Tuesday, May 15, 2007

What does this tell us about anything?

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Heini Halberstam, in the Chapter “Some Unsolved Problems of Higher Arithmetic” [Pages 191-203 in The Encyclopedia of Ignorance, Pergamon Press, Oxford, 1977], writes this:

“Turning to numbers that are the sums of two squares, these are only a littlem ore common than the primes…, and very little indeed is known about their finer distribution. For example, it is almost trivial to see that there is always such a number between n and n + n¼, yet literally nothing better is known…” [Page 201]

And this [ibid]:

“We know that, in a certain precise sense, most numbers are transcendental, yet the problem of deciding whether a given number is transcendental is profoundly difficult.” [Page 201]

Roger Penrose, in the same book, Chapter “Is Nature Complex?” [Page 160] writes:

“Though Nature [sic] is undoubtedly subtle, she is surely not malicious. This, at least, we have on the authority of Einstein…

That Nature can be usefully described, at least to a considerable degree according to the laws of number, has been in evidence for many centuries. But what is not so familiar to those without a mathematical background is that are several different kinds of number, many of which are nevertheless subject to the same arithmetical laws.”

Arithmetic (mathematics), in all its permutations, represents a reality that is as abstract and intangible as the theology of Jesuits. But it has “proofs” which theology does not.

Pi is infinite, and can be (almost) proven to be so. God is infinite, but there is no proof, so far, that can establish that “fact of faith.”

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Mathematicians, and their lackeys (which we mean descriptively not pejoratively), including physicists, resort to the “provable” abstractions of arithmetic to resolve issues of physical reality that belie the meta-reality, even though it appears – and we use the word “appears” advisedly – that physicists, cosmologists, and their ilk, are dealing with the meta-reality. (They are not.)

Psychiatry would call the mathematician’s province that place where they (mathematicians) go to escape from the world. It’s not just an escape from the practical reality of life – the vicissitudes of daily living; it’s an escape into a contrived reality that pretends to cope with profound issues affecting mankind.

But what are mankind’s ills that physical laws address? Hunger? Poverty? War? Disease? What?

When theologians tackle the idea of God and/or morality, they are net with opprobrium by scientists, generally.

But when science addresses issues that are not biological, geologic or in ways that are not beneficial to the plight of humankind, such as quantum physics, string theory, and all the other subsets of physics, no one (or rarely anyone) reproaches them, and they win Nobel and other prizes.

We don’t deny that the study of the transcendental ether is important -- some saying that it may even lead to the discovery of God.

But it seems strange that so many scientists, who don’t believe in God or a hereafter, would spend so much time and effort on the curiosities of the Universe which, for them, has bearing on their eventual physical mouldering….unless….unless they, deep down, want to prove that there is a God, or a life after this one, or something more than what we perceive as the human, sensory reality. (But that for another time.)

When one studies the laws of harmony and musical theory itself, the end result may end up being a Beethoven symphony or a Beatle tune.

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When one studies art – color, perspective, form, et cetera – one may produce a painting, as that by Monet, Titian, or Hockney.

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And if one studies literary manuals, one might even create a work of fiction (or non-fiction) like that of Shakespeare, Gogol ,or Updike.

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Those endeavors please the senses, and bring pleasure to an existence which is sometimes fraught with horrors of subtle or unimaginable kinds.

But what about mathematics, sometimes elegant in their construction? What sensory pleasures to they provide?

Yes, they stimulate the mind, so we give them that. And such stimulation can be quite as wonderful as that which one gets by looking at a Van Gogh painting, hearing a Verdi opera, or reading a Eco novel.

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But is mathematical stimulation as glorious as sensory stimulation? For some it is, but for the rest of us, it isn’t.

Thus, we see the pursuit of mathematics and physics, not so much as a useful mental endeavor but, rather, as an escape into and from the delectabilities of things mundane, but oh so very delicious mundanities.

