards in a series of
defined, well-separated steps. This is a smooth, continuous infinity
that describes geometrical objects. It is characterised not by the
whole numbers, but by the real numbers: the whole numbers plus all the
numbers in between that have as many decimal places as you please -
0.1, 0.01, √2, π and so on.

Cantor showed that this "continuum" infinity is in fact infinitely
bigger than the countable, whole-number variety. What's more, it is
merely a step in a staircase leading to ever-higher levels of
infinities stretching up as far as, well, infinity.

While the precise structure of these higher infinities remained
nebulous, a more immediate question frustrated Cantor. Was there an
intermediate level between the countable infinity and the continuum?
He suspected not, but was unable to prove it. His hunch about the
non-existence of this mathematical mezzanine became known as the
continuum hypothesis.

Attempts to prove or disprove the continuum hypothesis depend on
analysing all possible infinite subsets of the real numbers. If every
one is either countable or has the same size as the full continuum,
then it is correct. Conversely, even one subset of intermediate size
would render it false.

A similar technique using subsets of the whole numbers shows that
there is no level of infinity below the countable. Tempting as it
might be to think that there are half as many even numbers as there
are whole numbers in total, the two collections can in fact be paired
off exactly. Indeed, every set of whole numbers is either finite or
countably infinite.

Applied to the real numbers, though, this approach bore little fruit,
for reasons that soon became clear. In 1885, the Swedish mathematician
Gösta Mittag-Leffler had blocked publication of one of Cantor's papers
on the basis that it was "about 100 years too soon". And as the
British mathematician and philosopher Bertrand Russell showed in 1901,
Cantor had indeed jumped the gun. Although his conclusions about
infinity were sound, the logical basis of his set theory was flawed,
resting on an informal and ultimately paradoxical conception of what
sets are.

It was not until 1922 that two German mathematicians, Ernst Zermelo
and Abraham Fraenkel, devised a series of rules for manipulating sets
that was seemingly robust enough to support Cantor's tower of
infinities and stabilise the foundations of mathematics.
Unfortunately, though, these rules delivered no clear answer to the
continuum hypothesis. In fact, they seemed strongly to suggest there
might even not be an answer.

Agony of choice

The immediate stumbling block was a rule known as the "axiom of
choice". It was not part of Zermelo and Fraenkel's original rules, but
was soon bolted on when it became clear that some essential
mathematics, such as the ability to compare different sizes of
infinity, would be impossible without it.

The axiom of choice states that if you have a collection of sets, you
can always form a new set by choosing one object from each of them.
That sounds anodyne, but it comes with a sting: you can dream up some
twisted initial sets that produce even stranger sets when you choose
one element from each. The Polish mathematicians Stefan Banach and
Alfred Tarski soon showed how the axiom could be used to divide the
set of points defining a spherical ball into six subsets which could
then be slid around to produce two balls of the same size as the
original. That was a symptom of a fundamental problem: the axiom
allowed peculiarly perverse sets of real numbers to exist whose
properties could never be determined. If so, this was a grim portent
for ever proving the continuum hypothesis.

This news came at a time when the concept of "unprovability" was just
coming into vogue. In 1931, the Austrian logician Kurt Gödel proved
his notorious "incompleteness theorem". It shows that even with the
most tightly knit basic rules, there will always be statements about
sets or numbers that mathematics can neither verify nor disprove.

At the same time, though, Gödel had a crazy-sounding hunch about how
you might fill in most of these cracks in mathematics' underlying
logical structure: you simply build more levels of infinity on top of
it. That goes against anything we might think of as a sound building
code, yet Gödel's guess turned out to be inspired. He proved his point
in 1938. By starting from a simple conception of sets compatible with
Zermelo and Fraenkel's rules and then carefully tailoring its infinite
superstructure, he created a mathematical environment in which both
the axiom of choice and the continuum hypothesis are simultaneously
true. He dubbed his new world the "constructible universe" - or simply
"L".

L was an attractive environment in which to do mathematics, but there
were soon reasons to doubt it was the "right" one. For a start, its
infinite staircase did not extend high enough to fill in all the gaps
known to exist in the underlying structure. In 1963 Paul Cohen of
Stanford University in California put things into context when he
developed a method for producing a multitude of mathematical universes
to order, all of them compatible with Zermelo and Fraenkel's rules.

This was the beginning of a construction boom. "Over the past
half-century, set theorists have discovered a vast diversity of models
of set theory, a chaotic jumble of set-theoretic possibilities," says
Joel Hamkins at the City University of New York. Some are "L-type
worlds" with superstructures like Gödel's L, differing only in the
range of extra levels of infinity they contain; others have wildly
varying architectural styles with completely different levels and
infinite staircases leading in all sorts of directions.

For most purposes, life within these structures is the same: most
everyday mathematics does not differ between them, and nor do the laws
of physics. But the existence of this mathematical "multiverse" also
seemed to dash any notion of ever getting to grips with the continuum
hypothesis. As Cohen was able to show, in some logically possible
worlds the hypothesis is true and there is no intermediate level of
infinity between the countable and the continuum; in others, there is
one; in still others, there are infinitely many. With mathematical
logic as we know it, there is simply no way of finding out which sort
of world we occupy.

That's where Hugh Woodin of the University of California, Berkeley,
has a suggestion. The answer, he says, can be found by stepping
outside our conventional mathematical world and moving on to a higher
plane.

Woodin is no "turn on, tune in" guru. A highly respected set theorist,
he has already achieved his subject's ultimate accolade: a level on
the infinite staircase named after him. This level, which lies far
higher than anything envisaged in Gödel's L, is inhabited by gigantic
entities known as Woodin cardinals.

Woodin cardinals illustrate how adding penthouse suites to the
structure of mathematics can solve problems on less rarefied levels
below. In 1988 the American mathematicians Donald Martin and John
Steel showed that if Woodin cardinals exist, then all "projective"
subsets of the real numbers have a measurable size. Almost all
ordinary geometrical objects can be described in terms of this
particular type of set, so this was just the buttress needed to keep
uncomfortable apparitions such as Banach and Tarski's ball out of
mainstream mathematics.

Such successes left Woodin unsatisfied, however. "What sense is there
in a conception of the universe of sets in which very large sets
exist, if you can't even figure out basic properties of small sets?"
he asks. Even 90 years after Zermelo and Fraenkel had supposedly fixed
the foundations of mathematics, cracks were rife. "Set theory is
riddled with unsolvability. Almost any question you want to ask is
unsolvable," says Woodin. And right at the heart of that lay the
continuum hypothesis.

Ultimate L

Woodin and others spotted the germ of a new, more radical approach
while investigating particular patterns of real numbers that pop up in
various L-type worlds. The patterns, known as universally Baire sets,
subtly changed the geometry possible in each of the worlds and seemed
to act as a kind of identifying code for it. And the more Woodin
looked, the more it became clear that relationships existed between
the patterns in seemingly disparate worlds. By patching the patterns
together, the boundaries that had seemed to exist between the worlds
began to dissolve, and a map of a single mathematical superuniverse
was slowly revealed. In tribute to Gödel's original invention, Woodin
dubbed this gigantic logical structure "ultimate L".

