I was doing some probability calculations that include squaring a number between 0 and 1.
When I approximate 2/3 using 0.6 or 0.66 or 0.666 etc. I get an interesting series of growing same digit segments...
0.6^2=0.36
0.66^2=0.4356
0.666^2=0.443556
0.6666^2=0.44435556
0.66666^2=0.4444355556...
Hope it's OK to add a question here. I think to pertains to the topic.
What did cosmologists mean by "looks the same from everywhere"? Were they adjusting and calculating to compare "distant local" to "nearby local"? Or were they comparing raw values?
There was a time when both expansion...
OK, thanks; I was using "yes" meaning for all numbers of the set with no exceptions or conditions attached.
Is there an "exclusive yes" like exclusive or?
Here is what I think I know... :)
binary operation - defined on any set if it takes two elements from the set and returns a single element from the same set
additive identity - elements in a set remain unchanged with addition of the additive identity
multiplicative identity - elements in a set...
"In general, those mappings do not have two-sided inverses on the natural numbers..."
I have not been able to figure out what the left and right inverses mean; can you give me any help on that?
Natural numbers {1, 2, 3, ...}
Yes, what I meant to say was that every instance of addition or multiplication is defined on the naturals.
Can addition be defined as a mapping of naturals?
Does the inverse of that mapping exit without the definition of an additive inverse?
For every instance of addition or multiplication there is an inverse, closed on the naturals.
Not every instance of subtraction and division is defined, so not closed on the naturals.
This looks like two kinds of inverse.
Instance inverse - the inverse of instances of addition and...
My first thought is inverse polarity, but if the inverse wave form comprises -y values, any y=0 wouldn't have an inverse -y, so maybe the inverse wave form would not be strictly continuous? That seems asymmetric with respect to inversion...
edit-- I'm using the wrong term, inversion swaps the...
I'd like people here with formal training and professional experience to look at the night sky and report if they see Antares flashing, if they see Antares doing this while the other stars and planets are not doing so, and if they see the colors - red dot on top, blue and green areas near the...
So far, I don't think anyone in this thread has observed Antares and described here what they did or didn't notice except me. I have been requesting people do just that and have been watching for such posts.
Also per Wikipedia, it's "one of the largest stars visible to the naked eye. Its exact size remains uncertain, but if placed at the center of the Solar System, it would reach to somewhere between the orbits of Mars and Jupiter."
Uncertainty of size is because it is increasingly diffuse with...
Just to be clear, I thought it was Jupiter, but have since identified it is Antares.
Suggestions that the effect is Earth atmosphere, angle above horizon, or my eyes must explain why other objects (both planets and stars) at various angular elevations (including low ones) viewed both naked eye...
Stellarium is figured out, works properly.
Start with the Moon and there are four stars leading out to the left... the flashy object is the third one: Antares.
Please have a look.
After determining sidereal time, I realize Stellarium is automatically showing correct sidereal time for my location, but is still showing a night sky with the Sun under the horizon.
May have to find a different sky application.
Looks like Stellarium finds my location automatically but does not use that to fix the time. I just corrected the time and reloaded the web page... the time reverted back to 21:05 PM and showed a night sky.
I will correct the time to sidereal time this evening and see if I can correctly identify...
Stellarium right now, my local time 11:21 AM with the Sun up in the sky (I just checked) is indicating the time is 21:12 PM and showing the Sun under the horizon... with the location indicated "near Houston".
So yes, likely not Jupiter. Thanks everyone so far, would like to figure out what it is.
That is why I am asking... Jupiter is much more flashy than any other objects. The colors are particularly of interest.
I am in Houston. Early posts were from early evening looking SSW. The last post was from pre-dawn looking NNW.
Spotting it on a program to confirm it's Jupiter would be good...
I just looked now, naked eye and binoculars.
With naked eye there is a red dot at the top of the disc that appears and disappears every few seconds with a general flashiness near the bottom of the disc.
With binoculars, the general flashiness looks more green than blue, the red dot is easy to...
Been noticing this for a few evenings; didn't know it was Jupiter until this evening using https://stellarium-web.org/ (image from this evening).
Has been distinctly flashy more than other objects with a slight red flash at the top and a blue flash close to the bottom. Last night I looked with...
Me, too.
The abstracts are not just different in what is written... they have different dates.
