Playlist: • Lit Calculus Presented by Anthony Bosman, PhD. Math at Andrews University: math.andrews.edu Introducing limits, a central idea of Calculus, to make sense of instantaneous velocity and resolve Zeno's paradox.
Пікірлер: 21
@Raynaputi4 ай бұрын
Math is so cool. I always thought calculus was too heavy for me. After seeing a few examples, it's not too complicated. You presented this in a way that was enjoyable to watch and easy to understand. Thanks
@JJ-fr2ki7 ай бұрын
From mathematical philosopher to mathematical philosophers: There are several ways Calculus does solve many versions of Zeno’s Paradox. 1) Calculus offers a Style of Reasoning that sidesteps the material inferences of the old logical language with another that is fecund, accurate, and directs successful interventions. 2) Many cases can be solved as ratios of converging series’. These are not problematic. 3) There are many equivocations of the equal sign in math and the sciences, but so is the case for “is” or “reaches the finish line”. This vagueness is not vicious because it allows us in this case to accommodate a language with a tense less logic that treats objects like numbers in discrete mathmatics as the flowing changing things they are in the world. Unless you are willing to announce a skepticism of motion all together, and note this is very difficult because it amounts to a skepticism of momentum, force and power; all instantaneous properties of objects. You’ll have to rebuild physics. 4) There is nothing wrong with transfinite numbers and transfinite cardinalities. 5) Ask if you want elaboration on any, but this last point is the most important and the most subtle. It relates to a hidden equivocation in the false dilemma. “At any *instant* the arrow is where it is or where it is not. So *instantaneous* motion is impossible.” What is Zeno’s concept of the ‘instant’? He’s never experienced one. All he’s got is a kind of intuition about a smaller and smaller duration. The calculus makes explicit Zeno’s vague intuition with the concept of the limit and the payoff is tremendous. So regarding (1), why are we to cede authority to Zeno’s definition of ‘instant’ when the limit, ratios of limits, and transfinite numbers make explicit, including the limitations, of “instant” talk and yield unending inferential treasure. Philosophers eschew the the bewitchment of ancient conservative language and come to the world beyond the 17th century.
@unnamedexodus3902 Жыл бұрын
This helped me understand instantaneous velocity in physics. Thank you for such a great video. Please keep teaching.
@apopheniac42312 жыл бұрын
Thank you for a well-made video!
@alfredomulleretxeberria42393 жыл бұрын
Calculus exists under the assumption that Zeno's paradox does not exist and that it's possible to perform an infinite sum of infinitesimally small quantities. It's only stepping out of one game board and claiming it's winning by making up its own rules. *tips fedora*
@apopheniac42312 жыл бұрын
You don't need infinitesimally small quantities. The whole trick of calc is to sidestep them. Math is all about 'making up rules' and examining their consequences.
@norwayphilosopher Жыл бұрын
Correct. He set as premise something can be infinite in finite time, which is logically impossible
@elkanahgray98103 жыл бұрын
Calculus doesn't eliminate an infinitesimally small quantity...it just ignores it by limits! Calculus can't solve the Paradox because an infinite sum cannot be the addition of finite terms! good try though!
@gopackgo40362 жыл бұрын
Exactly, it's shocking this guy teaches calculus and can't even understand that the = sign in infinite sum does not mean = in the traditional sense of 1+1=2, it just means converging.
@apopheniac42312 жыл бұрын
0.333... = 1/3 0.999... = 1 Infinity is bigger than arithmetic. Cardinal correspondence is more fundamental than counting.
@norwayphilosopher Жыл бұрын
@@apopheniac4231 Wrong. One need to add infinite in finite time, which is logically impossible. 0.99999999... is not equal to 1. Limit of it is equal to 1.
@taylorfloyd47852 жыл бұрын
too bad that this isn't even in the ballpark of tackling zeno's paradox, why does a past moment compel a future moment, and why isn't it all static?
