Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9162 total)
1 online now:
Newest Member: popoi
Post Volume: Total: 915,817 Year: 3,074/9,624 Month: 919/1,588 Week: 102/223 Day: 0/13 Hour: 0/0


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   0.99999~ = 1 ?
onifre
Member (Idle past 2951 days)
Posts: 4854
From: Dark Side of the Moon
Joined: 02-20-2008


Message 166 of 237 (544424)
01-26-2010 8:54 AM
Reply to: Message 164 by Dr Adequate
01-26-2010 6:24 AM


But even then, I don't think that it's particularly a hazard for creative people.
Not true, there are studies that have shown a correlation between creativity and Bipolar disorders.
Hypomania:
quote:
A number of people with creative talents have reportedly experienced hypomania or other symptoms of bipolar disorder and attribute their success to it.
In the hypomanic state, people may feel that they cannot slow their minds down, and that their speeding thoughts are crafted exceptionally well. Some examples are speaking or writing in rhyme or alliteration without planning it first; quick responses to people talking; or the ability to improvise easily.
Hypomania appears to be found disproportionately in successful people, especially those in the arts.
Don't ask why I know this.
Sorry for off-topic reply.
- Oni

This message is a reply to:
 Message 164 by Dr Adequate, posted 01-26-2010 6:24 AM Dr Adequate has replied

Replies to this message:
 Message 167 by Dr Adequate, posted 01-26-2010 11:03 AM onifre has replied

  
Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 167 of 237 (544430)
01-26-2010 11:03 AM
Reply to: Message 166 by onifre
01-26-2010 8:54 AM


Not true, there are studies that have shown a correlation between creativity and Bipolar disorders.
But what you have quoted is something beginning: "A number of people with creative talents have reportedly experienced hypomania".
OK, what proportion of people "with creative talents" (how is this quantified?) have "reportedly experienced hypomania", and what proportion of people without creative talents have "reportedly experienced hypomania"?

This message is a reply to:
 Message 166 by onifre, posted 01-26-2010 8:54 AM onifre has replied

Replies to this message:
 Message 171 by onifre, posted 01-26-2010 1:29 PM Dr Adequate has not replied

  
AnswersInGenitals
Member (Idle past 151 days)
Posts: 673
Joined: 07-20-2006


Message 168 of 237 (544437)
01-26-2010 12:26 PM
Reply to: Message 161 by Rrhain
01-26-2010 2:13 AM


Trying to set things straight.
Let's use 0.9(n) to designate the number with n 9's after the decimal point (followed by zero's). Then, for any integer n, no matter how large, there is a number halfway between 0.9(n) and 1.0 that is different from 0.9(n) and 1.0. Thus, for all n, 0.9(n) and 1.0 are distinctly different numbers.
The error made in many of the above posts that try to prove that 0.99999.... is the same (is equal to) 1.0 is in confusing "converges to" and "is equal to". These are distinctly different attributes. In mathematical terms, the set of all 0.9(n) is an open set. Let's call this set SNo (for open set of strings of nines). !.0 lies on the boundary of this set but is not contained in it. Let SNc be the closure of SNo, i. e., the set SNo plus all its boundary points. This set does include 1.0 (and, of course, all the 0.9(n) for all n points), but it is distinct from (it is a different set than) SNo.
Now for a mea culpa. As erudite and definitive as the above sounds, there is a very good chance that I don't know what the hell I'm talking about. I'm really just throwing it out here to see if someone who does know what the hell they are talking about will comment on it.

This message is a reply to:
 Message 161 by Rrhain, posted 01-26-2010 2:13 AM Rrhain has not replied

Replies to this message:
 Message 169 by PaulK, posted 01-26-2010 12:48 PM AnswersInGenitals has not replied
 Message 170 by Dr Adequate, posted 01-26-2010 1:00 PM AnswersInGenitals has not replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 169 of 237 (544443)
01-26-2010 12:48 PM
Reply to: Message 168 by AnswersInGenitals
01-26-2010 12:26 PM


Re: Trying to set things straight.
quote:
The error made in many of the above posts that try to prove that 0.99999.... is the same (is equal to) 1.0 is in confusing "converges to" and "is equal to".
I don't think so. 0.999... IS the limit of 0.9(n) as n tends to infinity, and that is what we want to prove equal to 1. It's the series which converges to 1, not the number.
(That's not to say that there might not be similar confusion in some of the posts).

