Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts was removed, so supposedly could not have evolved by successive small modifications from earlier less complex systems through natural selection, which would need all intermediate precursor systems to have been fully functional. Irreducible complexity has become central to the creationist concept of intelligent design, but the concept of irreducible complexity has been rejected by the scientific community, which regards intelligent design as pseudoscience. Irreducible complexity is one of two main arguments used by intelligent-design proponents to support their version of the theological argument from design, used alongside specified complexity which adds mathematical support for it. The creation science argument that evolution cannot explain complex mechanisms because intermediate precursors would be non-functional predated its use in ID. In 1993 Michael Behe, a professor of biochemistry at Lehigh University, presented a variation of the same argument in a revised version of the school textbook Of Pandas and People. In his 1996 book Darwin's Black Box he called this concept irreducible complexity and said it made evolution through natural selection of random mutations impossible, or extremely improbable. This was based on the mistaken assumption that evolution relies on improvement of existing functions, ignoring how complex adaptations originate from changes in function, and disregarding published research. Evolutionary biologists have published rebuttals showing how systems discussed by Behe can evolve, and examples documented through comparative genomics show that complex molecular systems are formed by the addition of components as revealed by different temporal origins of their proteins. In the 2005 Kitzmiller v. Dover Area School District trial, Behe gave testimony on the subject of irreducible complexity. The court found that "Professor Behe's claim for irreducible complexity has been refuted in peer-reviewed research papers and has been rejected by the scientific community at large." (Wikipedia).
Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9
In this video I discuss irreducible polynomials and tests for irreducibility. Note that this video is intended for students in abstract algebra and is not appropriate for high-school or early college level algebra courses.
From playlist Abstract Algebra
Abstract Algebra | Irreducibles and Primes in Integral Domains
We define the notion of an irreducible element and a prime element in the context of an arbitrary integral domain. Further, we give examples of irreducible elements that are not prime. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://
From playlist Abstract Algebra
Irreducibility (Eisenstein's Irreducibility Criterion)
Given a polynomial with integer coefficients, we can determine whether it's irreducible over the rationals using Eisenstein's Irreducibility Criterion. Unlike some our other technique, this works for polynomials of high degree! The tradeoff is that it works over the rationals, but need not
From playlist Modern Algebra - Chapter 11
Abstract Algebra | Irreducible polynomials
We introduce the notion of an irreducible polynomial over the ring k[x] where k is any field. A proof that p(x) is irreducible if and only if (p(x)) is maximal is also given, along with some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal W
From playlist Abstract Algebra
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory
The chaotic complexity of natural numbers | Data structures in Mathematics Math Foundations 175
This is a sobering and perhaps disorienting introduction to the fact that arithmetic with bigger numbers starts to look quite different from the familiar arithmetic that we do with the small numbers we are used to. The notion of complexity is key in our treatment of this. We talk about bot
From playlist Math Foundations
Representation theory: Orthogonality relations
This lecture is about the orthogonality relations of the character table of complex representations of a finite group. We show that these representations are unitary and deduce that they are all sums of irreducible representations. We then prove Schur's lemma describing the dimension of t
From playlist Representation theory
Introduction to Complex Solutions of Polynomials (Precalculus - College algebra 35)
Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com A brief explanation of Complex Zeros/Roots, where they come from, how they are used, and why they come in conjugate pairs.
From playlist Precalculus - College Algebra/Trigonometry
Representation theory: The Schur indicator
This is about the Schur indicator of a complex representation. It can be used to check whether an irreducible representation has in invariant bilinear form, and if so whether the form is symmetric or antisymmetric. As examples we check which representations of the dihedral group D8, the
From playlist Representation theory
Exposing the Discovery Institute Part 3: Michael Behe
To start learning STEM for free, visit https://www.brilliant.org/ProfessorDaveExplains/ and the first 200 people will get 20% off Brilliant's annual premium subscription. Continuing this series exposing all the frauds at the religious propaganda mill "Discovery Institute", we arrive at Mi
From playlist Debunks/Discussions/Debates
Title: Computing real solutions to systems of polynomial equations using numerical algebraic geometry Symbolic-Numeric Computing Seminar
From playlist Symbolic-Numeric Computing Seminar
Finding ALL Solutions of Polynomials (Precalculus - College Algebra 37)
Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com How to completely factor a polynomial over the complex number system and find all of the solutions, including complex.
From playlist Precalculus - College Algebra/Trigonometry
RT8.3. Finite Groups: Projection to Irreducibles
Representation Theory: Having classified irreducibles in terms of characters, we adapt the methods of the finite abelian case to define projection operators onto irreducible types. Techniques include convolution and weighted averages of representations. At the end, we state and prove th
From playlist Representation Theory
Henniart: Classification des représentations admissibles irréductibles modulo p...
Recording during the thematicmeeting : "Algebraic and Finite Groups, Geometry and Representations. Celebrating 50 Years of the Chevalley Seminar " the September 23, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this
From playlist Partial Differential Equations
Visual Group Theory, Lecture 6.3: Polynomials and irreducibility
Visual Group Theory, Lecture 6.3: Polynomials and irreducibility A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achie
From playlist Visual Group Theory
[BOURBAKI 2017] 21/10/2017 - 1/4 - Oliver DUDAS
Splendeur des variétés de Deligne-Lusztig [d'après Deligne-Lusztig, Broué, Rickard, Bonnafé-Dat-Rouquier] ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter :
From playlist BOURBAKI - 2017
PotW: Prove that the Fraction is Irreducible [Number Theory]
If this video is confusing, be sure to check out our blog for the full solution transcript! https://centerofmathematics.blogspot.com/2018/10/problem-of-week-10-18-18-prove-that.html
From playlist Center of Math: Problems of the Week