4 ms·

It's not a very useful number. The name is very misleading because it uses the wrong prefix, and why is having a word for this particular number valuable? Just

by xlnt 18y ago

It's not a very useful number. The name is very misleading because it uses the wrong prefix, and why is having a word for this particular number valuable? Just say a googolplex+100 instead on the very rare occasions you want to refer to this particular number.

jsomers 18y ago
This is how one spoils a playful idea, and how imaginations fade.
- xlnt 18y ago
  Telling children the truth helps them learn to have genuinely good ideas. Lying to them to avoid hurting their feelings implies there is some reason they should feel bad or discouraged about making a mistake like this. There isn't.
  - iamdave 18y ago
    However I think we should applaud the lad for taking such a keen interest in mathematics at such an age, and having a willingness to expand his mind by way of creativity. Usefulness or not, he's showing the signs of a thinking man in the works.
    - xlnt 18y ago
      Yes. If I had an idea, and someone explained to my why it's no good, I'd be very pleased. I'd be glad they replied and told me something I didn't know. I'd consider it a reward; and a much more useful one than applause. I think that's the most sensible way to feel: applause is OK, but serious replies are even nicer.
      - LPTS 18y ago
        (kissing more of my karma away for saying true things) That's textbook autistic thinking. Almost verbatim, that's the difference between autistic and non autistic responses to praise. You are completely justified in thinking that way about yourself (and I think the same thing). But you also have to realize most people's brains aren't wired that way. Especially children who are also engaged in things like spontaneous sharing.
        xlnt 18y ago
        Why is autism called a mental illness if rational thinking is a textbook example? Anyhow, I agree that you should make personality-appropriate comments that the child will appreciate. (I upvoted all your comments in this thread now. Please don't worry about karma.)
        LPTS 18y ago
        Because autism involves (most likely) a deficiency in the mirror neurons which do not allow the children to learn from mimicking the social interaction of others. It's theorized that sometimes these deficient mirror neurons get replaced by other skills and pre-sensory processing, like logic, music, perfect pitch, etc, in the same way that some blind people have phenomenal hearing. Also it's debilitating for a lot of people, many of whom lack so many mirror neurons they never learn how to communicate.
        xlnt 18y ago
        As I understand it, "mirror neurons" are a silly idea. Researchers noticed that people, for example, running, and people observing running, have similar brain activity. Why might that be? Well, they say that certain neurons somehow mimic what one observes. They imply these neurons are somewhat autonomous. But there's another rather obvious possibility: the person running, and the person watching running, were both thinking about running. Their brain activity was similar because they were thinking about the same thing.
        LPTS 18y ago
        You don't understand it at all. The idea of mirror neurons is well proven. The only thing left to understand is if the mirror neuron problems result from or cause the autistic spectrum. It's not true that for two people thinking the same thing, their brain scan looks the same, so your intuition is flawed. They are sure mirror neurons exist, and they know where in the brain they are.
        18y ago
- gojomo 18y ago
  Then again, reflexive praise regardless of the merits of a child's idea can be harmful, too... "How Not to Talk to Your Kids: The inverse power of praise" http://nymag.com/news/features/27840/ http://nymag.com/news/features/27840/
  - hugh 18y ago
    Agreed. I suppose the important thing is to give praise in the right way. I think ideally praise should be phrased in such a way that gives them some gratification for doing what they've done, while challenging them to see if they can do something more. In this case, the kid has exercised enough creativity to realise that he can make up his own numbers, but not enough critical thinking to realise that the space of large numbers is huge enough that not every number should have a special name. Ideally, you'd want to use this as an opportunity to challenge the kid to see if he can work this out for himself. Ask him what other numbers he can think of, like a googolplex plus a thousand, or a googolplex minus one hundred, and see if he can figure out that there are far more numbers than there could possibly be catchy names for. Since the "interestingness" of that particular large number is apparent only in base ten, you could even use this as an opportunity to introduce him to other bases (or better still, to see if he can surmise their existence for himself).
- jraines 18y ago
  I think you can impart reason and judgment without killing imagination.
  - LPTS 18y ago
    Not in a six year old. It's called child development. Heard of it? Because if the child isn't old enough to gain reason and judgement you are just killing creativity, for no benefit. What age do reason and judgement hone to the right degree? Not 6, thats for damn sure. This is depressing. I could just see jraines and xlnt with a toddler. xlnt: "Now, Joey, it's Da-dee, not da-da. It's important to pronounce things preciesly" jraines: "I think you can impart precision without killing the kids language skills"
    - xlnt 18y ago
      When I was 4 I liked chess. By the time I was 6 I reasonably often beat my parents at chess, and had improved quite a lot. Doesn't chess require reason and judgment?
      - LPTS 18y ago
