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Author Topic:   Objective reality
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


(1)
Message 76 of 172 (559731)
05-11-2010 10:28 AM
Reply to: Message 75 by Straggler
05-11-2010 9:06 AM


Re: Supernatural Math
Straggler writes:
So you are saying that we discovered pi rather than invented it?
Yes, I am saying we discovered the relationship between a circle's diameter and it's circumference rather than invented it.
Are you saying we invented circles?
We certainly invented the name "Pi".
We certainly invented the useful notation of 3.14.....
We did not invent circles.
Therefore, we did not invent diameters.
Therefore, we did not invent circumferences.
Therefore, we did not invent any relationship that may or may not exist between diameters and circumferences.
Basic circles exist objectively (tree trunks, looking at the sun...).
They have objective (empirical) diameters and circumferences. Which can be used by the scientific method to develop general equations, this particular one we have named "Pi".
Have we determined the precise value of pi empirically or mathematically?
I do not think we have determined the "precise" value of Pi, have we? Do you mean, like, the ending decimal? It doesn't have one. Do you mean "precise" as in the exact relationship between a circles diameter and circumference? We haven't determined it at all, we've observed circles and identified general equations to represent them... and called one of them "Pi".
Would we expect an alien civilisation to get the same result assuming they could achieve the same levels of accuracy?
Yes. How could we possibly not? Decimal representation is merely a useful notation. The concept of Pi is a direct relationship concerning the diameter and circumference of a circle. As long as aliens have some sort of equivalent useful notation... how could their accuracy be different from ours?
Do you think an alien civilisation would, like us, have calculated pi to an extent that defies empirical usefulness and have gotten an identical result?
Perhaps, sure.
If so why? (as in why is the result identical not why would they bother to do this)
Because Pi (the theoretical value based on the general relationship between a circle's diameter and it's circumference) is objective. Basic circles are objective. Pi is derived by doing objective calculations upon objective observations to identify an objective conclusion. The perfect circle's perfect "Pi-value" does not have to exist within objective reality to be measured in order to identify the objective general relationship between the circumference and diameter of a circle ("Pi").
If this cannot be determined empirically is it still "science"? Is it still objective?
No, it would not be science or objective. But... why can it not be determined empirically?
Basic circles exist and can be observed empirically.
Diameters and circumferences can be observed and measured empirically.
These objective measurements can be used to show an empirical relationship.
This empirical relationship can be reduced to show a general empirical equation.
The result of this general empirical equation is called "Pi".
Pi is empirical.
(Note, I'm not saying that the exact value of Pi exists for some existing "perfect circle". I'm saying that Pi represents the general empirical relationship that can be observed in basic circles... and that this is empirical and scientific).
This general empirical equation may be used to identify a "perfect Pi" value for a "perfect circle"... but who cares? It does not negate the fact that the general equation was still derived empirically through observation.
What step are you missing?
Are you saying a perfect circle must necessarily exist in order to be specifically observed before the general relationship of a circles's diameter and circumference (Pi) can be considered empirical and objective?
Why would that be so?
Why can't objective, empirical observations lead to objective generalities?
What do you call those objective generalities when they are tested (time and time again) against reality and are always true?
Are you really suggesting that such an observationally based generality be called "subjective"?
Do you think Pi could possibly exist as we know it without empirical observations of circles?
Are you saying that a man in a box with 5 apples can only understand that 2 + 3 = 5 is objective, but cannot possibly understand that 2 + 4 = 6 is objective because he doesn't have 6 apples?
1+1+1+1+1=5 but 1+1+1+1+1+1 can't possibly = 6?
What sense does that make?

