maths treats reality as being continuous, but that is only an approximation valid for large scales
mathematical physics is all just models that come closer and closer to describing reality, not really discovering laws that the universe somehow runs on... this is hard to explain but I'm sure you know what I'm getting at
point is all our tools are only really good at describing things on a human scale, quantum mechanics is on a tiny scale blah blah relativity big scale maths/physics is middle ground and ugh so tired it's 4am I'll come back to this if the thread is alive tomorrow
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
What is the difference between .99999.... and 1? Subtract .99999... from 1. You get 0. (There is no such number as .000000...0001)
And if you subtract a number from another number and get 0, then they are the same number.
Another term for subtraction is "difference". With .9999... and 1, the difference is 0 - literally, there is no (0) difference.
I think actually if subtract 0.999... from 1 you get an infinitesimal
Except if you think about it such numbers are impossible. You can't have an infinite number of something and then something else; because the very act of going to the something else makes the infinite thing not infinite.
If I give you an infinite number of pennies and then punch you in the face, will I ever punch you in the face? No.
I think it's hard for someone not to rage at mario kart, while shouting "Fuck you Donkey Kong. Whose dick did you suck to get all those red shells?"
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MorgensternICH BIN DER PESTVOGELDU KAMPFAFFE!Registered Userregular
edited February 2010
You get an infiniteismal 0.0000.............1
BLOWS THE MIND
Morgenstern on
“Every time we walk along a beach some ancient urge disturbs us so that we find ourselves shedding shoes and garments or scavenging among seaweed and whitened timbers like the homesick refugees of a long war.” - Loren Eiseley
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RobchamThe Rabbit Kingof your pantsRegistered Userregular
MorgensternICH BIN DER PESTVOGELDU KAMPFAFFE!Registered Userregular
edited February 2010
Yes, I know it's not infinite if it ends.
Morgenstern on
“Every time we walk along a beach some ancient urge disturbs us so that we find ourselves shedding shoes and garments or scavenging among seaweed and whitened timbers like the homesick refugees of a long war.” - Loren Eiseley
What is the difference between .99999.... and 1? Subtract .99999... from 1. You get 0. (There is no such number as .000000...0001)
And if you subtract a number from another number and get 0, then they are the same number.
Another term for subtraction is "difference". With .9999... and 1, the difference is 0 - literally, there is no (0) difference.
I think actually if subtract 0.999... from 1 you get an infinitesimal
Except if you think about it such numbers are impossible. You can't have an infinite number of something and then something else; because the very act of going to the something else makes the infinite thing not infinite.
If I give you an infinite number of pennies and then punch you in the face, will I ever punch you in the face? No.
Actually, there are differently sized infinities
For example the infinity of natural numbers is smaller than the infinity of real numbers
the .999... = 1 thing reminds me of a dude in my math class that couldn't understand that the number of numbers between 3 and 4 is the same as the number of numbers between negative infinity and positive infinity.
Because of atomic limitations or planck distance or something.
Like, there's a difference between real and physical, dude.
the .999... = 1 thing reminds me of a dude in my math class that couldn't understand that the number of numbers between 3 and 4 is the same as the number of numbers between negative infinity and positive infinity.
Because of atomic limitations or planck distance or something.
Like, there's a difference between real and physical, dude.
Actually
The number of numbers between 3 and 4 is greater than the infinity of natural numbers
The integers are a countable infinity
The numbers between 3 and 4 include irrational numbers and are therefore uncountably infinite
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
I don't think the usefulness of matrix mechanics at least is "weird" at all. Ultimately all those processes are complexity reductions (or convenience functions) for underlying equation solving, which again is only a convenience form for pattern analysis - so if you accept that the universe is not in fact random, which we must for the purpose of this discussion, then even when the exact deterministic method can't be found, patterns must exist, which beings us back to equations and matrices.
The whole countably infinite vs uncountably infinite is a pretty good proof that mathematics is bunk.
Right except that the countable/uncountable distinction has a core place in Gödel's incompleteness theorems that have all kinds of ramifications in 'real world' disciplines such as computer science
[edit]Well, rather, similar concepts to the countable/uncountable distinction, at least
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
I don't think the usefulness of matrix mechanics at least is "weird" at all. Ultimately all those processes are complexity reductions (or convenience functions) for underlying equation solving, which again is only a convenience form for pattern analysis - so if you accept that the universe is not in fact random, which we must for the purpose of this discussion, then even when the exact deterministic method can't be found, patterns must exist, which beings us back to equations and matrices.
