6 ms·

They have encountered an interesting algorithmic problem here, very cool. To determine whether the universe as a whole has a preferred handedness, they had

by est31 4y ago

They have encountered an interesting algorithmic problem here, very cool. To determine whether the universe as a whole has a preferred handedness, they had to repeat the analysis for all tetrahedra constructed from their database of 1 million galaxies. There are nearly 1 trillion trillion such tetrahedra — an intractable list to handle one at a time. But a factoring trick developed in earlier work on a different problem allowed the researchers to look at the parity of tetrahedra more holistically: Rather than assembling one tetrahedron at a time and determining its parity, they could take each galaxy in turn and group all other galaxies according to their distances from that galaxy, creating layers like the layers of an onion. The linked earlier work: https://academic.oup.com/mnras/article/454/4/4142/993302 https://academic.oup.com/mnras/article/454/4/4142/993302

vlovich123 4y ago
Given there’s 100 billion-1 trillion galaxies estimated in the observable universe, isn’t 1 million a frighteningly small sample to draw conclusions from? How can we be sure that what we’ve observed is representative enough to extrapolate conclusions of? Moreover, how do we know if extrapolates to the universe homogeneously? What if the “opposite” asymmetry is present in the non observable universe such that on average the universe doesn’t actually have an asymmetry globally?
- nr2x 4y ago
  I'm guessing they thought of that.
- kaashif 4y ago
  Such an incredibly large scale asymmetry would still be interesting even if it weren't global for some reason. Even if there's a sampling thing going on, why should this particular sampling method have an asymmetry? Maybe there's no reason, or maybe there is a reason.
- graycat 4y ago
  > ... a frighteningly small sample to draw conclusions from? Just make the usual assumption: The data consists of random variables that are independent and have the same distribution. Or "independent and identically distributed", i.e., the i.i.d. case. Then can apply the theorems called the law of large numbers, either the weak version or the strong version. Then in the application of the law of large numbers, the number of samples is crucial, but, possibly surprisingly, the number of cases in all the data does not get involved, is not used in the law of large numbers, and is irrelevant. That is, to be more explicit, with this approach, we don't care how many galaxies there are, 10^12, 10^100, 10^1000, whatever. Right: With different approaches, might care a lot about (a) the number of galaxies there were in total, (b) the number of galaxies used in the analysis, i.e., if in (b) we had enough samples to characterize (a), to have a good approximation of the results we would get if we analyzed all of (a). For more, might claim that (A) the distribution we use in the law of large number is just that of ALL of the galaxies, a large number but not infinite (commonly a distribution is for infinitely many) and (B) drew the sample to be analyzed by rolling dice or some other mechanism that achieved independence so that, net, we have i.i.d. as wanted for the law of large numbers. So, here the distribution is not of some imaginary collection of infinitely many galaxies but just of the large but finitely many galaxies there are in THIS universe or THIS observable universe, or ..., this universe once we get tired of collecting data, start to run out of grant money, want to get home with the kids, want to watch the soccer matches, ...!
  - dotancohen 4y ago
    But these are _not_ independent datum. For one thing, these galaxies were observed and cataloged - something that already puts them on unequal footing with most of the universe' galaxies. Furthermore, of the catalogued galaxies, how were these particular galaxies selected for inclusion in the study? Humans are very bad at choosing things randomly - even when assisted by computers.
    - graycat 4y ago
      Take some independent random variables. Put them on a list, in a catalog, in a box, etc., and now they are still independent. That each random variable is about a galaxy and that they are all independent but now know that they are all visible only from the southern hemisphere of the earth, they are still independent. For such things will want to learn about the careful definition of independence and, for more, about conditional independence and the Radon-Nikodym theorem. There is a nice proof of this result by von Neumann in, e.g., the W. Rudin Real and Complex Analysis. > But these are _not_ independent datum You have not shown that. > ... unequal footing Your "unequal footing" is not part of probability theory. Pick a galaxy X. Note what you know about it. Now someone tells you it is in the catalog and also lets you see the other galaxies in the catalog. Now what more do you know about X than you did before???? Can read more about independence in Jacques Neveu, {\it Mathematical Foundations of the Calculus of Probability,\/}
