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[This is probably an absurd post, even more provisional in its judgments and ideas than most of my generally too-hasty postings. But I increasingly feel that I have to get my glimmers of understanding out there before I lose sight of some particularly fugitive insights or pseudo-insights.]
In the first days of recovery from total hip replacement surgery, I began but quickly abandoned a series of heavy-handed allegorical photographs, starting with the bright yellow “Fall Risk” wristband I found attached to my arm in the hospital and continuing to the initially accidental juxtaposition in my bedside table at the physical rehabilitation center, where my copy of The Outer Limits of Reason reposed in a drawer next to a package of Premium Adult Wipes.
The symbolism seemed appropriate for what I had been finding wrong with Noson S. Yanofsky’s book (subtitled What Science, Mathematics, and Logic Cannot Tell Us). Yanofsky’s summaries of the physical and computational limits of the universe that ensure that some questions are necessarily unanswerable were frequently frustrating when they should have been enlightening; however correct his understanding of the computational powers of reason and its instruments, again and again I would read his confident summation of some philosophical point and exclaim, “No! That isn’t what that means at all!”
Even when he acknowledges the existence of physical limits to rational analysis, Yanofsky seems almost oblivious to the extent to which reason is housed in a not very reliable physical system, surrounded by a distinctly unreliable matrix of cultural assumptions that it is reason’s role to unsettle whenever possible. Finding myself confined to bed in a situation in which all the bodily functions had been put under question, including the mental clarity with which I had been analyzing Yanofsky’s book pre-operation, made me wonder still more about the unexamined conditions in which science, mathematics, and logic can tell us anything. (I still haven’t tackled the whole thing, but I know what I think Yanofsky gets wrong when he talks about topics about which I know a modest amount. I need to give his book a fairer evaluation, one that discusses its virtues, which are many.)
Science, of course, had a great deal to do with the specific structures of the post-surgery situation into which I had been put—although the sheer range of personal responses and expectations of the multinational staff of the rehab center made me think that cultural anthropology was one of the sciences that was as important for my satisfactory navigation of the recovery process as any measurement of my vital signs or progress in physical therapy.
Specialists in the “hard” sciences, of course, think that for a cultural relativist to take such considerations into account must mean that the cultural relativist doesn’t believe in objective truth whatsoever, and a physicist, if I recall correctly, successfully published a memorable satirical paper in a philosophical journal to prove his point that social constructionists would believe any kind of nonsensical assertion about the social origins of scientific discovery. (The editors said that the paper’s thesis had struck them as open to serious disputation, but that it was logically argued from its initial dubious premises and it wasn’t their business to suppress debate on perspectives even if they found them questionable.)
In reality, of course, cultures are bounded by, if nothing else, the hard facts of the environment, which punishes sufficiently serious cultural miscalculations by the extinction of the holders of the beliefs—although enough of them survive under ordinary circumstances to ensure that the most dysfunctional of opinions endure, generation after generation. Everyday logic and culturally inflected assumptions operate on a “just good enough” principle akin to the “ecorithms” proposed as a mechanism of evolution in
Probably Approximately Correct, another one of those recent books I would be able to summarize more adequately and accurately had I not been in no shape to study its argument when I acquired it. (I believe, based on a first very fragmentary encounter, that the book’s hypothesis is primarily addressing the pre-linguistic internal algorithms of systems in nature and has nothing to do with language-based human cultures, but the notion provides a useful metaphor applicable to the larger question of culture.)
Edward Frenkel—who I now realize reviewed Probably Approximately Correct for the New York Times—views mathematics as a Platonic absolute in Love and Math: The Heart of Hidden Reality, but is acutely aware of the issues of cultural relativism, having had to overcome some of the most absurd cultural limitations of Soviet anti-Semitism just to be able to become a mathematician. What impresses him most is the extent to which mathematicians from the most diverse cultural backgrounds, whatever their other presuppositions, can contribute at once to one another’s perceptions of problems raised at the outer limits of mathematical theory, and the astonishing extent to which the discovery of new mathematical relationships suddenly illuminates the nature of an unsolved problem in the physical sciences, quantum physics in particular.
