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Author Topic:   Peanut Gallery
RAZD
Member (Idle past 1435 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


(1)
Message 946 of 1725 (603823)
02-07-2011 9:17 PM
Reply to: Message 866 by xongsmith
02-05-2011 12:49 PM


Re: How I see the strong confirmation bias
Hi xongsmith, thanks
None of the above...you just shrug & wait, accepting that you don't know.
And this would cover most of the cases, imho, as there are a lot of people that have made unconfirmed untested claims. Of course ones lost to history may never be known, and the best we can do is deal with the evidence in the here and now.
Seems the only instance listed so far is my listing of the FSM.
sadly so, and even here we have the problem of starting with a made up concept first ...
Making something up and then claiming and demonstrating it is made up is the epitomy of stupidity in this issue.
Worse, it is a logical fallacy,
http://onegoodmove.org/fallacy/begging.htm
quote:
The truth of the conclusion is assumed by the premises. Often, the conclusion is simply restated in the premises in a slightly different form.
http://onegoodmove.org/fallacy/affirm.htm
quote:
Any argument of the following form is invalid:
If A then B
B
Therefore, A
If it is a supernatural concept then it is made up
{X} is made up
Therefore it is a supernatural concept that is made up
But any number of made up concepts are not supernatural, so supernaturalness needs to be demonstrated not just assumed.
If you start with a concept that you make up, then you are starting with what you want to conclude (also known as begging the question) but haven't shown that it
http://theautonomist.com/.../permanent/fallacies.php#begging
quote:
Begging the question fallacy - Advancing an argument on the basis of statements which are assumed but need themselves to be proved, or assuming the conclusion or part of the conclusion in the premises of an argument. (Sometimes called circular reasoning.)
(bluegenes) made up concept {X}
(bluegenes) claims that it is a supernatural entity
therefore {X} is a supernatural entity that has been made up
Premise 2 has not been demonstrated to be anything other than assertion. Again any number of made up concepts are not supernatural, so supernaturalness needs to be demonstrated not just assumed.
bluegenes theory boils down to this: Every supernatural being that we can show has been made up is made up.
Whoop-ti-doo. Color me unimpressed.
Worse, every concept that can be shown to be made up so far has indeed been made up, but hasn't been shown to really be a supernatural concept.
At which point it doesn't really qualify as a scientific theory as it is an oxymoron.
Enjoy.

we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)

This message is a reply to:
 Message 866 by xongsmith, posted 02-05-2011 12:49 PM xongsmith has seen this message but not replied

crashfrog
Member (Idle past 1497 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 947 of 1725 (603827)
02-07-2011 10:14 PM
Reply to: Message 945 by RAZD
02-07-2011 8:31 PM


