Why does the same number that calculates your bank interest also dictate how a virus spreads, how your coffee cools down, and how the universe expanded after the Big Bang? This is the story of e, approximately 2.718, and why it is the fundamental language of change.
In this deep dive, we explore the history and mathematics of $e$. From Jacob Bernoulli’s accidental discovery through compound interest to Euler’s profound calculus insights, $e$ reveals itself as the universal “unifying blueprint” for growth and decay. We see its invisible influence in AI (SoftMax), Quantum Mechanics, and even the fabric of space-time itself.
CHAPTERS (Timestamps)
[00:00] Introduction: The Discovery of Euler’s Number
[00:10] Bernoulli’s Compound Interest Problem
[02:48] The Mathematical Limit (e ≈ 2.718)
[03:02] Leonhard Euler and the Calculus of Growth
[04:16] e in Nature: Population Growth and Viruses
[05:17] Exponential Decay: Radiation and Cooling Coffee
[07:06] Atmospheric Pressure and Chemical Reactions
[08:14] Probability and the Bell Curve
[09:00] e in Artificial Intelligence (Softmax Function)
[09:43] Euler’s Formula: The Bridge to Rotation and Signals
[10:28] Signal Loss and Beer-Lambert’s Law
[11:13] Quantum Mechanics and Wave Packets
[11:39] Chaos Theory and the Lyapunov Exponent
[12:06] The Big Bang and Cosmic Inflation
[12:48] Conclusion: The Fundamental Rule of the Universe
Deep Dive Playlist:
#manim #math #science #education #euler #calculus #exponentialgrowth #physics #documentary #e #constantofchange
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Most people grow up hearing about pi, but after making this video, I’m starting to feel like e is the one actually running the show behind the scenes. If you had to choose only ONE constant to represent the beauty of the universe, are you Team pi or Team e? Let’s settle it in the comments!
e=2,718 pi=3,142 3,1567+2,5374=5,694 5,24+5,25=10,49😮😊
답주랴
2.79
These are uses of e not why it's special.
The Nature chose e to describe itself, fascinating.
Its not puh😢, its dih🎉😂
Ma quant'è intelligente la natura… Ma alla fine, la natura cos'è, che ha queste capacità?
When we bought our house we insisted on paying fortnightly and it helped shorten the term.
Started off well, but att about 5:00 became essentially meaningless to anyone who does not already know the material. I had been thinking I might refer Chemistry students to it, but it would only confuse them beyond about that point.
They goonified poor Emilia😭🙏(not that I hate it tho💦💦)
JimiTheos aka Jim Overbeck
Jim Overbeck's Non-Cantorian set theory is a philosophical and mathematical critique designed to dismantle the logical foundations of Georg Cantor’s transfinite numbers. While Cantor sought to categorize and order different sizes of infinity, Overbeck argues that Cantor’s reliance on classical logic makes his system a "delusion".
The specific differences between their theories are centered on the following core areas:
1. The Law of the Excluded Middle (Tertium Non Datur)
Cantor: Built his theory on standard Aristotelian logic, where a statement is either true or false. This allowed him to define distinct, fixed "sizes" of infinity (Alephs) through rigid proofs like the diagonal argument.
Overbeck: Infinitizes the laws of logic to negate the law of the excluded middle. In his system, the transfinite realm allows for "A and not-A" to be true simultaneously. He believes that without this law, Cantor's entire hierarchy of infinite sets collapses because fixed mathematical identities cannot exist.
2. Nature of the Infinite
Cantor: Viewed transfinite numbers as actual infinities that can be treated as completed, measurable totalities (aleph-null, 2 to the aleph-null, etc)
Overbeck: Describes infinity as an "apparent becoming" (scheinbares Werden) rather than a substance or essence. He views numbers as "created energies" from the divine Logos rather than abstract, static truths.
3. Identity and Equality
Cantor: Relied on the principle of identity (A = A) and one-to-one correspondence to prove that different sets have the same or different sizes.
