(October 19, 2011 at 10:43 am)Pendragon Wrote: The only thing the math does is give 10 equal horses. After quantifying them in terms of money, we can let the math shine with much more detail. 1 prize stud worth $250,000 (who ran away) and is hanging out with 9 scrub mares worth $800 each. We shall have to see if they gave him some bad horse disease that brings his value down to 0 however.

Not to necro, but I want to nitpick this.
Of course turning things into numbers kills off a bunch of details. That's arguably what math is all about: getting the maximum mileage out of a very small bit of information (and conversely figuring out how little you can know while still being able to deduce something). We might lose a lot of information when we turn a knot into a polynomial (e.g. Alexander Polynomial, Jones Polynomial). But we do it anyway, because they're easier to work with than a horribly tangled diagram.

And if the health of the horses is something we find particularly important, we can find some notation of keeping track of that as well. Not all functors need be so forgetful.

So if I throw ten tennis balls into a bin, they aren't exactly the same as they were before I threw them? Ok. I can live with that. Math is supposed to be a description of reality after all, not the other way around.

I agree that math isn't completely objective. But I can't see where this subjectivity has any teeth. "I'm drank some coffee before I typed this sentence" was surely made from the same subjective basis. And I'm sure my coffee has some things in it (plastic leeched from the mug, maybe some of my hair?) that I don't consider to be coffee. My conception of coffee is no less perfect that my conception of n tennis balls in a bin. But I fail to see how we could insist on the existence of coffee while questioning the existence of numbers. I mean, coffee does exist, right?

(January 29, 2012 at 10:17 am)Categories+Sheaves Wrote:

(October 19, 2011 at 10:43 am)Pendragon Wrote: The only thing the math does is give 10 equal horses. After quantifying them in terms of money, we can let the math shine with much more detail. 1 prize stud worth $250,000 (who ran away) and is hanging out with 9 scrub mares worth $800 each. We shall have to see if they gave him some bad horse disease that brings his value down to 0 however.

Not to necro, but I want to nitpick this.
Of course turning things into numbers kills off a bunch of details. That's arguably what math is all about: getting the maximum mileage out of a very small bit of information (and conversely figuring out how little you can know while still being able to deduce something). We might lose a lot of information when we turn a knot into a polynomial (e.g. Alexander Polynomial, Jones Polynomial). But we do it anyway, because they're easier to work with than a horribly tangled diagram.

And if the health of the horses is something we find particularly important, we can find some notation of keeping track of that as well. Not all functors need be so forgetful.

So if I throw ten tennis balls into a bin, they aren't exactly the same as they were before I threw them? Ok. I can live with that. Math is supposed to be a description of reality after all, not the other way around.

I agree that math isn't completely objective. But I can't see where this subjectivity has any teeth. "I'm drank some coffee before I typed this sentence" was surely made from the same subjective basis. And I'm sure my coffee has some things in it (plastic leeched from the mug, maybe some of my hair?) that I don't consider to be coffee. My conception of coffee is no less perfect that my conception of n tennis balls in a bin. But I fail to see how we could insist on the existence of coffee while questioning the existence of numbers. I mean, coffee does exist, right?

The questions we were disputing were about math being objective, or subjective. If math is a description of reality, then it is subjective.

Speaking of subjective, our conceptions of reality are subjective as well, so your conception of coffee is not really coffee at all, and certainly not "perfect". Same as your conception of tennis balls in a bin. Nothing more than wild hallucinations.

However, the gaps left by our subjective understanding of reality does not mean there are gaps IN reality. Subjectivity always has teeth in the way it leaves holes in our understanding.
The fault is in us. But that fault allows a skeptic the room needed to question things considered "objective truth", as impossible for humans.

The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

(January 29, 2012 at 7:12 pm)Pendragon Wrote: However, the gaps left by our subjective understanding of reality does not mean there are gaps IN reality. Subjectivity always has teeth in the way it leaves holes in our understanding.
The fault is in us. But that fault allows a skeptic the room needed to question things considered "objective truth", as impossible for humans.

What gaps are you talking about? Show how these gaps follow from subjectivity plox?

If the ghost of Emmy Noether visits me in a dream tonight, and she gives me a complete and flawless conception of everything everywhere, that knowledge is also subjective, because it came from another one of my vivid hallucinations. But... with those assumptions from earlier, this knowledge may not have any of those gaps in it...

So there are gaps in our understanding. And our understanding is also subjective. Even if both are true, why does one imply the other?

(January 31, 2012 at 2:58 pm)Categories+Sheaves Wrote:

(January 29, 2012 at 7:12 pm)Pendragon Wrote: However, the gaps left by our subjective understanding of reality does not mean there are gaps IN reality. Subjectivity always has teeth in the way it leaves holes in our understanding.
The fault is in us. But that fault allows a skeptic the room needed to question things considered "objective truth", as impossible for humans.

What gaps are you talking about? Show how these gaps follow from subjectivity plox?

If the ghost of Emmy Noether visits me in a dream tonight, and she gives me a complete and flawless conception of everything everywhere, that knowledge is also subjective, because it came from another one of my vivid hallucinations. But... with those assumptions from earlier, this knowledge may not have any of those gaps in it...