Re: possibilities and probabilities
Indeed, which means you need to know that possibility before assuming that the 50:50 split is correct.
"The coin is not balanced" isn't an outcome in the outcome space, so, no, it's not a possibility we need to know about. If the coin isn't balanced that will emerge in the distribution of outcomes; the likelihood of one face will be less than the other.
We don't need to know, a priori, whether the coin is balanced or not - we can flip it and empirically determine the balance.
You said the probability was independent of time, thus both had to be true and false at the same time, unless you include time in the outcome space.
This is incorrect. Again, this equation:
which is the universal probability function for any event a, has no term for time.
I mean, do you think I'm lying to you about that? Prove me wrong. Where is the term for time in this equation? (Traditionally lower-case t is the symbol for "time", usually in seconds, in an equation.) If the mathematical basis for probability has no term for time, as you can plainly see, then what on Earth could be the basis for your conclusion that probabilities are dependent on whether the event was in the past or is in the future?
Which includes time factored into the outcome space.
No, it doesn't. As you can plainly see there's no factor of time in the function P(a), so clearly time is not being factored in. What is being "factored" is that half of the minutes in a day have one characteristic, and the other half have the opposite characteristic, and therefore the odds that a random minute out of the day has one characteristic and not the other is 1/2. Time is not a factor in this calculation; there is no term for time in P(a). If you disagree, show me the term for time in P(a).
Curiously, you had to intentionally manipulate your outcome space to achieve this result
Not really, and you've completely ignored the point.
Even if they are of equal area, there could be a higher probability that the pen will reside at the lower elevation of the floor than stay on the desk even though it was placed there.
So you agree that the outcomes are not equiprobable. Then why did you assert that they were equiprobable?
The area of the room could be 1000 times the area of the desk, and you could assume a random distribution of the pen around the desk you would not get better than 50% probability of the pen being on the desk.
Well, this is clearly inaccurate. The probability of the pen being on the desk decreases as the ratio of area of the desk to the area of the room decreases. Inversely it increases as the area of the desk increases relative to the area of the room, such that if the room is literally no larger than the desk (and therefore the surface of the desk is also the floor of the room) then the probability that the pen is on the desk given that it is in the room is 100%.
In other words the possibilities are not equiprobable. Rolling two dice and summing the result produces values between 2 and 12, but those values are not equiprobable; the odds of getting 7 aren't 1 in 11, they're 1 in 6.
I'll put you down for a (7) because "Absence of evidence is always evidence of absence" ...
I'm actually a 6 due to a position I hold about the maximum justifiable certainty of propositions, and 6 is the only logically tenable position on the Dawkins spectrum. Please correct your notes.
It asserts that a proposition is necessarily true because it has not been proven false (or vice versa).
I'm not asserting that a proposition is necessarily false because it has not been proven true; I'm asserting that absence of evidence is evidence of absence (not proof of absence) because when things are absent, an absence of evidence is the necessary result. Something that is absent is not present to give evidence.
When one man asserts the existence of blue fairies at the South Pole, and another man denies the existence of such fairies, the lack of any evidence for blue fairies at the South Pole does not equally support both their positions. Rather, that lack of evidence is evidence for the latter position. That's only a logical fallacy if you believe that conclusions can never be tentative.
It amuses me that this fallacy is used both pro and con.
It amuses me that you think that fallacies are the beginning and end of reason. The fact that some true things are also logical fallacies should indicate to you that logic has critical flaws that preclude it's use as a tool to understanding what is real in the universe. Logic is applicable only to axiomatic systems, which the universe is not. Empiricism is how we understand the universe, and empirically, an absence of evidence is evidence of absence.

This message is a reply to:
 Message 945 by RAZD, posted 02-07-2011 8:31 PM RAZD has seen this message but not replied

Straggler
Member (Idle past 95 days)
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 948 of 1725 (603841)
02-08-2011 6:16 AM
Reply to: Message 813 by RAZD
02-03-2011 10:20 PM


Subjective "Evidence" - Surely Not?
RAZD writes:
One of the problems that I have is that I cannot see a way to distinguish imagination from an unverified subjective experience (if you remember the discussions with Straggler) of the supernatural, particularly where one does not fully understand the experience....
I remember the discussions with Straggler very well. I remember your multi-thread "liar liar" tirade equally well.
Once again it seems you feel the need to raise the issue of subjective "evidence" in the context of a discussion about deities. I find it remarkable that you keep feeling the need to raise such "evidence" in the context of discussions about supernatural beings given your rather forthright stance on the absence of any link between the two. Not to mention the rampant accusations of "lying" that were made by you when it was suggested you might be making just such a connection to support your pro-supernaturalist arguments.
RAZD rather beligerently writes:
NEWS FLASH:
RAZD ARGUMENT ON THE VALUE OF SUBJECTIVE EVIDENCE HAS NOTHING TO DO WITH DEITIES!!!
.... for more on a logical argument regarding the value of subjective evidence that has nothing to do with deities stay tuned for more of my posts ....
Message 402
In the context of the great debate at hand the question of course is whether or not supernatural beings can legitimately be concluded to be the cause of such experiences.
To conclude supernatural causes for such human experiences is in itself an evidentially baseless conclusion. And one that flies in the face of all of the historical and psychological evidence regarding mankinds tendencies in this area.
In fact the whole "subjective evidence" argument amounts to nothing more than citing belief itself as a form of evidence.