- akiselev 4y ago
  A million galaxies in a survey of 1/20th of sky (I suspect, haven't run the numbers) manages to get most of the galaxies in our local Pisces–Cetus Supercluster Complex [1] that fall within the field of view, especially if the survey is pointed towards a less dense part of the PCSC. Since the supercluster complex is a galaxy filament [2], galaxies in the next nearest supercluster complex will be much farther away - just like the nearest star in the Andromeda galaxy is going to be orders of magnitude further away than the furthest star in the Milky Way (see artistic rendering in the Wiki page in [2]). Throw in gravitational lensing and the data becomes much noisier the further out you go [3]. [1] https://en.wikipedia.org/wiki/Pisces%E2%80%93Cetus_Supercluster_Complex https://en.wikipedia.org/wiki/Pisces%E2%80%93Cetus_Superclus... [2] https://en.wikipedia.org/wiki/Galaxy_filament https://en.wikipedia.org/wiki/Galaxy_filament [3] http://spiff.rit.edu/classes/ladder/lectures/wars/wars.html http://spiff.rit.edu/classes/ladder/lectures/wars/wars.html
  - codethief 4y ago
    Could you elaborate on how the information you provided answers GP's questions? I'm not really following you but I also don't know a lot about this topic.
- aortega 4y ago
  > isn’t 1 million a frighteningly small sample to draw conclusions from? Sample size in a survey will just give you more or less error. You can calculate exactly the expected error of such sample size.
- contravariant 4y ago
  Typically 1 million samples of anything is reasonable enough to get a good estimate, provided your sample is random. The probability that you've picked the exact 0.0001% of galaxies that had a specific pattern is vanishingly small.
  - vlovich123 4y ago
    I don’t follow. If there’s a persistent bias in the galaxies that are in our data set or there’s a bias in the person of the local portion of the universe we can observe, then the sample isn’t random. And since we can’t know what’s in the unobservable part of the universe…
    - Stupulous 4y ago
      In that sense you could argue that all of astrophysics is built off of a biased sample from which we can draw no conclusions. And you may well be right, I'd think, though it is unfalsifiable.
      - vlovich123 4y ago
        I don’t think it’s necessarily unfalsifiable to some degree. But there’s certainly parts of our astrophysics model that are already unfalsifiable and there’s no way around that. For example, the existence of the unobservable universe by definition is unfalsifiable. We kind of just assume the locality principle and that stars leaving our ability to observe them is expansion and not them hitting the edge of the universe and getting destroyed :).
    - naasking 4y ago
      > If there’s a persistent bias in the galaxies that are in our data set or there’s a bias in the person of the local portion of the universe we can observe, then the sample isn’t random. The Copernican principle is the default, unless we have some reason to doubt it in a particular case.
- gumby 4y ago
  There are a lot of theorems on sampling so though I’m no longer current in that area I presume the authors knew what they were doing. Especially as they had the maths chops to apply that factoring algorithm. But you can also consider a qualitative analysis. A standard assumption is that the Big Bang should be largely isotopic (else why not, which is the main point of the article). So where you look shouldn’t matter. Even if orientation were uniform in average (impossible to tell), non-uniform regions tell an interesting story. Now in reality we know the universe isn’t smoothly uniform: parts of it have curdled into galaxies, stars systems etc. Also there’s the puzzling imbalance between matter and antimatter. Why? This article points out another asymmetry, which could provide a clue.
amai 4y ago
There is another paper on „Efficient computation of N-point correlation functions in D dimensions“ at https://www.pnas.org/doi/10.1073/pnas.2111366119 https://www.pnas.org/doi/10.1073/pnas.2111366119 „This work considers NPCF estimation on isotropic and homogeneous manifolds in D dimensions. Under these assumptions (which encompass spherical, flat, and hyperbolic geometries), we show that any function of one position can be expanded in hyperspherical harmonics; a D-dimensional analog of the conventional spherical harmonics. “ So it seem they must assume a homogeneous and isotopic universe to be able to do their analysis.
- codethief 4y ago
  Very interesting point! (Though for non-homogeneous but still isotropic universes there still exist spherical harmonics, so homogeneity doesn't seem like a critical restriction here. Those are used, for instance, to analyze non-homogeneous alternatives to the usual FLRW cosmological model, e.g. Lemaître-Tolman-Bondi (LTB) models.)