And so we’ll address here, some of those delights that assuage the humdrummery of everyday life, and even the stilt of mathematics that afflicts us, and almost everyone else we know….so that we might pursue the ultimate question: Not what does reality consist of but why are we here?

17 comments:

Ennoia said...

"Number is the ruler of forms and ideas, and the cause of gods and demons." -- Pythagoras

Rich said...

I wish I could say the world as a whole was delicious, let alone for each and EVERY one of us. Of course, while we are here we should look into and discover what we can about it all.

Whatever this place is, it certainly keeps things under control. Through the use of time, space, etc, etc, etc it keeps things under control. I am not going to readily dismiss infinite possibilities bring infintite things with us sitting in just one of the possibilities (Ennoia I believe brought something along these lines up in another comment) but I will say that "in the end" it all seems to be controlled.

In other words, I cannot for a second believe that regardless of how many worlds, tries it all took, or whatever that this whole thing is not controlled (including us ultimately).

Perhaps becuase I rely too much on intuition/sesnses and the like that I believe this.

This DOES NOT mean I believe God controls everything although I do believe that whatever "runs this place" it is indeed at least somewhat intelligent...even DESPITE the "infinite" tries it took or the "infinite" other worlds/dimensions possibly existing that have "no intelligence."

The world itself is NOT the controller...although it can/does quite capably run on its own. Now why invoke something "sitting outside of it all?" Again, this place, regardless of how it got here or whatever, it does certainly seem controlled! NO DOUBT! Except when looking into the "quantum world" perhaps.

This DOES NOT mean there is no chance or probalitity....to us (at present) these do exist and experiments, etc, etc pretty much prove they exist...especially in the quantum world where probability certianly seems the rule.

I am of the belief that probability/chance, exists ONLY in the sense that we cannot figure it out...EVEN IN THE QUANTUM WOLRD. If we had the underlying "code" to this place (EVERYTHING including those other worlds, etc, etc, etc) I bet it would all be predictable and child's play. The result of this is that the future would ALREADY exist. Changing it, just causes another branch. The old one becoming obsolete or a file name pointing nowhere. Kinda like files in a computer...they exist but only really exist when they are called up and when changed...no big deal at all. Change it and do as you please with it (well almost).

Inifinity is also not really true. It is only infinite because we cannot see or calculate the end. Mathematics/arithmetic being a grear model of the world but still flawed in some way nonetheless. Numbers not telling the whole truth and nothing but the truth.

I certainly believe if given the "keys to this place" we would be able to KNOW the future and change it at will...or have MUCH greater control than we do now. BUT THIS IS NOT THE CASE! WHY???? We AGAIN, including everything, are firmly controlled or we just got unlucky in the "great scheme of things." Sitting at the bottom of the barrel of control over us and our environment.

We do NOT have free will! Or, if we do, it is an extrememly small amount (subject to more parameters and ONTROLS than Carter has little liver pills)! So, if this were the case, faith moves mountains even though I disagree with faith and most everything about this world...the "infinite amount" of reasons why I don't believe in free will. Perhaps extremely small "imperfections in the control of things" will allow us ,in the FAR, FAR, FAR future anyway, to be true Gods...controlling EVERYTHING!

RRRGroup said...

Rich:

We see some kind of determinism at work in your comment.

And we can't exactly rebut it, but maybe we should try, just for the heck of it.

Ennoia said...

I see more conflict than conviction in Rich's comments.

It doesn't make sense, to me at least, to suggest that the entire place is controlled, and that there is 'NO' free will -- and then, in almost the same breath, to suggest that having some knowledge would permit us to control things.

Did Rich have the option to comment, or was his decision pre-ordained somehow? Will my comments affect him, or has his reply already been somehow conjured up in advance?

Rich said...

Actually, what I meant was that FOR US things are indeed "ruled by probability"...no doubt! Experiments "confirm" this! But, I make the suggestion that this place when it was "created" certainly was done so WITH CONTROL...control implies no probability at least for whatever put this place here.

