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FQXi FORUM
October 15, 2019

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: The Janus of Mathematics by Burton J Smith [refresh]
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Author Burton J Smith wrote on Feb. 18, 2011 @ 14:29 GMT
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.

Download Essay PDF File

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Eckard Blumschein wrote on Feb. 19, 2011 @ 18:51 GMT
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

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Burton Smith replied on Feb. 20, 2011 @ 00:05 GMT
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

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Dan J. Bruiger wrote on Feb. 20, 2011 @ 00:14 GMT
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

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Burton Smith replied on Feb. 20, 2011 @ 15:43 GMT
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.

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Eckard Blumschein wrote on Feb. 20, 2011 @ 15:14 GMT
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

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Burt replied on Feb. 20, 2011 @ 23:23 GMT
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

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Eckard Blumschein replied on Feb. 21, 2011 @ 00:16 GMT
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

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Eckard Blumschein replied on Feb. 22, 2011 @ 06:27 GMT
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

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Steve Dufourny wrote on Feb. 20, 2011 @ 15:49 GMT
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

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Burton Smith replied on Feb. 20, 2011 @ 22:56 GMT
Aloha Steve:

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

Sincerely

Burt Smith

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Steve Dufourny replied on Feb. 22, 2011 @ 14:51 GMT
Aloha Burt Smith,

You have chance lol it is probably beautiful there.

You are welcome, sincerely

Steve

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Jennifer L wrote on Feb. 20, 2011 @ 17:08 GMT
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.

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Burt replied on Feb. 23, 2011 @ 01:59 GMT
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

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Don Limuti (digitalwavetheory.com) wrote on Feb. 22, 2011 @ 04:20 GMT
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

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Burt replied on Feb. 23, 2011 @ 02:06 GMT
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

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Anonymous replied on Feb. 23, 2011 @ 02:45 GMT
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

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Burt replied on Feb. 24, 2011 @ 16:06 GMT
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

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James Lee Hoover wrote on Feb. 24, 2011 @ 22:23 GMT
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

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Burt replied on Feb. 26, 2011 @ 16:21 GMT
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

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Anonymous wrote on Feb. 25, 2011 @ 02:26 GMT
Your analogy of natural flows and walking with the river is interesting. Could you expand a bit on this and how using a mathematics that flows with nature could alter science as we know it? How would this be different than the results of today's science which has it's own so called flow, a flow of continuously asking the same or similar question to demonstrate repeatability and achieve consensus? Would the results remain similar, but our perception, understanding, and use of the results be what is profoundly different?

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Burt replied on Feb. 28, 2011 @ 17:34 GMT
Aloha Anon: Thank you for your comments. You’ve asked three good questions.

Q. Your analogy of natural flows and walking with the river is interesting. Could you expand a bit on this and how using a mathematics that flows with nature could alter science as we know it?

A. It is my contention that the very foundation of modern mathematics is built upon axioms and postulates that...

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basudeba wrote on Mar. 7, 2011 @ 01:55 GMT
Dear Sir,

We fail to understand the rationale behind your groupings. While the definition of Categorization appears correct, the definition of Generalization given by you fails the test of exclusivity needed for differentiating between different groups. In fact it is nothing but Categorization by another name. You define Generalization as: “Drawing conclusions from the shared...

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Burt replied on Mar. 8, 2011 @ 18:06 GMT
Aloha:

I have to admit that this is the first time anyone accused me of talking like the famed Dr. Einstein, nor have I ever been chastised by a plurality referring to themselves as talking like the famed carpenter.

Apparently you are not familiar with scientific papers and their use of references. Those small superscripts found scattered throughout the essay can be deciphered on the final page titled references. There you will find all the information needed to locate the referred paper or book . The phase, sentence or sometimes the paragraph preceding the superscript are, if not in the actual words of the referenced author(s), are his or her thoughts or ideas on the subject matter at hand. The original essay contained over 85 references. Unfortunately, when the paper was submitted it was rejected due to excessive pages of references. After consultation with the referee it was decided that I could reduce the font size and place all I could on one page, prune the rest; or withdraw the paper. So I reduced the font size to 8, pruned nearly 40 references from the reference list, and got them all on one page. However, I left the essay untouched, other than re-numbering the references, as it was a bit late to re-write it, even if that had been allowed.

About half of the pruned references were from the first two pages of the essay. I realized that the concept of mathematics as a human invention going back to Ardipithecus ramidus was likely to upset any number of individuals that for one reason or another held certain books or beliefs inerrant. Cultural paradigm are quite effective filters; so if you have a problem with my definitions I refer you to references 10,11, 12, 19 as well as numerous papers by Robert Sieger, Stanislas Dehaene, Andreas Nieder, George Lakoff, and Rafele E. Núñez - and Merriam-Webster’s Dictionary as your definitions seem a bit esoteric.

You also appear poorly informed concerning subitization and tallying. I suggest you consult ref. #10, What counts by Brian Butterworth or “The Number Sense” by Stanislas Dehaene; or “The History of Mathematics,” by David E. Smith; vol. 1. (this one’s old but so is tallying).

