You just know that, when you see it expressed in this particular form, that people who think this are bugmen who just read that this was supposed to be amazing because "it combines each of these constants in a single equation" or whatever.
Understanding how exponentiation can be generalized to complex numbers, and that the nature of e^πix can be shown to be equivalent to a combination of trigonometric functions through deriving their Taylor series, and hence that there is a single natural base of 'continuous change' that gives rise to both exponential growth and cyclic recurrence depending on whether it's exponent is altered in a real or imaginary direction, that is substantial mathematical knowledge that illustrates how e^x may be considered the most important function in mathematics.
e^iπ + 1 = 0 is a specific case derived from this that is presented in this odd way as some bizarre curiosity, while even the trivially equivalent e^iπ = -1 gives more substantial insight (i.e. that iπ gives a 'half twist' when given to the complex exponential function).
My favorite explanation of Euler's formula is one that uses vector calculus. We create a model of a particle moving through the imaginary plane with its position being equal to z(t) = e^it. The velocity of the particle is equal to d/dt e^it = i*e^it and its acceleration is d/dt i*e^it = -e^it. Since the act of multiplying by i is the same as rotating a point about the origin 90deg, you can envision the velocity as a vector perpendicular to the position and the acceleration as a vector pointing towards the origin. At t=0, z is 1 and the velocity points directly upward and as t increases, you can imagine the particle moving in uniform circular motion about the origin.
But you can prove this more rigorously by turning the problem into a fairly simple system of differential equations and solving it. This is I believe the system to be solved:
z'(t) = [0 -1; 1 0] z, with z(0)=[1 0].
Modern math is fake and gay. Read Guenon(PBUH). Imaginary numbers don't exist. Neither do the reals. Only the positive integers exist and they're not infinite.
>Only the positive integers exist and they're not infinite
If they're not infinite, what do you suppose the biggest positive integer is?
>If they're not infinite, what do you suppose the biggest positive integer is?
Read Guenon's The Metaphysical Principles of the Infinitesimal Calculus. The positive integers can't be infinite because there are things that aren't positive integers. The infinite encompasses everything. Modern math is illogical and stupid.
2 months ago
Anonymous
Anything but applied mathematics is stupid mathematics.
2 months ago
Anonymous
Stupid hylic you shouldn't bother with Guenon since you wouldn't understand. An obsession with applications is one of the hallmarks of the modern degeneration.
I fricking hate that identity. It is a breathing symbol of everything wrong with math. The preference for language over what language denotates. The stilted refusal to do things efficiently over preference for doing things according to rigid convention. Deep ignorance of WHERE the math being used from comes from and how to develop similarly important breakthroughs. You might as well have told me that mathematics as a whole is unworthy of continuing as a medium for the discovery and elaboration and overwhelming of reality. It's one of the worst things I've ever seen.
It's a Reddit preference for involution (内卷) over exploration and conquest. It makes me angry in my temples. It makes me feel homicidal.
Modern math is fake and gay. Read Guenon(PBUH). Imaginary numbers don't exist. Neither do the reals. Only the positive integers exist and they're not infinite.
>Imaginary numbers don't exist.
You're posting on a board that exists only as information on a server using a device charged with a current whose phase time was calculated by an electrical engineer using imaginary numbers all so you can enjoy watching the most autistic people in the world debate the finer points of German Idealism.
Why is pic related profound to you? I mean sure it is curious that we have this relationship between these numbers that are curious enough in their own right. But I think you misunderstand the meaning of the word "profound", haha.
Book 23 of the Odyssey. I prattle about it on here but the theme of Odysseus’ identity and his connection to Ithaca and Penelope, one which many would find tenuous but through which he is able to reclaim his throne. That book struck me like lightning.
The shit near the start of the Analects about how to weed out someone of filial character.
More the general idea that you can tell someone's character by everything they do that is *not* signalling, from their perspective, and that they do when there is no reward or cost either way.
