# Innumeracy

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http://en.wikipedia.org/wiki/Innumeracy

It is my belief that the existence of various forms and degrees of innumeracy are central to understanding a whole host of disagreements on important issues. This is commonly understood in the context of people with lower levels of mathematical education but I believe this is a gross oversimplification.

I contend that this problem also applies to many mathematically educated individuals - as some forms of innumeracy involve visual and spatial reasoning in addition to logical and formula based reasoning. There are also people with little formal mathematical education but exceptional visual and spatial reasoning who are largely immune from some types of innumeracy.

The companion problem of innumeracy is the compartmentalization of innumeracy:

I have been caught off guard on many occasions throughout my life while encountering innumeracy. Looking back I can now see that I encountered innumeracy in the educational system going back as early as 5th grade science classes. I first specifically identified innumeracy as a significant issue when I was 17 years old attending a NSF summer camp on physics at Drake University during a heated argument with a applied mathematics professor. I had suspected there was a serious problem going back to when I was 15 but I had not actually encountered a PhD researcher displaying the symptoms until I was 17.

A few other such encounters happened during my undergraduate years with other kinds of innumeracy. Over the years I have continued to encounter new twists and variations on innumeracy - the worst examples being when I was in graduate school. I have come to believe that a huge research effort to expand on the idea is long overdue.

Such research would step on many toes because those who compartmentalize their innumeracy are largely immune from understanding they have a problem. Some of the really hard cases are those who are able to further cloak their problems in the appeal to authority granted them by advanced degrees, publication histories, and awards given by their peers.

A clear example of innumeracy was displayed by Nobel laureate Ilya Prigogine when took discontinuous functions  point particles  then substituted them with continuous functions to create indeterminism out of determinism on small scales  thus claiming small scale real objects are necessarily indeterministic. Someone with clear visual spatial reasoning would instantly understand the error. This is not an isolated case of this exact problem  I saw the same visual reasoning error repeated in graduate thermodynamics in a class of approximately 20 students  not just for a few minutes but over a several week period. I identified the underlying error in the first few seconds it was being discussed by the professor but could not get anyone else to recognize it for some 2-3 weeks. Someone finally confronted the professor outside of class and he quickly gave the answer and we moved on to other topics. The same error popped up again in a series of papers published as a result of work funded by the DOE and published in Foundations of Physics in the early 2000s. The error took about 15 minutes to identify - but over 2 years and 12 PhDs researching it plus journal editors and many hundreds of thousands of tax-payer dollars cannot fix a basic innumeracy problem.

I have not attempted to make a comprehensive list of innumeracy displays but here are some readily apparent ones  some are combined problems:

Inability to properly reason about 

Long spans of time

Short spans of time

Large distances

Short distances

Very fast speeds

Very slow processes  slow speeds

Large numbers of objects

Large numbers of very small objects

Small objects not requiring granularity

Geometric and exponential growth and decay

Internal versus external points of view and reference frames

Continuous versus discrete formulations and their information content

The information content and processing capability of large numbers of interconnected discrete objects

Connecting formula and geometric representation to actual objects

Finite versus infinite [open and closed systems]

Real numbers versus whole numbers

The traps inherent in assuming compact formulations contain the entire information content

The traps inherent in computer modeling without adequate data and testing and the extent to which they provide insight

Identifying cause and effect versus coincident, secondary, or parallel processes at work

Identifying fundamental versus secondary processes

Correctly identifying variables and naming them as such

In a larger work on this subject it would be important to identify fundamental versus composite issues of innumeracy. Some composite issues include problems outside of innumeracy as well.

There are some applications of this idea in many subject areas. I bring it up because it has been very important in my understanding of what has gone wrong in physics and cosmology. It is much easier to understand when applied to evolutionary biology  take for example cichlid fish which can create a new species in as little as 100 years:

http://en.wikipedia.org/wiki/Cichlid

A huge neglected area is general understanding of feedback processes which spans many innumeracies issues - evolution being a prime example and cichlid fish being a very good specific example.