Among other things, ultimate L provides for the first time a
definitive account of the spectrum of subsets of the real numbers: for
every forking point between worlds that Cohen's methods open up, only
one possible route is compatible with Woodin's map. In particular it
implies Cantor's hypothesis to be true, ruling out anything between
countable infinity and the continuum. That would mark not only the end
of a 140-year-old conundrum, but a personal turnaround for Woodin: 10
years ago, he was arguing that the continuum hypothesis should be
considered false.

Ultimate L does not rest there. Its wide, airy space allows extra
steps to be bolted to the top of the infinite staircase as necessary
to fill in gaps below, making good on Gödel's hunch about rooting out
the unsolvability that riddles mathematics. Gödel's incompleteness
theorem would not be dead, but you could chase it as far as you
pleased up the staircase into the infinite attic of mathematics.

The prospect of finally removing the logical incompleteness that has
bedevilled even basic areas such as number theory is enough to get
many mathematicians salivating. There is just one question. Is
ultimate L ultimately true?

Andrés Caicedo, a logician at Boise State University in Idaho, is
cautiously optimistic. "It would be reasonable to say that this is the
'correct' way of going about completing the rules of set theory," he
says. "But there are still several technical issues to be clarified
before saying confidently that it will succeed."

Others are less convinced. Hamkins, who is a former student of
Woodin's, holds to the idea that there simply are as many legitimate
logical constructions for mathematics as we have found so far. He
thinks mathematicians should learn to embrace the diversity of the
mathematical multiverse, with spaces where the continuum hypothesis is
true and others where it is false. The choice of which space to work
in would then be a matter of personal taste and convenience. "The
answer consists of our detailed understanding of how the continuum
hypothesis both holds and fails throughout the multiverse," he says.

Woodin's ideas need not put paid to this choice entirely, though:
aspects of many of these diverse universes will survive inside
ultimate L. "One goal is to show that any universe attainable by means
we can currently foresee can be obtained from the theory," says
Caicedo. "If so, then ultimate L is all we need."

In 2010, Woodin presented his ideas to the same forum that Hilbert had
addressed over a century earlier, the International Congress of
Mathematicians, this time in Hyderabad, India. Hilbert famously once
defended set theory by proclaiming that "no one shall expel us from
the paradise that Cantor has created". But we have been stumbling
around that paradise with no clear idea of where we are. Perhaps now a
guide is within our grasp - one that will take us through this century
and beyond.

Richard Elwes is a teaching fellow at the University of Leeds in the
UK and the author of Maths 1001: Absolutely Everything That Matters in
Mathematics (Quercus, 2010) and How to Build a Brain (Quercus, 2011)

within mutual service, Rich Murray
[hidden email] 505-819-7388 Skype audio, video rich.murray11

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Owen Densmore

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Administrator

Wow, thanks Rich. And the follow-on conversation on the website is also interesting.

I have to admit the Axiom of Choice has been puzzling to me, why its importance, how it is applied and so on.

-- Owen

On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray <[hidden email]> wrote:

"no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
on 8 August 1900, few of the assembled delegates seemed overly
impressed. According to one contemporary report, the discussion
following his address to the second International Congress of
Mathematicians was "rather desultory". Passions seem to have been more
inflamed by a subsequent debate on whether Esperanto should be adopted
as mathematics' working language.

Yet Hilbert's address set the mathematical agenda for the 20th
century. It crystallised into a list of 23 crucial unanswered
questions, including how to pack spheres to make best use of the
available space, and whether the Riemann hypothesis, which concerns
how the prime numbers are distributed, is true.
<snip>

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Bruce Sherwood

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Thanks, Rich, for the interesting note.

For another kind of completeness, I'll comment that I speak Esperanto.

In the period 1900-1905, approximately, there was a lot of interest
among French intellectuals in the possible use of a constructed
language for the purpose of international communications, with
Esperanto the leading contender. This led to a conference of
scientific groups that actually picked a language, Ido, which was a
modified Esperanto which supposedly "fixed" perceived failings of
Esperanto.

Roughly speaking, Ido rejected the unusual non-European structure of
Esperanto in favor of a more "naturalistic" scheme thought to appeal
more to educated Europeans, and possibly easier for Europeans to read
at sight (but likely to be more difficult to speak or write). The
whole affair was a major schism which damaged the movement to adopt an
easy-to-learn second language.

Both Esperanto and Ido still exist in globally dispersed communities,
but the Esperanto community has by far the largest number of speakers
of all the constructed languages. It is difficult to get good numbers,
but there are probably 50 to 100 thousand fluent speakers. I've even
known a number of native speakers of Esperanto, born to parents who
met in the Esperanto-speaking community and continued to speak the
language at home.

Few educated Americans have ever heard of Esperanto, and what they've
heard is in my experience mostly incorrect. Google Esperanto for vast
amounts of information, much of it accurate.

An interesting math connection: Sometime around 1900 Peano, of
mathematical fame, gave a talk in which he started in pure Latin,
progressively during the talk introduced various simplifications, and
by the end was speaking a much simplified Latin which he proposed for
international use.

Bruce

On Thu, Aug 18, 2011 at 9:41 AM, Owen Densmore <[hidden email]> wrote:

> Wow, thanks Rich. And the follow-on conversation on the website is also
> interesting.
> I have to admit the Axiom of Choice has been puzzling to me, why its
> importance, how it is applied and so on.
> -- Owen
>
> On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray <[hidden email]> wrote:
>>
>> "no one shall expel us from the paradise that Cantor has created",
>> Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
>>
>>
>> http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true
>>
>> Ultimate logic: To infinity and beyond
>>
>> 01 August 2011 by Richard Elwes
>> Magazine issue 2823.
>>
>> The mysteries of infinity could lead us to a fantastic structure above
>> and beyond mathematics as we know it
>>
>> WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
>> on 8 August 1900, few of the assembled delegates seemed overly
>> impressed. According to one contemporary report, the discussion
>> following his address to the second International Congress of
>> Mathematicians was "rather desultory". Passions seem to have been more
>> inflamed by a subsequent debate on whether Esperanto should be adopted
>> as mathematics' working language.
>>
>> Yet Hilbert's address set the mathematical agenda for the 20th
>> century. It crystallised into a list of 23 crucial unanswered
>> questions, including how to pack spheres to make best use of the
>> available space, and whether the Riemann hypothesis, which concerns
>> how the prime numbers are distributed, is true.
>> <snip>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>

Steve Smith

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

I appreciate your post Rich and owen and Bruce's responses.

I have a couple of observations:

1) I am always amazed (euphemism for offended) at our use of hyperbole
and superlatives in such things. We all know that mathematics and
science only has false-summits and that all "ultimates" are perpetual
"penultimates", and yet our rhetoric is always laced with absolutes and
mega-gigas and supra-ubers.