It's so fricking true.
People give themselves away all the time (including exposing positive traits), but anything that's a pre-established signal that they're aware of is an unreliable indicator. But these "small" things that are imperceptibly small ARE the solid indicators.
>pretty but useless expression of a handful of irrational numbers
versus >gigachad paradigmatic reality-defining equation that ended fallacious assumptions that all the universe's secrets are just waiting to be conclusively known if only we can just be smart and learned enough
The later chapters of Stanley Milgram's book "obedience to authority, an experimental view" go a long way to explain the origin of most evil in the world, and his other writings are very revealing about the invisible forces governing social behavior in collectives. I'd highly recommend pic-related.
But in terms of sheer profundity, a lot of Ron Maimon's stuff. I like his physics and mathematics writing, but his brief writings about religion and philosophy reconfigured my entire way of looking at the world to the point where I no longer consider myself an atheist. In retrospect this feels pretty profound.
there's more elsewhere, but I saved the text to some of his stuff here:
https://dimnaut.info/ethics/introtogod.html
https://dimnaut.info/ethics/do-atheists-have-a-standard-definition-of-God-If-not-what-is-it-that-they-disbelieve.html
https://dimnaut.info/ethics/is-it-possible-to-describe-God-mathematically.html
https://dimnaut.info/ethics/if-a-cell-inside-human-body-had-consciousness-would-it-be-aware-of-the-larger.html
https://dimnaut.info/ethics/could-believers-with-strong-faith-in-God-sometimes-exhibit-behavior-similar-to-Stockholm-Syndrome.html
https://dimnaut.info/ethics/whats-it-like-to-have-a-transcendent-spiritual-experience.html
https://dimnaut.info/ethics/if-god-doesnt-exist-why-did-he-talk-to-me-last-night.html
https://dimnaut.info/ethics/what-is-the-message-behind-marquis-de-sades-120-days-of-sodom.html
here's some more of his stackexchange writing I saved
https://dimnaut.info/maimon/stackex/phil/philosophy.html
https://dimnaut.info/maimon/stackex/chris/christianity.html
can you touch the numbers? are they in the room with us now?
no, they at best share similar properties to the real world, the thing inside your computer is not ones and zeros, its electrons and copper, the programs you claim your computer runs are just diagrams of the actual movements in the steel
your fricking soul is a number your moron, it's number whose digits encode your brain's internal computation within some computing cellular automaton, say rule 110. That's you, and you think therefore you are.
you better make peace with the platonic realm, anon, you're part of it
my soul is a number?
e^my soul, gives a single, definitive value?
5(my soul) = something else?
well anon if something being representable implies it to be equitable, perhaps i ought introduce you to the image i found, that i think depicts our situation very well
1 month ago
Anonymous
>e^my soul, gives a single, definitive value >5(my soul) = something else?
yeah, relative to the rule 110 algorithm, it's a single number, just look at pic. The first line is a sequence of 1's and 0's, which is a single number. With enough memory and time, you can encode any computer program into that number and rule 110 will run it by computing the subsequent lines. Doing e^(that number) would just scramble it, multiplying it by something else would also scramble it, fricking obviously.
1 month ago
Anonymous
That's an analogous representation and it only represents one of three parts that constitute his soul.
You just know that, when you see it expressed in this particular form, that people who think this are bugmen who just read that this was supposed to be amazing because "it combines each of these constants in a single equation" or whatever.
Understanding how exponentiation can be generalized to complex numbers, and that the nature of e^πix can be shown to be equivalent to a combination of trigonometric functions through deriving their Taylor series, and hence that there is a single natural base of 'continuous change' that gives rise to both exponential growth and cyclic recurrence depending on whether it's exponent is altered in a real or imaginary direction, that is substantial mathematical knowledge that illustrates how e^x may be considered the most important function in mathematics.
e^iπ + 1 = 0 is a specific case derived from this that is presented in this odd way as some bizarre curiosity, while even the trivially equivalent e^iπ = -1 gives more substantial insight (i.e. that iπ gives a 'half twist' when given to the complex exponential function).
