Lit Calculus 1: Zeno's Paradox

Presented by Anthony Bosman, PhD.

Introducing limits, a central idea of Calculus, to make sense of instantaneous velocity and resolve Zeno's paradox.

[Raynaputi]

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-frki]

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.

[unnamedexodus]

This helped me understand instantaneous velocity in physics. Thank you for such a great video. Please keep teaching.

[antoniopannuti]

So, the Zeno paradox deals with physical objects. The premises of the "calculus" reasoning
is that space and time can be divided "ad infinitum". In reality, when we reach planck scale, this is not certain. IMO, a "granularity" of space and time at a fundamental level will solve the Zeno paradox. Any take?

[taylorfloyd]

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?

[chrisg]

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.

[alfredomulleretxeberria]

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*

[elkanahgray]

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!

[gpdnrgi]

Hi I really need the name of the person talking in this video, it is for my math ia IB