Today I Learned

[Astronuc]

George Mitchell, former US Senator, came from humble roots. Quite a story.

http://thedianerehmshow.org/shows/2015-05-07/george-mitchell-the-negotiator

http://en.wikipedia.org/wiki/George_J._Mitchell

 

[Astronuc]

and I learned eating chili con carne y queso y frijoles is not a good thing before cycling a distance for speed in the sun.

Best to wait several hours.

Supposedly legumes are a good thing for the carbohydrates/sugar.

 

[collinsmark]

Today I learned that the true source of the elusive "perytons" (originally hypothesized to be from extragalactic origin) is likely from impatient office workers pining for warm and tasty snacks.

http://arxiv.org/pdf/1504.02165v1.pdf

Note Figure 7, which shows the frequency of "peryton" observations peak around local lunchtime.

 

[mfb]

Peryton thread for reference

Today I learned that the true source of the elusive "perytons" (originally hypothesized to be from extragalactic origin) is likely from impatient office workers pining for warm and tasty snacks.

http://arxiv.org/pdf/1504.02165v1.pdf

Note Figure 7, which shows the frequency of "peryton" observations peak around local lunchtime.

Today I learned astronomers are busy working out the power cycle of their microwave ovens (3.5) - not for their lunch but for actual science.

Rather, we believe that the operator had selected a power level of less than 100%, causing the magnetron power to cycle on and off on a 22-second cycle, the period specied in the manufacturer's service manual and confirmed by measurement.
[...]
We conjecture that on this occasion the operator inadvertently compromised the shielding by placing conducting material in the oven, perhaps Aluminium cooking foil that became caught between the door and the body of the oven, creating a unintended antenna, but we have yet to devise an acceptable test of this scenario.

 

[Astronuc]

It's never too late - More Than 75 Years After Enrolling, 94-Year-Old Set to Graduate West Virginia University
https://gma.yahoo.com/more-75-years-enrolling-94-old-set-graduate-190737454--abc-news-lifestyle.html

He studied engineering, physical education and industrial arts, and was close to graduation when he was drafted during World War II, serving in the Army Air Corps for three and a half years, WVU said.
. . . .
Brutto returned to school in 1946 but was forced to drop out again, this time to take care of his ill wife, according to WVU. He soon started working as a machinist in various factories.

 

[JorisL]

TIL there is an inequality named after one of my professors.
In fact I need it for an assignment which requires a continuity argument.

I don't like the fact that nobody hinted us to use that though. Luckily I found it before I set out to do just that.

 

[OmCheeto]

TIL that I started mentally cataloguing TV show scenes when I was about 5 years old.

I've been watching retro TV from 1956 through 1964, over the last few months.
It's quite strange, halfway through a 50 year old TV show, that you remember the gills in someones chest, and feathers flying around the room.
And a chicken man, in an amusement park flying saucer, that turned out to be real.
And some sissy guy, who kept calling for his mommy, when attacked by the serrated boomerang wielding alien creature.

Brains, are amazing.

 

[zoobyshoe]

Today I learned about the Banana Equivalent Dose (BED) of radioactivity:
http://en.wikipedia.org/wiki/Banana_equivalent_dose

A banana equivalent dose (abbreviated BED) is an informal expression of ionizing radiation exposure, intended as a general educational example to indicate the potential dose due to naturally occurring radioactive isotopes by eating one average-sized banana. One BED is often taken as 0.1 µSv, however, in practice this dose is not cumulative, as the principal radioactive component is excreted to maintain metabolic equilibrium. The BED is only an indicative concept meant to show the existence of very low levels of natural radioactivity within a natural food and is not a formally adopted dose quantity...

This part was interesting:

Although the amount in a single banana is small in environmental and medical terms, the radioactivity from a truckload of bananas is capable of causing a false alarm when passed through a Radiation Portal Monitorused to detect possible smuggling of nuclear material at U.S. ports.[6]

 

[OCR]

Today I learned that Johnny Carson graduated with a Bachelor of Arts Degree in radio and speech with a minor in physics in 1949.

 

[Astronuc]

Death toll in Amtrak derailment increased from 5 to 7. It appears the train was speeding (102 mph) where it should have been going slower. NTSB and Amtrak investigating.

