You should switch from calling it 'dungeons' to 'BASEments'

@jocabulous

3 жыл бұрын

badum tss

@david_ga8490

3 жыл бұрын

R/whoshhhh

@skrrrrrrrrt

3 жыл бұрын

David Gallego Álvarez huh

@zegichiban

3 жыл бұрын

I thought I like it being called dungeons, until I saw this comment.....

@sallylauper8222

3 жыл бұрын

aLL YOUR BASEMENT ARE BELONG TO US.

There's something about Neil's voice that has a "teacher that really cares about your learning" quality to it

@sillysausage4549

3 жыл бұрын

Strange. I find his corrupted English accent incredibly annoying. Sure he's a nice bloke, but the American pronounciations really grate on me.

@Liveitlarge247

3 жыл бұрын

He has a wicked T-shirt on too

@leif1075

3 жыл бұрын

For me a soothing sensual therapeutic quality!!!

@matthewmcbride2893

3 жыл бұрын

I completely agree. He seems earnest.

@Bronco541

3 жыл бұрын

@@sillysausage4549 I like how his accent is somewhere between English and American, its unique (somewhat, I'm sure there's plenty of people who move around a lot with similar accents). But more than that; he's enthusiastic and passionate about what he teaches.

New mathematical terms here - “pretty big”, “gigantic” and “really tiny”.

@skebess

3 жыл бұрын

We sometimes use this kind of terminology. Others include: almost everywhere, almost surely, almost never, always never, etc...

@duskyrc1373

3 жыл бұрын

And all three terms can apply to the same number, depending on context

@andrewboyd9948

3 жыл бұрын

@@duskyrc1373 bruh

@BoundlessxArts

3 жыл бұрын

@@skebess "70% of the time it works every time"

@JobvanderZwan

3 жыл бұрын

Nothing will ever top "the tooth number" though

There's a valuable treasure awaiting brave adventurers at the bottom of this dungeon, and his name is Neil Sloane

@Triantalex

6 ай бұрын

false.

If you listen to this without watching, it's like a madman just rattling off numbers.

@kasperrosenlund4187

3 жыл бұрын

That would describe a lot of Numberphile videos :D

@Vgamer311

3 жыл бұрын

It’s like that if you’re watching too.

@andybaldman

3 жыл бұрын

@@Vgamer311 lol!

@hayuseen6683

3 жыл бұрын

It stopped making sense after 40 seconds in, after that it was Numbers Station ramblings.

@not2tired

Жыл бұрын

This also works if you watch without listening

Neil sounds like a Half Life scientist

@zanvure330

3 жыл бұрын

Lol well said

@jschoete3430

3 жыл бұрын

How is that so precise haha

@ericschuster2680

3 жыл бұрын

the test chamberrrrrrrrr

@ionymous6733

3 жыл бұрын

i hear Professor Farnsworth from Futurama

@carltonleboss

3 жыл бұрын

He was the G-Man the entire time

Props to the editors and animators. This was pretty dense but their help made it understandable

How about ... 12 11 10 11 12 ...

@patrickhanlon932

3 жыл бұрын

It all depends on how you parenthesize it.

@jeremydavis3631

3 жыл бұрын

EDIT: This was my first impression. I've made another comment after thinking about it a bit more. Given that the size of a tower is unbounded and the size of a dungeon is asymptotically bounded (so that we only need two nested logarithms to get it to a friendly size), the combination should diverge to infinity, just slightly more slowly than the tower alone would. Calculating the terms of the sequence would be quite a bit harder, though.

@ShevkoMore

3 жыл бұрын

............... 12 12.. 11 11.. 10 10 10.. 11 11 11.. 12 12 12.. ...................

@jeremydavis3631

3 жыл бұрын

Oh, wait, I think my first impression was wrong. As Patrick Hanlon said, it depends on how you parenthesize it. If the last operation we do (assuming it makes any sense to talk about a "last" operation in an infinite sequence) is part of the tower, the result should be unbounded, since we're raising a large number to an unbounded power. If the last thing we do is part of the dungeon, it'll drag us back to the asymptote, and so it *might* be bounded. Proving that it actually *is* bounded for any given parenthesization strategy doesn't seem easy, though.