2) I have long been fascinated at the interplay between language and
deep understanding. I studied Esperanto alongside Greek and Latin and
Mathematics and Computer Languages in the hopes of finding the right
universal tool, or even a toolbox filled with appropriate tools to
think/communicate in qualitatively better ways. It was not for naught,
and perhaps if I did not have these in my toolbox I would either miss
them dearly or not know enough to miss them. But for the most part, my
improved thinking/communication feels quantitative, not qualitative.

3) Of the several auxiliary languages, I find Interlingua the easiest to
read/understand without any particular training... Esperanto seems to
rely heavily on Portuguese vocabulary/roots which are just (un)familiar
enough for me to find it difficult. In every case, I am not fluent
enough to feel I am able to *think* in these as alternate languages
while I do sometimes think in Spanish, in Mathematics, and in several
computer languages (for very narrow thinking unfortunately). I wish I
could think/percieve in musical structures or holographically, both of
which I have a formal understanding of but only limited intuition.

4) I found David Bohm's Rheomode and Dialogue even more compelling
because it went deeper than "merely" normalizing somewhat across
historical and cultural biases. Esperanto was a great 19th century idea
but I felt it did not go nearly far enough. I was (and am still to some
extent) enamored of his Holonomics and of course the Rheomode and
Dialogue, though the latter two seem under developed and somewhat naive.

- Steve

> Thanks, Rich, for the interesting note.
>
> For another kind of completeness, I'll comment that I speak Esperanto.
>
> In the period 1900-1905, approximately, there was a lot of interest
> among French intellectuals in the possible use of a constructed
> language for the purpose of international communications, with
> Esperanto the leading contender. This led to a conference of
> scientific groups that actually picked a language, Ido, which was a
> modified Esperanto which supposedly "fixed" perceived failings of
> Esperanto.
>
> Roughly speaking, Ido rejected the unusual non-European structure of
> Esperanto in favor of a more "naturalistic" scheme thought to appeal
> more to educated Europeans, and possibly easier for Europeans to read
> at sight (but likely to be more difficult to speak or write). The
> whole affair was a major schism which damaged the movement to adopt an
> easy-to-learn second language.
>
> Both Esperanto and Ido still exist in globally dispersed communities,
> but the Esperanto community has by far the largest number of speakers
> of all the constructed languages. It is difficult to get good numbers,
> but there are probably 50 to 100 thousand fluent speakers. I've even
> known a number of native speakers of Esperanto, born to parents who
> met in the Esperanto-speaking community and continued to speak the
> language at home.
>
> Few educated Americans have ever heard of Esperanto, and what they've
> heard is in my experience mostly incorrect. Google Esperanto for vast
> amounts of information, much of it accurate.
>
> An interesting math connection: Sometime around 1900 Peano, of
> mathematical fame, gave a talk in which he started in pure Latin,
> progressively during the talk introduced various simplifications, and
> by the end was speaking a much simplified Latin which he proposed for
> international use.
>
> Bruce
>
> On Thu, Aug 18, 2011 at 9:41 AM, Owen Densmore<[hidden email]> wrote:
>> Wow, thanks Rich. And the follow-on conversation on the website is also
>> interesting.
>> I have to admit the Axiom of Choice has been puzzling to me, why its
>> importance, how it is applied and so on.
>> -- Owen
>>
>> On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray<[hidden email]> wrote:
>>> "no one shall expel us from the paradise that Cantor has created",
>>> Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
>>>
>>>
>>> http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true
>>>
>>> Ultimate logic: To infinity and beyond
>>>
>>> 01 August 2011 by Richard Elwes
>>> Magazine issue 2823.
>>>
>>> The mysteries of infinity could lead us to a fantastic structure above
>>> and beyond mathematics as we know it
>>>
>>> WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
>>> on 8 August 1900, few of the assembled delegates seemed overly
>>> impressed. According to one contemporary report, the discussion
>>> following his address to the second International Congress of
>>> Mathematicians was "rather desultory". Passions seem to have been more
>>> inflamed by a subsequent debate on whether Esperanto should be adopted
>>> as mathematics' working language.
>>>
>>> Yet Hilbert's address set the mathematical agenda for the 20th
>>> century. It crystallised into a list of 23 crucial unanswered
>>> questions, including how to pack spheres to make best use of the
>>> available space, and whether the Riemann hypothesis, which concerns
>>> how the prime numbers are distributed, is true.
>>> <snip>
>> ============================================================
>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at http://www.friam.org
>>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

Bruce Sherwood

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Interesting reaction to Esperanto vocabulary, which has no Portuguese
roots at all except to the extent that there are many Romance-language
roots in Esperanto, which were borrowed mainly from French or Latin
forms.

A large number of constructed languages including Interlingua were
simplified Latin/Romance languages designed for immediate passive
readability by educated Europeans who already knew some European
languages (even speakers of English and German know lots of Romance
vocabulary). These Latinate languages however are not easy to master
for active use (speaking and writing) due to irregularities and the
requirement of a large vocabulary to be expressive.

Esperanto is unusual in making it possible to be very expressive even
with a rather small vocabulary, thanks to its non-European mechanism
for creating new words out of invariant particles which are themselves
words. It's rather like making molecules out of invariant atoms, and
it contributes to creative linguistic playfulness.

Bruce

On Thu, Aug 18, 2011 at 12:44 PM, Steve Smith <[hidden email]> wrote:

> I appreciate your post Rich and owen and Bruce's responses.
>
> 3) Of the several auxiliary languages, I find Interlingua the easiest to
> read/understand without any particular training... Esperanto seems to rely
> heavily on Portuguese vocabulary/roots which are just (un)familiar enough
> for me to find it difficult. In every case, I am not fluent enough to feel
> I am able to *think* in these as alternate languages while I do sometimes
> think in Spanish, in Mathematics, and in several computer languages (for
> very narrow thinking unfortunately). I wish I could think/percieve in
> musical structures or holographically, both of which I have a formal
> understanding of but only limited intuition.

Steve Smith

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Bruce -
> Interesting reaction to Esperanto vocabulary, which has no Portuguese
> roots at all except to the extent that there are many Romance-language
> roots in Esperanto, which were borrowed mainly from French or Latin
> forms.
Bruce-

Thanks for the correction...

It has been 30+ years since I studied Esperanto and the reaction is a
vestige of my naivette at the time having only border Spanish and a
smattering of Greek/Latin to draw from then.

I might not have known French from Portuguese at the time... though I
*think* I would have... I certainly do now! Or maybe it was just an
intuitive affinity alignment for me.... it is likely that I'd never
seen, or heard any Portuguese until I was introduced to it during my
Esperanto Class as one of the other Romance-languages which I probably
held limited to Italian, Spanish, French at the time...

Is there a reason I would have associated Esperanto with Brazil? Did
they have a strong interest/influence on it?