This message is a reply to:
 Message 75 by Straggler, posted 05-11-2010 9:06 AM Straggler has replied

Replies to this message:
 Message 77 by Straggler, posted 05-11-2010 11:05 AM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 77 of 172 (559736)
05-11-2010 11:05 AM
Reply to: Message 76 by Stile
05-11-2010 10:28 AM


Re: Supernatural Math
If this cannot be determined empirically is it still "science"? Is it still objective?
No, it would not be science or objective. But... why can it not be determined empirically?
How can we and the aliens agree on pi to 50 decimal places (or equivalent accuracy using whatever nomenclature they use) by empirical measurement?
Wiki writes:
Although practically a physicist needs only 39 digits of Pi to make a circle the size of the observable universe accurate to one atom of hydrogen
Stile writes:
Are you really suggesting that such an observationally based generality be called "subjective"?
No. I am suggesting (and attempting to make the argument in favour of) the idea that maths is objective whilst not being necessarily empirical.
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 76 by Stile, posted 05-11-2010 10:28 AM Stile has replied

Replies to this message:
 Message 78 by Stile, posted 05-11-2010 1:13 PM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 78 of 172 (559758)
05-11-2010 1:13 PM
Reply to: Message 77 by Straggler
05-11-2010 11:05 AM


Re: Supernatural Math
Straggler writes:
How can we and the aliens agree on pi to 50 decimal places (or equivalent accuracy using whatever nomenclature they use) by empirical measurement?
Aliens and us would agree on pi to whatever accuracy by using the same process (empirical observations of basic circles) to develop the same empircal general equation. Once the general equation is set the "theoretical perfect pi" is equivalent for both of us, it's just a matter of continuing the calculation to whatever accuracy you would like. 50 decimal places... or a million decimal places.
You seem to be asking the question of "how can a chair be a part of objective reality if Stile measures it's height to be 1.001 meters and Straggler measures it's height to be 1.002 meters?"
The question shows a difference in objective measuring techniques... it does not show that the chair's height is not objective. Do you agree that the chair's height (whatever it is) is still objective?
Different calculations of a specific "pi-value" derived from different measurements of different natural-circles does not indicate that Pi (the general relationship itself) is not objective.
The objective-ness of the general relationship does not rely upon specific general empirical measurements. It relys upon viewing *all* the general empirical measurements and identifying the general relationship as a whole. The culmination of *a lot* of general measurements objectively leads to an objective pattern... the general relationship. Which, being directly based on empirical observations, regardless of any individual's subjective ideas, is therefore empirical in itself.
It goes like this:
-We gather many, many observations (as accurate as possible) of circles (knowing that they are not perfect)
-we look at these observations and identify a general equation to represent the relationship between circumference and diameter
-we can say "if we had a 'perfect circle', then the relationship would be equal to Pi".
I am suggesting (and attempting to make the argument in favour of) the idea that maths is objective whilst not being necessarily empirical.
If you are also suggesting that math is objective... why are we discussing whether or not the aliens will have the same objective math? If math is objective... then shouldn't the aliens have the exact same math?
My only addition is that Pi can be tested through the scientific method. I fully admit that the "perfect, idealized concept of pi for a perfect circle" will never be measured in the real world... but that doesn't stop the scientific method from working. The scientific method isn't about idealized exactness, it's about describing the real world as accurately as possible.
I don't understand what we're arguing over. All your comments seem to imply that you want me to explain why/how math is objective. But if you're already agreeing to that... why are you asking the things you're asking?

This message is a reply to:
 Message 77 by Straggler, posted 05-11-2010 11:05 AM Straggler has replied

Replies to this message:
 Message 79 by Straggler, posted 05-11-2010 1:29 PM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 79 of 172 (559760)
05-11-2010 1:29 PM
Reply to: Message 78 by Stile
05-11-2010 1:13 PM


Re: Supernatural Math
You asked:
Stile writes:
I am extremely interested if anyone can describe a concept that is a part of "objective reality" that cannot be tested with the scientific method.
I am proposing that pi is such a concept and that it's objectivity distinct from the scientific method is demonstrated by the fact that an alien civilisation and us would agree on pi to an accuracy that lies beyond scientific empirical investigation.
All your comments seem to imply that you want me to explain why/how math is objective. But if you're already agreeing to that... why are you asking the things you're asking?
We seem to both agree that mathematics is objective. But you seem to think that it is objective because it is ultimately empirical.
I am merely questioning that assumption by pointing out that an objectively verifiable result of a quantity that can be determined mathematically to a degree of accuracy unachievable by empirical means would be shared by all intelligent beings in our universe.
Pi as a mathematical rather than an empirical construct seems to be part of the shared (i.e. objective) reality of our universe.

