Neil deGrasse Tyson Explains Exponentials 

I absolutely love these guys together! This is a rare friendship between comedian and astrophysicist. They always make my day and make learning THAT much better!!

Chuck really deserves more credit for just how well he actually learns everything they talk about. He might be confused at first but a few months later he applies it to something even harder!

Chuck is so funny! I love the blend of humor and science from this series.

11:24 Neil dropping the HARD F when it comes to banks

Is it possible that our innate linear thinking is what hampers our ability to grasp the spread of things like viral outbreaks? The penny doubled everyday is very similar to the speed of disease spread especially with modern travel capabilities. Thank you Neil and Chuck.

Neil: “Chuck I’m going to tell you how your brain is wired” Chuck: poorly 🤣🤣 Two absolute legends, I love watching and learning from your uploads, and the added comedy is class!👌🏻 keep them coming.

Most homeowners had no idea of the mortgage risk. However, all the bankers had the education to know what they were doing. Homeowners should have been protects and the bankers should have been allowed to fail.

Another exponential I like is time in seconds. We understand 1 second, 10 seconds and 100 seconds. 1,000 seconds is 16.67 minutes. 1,000,000 (million) seconds is 11.6 days. 1,000,000,000 (billion) seconds is 31.7 years. 1,000,000,000,000 (trillion) seconds is 317 centuries.

NDT “Chuck, I can hand you 5 million dollars right now” Chuck “I always knew I liked you!” 😂🤣

There is a VFX video made by the corridor crew , which uses CGI to portray accurate sizes of astronomical objects to help understand the scale better , I highly recommend watching it

'In ten days it will cover the earth', made my evening great, cheers chuck.

1 is making the science, space subjects more understandable, the other 1 is making the video funnier. And both of them are like legends about that. I saw StarTalk youtube channel just a few days ago, but i watched many of it's videos. Thanks Mr. Tyson and Mr. Nice for making these subjects funnier and more understandable :)

14:17 this has to be my favourite quote of all time it perfectly sums up why science is so hard the world is not made to be easily understood by us and we are not made to understand it.

Combination of Dr. Tyson and Chuck is like H2O, very crucial for survival of my sad soul. Much thanks.

I just found this channel last week. You guys, the content, and the way it is delivered is amazing.

Exponentials grow very fast. Factorials: Hold my beer.

Chuck totally unlocks Neil with the humor and really opens the conversation. You can see Neil explaining and Chucks gears turning. This is such a special relationship

“Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.”

Clock : 3 am Me : Sleeping NDT : BIIIIIIIIIIIIIIIIIIIIIIIIIIIIG NUMBERS....

Great video as usual. Please make a video describing all earth’s movements and their cycles (incl. rotation, revolution, precession, Nutation, around barycenter sun/moon etc). Thanks

"Mortgage" literally translates as "death pledge". In fairness, the original Latin "death pledge" meant that the debt would either terminate with your death or eventually be paid off. So it's not really as bad as the name "death pledge" makes it sound. But, still, as you pay off your mortgage, remember that "mort" means "death" and you're paying off your "death pledge". And, yeah, paying that mortgage probably will be the death of you too, eh?

I wish this video was exponentially longer, I could listen two these two for the rest of my life

The people who you claim cant think in terms of long term in regards to evolution are typically Religious, Ironically are the same people who think in terms of eternity. other than that, I love you two and your videos.

We all knew Dr. Tyson was brilliant as a scientist AND as a communicator of science to the general public. What is surprising, pleasantly, is how sublimely clever Chuck is, in his grasping of subject matters far removed from the everyday experience or the average "layman" level of understanding. He may play the fool, so to speak, for comedic effect but he is anything but. A worthy sidekick, a great comedian and really fun to watch him listen, learn and react. These two are the best science teachers a man could ask for!

Wow this is deep. Especially the discussion of floating interest rates and the 2008 collapse.

In Chuck's defense, he was probably taking into account real world conditions where the growth rate of the algae may have slowed due to algae dying from overcrowding

13:48 - This also explains why people refuse to believe that the foods we eat already are GMO, but it took thousands of years to perfect the current strains. The only reason people are concerned now is because we can see a change within a decade now, not 10 lifetimes.

Neil should talk about Knuth's Up-arrow Notation and extremely large transfinite numbers.

1:28 Swahili: Kimeumana! If you know you know.

It amazes me that a number as large as the quantity of atoms in the universe can be represented by the term 10^80

Every Vsauce opening: Hey Vsauce Michael here! Startalk: Chuuck

"Everything's big in astrophysics. Texas, you lose." I love the energy of this line.

I can't stop binging these StarTalk videos and I just bought your book lol so I know the line you were talking about. Absolutely love you guys!

