Geometry (a useful fiction)

What is the basis for reason? And mathematics?

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Obvious Leo
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Re: Geometry (a useful fiction)

Post by Obvious Leo » Thu Jul 09, 2015 12:18 am

Nicomedes wrote: I know what you mean, it's like absolute zero, just because we can't detect any movement with our present observations and instruments, doesn't mean we ought to conclude there is no movement, it just means our current observations and instruments aren't fine enough, in all likelihood.
Though I can't be certain, there's probably always some movement and variability going on, that's the way nature seems to operate.
It is both a more logical and a more physical statement to think of absolute zero as an unrealisable abstraction which cannot exist in the real universe, rather like a singularity or a mass moving at the speed of light. Newton's classical calculus can illustrate the way a system tends but the theory of limits does not mandate that zero and infinity must correspond to real physical states. Simple Galilean relativity shows that there can be no state of absolute motionlessness in physical reality. GR cannot quite accommodate this self-evident fact because it ignores the philosophy of the quantum, which explicitly states that a physically real entity cannot be infinitely divisible. It beggars belief that a simple truth known to the pre-Socratics should be so blatantly ignored by 21st century science but it certainly explains why spacetime physics makes no bloody sense.
Nicomedes wrote: I believe spatial dimensions are completely arbitrary concepts,
So did the Pythagoreans in a way but it was actually the great Persian philosopher/mathematicians who understood this best of all. The cloistered European houses of learning managed to import many of their mathematical tools from the Persians but they didn't bother to import the philosophy which was supposed to go with it. Presumably they felt they were in no need of philosophical instruction by a bunch of godless heathen when they had Aquinas to tell them what was what but unfortunately they made an error of judgement which was to send the science of physics into a conceptual cul-de-sac. Newton decided that Descartes was right and that his 3D space was physically real, despite Leibniz's furious protestations to the contrary. Physics will never make sense until the geeks wake up and realise that Leibniz was right and Newton was fucking WRONG.
Nicomedes wrote:don't think time ought to be considered the 4th dimension.
Time is history, the idea that everything collectively and individually has a past, present and future,
In that case you're a heretic like me. Minkwoski's 4D manifold explicitly implies that no metaphysical distinction exists between past, present and future. It goes without saying that if you mention the word "metaphysics" in a roomful of physicists they'll all quickly move away from you as if you just farted.
Nicomedes wrote:We simplify, simply because the world is infinitely more complicated than the brain can comprehend in its entirety,
I completely disagree with this. I reckon the universe is exactly what it appears to be, an infinite sequence of moments, which means that reality can only be said to exist in its own moment NOW. This presentist commitment reduces 3D space to an artefact of consciousness with which we examine our own past and this opinion is in complete accordance with the evidence. This is a cosmological model of such sublime austerity that it simply cannot be false.
Nicomedes wrote:Yeah reality seems orderly, but this can only be grasped so much, and we should be careful not to conflate what's going on internally with what's going on externally, like Plato, and modern physicists seem to be doing, but that being said, there's always going to be some overlap between the two.
Precisely. Events in the universe proceed in an orderly and causal fashion but the patterns of organisation we use to describe this order is entirely our own affair. This means that all the various waves. particles, forces, and fields which we invent and then collectively call the "laws of physics" are no such thing. These are merely the laws of physicists because nature itself is beholden only to the single meta=law of cause and effect.

