The Janus of Mathematics by Burton J Smith

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 characterizes of the items within a category", which makes Generalization a subset of Categorization. This is against the literal interpretation and common usage of these terms.

The above two nomenclatures are related to perceptions of different characteristics that define the objects. Since these characteristics have not been described individually, we have to assume that you refer to the totality of the identifying characteristics. This makes your third category redundant. You define "subitization or numerousness" as "The ability to rapidly ascertain if one group of items is larger/smaller than another". The terms "larger/smaller" are used only in dimension related descriptions, such as spread (one dimension), area (two dimensions) and volume (three dimensions) or descriptions related to the numbers associated with those objects. Further, the terms "larger/smaller" imply comparison with other objects, which is nothing but measurement and whose results are always expressed in terms of scalar quantities, which are nothing but numbers. Numbers are the perceived property of objects by which we differentiate between similars. After we perceive an object, if there are no similar perceptions, we designate the number associated with that object as one. If there are other similar perceptions, depending upon their sequence, we give each a name. These are the number sequences. You also appear to admit it when you say: "children, even babies have this ability", because even babies perceive, though they cannot use number sequence effectively. But then you contradict yourself when you say: "Numerals are not required."

If "subitization or numerousness" is related to numbers as described above, then it becomes one of the identifying characteristic of the objects and thus a subset of the earlier categories making its separate classification redundant.

Tallying is nothing but comparison, which is nothing but measurement and whose results are always expressed in terms of scalar quantities, which are nothing but numbers. Yet, you say "tallying does not require numerals, a mark or notation suffices" without realizing that it is a self contradictory statement. Numerals are nothing but notations. In fact you go on to support this view while arriving at an opposite conclusion.

When you say: "While subitization can help explain counting up to 4 and possibly 5, something else is required to count beyond that", you have unknowingly referred to a very important mechanism. After the perception of one, the perceptions of two and three arise very rapidly. Hence these are so named in Sanskrit. For this reason, even many animals show this prowess of counting up to three. The perception of four requires higher intelligence. But still it is not very difficult. The perception of 5 onwards requires definitely higher intelligence not only about numbers, but interactions. Use of fingers is nothing but a type of notation. Hence the reference to parietal lobe is without much significance. What you appear to be hinting at is the difference in the mechanism of perception of numbers up to 3 and may be 4 and the other numbers. You call the first category subitization. This classification reminds us of an anecdote related to Einstein:

Einstein had two dogs: one big and one small. He wanted to have a box for them to protect them from cold. He called a carpenter and told him to prepare the box with two doors for entry of the two dogs. The carpenter said that there is no necessity for two doors and one will suffice. Einstein said that two are needed because the big dog cannot enter through the small door. The carpenter replied that the small dog could enter through the big door. At this Einstein is reported to have said: Since the carpenter solved a problem which a Nobel Laureate like him could not solve, he deserved a Nobel Prize. It appears you are talking like Einstein and we are talking like the Carpenter.

Kindly review you article based on the above observation. The descriptions of historical developments by you are o.k.

Regards,

basudeba

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.

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

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

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.

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.....

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.

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

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

Dear Sir,

We will make your search simpler by pointing out that our essay appears at 10th from bottom in the list of essays for this competition. You are welcome to return our complements.

Regarding references, we repeat that "We are not impressed by name dropping or references." We do not follow others. We follow logic and proof only. Only these work in science, which requires verification of results. References being other people's opinions can be misleading. Many of the so-called Peers have been proved wrong. But neither logic nor proof has ever proved wrong. Hence we are not impressed by name dropping or references.

We did not threaten; "The judges panel will judge you from your answers." It was a logical statement. A scientist is expected to base his theories on proof and logic and not intemperate words or un-corroborative or misleading references. One who abandons logic or proof will be judged by the scientific community by his worth whatever that may be.

Just like you, we also "know little about FQXi other than what is displayed on their web site". So on this count we are on a level playing field.

Hence now at least we expect that you will give a specific replies to our comments (either proving it or disproving it) and not hide behind the references or else admit that you cannot reply to the points raised by us.

Regards,

basudeba.

Aloha Basudeba:

I have read your essay. Suffice to say, had I read it earlier my responses would have been different. Your essay indicates a search for truth, and I agree with much of which you write. However, your comments and criticisms to myself and others appears to indicate an 'intellectual arrogance' more common to academia, the media, and other self-anointed intelligentsia.

