What is a number?
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17-08-2016, 01:35 AM
RE: What is a number?
(17-08-2016 01:14 AM)Reltzik Wrote:  
(16-08-2016 08:55 PM)Bucky Ball Wrote:  So I don't know if I agree with this.
A circle is (can be) a finite and real object. A diameter can be measured, and is not undefined or only approximated. A circumference can be measured. So the idea that pi is something that is "only approximated" seems rather questionable, since pi x the diameter has a specific length, (the circumference of the specific circle in question).
Consider

First of all, pi is dependent on Euclidean geometry. If we have a non-euclidean geometry, then the ratio between circle and diameter is NOT pi. And anywhere we have a gravity well... which is basically everywhere in our universe... geometry is slightly off from Euclidean.

But that's not what is really being said about pi. It means that pi can only be calculated/measured to a degree of precision, rather than with complete precision. For every real-world circle, our ability to identify the length of its diameter or circumference are ALSO limited to a degree of precision. We might measure the diameter as 100cm, for example, but be off by quite a few manometers in our measurements. That means our ability to calculate pi from these real-world circles is also limited by these limits in our ability to measure. (Also, we draw imprecise circles.)

Even for theoretical circles with diameters that are defined as exact numbers, we can't calculate pi with perfect precision. Arbitrary precision, yes. However many digits we want to calculate pi out to, we can. We've sometimes get supercomputers doing ONLY this task, and they've gotten out to over 13,000,000,000,000 digits, far beyond the degree of precision that is required for any real problem. But while we can calculate it out to any degree of precision we wish, for any of these degrees of precision there WILL be error. It will be a very small error.... in pi's case, for these extreme super-computer-produced values, we have to get over a dozen TRILLION digits iin before there's ANY error... but the error will still be there. Very very small, but there. This is a problem not just for pi, but for every irrational number (and definitely for transcendental numbers look pi), because we don't even have the ability to represent and store an irrational number with complete and exact precision. That's why we always see pi written out as 3.14... or 3.14159... or so on. The ... indicates the imprecise part of pi, and no matter how precise we get, no matter how many digits we have before the ..., it is beyond human ability to calculate... or write down... the infinitely-many digits required for exact precision.

Hi,

Pre-apologies for maths ignorance. How does all the above fit in with Plato's theory of forms?

D.
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17-08-2016, 06:41 AM
RE: What is a number?
(17-08-2016 01:35 AM)Dworkin Wrote:  
(17-08-2016 01:14 AM)Reltzik Wrote:  First of all, pi is dependent on Euclidean geometry. If we have a non-euclidean geometry, then the ratio between circle and diameter is NOT pi. And anywhere we have a gravity well... which is basically everywhere in our universe... geometry is slightly off from Euclidean.

But that's not what is really being said about pi. It means that pi can only be calculated/measured to a degree of precision, rather than with complete precision. For every real-world circle, our ability to identify the length of its diameter or circumference are ALSO limited to a degree of precision. We might measure the diameter as 100cm, for example, but be off by quite a few manometers in our measurements. That means our ability to calculate pi from these real-world circles is also limited by these limits in our ability to measure. (Also, we draw imprecise circles.)

Even for theoretical circles with diameters that are defined as exact numbers, we can't calculate pi with perfect precision. Arbitrary precision, yes. However many digits we want to calculate pi out to, we can. We've sometimes get supercomputers doing ONLY this task, and they've gotten out to over 13,000,000,000,000 digits, far beyond the degree of precision that is required for any real problem. But while we can calculate it out to any degree of precision we wish, for any of these degrees of precision there WILL be error. It will be a very small error.... in pi's case, for these extreme super-computer-produced values, we have to get over a dozen TRILLION digits iin before there's ANY error... but the error will still be there. Very very small, but there. This is a problem not just for pi, but for every irrational number (and definitely for transcendental numbers look pi), because we don't even have the ability to represent and store an irrational number with complete and exact precision. That's why we always see pi written out as 3.14... or 3.14159... or so on. The ... indicates the imprecise part of pi, and no matter how precise we get, no matter how many digits we have before the ..., it is beyond human ability to calculate... or write down... the infinitely-many digits required for exact precision.

Hi,

Pre-apologies for maths ignorance. How does all the above fit in with Plato's theory of forms?

D.

To the best of my understanding of the Platonic Forms model, my observation of our inability to draw an exact circle or obtain an exact measurement would be a good example of objects in our world falling short of their exact form.
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18-08-2016, 09:06 AM
RE: What is a number?
(17-08-2016 06:41 AM)Reltzik Wrote:  
(17-08-2016 01:35 AM)Dworkin Wrote:  Hi,

Pre-apologies for maths ignorance. How does all the above fit in with Plato's theory of forms?

D.

To the best of my understanding of the Platonic Forms model, my observation of our inability to draw an exact circle or obtain an exact measurement would be a good example of objects in our world falling short of their exact form.

There are no Platonic forms. They exist in brains as ideas, as a result of learning about them, not "out there" in some perfect form. Although maybe a computer could make one (??)

Insufferable know-it-all.Einstein God has a plan for us. Please stop screwing it up with your prayers.
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18-08-2016, 01:48 PM
RE: What is a number?
(17-08-2016 06:41 AM)Reltzik Wrote:  
(17-08-2016 01:35 AM)Dworkin Wrote:  Hi,

Pre-apologies for maths ignorance. How does all the above fit in with Plato's theory of forms?

