BrainMeta'                 

Welcome Guest ( Log In | Register )

 
Reply to this topicStart new topic
> Mathematics: Invented or Discovered?, Why Platonism is wrong.
Rick
post Jul 27, 2010, 12:23 PM
Post #1


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



The Platonic view is that mathematics is a landscape, a world that is “out there,” pre-existing, and that mathematicians are discoverers, not inventors. That’s the view held by every mathematician I have heard who has an opinion on the topic, and they are all, of course, wrong, and I am (Surprise!) correct in saying that the ideal world is entirely of human construction.

The Platonic view is strangely seductive and reassuring, and Platonism accordingly drove early Christian philosophy (Plotinus, St. Augustine, St. Thomas Aquinus, Duns Scotus, etc.). However, consider this little anomaly at the center of the mathematical structure, the number zero to the power zero. How is it evaluated? Here’s where mathematicians fall back on contrived convention. Zero and every other number to the zeroeth power is defined as one. For non-zero numbers, this makes perfect sense. However, zero raised to any power but zero evaluates to zero! If you graph zero to the power x as a function of X, you will see a constant line of zero except at zero where it jumps up to one and then back to zero. The convention that zero to the zeroeth power equals one minimizes other impacts to the mathematical edifice.

Need more evidence? Consider that the Pythagorean theorem makes no sense to a student until (s)he constructs an understanding in his/her own mind. Everyone who understands that in a right triangle, a^2 + b^2 = c^2, has constructed that understanding for him or herself. Math’s a building project (artifact), not a mountain to be taken as given.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
GodConsciousness
post Jul 27, 2010, 12:36 PM
Post #2


Demi-God
*****

Group: Basic Member
Posts: 838
Joined: Sep 19, 2006
Member No.: 5683



I am curious about this Rick. On one hand, I agree with what you are saying in regards to the Platonic world of abstracted Ideals including mathematics- I tend to be more Aristotelian in this respect. Yet, I do feel that there is a mathematical organization or structure to the universe that we can discover- not because it exists in a world of disembodied Forms but due to an inherent mathematical organization in matter itself.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Jul 27, 2010, 04:14 PM
Post #3


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



The question is basically, "why are physical phenomena so conveniently modeled by mathematical formulae?" Take for example, the inverse square law of gravitation. It didn't have to be exactly a factor of two, did it? Why couldn't it have been an infinity of other factors such as 1.998? Why is it the simple integer two?

Or why are there so many linear equations in science (like f = m*a)? I don't suppose it was constructed that way in order to make it easy for us to understand. It must have been from necessity. However, if one continues on to advanced physics, the formulas grow rapidly incomprehensible. Consider string theory, for example.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Jul 27, 2010, 10:24 PM
Post #4


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Rick @ Jul 28, 2010, 01:14 AM) *

The question is basically, "why are physical phenomena so conveniently modeled by mathematical formulae?" Take for example, the inverse square law of gravitation. It didn't have to be exactly a factor of two, did it? Why couldn't it have been an infinity of other factors such as 1.998? Why is it the simple integer two?

Or why are there so many linear equations in science (like f = m*a)? I don't suppose it was constructed that way in order to make it easy for us to understand. It must have been from necessity. However, if one continues on to advanced physics, the formulas grow rapidly incomprehensible. Consider string theory, for example.
The gravity example is a good one, because it illustrates how mathematical descriptions of such phenomena are contrived and designed to fit our convenience. Gravity is poorly understood and possibly has origins in some high-dimensional space-time and penetrates a membrane to exhibit only a partial picture of its true nature and consequential influence. Thus the 'inverse square law of gravitation' might be better termed the 'inverse square law of gravitation as penetrating our particular dimensions or universe'.

So the equations are incomplete and merely models of natural phenomena to suit particular (human) purposes. They are invented. Related is the fact (huh!) that we are an infinity away from any description of the multiverse we find ourselves in. That is, the (likely) infinite complexity, large and small, means that no description, mathematical or other, will ever be the truth or close to it.

