The Janus of Mathematics by Burton J Smith

Burton Smith

Essay Abstract

Abstract: There are four general characteristics, intrinsic with hominids, but also other species, that are responsible for mathematics as we presently know it; sociability, categorization, generalization and subitization. Together they provided a sound policy for survival in a world of constant change. These traits not only grew into mathematics but also formulated a mental structure that was geared to simplifying, seeing patterns, and deducing results based on incomplete information and acting upon them. These basic traits, plus others, succeeded humans survived. Agriculture created a completely different environment, one where division of labor became a primary characteristic, where various human designed systems, including mathematics, took root and grew - systems that were often at variance with the natural world. Mathematics grew slowly at first, its primary role being accounting. With the invention of written numerals, and later writing, mathematics quickly became a major pragmatic tool in Mesopotamia and Egypt. Along the way it was forgotten that these tools were the product of human thinking, and were ascribed as divine gifts from the gods. Plato took this a step further and mathematics became a universe unto itself with numerals becoming nouns. A major point of agreement was that the monad, the generator of all numbers, was equality - all monads were identical. Unfortunately, there are no equalities in the Universe. Without equalities mathematical operands, with the exception of addition and subtraction, can not function. Number lines, infinities, negative values, zeros may exist in Plato's world but not in the Universe inhabited by humans. In our corner of the Universe there are flows; items flow from one form into another. The only discrete items are in human minds and the abstract systems they build. Analog thinking and computation may not be the final answer, but it will certainly be closer to truth.

Author Bio

Biological Statement: Burt Smith Married, three children. BS - Mathematics, minor astronomy - San Diego State College MS - Aquatic Biology - Western Kentucky University PhD - Agronomy, Range Management, Systems Ecology - University of Florida US Navy for two years. Five years as Research Engineer in Preliminary Design at General Dynamics Astronautics and Thiokol Chemical Corp. Self employed rancher in Utah and Nevada, 13 years. Research scientist at the US Forest Service research station in Albuquerque, 1 year. Extension Specialist at the University of Hawaii, Manoa with duties state-wide; 20 years. Organizations: AAAS, Triple 9, Mensa.

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[deleted]

Dear Burton,

You concluded: "Analog thinking and computation may not be the final answer, but it will certainly be closer to truth." This agrees with what I wrote in the first paragraph of my essay. I am facing a lot of distrust. May I ask you to check and possibly support my admittedly very basic and correspondingly rather unwelcome

criticism?

Regards,

Eckard

[deleted]

Eckard:

I'm not sure what your asking. I searched on your name and the response did not include any essays. It did include several comments you have made to other authors. If you wish to post comments on my article; that's part of the rules of this contest. Or are you taking a lot of flack on your comments and want some reinforcements?

Burt

Dan Bruiger

Hi, Burton

It was a pleasure to read your informative essay. We seem to think along similar lines, and you might enjoy reading mine ("topic/852").

Thanks and best wishes,

Dan

[deleted]

I read your essay with interest. We apparently share a basic interest in how the world of nature and humans work and that there is a difference.

I particularly liked your reference to time's arrow based on there being a back ground.

[deleted]

Dear Burton,

Having enjoyed reading your nice and even somewhat programmatic essay, I would have just a few minor and perhaps distracting questions besides my main desire to derive the consequences you are unfortunately just alluding to.

You concluded: "The problems arising from a mathematics that cannot duplicate the natural world would be subtle and possibly not contentious, if only we were

aware of its faults and planned accordingly. Unfortunately, our mathematics reflects our core behaviors; that of sociality, categorization, generalization and subitization. We draw lines around similar item, call them the same, project the traits of the average on all members, decide if a category is larger or smaller than another, and then ardently discuss what we've done; creating memes that now circle the globe in seconds. Changing our core behaviors is not likely to happen, changing our mathematics to better conform to reality is possible."

I made three suggestions for a better mathematics and for better interpretation of mathematical tools in physics, respectively.

You will find my essays via topics 369, 527, and 833 .

Regards,

Eckard

[deleted]

Aloha Eckard Blumschein:

In Hawaiian the word aloha has several meanings, but all in the traditional sense of warmth. I spent 20 years in the islands working with locals, and the aloha has endured.

I finally located your essay; Continuation Causes Superior but Unrealistic Ambiguity, #833. I could not find numbers 369 or 527. I searched using your last name, but to no avail. Either I was going at it all wrong or the FQXi search engine has some limitations, it presented other essays and while of interest, were not germane to the reason of my search. I read your essay and the discussion with various critics and found myself, contrarily to my initial expectations, agreeing with your major premises. I have no comments concerning the higher mathematics, which I usually comprehend, however, I'm not sufficiently cognizant of that rarified abstraction to criticize, much less make suggestions.