"All things originate from one another, and vanish into one another according to necessity and in conformity with the order of time"...Anaximander

"Life is what happens to you while you're making other plans"....John Lennon

"Shit happens"....Obvious Leo

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Arising_uk
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Re: Geometry (a useful fiction)

Post by Arising_uk » Thu Jul 09, 2015 2:03 am

Obvious Leo wrote:...
Precisely. Events in the universe proceed in an orderly and causal fashion but the patterns of organisation we use to describe this order is entirely our own affair. ...
Hmm... but how could we know this given 'events' are part of this fiction you say we create?
"All things originate from one another, and vanish into one another according to necessity and in conformity with the order of time"...Anaximander

"Life is what happens to you while you're making other plans"....John Lennon

"Shit happens"....Obvious Leo
You might like this one, "Experience is not what happens to you; it's what you do with what happens to you." - Aldous Huxley

Obvious Leo
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Re: Geometry (a useful fiction)

Post by Obvious Leo » Thu Jul 09, 2015 2:45 am

Arising_uk wrote:Hmm... but how could we know this given 'events' are part of this fiction you say we create?
Strictly speaking we can't know this for certain but unless one is willing to embrace solipsism we must assume that there is such a thing as an objective reality, even if we are inevitably constrained by only ever being able to construct our own subjective interpretation of it. In this regard I'm not a true Kantian because although I regard space as an observer construct I don't extend this conclusion to time and causation, as Kant did. These I regard as two different expressions of the same thing and as metaphysical first principles without which a comprehensible universe would be impossible. This aligns me more closely with Leibniz and Spinoza, as well as the later logicians/process philosophers like Whitehead and Peirce.
'

Scott Mayers
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Re: Geometry (a useful fiction)

Post by Scott Mayers » Fri Jul 10, 2015 12:57 am

I began an in-depth post the other day here and lost it all when I was somehow disconnected. Let me try again.

First off I have concern with most people today to presume that what we are only able to directly observe through our senses is all we can be certain of. It's nice to see here Obvious Leo who seems to have some good background on the scientific philosophy that I relate to from the past. But I disagree with his apparent distaste for how some of the present scientific philosophers/scientists are attempting to challenge the theoretical aspects, especially with how our present paradigm reflects most favorably for the pure observational restrictions for science regarding the extremes (the very large and very small).

In this respect, I question how the need to abandon the search for certainty with respect to logic, math, and the original intents of what is referred to as the 'logical positivist' movements at the beginning of the last century. To me, it appears that since the interpreted discoveries of the sciences revolving around Relativity and Quantum Mechanics appeared to conflict AND to how the arguments within the philosophies of the day acted to appear to defeat closure and spark an appeal to indeterminate factors lead to cause many to opt to abandon the traditional approach to seek a definitive logical argument(s) that could aid in making sense of our universe. For most, logic and math have taken a secondary role as simply a useful tool only. But how such 'tools' act functionally as being significant to backing observational data and to draw any certain conclusions requires at least a premise that places 'trust' that math/logic is sufficiently sound. Without this, any interpretations of science through the status empirical method falls short of its own 'soundness'. How can you assert even any degree of faith in the observations without questioning whether ALL the tools being used are just as real?

We also have to question how people interpret observations, not simply 'trust' that whomever raises the first interpretations have the best authority on the issues. Here, I question both those of on the side of Einstein and those for the later development of quantum mechanics. The present way is to simply accept these people's initial interpretations and evolve by building onto these without taking a step back to question some of the details. On this as well as to the logic question, I think that we've simply opted to preferentially preserve what appears to 'work' for mere practical sake, especially with regards to requiring students of the science to move past what seems like overwhelming depth and for institutions to concentrate on putting out more graduates who can actually get jobs. In this way, abandoning the under-riding scientific philosophy is demarcated from the regular active science. To me this is a cop-out and only creates difficulty for those wanting to reconcile philosophy with science, and reinstate logical analysis to be a function of determining scientific truth.

I originally argued with much more depth and details to this and my own positions. However, at least to begin, let me at least just start with this to allow better participation.

So, my question is to Obvious Leo's responses that appear to prefer the present abandonment of accepting logic/math as an essential function of truth and not simply a 'tool'? How do you reconcile that any observation-only approach as sufficient for trusting the outcomes of empirical science AND that we still use logic/math within it as supports while doubting these tools as being trustworthy or real? And the second question is how do we assure ourselves that given interpretations of our observations are justified without question?