This message is a reply to:
 Message 78 by Stile, posted 05-11-2010 1:13 PM Stile has replied

Replies to this message:
 Message 82 by Stile, posted 05-12-2010 9:39 AM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 80 of 172 (559951)
05-12-2010 7:24 AM
Reply to: Message 74 by cavediver
05-11-2010 9:04 AM


Re: Supernatural Math
cavediver writes:
Can you demonstrate that by the scientific method?
Irrespective of the language and symbols used, any suitably advanced intelligence will recognise this relationship.
Me personally? No, I've long forgotten my maths and theory for such things. But I do think that someone can.
If you do think it's objective, and you do think that "any suitably advanced intelligence will recognize this relationship"... how will they recognize it unless it is derived (somehow) from observations of reality?
If it is derived from observations of reality, how is it not testable by the scientific method?
If it is not derived from observations of reality... how can you be so sure that is, in fact, objective and aliens would recognize it?

This message is a reply to:
 Message 74 by cavediver, posted 05-11-2010 9:04 AM cavediver has replied

Replies to this message:
 Message 81 by Straggler, posted 05-12-2010 8:12 AM Stile has seen this message but not replied
 Message 83 by cavediver, posted 05-12-2010 10:23 AM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 81 of 172 (559957)
05-12-2010 8:12 AM
Reply to: Message 80 by Stile
05-12-2010 7:24 AM


Re: Supernatural Math
If you do think it's objective, and you do think that "any suitably advanced intelligence will recognize this relationship"... how will they recognize it unless it is derived (somehow) from observations of reality?
Which reality?
If it is derived from observations of reality, how is it not testable by the scientific method?
If the reality in question is not empirical but platonistic.
If it is not derived from observations of reality... how can you be so sure that is, in fact, objective and aliens would recognize it?
Because mathematical constructs exist in some sense that is objective but not empirical?
There is a platonistic view of maths that you seem to be unaware of here. I am not necessarily advocating it. Just countering your assumptions about what you seem to think is blatantly obvious.
cavediver writes:
Can you demonstrate that by the scientific method?
Irrespective of the language and symbols used, any suitably advanced intelligence will recognise this relationship.
Stile writes:
Me personally? No, I've long forgotten my maths and theory for such things. But I do think that someone can.
Why do you think that?
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 80 by Stile, posted 05-12-2010 7:24 AM Stile has seen this message but not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 82 of 172 (559969)
05-12-2010 9:39 AM
Reply to: Message 79 by Straggler
05-11-2010 1:29 PM