D.

To the best of my understanding of the Platonic Forms model, my observation of our inability to draw an exact circle or obtain an exact measurement would be a good example of objects in our world falling short of their exact form.

Reltzik,

Yes, exactly - if you will pardon the pun. Wink

I don't know if the forms theory has any credibility these days, and note Bucky Ball is unconvinced.

OK, this is dangerous waters, but it may be possible that such concepts as maths and logic forms are metaphysical. What I mean here (again danger warning) is that if sentient creatures ceased to exist anywhere in the universe, it would still be true that a square has 4 sides of equal length and that a circle is not an oval. Of course there does not have to be a perfect square or circle anywhere in the universe, as this would still be practically impossible, but the concept of such a thing would be available to a new sentience, if such a thought were to arise.

I'm not saying this is so, just possible?

D.
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18-08-2016, 04:16 PM
RE: What is a number?
(18-08-2016 01:48 PM)Dworkin Wrote:  What I mean here (again danger warning) is that if sentient creatures ceased to exist anywhere in the universe, it would still be true that a square has 4 sides of equal length and that a circle is not an oval.

I think that if we ceased to exist there would be no such tings as "square" and "circle". They are artificial constructions of our own creation.

#sigh
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18-08-2016, 04:22 PM
RE: What is a number?
(18-08-2016 01:48 PM)Dworkin Wrote:  
(17-08-2016 06:41 AM)Reltzik Wrote:  To the best of my understanding of the Platonic Forms model, my observation of our inability to draw an exact circle or obtain an exact measurement would be a good example of objects in our world falling short of their exact form.

Reltzik,

Yes, exactly - if you will pardon the pun. Wink

I don't know if the forms theory has any credibility these days, and note Bucky Ball is unconvinced.

OK, this is dangerous waters, but it may be possible that such concepts as maths and logic forms are metaphysical. What I mean here (again danger warning) is that if sentient creatures ceased to exist anywhere in the universe, it would still be true that a square has 4 sides of equal length and that a circle is not an oval. Of course there does not have to be a perfect square or circle anywhere in the universe, as this would still be practically impossible, but the concept of such a thing would be available to a new sentience, if such a thought were to arise.

I'm not saying this is so, just possible?

D.

.... I think whether Platonic forms exist in that sense hinges on the semantic question of how one defines the concept of existence, which, frankly, is something philosophers have tended to do a very poor job of. They seem to just assume if that what it means for something to exist is agreed upon by all (when it clearly isn't) and proceed as if it's an axiom.
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18-08-2016, 04:31 PM
RE: What is a number?
(11-08-2016 02:42 PM)Dworkin Wrote:  Hi,

This is one of those questions that takes us to the boundaries of reasoning.

https://welovephilosophy.com/2012/12/17/...ers-exist/

The link is an intro, but there is plenty of argument out there. What's your view?

D.

This reminds me of when they tried to label my kid dyslexic. I went to the PTA meeting with a few props. I held up a picture of the school taken from the North and one taken from the South and another from the East and also from the West. This is the school! and this is the school and twice more I showed them the school. Then I held up the letter P and announced it was the letter P. Then I spun it around and asked is this the letter P? No it is the letter b then one more turn? This is the letter P or b? NO! it has turned itself into a q. And now it is a d! Then I did the same thing with a picture of my son, from the front he is a boy, from the back he is still a boy and from above, sitting, standing, laying down he is still a boy. Why cannot this letter remain the letter P. Why cannot we the parents and teachers make a more sane method of education. There is nothing wrong with my son the problem is with the letters and the system that tries to say this is something different from itself when seen from a different side! etc...Dyslexic, my kid? No!
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18-08-2016, 04:32 PM
RE: What is a number?
(18-08-2016 04:16 PM)GirlyMan Wrote:  
(18-08-2016 01:48 PM)Dworkin Wrote:  What I mean here (again danger warning) is that if sentient creatures ceased to exist anywhere in the universe, it would still be true that a square has 4 sides of equal length and that a circle is not an oval.

I think that if we ceased to exist there would be no such tings as "square" and "circle". They are artificial constructions of our own creation.

So when one leaves the USA there are no longer miles, but kilometers? No gallons only liters? ETC.....
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18-08-2016, 04:35 PM
RE: What is a number?
(18-08-2016 04:32 PM)Born Again Pagan Wrote:  
(18-08-2016 04:16 PM)GirlyMan Wrote:  I think that if we ceased to exist there would be no such tings as "square" and "circle". They are artificial constructions of our own creation.

So when one leaves the USA there are no longer miles, but kilometers? No gallons only liters? ETC.....

Not when we leave the USA, when we cease to exist. And then yes, there are no longer miles, kilometers, gallons or liters.

#sigh
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18-08-2016, 04:40 PM
RE: What is a number?
Or if you'll excuse a third post in a row. The first college level math course I took assured us that 1+1 may not always =2. It just is said that it does and is a convention we use and all have to agree to it if we wish to study math etc... I don't remember the exact wording, but still 50 years later remember the concept. 1+1=2 only because we all agree that it does!
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