UKC

Did you know there are believed to be between 100,000,000,000 and 400,000,000,000 stars in our galaxy. I find this mind blowing but I can just about hold it together.

Did you also know there are about 100,000,000,000,000,000,000,000 atoms in an average sized apple. It's a big number, but we expect it to be.

Now take a humble deck of playing cards. If you think about how a deck of cards can be stacked in many different orders. How many order options exactly?

Well, did you know that that there are roughly the same number of possible orders to stack a deck of cards as there are atoms in the known mass of our galaxy.

Still struggling to wrap my head around that.

x10^67

8.07 x 10^67 Yeah, kinda nuts!

The universe is only 436.117x10^15 seconds old.

I used to watch a lot of Star Trek when I was a kid, I thought it was amazing the way the zipped around the universe and all that. I watched a lore video recently on youtube and was dumbfounded to learn they never even left the Milky Way, not even Voyager!

If you live to 85, you have 4420 weeks.  Tempus fugit.

That's wrong. You've written 1x10²³, which is the number of carbon atoms in ~2 g of graphite. What you wanted is 10²⁷ according to Google, but I think that is low more like 1.5x10²⁷ for a decent size apple.

I had a card game for Christmas, annoyingly* called More or Less. You take turns to read out a pair of numbers and the other players guess if the second "fact" is more or less than the first. Eg more stars in the universe or grains or sand on all the beaches.

*Annoying as many of the questions should be More or Fewer.

https://www.moreorlessgame.co.uk/

Yes, I read if you shuffle a pack of cards they will never have been in that sequence before, and never will be again ! 

Is that the number one is supposed to count up to in the presence of unruly children...?

Not true. It's unlikely, but not impossible. That's probability for you.

On the subject of numbers which blow your mind the numbers involved in the difference between a million and a billion blows mine.

If you think of numbers as seconds then a million seconds is roughly 12 days. A billion seconds equates to nearly 32 years!

Better off by far to be a billionaire than a mere millionaire.

Millionaire peasants 

This makes the half an hour sat in bank seem a bit lonely 

Courtesy of McGill University

'It seems unbelievable, but there are somewhere in the range of 8x10^67 ways to sort a deck of cards. That’s an 8 followed by 67 zeros. To put that in perspective, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before they would get even one billionth of the way to finding a repeat.'

as a total novice on stars, I found this a useful book:

https://www.goodreads.com/book/show/50884561-first-light?from_search=true&a...

I think that they've been clumsy with their words there.

There's a 1 in 8*10⁶⁷ chance that the first reshuffle will be a repeat, and a one in a billion chance that the repeat will happen before the end of the universe.

can I offer up the reduced Plancks constant 1.05 * 10 -34 Js which is very small indeded

mind blowingly small but no way near as mind blowing as the the consequences of Quantum Mechanics at that scale. 

imo big numbers are somewhat mundane in comparison.

There's only 52!

The number of trump supporters is still more mind blowing.

I don't want to further disillusion you but they never even left California!

Nice

Ha! (I've got the like button switched off) 

I believe you are right. 

£37,000,000,000.00 on a Track & Trace system that didn't work...

Another one foiled by poorly counting zeros.

Track & Trace cost closer to £37,000,000

Maybe a better example is Horizon which cost £1000,000,000

or worse still, the failed NHS IT system that cost £10,000,000,000

Look up Tree(3) think that was on here a while ago. Apparently it's a pretty big old number. Then you can do Tree(tree(3)^....) Tree(3) times.

Watched a few videos on it but they just basically explain it's so incomprehensibly big it'd be impossible to right it down in standard form with all the atoms in the universe or something.

I have trouble visualising how far current time measurement is away from approaching the Planck time

Trying to explain Avogadro’s to my children I used salt. Approx 60g in one mole is ~10^23 molecules. Reduce it to 6g and that’s ~10^22. Use a yeast balance to weight 0.6g (not a lot) and that’s ~10^21. A single grain is roughly 0.06g which is ~10^20. Which is still a huge, huge number.

'kind of' tying in with the number of permutations of playing cards, but more a probability thing...

I know that if I pick a random set of lottery numbers, it has exactly the same chance of winning as if I had picked 1,2,3,4,5,6,7.  It just seems very unlikely because I see order in it

I know this.  I know that 1,2,3,4,5,6,7 is as 'random' as 13,7,9,49,2,1,3

I know it, and I tell myself that I believe it.

But deep down, I secretly don't believe it.

Edited - I don't know if the lottery is still seven numbers between 1 and 49...it used to be, I think.

it’s more, 59. I think their thinking was: lottery tickets sales reducing, but most people who play it want to be a mega millionaire (*) , so increasing the range will decrease the chance of winning and hence make the Jack pot bigger. 
(*) most people who dont play it would be happy winning a stack of cash but not mega millions, but this cohort is not their target audience, as they probable still wouldn’t play it anyway. 

Yes, that's the number I thought it was 

Avocado's number - how many particles in a Guaca-mole.

'More or less' on Radio 4 dealt with this issue this week

Here's a surprisingly low number that will blow your mind...