@henryirvine7964

3 жыл бұрын

no

2:22 Took me a while to figure out that 11 was actually an equal sign rotated 270 degrees. because who says 90 degrees these days

@ChadTanker

3 жыл бұрын

every body does say 90 degrees because its shorter

@unnamed7225

3 жыл бұрын

@@ChadTanker Then what should everybody say for negative 90 degrees?

@cubixthree3495

3 жыл бұрын

@@unnamed7225 negative 90 degrees

@unnamed7225

3 жыл бұрын

@@cubixthree3495 ;-;

@wolfiy

3 жыл бұрын

@@cubixthree3495 3pi/2

Every time I see Mr Sloane's videos I can't take my eyes off his folders. Please can I ask, what are "Fat Struts" ? Thanks for the content y'all.

@eac-ox2ly

3 жыл бұрын

True

@lawrencecalablaster568

6 ай бұрын

Apparently they’re a mathematical structure in a lattice about which he has written a paper!

@Triantalex

6 ай бұрын

??

I got no idea wtf you're talking about but i like how you write stuffs on that brown papers

@binodbinod6814

3 жыл бұрын

Binod

@EHMM

3 жыл бұрын

E

Sloane is great. I love integer sequences.

@chrisdoyle1389

3 жыл бұрын

He's a Psycodelic Maths Professor,He has a Hendrix T-shirt on.

@christopherellis2663

3 жыл бұрын

@@chrisdoyle1389 psychedelic

If number explanations at the online encyclopedia of integer sequences (oeis) were like this, I would spend more time exploring it.

Never heard of this but that is what is so great about this channel, always bringing fascinating new concepts to the viewers attention. This has certainly inspired me to look more into different bases.

I love how I was so fooled by the first dungeon sequence. I compete in a lot of math competitions so I got very full of myself, and it was obvious the increment was always increasing by 1 and then it went like NOPE

@lawrencecalablaster568

Жыл бұрын

It’s so strange how it fits exactly up to 65 & then exponentially increases.

@19Szabolcs91

Жыл бұрын

@@lawrencecalablaster568 Sure is, but it has to do with how the difference in the sequence gets to be a 2-digit number, breaking the pattern. Similarly, the reason all 4 sequences started with 10, 11, 13, 16, 20 comes down to "'1" being the first digit.

So the "magic jump" in these sequences happens when the second units number increases from 1 to 2 (ie "10 sub x" to "20 sub x")

@rosiefay7283

3 жыл бұрын

Which shows just how fundamentally bogus this whole setup is. It confuses numbers with decimal representations.

@menachemsalomon

3 жыл бұрын

@@rosiefay7283 No, I don't think that's so. Firstly, when we're discussing different bases, only the first step is decimal. But Dustin is saying that the jump happens when the second place (not the units, the n^0 place, but one to the left, the n^1 place) goes to 2.

@Martykun36

2 жыл бұрын

​@@rosiefay7283 not really? it just means you have to settle on some "global base" first, and in this case it was 10. You can do the same process for any other base.

When you cross that threshold of having no idea what's going on, but there's still more than 10 minutes left in the video...

@GerSHAK

3 жыл бұрын

Hahaha :D

@Terri_MacKay

3 жыл бұрын

I got to the point where I was beginning to catch on...then he started talking about logs, and I was completely lost again. I am terrible at math, but find it fascinating. I understand a lot of the videos on this channel, but some just go right over my head.

@penfold1992

3 жыл бұрын

And then he starts referring to dollars!