On the issues where we agree (more or less), I've arrived from a different starting point than you have (this is an assumption, based on your Biography and your essay). I learned systems theory from several sources: practical experience, books, the late Howard Odum (system's ecology) as one of my mentors, 20 years of conducting numerous experiments and trials with willing ranchers, and visits to over 2000 operating ranches in North and Central America, Down Under and the Marianas.

Agriculture is not the natural world, but it is an ecotone between the natural world and the human abstract one we call civilization or society; especially so for pasture based livestock operations. Back in the early 1970's it dawned on me that present day math simply doesn't work on complex, dynamical systems, especially if living organisms are involved for the simple reason that they cannot be divided without destroying the system. Since I left Hawaii I've been attempting to make sense of "why math?" It had to be something that occurred early in our history and it had to have survival value. Fortunately, various cognitive scientist and anthropologists supplied the missing parts and strong suggestions. This essay of mine has been a long time arriving, but even so it was hurried and pruned for this event.

I would appreciate any comments you might care to make.

Sincerely

Burt Smith

[deleted]

Dear Burt Smith,

My essays 369 and 527 belong to the 1st and 2nd FQXi contest, respectively. Goto previous contests and then to read /discuss (not to winners).

You wrote: "changing our mathematics to better conform to reality is possible". Shouldn't you have an idea how? My suggestions are definitely hurting. While I need no warm words, high scores might attract helpful attention. Even more I appreciate factual criticism.

Perhaps I should read your essay more carefully. What do you mean with Janus? I just know him as having two faces.

Regards,

Eckard

Eckard Blumschein

Dear Burt Smith,

Maybe, you have no idea how to change mathematics to better conform to reality. This would explain why you did not yet respond.

I would nonetheless appreciate if you could say more about Janus, the Roman god of door, standing for January, for in and out, for left and right. See my recent reply to Doug Bundy at 833 as to admit that my request is not unfounded.

Regards,

Eckard

[deleted]

Aloha Eckard:

Believe it or not - I do have other demands on my time.

A brief discussion of the two faces of Janus and why it was applied to mathematics was pruned, along with several other items, so as to remain within the character limits of this contest. I had hoped that the discussion of pragmatic mathematics as opposed to the theoretical would suffice. I'm often wrong about such things.

You are correct in saying that I did not offer an alternative solution to mathematics as we presently know it. It would delight me no end to say that I had a solution, and for a slight consideration I would be willing to share it - but I don't.

I came to distrust mathematics in the 70's. The more I've worked with natural and ecotone systems (agriculture) the more I became convinced there was something basically wrong with math when applied to the natural world. As I mentioned in my essay, division in the natural world is very messy and is akin to death for any complex system; hence, it is not a proper operand for understanding the natural world. Multiplication as duplicator in addition is feasible, as is addition and subtraction. However, the information obtained is limited as to which pile is larger/smaller than another.

In your essay you have rejected analog computation as being out of date and too noisy. My experiences with analog computation in the 70's was that it was superior for modeling systems than were the digital behemoths of that time period. The vast sums that have been spent enhancing digital calculations make comparisons today difficult at best. Yet, there are groups working with analog; e.g. the Silicon Brain group at Stanford.(Ref, #54 in my essay.)

Other possibilities have to do with the way life changes over time, a slow morphing of form. Rivers flow and carry along all sorts of things besides water molecules; then there's the various forces found throughout our corner of the universe (electromagnetic, gravitation, etc.) and of course time. An orchestra combines the sounds from a large number of instruments into a unique sound - the composer starts the process and the conductor adds the finishing touches. Electromagnetic waves are capable of transporting such information vast distances; what we know about the reaches of the universe are carried on such waves. Are these, more natural (dare I say analog) phenomena, being investigated as possible calculation mediums? I hope so. The mathematics we have gets close on occasion - but close only counts in horseshoes.

Sincerely

Burt

[deleted]

Dear Burt,

Thank you for responding honestly. I agree on that a mathematical reduction of the the whole world, the wetware of the brain, and of other highly complex systems is inappropriate. I also agree with your insight that there is effectively no equality and no absolute symmetry in nature. Nonetheless I consider mathematics necessary and worth improvement.

Regards,

Eckard

[deleted]

Hello dear Burton J Smith,

Ver beautiful essay ful of rationality. The sortings and the synchro, we ignore indeed the false foundamentals.

I liked these words ,it is so important, I think that all the lost mathematicians must read that.

When you say about the universe finite and its series,it is so true,

after all these maths are there for helping physics.

Good luck in this contest

Steve

[deleted]

Aloha Steve:

Thank you for reading and your kind comments - they are appreciated.

Sincerely

Burt Smith

[deleted]

Aloha Burt Smith,

You have chance lol it is probably beautiful there.

You are welcome, sincerely

Steve

[deleted]

Dear Burton, What a refreshing paper, both in content and style. I too have long suspected a similar conclusion. During my PhD studies we ran statistics on all sorts of questions concerning livestock: their productivity, nutritional requirements, etc. We got some really great "answers" - at least great on paper. Attempting to apply the results back to an individual animal was a whole different ball game - usually ending in complete frustration. Each individual animal (system) was too unique with too many variables. This "problem" with individuality has resulted, in part, in the idea of cloning animals to ensure a consistent animal, which has resulted in individual animals that have a similar phenotype but are in fact, quite unique.