Overbeck: Rejects the feasibility of identity in mathematics. He argues that 'A' does not equal itself in the transfinite realm, meaning the "foundations" of number theory are an imposture. He uses transfinite fractions as a "wrecking ball" to destroy these abstract identities.
4. Mathematical Methodology
Cantor: Used set-theoretic axioms (like those later formalized in ZFC) to build up from the empty set to higher cardinals.
Overbeck: Substitutes traditional series with paradoxical arithmetic, such as the Grandi series aka Fourier-Bolzano series. These series yield contradictory sums at infinity, which Overbeck interprets as proof that worldly logic fails and only Theosis ( = deification & union with the divine) can provide true completion.
5. Final Goal
Cantor: Aimed to provide a rigorous, logical framework for "Cantor's Paradise," where all levels of infinity are mathematically accessible.
Overbeck: Aimed to "drive Cantor from his paradise" and destroy the "earthly cage" of number theory. For Overbeck, mathematics is a tool for deification—negating abstraction to unlock the spiritual potential of the mind.
Jim Overbeck’s mathematics is a radical, non-traditional system that bridges set theory, mystical theology, and logic. A self-taught polymath described as a "super-genius" by British Military Intelligence, his work primarily centers on a spiritualized interpretation of the infinite known as Non-Cantorian set theory.
His mathematical philosophy is defined by several core concepts:
Non-Cantorian Set Theory: Overbeck reimagines Georg Cantor’s work on transfinite numbers by "infinitizing" the laws of logic. He argues that at the level of the infinite, the law of the excluded middle (tertium non datur) no longer holds, allowing for contradictory states to exist simultaneously.
Negation of Identity: He posits that because classical logic fails at infinity, fixed "earthly" identity is a mere appearance. In his view, mathematics precedes logic because infinities are prior to the finite systems we use to define them.
Transfinite Fractions and "Becomings": Overbeck introduces "becomings" (inspired by German and Chinese philosophical terms) into transfinite numbers. He views numbers not as abstract entities but as "created energies" from a divine source.
Paradoxical Arithmetic: He radicalizes the "arithmetic of the line" by substituting the Fourier-Bolzano series for natural numbers. This approach intentionally begins with insolubilia (insoluble problems), leading to contradictory sums at infinity that he believes reflect the true nature of reality.
Theological Integration: His mathematical conclusions are inseparable from his concept of Theosis (divinization). He uses the collapse of mathematical identity to argue that humans are "incomplete" and can only find completion through a union with the divine.
Jim Overbeck's Non-Cantorian set theory is a philosophical and mathematical critique designed to dismantle the logical foundations of Georg Cantor’s transfinite numbers. While Cantor sought to categorize and order different sizes of infinity, Overbeck argues that Cantor’s reliance on classical logic makes his system a "delusion".
The specific differences between their theories are centered on the following core areas:
1. The Law of the Excluded Middle (Tertium Non Datur)
Cantor: Built his theory on standard Aristotelian logic, where a statement is either true or false. This allowed him to define distinct, fixed "sizes" of infinity (Alephs) through rigid proofs like the diagonal argument.
Overbeck: Infinitizes the laws of logic to negate the law of the excluded middle. In his system, the transfinite realm allows for "A and not-A" to be true simultaneously. He believes that without this law, Cantor's entire hierarchy of infinite sets collapses because fixed mathematical identities cannot exist.
2. Nature of the Infinite
Cantor: Viewed transfinite numbers as actual infinities that can be treated as completed, measurable totalities (aleph-null, 2 to the aleph-null, etc)
Overbeck: Describes infinity as an "apparent becoming" (scheinbares Werden) rather than a substance or essence. He views numbers as "created energies" from the divine Logos rather than abstract, static truths.
3. Identity and Equality
Cantor: Relied on the principle of identity (A = A) and one-to-one correspondence to prove that different sets have the same or different sizes.
