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Author Topic: Does mathematics give us a true reflection of reality?  (Read 1913 times)

Offline Alan McDougall

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In recent years, the limitations of mathematical models to express "the real workings of nature" have been the subject of intense discussion?

However, even the most advanced mathematical models are "only a rough approximation to reality", valid only within certain limits. The recent debate on chaos and anti-chaos has centered on those areas involving breaks in continuity, sudden "chaotic" changes which cannot be adequately conveyed by classical mathematical formulae.

What are your thoughts on the matter , do you think for instance that mathematics is a "Holy Cow" not to be messed with or a progressive advancement in the comprehension of what underpins reality and the best means of finding ultimate truth?

Not to bring religion into it, I would nevertheless like to post a quote of the great theoretical physicist Paul Dirac.

"I see God in the Beauty of his mathematics"

Alan
« Last Edit: 14/06/2016 16:00:42 by Alan McDougall »


 

Offline jeffreyH

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Re: Does mathematics give us a true reflection of reality?
« Reply #1 on: 14/06/2016 19:05:21 »
This is not meant to be a flippant answer but if you want a true reflection of reality look at a mirror. Mathematical theories accepted by the scientific community do not exist without some foundation in observation of natural processes. They may be several steps removed from the initial observations. Approximation is normally the best that can be expected. Absolute accuracy can be achieved easily if discussing macroscopic objects. I am holding one apple is a trivial example. When it comes to the motions of objects at any scale then approximation is all we can hope for. Unless others have differing views.
 

Offline Alan McDougall

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Re: Does mathematics give us a true reflection of reality?
« Reply #2 on: 14/06/2016 20:49:46 »
This is not meant to be a flippant answer but if you want a true reflection of reality look at a mirror. Mathematical theories accepted by the scientific community do not exist without some foundation in observation of natural processes. They may be several steps removed from the initial observations. Approximation is normally the best that can be expected. Absolute accuracy can be achieved easily if discussing macroscopic objects. I am holding one apple is a trivial example. When it comes to the motions of objects at any scale then approximation is all we can hope for. Unless others have differing views.

I am not sure that looking in the mirror would give me an accurate image of who I am. My brain fills in the gaps of my perception and is not a totally reliable source of my true reality. In fact I am mostly empty space at the fundamental level where mathematics can go and give an equation of my true reality as it fits into the grand order of the universe.

The macro level of me, might just be a construct of my expectations?
 

Offline evan_au

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Re: Does mathematics give us a true reflection of reality?
« Reply #3 on: 14/06/2016 22:35:15 »
Most mathematicians are somewhere on the spectrum from purely theoretical to the purely applied.
  • On the purely theoretical side, you can point to Galois (he died before the French revolution). In one night, he wrote down mathematics which today we use in CDs and Mobile Phones. So his purely theoretical description was useful in the real world, centuries later. His mathematics was true, regardless of whether we found an application for it (it will probably be replaced by another technique in the next generation of mobile phones - but that doesn't make it wrong).
  • Einstein was more on the Applied side. He used mathematical tools to describe how light, gravity and matter interacted in the real world, explaining the somewhat confusing results of previous experiments. His work would be ignored if it didn't accurately describe the experiments of the day; it has only grown in prestige as it has predicted the results of experiments for a century after he wrote it. No-one claims it is "True"; one day, it will probably be relegated to a "useful approximation for weak gravitational fields (like the Solar System)".
  • Chaos Theory is a relatively new field, which fundamentally challenges our most powerful computers. But it is everywhere, from the weather (we can now approximate 7-day forecasts) to Earth's magnetic field, the motion of planets in the Solar System, ecology and the economy. Sometimes chaotic systems spontaneously change state, and sometimes they are "pushed" by an external event (the proverbial "butterfly effect").
  • The majority of people are not mathematicians, but use mathematical tools to help them through life, whether that be deciding whether to buy more apples, doing the tax, selecting a car, or a myriad of things in the workplace. 
 
