[Xmca-l] Re: the ancients and the moderns

[Edward Wall]

Andy

      “World view” belonged to Bil, not me. 

      I think the history of mathematics fits rather well into what you found during your research (I agree with your reasoning about Copernicus and David’s view of the historical)); i.e. there was a lot of stirring and sharing. ’Actual’ Greek mathematics was, in a sense, rather fragile and, in a sense, substantially misunderstood after the fact. I would say that well before anything resembling Christianity and certainly well before the ‘Roman Church’ there were barely remnants of the Greek mathematical intellectual tradition. There were some early neo-platonists who tried, but reasonably unsuccessfully. However, texts (for example, Euclid) were saved, principally by Islamic scholars and there was developed a certain tradition of a proto-alegbra - mainly Islamic, at first - which spread into Europe. Most European mathematics, at this time of what little there was, was highly procedural; however some people - thinking, by the way, that they were continuing the Greek mathematical tradition (erroneously) began to make certain ‘symbolic’ generalizations that led, over a substantial amount of time, into modern mathematics. There has been some recovery of what seems to have been the original Greek mathematical intellectual tradition. Anyway mathematicians - probably mistakenly - view Euclid’s geometry as the Greek contribution and, in a way, as the only important ancient historical mathematical tradition (mainly because of a unique Greek mathematical methodology that is called ‘proof’).

     Interestedly, the beginnings of Davydov’s mathematics curriculum-  i.e. the measurement business -  is rather ‘Greek’ and Plato would have thought the way we think about ‘fractions' profoundly dubious. I have always whether the reason children struggle with such is because the Modern take is rather , in a sense, counter-intuitive given their experiences. Anyway Klein says all this better than I.

Ed

     

"The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth" - Niels Bohr




> On Apr 14, 2018, at  9:31 PM, Andy Blunden <andyb@marxists.org> wrote:
> 
> I am sure you are right, Ed, in that the history of
> mathematics must be in considerable measure one made up of
> scholars reading each other's work over vast expanses of
> time and space, and it is all much more complicated than I
> know. And Greek mathematics reached us not only via the
> Islamic world, but by the collaboration of Christian and
> Islamic scholars in Spain, I think. It was you invocation of
> "world view" which triggered my response.
> 
> In doing my research for "The Origins of Collective Decision
> Making" I found that academic historians wrote histories
> based on texts written by philosophers and it went: Ancient
> Greece, briefly Pliny, Gaius etc, then Condorcet and the
> philosophers of the French revolution, skipping blithely
> over a millennium and a half in which the common people
> developed and practised methods of collective decision
> making, upon which the French Philosophers of the 18th
> century could spin their elaborate and largely puerile and
> impractical theories. So, I wondered how much Copernicus
> owed to ancients Greeks who had already tried to measure the
> diameter of the Earth, and how much he owed to Italian and
> Dutch lens-makers and other artisans who developed very
> different approaches to understanding how Nature worked.
> Probably the "world view" that informed Galileo he owed to
> medieval Europe rather than Greek, Roman or Islamic scholars.
> 
> Andy
> 
> ------------------------------------------------------------
> Andy Blunden
> ttp://www.ethicalpolitics.org/ablunden/index.htm
> On 15/04/2018 5:53 AM, Edward Wall wrote:
>> Andy
>> 
>>      While there is much in what you say, a good bit of Greek mathematics was mediated through the Arabs. There is plenty of historical evidence. As regards it being mainly scripture, Plato has Socrates do considerable mathematics. Jacob Klein makes the point fairly well that there isn’t continuity re mathematics (ancient to modern); however that has little to do (in a sense) with the Roman Church. It has more to do with European adaptions of number. Nevertheless, my experience thinking in and outside mathematics classrooms, indicates a naive Greek view of number is alive and well.
>> 
>> Ed
>> 
>> "The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth" - Niels Bohr
>> 
>> 
>> 
>> 
>>> On Apr 14, 2018, at  12:34 AM, Andy Blunden <andyb@marxists.org> wrote:
>>> 
>>> Bill, I don't have any particular recommendation for your
>>> reading, but I have noticed a strange thing about how we
>>> view our intellectual history.