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Bruce Sherwood

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Yup. Esperanto is rather well known in Brazil (which still means that
the number of Brazilian speakers of Esperanto is small). In fact,
every week (in 10 minutes in fact) I meet on video Skype with
Esperanto-speaking friends I came to know in the Raleigh area when I
was at NCSU (I now live in Santa Fe), and a Brazilian group plans to
join us. However, it's never been the case that Portuguese has had a
major impact on the evolution of Esperanto.

Bruce

On Thu, Aug 18, 2011 at 3:12 PM, Steve Smith <[hidden email]> wrote:

> Bruce -
>>
>> Interesting reaction to Esperanto vocabulary, which has no Portuguese
>> roots at all except to the extent that there are many Romance-language
>> roots in Esperanto, which were borrowed mainly from French or Latin
>> forms.
>
> Bruce-
>
> Thanks for the correction...
>
> It has been 30+ years since I studied Esperanto and the reaction is a
> vestige of my naivette at the time having only border Spanish and a
> smattering of Greek/Latin to draw from then.
>
> I might not have known French from Portuguese at the time... though I
> *think* I would have... I certainly do now! Or maybe it was just an
> intuitive affinity alignment for me.... it is likely that I'd never seen,
> or heard any Portuguese until I was introduced to it during my Esperanto
> Class as one of the other Romance-languages which I probably held limited to
> Italian, Spanish, French at the time...
>
> Is there a reason I would have associated Esperanto with Brazil? Did they
> have a strong interest/influence on it?
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>

Grant Holland

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

In reply to this post by Rich Murray-2

Rich,

Wow. Thanks for passing on such a refreshing and informative article.

You get my vote for the most entertaining FRIAM post of the year (so far).

Grant

On 8/18/11 9:11 AM, Rich Murray wrote:

> "no one shall expel us from the paradise that Cantor has created",
> Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
>
> http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true
>
> Ultimate logic: To infinity and beyond
>
> 01 August 2011 by Richard Elwes
> Magazine issue 2823.
>
> The mysteries of infinity could lead us to a fantastic structure above
> and beyond mathematics as we know it
>
> WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
> on 8 August 1900, few of the assembled delegates seemed overly
> impressed. According to one contemporary report, the discussion
> following his address to the second International Congress of
> Mathematicians was "rather desultory". Passions seem to have been more
> inflamed by a subsequent debate on whether Esperanto should be adopted
> as mathematics' working language.
>
> Yet Hilbert's address set the mathematical agenda for the 20th
> century. It crystallised into a list of 23 crucial unanswered
> questions, including how to pack spheres to make best use of the
> available space, and whether the Riemann hypothesis, which concerns
> how the prime numbers are distributed, is true.
>
> Today many of these problems have been resolved, sphere-packing among
> them. Others, such as the Riemann hypothesis, have seen little or no
> progress. But the first item on Hilbert's list stands out for the
> sheer oddness of the answer supplied by generations of mathematicians
> since: that mathematics is simply not equipped to provide an answer.
>
> This curiously intractable riddle is known as the continuum
> hypothesis, and it concerns that most enigmatic quantity, infinity.
> Now, 140 years after the problem was formulated, a respected US
> mathematician believes he has cracked it. What's more, he claims to
> have arrived at the solution not by using mathematics as we know it,
> but by building a new, radically stronger logical structure: a
> structure he dubs "ultimate L".
>
> The journey to this point began in the early 1870s, when the German
> Georg Cantor was laying the foundations of set theory. Set theory
> deals with the counting and manipulation of collections of objects,
> and provides the crucial logical underpinnings of mathematics: because
> numbers can be associated with the size of sets, the rules for
> manipulating sets also determine the logic of arithmetic and
> everything that builds on it.
>
> These dry, slightly insipid logical considerations gained a new tang
> when Cantor asked a critical question: how big can sets get? The
> obvious answer - infinitely big - turned out to have a shocking twist:
> infinity is not one entity, but comes in many levels.
>
> How so? You can get a flavour of why by counting up the set of whole
> numbers: 1, 2, 3, 4, 5... How far can you go? Why, infinitely far, of
> course - there is no biggest whole number. This is one sort of
> infinity, the smallest, "countable" level, where the action of
> arithmetic takes place.
>
> Now consider the question "how many points are there on a line?" A
> line is perfectly straight and smooth, with no holes or gaps; it
> contains infinitely many points. But this is not the countable
> infinity of the whole numbers, where you bound upwards in a series of
> defined, well-separated steps. This is a smooth, continuous infinity
> that describes geometrical objects. It is characterised not by the
> whole numbers, but by the real numbers: the whole numbers plus all the
> numbers in between that have as many decimal places as you please -
> 0.1, 0.01, √2, π and so on.
>
> Cantor showed that this "continuum" infinity is in fact infinitely
> bigger than the countable, whole-number variety. What's more, it is
> merely a step in a staircase leading to ever-higher levels of
> infinities stretching up as far as, well, infinity.
>
> While the precise structure of these higher infinities remained
> nebulous, a more immediate question frustrated Cantor. Was there an
> intermediate level between the countable infinity and the continuum?
> He suspected not, but was unable to prove it. His hunch about the
> non-existence of this mathematical mezzanine became known as the
> continuum hypothesis.
>
> Attempts to prove or disprove the continuum hypothesis depend on
> analysing all possible infinite subsets of the real numbers. If every
> one is either countable or has the same size as the full continuum,
> then it is correct. Conversely, even one subset of intermediate size
> would render it false.
>
> A similar technique using subsets of the whole numbers shows that
> there is no level of infinity below the countable. Tempting as it
> might be to think that there are half as many even numbers as there
> are whole numbers in total, the two collections can in fact be paired
> off exactly. Indeed, every set of whole numbers is either finite or
> countably infinite.
>
> Applied to the real numbers, though, this approach bore little fruit,
> for reasons that soon became clear. In 1885, the Swedish mathematician
> Gösta Mittag-Leffler had blocked publication of one of Cantor's papers
> on the basis that it was "about 100 years too soon". And as the
> British mathematician and philosopher Bertrand Russell showed in 1901,
> Cantor had indeed jumped the gun. Although his conclusions about
> infinity were sound, the logical basis of his set theory was flawed,
> resting on an informal and ultimately paradoxical conception of what
> sets are.
>
> It was not until 1922 that two German mathematicians, Ernst Zermelo
> and Abraham Fraenkel, devised a series of rules for manipulating sets
> that was seemingly robust enough to support Cantor's tower of
> infinities and stabilise the foundations of mathematics.
> Unfortunately, though, these rules delivered no clear answer to the
> continuum hypothesis. In fact, they seemed strongly to suggest there
> might even not be an answer.
>
> Agony of choice
>
> The immediate stumbling block was a rule known as the "axiom of
> choice". It was not part of Zermelo and Fraenkel's original rules, but
> was soon bolted on when it became clear that some essential
> mathematics, such as the ability to compare different sizes of
> infinity, would be impossible without it.
>
> The axiom of choice states that if you have a collection of sets, you
> can always form a new set by choosing one object from each of them.
> That sounds anodyne, but it comes with a sting: you can dream up some
> twisted initial sets that produce even stranger sets when you choose
> one element from each. The Polish mathematicians Stefan Banach and
> Alfred Tarski soon showed how the axiom could be used to divide the
> set of points defining a spherical ball into six subsets which could
> then be slid around to produce two balls of the same size as the
> original. That was a symptom of a fundamental problem: the axiom
> allowed peculiarly perverse sets of real numbers to exist whose
> properties could never be determined. If so, this was a grim portent
> for ever proving the continuum hypothesis.
>
> This news came at a time when the concept of "unprovability" was just
> coming into vogue. In 1931, the Austrian logician Kurt Gödel proved
> his notorious "incompleteness theorem". It shows that even with the
> most tightly knit basic rules, there will always be statements about
> sets or numbers that mathematics can neither verify nor disprove.
>
> At the same time, though, Gödel had a crazy-sounding hunch about how
> you might fill in most of these cracks in mathematics' underlying
> logical structure: you simply build more levels of infinity on top of
> it. That goes against anything we might think of as a sound building
> code, yet Gödel's guess turned out to be inspired. He proved his point
> in 1938. By starting from a simple conception of sets compatible with
> Zermelo and Fraenkel's rules and then carefully tailoring its infinite
> superstructure, he created a mathematical environment in which both
> the axiom of choice and the continuum hypothesis are simultaneously
> true. He dubbed his new world the "constructible universe" - or simply
> "L".
>
> L was an attractive environment in which to do mathematics, but there
> were soon reasons to doubt it was the "right" one. For a start, its
> infinite staircase did not extend high enough to fill in all the gaps
> known to exist in the underlying structure. In 1963 Paul Cohen of
> Stanford University in California put things into context when he
> developed a method for producing a multitude of mathematical universes
> to order, all of them compatible with Zermelo and Fraenkel's rules.
>
> This was the beginning of a construction boom. "Over the past
> half-century, set theorists have discovered a vast diversity of models
> of set theory, a chaotic jumble of set-theoretic possibilities," says
> Joel Hamkins at the City University of New York. Some are "L-type
> worlds" with superstructures like Gödel's L, differing only in the
> range of extra levels of infinity they contain; others have wildly
> varying architectural styles with completely different levels and
> infinite staircases leading in all sorts of directions.
>
> For most purposes, life within these structures is the same: most
> everyday mathematics does not differ between them, and nor do the laws
> of physics. But the existence of this mathematical "multiverse" also
> seemed to dash any notion of ever getting to grips with the continuum
> hypothesis. As Cohen was able to show, in some logically possible
> worlds the hypothesis is true and there is no intermediate level of
> infinity between the countable and the continuum; in others, there is
> one; in still others, there are infinitely many. With mathematical
> logic as we know it, there is simply no way of finding out which sort
> of world we occupy.
>
> That's where Hugh Woodin of the University of California, Berkeley,
> has a suggestion. The answer, he says, can be found by stepping
> outside our conventional mathematical world and moving on to a higher
> plane.
>
> Woodin is no "turn on, tune in" guru. A highly respected set theorist,
> he has already achieved his subject's ultimate accolade: a level on
> the infinite staircase named after him. This level, which lies far
> higher than anything envisaged in Gödel's L, is inhabited by gigantic
> entities known as Woodin cardinals.
>
> Woodin cardinals illustrate how adding penthouse suites to the
> structure of mathematics can solve problems on less rarefied levels
> below. In 1988 the American mathematicians Donald Martin and John
> Steel showed that if Woodin cardinals exist, then all "projective"
> subsets of the real numbers have a measurable size. Almost all
> ordinary geometrical objects can be described in terms of this
> particular type of set, so this was just the buttress needed to keep
> uncomfortable apparitions such as Banach and Tarski's ball out of
> mainstream mathematics.
>
> Such successes left Woodin unsatisfied, however. "What sense is there
> in a conception of the universe of sets in which very large sets
> exist, if you can't even figure out basic properties of small sets?"
> he asks. Even 90 years after Zermelo and Fraenkel had supposedly fixed
> the foundations of mathematics, cracks were rife. "Set theory is
> riddled with unsolvability. Almost any question you want to ask is
> unsolvable," says Woodin. And right at the heart of that lay the
> continuum hypothesis.
>
> Ultimate L
>
> Woodin and others spotted the germ of a new, more radical approach
> while investigating particular patterns of real numbers that pop up in
> various L-type worlds. The patterns, known as universally Baire sets,
> subtly changed the geometry possible in each of the worlds and seemed
> to act as a kind of identifying code for it. And the more Woodin
> looked, the more it became clear that relationships existed between
> the patterns in seemingly disparate worlds. By patching the patterns
> together, the boundaries that had seemed to exist between the worlds
> began to dissolve, and a map of a single mathematical superuniverse
> was slowly revealed. In tribute to Gödel's original invention, Woodin
> dubbed this gigantic logical structure "ultimate L".
>
> Among other things, ultimate L provides for the first time a
> definitive account of the spectrum of subsets of the real numbers: for
> every forking point between worlds that Cohen's methods open up, only
> one possible route is compatible with Woodin's map. In particular it
> implies Cantor's hypothesis to be true, ruling out anything between
> countable infinity and the continuum. That would mark not only the end
> of a 140-year-old conundrum, but a personal turnaround for Woodin: 10
> years ago, he was arguing that the continuum hypothesis should be
> considered false.
>
> Ultimate L does not rest there. Its wide, airy space allows extra
> steps to be bolted to the top of the infinite staircase as necessary
> to fill in gaps below, making good on Gödel's hunch about rooting out
> the unsolvability that riddles mathematics. Gödel's incompleteness
> theorem would not be dead, but you could chase it as far as you
> pleased up the staircase into the infinite attic of mathematics.
>
> The prospect of finally removing the logical incompleteness that has
> bedevilled even basic areas such as number theory is enough to get
> many mathematicians salivating. There is just one question. Is
> ultimate L ultimately true?
>
> Andrés Caicedo, a logician at Boise State University in Idaho, is
> cautiously optimistic. "It would be reasonable to say that this is the
> 'correct' way of going about completing the rules of set theory," he
> says. "But there are still several technical issues to be clarified
> before saying confidently that it will succeed."
>
> Others are less convinced. Hamkins, who is a former student of
> Woodin's, holds to the idea that there simply are as many legitimate
> logical constructions for mathematics as we have found so far. He
> thinks mathematicians should learn to embrace the diversity of the
> mathematical multiverse, with spaces where the continuum hypothesis is
> true and others where it is false. The choice of which space to work
> in would then be a matter of personal taste and convenience. "The
> answer consists of our detailed understanding of how the continuum
> hypothesis both holds and fails throughout the multiverse," he says.
>
> Woodin's ideas need not put paid to this choice entirely, though:
> aspects of many of these diverse universes will survive inside
> ultimate L. "One goal is to show that any universe attainable by means
> we can currently foresee can be obtained from the theory," says
> Caicedo. "If so, then ultimate L is all we need."
>
> In 2010, Woodin presented his ideas to the same forum that Hilbert had
> addressed over a century earlier, the International Congress of
> Mathematicians, this time in Hyderabad, India. Hilbert famously once
> defended set theory by proclaiming that "no one shall expel us from
> the paradise that Cantor has created". But we have been stumbling
> around that paradise with no clear idea of where we are. Perhaps now a
> guide is within our grasp - one that will take us through this century
> and beyond.
>
> Richard Elwes is a teaching fellow at the University of Leeds in the
> UK and the author of Maths 1001: Absolutely Everything That Matters in
> Mathematics (Quercus, 2010) and How to Build a Brain (Quercus, 2011)
>
>
> within mutual service, Rich Murray
> [hidden email] 505-819-7388 Skype audio, video rich.murray11
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