by est31 4y ago

vlovich123 4y ago

Given there’s 100 billion-1 trillion galaxies estimated in the observable universe, isn’t 1 million a frighteningly small sample to draw conclusions from? How can we be sure that what we’ve observed is representative enough to extrapolate conclusions of? Moreover, how do we know if extrapolates to the universe homogeneously? What if the “opposite” asymmetry is present in the non observable universe such that on average the universe doesn’t actually have an asymmetry globally?

nr2x 4y ago
I'm guessing they thought of that.
kaashif 4y ago
Such an incredibly large scale asymmetry would still be interesting even if it weren't global for some reason. Even if there's a sampling thing going on, why should this particular sampling method have an asymmetry? Maybe there's no reason, or maybe there is a reason.
graycat 4y ago
> ... a frighteningly small sample to draw conclusions from? Just make the usual assumption: The data consists of random variables that are independent and have the same distribution. Or "independent and identically distributed", i.e., the i.i.d. case. Then can apply the theorems called the law of large numbers, either the weak version or the strong version. Then in the application of the law of large numbers, the number of samples is crucial, but, possibly surprisingly, the number of cases in all the data does not get involved, is not used in the law of large numbers, and is irrelevant. That is, to be more explicit, with this approach, we don't care how many galaxies there are, 10^12, 10^100, 10^1000, whatever. Right: With different approaches, might care a lot about (a) the number of galaxies there were in total, (b) the number of galaxies used in the analysis, i.e., if in (b) we had enough samples to characterize (a), to have a good approximation of the results we would get if we analyzed all of (a). For more, might claim that (A) the distribution we use in the law of large number is just that of ALL of the galaxies, a large number but not infinite (commonly a distribution is for infinitely many) and (B) drew the sample to be analyzed by rolling dice or some other mechanism that achieved independence so that, net, we have i.i.d. as wanted for the law of large numbers. So, here the distribution is not of some imaginary collection of infinitely many galaxies but just of the large but finitely many galaxies there are in THIS universe or THIS observable universe, or ..., this universe once we get tired of collecting data, start to run out of grant money, want to get home with the kids, want to watch the soccer matches, ...!
- dotancohen 4y ago
  But these are _not_ independent datum. For one thing, these galaxies were observed and cataloged - something that already puts them on unequal footing with most of the universe' galaxies. Furthermore, of the catalogued galaxies, how were these particular galaxies selected for inclusion in the study? Humans are very bad at choosing things randomly - even when assisted by computers.
  - graycat 4y ago
    Take some independent random variables. Put them on a list, in a catalog, in a box, etc., and now they are still independent. That each random variable is about a galaxy and that they are all independent but now know that they are all visible only from the southern hemisphere of the earth, they are still independent. For such things will want to learn about the careful definition of independence and, for more, about conditional independence and the Radon-Nikodym theorem. There is a nice proof of this result by von Neumann in, e.g., the W. Rudin Real and Complex Analysis. > But these are _not_ independent datum You have not shown that. > ... unequal footing Your "unequal footing" is not part of probability theory. Pick a galaxy X. Note what you know about it. Now someone tells you it is in the catalog and also lets you see the other galaxies in the catalog. Now what more do you know about X than you did before???? Can read more about independence in Jacques Neveu, {\it Mathematical Foundations of the Calculus of Probability,\/}
akiselev 4y ago