Obvious Leo
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Re: Geometry (a useful fiction)

Post by Obvious Leo » Fri Jul 10, 2015 1:49 am

Thank you for your thoughtful contribution, Scott. This thread is beginning to show promise as a useful exploration of mathematical philosophy and this is clearly a subject with which you have some familiarity. You raise a number of pertinent points to which I'd like to respond but right now is not a good time for me. I have a deadline to meet on a report which I have already procrastinated beyond the patience of my client and on the grounds of pragmatism I better force my responsibilities to take precedence over my preferences. I plan to give some further thought to your post and hope to respond within a day or so. Once again, welcome to the conversation.

surreptitious57
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Re: Geometry (a useful fiction)

Post by surreptitious57 » Sun Jul 12, 2015 9:17 am

The two most effective tools for understanding the Universe and how it functions are science and maths. Science is an inductive discipline
that uses evidence to validate its hypotheses while maths is a deductive discipline that uses proof to validate its hypotheses. Of these two
maths is the superior as its conclusions are absolute by default and as such require no human interpretation and which is why I think it was
discovered rather than invented. Science by contrast has to have its conclusions subject to revision and modification since evidence unlike
proof is not absolute by default. But it is still out side of maths the most objective means of understanding observable phenomena there is

But as noble as our attempts at understanding the Universe is it is important to see it from an external objective perspective to put it into
context. The various fine tuning constants known to physicists are evidence that our existence from a purely probabilistic perspective is at
the infinitesimal end of the spectrum. In other words it is incredibly unlikely that we do actually exist given all the variables. And so when
the Universe or at least this particular manifestation of it came in to existence just under fourteen billion years ago it was not a given that
an advanced species of primate would one day possess some degree of cognitive capability to be able to actually understand it. Far from it

But in spite of that we are not perfectly equipped to find all of the answers even though we want to. For we have mammalian brains which
are just as hard wired for emotion as they are for logic. We have this model the scientific method which as I have already said is subject to
continuous evaluation to hone out any imperfections in existing theory. And it is an on going process that is slow and repetitive but it is the
best we have. And because it is slow and repetitive we need to realise that we may not be able to find the answers to all the questions that
we are asking. A perfect model is way beyond us. Since we only have another five billion years before the Sun goes red giant and even if we
have colonised another world by then we shall eventually become extinct anyway as all species do. And all the knowledge we have acquired
will mean absolutely nothing. Now this may sound incredibly nihilistic but all it actually is is simply an objective assessment of what is going
to happen. As long as we attach zero emotional significance to that particular fact and do not allow our selves to be overwhelmed by it then
there is no reason why we cannot carry on investigating the Universe as we are. But we must interpret reality as it is not as we want it to be

Scott Mayers
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Re: Geometry (a useful fiction)

Post by Scott Mayers » Sun Jul 12, 2015 10:52 am

surreptitious57,

I understand you fairly. Yet I somewhat disagree with the argument that suggests no certainty can ever be found. It's circularity is akin to the very problematic interpretations of Gödel's Incompleteness Theorem. Should it be 'true' that

The interpretation of the following sentence is absolutely certain.
No certainty can ever be determined!

I believe this is a fault of logic to which I was hoping to discuss with Obvious Leo eventually as he seemed likely familiar with that era's philosophy. This error also suggests a problem with interpreting reality based on our ego by emphasizing "practice". In this way, inductive science alone cannot ever find closure. But what it CAN do is to suggest in a top-down manner how we might discover a bottom-up logical argument eventually.

Just as an example of math as you interpret as being a human invention, this implies that things like the number '3' by meaning does not exist without a mind to observe it. Yet, logically, you can induce original samples of collections of many countable objects as inferring what we mean by "3". In a reversal, bottom-up way, you can ask if any "three" things in our meaning can exist in some logical universal or group defined without us there to perceive it. And I say yes. You can opt to disagree but I don't think I nor nature will place any non-real existence of this. It is to me a kind of human collective solipsism to assert that only what we observe is what is real.

