I estimated 10^100, because a cubic light year is unfathomably large, and you probably wouldn't make it the largest number. Also, I have no internal concept of how many calories are in icecream... I've never bothered looking...

BETTER QUESTION
is it possible for a cube of icecream one light year on each side to even exist?
Answer, no, gravity would heat the center and it would boil, gas would escape into space, the whole thing would smell terrible.

Would a cube of icecream one light year on each side collapse into a black hole?
Absolutely, because the mass of a cubic lightyear of icecream is 7E50KG, corresponding to a Schwartzchild radius of 120 MILLION lightyears, your icecream black hole would consume, at the very least, our galaxy and a few neighboring ones, and quite possibly actually end the universe

(for perspective, the entire milky way is 6E42KG)
(I love Wolfram Alpha)

[EDIT]
would definitely destroy universe, 120 MLY is greater than the radius of the local supercluster, and once the local supercluster is consumed, the event horizon would expand by a couple orders of magnitude... you can see where this is going

 

Without wishing to appear a 'spoilsport' -- I thought the idea was to make an intuitive guess? --- Anyone can calculate it! Why are you 'cheating' your own exercise?!?!?! -- Oh well! - It's your thread after all -- and then there is the 'balm' of my guess being "correct" --- So... that'll have to qualify as a 'good go'

Very best regards
HP

I said 30 seconds of estimating (I did not say "guessing"). If I wanted a guess, I would have said guess and suggested a 2 second time limit. My whole point was to get to an approximation without a calculator.

I also said my 2 second gut feel (guess) in the Note3 of that same post. Define cheating as you wish (I guess you already have defined it) even though you did not read the rule book (or somehow managed to interpret the rules differently than everyone else).

 

Ok since we're doing spoilers -- I offer the following:

Average dietetic calories per litre of naturally sweetened ice Cream = 2,000 (Source: Online examination of several manufacturer's nutrition-info labels)

Litres per ly^3 ≈ 8.47*10^50 (Source: Simple arithmetic)

2000 Dietetic Cals * 8.47*10^50 Litres =1.694*10^54 Dietetic Cals per ly^3 (Source -- More simple arithmetic)

Wow! Wasn't that fun?

Best regards
HP

 

(or somehow managed to interpret the rules differently than everyone else).

HP did not interpret the rules differently than everyone else. To do so, no one could have interpreted them the same as she did. However, I agree with her interpretation, thus she did not interpret the rules differently than everyone else.

 

I said 30 seconds of estimating (I did not say "guessing"). If I wanted a guess, I would have said guess and suggested a 2 second time limit. My whole point was to get to an approximation without a calculator.

Whatever!

 

You know you're a nerd when you can calculate a cubic light year of ice cream in 3 lines.

 

Ok since we're doing spoilers -- I offer the following:

Average dietetic calories per litre of naturally sweetened ice Cream = 2,000 (Source: Online examination of several manufacturer's nutritional-info labels)

Litres per ly^3 ≈ 8.47*10^50 (Source: Simple arithmetic)

2000 Dietetic Cals * 8.47*10^50 Litres =1.694*10^54 Dietetic Cals per ly^3 (Source -- More simple arithmetic)

Wow! Wasn't that fun?

Best regards
HP

If you do four significant digits of estimating an unfamiliar unit of measurement (cubic light year) in your head (no calculator) within 30 seconds, you are some type of amazing savant.

 

If you do four significant digits of estimating an unfamiliar unit of measurement (cubic light year) in your head (no calculator) within 30 seconds, you are some type of amazing savant.

More idiot than savant but thanks for thoughts!

TTFN
HP

 

Magnet18's estimation question-

What is the maximum volume of icecream that can exist without collapsing into a black hole? (radius of sphere)
for hint you get this-

other than that the rules to Gophers original question apply, no calculators or googling, guess an order of magnitude

 

You know you're a nerd when you can calculate a cubic light year of ice cream in 3 lines.

I confess that I spent ≈ 100 seconds on the arithmetic -- But sans assistance of technology or paper -- So... I have my 'style points' please!

Best regards
HP

 

Magnet18's estimation question-

What is the maximum volume of icecream that can exist without collapsing into a black hole? (radius of sphere)
for hint you get this-

other than that the rules to Gophers original question apply, no calculators or googling, guess an order of magnitude

Not to 'nit pick' however this is not in the spirit of @GopherT 's exercizes! -- It is, rather, a straight forward math/physics exercise - The urge to merely calculate the answer is overwhelming! -- Please consider presenting it as a 'best answer' MC

Very best regards
HP

 

Fine then, do it without the hint

 

Absolutely, because the mass of a cubic lightyear of icecream is 7E50KG, corresponding to a Schwartzchild radius of 120 MILLION lightyears,

@magnet18

Are you certain about that? I get an EHR ≈ 110*10^6 ly for a spherical mass of 7*10^50kg -- I could be wrong -- it's been awhile -- Jeeze do I feel old

Best regards
HP

 

Fine then, do it without the hint

Yebut the The hint is merely a recitation well known relations -- 'unlearning' a fact - even temporary - is more difficult than learning it to begin with...

