.

Dear David,

.

Looks like I got in wrong again ... but not completely.

If I read you correctly, everything was wrong except the additions and subtractions (birth and death) operations which continue to be effected in nature despite the absence of human beings.

That’s less than I thought. I thought there would be some geometry as well, but, apparently not – no circles, no straight lines, no conical shapes, no waves, ... You didn’t mention it, but I suppose there are no triangles, no cylindrical designs and no zig-zags either.

By the way, what I meant was that the sun and the moon both have the shape of a circle, albeit an imperfect one. I was not referring to their movement in space. That’s my fault. I should have expressed myself more precisely.

Mind you, perhaps you, should have realised that only human beings could conceive of the movement of the sun and the moon in space as describing a circle or an ellipse or whatever. So I couldn’t possibly be referring to that because I had indicated that I was describing a situation in which there were no human beings – just me, a mathematically illiterate person hiding behind a curtain.

In the final analysis, it seems that the only maths to be found in nature, independently of mankind, are the adding and subtracting operations effected by birth and death.

Unless, of course, the imperfections you detect in nature (migrating birds that don’t fly straight, imperfectly designed mountain peaks and planar surfaces, seas and oceans which don’t make waves), are simply optical illusions caused by George’s magnifying lenses (if you happen to be looking through them), or, alternatively, errors produced by those mathematical models you employ to examine reality, since you indicate that they can only produce an abstraction of reality – not a reflection of it.

I guess it’s either an imperfection of nature , as you suggest, or George’s magnifying glasses that need cleaning, or, an error in the mathematical abstraction.

I wonder if George and One Under God share your opinion.

.

we are each..trying to describe..our own inner seeing..
revealing..our inner..to those without..[outside]revealing their own inner seeing

banjo..your correct..to a point..
and that is the point

[to try to describe]..

david<<..Mathematical models are an excellent tool for examining reality,>>..and they are..

but tools shape the substance
[think..art/woodwork etc]

taking art..[a method..of drawing..
sets up block shapes..to set up..THE proper proportion..

the golden mean..that at first..
only vaguely resembles the natural face/scene..or body..

via math..blocks circles/triangulations..
then the perspective..[vanishing point]..all..mechanical abstractions..[derivatives]..that yet draw our drawings..closer to that validated..of reality

[see the golden-mean]..

<<..but one must be aware..that it usually
is..only an abstraction of reality..and not a reflection of it...>>

you are both correct..and able to be made...to look not quite right..but so is it..with us all..as we each try..to block-out..or rather rough in..a bigger picture..

from our relatively narrower fields of affect..
via the individual minutia..into the real experiences..validating our smaller revelation..into words..

[lets include faulse memory..mechanistic law..ergo ego]
the mind-full..inner imagery from within..as seen via the material temporal values imposed from..without...[outside..as opposed by in-side].,.,

two dimensions..into a third..
out of 3rd..we get the 4th..inner space..[di-mention]

Dear Banjo,

I’m sure that George, OUG, you and I all see beauty in this world, all can feel love in our hearts for something, all see our own abstractions, all try to understand the world and share our humanity in many ways.

I hope we all see beauty in mathematics, and we all know mathematics at some level or other.

The fertilised ova from which we all come start their development in a geometric progression – 1,2,4,8,16.. cells.

"Mathematics is the language in which God has written the universe." - Galileo

At the start of the Second World War, mathematician G. H. Hardy felt a need to justify his belief that mathematics should be pursued for its own sake, rather than that of its applications. The resulting book, A Mathematician's Apology, is a defense of mathematics as a field. It’s a good read and can be found on the net.

The following explicitly connects pure mathematics with a search for the divine.

“Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece.

In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.”

Since mathematics is a part of my life and I think death is oblivion there is no aftermath for me.

.

Dear George,

.

I have no problems with your last post which I had not read before posting my last reply to David. It must have arrived while I was busy preparing my reply to David.

The only slight reservation I have is in relation to your comment : “Well, that is the whole point, we cannot “see” the world which has no observer that we can communicate with”.

I doubt that we observe any region in the world in its totality, 24h a day, 7 days a week but that does not prevent us from having access to a large number of them “through our senses and theories that adequately model physical reality” as you stipulate.

As for the more remote regions where there are no permanent observers, just the odd passing visitor every decade or so, I don’t think any reasonable person would entertain the slightest doubt as to the existence of the physical reality of those regions – even in the absence of “adequate models of physical reality leading to verifiable predictions”.

To return now to the question in hand as to whether pure mathematics is a product of the human imagination and, as such, not part of reality, that does, indeed, seem to be the case, except as regards the operations of additions and subtractions which are effected by life and death.

This is the result of an analysis of nature independently of mankind.

David has expressed doubt as to whether life and death should be considered as part of reality or not. But there is no doubt in my mind that they do. On the other hand, I thought I could discern signs of the application of geometry in nature (circles, triangles, cones, straight lines, flat surfaces, waves, zig-zags). David does not.