>>> 
>>> There is no direct connection between modern (i.e.,
>>> post-Copernicus) European thinking and the ancient Greeks.
>>> The only connections were mediated by the Romans, and after
>>> the decline of the Roman Empire by the Roman Church, and the
>>> Islamic world, and the heritage we received by this route
>>> was entirely scriptural. The legacy received via the Roman
>>> Church was of course a priestly one.
>>> 
>>> So I question whether there is any continuity in "world
>>> view" between the Greeks and the moderns, so the question of
>>> a "change" is problematic. So far as I can see modern,
>>> bourgeois consciousness arose out of the feudal societies
>>> which restored themselves after the Romans left. It is true
>>> that these societies were not particularly literate, so
>>> written records are mostly owed to the monasteries.
>>> 
>>> I am no historian, Bill, and maybe I'm missing something?
>>> 
>>> Andy
>>> 
>>> ------------------------------------------------------------
>>> Andy Blunden
>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>> On 14/04/2018 2:07 PM, Bill Kerr wrote:
>>>> Thanks Ed,
>>>> 
>>>> A good Samaritan sent me a copy of "The Ethnomethodological Foundations of
>>>> Mathematics”. I've ordered a copy of "Ethnographies of Reason.”
>>>> 
>>>> I looked up the other two. Once again, they are quite expensive. I am
>>>> interested in that change of world view that occurred b/w the Greeks and
>>>> the Moderns. I read a short book about Francis Bacon by Benjamin Farrington
>>>> that went into that .
>>>> 
>>>> Cheers, Bill
>>>> 
>>>> On Sat, Apr 14, 2018 at 9:38 AM, Edward Wall <ewall@umich.edu> wrote:
>>>> 
>>>>> Bill
>>>>> 
>>>>>    The book "The Ethnomethodological Foundations of Mathematics” - an
>>>>> ‘interesting' take on Godel’s First Incompleteness Theorem - is just a nice
>>>>> typeset copy of his dissertation (he may have a few extra things; I think I
>>>>> looked at it once and didn’t see much different but perhaps Michael thinks
>>>>> otherwise) which you can get from ProQuest for about $35 or whatever the
>>>>> going price is now. There are also a few articles which are reasonably
>>>>> available and, as MIchael, mentioned "Ethnographies of Reason.” If you like
>>>>> this sort of things, I would recommend The Ethics of Geometry by Lachterman
>>>>> and perhaps The Origin of the Logic of Symbolic Mathematics which takes on
>>>>> Husserl and Klein. There is, of course, a long list of other people who
>>>>> have interesting takes on some of this.
>>>>> 
>>>>> Ed Wall
>>>>> 
>>>>> "The opposite of a correct statement is a false statement. The opposite of
>>>>> a profound truth may well be another profound truth" - Niels Bohr
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>>>> On Apr 11, 2018, at  9:40 PM, Wolff-Michael Roth <
>>>>> wolffmichael.roth@gmail.com> wrote:
>>>>>> Bill, the book that I really found good (I have read all of his) is
>>>>>> "Ethnographies of Reason". Lots of good materials for helping readers
>>>>>> understand. Michael
>>>>>> 
>>>>>> On Wed, Apr 11, 2018 at 7:08 PM, Bill Kerr <billkerr@gmail.com> wrote:
>>>>>> 
>>>>>>> Michael wrote:
>>>>>>> the critique that E. Livingston articulates concerning
>>>>>>> social constructionism, which takes the social in a WEAK sense; and the
>>>>>>> social in the strong sense is not a construction.
>>>>>>> 
>>>>>>> I looked up Eric Livingston, The Ethnomethodological Foundations of
>>>>>>> Mathematics, referenced on p. 56 of your book. The price was $202, ouch!
>>>>>>> Publishers put marxist ideas from academics out of the reach of the
>>>>> poor.
