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Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org..../the-biggest-discove

00:05 Ramsey Numbers
One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935.
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../after-nearly-a-cent

06:21 Aperiodic Monotile
The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation.
CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com..../2023/03/23/its-a-sh
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../hobbyist-finds-math
- Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html

14:20 Three Arithmetic Progressions
Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern.
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../surprise-computer-s

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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/

Body language, both the speaker's and the audience's, is a powerful form of communication that is difficult to master, especially if the speaker is nervous. This video will teach you how to use your body language effectively, read the audience's body language and what to do when they look bored or disconnected. Use these tools to enhance your nonverbal communication abilities and better connect with your audiences.
Presented by Stanford graduate students Matt Levy, Colin Bailie, Jeong Joon Ha, and Jennifer Rosenfeld. Created as an exemplary final project in Lecturer JD Schramm's Strategic Communication course. Learn more about communication techniques and best practices on "Think Fast, Talk Smart: The Podcast." https://www.gsb.stanford.edu/i....nsights/think-fast-t

We all are, at times, the victims of one of the cruellest and most remorseless of all mental afflictions: obsessive thinking. But why?

FURTHER READING

You can read more on this and other subjects here: https://9qq0.short.gy/m0b8dK

“For some of us, today like every day, will mean another case of immersing ourselves, from the moment we wake up, in a by-now very familiar set of painful thoughts. We will dwell – once again – on how awful we look and more particularly, on how our nose is repulsively proportioned relative to the rest of our face. We will think – once again – of a website we inadvertently visited twelve years ago and how the police might be preparing to close in on, and arrest, us. We will think – once again – of how several of our neighbours (especially the people upstairs) might be colluding to ruin and disgrace us. Or we will think – once again – of something we said to a colleague which we fear they misconstrued and which may well lead them to seek disciplinary action against us at any moment…”

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Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015

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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman
SFX & Music: Jonny Hyman
Camerapeople: Derek Muller, Raquel Nuno
Editors: Derek Muller
Producers: Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett

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Adding Fractions?
Subtracting Fractions?
Multiplying Fractions?
Dividing Fractions?
Mixed Numbers?
Simplifying Fractions?

It's all here.

To support tecmath on Patreon: https://www.patreon.com/tecmath
It really helps and is appreciated!

The greatest problem of the modern education system is that it doesn't focus on systematically preparing students for many aspects of the real challenge out there: Life itself.

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⁣Gain a comprehensive understanding of SEO strategy, covering key elements such as crafting effective strategies, creating actionable roadmaps, leveraging competitive advantages, and presenting your plans to secure support and buy-in.

Herein we have compiled some of the most interesting psychological facts that will blow your mind! Human psychology explores the mind and behavior, and while there’s still a lot that we don’t know, there are some fascinating and surprising study findings about the secrets of the mind.

This video provides insightful explanations to why yawns are contagious, why food tastes better when someone else makes it, why we unintentionally believe what we want to believe, and so much more!

These psychology facts will explain or confirm some of the things you observe in yourself and others!


OTHER VIDEOS TO WATCH:

7 Subconscious Mistakes Your Brain Makes Every Day:
https://www.youtube.com/watch?v=1tEBf_qMrMM

17 Interesting Facts About Love:
https://www.youtube.com/watch?v=FrZxarhJX5E

15 Amazing Facts About The Human Body:
https://www.youtube.com/watch?v=FxBlYh7Sg-E


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Millions of Americans are administered anesthesia each year. Since 1846, doctors have used a variety of drugs to make patients unconscious for surgery, but even though the medications have changed, there's one thing that remains the same— it works. But how exactly?

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Following is the transcript of the video:

Narrator: When you go to sleep, if I pinched you, you'd be up. If I shook you, you'd be up, right? But under anesthesia, I'm gonna pinch you and do a full operation and you're not up. So it's really further on the spectrum of unconsciousness.

Narrator: When you wake up after being put under with general anesthesia you barely feel like any time has passed. You could have been out for an hour or a day and you wouldn't know the difference.

Fong: When you go to a natural sleep, people call your name, your alarm goes off, you wake up, right? This is not what is gonna happen during general anesthesia. You're gonna be unconscious.

Narrator: You're closer to being in a coma than being asleep.

Anesthesia was first used during surgery in 1846. The drug provided at that time was ether. Now anesthesiologists more commonly use a combination of drugs like propofol and fentanyl which interrupt neural pathways so you don't feel pain and you don't remember the surgery.

Fong: Three things that you need for general anesthesia are you need amnesia so that they don't remember, analgesia so they have pain relief and then operating conditions for the surgeon. Some surgeries you need the patient to be very relaxed so you would use a muscle relaxant. Other surgeries the patient just needs to be asleep and anesthetized but they don't need relaxation so how they do that varies upon the different medications that you're using. Some will depress excitatory neurons and some will enhance inhibitory neurons.

Narrator: Excitatory neurons, for example, get excited and send signals to other neurons to fire. Depressing them means less signals telling your brain you're in pain. Inhibitory neurons do the opposite. They make it harder for neurons to generate these electrical signals. In either case this means fewer active neurons overall which is important because when your body is being poked and prodded, neurons would typically fire to tell your brain you're in pain. If those neurons aren't firing, your brain doesn't know that your body is, well, being cut open.