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Re: Geometry (a useful fiction)

Post by surreptitious57 » Sun Jul 12, 2015 12:41 pm

I do not think that only what we observe is real but that only what we observe can be established as
being real. In science only what is observable can be tested and so anything which is non observable
is beyond its remit as untestable hypotheses are non scientific by definition. But that does not mean
that they are automatically false as they could actually be true but they would still be non scientific
I said that I think maths was discovered rather than invented so your final paragraph was superfluous

Scott Mayers
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Re: Geometry (a useful fiction)

Post by Scott Mayers » Sun Jul 12, 2015 12:54 pm

surreptitious57 wrote:I do not think that only what we observe is real but that only what we observe can be established as
being real. In science only what is observable can be tested and so anything which is non observable
is beyond its remit as untestable hypotheses are non scientific by definition. But that does not mean
that they are automatically false as they could actually be true but they would still be non scientific
I said that I think maths was discovered rather than invented so your final paragraph was superfluous
I was only initializing the point of your opinion on math prior to my opposite view, that math truly does represent something 'real': information. While you are correct on how most of today's paradigm has abandoned a logically positive reconstruction or reality, this is only because they redefined "science" back in the 1930s as a practical function and segregated logical analysis and theoretical physics to belong to a "philosophy-only" category. It segregated philosophy from science and is something I disagree with AND can prove was too prematurely decided.

I don't think that it is essentially 'wrong' to separate them but when those within "science" exist who may believe that science is alone sufficient to examining "truth", this is completely bad thinking. I understand its motives given the realities of the day. But we can now re-introduce a combination of the two approaches, still in a realistic and practical way, to find true closure on certain issues of knowledge about our reality.

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Re: Geometry (a useful fiction)

Post by surreptitious57 » Sun Jul 12, 2015 3:38 pm

The word truth is one that is laden with enormous psychological and philosophical baggage. So therefore it is important to separate
its two entirely different meanings namely the objective and the subjective. Now objective truth is what science is concerned with
and through the scientific method with regard to observation and experimentation and inter subjectivity and peer review attempts
to determine what is actually true regardless of interpretation. It is the most rigorous process known to exist so is incredibly useful
Whereas subjective truth on the other hand requires absolutely none of this methodological precision. Since all it does require is a
belief and nothing else. Now it is entirely possible of course for something that is subjectively true to also be objectively true. But
less it can be subject to the rigour of the scientific method then it cannot and indeed should not be regarded as being true as such
This is therefore why I place objective truth in a completely different category to subjective truth for they are not the same at all

Obvious Leo
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Re: Geometry (a useful fiction)

Post by Obvious Leo » Mon Jul 13, 2015 6:17 am

Scott Mayers wrote: For most, logic and math have taken a secondary role as simply a useful tool only.
I take issue with your implication that logic and maths are synonymous constructs. In fact I regard them as two entirely different things. I completely disagree with surreptitious that mathematics is discovered and place myself squarely in the "maths is invented" camp. Specifically maths is invented to model the patterns of organisation which the physicist observes in nature. Thus maths is intimately associated with the inductivism which is inherent in the scientific method, not the Platonist eternal verity which physics assumes a priori. Logic, on the other hand, is a process of deduction from metaphysical first principles.
Scott Mayers wrote: How can you assert even any degree of faith in the observations without questioning whether ALL the tools being used are just as real?
How can one have faith in an observation? An observation is a construct of the human consciousness and is therefore subjective by its very definition.

"It is the THEORY which determines what the observer will observe".....Albert Einstein.

Mathematical physics is intrinsically tautologous for this very reason. If we design our models specifically to predict what the observer will observe we can claim only a Pyrrhic victory when the observer duly goes ahead and observes what our models have predicted. Immanuel Kant observed the honourable German tradition of ensuring that his philosophy was unreadable but he summed up the problem of the observer quite well in his Jasche Lectures on Logic.