This message is a reply to:
 Message 813 by RAZD, posted 02-03-2011 10:20 PM RAZD has replied

Replies to this message:
 Message 955 by Blue Jay, posted 02-08-2011 3:59 PM Straggler has replied
 Message 956 by Jon, posted 02-08-2011 5:11 PM Straggler has replied
 Message 1005 by RAZD, posted 02-10-2011 2:25 PM Straggler has replied

Straggler
Member (Idle past 95 days)
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 949 of 1725 (603843)
02-08-2011 6:53 AM
Reply to: Message 923 by New Cat's Eye
02-07-2011 3:07 PM


Re: possibilities and probabilities
CS writes:
Its not that we simply have an absense of evidence for the pen, its that we have evidence of the empty desk.
Its not that we simply have an absense of evidence for supernatural beings, its that we have positive evidence of the human ability and inclination to invent such things.
Do you understand the difference between the theory that all supernatural concepts are derived from human imagination and the assertion that no supernatural beings exist?
Can you see how Bluegenes is talking about positive evidence for the former rather than playing the silly 'disprove' one god at a time that RAZ and Xongsmith seem determined to impose as necessary?
Can you see why the former approach is based on inductive scientific reasoning whilst the latter is just a debate tactic that amounts to nothing more than demanding that unfalsifiable beliefs be disproved?

This message is a reply to:
 Message 923 by New Cat's Eye, posted 02-07-2011 3:07 PM New Cat's Eye has not replied

Straggler
Member (Idle past 95 days)
Posts: 10333
From: London England
Joined: 09-30-2006


(1)
Message 950 of 1725 (603844)
02-08-2011 7:33 AM
Reply to: Message 819 by xongsmith
02-03-2011 11:15 PM


Re: The issue is settled?
X writes:
That is why Straggler's and bluegenes' hypothetical imagined beings are off topic.
Would you like to give us an example of a being that is not hypothetical or imagined and therefore is 'on-topic'?

This message is a reply to:
 Message 819 by xongsmith, posted 02-03-2011 11:15 PM xongsmith has replied

Replies to this message:
 Message 957 by xongsmith, posted 02-08-2011 5:49 PM Straggler has replied

Jon
Inactive Member


(1)
Message 951 of 1725 (603873)
02-08-2011 2:23 PM


Made up ≠ Non-existent!
That a concept is made up does not prevent said concept from existing, or even from being a part of the natural world (i.e., not supernatural).
Granted I am coming into this late, but it seems a bit silly to think we can disprove something merely by defining it in such a way that it is inherently disproven; and that is all it seems has been attempted:
Gods are made up; made up things don't exist; gods don't exist.
The error of this should be obvious.
Jon

Check out No webpage found at provided URL: Apollo's Temple!
Ignorance is temporary; you should be able to overcome it. - nwr

Replies to this message:
 Message 952 by Rahvin, posted 02-08-2011 2:43 PM Jon has replied
 Message 954 by Blue Jay, posted 02-08-2011 3:41 PM Jon has seen this message but not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 8.3


Message 952 of 1725 (603875)
02-08-2011 2:43 PM
Reply to: Message 951 by Jon
02-08-2011 2:23 PM


Re: Made up ≠ Non-existent!
That a concept is made up does not prevent said concept from existing, or even from being a part of the natural world (i.e., not supernatural).
Granted I am coming into this late, but it seems a bit silly to think we can disprove something merely by defining it in such a way that it is inherently disproven; and that is all it seems has been attempted:
Gods are made up; made up things don't exist; gods don't exist.
The error of this should be obvious.
You're absolutely right - even random guesses, completely made up ideas, can actually turn out to be relevant to reality.
But the issue isn't about proof or disproof. Nobody (that I'm aware of) thinks it's possible to actually prove that deities or any other made-up whatever do not exist. The simple fact is that what we think we know of reality is a small subset of the totality of reality, and even what we think we know isn't perfectly accurate.
Even if I see a pen on my desk, there's a chance I'm hallucinating, or that I'm trapped in the Matrix and the pen doesn't really exist, etc.
The real question is what's more likely.
When you completely make something up, how often does your fantasy translate into reality? What percentage of the time? Not reasoned predictions based on available evidence, but actual honest fantasy, where you make something up entirely in your mind? Even when your fantasy has some attachment to reality, how accurate is it?
Here's a test:
Draw a map. I have a place in mind, and I want you to draw a map of it. I'm not going to tell you what the place is, only that it's a real place in actual reality.
How likely is it that you'll draw anything even remotely like the place I've picked out? Sure, it's possiblethat by pure dumb luck or even some previously unknown mechanisms akin to psychic powers you could actually draw up a map that precisely or even slightly resembles the patch of reality I have in mind...but are you likely to?
Or is it more likely that whatever map you draw will have nothing at all to do with the actual territory?
Go ahead, though. Seriously, describe your map, and I'll tell you how accurately you've referred to my territory. We could even have all the participants join in, and see how often making things up actually correlates to reality.
(note - you and I have a similar basis of knowledge of reality. We both have access to tools like Google Earth. I've already told you that my territory is a real place; while you'll be making up your map, you're still drawing upon a wealth of information and prior probabilities in your guess. You actually have an infinitely greater chance of accurately mapping my territory than you would have a chance of completely making up a true total fantasy like the Flying Spaghetti Monster or the Invisible Pink Unicorn).