Probability is our lack of control/knowing of EVERYTHING! The "mechanisms" that run this place are EXTREMELY complex TO US...so naturally a lot of things seem free or not determined...including "our will."

I do leave room for the possibility that perhaps an extremely small amount of "free will" was given to us...with this perhaps over an extremely long time we, as a whole, will BE ALLOWED to figure most all of it out and be able to ACTUALLY CONTROL ourselves and our environment (space, time, etc, etc). Small changes can indeed create HUGE changes.

I am still of the opinion though that free will is an illusion of the senses/brain. We operate amongst a gazillion things THAT WE DO NOT CONTROL...I just bring this further and say we do not control anything. Easy to say...well we do control at least a few things here and there..."my argument" is that at the "end of the day" we DO NOT control anything. Following along the countless (seemingly infinite) CONTROLS of this place...to what adds up to we don't control a thing. MUCH MORE PRECISELY "IT" CONTROLS US (EVERYTHING)!

The answers to everything ARE ALREADY "OUT THERE." THERE IS NOTHING NEW UNDER THE SUN...so to speak...at least for our situation. Einstein did NOT discover E = MC2...it ALREADY EXISTED...whatever mechanisms of how this place works...ALLOWED HIM TO DISCOVER IT...just like I was allowed to write this. Discovery seems so special to us (our feelings adding to this --- even "our will" to survive) but really it is NOT ANYTHING SPECIAL! Why have "wrong" answers then or false discovery? Wrong and right, good and bad...I don't know...part of the conditions (mechanisms) running this place....what is "wrong" here, is "right" over there...."good" here, "bad" there...what we perceive is just the "machinery" running...us being feeling "parts" for whatever reason.

Of course then the natural question is if everything is determined than why have anything at all....well I will answer by saying that everything IS determined FOR US....but surely not for whatever has this place and us to exist. How critical are we to whatever this place wants is the question...I don't know. It gave us "the will to survive and carry on." I still cannot know the answer though...get it??? How can I ask this question or write any of this or there be "wrong answers" without "free will"...part of the "program" that's all...nothing special or maybe it is...? Why???...why anything at all? Outside of "our" ability to know...at least at present!

Ennoia said...

Rich,

I will agree that Einstein didn't 'invent' E=MC^2. But that doesn't imply that all creations are discoveries.

Did Beethoven 'discover' his 'Fifth'?

Did Shakespeare 'discover' Hamlet?

And, perhaps a more difficult one, did mankind 'discover' rocketry? Money?

Perhaps you would help me out by explaining whether you see any differences between 'inventions' vs. 'discoveries.'

Bruce Duensing said...

Another great blog which created some very penetrating responses.
I could not have thought of a more creative way to pose an important question. I enjoyed reading it.

RRRGroup said...

Thank you, Bruce, and your blog -- UFO Paradigm Probe -- is quite excellent in its erudition, so visitors here would do well to visit it (and comment).

Rich said...

Hi ennoia: I see 'inventions' and 'discoveries' as NOT examples of free will. They are NOT the products of us! Sort of like when you upgrade your computer or software...kind along these lines.

Here are two options:

We were just given an environment and body (universe) that has no free will. EVERYTHING IS DETERMINED, including possible changes (inventions, discoveries??) introduced into here/us! I know how would happen when either the universe is closed (determined) or open...black holes leading to another "place" (free will)...it could be done.

Or: We have SEVERELY limited free will and actually (can) exist somehow outside this world (individually or as a whole?????????). Stuck within an environment/body that is basically useless...other than perhaps experiencing what...?... sex, drugs, rock and roll...???? I don't know!

Ennoia said...