Re: Supernatural Math
Straggler writes:
Stile writes:
I am extremely interested if anyone can describe a concept that is a part of "objective reality" that cannot be tested with the scientific method.
I am proposing that pi is such a concept and that it's objectivity distinct from the scientific method is demonstrated by the fact that an alien civilisation and us would agree on pi to an accuracy that lies beyond scientific empirical investigation.
Okay, I think I understand.
But I'm pretty sure I've covered this already and I'm still not sure of any specific arguement against it, so I'll try again:
Stile in message 76 writes:
1. Basic circles exist and can be observed empirically.
2. Diameters and circumferences can be observed and measured empirically.
3. These objective measurements can be used to show an empirical relationship.
4. This empirical relationship can be reduced to show a general empirical equation.
5. The result of this general empirical equation is called "Pi".
6. Pi is empirical.
(Note, I'm not saying that the exact value of Pi exists for some existing "perfect circle". I'm saying that Pi represents the general empirical relationship that can be (generated from observations of) basic circles... and that this is empirical and scientific).
7. This general empirical equation may be used to identify a "perfect Pi" value for a "perfect circle"... but who cares? It does not negate the fact that the general equation was still derived empirically through observation.
I'm guessing that somewhere in the 4 to 7 range you think we lose the "scientific-ness" of the structure? But why?
Do you not think that making a general equation to represent an idealized concept off a bunch of empirically obtained data measurements is scientific?
I'm pretty sure that's exactly what the scientific method is... making observations and generalizing into idealized concepts.
Hypothesis - there is a relationship between the circumference and diameter of a circle
Observations - measure a bunch of circles to find their circumference and diameters
Analysis - look at all these values and attempt to identify a generalized, idealistic representation
Conclusion - circles follow a specific relationship between their circumference and diameter ("Pi")
What's not scientific?
Once the idealistic equation is identified, we can then represent a "perfect circle" and therefore a "perfect Pi" and do a calculation to any accuracy.
...maybe you don't think the idealistic equation is objective anymore? If not... then it doesn't go against the orignal statement anymore because it's not a part of objective reality.
...if you do think it's a part of objective reality, then you must agree that there's no other way to go then to identify this exact same idealistic equation. Once that's identified... any calculation of Pi can be made to millions of decimal places and will be exactly the same for any aliens.
Which means that an alien civilization would agree with us on Pi to a degree that goes beyond scientific empirical investigation.
Which goes back to a guy in a room with apples example. If this man has 5 apples, he can objectively (and scientifically) develop that 1+1+1+1+1=5. But you're saying that it's impossible for him to understand that 1+1+1+1+1+1=6 just because he doesn't physically have 6 apples??
I can understand you saying it's no longer a part of "objective reality" (within the box)... but then... it's not a part of my claim anymore.

This message is a reply to:
 Message 79 by Straggler, posted 05-11-2010 1:29 PM Straggler has replied

Replies to this message:
 Message 84 by Straggler, posted 05-12-2010 11:31 AM Stile has seen this message but not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 83 of 172 (559974)
05-12-2010 10:23 AM
Reply to: Message 80 by Stile
05-12-2010 7:24 AM


Re: Supernatural Math
But I do think that someone can.
Not by the scientific method Simply by mathematics.
If you do think it's objective, and you do think that "any suitably advanced intelligence will recognize this relationship"... how will they recognize it unless it is derived (somehow) from observations of reality?
Simple, they derive it from mathematics, which is the one example of an objective reality that does not depend upn the scientific method
If it is not derived from observations of reality... how can you be so sure that is, in fact, objective and aliens would recognize it?
A valid question - and I would say that you'd just have to appreciate the nature of formal systems to understand.
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 80 by Stile, posted 05-12-2010 7:24 AM Stile has replied

Replies to this message:
 Message 85 by Stile, posted 05-12-2010 3:43 PM cavediver has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 84 of 172 (559984)
05-12-2010 11:31 AM
Reply to: Message 82 by Stile
05-12-2010 9:39 AM