This message is a reply to:
 Message 951 by Jon, posted 02-08-2011 2:23 PM Jon has replied

Replies to this message:
 Message 953 by Jon, posted 02-08-2011 3:32 PM Rahvin has replied

Jon
Inactive Member


Message 953 of 1725 (603880)
02-08-2011 3:32 PM
Reply to: Message 952 by Rahvin
02-08-2011 2:43 PM


Re: Made up ≠ Non-existent!
The real question is what's more likely.
That question hardly seems relevant.
People accept as truth what they want to accept as truth; for some, probabilities figure into that; for others, they aren't important.
So who cares about what's likely? Statistics has little bearing on what is actual.
Jon

Check out No webpage found at provided URL: Apollo's Temple!
Ignorance is temporary; you should be able to overcome it. - nwr

This message is a reply to:
 Message 952 by Rahvin, posted 02-08-2011 2:43 PM Rahvin has replied

Replies to this message:
 Message 958 by Rahvin, posted 02-08-2011 6:00 PM Jon has replied

Blue Jay
Member (Idle past 2727 days)
Posts: 2843
From: You couldn't pronounce it with your mouthparts
Joined: 02-04-2008


Message 954 of 1725 (603881)
02-08-2011 3:41 PM
Reply to: Message 951 by Jon
02-08-2011 2:23 PM


Re: Made up ≠ Non-existent!
Hi, Jon.
Jon writes:
Gods are made up; made up things don't exist; gods don't exist.
The error of this should be obvious.
They haven't been using the strict rationalist approach to the debate that you describe here.
Rather, they've focused entirely on an empirical approach.
They haven't been focusing on showing that gods are made up: they've been focusing on showing that gods don't explain things that people say they explain, and concluding from that that gods are made up.
So, it's rather the reverse of the way you described it above:
Gods don't exist; things that don't exist are made up; gods are made up.
Okay, so it doesn't quite make sense backwards, but I think you get the idea.

-Bluejay (a.k.a. Mantis, Thylacosmilus)
Darwin loves you.

This message is a reply to:
 Message 951 by Jon, posted 02-08-2011 2:23 PM Jon has seen this message but not replied

Blue Jay
Member (Idle past 2727 days)
Posts: 2843
From: You couldn't pronounce it with your mouthparts
Joined: 02-04-2008


Message 955 of 1725 (603884)
02-08-2011 3:59 PM
Reply to: Message 948 by Straggler
02-08-2011 6:16 AM


Peanut Gallery of the Peanut Gallery
Hi, Straggler.
I would like to say that, by cutting and pasting excessive pyrotechnics from someone else's posts into your posts, you become just as guilty of excessive pyrotechnics as they are.
The exception is, of course, when the sample you cut-n-pasted from that someone else was actually cut-n-pasted by that someone else from one of their own earlier posts; in which case, you are guilty of exactly half the excessive pyrotechnics of that someone else.
But, ignoring the fact that this is incidentally just such a case, I still declare you guilty.
-----
Side Note: When stuff that happens in the Peanut Gallery thread draws gallery-style commentary itself (e.g., this post), maybe it's time to consider the possibility that the Peanut Gallery is no longer acting as a peanut gallery.

-Bluejay (a.k.a. Mantis, Thylacosmilus)
Darwin loves you.