My favorite explanation of Euler's formula is one that uses vector calculus. We create a model of a particle moving through the imaginary plane with its position being equal to z(t) = e^it. The velocity of the particle is equal to d/dt e^it = i*e^it and its acceleration is d/dt i*e^it = -e^it. Since the act of multiplying by i is the same as rotating a point about the origin 90deg, you can envision the velocity as a vector perpendicular to the position and the acceleration as a vector pointing towards the origin. At t=0, z is 1 and the velocity points directly upward and as t increases, you can imagine the particle moving in uniform circular motion about the origin.
But you can prove this more rigorously by turning the problem into a fairly simple system of differential equations and solving it. This is I believe the system to be solved:
z'(t) = [0 -1; 1 0] z, with z(0)=[1 0].
>Only the positive integers exist and they're not infinite
If they're not infinite, what do you suppose the biggest positive integer is?
>If they're not infinite, what do you suppose the biggest positive integer is?
Read Guenon's The Metaphysical Principles of the Infinitesimal Calculus. The positive integers can't be infinite because there are things that aren't positive integers. The infinite encompasses everything. Modern math is illogical and stupid.
Anything but applied mathematics is stupid mathematics.
Stupid hylic you shouldn't bother with Guenon since you wouldn't understand. An obsession with applications is one of the hallmarks of the modern degeneration.
I fricking hate that identity. It is a breathing symbol of everything wrong with math. The preference for language over what language denotates. The stilted refusal to do things efficiently over preference for doing things according to rigid convention. Deep ignorance of WHERE the math being used from comes from and how to develop similarly important breakthroughs. You might as well have told me that mathematics as a whole is unworthy of continuing as a medium for the discovery and elaboration and overwhelming of reality. It's one of the worst things I've ever seen.
It's a Reddit preference for involution (内卷) over exploration and conquest. It makes me angry in my temples. It makes me feel homicidal.
>It's a Reddit preference for involution
Euler's formula is not an involution wtf are you talking about
I specifically posted the Chinese term to indicate the Chinese sense of the word.
Didn't know math worked differently in China.
e^i(e^ix) != x no matter where you're from
It's also a sociological term. https://en.wikipedia.org/wiki/Neijuan
this will niether put food food on the table, nor get u laid, so its just some pitiful surrogate activity
Didn't ask?
Gauss was an idiot
Modern math is fake and gay. Read Guenon(PBUH). Imaginary numbers don't exist. Neither do the reals. Only the positive integers exist and they're not infinite.
I'm more of a [1+5^(1/2)]/2 guy myself.
>Imaginary numbers don't exist.
You're posting on a board that exists only as information on a server using a device charged with a current whose phase time was calculated by an electrical engineer using imaginary numbers all so you can enjoy watching the most autistic people in the world debate the finer points of German Idealism.
Why is pic related profound to you? I mean sure it is curious that we have this relationship between these numbers that are curious enough in their own right. But I think you misunderstand the meaning of the word "profound", haha.
I think it’s the most profound thing I’ve ever seen, and I have no idea what it means. I’m pretty sure that nobody has any idea what it means.
Book 23 of the Odyssey. I prattle about it on here but the theme of Odysseus’ identity and his connection to Ithaca and Penelope, one which many would find tenuous but through which he is able to reclaim his throne. That book struck me like lightning.
it was compressed down to very little space linguistically speaking so i doubt if anyone would ever get it
Whatever arises in dependence,
that is explained to be emptiness;
that is a dependent designation,
that itself is the middle way.
The shit near the start of the Analects about how to weed out someone of filial character.
More the general idea that you can tell someone's character by everything they do that is *not* signalling, from their perspective, and that they do when there is no reward or cost either way.