Hence my provisional conclusion, pending your opinion and that of One Under God, that pure mathematics is a product of the imagination and, as such, not part of reality, except as regards the operations of additions and subtractions.

I await yours and One Under God’s comments with interest .

.

its/sad..david sees..no afterlife..for*himself
and..neither..do i..for this present*..material-self[body]

BUT*..we..of ourselves..isnt everything
in fact..we each..are all..but micro-bits..of something..far greater

[much like..individual cells]..yet To-GETHER..
part of..a much larger..neurobio-logical/bio-structure..[the uni-verse][god]

lets quote..from..'gone_west'..again
hear*..what the departed..themselves reveal

<<..“‘Now..it is difficult..for you,to understand..our arrangements here;..it is..*very different..from what you..are usually taught.

It is not..however.;.so much that.;.the original teaching..of
the church..was wrong,..but that it has been..*misinterpreted..by its teachers.

At..the best,however,..
*they..only show..a part of*..the truth.

*Not even..here..do we know..*all the truth.

Truth..is like*..a diamond..with many facets.
Each facet..contains part,..but only part,*..*of the truth.

Some facets..are larger/smarter/more switched on..than others;
just like..all creeds..exist8..because of*..the ‘facet’.of truth,
however small,..which they..WE*..each..possess.

No faith../being/beast or presence..which had..*no element..of truth &*could exist..at/all..for any space of time..on earth.

Often,however,..the ‘facet’..[we each hold]..is very small.

The larger..then amount of truth..[first person/witness]...,the stronger that faith/proof..will,as a rule,grow...Thus the Roman Catholics..are..a numerous body,..but neither they..nor any Sect possess*..*all the truth...They simply form
one of..the communities..which exist/in the sets..where men believed...now live.

There..are also..Buddhists..and ‘heathen’..here,..and,indeed,..all religions.[people parts]

From this stage..we advance until..we have gathered..in all others/truths,..and then we shall really know..what is meant by God.

But..that is far hence.

“Since,however,..it is easier..for you to comprehend
the new facts..with which I am about to deal..if you can*..attach them to..*some..[egsisting]..theory..with which..you..already are acquainted,

I shall..thus..adopt
the general/plan..of Heaven,Purgatory,..and Hell.

Be under..no misunderstanding,..as depicted..by many personal/beliefs..these names are*..wholly misleading.
*But..if accepted..as a convenient..and rough [imprecise]. class-ification,..they will be helpful.

One fact,..however,..you must..clearly grasp.

So far as..I can discover..there is no evidence.of the eternity..of Hell.
Drop..that idea..and the rest will be easy..to understand.

At the same time.,.spirits may be..in what.I..will call Hell..for countless ages...For example,..Nero is there..still.. and likely to remain..there..for many..an earthly age.

“The officer..has just come up..from Hell,
and so that proves*..it is not a place of
perpetual torment...But as most spirits..who communicate with the living..are fairly spiritual
ones,..*they*..have never been..in Hell,..and so can tell you nothing of it.

Many do/not know
of its existence...For we do not know everything,!..only what,..is necessary for our own
progress.

They*..need no pains of Hell,
and so know not..of its existence.>>..

one big..living loving..biol-logical..*EL
light..sustaining/life..one cell..at a time

Dear david f,

Thanks for the Hardy quote.

My generation is younger than Hardy’s but also throughout my student and professional years, there was us, doing “exact” contemporary (pure) mathematics, and - as we used to say - theoretical physicists and applied mathematicians who were dressing their 20th century findings in 19th century mathematics.

Well, certainly an exaggeration, but there used to be a gap between proper, modern, mathematics, for instance differential geometry that I was working with, and outdated differential geometry that physicists were speaking when explaining and working with general relativity. Concepts like connections in principal bundles were something we strived on, but physicists did not find useful (and understand) these constructions. For instance, Lie groups, as formulated in 19th cenntury were very insightful but needed an input of 20th cdentory toplogy to make it the theory Lbullet-proof" (the same Dirac function until Laurent Schwarz fixed it).

This was the situation until Yang-Mills came and showed that these connections were nothing but what physicists called gauge fields in (physica) gauge theory (of elementary.particles).

[Apologies to Banjo, OUG and others who might not be familiar with these technical terms]

This was a fascinating experience for a pure mathematician like me, perhaps not unlike when centuries ago they found out that complex numbers (constructid just to defy the non-negativeness of squares) found important applications in various parts of physics. I wonder whether it was not this, Yang-Mills experience, that prompted Wigner to write about “unreasonable effectiveness of mathematics”.

Today, the new generation is different. No serious theoretical physicist can talk about gravitation theory, gauge theory or speculate about superstring theories without understanding much abstract, and “modern” concepts of pure mathematics that are now completely beyond my comprehension. So the gap - between “elegant” contemporary mathematics and mathematics applicable in theoretical physics is closing, or already closed. And that is good feeling that my PhD and habilitation, although dealing only with "elegancy" in approach to mathematics is needed, albeit very marginally in my case) in physics for progressive research.