        Another textbook autistic trait. This kid isn't wired like you. Normal children do not have those reasoning abilities at that age. You can't reasonably project from your experience to his, but are more likely to, because that's how people with autistic traits relate.
        xlnt 18y ago
        The original poster did not say how this child is wired. I think that parental expectations of children to dislike criticism is a large factor in why they usually grow up to dislike it.
        LPTS 18y ago
        The original poster indicated the child was engaged in spontaneous sharing, which indicates the child isn't on the spectrum. (Spontaneous sharing requires an ability to model the reaction of the person you share with, which requires the mirror neurons thought to be deficient in the autistic spectrum) Again, (and I don't mean any of this to sound harsh) your thoughts are not too relevant, because you can't use your kind of reasoning here. My dad (who is on the spectrum) ended up being horribly abusive to me throughout my childhood and teenage years because of thinking a lot like this. I don't want to conflate you and him, just to warn you that there is a really big trap it's easy for people with your personality traits to fall into around being overly logical, the projection that people with deficient mirror neurons have to resort to for relating to people, and how to treat and raise kids. You should recognize that you need the help of a person who doesn't share your mind-blindness to make appropriate judgements about children and how to relate to them. You absolutely cannot figure out how to treat kids on your own if you are on the spectrum. Using your logic, you should recognize it doesn't apply, and that you need a tool that isn't in your toolbox. Either a person who does have that skill who you listen to, or enough study of child psychology to reason your way to the right way to treat neurotypical kids.
- walterk 18y ago
  In this situation, there are things worth reinforcing (playing with language, initiative to name things, thinking about numbers), and some things that are not (false hopes of 'quadrupillion' becoming the next 'googol', or that significant contributions can be made so easily--the whole googol thing was serendipitous, not meritorious). It's a tricky situation, and I'm not sure what the best way to handle it is. But neither blind, effusive praise nor cold, harsh rejection are the best ways to go, here. If you had to pick one over the other, blind effusive praise it is, but there's definitely a middle ground here, one that selects for the things genuinely worth encouraging.
- jrockway 18y ago
  But hey, at least he proved on a web forum how he's smarter than a 6-year-old!
walterk 18y ago
Agreed, as a number it's not terribly useful, and in fact counterproductive for the reasons xlnt describes. Obviously you probably don't want to tell your son that, but as gojomo cautions, you might not want to praise him for it, either. (Edit: That is, if you do offer praise/encouragement, you'll want to do so in a way that avoids giving him false hopes that his number will become the next googol.) The thing is, simply naming a number isn't a great achievement, not even on the part of the mathematician's nephew who came up with 'googol'. It makes for an interesting story, but the thought processes involved are about as relevant to thinking mathematically as naming a pet dog is to understanding canine biology. But the initiative to name things is certainly valuable, and well worth reinforcing. The trick here is to lead your son towards an interest in the properties of numbers and away from any potential delusions of grandeur dependent on being the next 'googol' kid. Alternatively, or in concert with emphasizing the properties of numbers, you could also interest him in the properties of language and word construction, which he seems to have an aptitude for. Granted, your six year old would be pretty exceptional if you could get him interested in either!
LPTS 18y ago
You are very wrong about this xlnt. You should understand more about child development. It's a useful number because it gets a kid playing with math. Encourage them to teach themselves more about it, to play with it, but, for Christ's sake, do not give the child a terse answer more appropriate for a college student then a damn 6 year old. Your attitude is at the root of why the entire edifice of mathematics education to children is completely soul numbing.
- xlnt 18y ago
  I wasn't speaking to a child. I spoke about the content of the issue. What form to present it in, and which content the child would be interested to hear, is not my affair; it depends on the details of their situation and personalities. I cannot hope to comment accurately about that. Nor can you. In the future I would strongly encourage you to leave out remarks such as, "You should understand more about child development." I don't mind if you state that I'm wrong, for clarity, but you don't know anything about how many years I've spent learning about child development, or how much I know about it, so it's not wise to comment on that. PS I upmodded you back to 1. I don't think you intended to be hostile.
  - LPTS 18y ago
    Again, no offense, but the set of people who understand child development and the set of people who would say what you said do not intersect. So I can infer that you do not know child development.
    - xlnt 18y ago
      Sometimes unpopular ideas turn out to be true.
    - hugh 18y ago
      There are two questions here: (a) what's the actual value of this idea, and (b) what's the right thing to say to a child who has come up with an idea like this, in order to give them the correct amount of encouragement without over-praising them? As the cold-hearted over-educated curmudgeons of the internet, we're allowed to answer part (s) without worrying about part (b). The kid's dad has to worry about part (b) for himself, but I hope the kid's dad has enough perspective to realize the correct answer to part (a) is that it's worthless.