The last paragraph in my paper sums up what I was attempting to get across. In the distant past humans and any number of animal species used an inductive sort of logic to survive. It didn't have to work all the time, just most of the time. That trait persists, whether as a heritable trait, as I suspect, or as a cultural meme. Conclusions are drawn based on a general understanding of a category with little or no regard to the individualisms within that category. Classic examples are national boundaries drawn with little or no attention to the indigenous tribes that suddenly find themselves on both sides of the new border and react as might be expected.

Logic assumes that its propositions (premises) are true or false and thus determines the conclusion. At least in some logics, but since there are numerous logics being practiced, there is no doubt one where two negatives make a positive and thus anything can be proved true. Logic, like mathematics, is another human abstraction and may or may not have any relevance to the natural world.

In the real world I am aware of only one known truth and that is, thanks to Heraclitus via Plato, change is the only constant. Omar Khayyam added a twist to that with the moving finger, but that was it. Recently, technology began to measure in ten billionths of a meter and found identities to be rare, if they exist at all. Even if there are identities they would lie in different space-time locations hence would be subjected to slightly different forces or would act upon another body slightly differently. All of which fits the notion of constant change.

There may be other truths, as yet unknown. The sand piles of Per Bak (although it was Glen Held et.al. that apparently did the experimental work) illustrate the concept of equilibrium followed by a chaotic avalanche. Ilya Prigogine with self-organization, and of course general systems begun by Alexander Bogdanov and Ludwig von Bertalanffy and carried on by others such as G. M. Weinberg, H. T. Odum, Humberto Maturana and many others. Then there's the concept of emergent properties. That somewhat mystical property that often arises whenever a collection of parts begin to function in an organized manner. I have been fortunate to have experience a number of such events in trials that I, and others, initiated. The result is that I believe a complex, dynamical system can be guided in a given direction, baring such random events as Japan recently experienced. However, details cannot be predicted. The mind is an analog device, thus I expect that it will be eventually modeled; which appears to be going on at Stanford University, as mention in my paper.

There is the real world and there is the abstract one humans have devised. Agriculture allowed us to change our rules, but not the ones governing reality. And yes, I am a pessimist; as are many, if not most, practical ecologists.

One item of your essay: You say that "To measure the state of the system, the observer must cause at least one quantum of information (energy, momentum, spin, etc) to pass from him through the boundary to the system to bounce back for comparison."

If an object exists then it is there whether or not there is an observer. Vision, hearing and smell are passive senses. So unless one brings in "spooky action at a distance," or "God's Will" there doesn't appear to be a reason to assume that the observer somehow or other signals the target.

Sincerely

Burt Smith

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 contest "Is Reality Digital or Analog". Our Essay under the same name was published on 29-12-2010. We were associated with Academic Administration as a part of our profession before retirement. From our experience, we were concerned about the problems and directions of current science. One example is the extended run and up-gradation given to LHC, (which was set up to finally prove that Standard Model and SUSY were wrong), even when Tevatron is closing down. Thus, after retirement, we were more focused on foundational works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality.

Specifically we were concerned about the blind acceptance of the so-called "established theories" due to the rush for immediate and easy recognition even on the face of contradictions raising questions on the very theories. One example is the questions being raised on the current theories of gravitation after the discovery of Pioneer anomaly. While most students know about MOND, they are not aware of the Pioneer anomaly. Most of the finalists of this contest have either not addressed or insufficiently addressed this question. We hold that gravity is a composite force that stabilizes. This way we can not only explain the Pioneer anomaly and the deflection of the Voyager space-craft, but also the Fly-by anomalies.

Similarly, we were concerned about the blind acceptance of some concepts, such as inertial mass increase, gravitational waves, Higg's boson, strings, extra-dimensions, etc. Some of these are either non-existent or wrongly explained. For example, we have given a different explanation for ten spatial dimensions. Similarly, we have explained the charge interactions differently from the Coulomb's law. We have defined time, space, number and infinity etc., differently and derived all out formulae from fundamental principles. There are much more, which we had discussed under various threads under different Essays. We are the only entrant who defined "reality" and all other technical terms precisely and strictly used this definition throughout our discussion.

Though our essay was on foundational concepts and we derived everything from fundamental principles, it was basically alternative physics. Moreover, we are not known in scientific circles because we did not publish our work earlier. Hence it is surprising that even we got a community rating of 3.0 and (12 ratings) and Public Rating of 2.5 (2 ratings). We have no complaints in this regard. However, we have serious reservations about the manner in which the finalists were chosen.