Dennis May

Edited by dennislmay
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A clear example of innumeracy was displayed by Nobel laureate Ilya Prigogine when took discontinuous functions – point particles – then substituted them with continuous functions to create indeterminism out of determinism on small scales – thus claiming small scale real objects are necessarily indeterministic. Someone with clear visual spatial reasoning would instantly understand the error. This is not an isolated case of this exact problem – I saw the same visual reasoning error repeated in graduate thermodynamics in a class of approximately 20 students – not just for a few minutes but over a several week period. I identified the underlying error in the first few seconds it was being discussed by the professor but could not get anyone else to recognize it for some 2-3 weeks. Someone finally confronted the professor outside of class and he quickly gave the answer and we moved on to other topics. The same error popped up again in a series of papers published as a result of work funded by the DOE and published in "Foundations of Physics" in the early 2000's. The error took about 15 minutes to identify - but over 2 years and 12 PhDs researching it plus journal editors and many hundreds of thousands of tax-payer dollars cannot fix a basic innumeracy problem.

Prigogine was correct. A discontinuous step or jump function can be the weak limit of a series of continuous functions. For example, the famous Dirac Delta Function (which is a distribution, not a function), is the weak limit of a series of gaussian normal functions. Please look at: http://en.wikipedia...._delta_function. Prigogine had some non-standard ideas, but he was never innumerate.

What you call substitution (incorrectly, I might add) is in fact weak convergence of a series of functions. The error you saw was in your own head. Perhaps if you studied the mathematics more thoroughly you might not jump to such intemperate conclusions.

Ba'al Chatzaf

Edited by BaalChatzaf
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A clear example of innumeracy was displayed by Nobel laureate Ilya Prigogine when took discontinuous functions – point particles – then substituted them with continuous functions to create indeterminism out of determinism on small scales – thus claiming small scale real objects are necessarily indeterministic. Someone with clear visual spatial reasoning would instantly understand the error. This is not an isolated case of this exact problem – I saw the same visual reasoning error repeated in graduate thermodynamics in a class of approximately 20 students – not just for a few minutes but over a several week period. I identified the underlying error in the first few seconds it was being discussed by the professor but could not get anyone else to recognize it for some 2-3 weeks. Someone finally confronted the professor outside of class and he quickly gave the answer and we moved on to other topics. The same error popped up again in a series of papers published as a result of work funded by the DOE and published in "Foundations of Physics" in the early 2000's. The error took about 15 minutes to identify - but over 2 years and 12 PhDs researching it plus journal editors and many hundreds of thousands of tax-payer dollars cannot fix a basic innumeracy problem.

Prigogine was correct. A discontinuous step or jump function can be the weak limit of a series of continuous functions. For example, the famous Dirac Delta Function (which is a distribution, not a function), is the weak limit of a series of gaussian normal functions. Please look at: http://en.wikipedia...._delta_function. Prigogine had some non-standard ideas, but he was never innumerate.

What you call substitution (incorrectly, I might add) is in fact weak convergence of a series of functions. The error you saw was in your own head. Perhaps if you studied the mathematics more thoroughly you might not jump to such intemperate conclusions.

Ba'al Chatzaf

I suggest you read Bohm's book "Wholeness and the Implicate Order" where he outlines why such efforts destroy information content and fail to address the basic issues. What Prigogine did is basic innumeracy and numerous researchers called him on it. It is not difficult to apply the wrong math to the question and assume that correctly done wrong math proves something it does not.

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I suggest you read Bohm's book "Wholeness and the Implicate Order" where he outlines why such efforts destroy information content and fail to address the basic issues. What Prigogine did is basic innumeracy and numerous researchers called him on it. It is not difficult to apply the wrong math to the question and assume that correctly done wrong math proves something it does not.

NB: my bold

Which "numerous researchers" and in what articles in what refereed journals?