Amtrak derailment victims: CEO, Naval Academy student and software architect dead
http://news.yahoo.com/passengers-st...ain-derailment-in-philadelphia-153358441.html

Among the deceased are:

Rachel Jacobs, 39, the CEO of Philadelphia-based technology education company ApprenNet. Jacobs, a wife and mother of a 2-year-old, commuted to Philadelphia twice a week from New York, according to the CW affiliate.

Justin Zemser, 20, student at U.S. Naval Academy. The young man’s mother, https://gma.yahoo.com/amtrak-crash-victims-ceo-still-missing-navy-midshipman-152252891--abc-news-topstories.html , said her only son was heading home to Rockaway Beach, N.Y., after finishing his second year at the academy in Annapolis, Md.

Jim Gaines, a 48-year-old father of two who worked as a video software architect for the Associated Press, also died in the crash. He was returning home to Plainsboro, N.J., after attending meetings in Washington, D.C.

Peace be upon them and the families, friends and colleagues.

Profiles of Philadelphia Amtrak train derailment victims
http://news.yahoo.com/profiles-philadelphia-amtrak-derailment-victims-163042443.html

Navy Midshipman, AP Employee Among Dead In Amtrak Derailment
http://www.npr.org/2015/05/13/406505182/navy-midshipman-ap-employee-among-dead-in-amtrak-derailment

http://www.npr.org/sections/thetwo-...s-cars-roll-in-philadelphia-injuries-reported

"Amtrak Train 188 was traveling at 106 mph moments before it derailed Tuesday night. Investigators said the engineer applied the emergency brakes, but could only slow the train to 102 before it crashed seconds later. "You are supposed to enter the curve at 50 miles per hour," said Robert Sumwalt, NTSB board member."
Ref: http://news.yahoo.com/live-updates--amtrak-train-derailment-near-philadelphia-030241888.html

Engineer Applied Emergency Brake Before Fatal Amtrak Derailment
http://www.npr.org/sections/thetwo-...m-on-its-way-to-investigate-amtrak-derailment

 

[Enigman]

http://www.slate.com/content/dam/slate/blogs/future_tense/2014/08/WaterGallonsUsed.png.CROP.original-original.png

 

[mfb]

Today I learned: a vomitorium in ancient Rome was a gate crowds used to enter and exit a stadium.

 

[thankz]

that my first attempt at crab cakes are going to be delicious, in the oven right now.

here's the recipe:

lump crap
plain breadcrumbs
old bay
chives
egg whites
butter

 

[Stephanus]

Today I learned that 23! is 25,852,016,738,884,976,640,000 which has, coincidentally, 23 digits. The same coincidence does not occur in any other factorial except 1!.

Yep, if you use base 10 number

 

[zoobyshoe]

Yep, if you use base 10 number

And note I had to correct that a few posts later. There are actually three in a row: 22! has 22 digits, and 24! has 24 digits.

 

[Stephanus]

And note I had to correct that a few posts later. There are actually three in a row: 22! has 22 digits, and 24! has 24 digits.

Yes, yes, it's very cunning that you find it. It's interesting, beyond 24! say 25! I think it's 26 digits, and for 21! it's 20 digits. But it can only be manifested in base ten number.
Do you have any idea what is n?
n! is n digits in base n number?
Should program the computer to find out.

 

[Lisa!]

Now I'm 10 years old in PF years!

 

[zoobyshoe]

Yes, yes, it's very cunning that you find it. It's interesting, beyond 24! say 25! I think it's 26 digits, and for 21! it's 20 digits.

Yes, it's a strange and interesting little island.

But it can only be manifested in base ten number.
Do you have any idea what is n?
n! is n digits in base n number?
Should program the computer to find out.

That's beyond me. You go ahead and work on that.

 

[Stephanus]

Yes, it's a strange and interesting little island.
That's beyond me. You go ahead and work on that.