by xlnt 18y ago

jsomers 18y ago

This is how one spoils a playful idea, and how imaginations fade.

xlnt 18y ago
Telling children the truth helps them learn to have genuinely good ideas. Lying to them to avoid hurting their feelings implies there is some reason they should feel bad or discouraged about making a mistake like this. There isn't.
- iamdave 18y ago
  However I think we should applaud the lad for taking such a keen interest in mathematics at such an age, and having a willingness to expand his mind by way of creativity. Usefulness or not, he's showing the signs of a thinking man in the works.
  - xlnt 18y ago
    Yes. If I had an idea, and someone explained to my why it's no good, I'd be very pleased. I'd be glad they replied and told me something I didn't know. I'd consider it a reward; and a much more useful one than applause. I think that's the most sensible way to feel: applause is OK, but serious replies are even nicer.
    - LPTS 18y ago
      (kissing more of my karma away for saying true things) That's textbook autistic thinking. Almost verbatim, that's the difference between autistic and non autistic responses to praise. You are completely justified in thinking that way about yourself (and I think the same thing). But you also have to realize most people's brains aren't wired that way. Especially children who are also engaged in things like spontaneous sharing.
      - xlnt 18y ago
        Why is autism called a mental illness if rational thinking is a textbook example? Anyhow, I agree that you should make personality-appropriate comments that the child will appreciate. (I upvoted all your comments in this thread now. Please don't worry about karma.)
        LPTS 18y ago
        Because autism involves (most likely) a deficiency in the mirror neurons which do not allow the children to learn from mimicking the social interaction of others. It's theorized that sometimes these deficient mirror neurons get replaced by other skills and pre-sensory processing, like logic, music, perfect pitch, etc, in the same way that some blind people have phenomenal hearing. Also it's debilitating for a lot of people, many of whom lack so many mirror neurons they never learn how to communicate.
        xlnt 18y ago
        As I understand it, "mirror neurons" are a silly idea. Researchers noticed that people, for example, running, and people observing running, have similar brain activity. Why might that be? Well, they say that certain neurons somehow mimic what one observes. They imply these neurons are somewhat autonomous. But there's another rather obvious possibility: the person running, and the person watching running, were both thinking about running. Their brain activity was similar because they were thinking about the same thing.
        LPTS 18y ago
        You don't understand it at all. The idea of mirror neurons is well proven. The only thing left to understand is if the mirror neuron problems result from or cause the autistic spectrum. It's not true that for two people thinking the same thing, their brain scan looks the same, so your intuition is flawed. They are sure mirror neurons exist, and they know where in the brain they are.
        18y ago
gojomo 18y ago
Then again, reflexive praise regardless of the merits of a child's idea can be harmful, too... "How Not to Talk to Your Kids: The inverse power of praise" http://nymag.com/news/features/27840/ http://nymag.com/news/features/27840/
- hugh 18y ago
  Agreed. I suppose the important thing is to give praise in the right way. I think ideally praise should be phrased in such a way that gives them some gratification for doing what they've done, while challenging them to see if they can do something more. In this case, the kid has exercised enough creativity to realise that he can make up his own numbers, but not enough critical thinking to realise that the space of large numbers is huge enough that not every number should have a special name. Ideally, you'd want to use this as an opportunity to challenge the kid to see if he can work this out for himself. Ask him what other numbers he can think of, like a googolplex plus a thousand, or a googolplex minus one hundred, and see if he can figure out that there are far more numbers than there could possibly be catchy names for. Since the "interestingness" of that particular large number is apparent only in base ten, you could even use this as an opportunity to introduce him to other bases (or better still, to see if he can surmise their existence for himself).
jraines 18y ago
I think you can impart reason and judgment without killing imagination.
- LPTS 18y ago
  Not in a six year old. It's called child development. Heard of it? Because if the child isn't old enough to gain reason and judgement you are just killing creativity, for no benefit. What age do reason and judgement hone to the right degree? Not 6, thats for damn sure. This is depressing. I could just see jraines and xlnt with a toddler. xlnt: "Now, Joey, it's Da-dee, not da-da. It's important to pronounce things preciesly" jraines: "I think you can impart precision without killing the kids language skills"
  - xlnt 18y ago
    When I was 4 I liked chess. By the time I was 6 I reasonably often beat my parents at chess, and had improved quite a lot. Doesn't chess require reason and judgment?
    - LPTS 18y ago
      Another textbook autistic trait. This kid isn't wired like you. Normal children do not have those reasoning abilities at that age. You can't reasonably project from your experience to his, but are more likely to, because that's how people with autistic traits relate.
      - xlnt 18y ago
        The original poster did not say how this child is wired. I think that parental expectations of children to dislike criticism is a large factor in why they usually grow up to dislike it.
        LPTS 18y ago
        The original poster indicated the child was engaged in spontaneous sharing, which indicates the child isn't on the spectrum. (Spontaneous sharing requires an ability to model the reaction of the person you share with, which requires the mirror neurons thought to be deficient in the autistic spectrum) Again, (and I don't mean any of this to sound harsh) your thoughts are not too relevant, because you can't use your kind of reasoning here. My dad (who is on the spectrum) ended up being horribly abusive to me throughout my childhood and teenage years because of thinking a lot like this. I don't want to conflate you and him, just to warn you that there is a really big trap it's easy for people with your personality traits to fall into around being overly logical, the projection that people with deficient mirror neurons have to resort to for relating to people, and how to treat and raise kids. You should recognize that you need the help of a person who doesn't share your mind-blindness to make appropriate judgements about children and how to relate to them. You absolutely cannot figure out how to treat kids on your own if you are on the spectrum. Using your logic, you should recognize it doesn't apply, and that you need a tool that isn't in your toolbox. Either a person who does have that skill who you listen to, or enough study of child psychology to reason your way to the right way to treat neurotypical kids.
walterk 18y ago
In this situation, there are things worth reinforcing (playing with language, initiative to name things, thinking about numbers), and some things that are not (false hopes of 'quadrupillion' becoming the next 'googol', or that significant contributions can be made so easily--the whole googol thing was serendipitous, not meritorious). It's a tricky situation, and I'm not sure what the best way to handle it is. But neither blind, effusive praise nor cold, harsh rejection are the best ways to go, here. If you had to pick one over the other, blind effusive praise it is, but there's definitely a middle ground here, one that selects for the things genuinely worth encouraging.
jrockway 18y ago
But hey, at least he proved on a web forum how he's smarter than a 6-year-old!