There is an old story in India where an old sage challenges a king in South India in a game of chess. If the king won the sage would have to give everything he had but if the sage won the king would have to give grains of rice starting from one, doubling everyday till 64 days(because 64 squares on a chess board). The king thought linearly and accepted the challenge. The sage won. Till the first 15 days the king kept on giving rice and boasted about his kingdom's wealth but on the 20th day the king realizes that he has been tricked and asks the sage to forgive him. The sage forgives him and advices the king to think carefully before doing anything. Great story on exponentials!

Many of us who have engineered computer hardware or software understand these concepts, especially if you've started around the birth of the personal computer age in the late 70s / early 80's. Dealing with storage, throughput / bandwidth, random access memory capacities over the years absolutely solidifies an understanding of exponents and exponential growth.

Love u chuck been listening to start talk for years first time seeing u

I hit the thumbs up before I even watch the videos. Every one is entertaining, informative, and just simply a delight.

Hey Neil, can you do a video explaining what the maximum brightness that something could ever be?

I'm so happy I can hear you talk about the things you know

Man I love these videos, learning so much

A handful of words on "scale"... AND of course, I love these two!!! They're always fun and informative... When I have trouble dealing with the scale of a problem... depending on the particular problem, I try to visualize something more relatable to connect to it... Scale of the earth for instance... and then the sun... If you Scroogle it, the earth is around (not exact) 10,000 miles in diameter, which when one considers C= pi * D... comes to 30,000 miles (and some change) around... I consider the old-school rule to change oil every 3,000 miles or 3 months (of regular driving)... SO to drive straight through the earth, I'd change the oil 3 times and still have about 1000 miles to go... my state is around half that from where I live to Memphis (on the Miss... River)... SO in the "regular" habit of driving I do, it would take me about 10 months to make that journey... through... AND 31 or 32 months (2 and a half YEARS... or a tad more) to drive around it... Now... Take a dime and use it to draw a circle on a wall (or a paper you then tape to the wall... Let that dime-size circle represent Earth... If in the same "picture", the circle that would represent the sun would take up THE ENTIRE WALL from floor to ceiling... Note, please, that it's still NOT a perfect scale for precision, but you're now able to visualize (give or take) WELL within the "ball-park" of what you should think of in the comparison... AND a little closer to how it might connect or relate to your own life... Struggle with the millions, billions... trillions? Okay... A million dollars in $100 bills, is about 10,000 actual bills and bundled together, it weighs about 5 lbs... A billion would weigh 5000 lbs in $100's... So you couldn't carry it all in the bed of a full-ton dually... You'd need 2 duallies AND a half-ton pick-up to legitimately carry a billion dollars in $100's... Think about that... If you earned a dollar every second, you'd make 60 bucks a minute and 3600 every hour... It would still take you 32 YEARS to earn a billion dollars, and you STILL (at 3600/hour) would NOT LIVE LONG ENOUGH to earn a single trillion dollars... A trillion dollars would weigh about 5 million pounds in $100's... SO you'd need a FLEET of semi-trailers to load that cash and move it anywhere. Like I said, this ain't perfect or exactly precise. It's being able to "ball-park it" and find it relatable to something you CAN understand. ANYWAYS... I hope this helps someone... It takes a little repetition and practice, but it can be a useful practice guide. ;o)

Love that Mr.Tyson and Chuck do these videos ! watch these videos learn and laugh !

I’m frivolously but not exponentially really curious about that gold column behind Neil’s right shoulder.

One of the great examples is when you ask someone how tall a piece of paper would be if you could fold it in half 50 times. Your brain simply can't fathom that the answer is "it would stretch to the sun" but it would. Fascinating.

Always a pleasure watching star talk 👍🏼

I listened to your audio book of Astrophysics for People in a Hurry. I wasn't in a hurry, I was chilling at home. I don't remember the opening line, but I once knew it.

I thought i had a handle on exponentials but then i was presented to arrows notation and it blew my mind with things like Grahams number

Amazing when the brain make you go from ultra instinct, to slowing down time, then making you go rag doll mode all within seconds 😁

Wow, this is amazing, habari from Tanzania, where Serengeti is located.

It would be great for you guys to discuss the ways that the human brain is wired for exponential perception, like light and brightness

A bit late, everyone in the world needed this at the start of the Pandemic.

Been here from 100k subs I love that this channel is growing

Ironically, even though we THINK linearly, we SENSE things exponentially (or logarithmically). As an example, the difference in volume between a 1000 microwatt and a 2000 microwatt sound is not perceived as the same as the difference between a 2000 microwatt and 3000 microwatt sound. Instead, it takes a 4000 microwatt sound to be perceived as an equal increase in volume, and an 8000 microwatt sound for the next proportionate increase. So, instead of perceiving linearly (1000, 2000, 3000, 4000, etc.), we perceive logarithmically (1000 x 2º, 1000 x 2¹, 1000 x 2², 1000 x 2³, etc...). In this way, sense organs are useful over an enormous range of intensity.