This message is a reply to:
 Message 168 by AnswersInGenitals, posted 01-26-2010 12:26 PM AnswersInGenitals has not replied

  
Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 170 of 237 (544444)
01-26-2010 1:00 PM
Reply to: Message 168 by AnswersInGenitals
01-26-2010 12:26 PM


Re: Trying to set things straight.
Now for a mea culpa. As erudite and definitive as the above sounds, there is a very good chance that I don't know what the hell I'm talking about.
This.
You might want to look up the term "open set".

This message is a reply to:
 Message 168 by AnswersInGenitals, posted 01-26-2010 12:26 PM AnswersInGenitals has not replied

  
onifre
Member (Idle past 2951 days)
Posts: 4854
From: Dark Side of the Moon
Joined: 02-20-2008


Message 171 of 237 (544446)
01-26-2010 1:29 PM
Reply to: Message 167 by Dr Adequate
01-26-2010 11:03 AM


Left brained creativity
OK, what proportion of people "with creative talents" (how is this quantified?) have "reportedly experienced hypomania"
Since this is off-topic I figured you'd check out the link, which answered this question.
quote:
Famous individuals with hypomanic symptoms
Hypomania appears to be found disproportionately in successful people, especially those in the arts.
List of people affected by bipolar disorder: This is a list of people accompanied by verifiable source citations associating them with bipolar disorder (formerly known as "manic depression"). This list includes only: a) deceased persons; and b) living persons who have been frank about their condition. It does not include speculation about status of living people who have not publicly stated themselves to have bipolar disorder.
Obviously, due to privacy, hard numbers are not going to be available. We can only go with those who have publicly stated it.
The main point was in the symptoms, which, by understanding the symptoms, it should be easy to see the correlation between bipolar/hypomanic disorder and artists/creativity.
quote:
Symptoms:
Classic symptoms of hypomania include mild euphoria, a flood of ideas, endless energy, and a desire and drive for success.
In the hypomanic state, people may feel that they cannot slow their minds down, and that their speeding thoughts are crafted exceptionally well. Some examples are speaking or writing in rhyme or alliteration without planning it first; quick responses to people talking; or the ability to improvise easily.
People with hypomania are generally perceived as being energetic, euphoric, visionary, overflowing with new ideas, and sometimes over-confident and very charismatic, yet--unlike those with full-blown mania--are sufficiently capable of coherent thought and action to participate in everyday activities. A person in the state of hypomania might be immune to fear and doubt and have little social inhibition. People experiencing hypomania are often the "life of the party."
Radiohead front man Thom Yorke reportedly responded, "Hypomania? Yes, that's exactly what it was," when asked about his mental state after the release of the group's album OK Computer. Iggy Pop was diagnosed with hypomania during his stay in a mental hospital in the mid-1970s. It has also been suggested that Richey Edwards, the "fatalistic Manic Street Preacher" (Mojo, 2003), and the late Syd Barrett of the band Pink Floyd have experienced hypomania. In the biographical documentary An Unreasonable Man, Ralph Nader is described as having hypomania.
Evidence Linking Mania and Hypomania to Creativity:
From link:
quote:
Many artist, musicians, and writers have been diagnosed with bipolar or some other affective disorder during or after life: F. Scott Fitzgerald, Ernest Hemmingway, Samuel Clemens (Mark Twain), Ralph Waldo Emerson, Virginia Woolf, George Fredrick Handel, Robert Schumann, Peter Tchaikovsky, Kurt Cobain (Nirvana), Lord Byron, Emily Dickenson, John Keats, Alfred Lord Tennyson, and Vincent van Gogh. Other famous people like Patty Duke, Kitty Dukakas, Ted Turner and Robin Williams are currently living with bipolar disorder.
-furthermore-
Kreaplin (1921) hypothesized that mania might bring about changes in thought processes that would result in increased creativity of thinking; and his study suggest that mania can produce qualitative changes in thinking (ideas produced) (Weisberg, 1994).
Andreason (1970) completed the first study of mania and creativity using structured interview, matched control groups and strict diagnostic criteria. She found a high occurrence of mood disorder in the thirty creative writers she examined. Eighty percent had experienced at least one episode of major depression, mania or hypomania, and forty-three percent had a history of hypo manic or manic episodes. First degree relatives of the writers generally performed more creative work and often had mood disorders (Jamison, 1987, Fodor, 1999, Ghadirian et al., 2000).
-furthermore-
Richards and Kinney (1990) studied the relationship between mood disorder and creativity and found that fifty percent of bipolar groups experience greatest creativity when in mildly high mood states (Richards and Kinney, 1990).
Ludwig (1992) conducted an extensive biographical survey of 1,005 famous twentieth century artist, writers, and other professionals. Artist and writers experience and estimated three times the rate of psychosis, suicide attempts, mood disorders, and substance abuse than did comparably successful people in business, science, and public life. Poets were thirty times more likely to have had manic depressive illness than were their contemporaries and five times more likely to have taken their own life (Jamison, 1995).
Fodor (1998) found that students with high bipolar scores wrote about a peak performance obtained especially high Remote Associates Test scores in comparison with students in other conditions. The findings support the view that manic depressive inclination has a special benefit, namely higher creativity potential than what exist within the general population (Fodor, 1998).
Shapiro and Weisberg (1999) found the association between creativity and bipolar disorder is similar behavior symptoms . Scores were higher in those experiencing hypomania with no depression. Common behaviors found: cognitive abilities, lack of sleep, energy, impulsivity, bold attitudes, and depth of emotion (Shapiro and Weisberg, 1999).
And one more link, if you care to read it: Bipolar Disorder and the Creative Mind
quote:
It is clear that being bipolar does not mean that one will necessarily be creative. It is also clear that being bipolar is not a requisite for genius. However, Hagop S. Akiskal found that 9-10 percent of those bipolar patients he studied with less severe symptoms were artists and writers. The mind of a left-brained genius could be more vulnerable to mood swings, which manifest similarly to normal bipolar symptoms. Therefore the symptoms would not exist in all geniuses but in many. The connections in the brain that cause this genius may be different from those who express right brained talents. This would explain why geniuses in other fields do not show the same symptoms. It would also keep the link between mania and creativity that Ludwig's argument does not.
Left brained creativity could be a vulnerability factor to developing symptoms of bipolar disorder. Studies present a seemingly clear link between bipolar disorder and artistic creativity. This would account for the reason other individuals in creative fields, such as science, do not show the same results. Because talent is often focused, it is unlikely that a manic individual chooses art. Because not all bipolar minds are creative but many creative minds are bipolar, it seems likely that bipolar disorder generates vulnerability for bipolar symptoms. Because it is only a vulnerability factor, many people will not suffer from it while still having talent.
Not to drag this further off-topic, but from the above, you don't think there is enough evidence to suggest a correlation?
- Oni