A million galaxies in a survey of 1/20th of sky (I suspect, haven't run the numbers) manages to get most of the galaxies in our local Pisces–Cetus Supercluster Complex [1] that fall within the field of view, especially if the survey is pointed towards a less dense part of the PCSC. Since the supercluster complex is a galaxy filament [2], galaxies in the next nearest supercluster complex will be much farther away - just like the nearest star in the Andromeda galaxy is going to be orders of magnitude further away than the furthest star in the Milky Way (see artistic rendering in the Wiki page in [2]). Throw in gravitational lensing and the data becomes much noisier the further out you go [3]. [1] https://en.wikipedia.org/wiki/Pisces%E2%80%93Cetus_Supercluster_Complex https://en.wikipedia.org/wiki/Pisces%E2%80%93Cetus_Superclus... [2] https://en.wikipedia.org/wiki/Galaxy_filament https://en.wikipedia.org/wiki/Galaxy_filament [3] http://spiff.rit.edu/classes/ladder/lectures/wars/wars.html http://spiff.rit.edu/classes/ladder/lectures/wars/wars.html
- codethief 4y ago
  Could you elaborate on how the information you provided answers GP's questions? I'm not really following you but I also don't know a lot about this topic.
aortega 4y ago
> isn’t 1 million a frighteningly small sample to draw conclusions from? Sample size in a survey will just give you more or less error. You can calculate exactly the expected error of such sample size.
contravariant 4y ago
Typically 1 million samples of anything is reasonable enough to get a good estimate, provided your sample is random. The probability that you've picked the exact 0.0001% of galaxies that had a specific pattern is vanishingly small.
- vlovich123 4y ago
  I don’t follow. If there’s a persistent bias in the galaxies that are in our data set or there’s a bias in the person of the local portion of the universe we can observe, then the sample isn’t random. And since we can’t know what’s in the unobservable part of the universe…
  - Stupulous 4y ago
    In that sense you could argue that all of astrophysics is built off of a biased sample from which we can draw no conclusions. And you may well be right, I'd think, though it is unfalsifiable.
    - vlovich123 4y ago
      I don’t think it’s necessarily unfalsifiable to some degree. But there’s certainly parts of our astrophysics model that are already unfalsifiable and there’s no way around that. For example, the existence of the unobservable universe by definition is unfalsifiable. We kind of just assume the locality principle and that stars leaving our ability to observe them is expansion and not them hitting the edge of the universe and getting destroyed :).
  - naasking 4y ago
    > If there’s a persistent bias in the galaxies that are in our data set or there’s a bias in the person of the local portion of the universe we can observe, then the sample isn’t random. The Copernican principle is the default, unless we have some reason to doubt it in a particular case.
gumby 4y ago
There are a lot of theorems on sampling so though I’m no longer current in that area I presume the authors knew what they were doing. Especially as they had the maths chops to apply that factoring algorithm. But you can also consider a qualitative analysis. A standard assumption is that the Big Bang should be largely isotopic (else why not, which is the main point of the article). So where you look shouldn’t matter. Even if orientation were uniform in average (impossible to tell), non-uniform regions tell an interesting story. Now in reality we know the universe isn’t smoothly uniform: parts of it have curdled into galaxies, stars systems etc. Also there’s the puzzling imbalance between matter and antimatter. Why? This article points out another asymmetry, which could provide a clue.

amai 4y ago

There is another paper on „Efficient computation of N-point correlation functions in D dimensions“ at https://www.pnas.org/doi/10.1073/pnas.2111366119 https://www.pnas.org/doi/10.1073/pnas.2111366119 „This work considers NPCF estimation on isotropic and homogeneous manifolds in D dimensions. Under these assumptions (which encompass spherical, flat, and hyperbolic geometries), we show that any function of one position can be expanded in hyperspherical harmonics; a D-dimensional analog of the conventional spherical harmonics. “ So it seem they must assume a homogeneous and isotopic universe to be able to do their analysis.

codethief 4y ago
Very interesting point! (Though for non-homogeneous but still isotropic universes there still exist spherical harmonics, so homogeneity doesn't seem like a critical restriction here. Those are used, for instance, to analyze non-homogeneous alternatives to the usual FLRW cosmological model, e.g. Lemaître-Tolman-Bondi (LTB) models.)