Ba'al Chatzaf

Edited by BaalChatzaf
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It has been several years ago since I last discussed this on Atlantis_II but my recollection is that nearly all US based journals panned his work while Europeans praised his work. It wasn't just one or two comments in the US there were reviews of his work on line and in magazines calling out his fundamental error in discarding information content when doing mathematically incorrect substitutions. I find it remarkable that anyone would take his work in this area seriously since it is so boldly and obviously incorrect on the face of it. It is clear that Prigogine was working toward a philosophical end by whatever means. Bohm saw these kinds of efforts before Prigogine and preemptively showed why they necessarily are incorrect in not taking all variables into account - effectively a truncation error.

Prigogine’s work still being thought to be correct reminds me of von Neumann’s incorrect proof living long after it being successfully refuted because it had become part of the mainstream dialog for so long. Dialog lives long after the work or theory as been discredited. A very effective fact used in politics every day.

Dennis May

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It has been several years ago since I last discussed this on Atlantis_II but my recollection is that nearly all US based journals panned his work while Europeans praised his work. It wasn't just one or two comments in the US there were reviews of his work on line and in magazines calling out his fundamental error in discarding information content when doing mathematically incorrect substitutions. I find it remarkable that anyone would take his work in this area seriously since it is so boldly and obviously incorrect on the face of it. It is clear that Prigogine was working toward a philosophical end by whatever means. Bohm saw these kinds of efforts before Prigogine and preemptively showed why they necessarily are incorrect in not taking all variables into account - effectively a truncation error.

Prigogine's work still being thought to be correct reminds me of von Neumann's incorrect proof living long after it being successfully refuted because it had become part of the mainstream dialog for so long. Dialog lives long after the work or theory as been discredited. A very effective fact used in politics every day.

Dennis May

Aritcle Titles, Journal Names, volume, pages, authors and dates if you please.

And von Neuman's error (a rather subtle error) did not outlive J.S. Bell pointing it out.

Ba'al Chatzaf

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It has been several years ago since I last discussed this on Atlantis_II but my recollection is that nearly all US based journals panned his work while Europeans praised his work. It wasn't just one or two comments in the US there were reviews of his work on line and in magazines calling out his fundamental error in discarding information content when doing mathematically incorrect substitutions. I find it remarkable that anyone would take his work in this area seriously since it is so boldly and obviously incorrect on the face of it. It is clear that Prigogine was working toward a philosophical end by whatever means. Bohm saw these kinds of efforts before Prigogine and preemptively showed why they necessarily are incorrect in not taking all variables into account - effectively a truncation error.

Prigogine's work still being thought to be correct reminds me of von Neumann's incorrect proof living long after it being successfully refuted because it had become part of the mainstream dialog for so long. Dialog lives long after the work or theory as been discredited. A very effective fact used in politics every day.

Dennis May

Aritcle Titles, Journal Names, volume, pages, authors and dates if you please.

And von Neuman's error (a rather subtle error) did not outlive J.S. Bell pointing it out.

Ba'al Chatzaf

Three critical views I found required payment to read the entire text and I am not willing to do that. One was no longer on the Internet since the work is old. Another required payment but it was not clear what they thought of Prigogine's math.

Here is one book review with some of the flavor of what I read at the time:

http://www.quniverse.sk/buzek/zaujimave/p393_s.pdf

Though this review does not go into the specifics of the error generating Prigogine's conclusions it does indicate a lot of fly by night mathematics going on. Other views I read at the time indicated the specific kind of error Bohm warned of – truncation of information while moving to continuous functions.

A summary of why Prigogine's radical claims concerning indeterminism out of determinism hold no water – again inappropriate mathematics to reach a conclusion:

http://www.physics.nyu.edu/faculty/sokal/UCL-IPT-96-03.pdf

The author also notes - as a Google search will support - that interest in Prigogine's radical indeterminism claims are subjective – not objective - and primarily philosophical and religious – not scientific.

Ba'al Chatzaf wrote:

“And von Neuman's error (a rather subtle error) did not outlive J.S. Bell pointing it out.”

The error itself maybe not – just the conclusions resulting from the error. I heard the error of the conclusion repeated when I was in undergraduate and graduate school and even in written discussion of the memorial physics gathering for J.S. Bell. I still hear it all the time in various Internet discussions.