Eric Charles

The myth of knowledge

In reply to this post by Rich Murray-2

Shameless plug: I have started a academically-oriented blog. I suspect my most recent post, on 'The Myth of Knowledge', is relevant to many of the discussions that I have been part of on this list, and will be of interest to at least a few people here.

I now return you to your regularly scheduled posts (and second the point that the 'ultimate L' article was very cool).

Eric

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Owen Densmore

Re: The myth of knowledge

Administrator

Whoa, how about more? Why did you feel a need to start the blog? What is your goal? Why "psychology" or "fixing"? .. possibly Cognitive Science, or History of Science, or xx?

We need at least a trailer .. maybe the first post was it?

-- Owen

On Thu, Aug 18, 2011 at 6:03 PM, ERIC P. CHARLES <[hidden email]> wrote:

Shameless plug: I have started a academically-oriented blog. I suspect my most recent post, on 'The Myth of Knowledge', is relevant to many of the discussions that I have been part of on this list, and will be of interest to at least a few people here.

I now return you to your regularly scheduled posts (and second the point that the 'ultimate L' article was very cool).

Eric

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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Robert J. Cordingley

Re: The myth of knowledge

In reply to this post by Eric Charles

Interesting. It seems though it isn't knowledge that is core to your discussion but our 'knowing' - the human experience. What makes some things 'compiled' knowledge (in our experience, like riding a bike) and some things expressible knowledge (which we can teach, like nuclear physics)? Is it a physiological problem between muscle memory, the spinal cord, and the thing we call the brain?

Robert C
www.cirrillian.com

On 8/18/11 6:03 PM, ERIC P. CHARLES wrote:

Shameless plug: I have started a academically-oriented blog. I suspect my most recent post, on 'The Myth of Knowledge', is relevant to many of the discussions that I have been part of on this list, and will be of interest to at least a few people here.

I now return you to your regularly scheduled posts (and second the point that the 'ultimate L' article was very cool).

Eric
============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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Eric Charles

Re: The myth of knowledge

Not wanting to bring this thread to the list without evidence of greater interest, I have made posting on the blog more flexible, Robert has posted there, and I have replied on the blog.

Eric

On Fri, Aug 19, 2011 10:20 AM, "Robert J. Cordingley" <[hidden email]> wrote:

Interesting. It seems though it isn't knowledge that is core to your discussion but our 'knowing' - the human experience. What makes some things 'compiled' knowledge (in our experience, like riding a bike) and some things expressible knowledge (which we can teach, like nuclear physics)? Is it a physiological problem between muscle memory, the spinal cord, and the thing we call the brain?

Robert C
<a href="http://www.cirrillian.com" onclick="window.open('http://www.cirrillian.com');return false;">www.cirrillian.com

On 8/18/11 6:03 PM, ERIC P. CHARLES wrote:
Shameless plug: I have started a academically-oriented blog. I suspect my most recent post, on '<a moz-do-not-send="" href="http://fixingpsychology.blogspot.com/" onclick="window.open('http://fixingpsychology.blogspot.com/');return false;">The Myth of Knowledge', is relevant to many of the discussions that I have been part of on this list, and will be of interest to at least a few people here.

I now return you to your regularly scheduled posts (and second the point that the 'ultimate L' article was very cool).

Eric

============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at <a class="moz-txt-link-freetext" href="http://www.friam.org" onclick="window.open('http://www.friam.org');return false;">http://www.friam.org
============================================================
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Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

Rich Murray-2

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

In reply to this post by Grant Holland

each of us is all of single entire unified creative fractal
hyperinfinity ... . . . . Rich Murray 2011.08.19

thus, just as with the one-to-one matching of any minute subset of
real line continuum with entire continuum, obvious by glancing that
concentric circles bigger and bigger around a common center, can have
infinite straight radial lines from - to + through the center at 0,0

we see any seemingly individualized "minute" process within the
fractal hyperinfinity has the same order of hyperinfinity as the whole

we can lose the concepts of inner/outer and small/large in many global
multi-dimensional geometries in which the fractal variations can not
be used to establish these kind of properties -- not simple or
primary, but applicable to limited subsets after a lot of mathematical
stage setting

the same goes for before/now/after or simple/complex or cause/effect

this present moment -- of awareness (somewhere?) of writing, and
awareness (for, "my" here, an elsewhere and a hereafter) of seeing,
reading, comprehending little crooked black ma r k s this very in
s t a n t

for all sides, actually inside, highly prejudiced testimony supporting
purported sustaining reality of self/world

with severely circumscribed templates for communication/collaboration

however, actually no ground to describe measure understand limit
predict fear control the now moment movement

any holding on just more proof of already never is

now moment already timelessly locationlessly sizelessly open/vast

the shared cocreated self/world simulation already making timeless
"quantum" jumps in quality as well as quantity

we deliberately openmindedly boldly
choose/invite/allow/accept/enjoy/trust/share/celebrate/function/create/serve
transformations
of self/other simulation

here float
can do no other
God willing

within mutual service, Rich Murray
[hidden email] 505-819-7388
Skype audio, video rich.murray11

On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland
<[hidden email]> wrote:

Rich,

Wow. Thanks for passing on such a refreshing and informative article.

You get my vote for the most entertaining FRIAM post of the year (so far).

Grant

On 8/18/11 9:11 AM, Rich Murray wrote:

"no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Victoria Hughes

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

"God is a circle whose center is everywhere and whose circumference is nowhere."

attributed to various philosophers, beginning with Empedocles

a non-dual rephrase> " ... whose center is everywhere and circumference is now here".

or even "be the hologram you are, babe".