@Terri_MacKay

3 жыл бұрын

@@penfold1992 Yeah...what was that about?? Is "dollars" a math term I don't know about?? 🤔😂

@-johnny-deep-

3 жыл бұрын

@@penfold1992 - Yeah, that was odd. I guess he thought it would help people understand. I was understanding great until he temporarily threw me by saying "dollars" :-)

At first I was like "wait, this is a really simple pattern, 10, 11, 13, 16, 20... that just means that I have to add 1 the first time, 2 the second time, 3 the third time and so on and so on". But then I saw the numbers at 6:13. Oh boy was I wrong. This pattern is not as simple as I thought.

@martind2520

3 жыл бұрын

The third sequence does actually follow that pattern, so you weren't completely wrong.

@KnakuanaRka

3 жыл бұрын

Yeah, I think it starts like that, but I believe it stops working once you get beyond 20.

@-johnny-deep-

3 жыл бұрын

Yeah. Surprised that wasn't pointed out in the video.

7:01 : You forgot the paper change music !

@david_ga8490

3 жыл бұрын

Yep

@bobbyyie1310

3 жыл бұрын

@@david_ga8490 you don't want to attract headless creatures and such whilst in a dungeon.

Why does this guys office look like the inside of a circus tent?

@lukefreeman828

3 жыл бұрын

You mean "why do circus tents style themselves on this guys office?"

@HitHard1008

3 жыл бұрын

@@lukefreeman828 stop there.

@earthwormscrawl

3 жыл бұрын

Is it an office raised to the power of a circus tent, or a circus tent in base office?

@Eric4372

3 жыл бұрын

It’s the Whataburger wallpaper 😂

@omikronweapon

3 жыл бұрын

actually, this is the fírst time I realised he's just in a room with stripey wallpaper. My mind always interpreted it as him being in a tent, at some mathematical excavation xD I never questioned it...

If you love Neil sloane's numberphile videos, clap your hands (clap clap)

@LeoStaley

3 жыл бұрын

Clap clap! 👏

@emdivine

3 жыл бұрын

clap clap

@Sci0927

3 жыл бұрын

clap

@yashrawat9409

3 жыл бұрын

Clap

@verypotato6699

3 жыл бұрын

*Clapping intensifies*

At first I was surprised by the growth of these sequences. However, after some thought, I think there's an intuition to be had here. When interpreting a number in a base (e.g., interpreting 153 in base 10), you *are* performing an exponentiation in some sense, because you're interpreting it as 1x10^2 + 5x10^1 + 3x10^0. But the trick here is that, despite interpreting the numbers in all these different bases, *we are restricting ourselves to the 10 regular digits!* So unlike in, say, hexadecimal, where the number after 99 is 9A, here the number after 99 is still 100. As a result, the instant that one of these sequences increments its second term, or reaches a 3rd term, it starts to grow by a factor of the base (and the base has been increasing for some time). This helps it very quickly reach a fourth term, and thus grow by the cube of the base, etc. After that it's clear to see why it explodes. If we allowed as many digits as bases (e.g., 8, 9, A, B, ...), the terms would just grow by one each time and the sequence would stick to the triangular numbers.

@vsm1456

3 жыл бұрын

oh, that's cool

This does still end up pretty base 10-centric, even though it plays with many different bases. I looked a little into how it ends up when you keep it all in binary and only convert to base 10 at the very end, and it was pretty interesting, since for example, the 4th step is no longer 10_11_12_13, it's 10_11_100_101. The introduction of a third digit in the base so quickly means that you start to square numbers in the base conversion process sooner, so the numbers start to grow bigger sooner. However, since it's powers of 2 and not powers of 10, I suspect that the size of the growth rate changes will be smaller, so it's very possible that base 10 will catch up in terms of number size after a number of steps. An example (using bottom-up parentheses): Base 10, 7th step: 10_11_12_13_14_15_16 = 31 Base 2, 7th step: 10_11_100_101_110_111_1000 = A 68-digit binary number, 193825204350418564226 in base 10

You can´t just leave on a cliffhanger like that.

Yesss, more Neil Sloane and numbers :)

I’ve heard about sub used for counting variables (a1, a2, a3, etc), where a1 is term 1, a2 for term 2, etc. but I haven’t heard sub used this way.