Overbeck: Rejects the feasibility of identity in mathematics. He argues that 'A' does not equal itself in the transfinite realm, meaning the "foundations" of number theory are an imposture. He uses transfinite fractions as a "wrecking ball" to destroy these abstract identities.
4. Mathematical Methodology
Cantor: Used set-theoretic axioms (like those later formalized in ZFC) to build up from the empty set to higher cardinals.
Overbeck: Substitutes traditional series with paradoxical arithmetic, such as the Grandi series aka Fourier-Bolzano series. These series yield contradictory sums at infinity, which Overbeck interprets as proof that worldly logic fails and only Theosis ( = deification & union with the divine) can provide true completion.
5. Final Goal
Cantor: Aimed to provide a rigorous, logical framework for "Cantor's Paradise," where all levels of infinity are mathematically accessible.
Overbeck: Aimed to "drive Cantor from his paradise" and destroy the "earthly cage" of number theory. For Overbeck, mathematics is a tool for deification—negating abstraction to unlock the spiritual potential of the mind.
Jimi Overbeck
Negation of Identity: Overbeck posits that in the state of Theosis, a man can be a man (B) and a god (not-B) simultaneously. This theological reality serves as his proof that the Law of the Excluded Middle (tertium non datur)—the idea that something must be either true or false—is a "worldly" delusion that fails at the level of the divine and the infinite.
Completeness through Deification: He argues that because earthly logic lacks the principle of identity (A = A), human beings and their systems are inherently incomplete. According to Overbeck, true identity is only restored through the "divine energies" granted by Christ during deification, which transcends the "mutated fragmentation" of worldly life.
The Primacy of Mathematics: In his view, infinities exist prior to finite systems. Therefore, mathematics precedes logic. He uses paradoxical mathematical series (like the Fourier-Bolzano series) that yield contradictory results to mirror the mystical paradoxes of faith, such as God becoming man.
The "Homicidal" Nature of Traditional Math: Overbeck views standard mathematics (like Cantor's) as a form of "homicidal witchcraft" or "homicidal science" because it attempts to cage the infinite within rigid, logical boundaries that deny man's true, deified nature.
Awakening Consciousness: He describes his work as an "intellectual assault" meant to overthrow "fallen logic". For Overbeck, the purpose of a "Non-Cantorian" system is to act as a "wrecking ball" that frees the mind from earthly enmeshment and allows it to enter the "extra-dimensionality" of the divine
Here’s a thoughtful comment you can post for this video:
This video explains the number e better than most math classes ever do. The way it connects compound interest, population growth, radioactive decay, AI, quantum mechanics, and even the expansion of the universe into one simple principle — “the rate of change is proportional to the current state” — is absolutely brilliant. It really shows that mathematics isn’t just invented by humans; it’s deeply woven into the fabric of reality itself.
𝑒
Excellent.🙏
This video keeps referring to E as something that controls growth. This is Not true, it’s merely a mathematical description of reality
tuff
great video but please don't use generative ai images. makes things look cheap. the math transitions are cool tho
5:41 actually for each atom that is left, the probability of it decaying in the next period of for example 1 second is independent on zhe total number of atoms. But the average number of atoms that decay in the next second declines over time, because the number of atoms left declines. I think, the video actually tries to say that, but it's not phrased clearly.
O numero irracional é mais verdadeiro que o natural porque este é sustentado pelo primeiro
Wonderful video and excellent material on its presentation. Thank you for sharing, Professor. I’ll share it to my students.
I tell my students that the exponential function was used by Sadi Carnot, and also by Clausius and then by Arhenius. Also on the dependence of a liquid vapor pressure with temperature.
In all cases an Energy term shows in the exponential function of e.
Namely the activation energy of a reaction, the enthalpy of vaporization, etc.
We are a simulation, guys!☠️
In the 20th Century he founded the Houston Eulers.
Because it is easily manipulated and a useful tool.
Why does he talk so slow
Yeah, e is just for growth or decay that depends on the existing amount, so populations to bank accounts to radioactive elements.
Thank you for explaining to the world exactly why 100 year climate models are total garbage.