>>>>>>> Can this problem be solved or mitigated under capitalism?
>>>>>>> 
>>>>>>> On Thu, Apr 12, 2018 at 12:36 AM, Wolff-Michael Roth <
>>>>>>> wolffmichael.roth@gmail.com> wrote:
>>>>>>> 
>>>>>>>> Andy, to construct is a transitive verb, we construct something. It is
>>>>>>> not
>>>>>>>> well suited to describe the emergence (morphogenesis) of something new.
>>>>>>>> This is why Richard Rorty (1989) rejects it, using the craftsperson as
>>>>> a
>>>>>>>> counter example to the poet in the larger sense, the maker of new
>>>>> things.
>>>>>>>> He writes that poets know what they have done only afterward, when,
>>>>>>>> together with the new thing they have found themselves speaking a new
>>>>>>>> language that also provides a reason for this language.
>>>>>>>> 
>>>>>>>> I also direct you to the critique that E. Livingston articulates
>>>>>>> concerning
>>>>>>>> social constructionism, which takes the social in a WEAK sense; and the
>>>>>>>> social in the strong sense is not a construction.
>>>>>>>> 
>>>>>>>> Also interesting in this is the question of origins, and there the
>>>>> French
>>>>>>>> philosophers (Derrida and others) have had a lot of discussion. Mead's
>>>>>>>> fundamental point is that "before the emergent has occurred, and at the
>>>>>>>> moment of its occurrence, it does not follow from the past" (1932,
>>>>> xvii).
>>>>>>>> And concerning relations, Marx/Engels write (German Ideology) that the
>>>>>>>> animal does not relate at all, for it, the relationship does not exist
>>>>> as
>>>>>>>> relationship
>>>>>>>> 
>>>>>>>> m
>>>>>>>> 
>>>>>>>> Rorty, R 1989, *Contingency, Irony, and Solidarity*, CUP
>>>>>>>> 
>>>>>>>> On Wed, Apr 11, 2018 at 7:29 AM, Andy Blunden <andyb@marxists.org>
>>>>>>> wrote:
>>>>>>>>> Well, I can see that as an argument, Michael. My response:
>>>>>>>>> 
>>>>>>>>> The thing is, to interpret "construction" in an intellectual
>>>>>>>>> way, leads to the conclusion that to give construction a
>>>>>>>>> fundamental place in human evolution is "intellectualism,"
>>>>>>>>> and actually, interpreted that way, would be utterly absurd.
>>>>>>>>> But the fact is that all human actions are teleological,
>>>>>>>>> that is, oriented to a goal. Of course!! no hominid ever
>>>>>>>>> said to herself: "I think I will now take another step to
>>>>>>>>> evolving homo sapiens." AN Leontyev does exactly the same
>>>>>>>>> move in his criticism of Vygotsky.
>>>>>>>>> 
>>>>>>>>> Actually, I don't know just how the formation of social
>>>>>>>>> customs, speech and tool-making interacted in the earliest
>>>>>>>>> stages of phylogenesis, ... and nor do you. We do know that
>>>>>>>>> all three are intimately interconnected from the earliest
>>>>>>>>> times we have any real knowledge of, though.
>>>>>>>>> 
>>>>>>>>> As to "emergence," in my opinion "emergence" is the modern
>>>>>>>>> word for God. I don't know how this happens, so it must be
>>>>>>>>> Emergence.
>>>>>>>>> 
>>>>>>>>> Andy
>>>>>>>>> 
>>>>>>>>> ------------------------------------------------------------
>>>>>>>>> Andy Blunden
>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>> On 12/04/2018 12:18 AM, Wolff-Michael Roth wrote:
>>>>>>>>>> Andy, there is nothing of construction. Construction may be an effect
>>>>>>>> of
>>>>>>>>>> mind, but mind did not emerge as a construction. It is a
>>>>>>> manifestation
>>>>>>>>> of a
>>>>>>>>>> relationship.