Neil Sloane might be my favorite guest on Numberphile, glad to have him back!

His voice and tone are so relaxing and mesmerising!!

I love Neil Sloane, he’s becoming one of my favorite Numberphile hosts

All amazing stuff is here!

love neil's videos every time, this man is the integer wizard

I can't help but grin at the absurdity of the sequences that mathematicians come up with

Every year, my local university in NJ has a festival that features lots of school clubs, departments, and occasionally artists, researchers, vendors etc. I first met Neil at one of these special days. He had a table set up with sequences as puzzles where you had to figure out the next number and what the sequence was. If you were interested, he would talk to you about more sequences and the OEIS. I met him again another year. To my knowledge he is a regular attendee. Obviously they didn’t have any festival day this year. It’s a treat getting to see him talk about interesting sequences in video form regardless.

Your shirt looks great, we both love Jimi Hendrix

I noticed at the first way of bracketing, it is just +1,+2,+3,+4,etc. But top down it changes after the +4. That's a cool pattern.

I've wondered about the order of indeces since I was in high school. I'm so grateful I've found a video about it!

Love this guy's passion for his subject

With every episode is even more and more effort for the animations

3:57 - 4:00 I died of laughter Neil: plus 2 **awkward pause** uh - au - um dollars Me: *[Breaks into Laughter]*

He's back! Thaaaanks so much, more ASMR for me to sleep.

5:26 This relies on converting to decimal before reinterpreting it in the target base, the sequence would presumably be different if calculated using another base.

Omg I love videos with Neil

Is this the guy who knows the plot and character names of Avatar? What a legend!

Ok, neat to follow until... Wait, what? 1.1? a non-integer base?! :o

@Jordan-zk2wd

3 жыл бұрын

(you can even have imaginary and complex bases actually ^ ^)

@MrAlRats

3 жыл бұрын

There are numeral systems that use complex numbers as their base. For example, the Quater-imaginary numeral system which uses the imaginary number 2i as its base. It is able to almost uniquely represent every complex number using only the digits 0, 1, 2, and 3. No minus sign is used for negative numbers in this numeral system, as they have a different representation from their positive counterparts.

This video just shows how to get the sequence 10 11 13 16 20 from various different methods

@Meuszik

3 жыл бұрын

AND how using those methods produce radically different divergences _after_ 20.

Sloane's videos are my favorites

This is a delicious irony because the word dungeon comes from donjon, which was the main tower in a castle.

I barely understand the theory but watching Sloane having fun with secuences is awesome.

Wow, that's amazing! I thought that it was just a boring quadratic at first, and would've passed it off as such if it weren't for this video showing the cases past only a few iterations. What's going on here (I think), is that the bottom up approach starts getting "faster" with more digits, and the top down approach starts getting faster once to 10+X turns into 20+X.

Thanks for your video. If you can share a complete course about what is electricity and how to manipulate it. What are some useful devices that every system must have. How to make projects out of these devices. This would be great thing to have.

Officially, you're one of my favorite KZreadrs out here!

Good collection of books in background

One oddity w/ a "base computation" (a sub b) is that 'a' *isn't* really a numerical value, but a character string. If you do a top-down, you're constantly having these "represent in base ten" conversions.

I enjoyed this video way more than I probably should have.

5:00 Is it just a coincidence that if you add the right most digits of the descending numbers to the top number you get the end number. (not a math whiz)

@n0t10c

3 жыл бұрын

I was just coming here to post this

@SgtSupaman

3 жыл бұрын

No, it isn't a coincidence, because the left digit is a one, which means it is just equal to whatever the base is while the right digit is equal to itself, so you are adding the base + right digit. Calculating bases (which essentially means converting from whatever base into base 10) looks like this x^y*a + x^(y+1)*b + x^(y+2)*c + ... (where x is the base, y=0 because you are starting from the first position left of the decimal, and [a,b,c,...]=whatever value is in that position). It is the same thing that you learn as a child when you say a number like 13790 has a 1 in the 'ten thousands' place, a 3 in the 'thousands' place, a 7 in the 'hundreds' place, a 9 in the 'tens' place, and a 0 in the 'ones' place. That means that the number is equal to 10^0*0+10^1*9+10^2*7+10^3*3+10^4*1 (or 0+90+700+3000+10000).