This message is a reply to:
 Message 948 by Straggler, posted 02-08-2011 6:16 AM Straggler has replied

Replies to this message:
 Message 966 by Straggler, posted 02-09-2011 7:15 AM Blue Jay has replied

Jon
Inactive Member


Message 956 of 1725 (603888)
02-08-2011 5:11 PM
Reply to: Message 948 by Straggler
02-08-2011 6:16 AM


Literacy
Once again it seems you feel the need to raise the issue of subjective "evidence" in the context of a discussion about deities.
I'm confused, I thought RAZD made it clear that his discussion about subjective evidence has nothing to do with deities. Wasn't that the purpose of the News Flash that even you yourself quoted?
NEWS FLASH:
RAZD ARGUMENT ON THE VALUE OF SUBJECTIVE EVIDENCE HAS NOTHING TO DO WITH DEITIES!!!
.... for more on a logical argument regarding the value of subjective evidence that has nothing to do with deities stay tuned for more of my posts ....
Am I missing something here? Is RAZD telepathically communicating something to you without us, or even himself, being aware of it? If not, what makes you think his 'subjective evidence' talk has anything to do with 'deities'?
It's been made pretty clear that it doesn't.
Jon

Check out No webpage found at provided URL: Apollo's Temple!
Ignorance is temporary; you should be able to overcome it. - nwr

This message is a reply to:
 Message 948 by Straggler, posted 02-08-2011 6:16 AM Straggler has replied

Replies to this message:
 Message 965 by Straggler, posted 02-09-2011 7:12 AM Jon has replied

xongsmith
Member
Posts: 2587
From: massachusetts US
Joined: 01-01-2009
Member Rating: 7.0


Message 957 of 1725 (603892)
02-08-2011 5:49 PM
Reply to: Message 950 by Straggler
02-08-2011 7:33 AM


Re: The issue is settled?
Straggler writes:
X writes:
That is why Straggler's and bluegenes' hypothetical imagined beings are off topic.
Would you like to give us an example of a being that is not hypothetical or imagined and therefore is 'on-topic'?
Hey, I'm 5.7d. I dont think there is anything.
HOWEVER - just to throw some red meat onto the pile, YEAH:
Jesus Christ
I am certain there are some here in EvC who would argue that he is not hypothetical or made up.
I, like you & bluegenes, don't think there is anything more than subjective evidence supporting his existence. RAZD is most assuredly on our side as well.
But there are some here who disagree with us.

- xongsmith, 5.7d

This message is a reply to:
 Message 950 by Straggler, posted 02-08-2011 7:33 AM Straggler has replied

Replies to this message:
 Message 964 by Straggler, posted 02-09-2011 7:07 AM xongsmith has replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 8.3


Message 958 of 1725 (603894)
02-08-2011 6:00 PM
Reply to: Message 953 by Jon
02-08-2011 3:32 PM