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Offline Alan McDougall

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Re: Does mathematics give us a true reflection of reality?
« Reply #4 on: 15/06/2016 00:14:39 »
Most mathematicians are somewhere on the spectrum from purely theoretical to the purely applied.
  • On the purely theoretical side, you can point to Galois (he died before the French revolution). In one night, he wrote down mathematics which today we use in CDs and Mobile Phones. So his purely theoretical description was useful in the real world, centuries later. His mathematics was true, regardless of whether we found an application for it (it will probably be replaced by another technique in the next generation of mobile phones - but that doesn't make it wrong).
  • Einstein was more on the Applied side. He used mathematical tools to describe how light, gravity and matter interacted in the real world, explaining the somewhat confusing results of previous experiments. His work would be ignored if it didn't accurately describe the experiments of the day; it has only grown in prestige as it has predicted the results of experiments for a century after he wrote it. No-one claims it is "True"; one day, it will probably be relegated to a "useful approximation for weak gravitational fields (like the Solar System)".
  • Chaos Theory is a relatively new field, which fundamentally challenges our most powerful computers. But it is everywhere, from the weather (we can now approximate 7-day forecasts) to Earth's magnetic field, the motion of planets in the Solar System, ecology and the economy. Sometimes chaotic systems spontaneously change state, and sometimes they are "pushed" by an external event (the proverbial "butterfly effect").
  • The majority of people are not mathematicians, but use mathematical tools to help them through life, whether that be deciding whether to buy more apples, doing the tax, selecting a car, or a myriad of things in the workplace. 

Great response it sums up the whole question!

Thank you!

Alan
 

Offline jeffreyH

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Re: Does mathematics give us a true reflection of reality?
« Reply #5 on: 15/06/2016 00:51:15 »
Evan never disappoints.  ;D
 

Offline evan_au

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Re: Does mathematics give us a true reflection of reality?
« Reply #6 on: 16/06/2016 21:51:45 »
Quote from: Alan McDougall
Does mathematics give us a true reflection of reality?
It is known that humans and many animals have a fast-acting sense of number, called "Subitizing".
See: https://en.wikipedia.org/wiki/Subitizing

It is not a "True" reflection of reality, as it only has an accuracy of about 10%. But it is close enough for a bird to tell if an egg has fallen out of the nest (or a Cuckoo has added an egg to the nest).
https://en.wikipedia.org/wiki/Number_sense_in_animals

In their natural habitats, humans and animals deal with a large number of complex mathematical problems that require differential equations to solve accurately, including catching a ball, swinging from branch to branch, and walking.

The folding of proteins is a complex, multi-dimensional problem which is really hard to solve on a computer (but your cells do it every second). A citizen science project has allowed members of the public to discover the structure of important proteins, by turning it into a game (and competition).
See: http://fold.it/portal/

A more recent citizen science project examining a problem in quantum physics used a game on a smartphone. Despite the fact that the problem is extremely hard to solve on a computer, they found that some people quickly developed a sense of how this quantum system worked, and demonstrated methods that were far more effective than the researchers had been able to develop on their own.

...so our brains can do complex mathematics unconsciously!

Perhaps the mathematics we teach in high school seems irrelevant because it is too simple to deal with practical problems like catching a ball or catching a bus?
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #7 on: 28/06/2016 10:14:07 »
In recent years, the limitations of mathematical models to express "the real workings of nature" have been the subject of intense discussion?

However, even the most advanced mathematical models are "only a rough approximation to reality", valid only within certain limits. The recent debate on chaos and anti-chaos has centered on those areas involving breaks in continuity, sudden "chaotic" changes which cannot be adequately conveyed by classical mathematical formulae.

What are your thoughts on the matter , do you think for instance that mathematics is a "Holy Cow" not to be messed with or a progressive advancement in the comprehension of what underpins reality and the best means of finding ultimate truth?

Not to bring religion into it, I would nevertheless like to post a quote of the great theoretical physicist Paul Dirac.

"I see God in the Beauty of his mathematics"

Alan


What an odd question!