@LunchboxGaming

3 жыл бұрын

@@SgtSupaman Word...

5:56 - great visual animation here!

There seems to be a mistake on the brown paper at 9:53 Neil skipped 19 in base 14 and went straight to 19 base 13. the result should be 28 not 27.

@GenericInternetter

3 жыл бұрын

he also made a mistake in the introduction, where he did 12*5 instead of 12^5

@vladislav_sidorenko

3 жыл бұрын

@@GenericInternetter That is not a mistake. (a^b)^c = a^(b*c).

It's good to see I am not alone in my filing system, especially the heap of books (One of my heaps at home became unstable, collapsed, and broke a table!) I extend the heap system thus: 1) Place anything incoming on one of the heaps on my desk 2) When needed, search for the item in the heap and, when finished with it return it to the top of the heap. 3) When the heaps become too tall to see over a) Take off the top half b) scoop off the bottom half into the bin c) Return the top half. In that way the communication from the Vice Chancellor progresses at a steady pace to the bottom of the heap and to the destination it ultimately deserves.

7:00 "...natural way to make a dungeon. If you give me a bit of paper I'll show you." Taken out of context, it would sound like Neil is trying to get fundings for this esoteric long staircase just going up, another even longer coming down, and one more leading nowhere just for show.

I really enjoy Neil's insights and enthusiasm. I could totally imagine Sam Neil playing Neil Sloane in the bio pic of his life :)

10:02 I am delighted that the first five numbers of all 4 sequences are 10, 11, 13, 16, 20. I'm also appreciating that for two of the sequences the differences of sequential elements continue to be the natural numbers for a while longer.

I love this channel

Neil is always great

I realized that when you did the example for top to bottom and showed the sequence, I noticed something... I am just commenting right after seeing it so I don't know if you mentioned it in the video but... The sequence is 10, 11, 13, 16, 20, 25, 31, 38... I noticed the sequence is 10, then 10+1, then 10+2, 10+3...

There are two kinds of numberphile videos, either « the next number in the sequence is really big » or the « we still don’t know if the next number in the sequence exists, we’ve checked up to numbers that are xxx digits long »

It's interesting watching numberphile and getting a sense of the different mathematicians personalities. Some of them really like working towards some theory, some like real world implications, some like "giving it a go", and some like Klein bottles. But Neil Sloane more than anything seems to just like to play with numbers. There doesn't seem to need to be any greater meaning than saying "what if we play with weird rule X with these numbers". It makes sense why such a personality would create the OEIS.

@mostlyokay

3 жыл бұрын

I can't help but get a little dumbfounded by videos where he appears precisely because of that. In my mind here is no point in just finding number sequences without any connection to anything else in maths. But of course, time and time again results that were thought to be purely abstract and disjointed from other fields of maths have proven to be just the opposite.

Wow beautiful... Thanks old man math is truly amazing...

This is really cool. Like a entirely new way of thinking about numbers.

@gamespotlive3673

3 жыл бұрын

I don't know why I wrote this.

It's fascinating that all these sequences start with the same exact five numbers before diverging.

I don’t think this was addressed (or I just missed it) but in the sequence 10 9 8 7... With parentheses starting at the top, it’s not even possible to have an infinite sequence because before long the number being operated on will contain digits not defined in the base being converted to. It’s like saying 5 base 2.