Dennis May

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The author also notes - as a Google search will support - that interest in Prigogine's radical indeterminism claims are subjective – not objective - and primarily philosophical and religious – not scientific.

I am inclined to agree. Prigogine is engaging in a philosophic speculation. But that does not make him innumerate. He has a complete competent grasp of the mathematics. If he puts a strange interpretation on the math, that is not a mathematical error, that is a philosophical error.

In science, philosophy (other than some basic epistemology) is ka ka. The best thing that happened to physics was parting company from metaphysics.

To get good theories, follow Newton's rules as much as it is possible to follow them.

The theories should flow from the phenomena, not some crack brain a priorism pulled out of one's mental rectum.

Ba'al Chatzaf

Edited by BaalChatzaf
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The author also notes - as a Google search will support - that interest in Prigogine's radical indeterminism claims are subjective  not objective - and primarily philosophical and religious  not scientific.

I am inclined to agree. Prigogine is engaging in a philosophic speculation. But that does not make him innumerate. He has a complete competent grasp of the mathematics. If he puts a strange interpretation on the math, that is not a mathematical error, that is a philosophical error.

In science, philosophy (other than some basic epistemology) is ka ka. The best thing that happened to physics was parting company from metaphysics.

To get good theories, follow Newton's rules as much as it is possible to follow them.

The theories should flow from the phenomena, not some crack brain a priorism pulled out of one's mental rectum.

Ba'al Chatzaf

It would seem his philosophical inclinations drove him to where the math didn't really go - or at least the interpretation. His was likely a case of visual/spatial mathematical innumeracy and strong compartmentalization while still maintaining strong numeracy in other areas. I have seen this suprising kind of innumeracy many times since my undergraduate days and even more often when researching the history of physics.

Dennis May

Edited by dennislmay
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It would seem his philosophical inclinations drove him to where the math didn't really go - or at least the interpretation. His was likely a case of visual/spatial mathematical innumeracy and strong compartmentalization while still maintaining strong numeracy in other areas. I have seen this suprising kind of innumeracy many times since my undergraduate days and even more often when researching the history of physics.

Dennis May

Innumeracy is mathematical incompetence. You are confusing a difference in philosophy and interpretation with mathematical incompetence.

Did you read any of Prigogine's papers on far from equilibrium thermodynamics? They are mathematically sound as far as I can tell. As to the science I am not sufficiently grounded in thermodynamics to give a good judgement.

Ba'al Chatzaf

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It would seem his philosophical inclinations drove him to where the math didn't really go - or at least the interpretation. His was likely a case of visual/spatial mathematical innumeracy and strong compartmentalization while still maintaining strong numeracy in other areas. I have seen this suprising kind of innumeracy many times since my undergraduate days and even more often when researching the history of physics.

Dennis May

Innumeracy is mathematical incompetence. You are confusing a difference in philosophy and interpretation with mathematical incompetence.

Did you read any of Prigogine's papers on far from equilibrium thermodynamics? They are mathematically sound as far as I can tell. As to the science I am not sufficiently grounded in thermodynamics to give a good judgement.

Ba'al Chatzaf

I have not had issues with Prigogine's work except where he has made extraordinary claims.

I am postulating that innumeracy is a great deal more complex issue than what is normally expressed as simply "mathematical incompetence".

It is also important to understand one’s own limits as to numeracy. I am innumerate in several areas that I have observed others having great numeracy. For instance I cannot do square roots in my head like a professor I once had. I cannot memorize pages of numbers like a guy I knew in the Air Force. I cannot listen to a song one time and play it on the piano [and never had piano lessons] like a college student I once knew. Some forms of mathematical proofs entirely escape me as being proofs of anything. So numeracy and innumeracy form a large domain where it is unlikely anyone excels in all areas. I find visual/spatial innumeracy the one most interesting because it is the area in which I have personally observed the most radical disconnect between my own abilities and others who have mathematical backgrounds equal to or in many cases vastly superior to my own. The PhD or Nobel prize only gets you so far if you have a huge blind-spot.