Anyone who knows about maths knows that maths explains processes of reality and is simply explaining the process in more than just words alone which have ambiguity.  The Idea of maths is for a Universal understanding of process that should not be misunderstood once all the maths symbols are known.

To me it seems like you must have a problem with maths?  Otherwise you would  have not asked the question.


"I see God in the Beauty of his mathematics"

Preaching does not belong in a science forum and that is a diabolical quote.
 

Offline alancalverd

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Re: Does mathematics give us a true reflection of reality?
« Reply #8 on: 28/06/2016 10:41:28 »
It's interesting that science developed rapidly in those cultures that espoused a single Divine Plan rather than any polytheistic or animistic society. Many early scientists considered that they were looking for evidence of that Plan, and the abstract and eneral nature of mathematics was particularly appealing to those who though a god should not be constrained by material limits.   

Things have evolved to the point where we now think that the universe is more complicated and necessarily unpredictable than can be completely forecast by mathematical models, but those that we have are robust within known limits. At  this point, we need to drop the theistic approach, rather as we disembark the pilot once we have left harbour. Einstein said "God does not play dice with the universe" but Heisenberg pointed out that it only makes sense if he does, and we are now on the open sea. Apologies for the mixed metaphor, but I think the point is clear.

   
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #9 on: 28/06/2016 10:51:38 »
It's interesting that science developed rapidly in those cultures that espoused a single Divine Plan rather than any polytheistic or animistic society. Many early scientists considered that they were looking for evidence of that Plan, and the abstract and eneral nature of mathematics was particularly appealing to those who though a god should not be constrained by material limits.   

Things have evolved to the point where we now think that the universe is more complicated and necessarily unpredictable than can be completely forecast by mathematical models, but those that we have are robust within known limits. At  this point, we need to drop the theistic approach, rather as we disembark the pilot once we have left harbour. Einstein said "God does not play dice with the universe" but Heisenberg pointed out that it only makes sense if he does, and we are now on the open sea. Apologies for the mixed metaphor, but I think the point is clear.

   

Interesting Alan, I however do not believe the Universe is unpredictable, I think we have just not discovered everything yet and put the maths to it.
Our obvious main problem in science is the ''firmament'' of imagination because we are limited to how far we can travel and how fast we can travel to go and have a ''butchers'' of what if anything is beyond our visual boundary ''edge''.
I think once this achieved we will have a whole new set of ''numbers'' to ''play'' with and maths will be ''alive'' as ever.
I do know most maths ''works'' so science must have most things right and there is without doubt an importance between the maths/reality relationship.
 

Offline Alan McDougall

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Re: Does mathematics give us a true reflection of reality?
« Reply #10 on: 28/06/2016 12:37:03 »
In recent years, the limitations of mathematical models to express "the real workings of nature" have been the subject of intense discussion?

However, even the most advanced mathematical models are "only a rough approximation to reality", valid only within certain limits. The recent debate on chaos and anti-chaos has centered on those areas involving breaks in continuity, sudden "chaotic" changes which cannot be adequately conveyed by classical mathematical formulae.

What are your thoughts on the matter , do you think for instance that mathematics is a "Holy Cow" not to be messed with or a progressive advancement in the comprehension of what underpins reality and the best means of finding ultimate truth?

Not to bring religion into it, I would nevertheless like to post a quote of the great theoretical physicist Paul Dirac.

"I see God in the Beauty of his mathematics"

Alan


What an odd question!

Anyone who knows about maths knows that maths explains processes of reality and is simply explaining the process in more than just words alone which have ambiguity.  The Idea of maths is for a Universal understanding of process that should not be misunderstood once all the maths symbols are known.

To me it seems like you must have a problem with maths?  Otherwise you would  have not asked the question.


"I see God in the Beauty of his mathematics"

"Preaching does not belong in a science forum and that is a diabolical quote.


Quote
"Preaching does not belong in a science forum and that is a diabolical quote.