“(...) Truth, it is said, consists in the agreement of cognition with its object. In consequence of this mere nominal definition, my cognition, to count as true, is supposed to agree with its object. Now I can compare the object with my cognition, however, only by cognising it. Hence my cognition is supposed to confirm itself, which is far short of being sufficient for truth. For since the object is outside me, the cognition in me, all I can ever pass judgement on is whether my cognition of the object agrees with my cognition of the object”.

The true illuminati in the priesthood of physics were utterly shattered by the discovery of the Higgs boson at the LHC. They are yet a small handful but a growing number of physicists are waking up to the fact that they're barking up the wrong tree.
Scott Mayers wrote: We also have to question how people interpret observations, not simply 'trust' that whomever raises the first interpretations have the best authority on the issues
Bingo. You've nailed the problem in a nutshell. An observation is just raw data and thus has no explanatory authority. The data still needs to be interpreted so it is the narrative of physics which counts. The model-building paradigm laid out by Bohr established spacetime as the underpinning narrative of physics and everything that's happened since then has simply been tacked onto this narrative by brute mathematical force. Ptolemy would weep tears of joy to discover that his methodology for physics has lasted for 2000 years. The mathematical extravaganza which is modern physics is nothing more than the 20th century equivalent of the Ptolemaic epicycles, an attempt to prop up an absurd hypothesis with a vast suite of supplementary hypotheses of escalating absurdity.
Scott Mayers wrote: On this as well as to the logic question, I think that we've simply opted to preferentially preserve what appears to 'work' for mere practical sake, especially with regards to requiring students of the science to move past what seems like overwhelming depth and for institutions to concentrate on putting out more graduates who can actually get jobs. In this way, abandoning the under-riding scientific philosophy is demarcated from the regular active science. To me this is a cop-out and only creates difficulty for those wanting to reconcile philosophy with science, and reinstate logical analysis to be a function of determining scientific truth.
You've touched on one of my favourite gripes and this is a subject I have written on at considerable length. The constraints of academia is the single most serious impediment standing between physics and a true cosmological model. However this is probably a subject for another day.
Scott Mayers wrote:So, my question is to Obvious Leo's responses that appear to prefer the present abandonment of accepting logic/math as an essential function of truth and not simply a 'tool'? How do you reconcile that any observation-only approach as sufficient for trusting the outcomes of empirical science AND that we still use logic/math within it as supports while doubting these tools as being trustworthy or real?
Firstly logic and maths must be regarded as two entirely separate tools. If the maths are describing a universe which doesn't make sense then it is an act of the ultimate hubris to therefore conclude that we must live in a universe which doesn't make sense. Logic demands that the maths are not describing the real universe, which means we have made a false a priori assumption. As I have stated at considerable length for many years in countless different forums this false a priori assumption was originally made by Newton. SPACE DOES NOT PHYSICALLY EXIST, as Leibniz insisted from the outset. If we take 3D space out of our physical models and put it into the consciousness of the observer where it belongs then every single paradox and counter-intuitive absurdity in physics simply vanishes back into the luminiferous aether which gave birth to it.
Scott Mayers wrote:And the second question is how do we assure ourselves that given interpretations of our observations are justified without question?
I think I've covered this point. No such assurance is possible, even in principle.

Scott. I reckon we'll make a lot of progress in our discussions on these weighty matters but we'll make it a hell of a lot faster if you read the synopsis of my philosophy first. Most of the points I make in the various threads on physics in which I participate are addressed in it. Ignore the mathematical typo in my experiment. I'm aware of it and will correct it in my next revision. ( 0.000033 seconds should read 0.0000133 seconds.)

https://austintorney.wordpress.com/2015 ... n-de-jong/

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Re: Geometry (a useful fiction)

Post by surreptitious57 » Tue Jul 14, 2015 9:36 am

Obvious Leo : how do you know that three dimensional space is a mental construct and not
actually independent of human interpretation ? How can you be a hundred per cent certain
on the reliability of your sense organs in respect of this ? Why does human life have to have
meaning ? What do you think of the idea that time is actually what space is expanding into ?