Fong: Basically it interrupts the pathways and the communication between your neural networks. We're aiming for them to be not in pain by looking at their vital signs, their heart rate, their blood pressure. Then we want to make sure that they're unconscious.

Narrator: Without anesthesia, many important surgeries wouldn't be possible because they'd be way too traumatic.

Fong: Surgery didn't move forward, really, until anesthesia moved forward. You know, you watch those old movies. They give you a swig of alcohol, they put a tourniquet and they hack your leg off. People don't do well with that, right? If you had a bad heart, that would be the end of that.

Narrator: After the procedure is complete the doctors stop administering the meds and the most powerful effects of the drugs wear off but even though you're conscious again you might continue to experience some of the drugs side effects.

At $2 billion per aircraft, the Northrop B-2 Spirit is the most expensive plane ever built. But how does this giant become invisible to radar? And why does it look like it flew straight out of a sci-fi movie?

For more megaprojects content, be sure to subscribe to MegaBuilds!

0:00 The Insane Engineering of the B-2 Bomber
0:52 The Cold War
2:09 The ATB Program
4:42 The B-2's Design & Engineering
9:32 Capabilities & Performance
11:50 The Cost & Future of the B-2

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Dr. Cal Newport and Dr. Andrew Huberman discuss the concept of time blocking, fixed schedule productivity and deep work.

Cal Newport, Ph.D. (@CalNewportMedia) is a professor of computer science at Georgetown University and bestselling author of numerous books on focus and productivity and how to access the deepest possible layers of your cognitive abilities in order to do quality work and lead a more balanced life. Dr. Andrew Huberman is a tenured professor of neurobiology and ophthalmology at Stanford University School of Medicine and host of the Huberman Lab podcast.

Watch the full episode: https://youtu.be/p4ZfkezDTXQ
Show notes: https://www.hubermanlab.com/ep....isode/dr-cal-newport

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Timestamps
00:00 Introduction to Time Management Strategies
00:11 The Philosophy of Time Blocking vs. To-Do Lists
01:31 Adopting a Fixed Schedule for Productivity
02:17 Incorporating Exercise into a Busy Schedule
03:30 Managing Insomnia and Productivity
06:41 Deep Work: The Key to Long-Term Success
07:54 Looking Ahead: Planning for Decades, Not Days
08:51 Conclusion and Invitation to Watch Full Episode

#hubermanlab #calnewport #productivity the Huberman Lab podcast is for general informational purposes only and does not constitute the practice of medicine, nursing or other professional health care services, including the giving of medical advice, and no doctor/patient relationship is formed. The use of information on this podcast or materials linked from this podcast is at the user’s own risk. The content of this podcast is not intended to be a substitute for professional medical advice, diagnosis, or treatment. Users should not disregard or delay in obtaining medical advice for any medical condition they may have and should seek the assistance of their health care professionals for any such conditions.

Want my books for free? Go here: https://www.acquisition.com/audiobooks
The easiest business I can help you start (free trial): https://www.skool.com/games

If you’re new to my channel, my name is Alex Hormozi. I’m the founder and managing partner of Acquisition.com. It’s a family office, which is just a formal way of saying we invest our own money into companies. Our 10 portfolio companies bring in over $250,000,000+ per year. Our ownership stake varies between 20% and 100% of them. Given this is a YT channel, and anyone can claim anything, I’ll give you some stuff you can google to verify below.

How I got here…

21: Graduated Vanderbilt in 3 years Magna Cum Laude, and took a fancy consulting job.
23 yrs old: Left my fancy consulting job to start a business (a gym).
24 yrs old: Opened 5 gym locations.
26 yrs old: Closed down 6th gym. Lost everything.
26 yrs old: Got back to launching gyms (launched 33). Then, lost everything for a 2nd time.
26 yrs old: In desperation, started licensing model as a hail mary. It worked.
27 yrs old: "Gym Launch" does $3M profit the next 6 months. Then $17M profit next 12 months.
28 yrs old: Started Prestige Labs. $20M the first year.
29 yrs old: Launched ALAN, a software company for agencies to work leads for customers. Scaled to $1.7mmo within 6 months.
31 yrs old: Sold 75% of UseAlan to a strategic buyer in an all stock deal.
31 yrs old: Sold 66% of Gym Launch & Prestige Labs at $46.2M valuation in all-cash deal to American Pacific Group. (you can google it)
31 yrs old: Started our family office Acquisition.com. We invest and scale companies using the $42M in distributions we had taken + the cash from the $46.2M exit.
32 yrs old: Started making free content showing how we grow companies to make real business education accessible to everyone (and) to attract business owners to invest or scale their businesses.
34 yrs old: I became co-owner of https://Skool.com to help the many people who want to start a business online do so.

Today: Our portfolio now does $200M/yr between 10 companies. The largest doing $100M/yr the smallest doing $5M per year. Our ownership varies between 20% and 100% ownership of the companies. Many of them we invested in early and helped grow (which is how we make our money - not youtube videos).

To all the gladiators in the arena, we’re all in the middle of writing our own stories. The worse the monsters, the more epic the story.

You either get an epic outcome or an epic story. Both mean you win.

Keep crushing. May your desires be greater than your obstacles.

Never quit,

Alex

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