That diabolic quote was made by one of the greatest minds, greatest physicist and mathematical in all of history namely Paul Dirac who was the first scientist to postulate the existence of antimatter long before it was proved true.

Educate yourself before making stupid remarks

Taking that as preaching is the height of idiotic nonsense and your use of "Diabolic" shows that it is you not me, who is believer in these things such as the Devil (Diabolic) himself.

Try to actually post some lucid and meaningful instead of your constant river of stupid rubbish.  [:(!]
« Last Edit: 28/06/2016 12:40:56 by Alan McDougall »
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #11 on: 28/06/2016 13:22:26 »
In recent years, the limitations of mathematical models to express "the real workings of nature" have been the subject of intense discussion?

However, even the most advanced mathematical models are "only a rough approximation to reality", valid only within certain limits. The recent debate on chaos and anti-chaos has centered on those areas involving breaks in continuity, sudden "chaotic" changes which cannot be adequately conveyed by classical mathematical formulae.

What are your thoughts on the matter , do you think for instance that mathematics is a "Holy Cow" not to be messed with or a progressive advancement in the comprehension of what underpins reality and the best means of finding ultimate truth?

Not to bring religion into it, I would nevertheless like to post a quote of the great theoretical physicist Paul Dirac.

"I see God in the Beauty of his mathematics"

Alan


What an odd question!

Anyone who knows about maths knows that maths explains processes of reality and is simply explaining the process in more than just words alone which have ambiguity.  The Idea of maths is for a Universal understanding of process that should not be misunderstood once all the maths symbols are known.

To me it seems like you must have a problem with maths?  Otherwise you would  have not asked the question.


"I see God in the Beauty of his mathematics"

"Preaching does not belong in a science forum and that is a diabolical quote.


Quote
"Preaching does not belong in a science forum and that is a diabolical quote.

That diabolic quote was made by one of the greatest minds, greatest physicist and mathematical in all of history namely Paul Dirac who was the first scientist to postulate the existence of antimatter long before it was proved true.

Educate yourself before making stupid remarks

Taking that as preaching is the height of idiotic nonsense and your use of "Diabolic" shows that it is you not me, who is believer in these things such as the Devil (Diabolic) himself.

Try to actually post some lucid and meaningful instead of your constant river of stupid rubbish.  [:(!]


Wasn't Dirac the scientist with the ''child like'' drawings?


added-

"I see God in the Beauty of his mathematics"


The correct and none sexist objective statement would have been , I ''see'' space and it's beauty of mathematics that the matter occupying  space shows me. 


« Last Edit: 28/06/2016 13:30:31 by Thebox »
 

Offline Alan McDougall

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Re: Does mathematics give us a true reflection of reality?
« Reply #12 on: 28/06/2016 13:38:25 »
In recent years, the limitations of mathematical models to express "the real workings of nature" have been the subject of intense discussion?

However, even the most advanced mathematical models are "only a rough approximation to reality", valid only within certain limits. The recent debate on chaos and anti-chaos has centered on those areas involving breaks in continuity, sudden "chaotic" changes which cannot be adequately conveyed by classical mathematical formulae.

What are your thoughts on the matter , do you think for instance that mathematics is a "Holy Cow" not to be messed with or a progressive advancement in the comprehension of what underpins reality and the best means of finding ultimate truth?

Not to bring religion into it, I would nevertheless like to post a quote of the great theoretical physicist Paul Dirac.

"I see God in the Beauty of his mathematics"

Alan


What an odd question!

Anyone who knows about maths knows that maths explains processes of reality and is simply explaining the process in more than just words alone which have ambiguity.  The Idea of maths is for a Universal understanding of process that should not be misunderstood once all the maths symbols are known.

To me it seems like you must have a problem with maths?  Otherwise you would  have not asked the question.


"I see God in the Beauty of his mathematics"

"Preaching does not belong in a science forum and that is a diabolical quote.


Quote
"Preaching does not belong in a science forum and that is a diabolical quote.

