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No, it just shows that society is dynamic and evolutionary (except in the USA).It shows that the models don't take dynamics of the society into account, which makes them inaccurate and can only be good for a short period of time.
Complex Integration and Finding Zeros of the Zeta Function
In this video we examine the other half of complex calculus: integration. We explain how the idea of a complex line integral arises naturally from real definite integrals via Riemann sums, and we examine some of the properties of this new sort of integral. In particular, we consider some complications that arise when trying to apply the fundamental theorem of calculus to complex functions.
We then bring these ideas to the central focus of this series: the zeta function and the Riemann hypothesis. By the end of the video, we will be able to use complex integrals to approximate the location of the zeroes of the zeta function (or those of any other complex function for that matter)!
Analytic Continuation and the Zeta Function
Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for complex inputs and make sense of what it is the Riemann Hypothesis is claiming.
Chapters:
00:00 zetamath does puzzles
00:23 Recap
02:40 Bombelli and the cubic formula
08:45 Evaluating real functions at complex numbers
12:33 Maclaurin series
21:22 Taylor series
27:19 Analytic continuation
35:57 What goes wrong
48:19 Next time
The Basel Problem Part 1: Euler-Maclaurin Approximation
This is the first video in a two part series explaining how Euler discovered that the sum of the reciprocals of the square numbers is π^2/6, leading him to define the zeta function, and how Riemann discovered the surprising connection between the zeroes of the zeta function and the distribution of the primes, leading ultimately to his statement of the Riemann Hypothesis. This video focuses on how Euler developed a method to approximate this sum to 17 decimal places, as well as how the Bernoulli numbers naturally appear as part of this problem.
The Basel Problem Part 2: Euler's Proof and the Riemann Hypothesis
In this video, I present Euler's proof that the solution to the Basel problem is pi^2/6. I discuss a surprising connection Euler discovered between a generalization of the Basel problem and the Bernoulli numbers, as well as his invention of the zeta function. I explain Euler's discovery of the connection between the zeta function and the prime numbers, and I discuss how Riemann's continuation of Euler's work led him to state the Riemann hypothesis, one of the most important conjectures in the entire history of mathematics.
Sections of this video:
00:00 Intro
01:24 Euler's Basel proof
23:20 The zeta function and the Bernoulli numbers
32:01 Zeta and the primes
48:15 The Riemann hypothesis
A Youtube channel seems to be dedicated to explain this problem, and I find it as one of the best explanation online.If you are serious to understand this problem, this video is a good place to start.
https://www.youtube.com/c/zetamath/videos
Factorials, prime numbers, and the Riemann Hypothesis
Today we introduce some of the ideas of analytic number theory, and employ them to help us understand the size of n!. We use that understanding to discover a surprisingly accurate picture of the distribution of the prime numbers, and explore how this fits into the broader context of one of the most important unsolved problems in mathematics, the Riemann Hypothesis.
Hamdani,Have you built the motor yourself, or do you know someone who has built it? Do you know a working prototype of it?
I am so pleased that you are investigating magnetic force fields. We also need to explain the magnoflux spin effect of the magnetic field please.
So the question now is, what's all the fuss? Who would deny that?It seems that some people are convinced that consciousness can have effects on matter without physical interface which can be analyzed, modeled, and manipulated. This would make consciousness looks magical. But that's how magic tricks are usually done. Show audiences the beginning and the end of a process while hiding something in between. Some misdirections can amplify the effects of mythical confusions.
https://en.wikipedia.org/wiki/Riemann_hypothesis
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
1/2
. Many consider it to be the most important unsolved problem in pure mathematics.[1] It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is named.
The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ(s) = 0 when s is one of −2, −4, −6, .... These are called its trivial zeros. The zeta function is also zero for other values of s, which are called nontrivial zeros. The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that:
The real part of every nontrivial zero of the Riemann zeta function is
1/2
.
Thus, if the hypothesis is correct, all the nontrivial zeros lie on the critical line consisting of the complex numbers
1/2 + i t, where t is a real number and i is the imaginary unit.