Dennis May

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It is my contention that highly-talented people tend to gravitate to different disciplines, and that is a good thing. Although, as I believe Heinlein said, "specialization is for insects."

Now, that is a very mean thing to say, or take, but there is some truth in it.

When people develop profuse talents in certain areas, they develop a certain type of communication. This works well with like-minded individuals, more-or-less, but even then, problems occur. Still (at least in my case), one has to bridge gaps and attempt to communicate back. No criticism, just expressing lack-of-full-understanding<tm>.

The premise of this thread is built upon an assumption, and I do believe there is some frustration backing it.

What I would say to the writer is that there are other people reading it that have undergone similar frustrations, but live outside the world of math. For instance, were I to say something like "There are a lot of guitar players that are inundated by their obsession with vintage gear; they think that only if they had the perfect instrument they might play better (and they might, for that matter). . " and so on and so forth, it would relate to guitar people, but only in a highly-limited way to others.

In forum writing, this just happens, and then (as it already has), others with similar skill-sets will begin sharing their equal frustrations.

My interest tends to lie outside of those boundaries, because, well, I don't think it relates to any kind of built knowledge from any discipline. Meaning, I think the frustration is more of a general type. Meaning, the next step, frustration being what it is, find a way to convey this in a way outside of math (in this case).

best,

rde

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It is my contention that highly-talented people tend to gravitate to different disciplines, and that is a good thing. Although, as I believe Heinlein said, "specialization is for insects."

Now, that is a very mean thing to say, or take, but there is some truth in it.

When people develop profuse talents in certain areas, they develop a certain type of communication. This works well with like-minded individuals, more-or-less, but even then, problems occur. Still (at least in my case), one has to bridge gaps and attempt to communicate back. No criticism, just expressing lack-of-full-understanding<tm>.

The premise of this thread is built upon an assumption, and I do believe there is some frustration backing it.

What I would say to the writer is that there are other people reading it that have undergone similar frustrations, but live outside the world of math. For instance, were I to say something like "There are a lot of guitar players that are inundated by their obsession with vintage gear; they think that only if they had the perfect instrument they might play better (and they might, for that matter). . " and so on and so forth, it would relate to guitar people, but only in a highly-limited way to others.

In forum writing, this just happens, and then (as it already has), others with similar skill-sets will begin sharing their equal frustrations.

My interest tends to lie outside of those boundaries, because, well, I don't think it relates to any kind of built knowledge from any discipline. Meaning, I think the frustration is more of a general type. Meaning, the next step, frustration being what it is, find a way to convey this in a way outside of math (in this case).

best,

rde

Dennis

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Oh, this one? I change them frequently.

This particular model has a semi-venerable history. Originally, it was dedicated, in a post, to George H. Smith, when he was in the heat of battle, sort of (it is hard to judge, being that GHS has Massive Ninja Power<tm>). It is an electronic roasting spit. Do the math.

rde

By tomorrow, It Will Be Gone<tm>

Edited by Rich Engle
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I believe it was on sale also, but that would involve all those math thingys ~ ~

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Oh, this one? I change them frequently.

This particular model has a semi-venerable history. Originally, it was dedicated, in a post, to George H. Smith, when he was in the heat of battle, sort of (it is hard to judge, being that GHS has Massive Ninja Power<tm>). It is an electronic roasting spit. Do the math.

rde

By tomorrow, It Will Be Gone<tm>

I thought it was something like that but the depth of the pan under it didn't seem right to me. It must catch a lot of meat dripping

in addition to housing the heating element. George can handle the heat and dish it out as well.

Dennis

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I am postulating that innumeracy is a great deal more complex issue than what is normally expressed as simply "mathematical incompetence".

In other words, you have substituted your definition of the word "innumeracy" for the definition that other writers on the subject use. What makes your definition right and other people's definition wrong? John Allen Paulos has written several books on the subject. Why is he wrong and you right?