So far, no. Only base 2 and 2! is two digits 10
This is the list that I make. For each base. Remember, A -> 10, B -> 11, C -> 12. Maximum is 62 base number
base; len; result
2: 2; 10
3: 2; 20
4: 3; 120
5: 3; 440
6: 4; 3200
7: 5; 20460
8: 6; 116600
9: 6; 612700
10: 7; 3628800
11: 8; 205940A0
60: 47; 1K34lTABjkLQij9TkGanwv0XwJVAfZ89`00000000000000
61: 47; b2tipGOC8axb22OlaFskBeQEgCbeEuo6`vixIIk7DhScsx0
62: 48; I0YAwAmEHVRb1wt5AfbjF1UTOi1IvOT64r2X5ZK2cbErxG00
But with higher base number, the digits seems left behind. I think there's no such n! is n digits for n base number. But can it be proven otherwise?

 

[zoobyshoe]

Today I learned the Stephanus theorem:

there's no such n! is n digits for n base number

Will it be proven?

 

[Stephanus]

Today I learned the Stephanus theorem:

there's no such n! is n digits for n base number

Will it be proven?

Naah, it's not a theorem. It's not mine either.
It's this':

[FONT=Courier New]  for n:=2 to 62 do begin
    FBase:=n;
    for m:=1 to n do FNumber[m]:=0;
    FNumber[0]:=1;
    FNumber[1]:=1;
    for f:=1 to n do Multiply(f);       
  end;

Part of the code.

 

[Stephanus]

Congratulations! You are correct. Also, 24! is a 24 digit number. It's a hat trick: 22!, 23!, 24! .

Yes zoobyshoe, I remember saw your post earlier.

 

[OmCheeto]

Now I'm 10 years old in PF years!

Congratulations!

Yes, yes, it's very cunning that you find it. It's interesting, beyond 24! say 25! I think it's 26 digits, and for 21! it's 20 digits. But it can only be manifested in base ten number.
Do you have any idea what is n?
n! is n digits in base n number?
Should program the computer to find out.

Yes!
And please find out what Lisa! is in base 36.
Thanks!

Oh, never mind. It's her birthday. I'll do it.

Lisa₃₆ = 1,004,122₁₀
1,004,122! = ∞?
Stupid google calculator...

hmmmm...

per wiki:

1,000,000! ≈ 8.263931688×10^5,565,708
1,723,508! ≈ 5.290070307×10^10,000,001
​

hmmm...

In his book The Emperor's New Mind, Penrose estimates the number of baryons in the observable universe to be of the order of 10⁸⁰​

So Lisa₃₆!, is a lot.

ps. TIL that sometimes, wiki gets things right; "The calculator seen in Mac OS X handles up to 92!"
My calculator claims 93! is; "Not a number"

 

[mfb]

2 is the only number n such that n! has n digits in base n.
There is an intuitive way to see this: n^(n-1) is the smallest number with n digits in base n, but we only have n! = n(n-1)(n-2)*...*2*1 < n*n*...*n*1 = n^(n-1) with n=2 as exception.

You can also prove it via the stirling formula.

 

[Stephanus]

All in base ten
Has to make the software by hand. Delphi has no variable that can handle that much.
You can check my software with calculator for low number, but for higher number, I don't know if there's bug or not. Beside, who know?

10!: 3,628,800
20!: 2,432,902,008,176,640,000
30!: 265,252,859,812,191,058,636,308,480,000,000
100!: 93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000
200!: 788,657,867,364,790,503,552,363,213,932,185,062,295,135,977,687,173,263,294,742,533,244,359,449,963,403,342,920,304,284,011,984,623,904,177,212,138,919,638,830,257,642,790,242,637,105,061,926,624,952,829,931,113,462,857,270,763,317,237,396,988,943,922,445,621,451,664,240,254,033,291,864,131,227,428,294,853,277,524,242,407,573,903,240,321,257,405,579,568,660,226,031,904,170,324,062,351,700,858,796,178,922,222,789,623,703,897,374,720,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
300!: 306,057,512,216,440,636,035,370,461,297,268,629,388,588,804,173,576,999,416,776,741,259,476,533,176,716,867,465,515,291,422,477,573,349,939,147,888,701,726,368,864,263,907,759,003,154,226,842,927,906,974,559,841,225,476,930,271,954,604,008,012,215,776,252,176,854,255,965,356,903,506,788,725,264,321,896,264,299,365,204,576,448,830,388,909,753,943,489,625,436,053,225,980,776,521,270,822,437,639,449,120,128,678,675,368,305,712,293,681,943,649,956,460,498,166,450,227,716,500,185,176,546,469,340,112,226,034,729,724,066,333,258,583,506,870,150,169,794,168,850,353,752,137,554,910,289,126,407,157,154,830,282,284,937,952,636,580,145,235,233,156,936,482,233,436,799,254,594,095,276,820,608,062,232,812,387,383,880,817,049,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