So there are gaps in our understanding. And our understanding is also subjective. Even if both are true, why does one imply the other?

Understanding comes not just from our own crippled viewing point, but also from many others, so that a greater, clearer picture may emerge. I guess this is the essence of the scientific method.

Unfortunately, "understanding" can come from group manipulations, where under pressure, sometimes minor pressure, people will agree they saw something just to "go along".

So our "understanding" will be potentially far better, or worse than our own individual view.

The subjective aspects of what we saw, what we remembered we saw and heard, the faulty aspects of how tired, drunk, or high...etc give one great pause as to how much trust to place in ones own, or anyone's version of reality.

However, you did agree that understanding itself is subjective, and capable of being wrong. Even if we have corrected this viewpoint with as many observation aspects as we can currently find, there is always the chance that the understanding can be invalidated with new observational points. (also the scientific method)

The gaps between what we understand, to what we do not understand are huge, and the greasy little uncertainly in our own subjective position makes it suck a bit more.

Want more gaps?

(January 30, 2012 at 10:17 am)Rhythm Wrote: The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

Ever hear of Dyslexia? Right off the bat you are wrong. Why is it that every kid does not score a perfect 100 on their math? Do your kids?

Hmmm right down to the last detail....

I know you are a rational person, but this is delusional. Numbers/math is shared by every human down to the last detail?
Care to prove this?

(January 31, 2012 at 11:37 pm)Pendragon Wrote:

(January 30, 2012 at 10:17 am)Rhythm Wrote: The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

Ever hear of Dyslexia? Right off the bat you are wrong. Why is it that every kid does not score a perfect 100 on their math? Do your kids?

Hmmm right down to the last detail....

I know you are a rational person, but this is delusional. Numbers/math is shared by every human down to the last detail?
Care to prove this?

Truly. Even mathematicians aren't all in agreement with various aspects of the formalism. There are a myriad of problems associated with set theory for example. For example, there were very prominent mathematicians who renounced Georg Cantor's ideas about set theory in the time when it was invented. And there are still mathematicians today who do not accept these ideas completely. They do contain flaws and inconsistencies without a doubt.

People seem to have a truly naive idea of mathematics. It's not nearly as cut-and-dry as people seem to think. It's highly subjective. I personally don't believe that aliens would necessarily have created the same mathematics that we have. Sure, it's going to have some similarities. Our mathematics isn't that lame. But it's far from perfect too.

So I agree with the issues brought up by Pendragon. Neither science, nor mathematics is anywhere near as clear-cut or as well-defined as many atheists would like to believe.

I'm mean this shouldn't send anyone running off to suddenly believe in something as stupid as the bible, for example. But the point is that math and science both are no where near complete or perfect enough to rely upon to offer us any real 'truths' of the nature of reality.

So pitting a belief in a God with a belief in Mathematics is truly naive.

One has nothing to do with the other truly.

(February 1, 2012 at 12:11 am)Abracadabra Wrote:

(January 31, 2012 at 11:37 pm)Pendragon Wrote:

(January 30, 2012 at 10:17 am)Rhythm Wrote: The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

Ever hear of Dyslexia? Right off the bat you are wrong. Why is it that every kid does not score a perfect 100 on their math? Do your kids?

Hmmm right down to the last detail....

I know you are a rational person, but this is delusional. Numbers/math is shared by every human down to the last detail?
Care to prove this?

Truly. Even mathematicians aren't all in agreement with various aspects of the formalism. There are a myriad of problems associated with set theory for example. For example, there were very prominent mathematicians who renounced Georg Cantor's ideas about set theory in the time when it was invented. And there are still mathematicians today who do not accept these ideas completely. They do contain flaws and inconsistencies without a doubt.

People seem to have a truly naive idea of mathematics. It's not nearly as cut-and-dry as people seem to think. It's highly subjective. I personally don't believe that aliens would necessarily have created the same mathematics that we have. Sure, it's going to have some similarities. Our mathematics isn't that lame. But it's far from perfect too.

So I agree with the issues brought up by Rhythm. Neither science, nor mathematics is anywhere near as clear-cut or as well-defined as many atheists would like to believe.

I'm mean this shouldn't send anyone running off to suddenly believe in something as stupid as the bible, for example. But the point is that math and science both are no where near complete or perfect enough to rely upon to offer us any real 'truths' of the nature of reality.

So pitting a belief in a God with a belief in Mathematics is truly naive.

One has nothing to do with the other truly.

It seems you are agreeing with Pendragon, not rhythm.

yes? not sure about aspects of your post.

(February 1, 2012 at 12:15 am)Pendragon Wrote: It seems you are agreeing with Pendragon, not rhythm.

yes? not sure about aspects of your post.

Yes, that's right. Sorry about the mistake. I've edited the post.

(February 1, 2012 at 12:25 am)Abracadabra Wrote:

(February 1, 2012 at 12:15 am)Pendragon Wrote: It seems you are agreeing with Pendragon, not rhythm.

yes? not sure about aspects of your post.

Yes, that's right. Sorry about the mistake. I've edited the post.

Just want to be clear. Seems rhythm may have strayed a bit from his usual formidable self.

Just want to be ready when he comes, though it was a rather lame post on his part. Waiting for him to shoot some fire.