That sounds so, so ...... Objectivist....!

See http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Consequences-Vintage/dp/0679726012 for a review of his book on the subject. He is a blurb on the use of the term as defined by the people who coined the term in the first place:

"Innumeracy is a neologism coined by analogue with illiteracy; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy. [12]"

The term belongs to Douglas Hofstadter who made it up in the first place. It is his word, not yours.

Ba'al Chatzaf

Edited by BaalChatzaf
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I am postulating that innumeracy is a great deal more complex issue than what is normally expressed as simply "mathematical incompetence".

In other words, you have substituted your definition of the word "innumeracy" for the definition that other writers on the subject use. What makes your definition right and other people's definition wrong? John Allen Paulos has written several books on the subject. Why is he wrong and you right?

That sounds so, so ...... Objectivist....!

See http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Consequences-Vintage/dp/0679726012 for a review of his book on the subject. He is a blurb on the use of the term as defined by the people who coined the term in the first place:

"Innumeracy is a neologism coined by analogue with illiteracy; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy. [12]"

The term belongs to Douglas Hofstadter who made it up in the first place. It is his word, not yours.

Ba'al Chatzaf

That's the beauty of language - it evolves to fit the need of users. I view the original intent as too narrow and self serving.

Dennis

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That's the beauty of language - it evolves to fit the need of users. I view the original intent as too narrow and self serving.

Dennis

Which no doubt furthers some particular intent and interest that YOU have.

Ba'al Chatzaf

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That's the beauty of language - it evolves to fit the need of users. I view the original intent as too narrow and self serving.

Dennis

Which no doubt furthers some particular intent and interest that YOU have.

Ba'al Chatzaf

Exactly.

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I am postulating that innumeracy is a great deal more complex issue than what is normally expressed as simply "mathematical incompetence".

In other words, you have substituted your definition of the word "innumeracy" for the definition that other writers on the subject use. What makes your definition right and other people's definition wrong? John Allen Paulos has written several books on the subject. Why is he wrong and you right?

That sounds so, so ...... Objectivist....!

It would not be fair to Objectivists to equate my methodology with those of Objectivists. I was intensely interested in innumeracy long before I first ever heard of Ayn Rand - when I was 30 years old. As a few regulars on Objectivist Living should be able to attest - I am interested in the ideas of Ayn Rand but I do not qualify as a little o or big O Objectivist.

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• 3 years later...
The Unexpected Power of Baby Math: Adults Still Think About Numbers Like Kids

http://www.sciencedaily.com/releases/2014/01/140122134231.htm

"Educated adults understand numbers "linearly," based on the familiar number

line from 0 to infinity. But children and uneducated adults, like tribespeople

in the Amazon, understand numbers "logarithmically" -- in terms of what

percentage one number is of another."

Well that makes sense - innumeracy originating in early

development. The sense of sound is logarithmic, the article

below indicates all senses and our nervous system is built around

logarithmic scaling.

http://web.mit.edu/newsoffice/2012/thinking-logarithmically-1005.html

It would be my view that the difference between those stuck thinking

to verbal analytic thinking versus visual analytic thinking. In my

experience those physicists most likely to fall into innumeracy are those

most comfortable with rules based formulaic physics but largely crippled

in laboratory physics, physical models, and general engineering spatial

skills.

Dennis

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From Ba'al Chatzaf 23 January 2011 - 06:53 AM:

"Innumeracy is a neologism coined by analogue with illiteracy; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy. [12]"

Unless the previous researchers identified this logarithm sensory/neural link

in their discussions of innumeracy [i have not read their work] they did - in my

opinion - miss the boat on a fundamental understanding of the subject

matter at hand. More work in their area should involve visual

analytic versus verbal analytic thinking skills in overcoming

innumeracy [innumeracy with my expanded definition].

There is necessarily a high correlation of genetics and brain

development related to this issue.