>>>>>>>>>> 
>>>>>>>>>> Emergence means that what comes after cannot be predicted on the
>>>>>>> basis
>>>>>>>> of
>>>>>>>>>> what comes before. The construction metaphor implies that (e.g., the
>>>>>>>>>> craftsman in the Marx/Engels case who is superior to the bee, an
>>>>>>>> example
>>>>>>>>>> that Vygotsky takes up).
>>>>>>>>>> 
>>>>>>>>>> Construction smacks of intellectualism, precisely the intellectualism
>>>>>>>>> that
>>>>>>>>>> Vygotsky made some moves to overcome at the end of his life
>>>>>>>>>> 
>>>>>>>>>> m
>>>>>>>>>> 
>>>>>>>>>> On Wed, Apr 11, 2018 at 7:09 AM, Andy Blunden <andyb@marxists.org>
>>>>>>>>> wrote:
>>>>>>>>>>> All of those quotes make my point, Michael, in ever so
>>>>>>>>>>> slightly different words.
>>>>>>>>>>> 
>>>>>>>>>>> a
>>>>>>>>>>> 
>>>>>>>>>>> ------------------------------------------------------------
>>>>>>>>>>> Andy Blunden
>>>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>>>> On 12/04/2018 12:02 AM, Wolff-Michael Roth wrote:
>>>>>>>>>>>> I do not think mind is a construction,
>>>>>>>>>>>> 
>>>>>>>>>>>> Vygotsky (1989) writes: "Any higher psychological function ... was
>>>>>>>> the
>>>>>>>>>>>> social relation between two people" (p.56)
>>>>>>>>>>>> 
>>>>>>>>>>>> And Mikhailov (2001) suggests: "the very existence of the
>>>>>>>>>>>> mind is possible only at the borderline where there is a continual
>>>>>>>>>>>> coming and going of one into the other, at their dynamic interface,
>>>>>>>>>>>> as it were—an interface that is defined ... by the single process
>>>>>>> of
>>>>>>>>>>> their
>>>>>>>>>>>> [self and other] mutual generation and mutual determination"
>>>>>>>> (pp.20-21)
>>>>>>>>>>>> Bateson (1979): Mind is an effect of relations, an aggregate
>>>>>>> effect,
>>>>>>>>> like
>>>>>>>>>>>> stereo (spatial) vision
>>>>>>>>>>>> is the emergent effect of two eyes with planar images.
>>>>>>>>>>>> 
>>>>>>>>>>>> Mead (1932): "the appearance of mind is only the culmination of
>>>>>>> that
>>>>>>>>>>>> sociality which is found throughout the universe" (p.86).
>>>>>>>>>>>> 
>>>>>>>>>>>> Nobody says anything about construction. The to eyes don't
>>>>>>> construct
>>>>>>>>>>>> stereovision and space. It is an emergent phenomenon,
>>>>>>>>>>>> an ensemble effect deriving from relations.
>>>>>>>>>>>> 
>>>>>>>>>>>> m
>>>>>>>>>>>> 
>>>>>>>>>>>> 
>>>>>>>>>>>> On Wed, Apr 11, 2018 at 6:47 AM, Andy Blunden <andyb@marxists.org>
>>>>>>>>>>> wrote:
>>>>>>>>>>>>> I always thought that the mind was a construction of human
>>>>>>>>>>>>> culture. But of course, that was not what Spinoza thought.
>>>>>>>>>>>>> 
>>>>>>>>>>>>> Andy
>>>>>>>>>>>>> 
>>>>>>>>>>>>> ------------------------------------------------------------
>>>>>>>>>>>>> Andy Blunden
>>>>>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>>>>>> On 11/04/2018 11:44 PM, Wolff-Michael Roth wrote:
>>>>>>>>>>>>>> No, I am not saying that there were human beings. Anthropogenesis
>>>>>>>> and
>>>>>>>>>>>>>> generalized (societal) action *come* together. But we have to
>>>>>>>> explain
>>>>>>>>>>>>>> culture and cognition as emergent phenomena not as
>>>>>>> *constructions*
>>>>>>>> of
>>>>>>>>>>> the
>>>>>>>>>>>>>> mind. m
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> On Wed, Apr 11, 2018 at 6:15 AM, Andy Blunden <
>>>>>>> andyb@marxists.org>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>> So, Michael, you are saying that there were human beings
>>>>>>>>>>>>>>> before there was culture. And I gather you do not count
>>>>>>>>>>>>>>> tools as units of culture.