The same difficulties of today's mathematics are found in the form of modeling. As you are certainly aware, models do well to explain the past, but have a huge confidence error in predicting the future. In dealing with climate change, models are able to tell us that in certain areas in certain seasons, the weather will get warmer and dryer or cooler and wetter, but little else. And after a particular weather event, it is impossible to say that the event was the result of climate change. My point is, without getting into a discussion on climate change or animals per se, that mathematics is missing something very fundamental - that the individual (system) is operating with little concern for the mean.

[deleted]

Aloha Jenniver L.

Quite so; few individuals wish to be average. However, most like to know where the average is so they can decide what, if anything, to do about it. Since the average comes with a consensual agreement as to its characteristics most individuals can find enough wiggle room to shift themselves from above to below or vice versa, depending on subject matter.

Outliers, or the "lunatic fringe" as its sometimes called, present a different situation as they are events or items that are not suppose to occur with any regularity; yet often do. They are typically viewed as an inconvenience at best and disruptive at worst. But the fact remains it is

the "lunatic fringe" that is responsible for many, if not most, of the major changes, good or ill, that occur.

Sincerely

Burt Smith

[deleted]

Burt,

Your statement "Without equalities mathematical operands, with the exception of addition and subtraction, can not function." I do not believe that even addition and subtraction are exceptions see http://www.zenophysics.com/DWT/17__Math-Physics.html

Thanks for your paper.

Don Limuti

[deleted]

Aloha Don:

One can add up the number of items in a junk yard and compare the total to the total of items in another junk yard and determine which one has more items. Not a great deal of information is obtained but of some value, especially if one is in the junk yard cleaning up business.

Haven't looked at your suggested site, but will.

Thanks for your comments

Sincerely

Burt Smith

[deleted]

Burt,

Yes in math 1plus1 = 2 This corresponds to the addition of your Junk items. Your use of the term "item" indicates that you have turned the junk into numbers.

But in physical reality I have reason to believe that 1 lb. of junk plus 1 lb. of junk > 2 lb. of junk.

I believe there is a big divide between physics and math. I also think we are poking at the same thing. And thanks for your reply.

Don Limuti

[deleted]

Aloha Don:

Sorry, but the use of the word item does not automatically imply numbers. Item has several definitions, one of which is "an object of attention, concern or interest" which is the meaning I intended, and I thought was clear from the context - apparently it wasn't.

Adding a measurement (noun) to a numeral, I believe reduces the numeral to an adjective, and the onus of accuracy then falls on the noun, pounds in this case, to guarantee that "a pound is a pound the world around." Since a pound is, by definition, a fraction of the standard kilogram kept in France, the ultimate onus is on that platinum-iridium chunk - which I understand has loss a little weight since it was first cast. Not that it will change anything as there's a greater difference in the weight or an item from mountain top to sea level than in the few micrograms the standard lost.

And yes, I think we are, more-or-less, poking at the same things.

I have read the items at your web site. You've obviously spent a great deal of thought and time in the formulation of the theory. You're to be congratulated.

Sincerely

Burt Smith

James Hoover

If one can't step into the same river twice, one can walk with the river - go with the flow. It may not be exactly the same river one steps into each time but it's certainly closer than if one proceeds cross-wise.

Burt,

Wise words above. Your approach is different than mine. Mine borrows from models in positing the point of analogue reality. Yours less so.

Jim Hoover

[deleted]

Aloha Jim

Thank your for your comments, they are appreciated.

In your essay you discuss different models, apparently all digital, which are said to be analogues of real events. I had a little trouble with the apparent interchange of analog with analogue. And while my dictionary gives that as a major definition, I have always thought of analog as a flow, but not an infinite flow as some contend. For if the universe is finite then nothing in it can be infinite - or so it would appear. Which raise a point, if flows are not infinite then is the difference between discrete and analog a measurement, time, or both? A bullet is a discrete item, a machine-gun spits out a stream of them, but they are still discrete items. So would an analog item in the same context be a long spear, lance or sword; or would it have to be much longer? At what point could we draw a line and say this is discrete and that is analog? Perhaps that's the whole point of this contest; to get one further away from the box than they presently are.

I agree with some of your positions, such as models depict whatever hypothesis one wants to pose. Just as statistics, experiments, or argument can be presented to favor any preconceived viewpoint. But that's the beauty of living in the abstract world we've constructed for ourselves. I disagree that doing more of what we've done in the past is going to be much help. We need a new tool, we need a math that better approximates nature; and that math may very well require a machine as its foundation.

You mentioned that you have a column; is it on the web?

We've enjoyed our stay in your state and expect to return.

Sincerely

Burt Smith