The first sequence is A121263 in the OEIS. In Mathematica: define the rebase function, rebase[v_] := Join[Drop[v, -2], {FromDigits[IntegerDigits[v[[-2]]], Last[v]]}] Then define the dungeon number function to apply this recursively to a list of numbers: dun[n_] := First[Nest[rebase, Range[10, 9 + n], n - 1]]. Now make a table: dun[#] & /@ Range[20] which gives {10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 65, 87, 135, 239, 463, 943, 1967, 4143, 8751, 18479}.

9:54 Brady and Neil got different answers... Which really emphasizes how math can be more slippery than metal on ice

@thedystopyansociety

3 жыл бұрын

27 seems to be correct in this case. Drove me a bit mad trying to figure out how they arrived at 28 in the graphic.

A visit with Neil Sloane is a great way to lift our mathematical spirits out of the dungeons, for sure.

Dont forget to place torches when you dig that deep

Best use of the brown paper yet.

Neil Sloane is by far my favourite guest on Numberphile :)

When you're watching a bunch of videos on Dungeons and Dragons and your recommendations get a little weird. Hi, I wasn't expecting this but this channel seems fun

If you go from top to bottom, we're writing it in base ten (decimal), wouldn't this affect something? If you go bottom to top, it doesn't matter because we only care for the value.

Can u get more of this guy and OEIS and Amazing graphs?

COOL CONCEPT!

Is the "slow" growing parenthesizing starts as a quadratic function because there are two digits, so the second power of the new base is the largest that ever gets accumulated into the next number in the sequence. But the moment the sequence reaches three digits, suddenly the third power of each consecutive new base comes into play. That causes four digit numbers to be reached even faster, and then it explodes.

Good video👍👍

interesting, thankyou

This is very interesting 👍

To fix the ambiguity of the towering numbers, this is why we need the triangle of power, which replaces exponents, logs, and roots with a single notation, and shows no ambiguity for things like this, as well as more clearly showing the relationship between the 3 notations. For those who don't know what this notation is, 3Blue1Brown did a fantastic video on it, and I highly recommend anyone watch it.

Great video, as usual. But I missed the requisite elevator music during the paper change at 7:01.

3:05 This is reasonable. The "rebasing" operation treats its first (top, left) operand as a digit-string, and evaluates it in the base given by its second (bottom, right) operand, and gives you a number. So anything with a subscript is a digit-string, not a number. So in a stack of dungeons every level is a digit-string except the bottom one, so you have to start at the bottom and work up.

Hoping its a series of videos

10:41 So towers are clearly made out of timber, since you can take them apart log by log. ∗Ahem∗

Does the AsubB notation ask you to "remember" any information about what base the result was written in or is the result simply taken to be a new base 10 number for all intents and purposes? That is, are those massive results regarded as large base 10 numbers or is it accurate to say "No it's just 10 (in base 10), but we wrote it as if it was in different bases a bunch of times?"

Why can't negative numbers be considered prime? I understand that to classify a negative as a prime, this would interfere with already established theorems and axioms; but what about giving negative primes their own classification under for n

I'd like to see a further exploration on this topic. *How* do these numbers grow? If we bebin at timestamp 10:12, we see series where each number is 1, then 2, then 3, then 4 more than the previous number before the divergence. But what is the pattern of divergence? And in the second pair of the series, does it end at base 2? Is there a meaningful base one, or base zero?

please make a video on Bowers' Exploding Array Function (BEAF), Bird's Array Notation (BAN) and the Extensible-E System

1:08 The point is that the reason why top down is the official way is that bottom up notates something which already has a notation. (a^b)^c=a^bc, so the (a^b)^c notation is needless.

This video taught me how to count in bases higher than base 10, despite that not being it's main goal.

Pretty interesting how in some cases the subtractions of x and the next x number grows from 1 to n.

these things just blow my mind that someone was just sitting around and said hey we have been doing this counting up thing...lets go down?

“Single digits don’t change.” I’d count ceasing to exist in some cases a “change”!

The "re-basing" I find reminiscent of the hydra problem, although obviously this sequence does not grow as quickly.

Quickest I've ever gotten lost on a Numberphile video!