*Tibees goes to stay on ISS until she comes up with grand unification theory! 🚀🌎

I looove this new "stuck until I learn" format

imagine waiting in line to the toilet and hearing from the closed door "There's one very specific problem from the book that I want to solve on this trip and that is to compute the hypervolume of a fractal hypersphere, of dimension 4.5" :)

Instructions unclear, I have been on this train for four years, and still can't comprehend it.

I'm not an actor but I get pleasure watching actors. I'm not a footballer but I get pleasure watching football. I'm not a mathematician , but I get pleasure in watching clever people do maths and Toby's approach is unique and compelling. Another great video, thank you for creating it.

Toby is the coolest person I don't know.

0:48 train of thought, what a coincidence

Could listen to her voice and talking about the fabric of reality all day and night long. so relaxing

This video feels like a very comfortable sofa.

Australia definitely needs more railways and more trains.

This was exactly what I wanted: the 4D shorts to become a full video

Math & Imagination breaks the boundaries of dimensions, the boundaries that we cannot break as a 3D being are already broken.

Next Video - Trapped on Earth until I learn how to escape but seriously, great video, the idea of learning random things because they sound cool is great

root(2/pi) makes me think of 2 things, in particular. The first is the fourier transform and the second is the Gaussian distribution.

I have travelled this route a few times. Nice to see the landscapes again as a backing to your voice. I really liked going over the rivers as the landscape changes dramatically around them.

Oh "Train of thought" would have been a great title for this video. :)

Very glad to hear it is not just me struggling with The Three Body Problem 😊

I'm loving this miniseries you have going here. If you don't mind, more of this would be great. This is such a wild but apt way to understand science. If I wasn't already a huge fan of it, I would've wanted something like this to understand science back in the day. I'm glad you got to read Three-Body Problem, one of my favourite science fiction novels. It inspired me to write my own science fiction novel with a similar premise, but it heavily evolved into something I'm quite proud of. Almost all your videos remind me of it in some way. I should probably go back and write more.

You are so good. The video editing was amazing.

I'm a big fan of both physical and mental explorations, so this video is mesmerizing in a weirdly relatable way for me. I found your channel from a comment you left on another video 7 years ago about being an aspiring physics youtuber and I wondered if the aspiration was still going strong--which it clearly is! So cool to find such neat and recent content at the end of that search. I'm glad you're still having fun making these informative videos, keep it up!!

Love the video! Thank you. Your stop at Tully (7:10) reminded me of a joke my brother told me long ago. He was rushing home for Christmas from Cornell University, and he passed through Tully, NY. He told me he just had to stop somewhere in Tully to pick up a souvenir, a "Tullyphone" book. Australia is so beautiful!

I love these videos where you have to figure it out before you get to continue. Love your content!

Thanks for this wonderful train trip. Looking forward to more. Hope your mogs aren't too lonely without you. Hugs

Toby's Next Video: *Flying in a plane until I understand the Universe*

Loving this long form content that takes a deeper dive into some of these topics! Its also giving the message that learning can be done anywhere

Thank you, Toby 💞

Hello Tibees! Gamma function has a recursive property that allows us to calculate gamma of factions. I believe it's gamma(x+1)=x * gamma(x). If you do this on your example, you will get to something that involves gamma(0.25). From this, there are some useful properties I forgot

You're such a nice person, I could hear you talking in your calm voice for hours, also i can follow the hole time your expressions, thats amazing Thx😊

This was fascinating! Extremely well done!

Thank you, Toby! ❤👸

"The train had to wait for an hour for the northbound train...". Being a mathematician from the Netherlands, I find this harder to comprehend than a hypersphere.

Wow this travel documentation is something special. To go on a journey together with you and your thoughts is intriguing. I bow to your idea of this train of thought.

I really enjoy your Art. I have been working on a problem/ I looked up one day and wondered if it would be possible to be on a moon that orbit a planet so large that a person’s field of vision (horizon) would only see the planets surface which the moon orbits. Imagine if the sky was replaced with the surface of Jupiter. 🕊️

Please do more of these types of videos, they're really delightful :)

Thank you for sharing this journey

Absolute perfection, I could listen endlessly

imagine for example going through a wormhole, as you approach it, you look around, you see the familiar 3d world, as you approach the point of least radius, where light orbits its, you will see the inside and the outside covers exactly half and half of your visual field, as you go further in, the interior fills more and more of your visual field until it fills just as much of it as your familiar 3d world you entered from. try to imagine such things first. then try to go beyond.