This takes us into the central debate of a question that may turn out to be one of the insoluble problems to which Yanofsky refers: Mathematics is a cultural construct. (It has to be, because the simple use of Arabic numerals and agreed-upon meanings for the letters of several alphabets is a cultural construct—although the relationships expressed by the equations would be identical if numerals and letters from some other cultural background were substituted. Suddenly I want to go tackle Joseph Needham’s Science and Civilization in China, a multivolume work that Needham claimed only he and his wife had ever read in its entirety.)
Mathematics, as it is written down on chalkboards or computer screens, is a cultural construct, but it reflects relationships in the order of the universe, far, far beyond the simple arrangement of discrete objects from which basic arithmetic presumably arose in immeasurable depths of prehistory. If mathematics in its essence is cross-cultural, is it also direct perception of the nature of reality? If the math only makes sense when there are ten dimensions and not four or eleven or twenty, are there then really ten dimensions, even if we can never prove this by experiment? Or are there areas in which mathematics leads us astray, as its elegant logic shades off into sheer fantasy?
Good question, and few people are qualified even to hazard a well-informed guess, much less an argument in favor of one side or the other.
D. Fox Harrell’s Phantasmal Media: An Approach to Imagination, Computation, and Expression may or may not shed light on that problem, but it certainly confronts some of the most vexing questions of cultural presuppositions and inflections, and offers insights into the uses of digital media to explore and reveal “cultural phantasms” in ways that almost certainly rhyme with the concerns of Afrofuturism, even though the word does not seem to appear in Harrall’s text. (I await the arrival of the catalogue of the Studio Museum’s current exhibition on that topic, The Shadows Took Shape, a title borrowed from a Sun Ra album.)
Harrall does cite a digital work by Guillermo Gómez-Peña and Ali Dagar, The Chica-Iranian Project, that mashes up Mexican and Kurdish mythologies and ethnic signifiers under such rubrics as “Test your ethnic profiling skills!” This takes us off into indisputably different territory from the epistemology with which this blog post began, but Harrell gets to “Cultural Phantasms” by way of a chapter titled “Expressive Epistemologies.”
Nonetheless, all of this deserves to be discussed under the rubric of cultural inflections, for we have gotten a long way away from mathematics and the outer limits of reason.
In the first days of recovery from total hip replacement surgery, I began but quickly abandoned a series of heavy-handed allegorical photographs, starting with the bright yellow “Fall Risk” wristband I found attached to my arm in the hospital and continuing to the initially accidental juxtaposition in my bedside table at the physical rehabilitation center, where my copy of The Outer Limits of Reason reposed in a drawer next to a package of Premium Adult Wipes.
The symbolism seemed appropriate for what I had been finding wrong with Noson S. Yanofsky’s book (subtitled What Science, Mathematics, and Logic Cannot Tell Us). Yanofsky’s summaries of the physical and computational limits of the universe that ensure that some questions are necessarily unanswerable were frequently frustrating when they should have been enlightening; however correct his understanding of the computational powers of reason and its instruments, again and again I would read his confident summation of some philosophical point and exclaim, “No! That isn’t what that means at all!”
Even when he acknowledges the existence of physical limits to rational analysis, Yanofsky seems almost oblivious to the extent to which reason is housed in a not very reliable physical system, surrounded by a distinctly unreliable matrix of cultural assumptions that it is reason’s role to unsettle whenever possible. Finding myself confined to bed in a situation in which all the bodily functions had been put under question, including the mental clarity with which I had been analyzing Yanofsky’s book pre-operation, made me wonder still more about the unexamined conditions in which science, mathematics, and logic can tell us anything. (I still haven’t tackled the whole thing, but I know what I think Yanofsky gets wrong when he talks about topics about which I know a modest amount. I need to give his book a fairer evaluation, one that discusses its virtues, which are many.)
Science, of course, had a great deal to do with the specific structures of the post-surgery situation into which I had been put—although the sheer range of personal responses and expectations of the multinational staff of the rehab center made me think that cultural anthropology was one of the sciences that was as important for my satisfactory navigation of the recovery process as any measurement of my vital signs or progress in physical therapy.