Re: Made up ≠ Non-existent!
The real question is what's more likely.
That question hardly seems relevant.
People accept as truth what they want to accept as truth; for some, probabilities figure into that; for others, they aren't important.
So who cares about what's likely? Statistics has little bearing on what is actual.
Statistics in general is not relevant.
The subset of statistics known as probability is extremely relevant.
We can never be absolutely certain of anything. We're human; we can hallucinate, we can only draw conclusions from available data rather than all relevant data, the available data can be itself flawed, and so on.
Probability helps us determine which of all the myriad hypotheses are most likely to be true.
Now, in everyday life, most of us dont think that way; we have our internal set of beliefs about the world, some based on fact, some based on opinion, and some based on fiction, and we don;t really think about it more deeply than that.
But when you say "I believe that x is true," what you're actually saying is that "I estimate that the probability of x being true is greater than the probability that x is not true." For instance, I estimate that the probability that the Sun will rise in teh East tomorrow to be greater by far than the sum total of all alternatives, including that the Sun could rise in the North, or could not rise at all, etc. I estimate that the probability that the Sun will rise in the East tomorrow is so much greater than any of the alternatives that I consider all competing hypotheses to be absurd on the basis that the probability of any of them being true is infinitisimally small.
This is, of course, different from the other colloquial usage of the term "belief;" "I believe in democracy" means that I think democracy is good, and has nothing to do with whether or not I think democracy actually exists in reality or not.
We even have actual equasions to help us determine relative probabiltiies when we're trying to figure out how a given observation affects the likelihood of competing hypotheses being correct. One such is called Bayes Theorem, which states that the probability of a given hypothesis being the most accurate of all choices given a specific event is equal to the probability of that hypothesis being true prior to the event, multiplied by the probability of the event occurring if we assume that the hypothesis were true, divided by the probability of the event occurring across all competing hypotheses.
That's a lot of words. It looks more like this:
p(h|b)=p(h)*p(b|h)/p(b) Where:
p(h|b) is the probability of hypothesis h given event b
p(h) is the prior probability of hypothesis h, the probability that the hypothesis is true without considering event b.
p(b|) is the probability of event b occurring given that hypothesis h is true
and p(b) is the probability of event b occurring across all possible hypotheses
Typically we express the theorem once for each competing hypothesis, and figure out how a given event updates the likelihood of each. When an event (which can be an observation, or an experiment, etc) modifies the relative likelihoods of various competing hypotheses, we call it "evidence."
This is the rational and mathematically accurate way to gauge the appropriate strength of one's beliefs.
The more likely a given event is to occur given a specific hypothesis compared to how likely it is to occur across all competing hypotheses, the more likely that hypothesis is to be true if the event is observed. If an event can only happen if one single hypothesis is true, then that event would be extremely strong evidence for that hypothesis.
If an event is just as likely to happen whether the hypothesis is true or false, then p(b|h) will be equal to p(b), they'll cancel out of the equasion, and we'll be left with p(h|b) = p(h), which means the probability of hypothesis h doesn't change at all if event b happens. This is what we call "irrelevant information." The likelihood that the price of tea in China will be 5 Yen if the Sun rises in the South tomorrow is the same as if the Sun rises in the East, or West, or doesn't rise at all. That means that the price of tea in China is irrelevant to the various competing hypotheses regarding the Sun's rise tomorrow.
See how this works? It's the mathematical, fully verbose explanation of the normally intuitive process of determining one's beliefs...and it's far more consistent and accurate than human intuition.
Probability is absolutely relevant, even if most people don't typically think in those terms.

This message is a reply to:
 Message 953 by Jon, posted 02-08-2011 3:32 PM Jon has replied

Replies to this message:
 Message 959 by Jon, posted 02-08-2011 7:11 PM Rahvin has replied

Jon
Inactive Member


Message 959 of 1725 (603899)
02-08-2011 7:11 PM
Reply to: Message 958 by Rahvin
02-08-2011 6:00 PM


Re: Made up ≠ Non-existent!
Statistics in general is not relevant.
The subset of statistics known as probability is extremely relevant.
Sorry, but statistics and probability are only meant to describe reality; they do not define it.
What is probable or what is more likely has little bearing on what actually is.
Jon

Check out No webpage found at provided URL: Apollo's Temple!
Ignorance is temporary; you should be able to overcome it. - nwr

This message is a reply to:
 Message 958 by Rahvin, posted 02-08-2011 6:00 PM Rahvin has replied

Replies to this message:
 Message 960 by Rahvin, posted 02-08-2011 7:50 PM Jon has seen this message but not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 8.3


Message 960 of 1725 (603901)
02-08-2011 7:50 PM
Reply to: Message 959 by Jon
02-08-2011 7:11 PM


Re: Made up ≠ Non-existent!
Sorry, but statistics and probability are only meant to describe reality; they do not define it.
What is probable or what is more likely has little bearing on what actually is.
Perhaps you misunderstand.
Probability does not affect reality.
Bayes Theorem is just one of those tools we have to make our internal maps more accurately represent the territory of reality.
It's like any other form of math. Numbers don't create reality, but by using numbers to represent reality in a way that we can better organize and explain it, we can discern much, much more about the real world and how it behaves. What's more, we can actually use those predictions to test our hypotheses.
What exists in reality exists regardless of whether we use math or not, whether we believe it exists or not. Math just helps us map the territory.

This message is a reply to:
 Message 959 by Jon, posted 02-08-2011 7:11 PM Jon has seen this message but not replied

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