Infinitesimal Monad (extra footage)

Extra footage with Professor Carol Wood.

NUMBERPHILE

Videos by Brady Haran

[sserpxeadnap]

Please please do more videos with Professor Wood!! Extremely enjoyable

[reallyWyrd]

I gotta go study the hyper-reals so I can start messing with people. I want to draw little funnel shapes over each integer on the number line and then be like, "and here, you see this funnel shape? This is the whirlpool draining away your sanity."

[cmdtuts]

Professor Carol Wood is a fascinating person, it would be great to see more of her in the future.

[mondoke]

I just love how after years of talking about science with lots of scientists for a living, there are still topics that make blow Brady's mind.

[fantiscious]

Me: *finishes watching the previous video, sees this one*
Me: Oh, another one!

Professor Wood: **immediately starts with** "Well it's worse than that"

Me: _OH NO_

[garethdean]

Glorious. I want to print this video onto a custom cake and eat it.

[SpamDestroyer]

I love how this immediately starts off with "It's worse than that!"

[ffhashimi]

I think this woman is an amazing teacher

[unclvinny]

Dr. Wood is great, hope you can do more videos with her.

[VladVladislav]

-"even K!"
- brain exploded

[kmdash]

I don't know why, but I really like infinitesimals.

[BewilderedBird]

I really, really like this approach to calculus. In fact, I think the deltas and epsilons are much less intuitive and contribute to much of the confusion to calculus students. This infinitesimal approach is much closer to what Leibniz was thinking when he discovered/invented calculus and makes more intuitive sense.

[firstlast-wgon]

I picture numbers in this context like this; "1" is just a letter describing the peak of a 'concentration' of many little unique entities that we label "numbers", "1" does not refer to a singular object (like one donut) but rather the highest 'concentration' of unique entities. For example, you can have those infinitesimals close or far away from "1" on the number line, all that really means is the entity is bigger, or as I call it more concentrated. If you applied this constantly then numbers are more like bumps than a long sequence, you know like 1 2 3 4, it's more like a series of completely unique patterns that peak at certain points.

This post literally means nothing but it's a cool idea, it could be shifted into a 3D representation of numbers too.

[okoyoso]

Do a video on the smooth infinitesimal analysis too! It's similar to non-standard analysis in that it uses infinitesimals.

[zachsmith]

<3 at 1:26 'it removes all the epsilons and deltas...' as someone who's more into algebra this is wonderful!

[micknamens]

Positive infinity is usually considered as the limit of N, which is supposed to be unique. What is the relationship between infinity and K, or K+1 ?

[FishKungfu]

The infinitesimal monad set is really cool and I like it, but it agitates me at the same time.

[levinb]

1:11 Her thesis advisor was ABRAHAM No wonder!!!

[BluRey]

She is correct. This lines up with Fractals, Omega Code, Menger Cube and String Theories. She deserves an Honorary Cosmological Degree.

[Kram]

What happened there at 4:00 - 4:02 ?
It's just blacked out and you begin to say something mid-sentence after that?