The linked abstract alone is "Date: received 1 Mar 2021, last revised 3 Mar 2021"
The PDF linked paper with the different abstract is "work in progress 31.10.2019"
Two-marble probabilities
BB 1/4
BW 1/2
WW 1/4
Three-marble probabilities of selecting a black
B BB 1
B BW 2/3
B WW 1/3
Probability of selecting a black marble if we add a black marble to the two marble bag
(1 x 1/4) + (2/3 x 1/2) + (1/3 x 1/4) = 2/3
Three marbles with 2/3 probability of...
Knowing a 6 was showing, I meant counting all the row-column intersections for which 6 occurs within the face sums' ordered pairs, e.g., (1,6) (2,6), (3,6)...(6,3), (6,2), (6.1). Counting each intersection once I get eleven. The two die are independent so I should have counted (6,6) twice, or...
I'm not following your meaning of multiplying by 1/2. The two cells of interest are the two that show 7 where the row and column labels match the known or assumed face. For a face up of 6, those two would be (1,6) and (6,1)... for all face up n=1-6 the two cells that show 7 will be on the same...
Yes... the second may be more generally P(a+b=7 |a V b where row a = col b)
If the second were P(a+b=7 |all a + all b where row a = col b) then knowing or assuming that a face is n, does the possibility (n,n) needed to be counted independently for row n and col n so that it is counted twice...
Scenario 1]
The dice are rolled out of your sight and you are then asked the p(7), before you are allowed to look at the results.
Calculate p(7) by looking at table of 36 possibilities and counting the number of sum cells totals that equal 7, there are six of them, so
p(7) = 6/36 = 1/6...
Considering a kind of object, looks to me like "all" might be finite or infinite, and "infinite" might be some or all.
With natural numbers 1, 2, 3..., it looks to me like "all" does mean infinite and infinite does mean all. So no new guests in the form of a natural number.
I'm not seeing a...
Let the room numbers and occupants be unique and paired natural numbers such that:
1 is in room 1, 2 is in room 2, 3 is in room 3...
Is there any question that the hotel now contains all of the natural numbers?
If posed a unique natural number not yet a guest shows up, what is this number?
"We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the "time of the stationary system" at the places where they happen to be. These clocks...
That's all kind of what I've been thing, too.
What remains is the justification for the process between the moving and rest clocks. He is careful to describe the process between clocks at rest, but then applies that concept to relatively moving clocks.
Since we will learn later that clocks in...
OK, that's what I have been thinking, too.
Section 2 presents the moving rod AB wrt the "stationary system".
Let me show you the problematic paragraph - tenth paragraph of section 2, regarding the clocks placed on the ends of the moving rod AB...
"We imagine further that at the two ends A and...
My title just shows the part of the 1905 paper about which I'm asking, not suggesting losing the observer.
I think I understand how distant clocks at rest wrt to an IFR are synchronized. What I am not understanding is how that process is extended to collocated clocks in relative motion.
What I...
Of course you all anticipate that my questions arise because the next section places clocks on the ends of the rod AB moving with respect to the system at rest, having those moving clocks indicating the time values of local at rest clocks using the synchronization process. His original example...
1905 paper, looks to me like:
Postulates:
- principle of relativity
- definite velocity of c
Definition of inertial frame coordinate system
- using rigid rods to identify position of A at rest WRT to the IFR coordinates
Seems clear that rigid rods may be used to identify the place of other...
Even before considering Many Worlds, Schrodinger’s cat has always presented the discrete yet potentially confounding not necessarily binary outcome. To measure unconfounded binary outcome, a cat must be prepared so as to be in the ultimate of its nine lives.
Regarding flux, I find Dr. Sten Odenwald, NASA Astronomer writing in 2015, updated 2017:
SN 1987A produced a neutrino pulse of 10^58 neutrinos, which was reduced to only 24 detected on Earth due to the inverse-square law at the distance to SN1987A, and the fact that neutrinos interact very...
I keep seeing the reassuring "safe distance" from Betelgeuse in the event of supernova. This may be a relief to those worrying the Earth's magnetosphere or atmosphere might be at risk. However, anyone here authoritatively know about supernova neutrinos having an effect on the Sun, and if so...
I've read around here that a photon has no position operator,
that in relativistic field theory photons can't be enumerated,
that only interactions may be measured...
maybe the concept of "travel" applied to a photon is highly problematic?
See if this helps...
"Heisenberg's uncertainty principle for conjugate pairs of observables follows directly from the fact that those observables are essentially the Fourier transforms of each other."
Mathpages
Maybe Relativity? Points' neighborhoods in spacetime are within the hyperbolic bounds of light rays from them, the absolute magnitudes of spacetime intervals between them non- transitive (Minkowski).
Alice and Bob - null separated
Bob and Carol - null separated
Alice and Carol - may be...