This message is a reply to:
 Message 167 by Dr Adequate, posted 01-26-2010 11:03 AM Dr Adequate has not replied

  
Jon
Inactive Member


Message 172 of 237 (544457)
01-26-2010 3:07 PM
Reply to: Message 144 by Stile
01-25-2010 9:27 AM


Re: Real Numbers and Real Ity
Stile writes:
Jon writes:
1 = 3/3 = 1/3 + 2/3 = 0.3333| + 0.6666| = 0.9999| ≠ 1
I don't understand this.
You went logically along until the very end. I don't (logically) see any reason why you put a "≠" in instead of a "=" at the end. What would make you do so?
Yes. I was 'quoting' (sans-any-reasonable-indication-that-it-was-a-quote ) the paradoxical hypothetical that Dr. A had come up with (Message 119). My point was as Dr. A's point; in a system where 0.9999| ≠ 1, there is a paradox.
My extension of this was that Mother Nature doesn't have paradoxes in the first place that she must then fix with some 'distinctness' criteria that closes the paradox by equating the apparently unequal. But, I will not go further into this here, because I have started a (still un-promoted) topic (Message 1) which is meant to address the relationship of our Math system to Reality.
The rest of your post seems to have been based on your understandable misreading of my horribly ambiguous statement, and so I think we can discount it.
Thanks,
Jon