Rich,

I wasn't going to reply to you, but I guess it was pre-determined that I do so... ;)

The universe has a set of laws which determine how matter behaves. My lawn grows, but it wouldn't even be there to grow if it weren't for the planting of grass seed. The choice to plant that grass seed was not determined by the physical laws of the universe. Mankind may just as easily have decided that a yard full of mulch looked better. And when I patch the lawn as a result of my dog's digging, I have all sorts of choices as to which kind of seed to use. I am certainly limited to choosing from an available type, but those types change -- especially now with genetic engineering.

Yes, our choices are limited to what is physically possible. I cannot drink something that isn't wet. I cannot jump into the air without expecting to fall back down to the ground. I cannot split H20 into anything other than Hydrogen and Oxygen. But I still have the choice as to what I want to drink, whether I want to jump, and whether or not I want to split water molecules.

Rich said...

Hi Ennoia, it was predetermined that I answer you...true.

"The choice to plant that grass seed was not determined by the physical laws of the universe."

The "laws of the universe" tend to get a bit fuzzy the smaller things get.

Experiments bascially prove that the quantum world is essentially unpredictable. I will agree with the experiments...subject to the limits of the current configuration of the world, us and the machines we build to examine the quantum world.

"My argument" is that somehow if we could step "outside" this place we would be able to see that EVEN in the quantum world EVERYTHING IS TOTALLY PREDICTABLE...ABSOLUTE CERTAINTY! In other words, imagine a software program written to EXECUTE "absolute randomness," EVEN to machines designed to measure the output of such program....without being able to examine the SOURCE CODE, sure it WILL indeed APPEAR to be TOTALLY random! EXTREMELY DIFFICULT, if not impossible, to figure out that it is NOT RANDOM...especially if you had no idea what you were dealing with or had NO ACCESS TO IT!

Chance/probability in the macro and micro world being the result of our inability to know/control EVERYTHING (like OWNING the source code to ourselves and the world). We may never be able to as long as we are "in here"...we're just "living the program," so to speak.

I welcome rebuttals...even though I am essentially dealing with the unprovable.

Thanks for your thoughts Ennoia...I appreciate that you got back to me.

Ennoia said...

Experiments bascially prove that the quantum world is essentially unpredictable.

I am going to assume that you are referencing Schrödinger's cat.

In that case, the cat is both dead and alive at once. It is only the act of observing -- a choice of free will -- which will dictate whether the cat is alive or dead.

If we were to, as you say, step 'outside', would we see the cat as both dead and alive at once? That is a logical contradiction.

Quantum physics, as I understand it, does not support your conclusion.

Rich said...

"It is only the act of observing --a choice of free will -- which will dictate whether the cat is alive or dead.

If we were to, as you say, step 'outside', would we see the cat as both dead and alive at once? That is a logical contradiction."

Hi ennoia, when you talk of "choice"...choice IS governed by COUNTLESS things including the things we feel we have control over...these things run "past and present." Observing the cat CAN ONLY TAKE PLACE should ALL conditions ALLOW one to observe the cat.

You can argue that well one has control over at least some of these conditions. The thing is if we do not control most things...then how do we ACTUALLY control anything at all?

IS THERE A SEPERATE RULE THAT WHATEVER GOVERNS THE UNCONTROLLABLE (for us anyway) DOES NOT AFFECT OUR THOUGHTS/MIND? That our thoughts somehow transcend the uncontrollable?

The easy way around this is to say well we do not control MANY MANY things and ONLY FEEL like we control at least some things. Hence, WE DO NOT CONTROL ANYTHING. Otherwise AGAIN can our minds/thoughts somwehow transcend the "MOSTLY uncontrollable" environment/body we live...with different rules governing our thoughts and environment/body/brain? Also, EVEN if we could leave (or exist "outside") our bodies/environment WOULD STILL NOT MEAN WE CONTROL OURSELVES...easy...most of us (even the suicides I'll bet) DO NOT CONTROL WHEN THEY DIE...why believe the control STOPS at death or "leaving our bodies/brain."

The microworld (let alone the macroworld) at present CERTAINLY appears to be random. My belief, of course, is that at the "end of the day" even this world is not random. TOTALLY PREDICATBLE....just not by us (currently or perhaps forever??).