Best regards
HP

 

I saw this video a few weeks ago, and maybe here's a good chance to post it here. It's 19 minutes long, but very much worth watching, I think:

The numbers discussed near the end are so mind-boggling that one quickly loses all of one's "estimation skills" when attempting to assimilate their dimensions.

 

it depends on whether the ice cream chocolate or vanilla or regular or low fat.

 

I saw this video a few weeks ago, and maybe here's a good chance to post it here. It's 19 minutes long, but very much worth watching, I think:

The numbers discussed near the end are so mind-boggling that one quickly loses all of one's "estimation skills" when attempting to assimilate their dimensions.

The presenter's ignorance (or, more likely, feigned ignorance) is exasperating! -- His conflation of Number Theory with mere nomenclature and 'gaming/sport culture' --- and, much worse, 'numbers' with 'functions' is frankly offensive! --- The degree of intellectual cowardice (in the face of truly abstract concepts) exhibited by many (otherwise intelligent) people is appalling! Such individuals would do well to accept - if not embrace - the oh, so humiliating fact that reality was neither fashioned for, nor specially tailored to, their emotional needs/cognitive limitations - nor, for that matter, those of humanity in general! Once again, it would appear a matter of insecurity, denial and, so it seems, something akin to stark horror at the merest notion of an indifferent reality -- Scuse me while I hurl

With jaded regards
HP

PS @cmartinez It is likely unnecessary that I say this - however I feel that I should! --- My 'gripe' is entirely with the presenter's attitude and the contents of his presentation --- and in no way with your decision to link same! - I, for one, greatly appreciate your efforts in bringing stimulating discourse to these fora!

 

The presenter's ignorance (or, more likely, feigned ignorance) is exasperating! -- His conflation of Number Theory with mere nomenclature and 'gaming/sport culture' --- and, much worse, 'numbers' with 'functions' is frankly offensive! --- The degree of intellectual cowardice (in the face of truly abstract concepts) exhibited by many (otherwise intelligent) people is appalling! Such individuals would do well to accept - if not embrace - the oh, so humiliating fact that reality was neither fashioned for, nor specially tailored to, their emotional needs/cognitive limitations - nor, for that matter, those of humanity in general! Once again, it it would appear a matter of insecurity, denial and, so it seems, something akin to stark horror at the merest notion of an indifferent reality -- Scuse me while I hurl

With jaded regards
HP

PS @cmartinez It is likely unnecessary that I say this - however I feel that I should! --- My 'gripe' is entirely with the presenter's attitude and the contents of his presentation --- and in no way with your decision to link same! - I, for one, greatly appreciate your efforts in bringing stimulating discourse to these fora!

so... I take it you did not like it? ... jokes aside, in another post I had a similar discussion with WBahn, in which he considered the presenter (and his arguments) as too infantile and naïve. Well, the thing is that we are not their target audience, but rather teenagers, or adults that have an interest in science and engineering but have no extensive, or formal education. But have a genuine interest in the subject. If these sort of circus-like presentations piques their minds and imagination, then so much the better, I say.

On the other hand, (although I have an engineering degree) I have to admit that I'm not as versed in high-level mathematics as I though I was... I had completely forgotten about the ↑ notation, for instance, and had never heard about Graham's number. Also, I found the two mathematician's duel at the end rather interesting (hey... the Mexican won! )... it made me realize that a number does not have to have a definite value, but rather a clear definition (maybe that's a subject for another thread) for it to be considered a number.

With my deepest appreciation of your honest response and sincerity, and respect for your well meaning.
cmartínez

PS: Sometimes hurling helps one get rid of the bad vibes that would refuse to leave one's body otherwise...

 

part of my slide rule collection....flanked by my TWO William Orr Technical Writing Award plaques.

 

Magnet18's estimation question-

What is the maximum volume of icecream that can exist without collapsing into a black hole? (radius of sphere)
for hint you get this-

other than that the rules to Gophers original question apply, no calculators or googling, guess an order of magnitude

@magnet18 So I'll just say the minimum volume that will collapse cuz otherwise it's transfinite infinitesimal number less than that to say the maximum volume that won't collapse.

From what you're saying ice cream's density is 8.26E11 kg per cubic km.

So The mass for inital sphere radius equal to schwarzschild radius is ~ 2.97E38 kg.
So radius is ~ 4.41E8 km.
So the initial volume of the smallest sphere of that ice cream that will collapse is 3.6E26 cubic km.

I used calculator but I say if it's right I did well anyhow cuz I did it in less than two minutes and no references to anything! It's just simultaneous solution but tricky so I say tnx for good question!