>>>>>>>>>>>>>>> Do we have to await a Psychologist to invent the word
>>>>>>>>>>>>>>> "meaning" before we can poke a stick into an ant-hill?
>>>>>>>>>>>>>>> Creationism makes more sense, Michael, at least it offers
>>>>>>>>>>>>>>> /some/ explanation for the existence of human life.
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> Andy
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> ------------------------------------------------------------
>>>>>>>>>>>>>>> Andy Blunden
>>>>>>>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>>>>>>>> On 11/04/2018 9:57 PM, Wolff-Michael Roth wrote:
>>>>>>>>>>>>>>>> Hi Bill,
>>>>>>>>>>>>>>>> it is not so much "socially constructed." My key point in the
>>>>>>>> book
>>>>>>>>> is
>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>> it is social BEFORE there can be any construction. It is
>>>>>>> social,
>>>>>>>>> and
>>>>>>>>>>>>> this
>>>>>>>>>>>>>>>> is where I refer to a Vygotsky that has not been taken up,
>>>>>>>> because
>>>>>>>>>>>>> "every
>>>>>>>>>>>>>>>> higher psychological function ... was a social relation between
>>>>>>>> two
>>>>>>>>>>>>>>>> people." That is, in this specific case, mathematics is social,
>>>>>>>> was
>>>>>>>>>>> the
>>>>>>>>>>>>>>>> relation between two people before you see it in individuals...
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> I think the construction metaphor breaks down when you look at
>>>>>>>> our
>>>>>>>>>>>>>>> species
>>>>>>>>>>>>>>>> becoming human. So before there was culture, before we used
>>>>>>>> tools,
>>>>>>>>>>>>> where
>>>>>>>>>>>>>>>> were those tools for constructing anything of the likes that
>>>>>>>>>>>>>>>> constructivists say that we use to construct? How can a hominid
>>>>>>>>>>>>> construct
>>>>>>>>>>>>>>>> "meaning" of the branch as tool to start digging for roots or
>>>>>>>>> fishing
>>>>>>>>>>>>> for
>>>>>>>>>>>>>>>> termites? And how do they construct meaning of the first
>>>>>>>>> sound-words
>>>>>>>>>>>>> when
>>>>>>>>>>>>>>>> they do not have a system that would serve as material and tool
>>>>>>>> for
>>>>>>>>>>>>>>>> building anything like "meaning?"
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> So yes, a learning theory has to be able to explain learning
>>>>>>> from
>>>>>>>>>>>>> before
>>>>>>>>>>>>>>>> culture (phylogenesis), before language and meaning
>>>>>>>> (ontogenesis).
>>>>>>>>>>>>>>>> And about eclecticism---I think we would be a step further if
>>>>>>> we
>>>>>>>>>>>>> listened
>>>>>>>>>>>>>>>> to and pondered A.N. Leont'ev's complaint about the "eclectic
>>>>>>>> soup
>>>>>>>>>>>>>>>> [eklekticheskoj pokhlebke] ... each to his own recipe" that
>>>>>>>>>>>>> psychologists
>>>>>>>>>>>>>>>> are trying to cook (in his foreword to *Activity.
>>>>>>> Consciousness.
>>>>>>>>>>>>>>>> Personality*).