It's so fricking true.
People give themselves away all the time (including exposing positive traits), but anything that's a pre-established signal that they're aware of is an unreliable indicator. But these "small" things that are imperceptibly small ARE the solid indicators.
https://readberserk.com/
>pretty but useless expression of a handful of irrational numbers
versus
>gigachad paradigmatic reality-defining equation that ended fallacious assumptions that all the universe's secrets are just waiting to be conclusively known if only we can just be smart and learned enough
great answer anon but dont fall in the same trap as the OP. Generalize!
I'm a layperson. My understanding is derived only through secondary sources. I can't math!
Practice
The later chapters of Stanley Milgram's book "obedience to authority, an experimental view" go a long way to explain the origin of most evil in the world, and his other writings are very revealing about the invisible forces governing social behavior in collectives. I'd highly recommend pic-related.
But in terms of sheer profundity, a lot of Ron Maimon's stuff. I like his physics and mathematics writing, but his brief writings about religion and philosophy reconfigured my entire way of looking at the world to the point where I no longer consider myself an atheist. In retrospect this feels pretty profound.
there's more elsewhere, but I saved the text to some of his stuff here:
https://dimnaut.info/ethics/introtogod.html
https://dimnaut.info/ethics/do-atheists-have-a-standard-definition-of-God-If-not-what-is-it-that-they-disbelieve.html
https://dimnaut.info/ethics/is-it-possible-to-describe-God-mathematically.html
https://dimnaut.info/ethics/if-a-cell-inside-human-body-had-consciousness-would-it-be-aware-of-the-larger.html
https://dimnaut.info/ethics/could-believers-with-strong-faith-in-God-sometimes-exhibit-behavior-similar-to-Stockholm-Syndrome.html
https://dimnaut.info/ethics/whats-it-like-to-have-a-transcendent-spiritual-experience.html
https://dimnaut.info/ethics/if-god-doesnt-exist-why-did-he-talk-to-me-last-night.html
https://dimnaut.info/ethics/what-is-the-message-behind-marquis-de-sades-120-days-of-sodom.html
here's some more of his stackexchange writing I saved
https://dimnaut.info/maimon/stackex/phil/philosophy.html
https://dimnaut.info/maimon/stackex/chris/christianity.html
:O c==3
8====D + () = 😀
>penis 😐 c==3
>penis (japan) :O c==3
Allt the equations posted in this thread filtered me. What is there to get from these? What's the point in studying math at this level?
This is a great synopsis of the relevant section in "An Investigation of the Laws of Thought."
I can use arithmetic to simulate any computer program. If you're saying numbers don't exist, then by extension computer programs don't exist.
can you touch the numbers? are they in the room with us now?
no, they at best share similar properties to the real world, the thing inside your computer is not ones and zeros, its electrons and copper, the programs you claim your computer runs are just diagrams of the actual movements in the steel
your fricking soul is a number your moron, it's number whose digits encode your brain's internal computation within some computing cellular automaton, say rule 110. That's you, and you think therefore you are.
you better make peace with the platonic realm, anon, you're part of it
my soul is a number?
e^my soul, gives a single, definitive value?
5(my soul) = something else?
well anon if something being representable implies it to be equitable, perhaps i ought introduce you to the image i found, that i think depicts our situation very well
>e^my soul, gives a single, definitive value
>5(my soul) = something else?
yeah, relative to the rule 110 algorithm, it's a single number, just look at pic. The first line is a sequence of 1's and 0's, which is a single number. With enough memory and time, you can encode any computer program into that number and rule 110 will run it by computing the subsequent lines. Doing e^(that number) would just scramble it, multiplying it by something else would also scramble it, fricking obviously.
That's an analogous representation and it only represents one of three parts that constitute his soul.
>can you touch the numbers?
Reminded me of this.
>a proof for the law of cosines that puts completing the square and pythagorean theorem into one big interconnected statement