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Re: Geometry (a useful fiction)

Post by Obvious Leo » Tue Jul 14, 2015 10:53 am

surreptitious57 wrote:Obvious Leo : how do you know that three dimensional space is a mental construct and not
actually independent of human interpretation ?
I am merely accepting the mainstream view of various sciences which are better qualified than physics to take an informed position on this matter. The notion of the cognitive map has been central to the psychology of perception for almost 100 years. How our senses receive and order visual information is very well understand and developments in cognitive neuroscience over recent decades have established the general mechanism by which this information is processed. In fact last year's Nobel prize for medicine was awarded to a team which used functional MRI imaging to specifically uncover the neural network system responsible for constructing 3 dimensional space. To a psychologist or a neuroscientist Kant was merely making a long-winded statement of the bloody obvious.
surreptitious57 wrote: How can you be a hundred per cent certain
on the reliability of your sense organs in respect of this ?
The sense organs have nothing to do with it because we don't see with our eyes. We see with our minds.
surreptitious57 wrote:Why does human life have to have
meaning ?
It doesn't. But it does require an explanation. Newtonian physics is a creationist paradigm which relies on the god hypothesis but this should make any philosopher reach for his hemlock because this cop-out defines the universe as unknowable.
surreptitious57 wrote:What do you think of the idea that time is actually what space is expanding into ?
The "expanding space" is not a physical statement and, as Leibniz pointed out, the Cartesian space can have no ontological currency on the grounds of insufficient reason. It is simply unnecessary and the universe is a hell of a lot simpler without it.

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Re: Geometry (a useful fiction)

Post by Hobbes' Choice » Tue Jul 14, 2015 11:44 am

surreptitious57 wrote:Obvious Leo : how do you know that three dimensional space is a mental construct and not
actually independent of human interpretation ? How can you be a hundred per cent certain
on the reliability of your sense organs in respect of this ? Why does human life have to have
meaning ? What do you think of the idea that time is actually what space is expanding into ?
It's more about the way we choose to model what we experience, than the actual reality "out there".

It is probably highly unlikely that evolution has provided us with the exactly correct and perfect means of experiencing what is real. In fact as science has increased we now appreciate a lot more about what we are incapable of experiencing; infra-red, microwaves, radio waves. The microscopic and macroscopic worlds. When we bear witness to all this other stuff we can only do so by proxy with our common senses. We might be able to 'see' a microwave on an oscilloscope to know it is there, but that is not what it looks like (in reality).
So nature has provided us with a range of senses, but none of these could ever possibly give us access to, as Kant would have it, the "thing in itself". To help the limits of our sense we invent geometry and maths to measure, quantify and compare. We have basic intuitions about time and space, but these are constructed by our sensations, and are naturally limited to the equipment provided by nature, with which we are bound to struggle.

This is all perfectly okay if we wish to keep our conception of reality in the human scale, and maybe we will never be able to reach out very far beyond that. But whatever lies beyond will be ultimately unknown to us.

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Re: Geometry (a useful fiction)

Post by Scott Mayers » Tue Jul 14, 2015 12:36 pm

Damn! I just made a carefully long post which ended up being lost again! There's got to be a way to recover this because our computer memory holds this even if we get disconnected while we are continuing to write. Yet, I don't know if the 'disconnect' erases that memory completely or if its maintained somewhere in our computer memory. Anyways, I'll have to try again. But I'll have to take a break.

Note that I tried the 'preview' assuming that this should automatically save AND connect, but it doesn't work. Some have suggested this particular advise already and why I presumed it should work. I should have saved it through copying first! I hope this helps others who might have this same problem. I'm guessing that we have to be connected to have the work 'saved' through the site or it is discarded regardless by the browsers. A fix should be made to require the local computer to save this in buffer and accessible later with a warning prompt!

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