Re: Supernatural Math
I'm guessing that somewhere in the 4 to 7 range you think we lose the "scientific-ness" of the structure? But why?
Because (in my role of arguing the platonic objective mathematical reality) I dispute that measuring empirical circles is the way to establish the value of pi at all. The fact that we and the aliens may have discovered the concept of pi through some poor empirical manifestation leading to a shoddy physical approximation does not mean that pi itself is an empirical quantity. Indeed no empirical circle will ever give us an accurate value of pi. We and the aliens can independently go off an measure as many physical circles as we wish. We can average our results and no doubt come to some limited agreement on a value for pi. Perhaps to a few decimal places in our nomenclature. Thus we would establish that pi is an objectively measurable and verifiable empirical quantity. That would be the empirical methodology would it not?
But we and the aliens would both be better off laying our rulers aside and simply trusting the objectivity of the mathematics. If we did we would both agree on a value for pi that defies empirical investigation. We would agree to an accuracy that makes any empirical agreement from which objectivity might be claimed pale into insignificance. Mathematically we would independently agree to such an extent that the objectivity of the quantity in question would be all but indisputable.
Which goes back to a guy in a room with apples example. If this man has 5 apples, he can objectively (and scientifically) develop that 1+1+1+1+1=5. But you're saying that it's impossible for him to understand that 1+1+1+1+1+1=6 just because he doesn't physically have 6 apples??
No. If anything I am saying that the 1+1+1+1+1+1=6 conclusion is independent of how many apples he has or even the existence of apples at all. Because it is not an empirical conclusion as such.
If you add 13 heffalumps to 6 heffalumps how many heffalumps do you have? But has anyone ever added heffalumps together? Or indeed ever empirically encountered a heffalump? So how do we know that 13 heffalumps + 6 heffalumps will give us 19 heffalumps? Are we simply applying inductive reasoning? Is it possible that 6 heffalumps + 13 heffalumps will NOT give us 19 heffalumps?
If our reasoning is purely inductive (which empirically it would have to be be given that we have never even seen 1 heffalump never mind counted different numbers of them) then we would have to say that Yes — It is quite possible that heffalumps will behave differently to every other addable entity we have ever encountered (e.g. apples). We would have to acknowledge the possibility that 13 heffalumps + 6 heffalumps will give us 74 heffalumps because until we actually make the observation any un-refuted answer is possible.
But you and I both know that regardless of empirical observation we can say with mathematical certainty how many heffalumps we will end up with. So why do you think that is?

This message is a reply to:
 Message 82 by Stile, posted 05-12-2010 9:39 AM Stile has seen this message but not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 85 of 172 (560020)
05-12-2010 3:43 PM
Reply to: Message 83 by cavediver
05-12-2010 10:23 AM


Re: Supernatural Math
cavediver writes:
Stile writes:
If it is not derived from observations of reality... how can you be so sure that is, in fact, objective and aliens would recognize it?
A valid question - and I would say that you'd just have to appreciate the nature of formal systems to understand.
I think this is the heart of the matter.
And I think I've figured out my own confusion.
My early guess would be that the formal system is part of the development of the equations. But if the equations are based on original observations of the real world... and result in explanations about the real world that can be tested (say, like, quantum theory prediction/confirmation type stuffs) ...then that would see to be well within the realm of "scientific study".
Of course, there are pure theoretical maths and physics that do not have results that are testable in the real-world. But these are all based upon the same rules and regulations that other concepts that are testable use.
So I do agree that these purely theoretical maths and physics are objective based on the objectively known rules of reality. But I do not agree that they are within the "known to be a part of objective reality" category I'm thinking of when I state:
(Back to my original-original wording in Message 437, the post-linked-to in order to create this thread)
Stile writes:
I'm trying to say there is always a scientific test for those things that fall into the "known to exist within objective reality" category and do not fall into either of the 2 following categories.
So... all this seems to have been a confusion over my use of the word "objective". I'm attempting to differentiate between "objective based off of known rules" and "known to be a part of objective reality" and I don't think I've been doing a good job at keeping it straight.
I will try to explain my confusion through the use of my own man in a box with 5 apples example:
His known objective reality contains scientific proof for 1+1+1+1+1=5, but does not show that 1+1+1+1+1+1=6.
Although 1+1+1+1+1+1=6 is objective, it is not "scientifically testable" in the sense that buddy doesn't have 6 apples. It is "objective based off of known rules".
Since it cannot be tested... it then is not a part of known objective reality... in which case my statement doesn't apply.
Bringing this back to advanced mathematical concepts (purely theoretical):
They are only "objective based off of known rules" and are not "known aspects of objective reality" (as I've been defining the terms). Therefore, my original statement does not apply.
For Pi, specifically, I think it may actually be a part of "known objective reality" since it can be scientifically tested and verified within some degree (as all scientific tests include possible errors). So maybe Pi was a bit of a poor example to attempt and flush out this confusion.
Hope this clears up some things.

