152 - You won't believe how big this number is (not clickbait) ✖️➕➗
Hey there, ! Sorry, it was clickbait :D
What's the biggest number you can think of?
No, no, not something like 'infinity' or 'infinity+1' or something.
What's the biggest number you can represent that has an actual value?
Have you heard of BODMAS?
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Let's start with 1, and go from there, hey?
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We could, well, count from 1 and just go up from there (1, 2, 3, 4, 5 etc.) but that would probably take a long time to get to a really really big number
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We could also add numbers from 1 (1+5=6, 6+5=11, 11+5=16 and so on and so forth), but that probably doesn't grow too quickly either
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We could multiply some really big numbers, which might get us preeetty high up too (like...15,312,334 x 101,239 or something?)
Let's go bigger.
Have you heard of Googolplex?
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One of the easiest ways to make bigger numbers is just to add 0's!
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10, for example, can then go to 100, then 1000, then 10000...you get the drift
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Instead of just adding 0's, we could instead just use exponentiation - essentially just count the number of 0's (aka putting a number 'to the power of')
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So, it could be 10^2 = 100, 10^3 = 1,000, 10^4 = 10,000 etc.
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The number googol was, uh, invented (?) by Edward Kasner in 1938 after he asked his 9-year old nephew what he should call 10^100
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The bigger number we could do is have 10^(10^100) = 10^googol (a googlplex!) and DAYUM that'd be a massive number of 0's!
That's a big number...let's go bigger.
Have you heard of Graham's number?
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Instead of just adding 0's, is there another way that we can create a system to make...really BIG numbers?
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I'm going to screw up a bit of the notation here but here we go:
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Adding, is like counting a number of times in one step (3 + 3 = 3 4 5 6)
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Multiplying, is like adding a number of times in one step (3 x 3 = 3 + 3 + 3)
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Exponentiation, is like multiplying a number of times (3 ^ 3 = 3 x 3 x 3 = 27)
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What happens when we go higher?
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Tetration, is like exponentiation, but happening a number of times (3^^3 = 3 ^ 3 ^ 3 ^ 3 = 3 ^ 3 ^ 27 = 3 ^ 7,625,597,484,987 = a 3.6 trillion digit number)
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We're already at a MASSIVE number, but can we go further?
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Pentation, is like tetration, but happening a number of times (3^^^3 = 3^^(3^^3)) = I don't know how many digits this had, but, well, it's big. It's at this point that my brain ceases to be able to understand what the hell is happening here but I'm just along for the ride.
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So let's keep going?
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Hexation, is like pentation, but happening a number of times (3^^^^3) <- I get lost right about here, but just imagine it's...just...really really big.
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And that's just the start.
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Ronald Graham (a living American mathematician) was trying to solve a graph theory problem (honestly it's not going to add to your understanding here so don't worry) and came up with a system (called the hyperoperational system) to create a mind-bogglingly big number to serve as the 'upper bound' for the problem.
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With g1 = 3^^^^3 (i.e. a hexated 3), g2 = 3[^...g1 times...^]3, g3 = 3[^...g2 times...^]3 etc, Graham decided that his number would be g64 = 3[^...g63 times...^]3
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Can you see how ridiculous this gets? The magnitude of this number is just...it's just SO big. Even just the number of arrows that you put between the 3's, when it gets to g2, is just an INCREDIBLY CRAZY BIG number. The mind just can't keep it all in.
I honestly lost you (and myself) trying to explain this all - once you get to tetration or pentation the mind melts, so I'm guessing you that you skipped most of it to come down here.
Anyway, that's enough for this lesson. Your homework is to look up an even bigger set of numbers (the Busy Beaver set of numbers) which is technically computable and humungously large, but difficult to actually work out.
Chat soon :)
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✔️Real Life Recommendations
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Predator - I wanna watch Prey because it's been getting some #hype, but I thought it would make sense to watch Predator first - which was a great idea because it's such a CLASSIC. Featuring some fantastic quotes from Arnold Schwarznegger including "Get to the choppah!", as well as some great supporting actor performances as well. One thing I loved was how the Predator was hidden for a bunch of time, and was scarier by the fact of not being able to see or hear it. In addition, the movie shows you the thinking, the traps, the set-up, and then how those plans can fail, and how Arnold adapts. I'll let y'all know when I've watched Prey as well :)
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Robata - a wonderful Japanese restaurant that has a modern vibe at the end of Exhibition St in the city. I recently went for a friend's 30th and they had some tasty pickled food, a great chicken yakitori, and some delicious pork cutlet! Add some sake in there and baby you've got a great dinner out! Highly recommended.
🚌 Adventures on the Information Super-Highway
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The case of the fake IMDB credits - an interesting corollary of the concept of a 'Metaverse' is people gaming their online presence so that they can seem more famous than they are. In this instalment, find out how Indian dudes are getting their own information panels on Google.
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The looming copper crunch and why recycling can’t fix it - something to keep an eye on, the part that we usually don't monitor - the resource constraints of more sophisticated technologies, how much we've already wasted, and the lead time to open up a new copper mine.
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When efficiency hurts more than it helps - the strive to become so damn efficient in everything you try to do means that you actually become less efficient overall because you don't have any idle capacity to add a new 'queue' to complete things. What this means is...
The closer you get to full capacity utilization, the longer your queues get. If you’re using 100% of capacity all time, your queues grow to infinity.
That's probably why it feels like there's always more to do, and never enough time to do things.