7:40 "As a astrophysicist we are steeped in it. We are Baptist in it. So we have a easier time." Not just Astrophysicist. As chemists we routinely deal with sizes, scales, and lengths of time that are ridiculously small. I remember earlier on in my training doing drills in exponentials. Converting back and forth between exponential notation to chemical concentration and back over and over. Now it's like my brain as a zoom function, can easily imagine zooming in to picture things that are super small, or zooming out to picture things that are super large.

I love that were diving into this topic again.

A few key exponents that hit us in real life on a regular basis: - interest rates - inflation - population growth - infection spread - social media disinfo spread

Humans often rely on linear thinking because it allows us to easily predict outcomes based on past experiences. However, this approach can fall short when dealing with unpredictable situations or systems that do not follow straightforward logic. How can we balance our natural inclination for linear thinking with the need for more flexible approaches in complex problem-solving?

I'm developing a cure for allergies and addiction. It's proven to work. However, converting my alternative formulas is an issue. This video gave me insight about translating my concepts to linear brains. To most people, they believe my severe allergies disappearing was a miracle even though I can do a disertation on the neurology and physics involved. Thanks.

That “start with a penny and double it” thing is an idea I had years ago for a game show. Similar to Jeopardy!, it has 30 questions with the first right answer awarding 1 cent, then every question after that will double the amount if right, or halve it if wrong. If someone gets all questions right, they get a total over $5 million (or add a 31st bonus question to bring it up to $10.7 million).

Thank you for the video! Now whan Chuck is almost ready, next big number theme is Knuth's up-arrow notation and Graham's number? To proove we can create integers without any phisical meaning.

An excellent example that a professor of trigonometry gave us (who from Argentina communicated by mail with Carl Sagan several times): Suppose that a newspaper sheet is 1 millimeter thick, fold the newspaper 50 times ... you will reach the belt of asteroids !!!, Greetings from Argentina. Un excelente ejemplo que nos dió un profesor de trigonometría (que desde Argentina, se comunicó por correo con Carl Sagan varias veces): Supongan que una hoja de perióico mide 1 milimetro de espesor, plieguen el diario 50 veces... llegarán al cinturon de asteroides!!!, Saludos desde Argentina

As much as these type of videos may make others feel small, they make me feel large, for I can witness them.

12:50 Exactly, bro. In fact, 1000 seconds is about 16.67 minutes whereas a million seconds is equivalent to about 12 days. And a billion seconds is equivalent to about 32 years. That's the power of exponentials.

According to Wikipedia, the total area of Alaska is 1,717,856 km^2, while the area of Texas is 695,662 km^2. Dividing the former number by the latter we get about 2.5, not five.

Thanx guys. Massively appreciated

Arithmetic starts getting weird at exponents. Counting, the most basic arithmetic, makes perfects sense -- just add one at every new step to what you had at the last step. Adding is a lot like counting, but you can do it in bunches: start with 5, glom 3 to it and you've got 8. And multiplying is just a ramped up form of addition. If you have 5 sets of 3, you're basically adding by 3 -- 3, 6, 9, 12, etc -- 5 of which gets you to 15. What these operators have in common so far, is that both numbers, 5 and 3, show up in the answer. That 3 is still sitting there next to the 5 inside the 8 you got after you added them together. Same goes for multiplying -- there's still 3 5s (as well as 5 3s) right there in the 15 you got when you did times. But now we come to exponents where, still working with 5 and 3, we would get 5^3, which means 3 copies of 5 multiplied together, so 5x5x5 which is 125. This is how exponents aren't like the other bois and girls -- there's no 3 in 125. Where did it go? 125 can only be divided by 5. It's like there never really was a 3. Really, the 3 is outside of the value, just working as a note off to the side to let you know how many of the numbers that you _are_ working with need to go into play.

You can see all the planets and the universe "to scale" in VR, universe in a sandbox. Highly recommended.

These are so much fun to watch. And I learn things too, I can tell the guy's are just having a good time too, maybe that's why this is so great

I really want to see neil talk about arrow notation which makes number increase at an even greater rate is size. Is still using exponents but the exponents themselves grow exponentially.

I speak to people about exponentials all of the time .. most recently when discussing population growth & now Spotted Lantern Fly growth / spread .. I think the lantern flies will give people a better sense of it.

I watched the preview on mousing over, and thought "what kind of torture is going on here?" So now I'm watching. If only school was this fun! This reminds me when I was reading Asimov decades ago. Unfortunately he only authored around 500 books.

Great stuff!👌🏾😊

Chuck with a new mic, Nice!