On Aug 19, 2011, at 5:11 PM, Rich Murray wrote:

each of us is all of single entire unified creative fractal
hyperinfinity ... .   .    .    . Rich Murray 2011.08.19

thus, just as with the one-to-one matching of any minute subset of
real line continuum with entire continuum, obvious by glancing that
concentric circles bigger and bigger around a common center, can have
infinite straight radial lines from - to + through the center at 0,0

we see any seemingly individualized "minute" process within the
fractal hyperinfinity has the same order of hyperinfinity as the whole

we can lose the concepts of inner/outer and small/large in many global
multi-dimensional geometries in which the fractal variations can not
be used to establish these kind of properties -- not simple or
primary, but applicable to limited subsets after a lot of mathematical
stage setting

the same goes for before/now/after or simple/complex or cause/effect

this present moment -- of awareness (somewhere?) of writing, and
awareness (for, "my" here, an elsewhere and a hereafter) of seeing,
reading, comprehending little crooked black ma r k    s this very in
s t   a    n      t

for all sides, actually inside, highly prejudiced testimony supporting
purported sustaining reality of self/world

with severely circumscribed templates for communication/collaboration

however, actually no ground to describe measure understand limit
predict fear control the now moment movement

any holding on just more proof of already never is

now moment already timelessly locationlessly sizelessly open/vast

the shared cocreated self/world simulation already making timeless
"quantum" jumps in quality as well as quantity

we deliberately openmindedly boldly
choose/invite/allow/accept/enjoy/trust/share/celebrate/function/create/serve
transformations
of self/other simulation

here float
can do no other
God willing

within mutual service, Rich Murray
[hidden email] 505-819-7388
Skype audio, video rich.murray11

On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland
<[hidden email]> wrote:

Rich,

Wow. Thanks for passing on such a refreshing and informative article.

You get my vote for the most entertaining FRIAM post of the year (so far).

Grant

On 8/18/11 9:11 AM, Rich Murray wrote:

"no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Rich Murray-2

Re: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

Thanks, Tory,

great to appreciate http://toryhughes.com/news/
re your art show now at StarBucks on the Plaza this month

I've been artistically doing science:

Richat Structure, Mauritania -- Cox geoablation via Boslough comet
fragment air burst directed 6,000 K high pressure directed jets: Rich
Murray 2011.08.17
http://rmforall.blogspot.com/2011_08_01_archive.htm
Thursday, August 18, 2011
[ at end of each long page, click on Older Posts ]
http://groups.yahoo.com/group/astrodeep/message/93
[ you may have to Copy and Paste URLs into your browser ]

10 m broken rock hill with black glazes, W of Rancho Alegre Road, S of
Coyote Trail, W of Hwy 14, S of Santa Fe, New Mexico, tour of 50
photos 1 MB size each via DropBox: Rich Murray 2011.07.28 2011.08.03
http://rmforall.blogspot.com/2011_08_01_archive.htm
Wednesday, August 3, 2011
[ at end of each long page, click on Older Posts ]
http://groups.yahoo.com/group/astrodeep/message/92
[ you may have to Copy and Paste URLs into your browser ]

HUDF center top left, #90 astrodeep200407aab10ada.png 3.68 MB
1244X1243 1 of 4 identical views with different color schemes
2008.12.12 #88-91 on rmforall at flickr.com: Rich Murray 2011.01.09
http://rmforall.blogspot.com/2011_01_01_archive.htm
Sunday, January 9, 2011
[ at end of each long page, click on Older Posts ]
http://groups.yahoo.com/group/astrodeep/message/80
[you may have to Copy and Paste URLs into your browser]

within mutual service, Rich Murray
[hidden email] 505-819-7388
Skype audio, video rich.murray11

On Fri, Aug 19, 2011 at 4:38 PM, Victoria Hughes
<[hidden email]> wrote:

"God is a circle whose center is everywhere and whose circumference is
nowhere."
attributed to various philosophers, beginning with Empedocles
a non-dual rephrase> " ... whose center is everywhere and circumference is
now here".
or even "be the hologram you are, babe".

On Aug 19, 2011, at 5:11 PM, Rich Murray wrote:

each of us is all of single entire unified creative fractal
hyperinfinity ... .   .    .    . Rich Murray 2011.08.19
>
thus, just as with the one-to-one matching of any minute subset of
real line continuum with entire continuum, obvious by glancing that
concentric circles bigger and bigger around a common center, can have
infinite straight radial lines from - to + through the center at 0,0

we see any seemingly individualized "minute" process within the
fractal hyperinfinity has the same order of hyperinfinity as the whole

we can lose the concepts of inner/outer and small/large in many global
multi-dimensional geometries in which the fractal variations can not
be used to establish these kind of properties -- not simple or
primary, but applicable to limited subsets after a lot of mathematical
stage setting

the same goes for before/now/after or simple/complex or cause/effect

this present moment -- of awareness (somewhere?) of writing, and
awareness (for, "my" here, an elsewhere and a hereafter) of seeing,
reading, comprehending little crooked black ma r k    s this very in
s t   a    n      t

for all sides, actually inside, highly prejudiced testimony supporting
purported sustaining reality of self/world

with severely circumscribed templates for communication/collaboration

however, actually no ground to describe measure understand limit
predict fear control the now moment movement

any holding on just more proof of already never is

now moment already timelessly locationlessly sizelessly open/vast

the shared cocreated self/world simulation already making timeless
"quantum" jumps in quality as well as quantity

we deliberately openmindedly boldly
choose/invite/allow/accept/enjoy/trust/share/celebrate/function/create/serve
transformations
of self/other simulation

here float
can do no other
God willing

within mutual service, Rich Murray
[hidden email] 505-819-7388
Skype audio, video rich.murray11

On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland
<[hidden email]> wrote:

Rich,
>
Wow. Thanks for passing on such a refreshing and informative article.

You get my vote for the most entertaining FRIAM post of the year (so far).

Grant

On 8/18/11 9:11 AM, Rich Murray wrote:

"no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Eric Charles

Re: The myth of knowledge

In reply to this post by Eric Charles

Resend: I have not seen this post yet, apologies if it is a repeat.

Owen,
Alas, the first post was not a trailer (Nick has been haranguing me about this). Instead, the first post was an attempt to crudely connect my blog with the other blogs I have been actively commenting on for the past year or so (to try to get some instant gratification in terms of traffic and comments, and to acknowledge others' influence in the current endeavor). So, here it goes...

I struggled to pick a good title. "Fixing Psychology" seemed appropriate to the things I am likely to write about, and also a touch provocative... which I liked. For the past hundred years or so, psychology has been in a state like physics was shortly before Einstein - from the outside things look fine, but inside there are hosts of cracks in the system, and the patches aren't holding very well. As late as the 1970's you could still find water cooler conversation in psychology departments between people wondering what subfield the next "Newton" of psychology would come from - What type of theory would eventually emerge to unify the field? What type of person would create it? However, that hope has been almost totally abandoned and psychology continues to fragment. Also, as a result of that fragmentation some of the most scientifically 'solid' areas of psychological research (learning theory and perceptual research) have become very marginalized. The few things that presently serves as a 'foundation' for the field are not ideal. So in that sense, psychology needs fixing in two ways: 1) We need to work towards unity, rather than division. 2) We need a better foundation to build that unity on.