walterk 18y ago

Agreed, as a number it's not terribly useful, and in fact counterproductive for the reasons xlnt describes. Obviously you probably don't want to tell your son that, but as gojomo cautions, you might not want to praise him for it, either. (Edit: That is, if you do offer praise/encouragement, you'll want to do so in a way that avoids giving him false hopes that his number will become the next googol.) The thing is, simply naming a number isn't a great achievement, not even on the part of the mathematician's nephew who came up with 'googol'. It makes for an interesting story, but the thought processes involved are about as relevant to thinking mathematically as naming a pet dog is to understanding canine biology. But the initiative to name things is certainly valuable, and well worth reinforcing. The trick here is to lead your son towards an interest in the properties of numbers and away from any potential delusions of grandeur dependent on being the next 'googol' kid. Alternatively, or in concert with emphasizing the properties of numbers, you could also interest him in the properties of language and word construction, which he seems to have an aptitude for. Granted, your six year old would be pretty exceptional if you could get him interested in either!

LPTS 18y ago

You are very wrong about this xlnt. You should understand more about child development. It's a useful number because it gets a kid playing with math. Encourage them to teach themselves more about it, to play with it, but, for Christ's sake, do not give the child a terse answer more appropriate for a college student then a damn 6 year old. Your attitude is at the root of why the entire edifice of mathematics education to children is completely soul numbing.

xlnt 18y ago
I wasn't speaking to a child. I spoke about the content of the issue. What form to present it in, and which content the child would be interested to hear, is not my affair; it depends on the details of their situation and personalities. I cannot hope to comment accurately about that. Nor can you. In the future I would strongly encourage you to leave out remarks such as, "You should understand more about child development." I don't mind if you state that I'm wrong, for clarity, but you don't know anything about how many years I've spent learning about child development, or how much I know about it, so it's not wise to comment on that. PS I upmodded you back to 1. I don't think you intended to be hostile.
- LPTS 18y ago
  Again, no offense, but the set of people who understand child development and the set of people who would say what you said do not intersect. So I can infer that you do not know child development.
  - xlnt 18y ago
    Sometimes unpopular ideas turn out to be true.
  - hugh 18y ago
    There are two questions here: (a) what's the actual value of this idea, and (b) what's the right thing to say to a child who has come up with an idea like this, in order to give them the correct amount of encouragement without over-praising them? As the cold-hearted over-educated curmudgeons of the internet, we're allowed to answer part (s) without worrying about part (b). The kid's dad has to worry about part (b) for himself, but I hope the kid's dad has enough perspective to realize the correct answer to part (a) is that it's worthless.