Chuck plays the dumb sidekick but he is no slouch mentally and brings so much comedic relief to all this lofty mathematics, I love these guys together

that is a great observation about the models of the solar system and how they exaggerate the planets

As soon as he said Moorgate rate I knew I knew I needed an analogy.

There is an Indian legend about the invention of Chess game, that explains exponential. To compensate a name named Sessa for the invention of the game of chess, the King of Taligana offered him a reward of his choice. Sessa asked to be granted a grain of wheat for the first square of the chessboard and the double for every square thereof. The King, unable to think exponentially, accepted the request just to discover soon that the final amount of wheat he granted as reward was impossible to pay (something like 36 billions of billions of grains). Once the King recognised the mistake, Sessa retired his request and the King appointed him governor of a province.

Some of this conversation reminds me of a comic in MAD magazine many years ago. The boss comes out of his office screaming about a fifty cent long distance telephone call. His secretary says "But you deal in hundreds of thousands of dollars every day, why are you so upset about fifty cents?" He replies, "I have no comprehension of a hundred thousand dollars but fifty cents I can understand!"

This time it took Chuck five seconds to send Neil into his first fit of laughter in the convo. Isn't that a new record?

Jul 27: Neil: How many earths would fill the Sun? Chuck: Idk. Neil: 1 million! Literally a week later: How many Earths would fill the Sun? Chuck: Idk.

I heard you talk about the 4th dimension and I would like to say . I had a thought and it was “ everything is already in existence it’s just yet to be discovered “ in other words a Tesla vehicle was already in existence because the materials were on earth already…. But Neil thanks for inspiring me

I own your book Astrophysics For People in a Hurry in hardback, and that is not the opening line from the first chapter or the preface.

About the idea of a million, I found it easier to process this from a salesperson point of view. I have a product that I market for $1,000. My goal is to sell one thousand units to reach gross sales of $1M. That math seems not so confusing for me like this. That's exponentially appealing!

the other day i was so facinated by the POWER of exponential change when a friend asked me how many times do i have to fold a thickness of 0.1mm newspaper to reach the moon. I guess I will leave my comment here cause you will be surprised when you find out the answer yourself....

I was thinking about this the other day. I read somewhere that the largest black holes will eventually evaporate after something like 10^100 years from now. Which means after 10^99 years, that unfathomable amount of time has to elapse again another ten times over before you get to 10^100. It’s impossible to visualize how much time that is

I met Chuck. He's a wonderful family man. He and Neil make a great team.

I absolutely LOVE these explainer videos

Just to be *that* guy, a penny a day exponentially multiplied by 2 for 30 days is not ten million dollars. It's actually $5,368,709.12 on the 31st day, plus roughly the same amount you've already been given (for instance on the tenth day you get given $5.12 which enables you to have made $10.23 in total) so the total figure is more or less $10,737,418.24 and not the $20,000,000 stated in this video. But still, take the penny. #JustSaying :-)

I love these guys together. I learn so much, and laugh too! I wish I had Neil for a teacher

love this! you guys are hilarious and educational!

Sir I have one question for you does multiverse is exists ❓

I've always wondered. If we don't know where all antimatter is, then could we instead blame black holes for the odd distribution?

Absolutely brilliant!!

Alaska is the largest state in the United States in terms of land area at 570,380 square miles (1,477,300 km2), over twice (roughly 2.47 times) as large as Texas. before the Ice melted, it was almost twice that size. It's losing ice exponentially, But the ice loss, around the world approaches something factorial. Factorials grow faster than exponential functions, but much more slowly than doubly exponential functions. However, tetration and the Ackermann function grow faster. I've heard remarks that ice loss is tetration, and that seriously scares me.

This is the time when we need to evolve as a species to understand exponentials, the world beyond 3D, etc. I mean the exponential thing isn't difficult, just by doing exercises in math at school you realize that exponentials are just way bigger than you can imagine so just overestimate when asked for an estimation, and in a life or death situation (like in 2008), take out your calculator.

yeah i can't get my head round how big the sun is too.. thankyou for making and sharing these great videos 🙂 x

Hi Tyson, could Benfords Law be a subject you would take up sooner or later on your channel.......ex distances from the stars to earth etc. fits, and how does that and what does that say about the univerrs.........

I am so glad he talked about the "one penny today" story - after one month of doubling you've netted 20,000,000 dollars.

"Oh Lord" feels like the appropriate reaction 😂

Alaska is 2.47 times the area of Texas not 5. Secondly I don’t know which “close-packing” Neil used but regarding of that, current solar volume is 1.41x10^18 km3. If we take the average Sun-Earth distance of 1.496x10^8 km as the new radius of the red giant Sun we obtain a sphere of 14x10^24 km^3. Which divided by the current volume gives an increase of almost 10 millions Suns (not 1 million). It’s nice to throw some numbers around but they better be kinda close at least