This message is a reply to:
 Message 83 by cavediver, posted 05-12-2010 10:23 AM cavediver has not replied

Replies to this message:
 Message 86 by Straggler, posted 05-12-2010 5:45 PM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 86 of 172 (560027)
05-12-2010 5:45 PM
Reply to: Message 85 by Stile
05-12-2010 3:43 PM


Re: Supernatural Math
I still think you are missing the point of the Platonist view of mathematics. Whether any of us adhere to this view or not it is worth understanding what it is that this suggests.
Wiki writes:
Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's belief in a "World of Ideas" (typified by Plato's cave): the everyday world can only imperfectly approximate an unchanging, ultimate reality. Wiki on maths
This suggests that mathematics is both independent of, and indeed arguably more objective than, empirical reality.
Stile writes:
I will try to explain my confusion through the use of my own man in a box with 5 apples example:
His known objective reality contains scientific proof for 1+1+1+1+1=5
Actually no. Empirically all your box man can say is that 1 apple + 1 apple + 1 apple + 1 apple + 1apple + 1 apple = 6 apples. He cannot empirically conclude with certainty that this same relationship applies to pears, bananas or indeed anything else he hasn't actually observed.
Although 1+1+1+1+1+1=6 is objective, it is not "scientifically testable" in the sense that buddy doesn't have 6 apples. It is "objective based off of known rules".
How does he know these rules?
Since it cannot be tested... it then is not a part of known objective reality... in which case my statement doesn't apply.
If you simply define objective to mean that which can be empirically verified then it is hardly surprising that you only consider things which can be empirically verified as being objective.
The question of this thread is surely to ask whether that definition of objective is justified. A mathematical platonist would say not.

This message is a reply to:
 Message 85 by Stile, posted 05-12-2010 3:43 PM Stile has replied

Replies to this message:
 Message 87 by Stile, posted 05-13-2010 8:14 AM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 87 of 172 (560099)
05-13-2010 8:14 AM
Reply to: Message 86 by Straggler
05-12-2010 5:45 PM


Re: Supernatural Math
Straggler writes:
Actually no. Empirically all your box man can say is that 1 apple + 1 apple + 1 apple + 1 apple + 1apple + 1 apple = 6 apples.
Actually, he can't even do that. He's only got 5 apples. But I understand your point.
How does he know these rules?
He is intelligent. We are talking about intelligent aliens, right?
He has an apple, and decides to call it "1".
He then holds two apples and decides to call that "2".
...
He sees that when he holds 2 apples and then holds another 3 apples.. he ends up with "5".
...
Through these observations he can scientifically test and construct simple math.
Straggler writes:
Stile writes:
Since it cannot be tested... it then is not a part of known objective reality... in which case my statement doesn't apply.
If you simply define objective to mean that which can be empirically verified then it is hardly surprising that you only consider things which can be empirically verified as being objective.
Exactly. Although I don't so much restrict "knowing to be a part of reality" to be only that which is "empirically verified" so much as I don't know of any other successful method to do such.
If you go back and read my original posts on the matter from the other thread, you'll see that I fully intended it to be a simple statement of totality that is futile to argue against. It wasn't meant to spark debate or even be debated. Imagine my surprise when so much has come out of it...
The question of this thread is surely to ask whether that definition of objective is justified. A mathematical platonist would say not.
That may very well be your intention. But it was never mine. I simply wanted to defend my original statement. And explain it, and understand the rest of the discussion.
This suggests that mathematics is both independent of, and indeed arguably more objective than, empirical reality.
Oh, I understood the idea. I just didn't understand how it defied my original statement. Which is what I thought everyone was trying to show me and caused me even more confusion.
I fully agree that anything that is "objective" (blanket term) is not necessarily scientifically testable.
Like I explained in the earlier thread, my morality is "objective" in a way as well... but it is certainly not scientifically testable.