That diabolic quote was made by one of the greatest minds, greatest physicist and mathematical in all of history namely Paul Dirac who was the first scientist to postulate the existence of antimatter long before it was proved true.

Educate yourself before making stupid remarks

Taking that as preaching is the height of idiotic nonsense and your use of "Diabolic" shows that it is you not me, who is believer in these things such as the Devil (Diabolic) himself.

Try to actually post some lucid and meaningful instead of your constant river of stupid rubbish.  [:(!]


Wasn't Dirac the scientist with the ''child like'' drawings?


added-

"I see God in the Beauty of his mathematics"


The correct and none sexist objective statement would have been , I ''see'' space and it's beauty of mathematics that the matter occupying  space shows me. 


What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"

More quotes from Paul Dirac of which you know nothing but still make stupid remarks about him.

Quote
God used beautiful mathematics in creating the world.

Quote
Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

I cannot tolerate your continual nonsense anymore so you are the second person I put on my ignore option
« Last Edit: 28/06/2016 13:42:25 by Alan McDougall »
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #13 on: 28/06/2016 17:07:33 »






What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"

There is nothing wrong with he or she but there is something wrong when Dirac defines ''god'' as his, it does not say her mathematics or politically correct their mathematics it says his mathematics, that a bit sexist and is saying ''god'' is a man suggesting the ''creator'' is not a women or could be a women.


 

Offline IAMREALITY

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Re: Does mathematics give us a true reflection of reality?
« Reply #14 on: 28/06/2016 17:31:19 »






What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"


There is nothing wrong with he or she but there is something wrong when Dirac defines ''god'' as his, it does not say her mathematics or politically correct their mathematics it says his mathematics, that a bit sexist and is saying ''god'' is a man suggesting the ''creator'' is not a women or could be a women.

That's a very good point!  Since god is a fictional character, I guess some impose their own preferred gender upon it.  Even if it were real, it wouldn't have a gender, so I guess the right thing to say would be "Its".  (At the most, it would simply be a force that is a catalyst for creation, and forces most definitely don't have genders and would go by its)
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #15 on: 28/06/2016 21:57:18 »






What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"


There is nothing wrong with he or she but there is something wrong when Dirac defines ''god'' as his, it does not say her mathematics or politically correct their mathematics it says his mathematics, that a bit sexist and is saying ''god'' is a man suggesting the ''creator'' is not a women or could be a women.

That's a very good point!  Since god is a fictional character, I guess some impose their own preferred gender upon it.  Even if it were real, it wouldn't have a gender, so I guess the right thing to say would be "Its".  (At the most, it would simply be a force that is a catalyst for creation, and forces most definitely don't have genders and would go by its)


Yes I agree ''it's'' would be a better term with ''it'' meaning just about anything.

 

Offline Alan McDougall

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Re: Does mathematics give us a true reflection of reality?
« Reply #16 on: 28/06/2016 22:41:31 »


What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"

There is nothing wrong with he or she but there is something wrong when Dirac defines ''god'' as his, it does not say her mathematics or politically correct their mathematics it says his mathematics, that a bit sexist and is saying ''god'' is a man suggesting the ''creator'' is not a women or could be a women.


Cant you write even one post that makes sense? This one is again ambiguous, rambling back on itself and circular non-logic.

"And to again to return to your stupid remark that I was preaching and that the quote was diabolic".

Is was Paul Dirac who said he "Saw God in the beauty of his mathematics ( Not me, go to his grave and admonish him there for preaching and apologise to me for saying I was preaching)

You uses the Term "Diabolical" therefore you believe in Satan also called the Devil.

If anyone were preaching it was Paul Dirac not me, get that into you skull!!
« Last Edit: 28/06/2016 22:43:58 by Alan McDougall »
 

Offline alancalverd

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Re: Does mathematics give us a true reflection of reality?
« Reply #17 on: 28/06/2016 22:52:20 »
politically correct their mathematics
"politically correct" but etymologically wrong. The neuter 3rd person singular in English is "it". We always refer to animals with a gendered pronoun because they are gendered, but for reasons lost in the mist of history, the default gender varies - usually "he" except for cats. And the species noun is gendered too: dog, goose, duck.... And just to make it interesting, boats, aeroplanes and vehicles are always "she".