How many times would you need to fold a sheet of paper for it's thickness to reach the Moon?

About 40?

Absolutely excellent estimation!

42.

https://bigthink.com/starts-with-a-bang/fold-paper-reach-moon

They are not talking about probability at all. Its simple permutations. 52 cards so possible unique arrangements is 52! = 8.0658 x10^67

That's pretty astounding.

But what I find even more astounding (and I don't know why it should be) is that the thickness after 103 folds would exceed the size of the observable universe!

https://wonderopolis.org/wonder/can-you-fold-a-piece-of-paper-more-than-sev...!

Indeed, that's the problem.

What they said was " To put that in perspective, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before they would get even one billionth of the way to finding a repeat.'"

I think that's clumsy use of words, as they are not acknowledging the fact that whilst it's unlikely, the hypothetical person might, in fact, find a repeat before the universe ended.

To use an analogy with smaller numbers, it's like saying "if you asked a stranger to pick a random number between one and ten, then asked five other strangers to pick a random number between one and ten, you would be half way to finding a repeat" when in fact there would be a 50% chance you already had a repeat.

Tree 3 is a good call as is Graham's Number. An explanation of both can be found on Numberphile (YouTube).

My personal favourite 'big number' is centered around the Rubik's Cube; any scramble can be solved in <=20 moves aka God's Number. I came across its partner - The Devil's Number, which is the fewest number of moves required to achieve every possible permutation. This number is big and currently unknown afaik.

- 

The Birthday Paradox - if you have 23 people in a room together, there's a 50% chance that two of them have the same birthday.
https://betterexplained.com/articles/understanding-the-birthday-paradox/

And here's a real world mind-blowing (but surprisingly not quite as unlikely as you might think) coincidence - in September 2009 the Bulgarian national lottery drew the same winning numbers on two consecutive weeks: http://news.bbc.co.uk/1/hi/8259801.stm

Yep.  I always think that the average lifespan of 1000 months tends to focus the mind somewhat!

Re the pack of 52! cards and atoms in the galaxy, if you step up to the tarot pack weighing in at 78! cards, the number of variants is around  4,817,692,279,497,248,276,615,783,438,745,600,000 visible universes' worth of atoms.

Apparently one visible universe worth of atoms is around 57! - 58! or thereabouts.

If we live in a inflating torus shaped universe then its gravitional entropy (if we could count its microstates) must be greater than 3.26 x10^122. ( perimeter institute lecture by Neil Thurock youtube.com/watch?v=rsI_HYtP6iU&)

I felt OK about this until I realised how far through I am!

Indeed, and I don't think the last 250 come with guarantees attached.  At least, I can't find mine! 😂

There is only one Donald Trump (thankfully)

This is not scientific but it blows my mind to think that the first episode of Dr Who I watched in 1963 (the repeated episode as I missed the first transmission with all the fuss about Kennedy going on) is

as far away in time from us now as

1903 was from me in 1963. 

That blows my mind, as well as the fact that this year is 120 years since my Grandad was born.

Similarly, the number of years between the end of the Second World War and me being born is about the same as the number of years I’ve dabbled on this forum!  

It's things like that that show how short human lifespan really is plus the phenomenal rate of technological change in the 20th Century. Take Yuri Gagarin's first space flight (1961)  and the Wright brothers' first powered flight (1903). We are now a longer span of time beyond Gagarin's mission than he was ahead of the Wrights.

If you take a historical figure like Julius Caesar who died in 44BC and consider the Biblical 'three score years and ten' lifespan then he's only separated from us by about 30 human lifetimes. We're only 6 lifetimes away from Elizabeth 1st by the same calculation.

Another very big number is found in the possible moves in a game of chess, 10 followed by 123 zeros! 

https://www.liverpoolmuseums.org.uk/stories/which-greater-number-of-atoms-u...

It worked perfectly; it made £37,000,000,000.00 (or whatever the figure was) for someone's mates.

In reply to broken spectre:

You'd need pretty thin paper (or absurdly long one) to manage the requisite number of folds.  For a long time it was generally believed that you couldn't fold a piece of paper more than 8 times. An American high school student called Britney Gallivan tested that and managed (I think) 12 folds, using a 4000' long piece of tracing paper.  Even more impressively, she worked out an equation that describes the minimum length for a piece of paper of a particular thickness for it to be possible to fold it n times. 

L=πt/6(2ⁿ+4)(2ⁿ-1)

​​​​​​

Good wind up Sir! You almost had me there!

The magnetic field of magnetars.

Magnetars are neutron stars with extremely strong magnetic fields.

The magnetic field of the Earth is 30 – 60 microteslas.

The strongest manmade magnetic field is about 45 teslas.

The magnetic field of a magnetar is about 10,000,000,000 teslas.

At a distance of half the distance to the Moon the magnetic field of a magnetar would wipe the magnetic information from all credit cards on Earth and at 1000 km the magnetic field would distort the electron clouds of atoms and all life world be destroyed.