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 144 by Stile, posted 01-25-2010 9:27 AM Stile has seen this message but not replied

  
Jon
Inactive Member


Message 173 of 237 (544476)
01-26-2010 6:04 PM
Reply to: Message 139 by Son Goku
01-25-2010 5:14 AM


Re: Totally right!
The fact that 0.999.. < 1.1 shows that it cannot grow to infinity.
I think there is a fine difference between growing to infinity and infinitely growing. I would say that the latter is possible in respects 0.9, etc., while still maintaining it has a value less than 1.0. Afterall, the number we are working with is infinite, is it not? With no proof eliminating infiniteness (not quite the same as infinity, I don't think), starting with 0.0 and adding the 0.9 cuts the remaining distance between 0.0 & 1.0 to 1/10 its previous size, no?
1.0 - 0.0 = 1.0
1.0 - 0.9 = 0.1
(1/10)(1.0) = 0.1
0.1 is 1/10 of 1.0
Now, if we add another 9, so 0.99, the remaining 1/10 distance is cut itself to 1/10 of its former size. I won't do the proof for that, but it seems more intuitive to me that as we added 9s, the distance between 1.0 and 0.0 would simply become infinitely smaller, but never be a gap bridgeable through the adding of infinite 9s or without rounding. (I hear the word 'Zeno' being whispered in my ear, but I am not sure why.) It seems that left as it is, Math can end up describing a paradoxical nature... or, a reality that is not Reality.
I see no reason why Math could not permit such infinite divisions in contradiction to Reality, which clearly does not. (Damn, there's that 'Zeno' whisper sound again.) Now, I realize that it doesn't work this way, and so long as the MATHSYSTEM maintains the DISTINCTness criterion it too will not permit such infiniteness. But that it needs a check-sub-system to eliminate contradictions with Reality should be a good sign that the MATHSYSTEM and its parts do not follow necessarily from Reality (REALWORLDSYSTEM), just that we have found a way to make the system both internally consistent and eliminate its contradictions to Reality. Anyway, more on this relationship when my dern thread gets (if ever) promoted.
Jon
Edited by Jon, : zeros and such

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 139 by Son Goku, posted 01-25-2010 5:14 AM Son Goku has not replied

Replies to this message:
 Message 175 by lyx2no, posted 01-26-2010 7:49 PM Jon has not replied
 Message 176 by Dr Adequate, posted 01-26-2010 8:03 PM Jon has replied
 Message 183 by Rrhain, posted 01-27-2010 2:45 AM Jon has not replied

  
Apothecus
Member (Idle past 2411 days)
Posts: 275
From: CA USA
Joined: 01-05-2010


Message 174 of 237 (544483)
01-26-2010 6:44 PM
Reply to: Message 157 by RAZD
01-25-2010 6:29 PM


Re: ~ to the 10th power?
It might be interesting to see how people think which explanations are the ones that best convince them -- Huntard and Straggler and any other lurkers who had trouble with this issue.
Aside from a couple off-topic posts, I've lurked here for a while. With regard to this thread, it seems to me that in order to not be found at night in a deserted lot in Chippewa Falls, naked, shivering, malnourished and bleeding from multiple self-inflicted shiv gashes, you need to fall into one of the following categories:
1. Geniune, honest mathematician
2. Not a mathematician, but still really smart with things like physics or drink mixology
3. Not a mathematician but with a rudimentary grasp of calculus or other maths (thus not too intellectually invested in your own opinion either way)
4. Don't care, but like to rattle the animals' cages all the same
I think I fall somewhere in the #3 category. I can grasp the concept as put forth, and since I'm blatantly ignorant to most of the rationale for objecting to why 0.9999.... should not equal 1, I can happily whistle "Bolero" as I scroll through this thread. It seems like a very straightforward idea on the surface, and as a committed #3, the surface is all I really care to see.
Thanks for this discussion.
Have a good one.