Dennis

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From Ba'al Chatzaf 23 January 2011 - 06:53 AM:

"Innumeracy is a neologism coined by analogue with illiteracy; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy. [12]"

Unless the previous researchers identified this logarithm sensory/neural link

in their discussions of innumeracy [i have not read their work] they did - in my

opinion - miss the boat on a fundamental understanding of the subject

matter at hand. More work in their area should involve visual

analytic versus verbal analytic thinking skills in overcoming

innumeracy [innumeracy with my expanded definition].

There is necessarily a high correlation of genetics and brain

development related to this issue.

Dennis

A good point. Here is an historical instance. Michael Faraday who invented the field concept did not own ten lines of mathematics. He worked as a book binder when he was a lad He made a good impression on Humphry Davy, a leading scientist in England who hired him on as a lab assistant. Faraday went from success to success. He was genius at experimenting and designing experiments. He also had a supreme talent of -visualization-. His right brain genius is what enabled him to see lines of force and fields in space without a single line of calculus. James Clark Maxwell appreciated the nature of Faraday's genius and he put his superlative mathematical talent to work on Faraday's visually original ideas. The result was classical electrodynamics.

Faraday would have flunked the math section of the SATs. So your remark about looking the wrong way at math talent has some evidence. Faraday would have been classified as innumerate. Fortunately that was not how he was judged.

Ba'al Chatzaf

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From Ba'al Chatzaf 23 January 2011 - 06:53 AM:

"Innumeracy is a neologism coined by analogue with illiteracy; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy. [12]"

Unless the previous researchers identified this logarithm sensory/neural link

in their discussions of innumeracy [i have not read their work] they did - in my

opinion - miss the boat on a fundamental understanding of the subject

matter at hand. More work in their area should involve visual

analytic versus verbal analytic thinking skills in overcoming

innumeracy [innumeracy with my expanded definition].

There is necessarily a high correlation of genetics and brain

development related to this issue.

Dennis

A good point. Here is an historical instance. Michael Faraday who invented the field concept did not own ten lines of mathematics. He worked as a book binder when he was a lad He made a good impression on Humphry Davy, a leading scientist in England who hired him on as a lab assistant. Faraday went from success to success. He was genius at experimenting and designing experiments. He also had a supreme talent of -visualization-. His right brain genius is what enabled him to see lines of force and fields in space without a single line of calculus. James Clark Maxwell appreciated the nature of Faraday's genius and he put his superlative mathematical talent to work on Faraday's visually original ideas. The result was classical electrodynamics.

Faraday would have flunked the math section of the SATs. So your remark about looking the wrong way at math talent has some evidence. Faraday would have been classified as innumerate. Fortunately that was not how he was judged.

Ba'al Chatzaf

Very interesting, I had not heard about Faraday's history but it does not surprise me at all based on my own experiences.

The same problem exists in the engineering sciences. Many recent graduates of engineering find themselves involved

in factory machinery or other machinery specifications work. Many of the best engineering students sail through on their

mathematical abilities and ability to follow rules based formulas and specified procedures to arrive at solutions. When

confronted with new problems requiring visualization skills and original solutions many are helpless. This gives a very bad

impression of engineering to maintenance men in those factories who do not have the mathematical background or

education but often know the possible set of solutions through experience and hands-on spatial skills.

A good example happened about ten years ago when I was in a factory in Arkansas. I was dressed in an hourly worker

smock and beard net [you have to go way out of your way to get an engineering smock and safety hat] and I am older than

and look more like Larry the Cable Guy than most engineers seen in that factory. While taking some measurements and

photos of equipment modifications done in the factory the maintenance man for the line came up to me and

wanted assurances that some idiot engineer wasn't going to ruin the piece of equipment by putting on a bunch of

unnecessary guarding. I assured him I would do my best to make sure someone doesn't screw it up and make his job harder.

Since I don't look the part I got feedback at many plants from maintenance men who all seemed to believe I was just an hourly

safety assistant of some kind. They all have such a bad impression of know nothing engineers that most "pretty boy" young

engineers never get told what is really going on because it is commonly viewed as a waste of time to try to explain things

to them since they don't know anything and aren't going to last anyway.

Dennis