I appreciated your comments, tho I do not agree with them. Many of the thoughts expressed in the paper are not exclusively mine, as I hope I’ve made clear. Some come from the frontiers of cognitive science, others from anthropology and animal behavior that are increasing not in agreement with the image of “the divine human.” I have attempted to show that not only are there two faces of mathematics (pragmatic and theoretical) but also two faces of the world we live in; the real one and the abstract one we’ve built to protect us from our perceptions of the real one. The continual use of the tool that got us into our current predicament is not the solution.

Sincerely

Burt Smith

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basudeba replied on Mar. 9, 2011 @ 03:07 GMT
Dear Sir,

We thank you profusely for describing us properly. In fact we are "not familiar with scientific papers and their use of references". We have admitted so in the Author Biography in our essay.

We don't understand the cult of incomprehensibility perpetuated by the theoretical physicists of "mainstream science", which has failed to deliver anything new over the last several decades though the experimental physicists have done wonderful innovations. One example, LHC experiment designed by experimental physicists that proves Standard Model and SUSY developed by theoretical physicists wrong. We also don't understand the blind acceptance of "references" without applying one's mind to judge its veracity. In our unscientific terminology, we call it superstition. Add the cult of reductionism to the mix and you get a recipe to "scientific failures" and a sure way to lead to cozy life at public expenses by fooling the gullible public with incomprehensible "dogma".

We are not impressed by name dropping or references. We have given specific comments on your essay only because it is being debated on a public forum. We may not be a scientists or we may not understand much, but we have a right to comment. We expect you to give a specific reply to our comments (either proving it or disproving it) or else admit that you cannot reply to the points raised by us. The judges panel will judge you from your answers.

Regards,

basudeba.

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Burt replied on Mar. 12, 2011 @ 19:24 GMT
Aloha Basudeba:

You are correct this is a public forum and as such one can comment or, in your case, criticize to your heart’s content.

However, since you admit that you “are not familiar with scientific papers and their use of references” I am somewhat of a loss how to proceed. I had hoped that if I read your essay some light might shine, but a search of basudeba in the FQXi search engine failed to locate it.

So I’m left with your comments about references, one being; “We are not impressed by name dropping or references.” You criticize my definitions, which I informed you was referenced, (one being Merriam-Webster’s Dictionary) and provide one of your own, without reference of course, as if you are one of the anointed few. This may work in the esoteric world of the intelligentsia, but has no place in science, which requires verification of results - hence, the requirement for references.

Finally, your veiled threat; “The judges panel will judge you from your answers.” I know little about FQXi other than what is displayed on their web site, but I’m led to believe that they are a scientific organization. Consequently, I assume that the judges they appoint to review the top contenders are scientist in one field or another and are, as stated in the rules, peers.

Sincerely

Burt Smith

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Sridattadev wrote on Mar. 7, 2011 @ 19:45 GMT
Dear Burton,

Wisdom is more important than imagination is more important than knowledge for all the we know is just an imagination chosen wisely.

Please read Theory of everything at your convenience posted by me in this contest.

Who am I? I am virtual reality, I is absolute truth.

Love,

Sridattadev.

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Burt replied on Mar. 8, 2011 @ 18:08 GMT
Aloha Sridattadev Kancharia:

I have read your essay but have no comment other than a belief is sacred to the believer, but not necessarily to others.

Thank you for your comments

Sincerely

Burt Smith

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Sridattadev replied on Mar. 9, 2011 @ 21:40 GMT
Dear Burt,

I absolutely agree with you and respect your understanding, I just wanted to share this belief or realization that we are all connected. I wish you all the best as well.

Love,

Sridattadev.

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Michael Jeub wrote on Mar. 9, 2011 @ 03:13 GMT
It was nice to learn the term subitization. You use many names and people of history looking back (one face of Janus) but not much looking forward, (the other face).

As far as the loci of thought is concerned there are the ideas about the heart, and how the brain was not the center of thought. It was the heart, Aristotle as well as the ancient Egyptians seemed to believe. I found that such a striking idea when I first heard of it a few years ago, and is this what triggers the procreation and survival.....

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Peter Jackson wrote on Mar. 11, 2011 @ 19:34 GMT
Aloha Bert

A very different and refreshing new angle. and perhaps some of the truest words here in;

"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."

Worth top marks in themselves. I've followed that through with logic for the model in my essay. It is an astonishingly falsifiable and vastly simplified physics, of SR from QM, yet shrouded from initial view by over reliance on maths. As a Mensa member I think you will see it, but it takes dynamic visualization skills 3 from 4 don't possess.

The solution is consistent with top essay Edwins, Regazas maths and many other reality based essays.

I hope you'll try, and comment.

Many thanks

Peter

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Burt replied on Mar. 15, 2011 @ 17:33 GMT
Aloha Peter:

I have read your essay, and agree that there appears to be an over reliance on mathematics. Beyond that I do not feel qualified to comment.

Sincerely

Burt Smith

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basudeba wrote on Mar. 20, 2011 @ 06:05 GMT
Sub: Possibility of manipulation in judging criteria – suggestions for improvement.

Sir,

We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

“We are a non-professional and non-academic entrant to the Essay...

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