Love your contents as always

It's been years since I've read the Rucker, and Pickover books. I never tried to do the exercises in the Pickover book which were a bit daunting after being out of university for so long. Now I'm inspired to re-read, and twist my brain into higher dimensions again!

You’re living the dream! Just understanding and mastering a subject for its own sake is what I want to do

Good to see you Toby! ☺️

Omg your videos are brilliant ❤ a gem

The 2nd book, "The Dark Forest", is asking us "How to visualize the 4th dimension?" from a human perspective. More closely related to what we are trying to learn in this video.

I learned to sing and play the guitar during a bicycle trip in Tassie, New Zealand, South America, Spain, visited libraries to work on a new philosophically derived universal language, learned biochemistry in a treehut near Byron Bay and a cosy wooden house in a secluded valley in New Zealand, and just philosophy, programming, inventions, physics theories, math, GPU programming in smaller episodes. Now I have a bungalow close to nature in the Netherlands. It's a great life, interesting to see this in someone else :) Thank you for sharing, good luck and enjoy!

Stressful way to film, congratulations for the result! 👍

Great idea. Good job! Thanks!

Cool to see you went through Bundaberg! I hope you liked it here even if you didn't stay for long

this video format is awesome

I am happy to see that you popped up on my feed. Are you better now. I have been looking forward to your return.

Watching this again, I am reminded of 'Stanboul train' a novel by graham Greene. Your work ethic seems tough with you working in bed, seated and standing during the day. From your videos your preferred relaxation is really energetic ! Glad you had a good trip. Really attractive ! thank you for having us along for the ride !

Loving the recent inspired videos

Think of a jawbreaker, each layer has no gap in between it because it is like a varnish, each layer is like a varnish.

Like, the symbolism?! Half-factorials, gamma functions, hyper volumes and fractal hyperspheres. The concept of the volume malleability with regards to hyperspheres and hypercubes is amazing.

Thanks!

Enjoyed this video. The parts without the mathematics reminded me of travelling on a Train in the Andes in south America, falling asleep next to a woman I didn't know who was working away on her laptop, I am able to understand your preference for your single seat with bed conversion Toby. Martin Gardner published articles on Hyper spheres and I think they are outside spatial reality in the same way Engineering equations used in analysis are not restricted in the number of interconnected inputs( 'dimensions'). Pressure, time, energy, size, temperature, friction, force, mass ......

I really enjoy this format. I like the peace. I like taking a break to hear about suger farms and look at deer. I only wish it were longer.

I am loving these challenges ❤❤❤❤

This is my new favorite ASMR channel 😊

Loved all the train terminology subtly being used

- Nice video Professor Rapunzel🧝‍♀ ... i mean Professor Tibees... - I always liked your interest in higher dimensions... 4:29 - It's very interesting to think that a ball can take up a tiny space inside a higher dimensional box ... and still be touching all the sides of it... like it's small but very big at the same time... 21:25 - looks like you enjoyed your train ride ... except for the part where you struggled not to get thrown around the room, right? 😎 ... 19:38

🙏 ty for helping me relax

Fantastic video and some AWESOME socks at 21:21 😉

I like this new style of videos where there is a second theme beside the maths!

Fascinating video! I hope the algorithm suggests this to every kind of person imaginable

Holy moly, she got serious again!

My dad told me that a physics professor of his at the University of Rome (and associate of Enrico Fermi's) would think about Maxwell's Equations every time he rode on a train and would never get bored. Now you look crazy if you're not looking at your phone.

Landed in Cairns almost a decade ago, great memories, even if I do not recall thinking about 3-spheres

in 15:45 the graphic showed that the (1/2)! = sqrt(pi) thats actuallly slightly wrong, the factorial of a half is HALF the square root of pi

You are a delight! Thank you for sharing. Authenticity is perhaps the most precious treasure of modern life.

This is so soothing

Bernouli seen the function of a train and seen the equatorial into geers which is how he developed the computer by image

14:40 Australia is really beautiful. Hope I can go there some day

Your voice brings me immediate calm.

Tully is the wettest place in Australia 🇦🇺.