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>>>>> Michael
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> On Tue, Apr 10, 2018 at 7:15 PM, Bill Kerr <billkerr@gmail.com
>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>> One interpretation of Vygotsky (Wolff-Michael Roth) argues
>>>>>>> that
>>>>>>>>> all
>>>>>>>>>>>>>>>>> knowledge is socially constructed and that ethnomethodology,
>>>>>>>>> paying
>>>>>>>>>>>>>>>>> detailed attention in the now, is the best or only way of
>>>>>>>>> detecting
>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>> evaluating what is going on . Human activity can’t be reduced
>>>>>>> to
>>>>>>>>>>>>>>> individual
>>>>>>>>>>>>>>>>> actions. Anything individual originates in the social, be it
>>>>>>>>> words,
>>>>>>>>>>>>>>>>> mathematics or by implication computer science (mentioned not
>>>>>>> in
>>>>>>>>> the
>>>>>>>>>>>>>>>>> original but because it is a current interest of mine).
>>>>>>> Moreover
>>>>>>>>>>>>>>> internal
>>>>>>>>>>>>>>>>> representations or schemas seem to be denied because that
>>>>>>> would
>>>>>>>>> be a
>>>>>>>>>>>>>>>>> capitulation to dualism, emphasising brain / mind activity
>>>>>>>> whereas
>>>>>>>>>>> the
>>>>>>>>>>>>>>> real
>>>>>>>>>>>>>>>>> deal is an integrated thinking body.
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> This world view is critical of other learning theories be they
>>>>>>>>>>>>>>>>> behaviourist, cognitivist, enactivist or constructivist.
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> The question that I want to explore here is the pragmatic one
>>>>>>> of
>>>>>>>>>>>>> whether
>>>>>>>>>>>>>>>>> and how learning theory (an abstraction) makes a difference in
>>>>>>>>>>>>> practice,
>>>>>>>>>>>>>>>>> for busy, hard working (usually overworked) teachers. An
>>>>>>>>> alternative
>>>>>>>>>>>>>>>>> epistemology/ies which might appeal more in practice to real
>>>>>>>>>>> teachers
>>>>>>>>>>>>>>> under
>>>>>>>>>>>>>>>>> pressure is an eclectic one centred around the issue of “what
>>>>>>>>>>> works”.
>>>>>>>>>>>>>>>>> I believe I am better read on learning theory than most
>>>>>>>> teachers.
>>>>>>>>>>> See
>>>>>>>>>>>>>>>>> http://learningevolves.wikispaces.com/learning%20theories
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> Up until now I've developed an eclectic / pragmatic approach
>>>>>>> to
>>>>>>>>>>>>> putting
>>>>>>>>>>>>>>>>> learning theory into practice. Take something from Seymour
>>>>>>>>> Papert's
>>>>>>>>>>>>>>>>> constructionism, something from Dan Willingham's cognitivism,
>>>>>>>>>>>>> something
>>>>>>>>>>>>>>>>> from Dan Dennett's behaviourism, something from Andy Clarke’s
>>>>>>>>>>>>> enactivism
>>>>>>>>>>>>>>>>> and roll them altogether in an eclectic mix. The authors in
>>>>>>> this
>>>>>>>>>>> list
>>>>>>>>>>>>>>> could
>>>>>>>>>>>>>>>>> be multiplied. My underlying belief was that it was not
>>>>>>> possible
>>>>>>>>> to
>>>>>>>>>>>>>>> develop
>>>>>>>>>>>>>>>>> a unified learning theory, that human learning was too complex
>>>>>>>> for
>>>>>>>>>>>>>>> that. As
>>>>>>>>>>>>>>>>> Marvin Minsky once said in 'Society of Mind', "the trick is
>>>>>>>> there
>>>>>>>>> is
>>>>>>>>>>>>> no
>>>>>>>>>>>>>>>>> trick", I think meaning no overarching way in which human's
>>>>>>>> learn.
>>>>>>>>>>>>>>>>> One big surprise in reading Wolff-Michael Roth is his serious
>>>>>>>>>>> attempt
>>>>>>>>>>>>> to
>>>>>>>>>>>>>>>>> put an end to such eclectism and develop what appears to be a
>>>>>>>>> unfied
>>>>>>>>>>>>>>>>> learning theory.
>>>>>>>>>>>>>>>>> 
>