Visualizing the Riemann zeta function and analytic continuation
Even if a highly ultimate technology, would comunicante trough physical means.We usually call them interfaces. They can be biological neurons, implanted electrodes, or non-invasive brain wave sensors.
There a wire or even light it's not different from my hands.
Science is less concerned about why or what some ultimate truth might be and more concerned with having an explanation and a model that is useful for making predictions.What does science say that can be used to answer the question in the op?
Lenin, Mao and Hitler had very good models of reality that helped them persuade millions of individuals to do all sorts of things that you might consider immoral.The collapse of the systems that they built show that their models of reality are not as good as you'd like to think.
Here is the visualization of the second experiment, which start from the first as described before. If the charged particle is stationary to the wire, no magnetic force is received.The difficulty in working with electrically charged particles/objects is that they are attracted to even neutral objects due to electric displacement. An electrically charged metal ball is attracted to the plastic hose even when it's empty and electrically neutral.
Next, the wire is zoomed to show the electrons and metal atoms inside.
From the picture above, the electrons inside the wire move to the left with speed v, but particle q doesn’t receive magnetic force.
Now if the wire is moved to the right with speed v, the speed of electrons becomes 0, while the speed of the metal atoms = v. It is shown that magnetic force F is produced downward.
The picture above is equivalent to the picture from previous post.
Here we can conclude that electron’s movement is not responded by the particle, while atom’s movement produces magnetic force to the particle. It seems that for a long time we had missed the difference between atoms and free electrons which cause electric current and produce magnetic force.
For the second experiment, we will study the effect of the movement of charged particles inside a conductor (or convector) toward the test particle. We will study the hypothesis that magnetic force is not only affected by the magnitude of electric charge that moves inside a conductor (or convector), but also affected by the mass of the particle.
Electric current in a copper wire is produced by the flow of electrons inside. The charge and mass of electrons are always the same, so we need some other particles as electric current producers to get reference. For that we will replace the conductor by a hose filled by electrolyte solution that contains ions, since ions are also electrically charged and have various masses. Some of electrolytic solutions that will be used are NaCl, H2SO4, HCl, CuSO4, FeCl3.
My previous experiment didn't produce conclusive result yet. I'll try again if I can find a way to improve the experimental setup and increase the signal over noise ratio.Some of electrolytic solutions that will be used are NaCl, H2SO4, HCl, CuSO4, FeCl3.\What happened when you used them?
In the english version of wikipedia for the same subject(magnetic field), the Einsteinian model is lost (i dont know why) :I think it's moved to a separate article.
https://en.wikipedia.org/wiki/Magnetic_field
hamdani yusuf, i dont really understand your claim.Where did I say that?
You say that nobody understand the magnetic force.
In order to have a revolution, you need to persuade a few million individuals to behave in a certain way, beheading aristocrats or marching across China, for instance. And the leaders of the revolution are subject to your judgement of morality.With more knowledge and more accurate and precise model of reality, we can avoid and prevent more immoral actions. We forgive but not forget. Any moral rule involving reward and punishment system is meaningless if it doesn't help making life easier for future conscious beings.
Problem is that society evolves, so what may appear to be in the short term interest of the peasant army may pave the way for repression of their descendants.
SpaceX's Starship launch vehicle has the potential to explore the solar system in a bold, new -- and supersized -- way. Planetary scientist Jennifer Heldmann talks about how reusable, large-scale spacecraft like Starship could help humanity achieve its next galactic leaps and usher in a new era of space exploration, from investigating the solar system's many ocean worlds to launching bigger telescopes that can see deeper into the universe.
Veganism will win, but you're wrong about why
Loose workings for how many cows my dairy consumption will kill (for a reason unknown to me, this text didn't render on the video, sorry): Based on my current rate of dairy consumption (1 litre milk + 500g of cheese per week) I’ll consume another 15,600 litres of milk if I reach 82. The average cow produces 49,780 litres of milk throughout its life, and for every cow there is a culled bull and a child that’s taken away.
Timestamps:
00:00 Why Make it Easy?
02:48 Can They Suffer?
06:53 Unnecessary Harm
16:02 An Arbitrary Definition
19:34 Two Sovereign Masters
27:58 Why Not Vegan?!