This message is a reply to:
 Message 86 by Straggler, posted 05-12-2010 5:45 PM Straggler has replied

Replies to this message:
 Message 88 by Straggler, posted 05-13-2010 8:44 AM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 88 of 172 (560106)
05-13-2010 8:44 AM
Reply to: Message 87 by Stile
05-13-2010 8:14 AM


Re: Supernatural Math
Stile original statement writes:
All things that are collectively agreed to exist within objective reality are testable and verifiable through the scientific method.
Through these observations he can scientifically test and construct simple math.
Can he?
If he only has five apples on what empirical basis does he conclude that the number 6 exists?
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 87 by Stile, posted 05-13-2010 8:14 AM Stile has replied

Replies to this message:
 Message 89 by Stile, posted 05-13-2010 10:13 AM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 89 of 172 (560112)
05-13-2010 10:13 AM
Reply to: Message 88 by Straggler
05-13-2010 8:44 AM


Re: Supernatural Math
Straggler writes:
Can he?
If he only has five apples on what empirical basis does he conclude that the number 6 exists?
Forgive me, this is the same confusion I've been trying to battle since the beginning. I will attempt to be extremely explicit.
He does not have an empirical basis to conclude that the number 6 exists.
He does have an "objective" basis to conclude that the number 6 exists (extending the rules he's scientifically and empirically tested and shown to be "a known part of objective reality" with his 5 apples).
But "6 apples" is not within his "known to be a part of objective reality" category.
His number 6 would be equivalent to "purely theoretical maths/physics".
So he certainly can conclude that the number 6 exists. It just isn't included in his "known to be a part of objective reality" category.
Let's move this back to Pi.
Let me know where if/why you think the "known to be a part of objective reality" area is not valid, I think it all comes back at the end:
1. Basic circles exist and can be tested.
2. Basic geometry exists and can be tested (hexagons...)
3. Basic math exists and can be tested (addition gives us simple math... speed/velocity/acceleration measurements can give us basic derivatives and integration...)
4. Analysis of simple geometric shapes (equilateral triangle, square, pentagon, hexagon... any Regular Polygon where the sides are all the same length) gives us an equation showing a relationship between distance from a shape's centre, it's number of sides, and it's perimeter.
5. Taking the limit of this equation as the number of sides goes to infinity (a circle...), we'll end up with our same circle equation of Circumference=SomeConstant*diameter.
6. This equation can be scientifically tested and verified against basic circles existing in nature. Will it be perfect? Of course not, but that's not a requirement of science.
7. That "SomeConstant" will also be the theoretical Pi value for a perfect circle that all aliens will be able to duplicate to any requested accuracy.
I agree that we'll both (humans and aliens) be able to calculate Pi beyond our "known to be a part of objective reality" category. But this doesn't stop us from both having an "objective" (general usage) value of Pi that we can calculate to whatever accuracy we want.
Hope that clarify's my thinking and usage of terms.

This message is a reply to:
 Message 88 by Straggler, posted 05-13-2010 8:44 AM Straggler has replied

Replies to this message:
 Message 90 by Straggler, posted 05-13-2010 11:05 AM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 90 of 172 (560114)
05-13-2010 11:05 AM
Reply to: Message 89 by Stile
05-13-2010 10:13 AM


Re: Supernatural Math
Stile initial statement writes:
All things that are collectively agreed to exist within objective reality are testable and verifiable through the scientific method.
Stile writes:
He does not have an empirical basis to conclude that the number 6 exists.
What is the largest number that we have an empirical basis for?
Does infinity exist?
Does infinity have an empirical basis?
So he certainly can conclude that the number 6 exists. It just isn't included in his "known to be a part of objective reality" category.
Why ever not?
Edited by Straggler, : No reason given.
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 89 by Stile, posted 05-13-2010 10:13 AM Stile has replied

Replies to this message:
 Message 91 by Stile, posted 05-13-2010 12:14 PM Straggler has replied

  
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