Fortunately the closest known magnetar is about 9,000 light year away.

Dave

Utter Tosh.  I went out and counted them last night - I thought there were 398,397,010,589.***

Did you also know there are about 100,000,000,000,000,000,000,000 atoms in an average sized apple. It's a big number, but we expect it to be.

Well!!  Bugger my cucumber.  I've just proved that estimate wrong.   I just ate a bite out of my apple....  Scientists, my a)(*e !!!  Must have been at least 987,000,000,000,000,000,000 atoms in that bite......

***  I've just spotted two new ones I didn't notice.   Add that to the score.

398,397,010,590

You probably got caught by the Froggatstar (have you seen the scenery). It is actually a very tight binary.    Take it you have read The Three Pebble Problem?

You are assuming rearrange=shuffle.

I think it's accurate as a shuffle is a random rearrangement, but you can have systematic  rearrangements

Ah, but a shuffle might not in fact be a rearrangement, if all the cards managed to end up back in their original order. What are the chances of that though? 1 in ~10^67 perchance?

There are more real numbers packed between 0 and 1 than there are natural numbers.  Both are infinite as well. Infinite comes in different sizes.

If after a thorough shuffle any arrangement is equally likely then the chance will be 1 in n! where n is the size of the pack. If the shuffle is imperfect, the chance could be zero - imagine actually doing the shuffle and stopping after first swap of cards.

That reminds me of  Hilbert's Hotel: a fully occupied hotel with an infinite number of rooms can still take on more guests, even an infinite number of them.

Better tell Rishi about it; could be a solution to the asylum seeker problem...

They could call it the "Kigali Hotel" so those lefty ECHR lawyers wouldn't think it was in Rwanda.

It occurred to me that if you managed to "find" the longest infinitely long number in decimal it would be a fair bit longer writ in binary

Does binary 1/0 = infinity count?

And if you were to represent it in Roman numerals it would need an infinite number of different symbols.

Or would it?

I'm guessing that question doesn't have an answer.

It would be just the same - infinitely long, but the same infinity not a bigger one.  Whichever base you're using you could write it by chalking one digit on each of the bedroom doors in Hilbert's Hotel.

it would be the same infinity value but it must be longer in digits.  How many pairs of walking boots would you need to chalk this number on an infinitely long blackboard?  Infinite?

It's more digits, but also the same number of digits.  I realise that doesn't make sense, but that paradox is really the whole point of the hotel analogy.  The hotel is completely full, but also has room to accommodate an infinite number of new guests.

Yup.

I think that's a reasonable assumption to make here

You can have systematic rearrangements, but systematic means ordered, and therefore a tendency to repeat patterns. 

For a trivial example, you could rearrange by systematically taking one card off the top and putting it on the bottom, and you'd have a repeat in less than a minute.

It seems to me that you would have to design your system specifically not to repeat in order to cycle though all the possible permutations - and if that's what they were trying to say, they've been even more clumsy with their words than I first thought!

I'm not a sir, and I don't understand your comment.  What part of my post was a wind up?

Just one single symbol, surely...?

Which one would that be then?

∞

The lemniscate.

Since when was that a Roman numeral?

I think you know exactly what they were saying but are criticising their language choice. 

I disagree with you, as the kids will say, 'end of'

Since when did the Romans have symbols able to cope with the required number concept?

Or even zero?

Not that you can ever have enough symbols, Roman or otherwise, to represent infinity. Expect for something abstract like the lemniscate. So it's a bit of a pointless discussion, isn't it?

What is zero in Roman numerals?

Nero

Closest they could get to it

🤣

The paper is folded on the same axis each time, so it looks more like its been wound up. Folding where you alter the axis by 90 degrees each time is much more difficult as it actually requires the material to stretch.

Does that disprove the equation(s)?  I don't claim to be a expert (or even especially knowledgeable) but it is a fairly well known piece of work and thought it might be of interest and relevance given the topic.  Perhaps I was wrong.

Not a numeral is it, just like three is not a numeric digit 

is probably what you meant

And how you can slander three by comparing it with that scandalous Emperor is disgraceful!

Although with Hilbert you aren't actually dealing with infinities of different sizes. They are both "countable" infinities. Cantor's proof of uncountable infinities existing is brilliant in its simplicity.

I assume that's the same as "the optimum number of bikes is always n+1"...?

The billion number that does my head in is this:

Ignoring inflation and interest and all that stuff, if you had been putting £1 million in the bank every year since the Norman Conquest in 1066, you still wouldn't be a billionaire....

Yes. Its like if you counted at a rate of one per second.

It would take about 11 and half days to reach one million but nearly 32 years to reach a one billion.

Dave

And that's ignoring the old British Billion, which meant bi-million, as in million squared. That would take 317 centuries. 

How many ways to fold a protein? That's got to be a very big number, which is why what AlphaFold does is so impressive.

1

Multiply any number by it and it remains the same.  (see 0 with addition).

If you donated a £1m every year from 1066 to the Conservative party you'd be a trillionaire.

No one has mentioned the truly awesome number that is .......

e