Essay Abstract

One reason for the "unreasonable effectiveness of mathematics" is that it is never compared to nature itself, which is ambiguous, but to well-defined idealized versions (models). Math is consistent with nature in unfamiliar situations because it is consistent within itself.

Author Bio

Dan Bruiger is an independent researcher and amateur astronomer, with undergraduate studies at UCLA and UC Berkeley. He is the author of Second Nature: the man-made world of idealism, technology, and power, Trafford/Left Field Press 2006. He is currently preparing a new book for publication, The Found and the Made. He resides in the small community of Hornby Island, British Columbia and dances Argentine tango.

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5 days later

Dear Dan Bruiger,

You wrote: "We cannot exhaustively know a natural reality, although we can exhaustively describe a theory of physics and list its elements and propositions.'

Abstract we cannot know or do anything. This is what real me thinks: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

Warm regards,

Joe Fisher

7 days later

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  • Post #3

Dan,

There's a lot of quotable material here, steeped in wisdom. Math and physics must be considered in their context as embodied cognition. I assume you are saying that they and their relationship come about due to reasoning. You provide a kind of wariness to ascribing reality to our theory and modeling. That is good. I propose that wariness too but not so eloquently.

Good job.

Jim

    6 days later

    Dan, your thoughtful and carefully worded essay looks like a search for a way to share a vision or larger idea about the nature of science and reality with the world. You clearly have thought deeply about issues of how our perceptions of reality are fundamentally distinct from that reality, and about how physics and even more so math in abstracting from that reality impose on it our own perceptions and inventions of order.

    Your paper has many gems, such as "Evidently nature has its own order consistency, apart from the human need to perceive it. ...[which need is perhaps] why science has taken such refuge in mathematics as the sheer embodiment of reason and order, even as the ontological basis of nature. The alternative is uncertainty and perhaps an inexplicable universe."

    You seem very aware of the limitations of science, and how those limitations impact the choice of problems and range of solutions that scientists take up, and the ways this contributes to the illusion that "math applies in unfamiliar domains because ... a parallel mathematical domain is simply there already, waiting for us." Near the end you write "Mathematicians can no longer afford to ignore the genetically inbuilt relation of math to physical reality (the real pre-established harmony) or its significance as a conscious human creation."

    Your essay has deepened and fleshed out the question of the contest and laid out a case for the resolution of that question to tilt in a certain direction. What is missing here, although I can see you reaching for it, is a deep and specific explanation of how physics uses mathematics to model the world, how that has shaped mathematics, and why mathematics has been such a troublesome tool and companion.

    Please allow me to direct your attention to the contest submissions by David Hestenes ("Modeling the Physical World with Common Sense and Mathematics") on the former and Robert MacDuff ("A Mathematics of Science") on the latter.

    Rob's essay in particular addresses the radical idealization embedded in contemporary math - by proposing an alternative system which intrinsically conserves information about the properties of models of observable phenomena, such as grouping properties of quantities, much as Euclid's geometry encodes information about the structures being reasoned about.

    This radical departure from the mathematics of the past few centuries opens the way to broadening the range of questions science will have the tools to address. It has had a profound impact on K-12 teachers and their students but has met stubborn resistance from academics of all stripes due I'm sure to the huge investment they have in the paradigm that Rob's work is threatening to overturn.

      Dear Christopher,

      Thank you for your appreciative and thoughtful comments, and for directing me to the two papers you mentioned. Both refer significantly to Kant. David Hestenes' paper says right at the outset that "Kant shifted the focus of epistemology from structure of the external world to structure of mind." This is exactly what I think needs to happen in both physics and math. A science that does that is what I call "second-order" science, because it necessarily refers to its own sources, methods, structure, epistemology, etc. It seems that historically, then, natural philosophy did not follow Kant's advice but rather defined itself as "first-order" science, strictly embracing a third-person description of the world, leaving reflection on its methods to philosophy, psychology, sociology, etc.

      I am not a mathematician, physicist, or any other kind of specialist, but I can see the importance of opening up fundamental questions such as these papers propose. I am very interested in the human need for certainty and how it shapes society. (Think of "security" issues, for example.) As forms of cognition, both physics and math seem to serve that need; conversely, re-thinking them might provide alternative models for society and governance.

      Thanks again,

      Dan

      15 days later

      Dan,

      Time grows short, so I am revisiting essays I've read to assure I've rated them. I find that I rated yours on 3/22, as I sometimes do when I can immediately relate to it. I find that somehow it attributed my comments to an anonymous responder. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

      Jim

      Dan,

      This is a very nice essay.

      It reminds me of the drunken man looking for his car keys under the lamp post. When asked where he dropped them he replied "over there" and pointed away from himself. When asked why he was looking here, he replied "the light is better". We like to use the tools that work for us.

      The best description of it that I can give is "thoughtful". Nothing you have written is particularly profound taken alone, but as a complete whole it is an excellent proposition ... very well argued.

      Best Regards and Good Luck,

      Gary Simpson

      Dan,

      It was a great pleasure to read your essay. I was reminded how close our philosophies have proved previously as I agreed every sentence. Of course scoring shouldn't be all about agreement so your max score will be also genuinely for the excellent clarity, content, organisation style etc. etc.

      I particularly like your 'maths is simulation' view. Just as astronomy, many simulations use flawed input and can fool us. My own essay identifies a key case where we've been fooled (the great red & green sock switch con trick) which has fundamental implications across physics. I hope you can get to read and score it as I'm sure you'll like it.

      Very best wishes

      Peter

        Hi, Peter

        Thanks for your appreciation, gratefully received. Due to personal circumstances, I haven't had much time to read the essays this year, let alone comment or vote (actually I never vote). I will try to make time to read yours.

        thanks,

        Dan

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