A set of thirty-five finalists (the "Finalists") have been chosen based on the essays with the top Community ratings that have each received at least ten ratings. The FQXi Members and approved Contest entrants rate the essays as "Community evaluators". Since many of the FQXi Members are also approved Contest entrants, this effectively makes the contestant as the judge for selection of the finalists. This process not only goes against the foundational goals of the Contest, but also leaves itself open for manipulation.

Most contestants are followers of what they call as "mainstream physics". Thus, they will not be open to encourage revolutionary new ideas because it goes against their personal beliefs either fully (like our essay) or partially (like many other essays that did not find place in the final list. One example is Ms Georgina Parry. There are many more.) The prime reason for such behavior is cultural bias and basic selfish instinct of human beings. Thus, truly foundational essays will be left out of the final list.

In support of the above, we give a few examples. While there are some really deserving contestants like Mr. Julian Barbour, who really deserve placement in the final listing, the same cannot be said for many others. Mr. Daniele Oriti, who tops the list of finalists, says that whether reality is digital or analog "refers, at least implicitly, to the 'ultimate' nature of reality, the fundamental layer." He admits that "I do not know what this could mean, nor I am at ease with thinking in these terms." Then how could he discuss the issue scientifically? Science is not about beliefs or suppositions. His entire essay exhibits his beliefs and suppositions that are far from scientific descriptions. He admits it when he talks about "speculative scenario". Yet, his essay has been rated as number one by the Community.

The correspondence between us and Mr. Efthimios Harokopos under his Essay and our comments under the various top ranking finalists show the same pattern. One example is Mr. Paul Halpern. We have raised some fundamental questions under the essay of Mr. Hector Zenil. If the answers to these questions are given, most of the finalists will be rejected. If the idea is to find out the answers to these questions, then also most of the finalists will be rejected.

The public that read and rated the essays are not just laymen, but intelligent persons following the developments of science. Their views cannot be ignored lightly. Mr. Daniele Oriti, who tops the list of finalists as per community rating, occupies 35th place in public rating. Mr, Tejinder Singth, who is 7th among the list of finalists as per community rating, occupies 25th place in public rating. If public rating is so erroneous, it should be abolished.

Secondly, the author and interested readers (including FQXi Members, other contest entrants, and the general public) are invited to discuss and comment on the essay. Here personal relationship and lobbying plays an important role. An analysis of the correspondence between various contestants will show that there was hectic lobbying for mutual rating. For example: Eckard Blumschein (Finalist Sl. No. 15) had written on Mar. 15, 2011 to Mr. Ian Durham (Finalist Sl. No. 3) "Since you did not yet answered my question you give me an excuse for not yet voting for you." There are many such examples of open lobbying. One of the first entrants visited most contestants and lobbied for reading his essay. Thus, not only he has received the highest number of posts under his Essay, but has emerged as one of top contenders.

The above statement gets further strengthened if we look at the voting pattern. More than 100 essays were submitted between Feb.1-15. Of these 21 out of 35 are the finalists. Of these the essays of 14 contestants were published in 5 days between Feb. 14-18. Is it a mere coincidence? For some contestants, maximum rating took place on the last day. For example, on the last date alone, Mr. Paul Halpern rose from 14th place to 5th place, Mr. Donatello Dolce rose from 35th place to 14th place, and Mr. Christian Stoica came into the top 35. All these cannot be coincidental.

Thirdly, no person is allowed to submit more than one essay to the Contest, regardless if he or she is entering individually or as part of a collaborative essay. Yet, we suspect that some have indulged in such activities. For example, we commented below the essay of one contestant on March 4. We got a reply from the next contestant the same day. The correspondence continued. The original contender has not replied to us. In fact he has only replied twice in 20 posts. This is surprising.

In view of the above, we request you to kindly review your judging process and forward all essays to an independent screening committee (to which no contestant or their relatives will be empanelled), who will reject the essays that are not up to the mark and select the other essays without any strict restriction on numbers to the final judges panel. This will eliminate the problems and possibilities discussed by us. This will also have the benefit of a two tier independent evaluation.

Our sole motive for writing this letter is to improve the quality of competition. Hence it should be viewed from the same light".

Regards,

Basudeba.