@norwayphilosopher Жыл бұрын
facts are the opposite of what being told. On atomic level no objects move. Movement is in fact an illusion and quantum theory and experiments prove that there are no particles out there. On a TV or computer screen nothing moves. Same illusion. limit of a sum is not a sum. Zenos paradox is about one cannot reach this limit no matter how many decimal numbers are added. One needs to add infinite in finite time, which is logically impossible. 0.99999999... is not equal to 1. Limit of it is equal to 1. OCTOBER 23, 2015 'Zeno effect' verified-atoms won't move while you watch by Bill Steele, Cornell University One of the oddest predictions of quantum theory - that a system can't change while you're watching it - has been confirmed in an experiment by Cornell physicists. Their work opens the door to a fundamentally new method to control and manipulate the quantum states of atoms and could lead to new kinds of sensors. The experiments were performed in the Utracold Lab of Mukund Vengalattore, assistant professor of physics, who has established Cornell's first program to study the physics of materials cooled to temperatures as low as .000000001 degree above absolute zero. The work is described in the Oct. 2 issue of the journal Physical Review Letters Graduate students Yogesh Patil and Srivatsan K. Chakram created and cooled a gas of about a billion Rubidium atoms inside a vacuum chamber and suspended the mass between laser beams. In that state the atoms arrange in an orderly lattice just as they would in a crystalline solid.,But at such low temperatures, the atoms can "tunnel" from place to place in the lattice. The famous Heisenberg uncertainty principle says that the position and velocity of a particle interact. Temperature is a measure of a particle's motion. Under extreme cold velocity is almost zero, so there is a lot of flexibility in position; when you observe them, atoms are as likely to be in one place in the lattice as another. The researchers demonstrated that they were able to suppress quantum tunneling merely by observing the atoms. This so-called "Quantum Zeno effect", named for a Greek philosopher, derives from a proposal in 1977 by E. C. George Sudarshan and Baidyanath Misra at the University of Texas, Austin,, who pointed out that the weird nature of quantum measurements allows, in principle, for a quantum system to be "frozen" by repeated measurements. Previous experiments have demonstrated the Zeno Effect with the "spins" of subatomic particles. "This is the first observation of the Quantum Zeno effect by real space measurement of atomic motion," Vengalattore said. "Also, due to the high degree of control we've been able to demonstrate in our experiments, we can gradually 'tune' the manner in which we observe these atoms. Using this tuning, we've also been able to demonstrate an effect called 'emergent classicality' in this quantum system." Quantum effects fade, and atoms begin to behave as expected under classical physics. The researchers observed the atoms under a microscope by illuminating them with a separate imaging laser. A light microscope can't see individual atoms, but the imaging laser causes them to fluoresce, and the microscope captured the flashes of light. When the imaging laser was off, or turned on only dimly, the atoms tunneled freely. But as the imaging beam was made brighter and measurements made more frequently, the tunneling reduced dramatically. "This gives us an unprecedented tool to control a quantum system, perhaps even atom by atom," said Patil, lead author of the paper. Atoms in this state are extremely sensitive to outside forces,l he noted, so this work could lead to the development of new kinds of sensors. The experiments were made possible by the group's invention of a novel imaging technique that made it possible to observe ultracold atoms while leaving them in the same quantum state. "It took a lot of dedication from these students and it has been amazing to see these experiments be so successful," Vengalattore said. "We now have the unique ability to control quantum dynamics purely by observation." The popular press has drawn a parallel of this work with the "weeping angels" depicted in the Dr. Who television series - alien creatures who look like statues and can't move as long as you're looking at them. There may be some sense to that. In the quantum world, the folk wisdom really is true: "A watched pot never boils."
@chrisg30307 ай бұрын
I ask a fellow passenger "Does this train go to Cambridge?" "Yes" comes the reply, but a bit later the train rushes through Cambridge station without even slowing down. The fellow passenger shrugs and says "But it does go to Cambridge, it just doesn't stop there." Zeno messes with our useful but fictitious convention of modeling motion as a series of stops.
@vikrantirannajakarwar5929 Жыл бұрын
Appealing solution to the paradox❤
@norwayphilosopher Жыл бұрын
Wrong solution as he set as premise something can be infinite in finite time, which is logically impossible
@nataraja30308 ай бұрын
oh my god! this is so profound.
@danschaben38712 жыл бұрын
Tough crowd in the math world.
@user-gp4dn6rg2i Жыл бұрын
Hi I really need the name of the person talking in this video, it is for my math ia IB
@MathatAndrews Жыл бұрын
Anthony Bosman, PhD www.andrews.edu/cas/math/faculty/bosman-anthony.html