Ralph Waldo Emerson creates interesting thoughts whilst thinking about our shared nature. Just a shy suggestion. Trains to new thoughts...and questions. Loved the landscapes!

The Three-Body Problem is in my top 3 sci-fi books for sure! What a great companion book for this journey too!

Tibees was an unexpected contender for my new favorite railway KZfaqr.

Wonderful concept.

love it!

Yes tebee u answered the question

i wish i had something more intelligent to comment about the content of this video, but i am just very impressed that you go out of your way to understand and investigate these complex mathematics topics. like i know you have an honours degree and started a phd, but i have never met someone who studied math like you, and as someone who actively avoided pure math and failed physics throughout my whole schooling, you make this incredibly approachable. science communicator pro!!!

Loved this on Nebula ❤

I don't understand any of this. Yet... Hearing her soft voice, seeing her beauty and intellect is just mesmerising.

Its 2AM in Norway and im watching the snow fall as i get lost in Tibees voice talking about things that are way above what im capable of comprehending.... But its so facsinating.

Hey Tibees, don't know if you figured this out, but the gamma function obeys the property n! = n * (n - 1)! So you can reduce the input to nicer values such as Gamma(1/2)

Awesome, awesome!

I love the Three body program!

It would take me a lot of time and effort to explain the peace and enthusiasm I feel with these format of sciency-vloggy-introspective videos.

Love tibees❤️❤️❤️

train of thought. love it.

Tibees, you make me jealous. You seem to have too much fun with these "until I learn it" series, I wish I could visit the Land of Oz to have fun like you do. Keep up the great work. Your videos are the highlight of my retirement.

Next video: Riding a "short horse" until i understand Schrödinger's Cat experiment.

4:25 the face Tibees makes when she thinks about the possibility that I might leave one or more comments under her video, but the possibilities on the probability distribution have not yet collapsed into a measured comment particle. At least I left the string theory out of this one.

Thank you Tibees! This one of the most enthralling videos exploring fractal dimensions. I am not too good in the subject, but when you mentioned the Gamma function, it sounded like it is an interpretation of what intermediate factorial values are. Is this the case? Is it just one kind of interpolation for factorials? If it is interpretative, why is it used in something non-interpretative, like determining the area of a fractal dimension?

LOL! I wouldn't be able to do this in Denmark 😂 You are cool Tibee. I also like this new format with challenges 😎Also 1:17 AAAAARGH my eyes! White screen of much blindness 😵‍💫

Hello Toby, I'm a big fan all the way from Kenya, always excited to see your content... I might not be as learned as you but I also have a huge obsession about extra-dimensions and their relationships to our 3d reality. 😅😅 I believe this should be a frontier fundamental topic taken seriously in the scientific community since it has a lot yet to be understood and applied properly. Nway, my observation from my very limited knowledge on dimensions is... If 1d has length, L¹ (e.g. 5cm) to describe total spacial magnitude covered over straight line. 2d has area L², (e.g. 25cm²) measuring total spacial magnitude occupied with perimeter 4L¹, (20cm) to describe the boundary encircling the spacial area. 3d has volume L³, (125cm³) to describe the total of spacial magnitude occupied plus has a surface area 6L² (150cm²) to describe the area of boundary surrounding it... This therefore means 4d beings have L⁴, (625cm⁴) to calculate total spacial magnitude occupied with a 3d volumetric space boundary, L³ around it. Volumetric surface boundary of a 4d hypercube = (L³) * the 8 3d cells in tesaract/hypercube= 8L³. (1000cm³)... 🤯🤯🤯 In summary, Dimensional space boundaries: Perimeter of a square, 2d = 4L¹ Surface area of a cube, 3d =6L².... Volumetric surface of a hypercube, 4d = 8L³ 4L¹, 6L², 8L³.... interesting sequence for higher dimensional surfaces/boundaries... My question is... can we 3d beings even try to imagine or recreate what volumetric surface boundary of 4d hyperobject/beings would look like? Coz my brain can't fathom that.

wow, just wow!

Haha... I do it too.. This one time I ended up all the way down in Stuttgart.😅

Omg.. i thought you already understood all about hyperspheres, hyperdimensions, hyperdirections and all the other hyperduperstuff ... 🤨😯🥺 YOU are the HYPER !!!

Nice topic and very cool train journey! Hyper-spheres are cool: note that the volumes of all even-dimensional unit hyper-balls sum up to e^pi :)