I don't think it would be 'weird' if these 'pure' mathematical bits and pieces didn't then turn out to have predictive power
That is the crux of the weirdness
Not only does mathematics describe our observational results
It also predicts stuff we haven't observed yet
the .999... = 1 thing reminds me of a dude in my math class that couldn't understand that the number of numbers between 3 and 4 is the same as the number of numbers between negative infinity and positive infinity.
Because of atomic limitations or planck distance or something.
Like, there's a difference between real and physical, dude.
Actually
The number of numbers between 3 and 4 is greater than the infinity of natural numbers
The integers are a countable infinity
The numbers between 3 and 4 include irrational numbers and are therefore uncountably infinite
Right, sorry he was saying that uncountably infinite numbers were impossible.
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
I don't think the usefulness of matrix mechanics at least is "weird" at all. Ultimately all those processes are complexity reductions (or convenience functions) for underlying equation solving, which again is only a convenience form for pattern analysis - so if you accept that the universe is not in fact random, which we must for the purpose of this discussion, then even when the exact deterministic method can't be found, patterns must exist, which beings us back to equations and matrices.
I don't think it would be 'weird' if these 'pure' mathematical bits and pieces didn't then turn out to have predictive power
That is the crux of the weirdness
Not only does mathematics describe our observational results
It also predicts stuff we haven't observed yet
It's rad as hell, sure, but I don't know about "weird".
the .999... = 1 thing reminds me of a dude in my math class that couldn't understand that the number of numbers between 3 and 4 is the same as the number of numbers between negative infinity and positive infinity.
Because of atomic limitations or planck distance or something.
Like, there's a difference between real and physical, dude.
Actually
The number of numbers between 3 and 4 is greater than the infinity of natural numbers
The integers are a countable infinity
The numbers between 3 and 4 include irrational numbers and are therefore uncountably infinite
Right, sorry he was saying that uncountably infinite numbers were impossible.
Oh, yeah it's a difficult concept to grasp at first
I had an argument with a dude in my logic class about it after we looked at Cantor's argument
His point was that a countable infinity is pragmatically uncountable anyway so there's no difference
I think that a better description would be 'enumerable' infinity and 'innumerable' infinity
bongi on
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MorgensternICH BIN DER PESTVOGELDU KAMPFAFFE!Registered Userregular
edited February 2010
But when you do grasp the ide aof infinite numbers, you truly do have a Matrixesque type moment where there is no spoon.
It's a great feeling.
Morgenstern on
“Every time we walk along a beach some ancient urge disturbs us so that we find ourselves shedding shoes and garments or scavenging among seaweed and whitened timbers like the homesick refugees of a long war.” - Loren Eiseley
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
I don't think the usefulness of matrix mechanics at least is "weird" at all. Ultimately all those processes are complexity reductions (or convenience functions) for underlying equation solving, which again is only a convenience form for pattern analysis - so if you accept that the universe is not in fact random, which we must for the purpose of this discussion, then even when the exact deterministic method can't be found, patterns must exist, which beings us back to equations and matrices.
I don't think it would be 'weird' if these 'pure' mathematical bits and pieces didn't then turn out to have predictive power
That is the crux of the weirdness
Not only does mathematics describe our observational results
It also predicts stuff we haven't observed yet
There may be a very simple explanation for this phenomenon that we just can't see. Nature is full of phenomena that seem to be complex and mysterious but can actually have very simple rules governing them. For example, flocks of starlings or schools of fish moving in unison appears to require some higher organization that surely these simple beasts lack. But really the problem is simply one of perception. The behavior looks complex, so we tend to assume it is. However it's been shown that a few very simple rules can effectively lead to the same behavior. Here's one example I found with a quick search: http://www.red3d.com/cwr/boids/
I was talking about this with usagi last night. People trained in advanced mathematics that like to play around with it will often talk of the beauty of a particular set of numbers or a formula, and maybe this is just their finely tuned brain instinctively recognizing number sets or formulas that are likely to be useful even if they don't know what they're a solution for yet. Nothing mystical or even arguably weird, just a process that we don't fully understand yet.