 

[Stephanus]

2 is the only number n such that n! has n digits in base n.
There is an intuitive way to see this: n^(n-1) is the smallest number with n digits in base n, but we only have n!=n(n-1)(n-2)*...*2*1 < n*n*...*n*1 with n=2 as exception.

You can also prove it via the stirling formula.

You're right mfb!. I tought 1 is also the answer beside 2. But I just realized that there's no base 1

 

[OmCheeto]

All in base ten
Has to make the software by hand. Delphi has no variable that can handle that much.
You can check my software with calculator for low number, but for higher number, I don't know if there's bug or not. Beside, who know?

10!: 3,628,800
20!: 2,432,902,008,176,640,000
30!: 265,252,859,812,191,058,636,308,480,000,000
...

um... given that the numbers >92! are not numbers...

What is the highest factorial you can calculate, if all the baryons and neutrino's were converted into binary bits?
Given that it is predicted that neutrinos outnumber baryons by a billion to 1.

"So the total number of neutrinos in the observable universe is about 1.2 x 10⁸⁹ !"
​

 

[Stephanus]

What is the highest factorial you can calculate, if all the baryons and neutrino's were converted into binary bits?
Given that it is predicted that neutrinos outnumber baryons by a billion to 1.

"So the total number of neutrinos in the observable universe is about 1.2 x 10⁸⁹ !"​

What is this? Are you reading my mind?
A week ago I created a thread about neutrino.
Yes, you're right OmCheeto, neutrinos outnumber baryons, but baryon are still heavier then neutrino.

https://www.physicsforums.com/threads/are-neutrinos-much-more-abundant-than-atoms.813792/

But to calculate the factorial of 1.2E89 is a very difficult trick. Try if I can solve this. But I think, I might take 1 week. I'm still searching the algorithm of 4 pegs Hanoi Tower.
​

 

[OmCheeto]

What is this? Are you reading my mind?
A week ago I created a thread about neutrino.
Yes, you're right OmCheeto, neutrinos outnumber baryons, but baryon are still heavier then neutrino.

https://www.physicsforums.com/threads/are-neutrinos-much-more-abundant-than-atoms.813792/

But to calculate the factorial of 1.2E89 is a very difficult trick. Try if I can solve this. But I think, I might take 1 week. I'm still searching the algorithm of 4 pegs Hanoi Tower.
​

Actually, I meant to say, the inverse of the factorial. In other words, find x when x! = 1e89.

But that should probably be asked in the maths section of PF.

TIL, that in the 1964 TV version of "I Robot", they pronounced "robot" as "row butt".
I kind of giggled, like a minion.
But then I thought about the origin of the word, and decided it should be pronounced "row boat".
That made me giggle too.

I also learned today, that Leonard Nimoy played different rolls in both the 1964 and 1995 "The Outer Limits" versions. (I thought I was losing my mind for a moment. I'd seen the 1995 version 3 months ago, and didn't know there was a previous one.)

I also learned that "I Robot", was a story originally written by someone named Eando Binder, and not Isaac Asimov.
Then I learned that Eando was not really a person, but two people: Earl and Otto Binder.
That made me giggle again.

It's been a funny day.

 

[Stephanus]

2 is the only number n such that n! has n digits in base n.
There is an intuitive way to see this: n^(n-1) is the smallest number with n digits in base n...

How foolish I am. Of course. Should have take a momen to think rather than find the answer through coding.

Actually, I meant to say, the inverse of the factorial. In other words, find x when x! = 1e89

" So the total number of neutrinos in the observable universe is about 1.2 x 10⁸⁹!"

So the "!" is only an exclamation mark
I tought you want me to search 1.2E89!, instead what is X! = 1.2E89, I think, x is somewhere around 100 or 110, but I have to use software to find that.
Give me time.