Specialists in the “hard” sciences, of course, think that for a cultural relativist to take such considerations into account must mean that the cultural relativist doesn’t believe in objective truth whatsoever, and a physicist, if I recall correctly, successfully published a memorable satirical paper in a philosophical journal to prove his point that social constructionists would believe any kind of nonsensical assertion about the social origins of scientific discovery. (The editors said that the paper’s thesis had struck them as open to serious disputation, but that it was logically argued from its initial dubious premises and it wasn’t their business to suppress debate on perspectives even if they found them questionable.)
In reality, of course, cultures are bounded by, if nothing else, the hard facts of the environment, which punishes sufficiently serious cultural miscalculations by the extinction of the holders of the beliefs—although enough of them survive under ordinary circumstances to ensure that the most dysfunctional of opinions endure, generation after generation. Everyday logic and culturally inflected assumptions operate on a “just good enough” principle akin to the “ecorithms” proposed as a mechanism of evolution in
Probably Approximately Correct, another one of those recent books I would be able to summarize more adequately and accurately had I not been in no shape to study its argument when I acquired it. (I believe, based on a first very fragmentary encounter, that the book’s hypothesis is primarily addressing the pre-linguistic internal algorithms of systems in nature and has nothing to do with language-based human cultures, but the notion provides a useful metaphor applicable to the larger question of culture.)
Edward Frenkel—who I now realize reviewed Probably Approximately Correct for the New York Times—views mathematics as a Platonic absolute in Love and Math: The Heart of Hidden Reality, but is acutely aware of the issues of cultural relativism, having had to overcome some of the most absurd cultural limitations of Soviet anti-Semitism just to be able to become a mathematician. What impresses him most is the extent to which mathematicians from the most diverse cultural backgrounds, whatever their other presuppositions, can contribute at once to one another’s perceptions of problems raised at the outer limits of mathematical theory, and the astonishing extent to which the discovery of new mathematical relationships suddenly illuminates the nature of an unsolved problem in the physical sciences, quantum physics in particular.
This takes us into the central debate of a question that may turn out to be one of the insoluble problems to which Yanofsky refers: Mathematics is a cultural construct. (It has to be, because the simple use of Arabic numerals and agreed-upon meanings for the letters of several alphabets is a cultural construct—although the relationships expressed by the equations would be identical if numerals and letters from some other cultural background were substituted. Suddenly I want to go tackle Joseph Needham’s Science and Civilization in China, a multivolume work that Needham claimed only he and his wife had ever read in its entirety.)
Mathematics, as it is written down on chalkboards or computer screens, is a cultural construct, but it reflects relationships in the order of the universe, far, far beyond the simple arrangement of discrete objects from which basic arithmetic presumably arose in immeasurable depths of prehistory. If mathematics in its essence is cross-cultural, is it also direct perception of the nature of reality? If the math only makes sense when there are ten dimensions and not four or eleven or twenty, are there then really ten dimensions, even if we can never prove this by experiment? Or are there areas in which mathematics leads us astray, as its elegant logic shades off into sheer fantasy?
Good question, and few people are qualified even to hazard a well-informed guess, much less an argument in favor of one side or the other.
D. Fox Harrell’s Phantasmal Media: An Approach to Imagination, Computation, and Expression may or may not shed light on that problem, but it certainly confronts some of the most vexing questions of cultural presuppositions and inflections, and offers insights into the uses of digital media to explore and reveal “cultural phantasms” in ways that almost certainly rhyme with the concerns of Afrofuturism, even though the word does not seem to appear in Harrall’s text. (I await the arrival of the catalogue of the Studio Museum’s current exhibition on that topic, The Shadows Took Shape, a title borrowed from a Sun Ra album.)
Harrall does cite a digital work by Guillermo Gómez-Peña and Ali Dagar, The Chica-Iranian Project, that mashes up Mexican and Kurdish mythologies and ethnic signifiers under such rubrics as “Test your ethnic profiling skills!” This takes us off into indisputably different territory from the epistemology with which this blog post began, but Harrell gets to “Cultural Phantasms” by way of a chapter titled “Expressive Epistemologies.”
Nonetheless, all of this deserves to be discussed under the rubric of cultural inflections, for we have gotten a long way away from mathematics and the outer limits of reason.