I'm afraid that mathematics is as contrived as astrology and we need to move on from the present position to something more philosophically enlightening to deal with the mysteries of nature. Of course, to get through the day, the equations work quite well, and we do have buses, trains and planes to catch - just as biologists have no idea what life is, because it is a meaningless term intrinsically and merely packages a set of descriptions together in an arbitrary way to (unsuccessfully in my view) help understand a complex emergent state. We might even view consciousness similarly one day!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Aug 02, 2010, 02:19 PM
Post #5


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



The very necessity of postulating dark matter to patch up the error of the inverse square law to hold the galaxies together should tell us something about the sorry state of contemporary physics.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 02, 2010, 07:14 PM
Post #6


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Rick @ Aug 02, 2010, 11:19 PM) *

The very necessity of postulating dark matter to patch up the error of the inverse square law to hold the galaxies together should tell us something about the sorry state of contemporary physics.
This could solve that issue: http://www.physorg.com/news199591806.html
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Aug 03, 2010, 08:52 AM
Post #7


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



I like that new model, but it still does not explain the need to postulate dark matter. It takes care of dark energy only.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 03, 2010, 08:14 PM
Post #8


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Rick @ Aug 03, 2010, 05:52 PM) *

I like that new model, but it still does not explain the need to postulate dark matter. It takes care of dark energy only.
Matter - energy .... different patterns, still snowflakes.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Aug 04, 2010, 08:18 AM
Post #9


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



Spoken like an artist, not a scientist. Nothing inherently wrong with that, of course, but this thread is somewhat non-arty.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 04, 2010, 07:14 PM
Post #10


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Rick @ Aug 04, 2010, 05:18 PM) *

Spoken like an artist, not a scientist. Nothing inherently wrong with that, of course, but this thread is somewhat non-arty.
Maybe mathematics is art, you know 'creation' rather than 'exposition'.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Aug 05, 2010, 05:45 PM
Post #11


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



Hmmm. I thought artists rebelled against rules. Math is nothing but rules!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Homegamek
post Aug 05, 2010, 06:43 PM
Post #12


Aspiring
**

Group: Basic Member
Posts: 99
Joined: Jun 26, 2010
Member No.: 32873



.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 06, 2010, 04:50 AM
Post #13


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Hey Hey @ Aug 05, 2010, 04:14 AM) *
QUOTE(Rick @ Aug 04, 2010, 05:18 PM) *
Spoken like an artist, not a scientist. Nothing inherently wrong with that, of course, but this thread is somewhat non-arty.
Maybe mathematics is art, you know 'creation' rather than 'exposition'.
QUOTE(Rick @ Aug 06, 2010, 02:45 AM) *
Hmmm. I thought artists rebelled against rules. Math is nothing but rules!
But if mathematics is invented (created) then surely the two (art-math) have some relationship, though one might need to be less stifled about the definitions of each. Unless, of course, your original question was pure rhetoric and without real intellectual intent.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
GodConsciousness
post Aug 06, 2010, 05:23 AM
Post #14


Demi-God
*****

Group: Basic Member
Posts: 838
Joined: Sep 19, 2006
Member No.: 5683



A true Platonist would revel in the intersections of mathematics and art!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 06, 2010, 05:32 AM
Post #15


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



Look, most things out there are constructs. Gravity is a construct and the equations fit the constructs, having no further relevance or meaning. Humans have invented most mathematics and equations become discarded (sometime slowly due to a misguided respect for the inventor or to do with the limitations of holding more complex descriptions in the average human mind). Newton's description of gravity was based on a failure to understand the nature of gravity. By that I don't mean the actual basis of the phenomenon, but that it is likely not a phenomenon, rather an emergent observation of something likely never describable. That is not to say that the equations do not help in applications that humans derive, or that we will not be able to exploit the increasingly complex descriptions of the delusion over time. But we will never actually know the nature of what creates the observations.