Many of my past and in-progress publications are along these lines, but I was hoping that a blog would provide a place to develop parts of more long-term projects, to test run new ideas, and to develop responses too long to be a 'comment' somewhere else. In particular, I am hoping to generate feedback and reactions while the works are still in progress, and to stimulate discussion more generally. Among the long term projects are: 1) A Perception-Action textbook I am trying to produce through massively multi-authored means through the International Society for Ecological Psychology. The book would have perception at its core, but connect to social psychology, cognitive psychology, and other areas commonly thought of in a disjointed fashion. 2) A book on "Natural Design" in which I am trying to tie 40 years worth of Nick's work into a coherent story showing the connection between evolutionary biology, behavior, and psychology. 3) The most long term, an Introductory Psychology textbook that presents psychology in a unified rather than fragmentary way. Also, on the "service" side of my job, I am heading a taskforce for the 'Society of General Psychology' trying to find ways to support early career psychologists who are trying to pursue general interests against the pressures to narrowly specialize.

One thing not to under-emphasize, is that very few of the ideas I will be proffering are that new. There was a false-start towards a psychology influenced by American Pragmatism in the early 1900's. It remains the most coherent framework for a science of psychology, and so most of what I'll be promoting to "fix" psychology are other people's ideas that are a hundred years old. In some places I will be very explicit about that historic context, in other places I will just try to explain how things look from that point of view. Also, my desire to simply stimulate discussion should not be under-emphasized. If I could get any reasonable number of people to start thinking seriously about unifying psychology, I would be pretty happy, even if they didn't like my suggestions for how to do it.

Was that what you were looking for?

Eric

On Thu, Aug 18, 2011 11:20 PM, Owen Densmore <[hidden email]> wrote:

Whoa, how about more? Why did you feel a need to start the blog? What is your goal? Why "psychology" or "fixing"? .. possibly Cognitive Science, or History of Science, or xx?

We need at least a trailer .. maybe the first post was it?

-- Owen

On Thu, Aug 18, 2011 at 6:03 PM, ERIC P. CHARLES <epc2@...> wrote:
Shameless plug: I have started a academically-oriented blog. I suspect my most recent post, on '<a href="http://fixingpsychology.blogspot.com/" target="" onclick="window.open('http://fixingpsychology.blogspot.com/');return false;">The Myth of Knowledge', is relevant to many of the discussions that I have been part of on this list, and will be of interest to at least a few people here.

I now return you to your regularly scheduled posts (and second the point that the 'ultimate L' article was very cool).

Eric

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Meets Fridays 9a-11:30 at cafe at St. John's College
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Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

Eric Charles

Re: The myth of knowledge

Forwarded to list at Owen's request...

Owen,
I'll meditate on a more thorough answer, but the quick one is: Yes, psychology is "fragmented in the sense of having little or no basis upon which psychologists agree." The original umbrella organization, the American Psychological Association now has 56 Divisions! The original idea was to create "Unity Through Division" (and a multi-volume history of the APA is so titled), but it has not worked. Instead, it has only lead to greater fragmentation. There is no framework nor even a set of core phenomenon, core experiments, or core findings that holds things together.

Eric

On Sat, Aug 20, 2011 12:34 PM, Owen Densmore <[hidden email]> wrote:

Not a duplicate, at least for me, so I'm really glad you did resend! And, yes, that was exactly what I was looking for. I had no idea that psychology was, at least from the inside, fragmented as you describe.

The unification theme is subtle: upon what "axis" does a multidimensional system unify?

I'm reading a wonderful book by Timothy Gowers, a Fields medalist mathematician, who wrote The Princeton Companion to Mathematics. (There is no Nobel prize in mathematics: <a href="http://goo.gl/mj7f" onclick="window.open('http://goo.gl/mj7f');return false;">http://goo.gl/mj7f) He was concerned not about how to unify mathematics, but show what that unified structure was. It's not a "math book" per se, but a series of ever-deeper plunges into the structure and scope of the areas of mathematics, and how they overlap.

It is a "companion" in that it claims no authority or completeness as an encyclopedia might. Rather it is a very human guide, with a point of view (opinions) and gaps. It was as much orchestrated by TG as written .. it had a web-site with many commentators, and has several sections of the book written by experts in particular areas.

One is struck by the fact that even though there are many fields, this is not considered fragmentation because they all accept certain fundamentals.

Psychology is "fragmented" to we novices in that there are many fields. And a "Companion" would certainly be useful for us. But is it fragmented in the sense of having little or no basis upon which psychologists agree?

-- Owen

Links:

Gowers' home page <a href="http://gowers.wordpress.com/" onclick="window.open('http://gowers.wordpress.com/');return false;">http://gowers.wordpress.com/

Polymath Project: <a href="http://polymathprojects.org/" onclick="window.open('http://polymathprojects.org/');return false;">http://polymathprojects.org/ (Shows community process in math)

Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

Nick Thompson

Re: The myth of knowledge

Oh, dear, Eric. You have just confirmed Owen’s worst suspicions about psychology.

Next we will be hearing from the pomo crowd that the reason psychologists cannot agree is that there is no such thing as human psychology, that the study of human behavior is like the study of English literature, and that we should no more expect psychology to converge on a common approach than we would expect literary criticism to converge on a common view of what good fiction is. It’s just power and politics all the way down.

[sigh]

Nick

From: [hidden email] [mailto:[hidden email]] On Behalf Of ERIC P. CHARLES
Sent: Saturday, August 20, 2011 5:42 PM
To: Owen Densmore
Cc: friam
Subject: Re: [FRIAM] The myth of knowledge

Not a duplicate, at least for me, so I'm really glad you did resend! And, yes, that was exactly what I was looking for. I had no idea that psychology was, at least from the inside, fragmented as you describe.

The unification theme is subtle: upon what "axis" does a multidimensional system unify?

I'm reading a wonderful book by Timothy Gowers, a Fields medalist mathematician, who wrote The Princeton Companion to Mathematics. (There is no Nobel prize in mathematics: http://goo.gl/mj7f) He was concerned not about how to unify mathematics, but show what that unified structure was. It's not a "math book" per se, but a series of ever-deeper plunges into the structure and scope of the areas of mathematics, and how they overlap.

It is a "companion" in that it claims no authority or completeness as an encyclopedia might. Rather it is a very human guide, with a point of view (opinions) and gaps. It was as much orchestrated by TG as written .. it had a web-site with many commentators, and has several sections of the book written by experts in particular areas.

One is struck by the fact that even though there are many fields, this is not considered fragmentation because they all accept certain fundamentals.

Psychology is "fragmented" to we novices in that there are many fields. And a "Companion" would certainly be useful for us. But is it fragmented in the sense of having little or no basis upon which psychologists agree?

-- Owen

Links:

Gowers' home page http://gowers.wordpress.com/

Polymath Project: http://polymathprojects.org/ (Shows community process in math)

Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601