English is a lot more interesting (and more useful) than political correctness. Think thatched cottages rather than concrete tower blocks.

Anyway, here's the big secret about the judaeochristian god: she's black. And a weak lefthander.
« Last Edit: 28/06/2016 22:55:12 by alancalverd »
 

Offline IAMREALITY

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Re: Does mathematics give us a true reflection of reality?
« Reply #18 on: 28/06/2016 23:00:56 »


What has sexism have to do with is?? Are you a male or a female or something in between?
What on earth is wrong with "He" or She"

There is nothing wrong with he or she but there is something wrong when Dirac defines ''god'' as his, it does not say her mathematics or politically correct their mathematics it says his mathematics, that a bit sexist and is saying ''god'' is a man suggesting the ''creator'' is not a women or could be a women.


Cant you write even one post that makes sense? This one is again ambiguous, rambling back on itself and circular non-logic.

"And to again to return to your stupid remark that I was preaching and that the quote was diabolic".

Is was Paul Dirac who said he "Saw God in the beauty of his mathematics ( Not me, go to his grave and admonish him there for preaching and apologise to me for saying I was preaching)

You uses the Term "Diabolical" therefore you believe in Satan also called the Devil.

If anyone were preaching it was Paul Dirac not me, get that into you skull!!

I'm not sure why you're attacking the poster like this.  They weren't admonishing you to begin with, and they specifically call out Dirac, and the word choice the dude chose to use.  They were just making a substantive point.

And the point was clear and simple to understand.  And that's that Dirac says that God was a he, by referencing the pronoun 'his' in his quote.  The poster was objecting to it on the grounds that why does god have to be a he and not a she.  Why not 'her' mathematics etc.  But the correct choice would be it.  "Its" mathematics.  That's the correct choice since god has no gender (and, well, is quite a fictional thing to begin with, but I digress...)
« Last Edit: 28/06/2016 23:03:15 by IAMREALITY »
 

Offline Thebox

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Re: Does mathematics give us a true reflection of reality?
« Reply #19 on: 28/06/2016 23:02:40 »
politically correct their mathematics
"politically correct" but etymologically wrong. The neuter 3rd person singular in English is "it". We always refer to animals with a gendered pronoun because they are gendered, but for reasons lost in the mist of history, the default gender varies - usually "he" except for cats. And the species noun is gendered too: dog, goose, duck.... And just to make it interesting, boats, aeroplanes and vehicles are always "she".

English is a lot more interesting (and more useful) than political correctness. Think thatched cottages rather than concrete tower blocks.

Anyway, here's the big secret about the judaeochristian god: she's black. And a weak lefthander.

Thank you for the English lesson, I nearly put ''it'', but then I though even if I said ''if'' I would still be defining ''it'' as being something by calling it, an ''it''.  We could say this ''thing'' but then that reminds of a horror movie, so how about virtual being?

 

Offline jeffreyH

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Re: Does mathematics give us a true reflection of reality?
« Reply #20 on: 28/06/2016 23:27:34 »
Let calmness and tranquility proceed your posts, lest you intend to offend your hosts. All things in moderation.
 

Offline IAMREALITY

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Re: Does mathematics give us a true reflection of reality?
« Reply #21 on: 28/06/2016 23:39:47 »
Let calmness and tranquility proceed your posts, lest you intend to offend your hosts. All things in moderation.

Is this your own? I love it!
 
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Offline jeffreyH

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Re: Does mathematics give us a true reflection of reality?
« Reply #22 on: 29/06/2016 02:05:35 »
Let calmness and tranquility proceed your posts, lest you intend to offend your hosts. All things in moderation.

Is this your own? I love it!

In years gone by. A poet was I. Yes it was my own.
 

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Re: Does mathematics give us a true reflection of reality?
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