The cat is it dead or alive?

This sentence is false. Therefore it is true but wait therefore it is false but wait therefore it is true, etc, etc, etc...where does this "infinite" logic problem end?? Not with us it seems! So much for logical contradiction!

Ok, so we observe, the cat and somehow ---- SOMEHOW ---- cause the cat to become dead or alive....hahaha. MAKES me laugh. Act of observation changes the result....ok, again, the choice "we made to observe" and mechanics of observation NEED NOT BE OURS...and "my belief" is that they aren't and neither is the result...right!

Ennoia said...

Rich,

The double-slit experiment may very well involve factors yet unknown to science. That doesn't mean that logic must turn itself inside out in order to accept the results.

Quantum Mechanics involves probabilities. Undoubtedly there are forces at work in the universe which I have no control over. But that doesn't mean that I have no control over my life. It's not an either-or proposition.

If I 'will' my arm to move, I notice that it moves. It might also twitch uncontrollably from time to time, and I will agree that I have no control over that twitch. But I certainly do have control over my arm in normal circumstances.

I am also curious whether you feel you even have the choice to change your thinking on this issue. If I can't change your 'pre-determined' mindset, perhaps I am just wasting my time.

Indeed, you might also believe that my mindset is pre-determined, or maybe you doubt that I exist at all. Are you a solipsist hiding in a determinist's clothing?

Rich said...

I could concede YOU changed my mind ennoia. Would that be my will? Wait, I can decide whether or not to accept your answer or not. See the problem is that ALL of our actions RELY on previous actions of our environment/bodies and so forth. If, I REALLY had free will, I wouldn't need to accept or deny your answer or go somewhere in between. I WOULD ALREADY KNOW IT. So would you!

You say it is not either - or.

If the world is ALL based on probability...how would YOU, your thoughts, your decisions sit UNTOUCHED from probability?

If the world is ALL determined? Again, the same question...?

And lets say the world is a "mixture" of BOTH...which most of us can probably easily believe. BELIEVE being the keyword. I can control my arm but not the weather. Again, the same question...?

How are your thoughts, decisons,etc....or YOU....NOT affected by ANYTHING. Do you somehow transcend ALL what makes the world go around?

Oh wait, we are affected by some things but not others. My decisions, thoughts remain outside of the affected things of the world. I AM SPECIAL! I would like to know the SPECIAL law covering this....????

When someone is suffering, tortured or dying though, they are not NOT SO SPECIAL. Right! Remember anything BEFORE you were born? Will you remember anything after your death? Did you control the who, what, where, why, when and how of your birth? Oh wait, we are special...just not special enough to control the more important things. But, we somehow control our arm(s) though...a relief, I'll sleep good tonight "knowing I control" my arms...OR WILL I?

YES there indeed may involve factors yet unknown to science (to us). What does this have to do with you or I or anyone/anything, if anything at all...we do not know.

Is your existence ennoia really yours? I know mine isn't. Far, far, far, far, far, far , far, far, far, far, far, far, far, far, far, far, far, far, far, far, far, too many things tell me it isn't. I conclude I am not mine.

Ennoia said...

So we are to assume that because we can't change the weather, we can't change anything? How absurd!

As for my thoughts and as they relate to my death... I think it is also absurd to talk about such things. We know memories are stored within the brain. Without that brain, and the memories and identity stored within, it becomes absolutely meaningless for me to speak of my 'self' after my death. It is a tempting lure of the ego to think otherwise -- but that doesn't make it true in the least.

The "Prime Mover" is within you, Rich. Indeed, it is withing any creature which is capable of making decisions.

Rich said...

Ennoia, don't ever stop being you even if you have no choice in the matter.

I am going to now read the most recent topic of this blog and then go here: http://paradigmprobe.blogspot.com/

All things come to an end whether we want them to or not...tells me all I need to know.