Originally posted by twhiteheadWhat if you got said wisdom on an infinitely wide bandwidth forum? Wouldn't that give you that infinite wisdom in an infinitely small amount of time?
It would take an infinite amount of time to share infinite wisdom. I don't think you are going to manage in one small YouTube video.
Originally posted by JS357Well, wisdom is to do with information and information is measured in bits, which makes it countable. Bandwidth is measured in frequency and as far as we know isomorphic to the reals - a countable infinity divided by an uncountable one comes out to zero. Although there's some controversy about whether space-time is continuous, if it is not then you have countable infinity divided by finite and it takes an infinitely long time.
Doesn't that depend on their respective aleph numbers (cardinality)?
Originally posted by DeepThoughtI wonder if the speed of light in a vacuum enters into the calculations. If there were a vacuum such as inside sunhouse's cranium perhaps wisdom would never penetrate.🙂
Well, wisdom is to do with information and information is measured in bits, which makes it countable. Bandwidth is measured in frequency and as far as we know isomorphic to the reals - a countable infinity divided by an uncountable one comes out to zero. Although there's some controversy about whether space-time is continuous, if it is not then you have countable infinity divided by finite and it takes an infinitely long time.
Originally posted by DeepThoughtNot so. Just because computer programmers like to measure information in bits doesn't mean information is inherently countable. It only means computers can only store countable information.
Well, wisdom is to do with information and information is measured in bits, which makes it countable.
Bandwidth is measured in frequency and as far as we know isomorphic to the reals - a countable infinity divided by an uncountable one comes out to zero. Although there's some controversy about whether space-time is continuous, if it is not then you have countable infinity divided by finite and it takes an infinitely long time.
If spacetime is continuous then the information carried in a photon could be uncountably infinite.
Originally posted by twhiteheadSince we are talking about wisdom the relevant type of information is a string of symbols and that is countable. Even if the information is continuous it can still measured in bits, it just depends on whether you take your log relative to base 2 or use a natural logarithm when it's Boltzmann's constant in natural units.
Not so. Just because computer programmers like to measure information in bits doesn't mean information is inherently countable. It only means computers can only store countable information.
[b]Bandwidth is measured in frequency and as far as we know isomorphic to the reals - a countable infinity divided by an uncountable one comes out to zero. Althou ...[text shortened]... spacetime is continuous then the information carried in a photon could be uncountably infinite.
Originally posted by DeepThoughtBut the final digit of e has not been revealed.
Since we are talking about wisdom the relevant type of information is a string of symbols and that is countable. Even if the information is continuous it can still measured in bits, it just depends on whether you take your log relative to base 2 or use a natural logarithm when it's Boltzmann's constant in natural units.
Originally posted by DeepThoughtWhy? Explain your reasoning rather than just stating it as fact. I see no reason why wisdom must be either in strings or countable.
Since we are talking about wisdom the relevant type of information is a string of symbols and that is countable.
Even if the information is continuous it can still measured in bits,
No, it can't. The reals are not countable.
it just depends on whether you take your log relative to base 2 or use a natural logarithm when it's Boltzmann's constant in natural units.
I don't understand. Please expand on that. How would you store PI in bits?
Originally posted by twhiteheadHow do you communicate wisdom? Language consists of words that can be mapped to symbols in one way or another and so that information is at most countably infinite. Entropy is a measure of information, it's defined as the sum over states of the probability of a state times the log of the probability of a state. The choice of base affects the units that the resultant measure of entropy has, in base 2 that comes out in bits. If the variable that is the information carrier can vary continuously the result need not be an integer. So the bit "count" doesn't have to be an integer.
Why? Explain your reasoning rather than just stating it as fact. I see no reason why wisdom must be either in strings or countable.
[b]Even if the information is continuous it can still measured in bits,
No, it can't. The reals are not countable.
it just depends on whether you take your log relative to base 2 or use a natural logarithm when ...[text shortened]... n natural units.
I don't understand. Please expand on that. How would you store PI in bits?[/b]