This message is a reply to:
 Message 157 by RAZD, posted 01-25-2010 6:29 PM RAZD has seen this message but not replied

Replies to this message:
 Message 177 by Jon, posted 01-26-2010 8:05 PM Apothecus has seen this message but not replied

  
lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 175 of 237 (544491)
01-26-2010 7:49 PM
Reply to: Message 173 by Jon
01-26-2010 6:04 PM


Re: Totally right!
Is Zeno by any chance whispering "For get about that turtle race thing: I was wrong."? Zeno couldn't solve it, but a lot of maths have been discovered since his day.
Now, if we add another 9, so 0.99, the remaining 1/10 distance is cut itself to 1/10 of its former size. I won't do the proof for that
A proof for that? You are so out of your league.

You are now a million miles away from where you were in space-time when you started reading this sentence.

This message is a reply to:
 Message 173 by Jon, posted 01-26-2010 6:04 PM Jon has not replied

  
Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 176 of 237 (544493)
01-26-2010 8:03 PM
Reply to: Message 173 by Jon
01-26-2010 6:04 PM


Re: Totally right!
I think there is a fine difference between growing to infinity and infinitely growing. I would say that the latter is possible in respects 0.9, etc., while still maintaining it has a value less than 1.0. Afterall, the number we are working with is infinite, is it not?
NO.
I see no reason why Math could not permit such infinite divisions in contradiction to Reality, which clearly does not. (Damn, there's that 'Zeno' whisper sound again.) Now, I realize that it doesn't work this way, and so long as the MATHSYSTEM maintains the DISTINCTness criterion it too will not permit such infiniteness. But that it needs a check-sub-system to eliminate contradictions with Reality should be a good sign that the MATHSYSTEM and its parts do not follow necessarily from Reality (REALWORLDSYSTEM), just that we have found a way to make the system both internally consistent and eliminate its contradictions to Reality. Anyway, more on this relationship when my dern thread gets (if ever) promoted.
Pure gibberish.

This message is a reply to:
 Message 173 by Jon, posted 01-26-2010 6:04 PM Jon has replied

Replies to this message:
 Message 178 by Jon, posted 01-26-2010 8:13 PM Dr Adequate has replied

  
Jon
Inactive Member


Message 177 of 237 (544494)
01-26-2010 8:05 PM
Reply to: Message 174 by Apothecus
01-26-2010 6:44 PM


Re: ~ to the 10th power?
Apothecus from Minnesotecus writes:
... Chippewa Falls...
Hello my fellow Minnesotan Always good to be able to add some more cold, frigid sanity around here
Jon

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 174 by Apothecus, posted 01-26-2010 6:44 PM Apothecus has seen this message but not replied

  
Jon
Inactive Member


Message 178 of 237 (544495)
01-26-2010 8:13 PM
Reply to: Message 176 by Dr Adequate
01-26-2010 8:03 PM


Re: Totally right!
Afterall, the number we are working with is infinite, is it not?
NO.
It's not? How many decimal places does 0.9999| go out to?
Jon

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 176 by Dr Adequate, posted 01-26-2010 8:03 PM Dr Adequate has replied

Replies to this message:
 Message 179 by Dr Adequate, posted 01-26-2010 9:44 PM Jon has replied

  
Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 179 of 237 (544500)
01-26-2010 9:44 PM
Reply to: Message 178 by Jon
01-26-2010 8:13 PM


Re: Totally right!
It's not?
Of course not.
How many decimal places does 0.9999| go out to?
Infinitely many, of course.

This message is a reply to:
 Message 178 by Jon, posted 01-26-2010 8:13 PM Jon has replied

Replies to this message:
 Message 180 by Jon, posted 01-26-2010 11:05 PM Dr Adequate has not replied

  
Jon
Inactive Member


Message 180 of 237 (544530)
01-26-2010 11:05 PM
Reply to: Message 179 by Dr Adequate
01-26-2010 9:44 PM


Re: Totally right!
Dr. A writes:
It's not?
Of course not.
How many decimal places does 0.9999| go out to?
Infinitely many, of course.
Care to explain?

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 179 by Dr Adequate, posted 01-26-2010 9:44 PM Dr Adequate has not replied

Replies to this message:
 Message 181 by bluescat48, posted 01-26-2010 11:37 PM Jon has not replied
 Message 184 by Rrhain, posted 01-27-2010 2:57 AM Jon has not replied
 Message 194 by xongsmith, posted 01-27-2010 12:07 PM Jon has not replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024