So, I feel, much mathematics is of little worth in the bigger picture and simply gets us through the day (as applied math, helping planes to fly; or pure math, entertaining like a playstation game). As as for statistics (spit) ... well, humans manipulate everything else for their own ends, so why not?
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 06, 2010, 05:40 AM
Post #16


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Homegamek @ Aug 06, 2010, 03:43 AM) *

.
Unlike a point particle, taking no space, your point (period) has taken up (physical) space in the discussion, yet is valueless. Please do not do that Enki, or I will delete them. And if that doesn't work I will ask Shawn to ensure that your new identity is banned. Your resumed irritating habit will not be tolerated.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 06, 2010, 05:44 AM
Post #17


Supreme God
*******

Group: Basic Member
Posts: 7763
Joined: Dec 31, 2003
Member No.: 845



QUOTE(GodConsciousness @ Aug 06, 2010, 02:23 PM) *

A true Platonist would revel in the intersections of mathematics and art!
Yes, but would also likely waste our time with tub-thumping! Look at for Lindsay!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
P JayS
post Apr 27, 2013, 03:08 AM
Post #18


Demi-God
*****

Group: Basic Member
Posts: 588
Joined: Apr 04, 2012
Member No.: 34146



QUOTE(Rick @ Jul 27, 2010, 12:23 PM) *

The Platonic view is that mathematics is a landscape, a world that is “out there,” pre-existing, and that mathematicians are discoverers, not inventors. That’s the view held by every mathematician I have heard who has an opinion on the topic, and they are all, of course, wrong, and I am (Surprise!) correct in saying that the ideal world is entirely of human construction.

The Platonic view is strangely seductive and reassuring, and Platonism accordingly drove early Christian philosophy (Plotinus, St. Augustine, St. Thomas Aquinus, Duns Scotus, etc.). However, consider this little anomaly at the center of the mathematical structure, the number zero to the power zero. How is it evaluated? Here’s where mathematicians fall back on contrived convention. Zero and every other number to the zeroeth power is defined as one. For non-zero numbers, this makes perfect sense. However, zero raised to any power but zero evaluates to zero! If you graph zero to the power x as a function of X, you will see a constant line of zero except at zero where it jumps up to one and then back to zero. The convention that zero to the zeroeth power equals one minimizes other impacts to the mathematical edifice.


Need more evidence? Consider that the Pythagorean theorem makes no sense to a student until (s)he constructs an understanding in his/her own mind. Everyone who understands that in a right triangle, a^2 + b^2 = c^2, has constructed that understanding for him or herself. Math’s a building project (artifact), not a mountain to be taken as given.

0^0 = (0, 1)
0^1 = 0

0 * 0 = 1: With gravity 1 is razed to 0. With reverse gravity 0 is raised to 1.
1/0 = 0 : 1.0 -> 0.9 -> 0.8 -> 0.7 -> 0.6 -> 0.5 -> 0.4 -> 0.3 -> 0.2 -> 0.1 -> 0 downward gravity.
1/0 = 1 : Reverse gravity raises from 0 in the opposite direction to 1. Without reverse gravity nothing could stand.

0 * 0 = 0:
Gravity Neutral : 0.5 <-> 0.4 <-> 0.3 <-> 0.2 <-> 0.1 <-> 0 <-> 0.1 <-> 0.2 <-> 0.3 <-> 0.4 <-> 0.5

Here the balance of 1 is divided into 2 across 0 equally. The extent of the matter in any direction is 1/2 = 0.5. Thus we learn what the basic radius is for any pi circumference in time virtually without any gravity at all or gravity in neutral.

This makes the diameter d = 2r = 1. The basic unit of time is 1 second. The perimeter of the pi circumference in averaged phi space = 3 along with the concentric square and inscribed hexagon of the Geometric Spencer Construction.

Presently 0*0=0. This assumption deals with Pi/d=pi and the radius in accord with a unit of time as 1 second is r=1/2.

For 0*0=1 it becomes necessary to know in which direction the primary force of gravity is that is being discussed, downward or reverse.

When it comes to 0^0=1, zero is simply the exception to the rule using the direction of gravity.

P.j.S .!.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post

Reply to this topicStart new topic
1 User(s) are reading this topic (1 Guests and 0 Anonymous Users)
0 Members:

 



Lo-Fi Version Time is now: 19th April 2014 - 04:39 PM


Home     |     About     |    Research     |    Forum     |    Feedback  


Copyright © BrainMeta. All rights reserved.
Terms of Use  |  Last Modified Tue Jan 17 2006 12:39 am

Consciousness Expansion · Brain Mapping · Neural Circuits · Connectomics  ·  Neuroscience Forum  ·  Brain Maps Blog