Posts
it would still be less pepperoni than before! I don't about you, but I am pro more pepperoni.
mathematics and physics are becoming more closely and spookily entwined all the time
mathematical physics is all just models that come closer and closer to describing reality, not really discovering laws that the universe somehow runs on... this is hard to explain but I'm sure you know what I'm getting at
point is all our tools are only really good at describing things on a human scale, quantum mechanics is on a tiny scale blah blah relativity big scale maths/physics is middle ground and ugh so tired it's 4am I'll come back to this if the thread is alive tomorrow
kpop appreciation station i also like to tweet some
The success of ('pure' mathematical) symmetries in not only classifying known fundamental particles, but also in predicating the properties of unknown ones
Or the success of matrix mechanics in classifying quantum mechanical phenomena and predicting novel results
This is not really a question that I am expecting you to answer
It's fucking weird
And if you subtract a number from another number and get 0, then they are the same number.
Another term for subtraction is "difference". With .9999... and 1, the difference is 0 - literally, there is no (0) difference.
me
Tumblr blargh
I think actually if subtract 0.999... from 1 you get an infinitesimal
Except if you think about it such numbers are impossible. You can't have an infinite number of something and then something else; because the very act of going to the something else makes the infinite thing not infinite.
If I give you an infinite number of pennies and then punch you in the face, will I ever punch you in the face? No.
BLOWS THE MIND
I am the main wizard here
I train other wizards to wreck your shit
Tumblr blargh
Actually, there are differently sized infinities
For example the infinity of natural numbers is smaller than the infinity of real numbers
Because of atomic limitations or planck distance or something.
Like, there's a difference between real and physical, dude.
also used as an industrial solvent! and it's deadly if you inhale it!
Actually
The number of numbers between 3 and 4 is greater than the infinity of natural numbers
The integers are a countable infinity
The numbers between 3 and 4 include irrational numbers and are therefore uncountably infinite
I don't think the usefulness of matrix mechanics at least is "weird" at all. Ultimately all those processes are complexity reductions (or convenience functions) for underlying equation solving, which again is only a convenience form for pattern analysis - so if you accept that the universe is not in fact random, which we must for the purpose of this discussion, then even when the exact deterministic method can't be found, patterns must exist, which beings us back to equations and matrices.
CAANTOOOOOOORRR
The .99999... = 1 thing has been backed up by mathematicians, though, so I think I'll go with the experts and not random internet people. Sorry.
Right except that the countable/uncountable distinction has a core place in Gödel's incompleteness theorems that have all kinds of ramifications in 'real world' disciplines such as computer science
[edit]Well, rather, similar concepts to the countable/uncountable distinction, at least
I don't think it would be 'weird' if these 'pure' mathematical bits and pieces didn't then turn out to have predictive power
That is the crux of the weirdness
Not only does mathematics describe our observational results
It also predicts stuff we haven't observed yet
Right, sorry he was saying that uncountably infinite numbers were impossible.
it's funny when people get confused by that
it really makes perfect sense as long as you look at it logically
It's rad as hell, sure, but I don't know about "weird".
statement A: You are what you eat
Axiom X: bongi is a butt
Take axiom X. QED.
It all comes down to picking the right axioms.
does this mean that he eats assholes or that he eats buttcheekflesh
or both
ed: best totp or bestest totp
Oh, yeah it's a difficult concept to grasp at first
I had an argument with a dude in my logic class about it after we looked at Cantor's argument
His point was that a countable infinity is pragmatically uncountable anyway so there's no difference
I think that a better description would be 'enumerable' infinity and 'innumerable' infinity
It's a great feeling.
funnily enough I didn't really "get" infinity until an argument about
wait for it
the .99999... = 1 thing
There may be a very simple explanation for this phenomenon that we just can't see. Nature is full of phenomena that seem to be complex and mysterious but can actually have very simple rules governing them. For example, flocks of starlings or schools of fish moving in unison appears to require some higher organization that surely these simple beasts lack. But really the problem is simply one of perception. The behavior looks complex, so we tend to assume it is. However it's been shown that a few very simple rules can effectively lead to the same behavior. Here's one example I found with a quick search: http://www.red3d.com/cwr/boids/
I was talking about this with usagi last night. People trained in advanced mathematics that like to play around with it will often talk of the beauty of a particular set of numbers or a formula, and maybe this is just their finely tuned brain instinctively recognizing number sets or formulas that are likely to be useful even if they don't know what they're a solution for yet. Nothing mystical or even arguably weird, just a process that we don't fully understand yet.