expansion - How can an infinite universe expand?

I understand the expansion of the universe as actually an increase in the ratio of space to matter. Is this a correct understanding?

It isn't wrong. The ratio is increasing. But it isn't a "correct understanding". It's merely an observation of one of the results of the expansion of space.

If the universe is infinite how can it expand?

I don't know. Nor do I know how big bang cosmology can be reconciled to an infinite universe. If you look around on the internet, you can find articles like this which say this:

"The linear dimensions of the early universe increases during this period of a tiny fraction of a second by a factor of at least 10$^{26}$ to around 10 centimetres (about the size of a grapefruit)".

However in 2013 results from the WMAP mission appeared to confirm that space is flat. Then a non-sequitur crept in. See this article and pay careful attention to this:

"We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

That's a massive error. It absolutely doesn't suggest that the universe is infinite in extent. Or that the Universe is much larger than the volume we can directly observe. But this myth has legs, and people repeat it ad-infinitum, even though they can't explain how it fits in with Big Bang cosmology. What you tend to hear is that the observable universe was the size of a grapefruit, but it absolutely doesn't satisfy. Moreover there's a dreadful flaw lurking in the shadows. Take a look at the stress-energy-momentum tensor, and note the energy-pressure diagonal. A gravitational field is something like a spatial pressure gradient, and you can think of space as having an innate "pressure". So you can reason that the universe must expand. As to why Einstein didn't, I just don't know. But anyway, for an analogy, squeeze a stress-ball down in your fist, and let go. It expands because of the pressure. However if that material was infinite in extent, the pressure is counter-balanced at all locations. So it can't expand. In similar vein, in my opinion, an infinite universe can't expand.

People claim the universe must be infinite because of the cosmological principle. But this is merely an assumption. There's an assumption that the universe is homogeneous and isotropic, but this isn't fact. You cannot use it to make sweeping claims about an infinite universe that was always infinite. For all we know some observer 50 billion light years away might be looking up at the night sky wondering why half of it is black. Or a mirror-image of the other. Or some kind of edge.

It is said that in days gone by, people could not conceive of a world that was curved. They could only conceive of a world with an edge. Nowadays I rather fancy that there are some people who cannot conceive of a world that is not curved. They cannot conceive of a world with an edge.

Edit:

See The Foundation of the General Theory of Relativity: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Energy is the source of the stress-energy tensor. Matter is only a source because of the energy-content. Also see Inhomogeneous and interacting vacuum energy which refers to spatial energy. An interesting read is the article Universe 156 billion light-years wide
featuring Neil Cornish. This isn't entirely accurate, but the compound interest and the hall of mirrors concepts are of interest. As for the non-sequitur, see this interview with Joseph Silk:

"We do not know whether the Universe is finite or not."

I hope nobody will argue with that. Reading on:

"To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite".

This is akin to the old Asteroids game. But the Planck mission found no evidence of any torus. Reading on further:

"So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."

I dispute that. There is a third possibility. A flat finite universe with no intrinsic curvature. If anybody can cite some reliable sources that support the assertion that a flat universe must be infinite, I'd like to see them.

Would humans hear gravity waves from a binary BH fusion nearby?

Gravity would warp your entire body, or at least tug on it, because bodies that aren't bound together by gravity largely resist it's deformation, at least that's the major point I'm working on here.

That being said, it should pull on some structure in your ear, be it the bones or the tiny Philae (I believe that's the right word, edit if not), either way it results in a deviation from their original position.

Depending on proximity you might also be able to feel it, in likeness to standing in front of a large speaker. However the ears would be far more sensitive.

I hope I've answered your question :)

biochemistry - What effect has changing pH and salt concentration on protein complexes?

The formation of protein complexes or aggregates in aqueous buffers is determined by a number of factors: physical properties of the protein itself, pH, temperature, type and concentration of the used cosolvent (salt). Solutes are often roughly divided by type into chaotropes ('disorder-making'), which destabilise protein structures and kosmotropes ('order-making'), which stabilize them. [1, 2]

Chaotropic salts interfere with intramolecular interactions mediated by non-covalent forces such as hydrogen bonds, van der Waals forces, and hydrophobic interactions, which, at high cosolvent concentrations, results in protein denaturation.

Kosmotropic salts, on the other hand, cause water molecules to favorably interact, which also stabilizes intermolecular interactions in proteins. The salt molecules readily interact with water from the protein's hydratation shell and remove it from the protein surface, which produces thermodynamically unfavourable interactions that are reduced when proteins associate to form complexes. With increase in salt concentration the protein precipitation (salting out) increases.

Both cations and anions have been ranked separately by their capacity to precipitate proteins, to form a Hofmeister series [3, 4] (first set in 1888 but still hotly debated), e.g.:

SO₄²⁻ > H₂PO₄⁻ > CH₃COO⁻ > Cl⁻ > Br⁻

At large salt concentrations protein solubility is given by the empirical Cohn equation [6]:

lnS = α − βc

where S is the protein solubility, c is the salt's ionic strength, α and β are empirical constants characteristic of particular salt.

Salting-out agents are very widely used in protein purification (to concentrate proteins eg. with ammonium sulfate), chromatography or crystalization.

The influence of pH on protein-protein interactions in solution works through altering of the electrostatic properties of protein surfaces. At pH equal to the protein's isoelectric point (pI), where its net charge is neutral, charge repulsions of similar molecules are relatively low and many proteins will aggregate. Very low and very high pH will case proteins to denature; during digestion, for instance, proteins are in extremely low and then extremly high pH that exposes their backbones for enzymatic degradation.

For more information, please refer to:

1. Martin Chaplin, Kosmotropes and Chaotropes, http://www.lsbu.ac.uk/water/kosmos.html




2. Zangi R. Can salting-in/salting-out ions be classified as chaotropes/kosmotropes? J Phys Chem B. 2010 Jan 14;114(1):643-50.




3. Pace CN, Treviño S, Prabhakaran E, Scholtz JM. Protein structure, stability and solubility in water and other solvents. Philos Trans R Soc Lond B Biol Sci. 2004 Aug 29;359(1448):1225-34; discussion 1234-5.




4. Shimizu S, McLaren WM, Matubayasi N. The Hofmeister series and protein-salt interactions. J Chem Phys. 2006 Jun 21;124(23):234905.




5. Zhang Y, Cremer PS. Interactions between macromolecules and ions: The Hofmeister series. Curr Opin Chem Biol. 2006 Dec;10(6):658-63. Epub 2006 Oct 10.




6. Ruckenstein E, Shulgin IL. Effect of salts and organic additives on the solubility of proteins in aqueous solutions. Adv Colloid Interface Sci. 2006 Nov 16;123-126:97-103. Epub 2006 Jun 30.

positional astronomy - Why do stars seem not to move relative to each other?

They do move - just far too slowly for you to detect by eye even over several human lifetimes.

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space

Douglas Adams, "The Hitch-hikers Guide to the Galaxy"

Even the closest stars are a very, very, very long way away so their apparent movement relative to each other is going to be very small.

You can see the same effect when looking out of a moving vehicle through the side windows. You see the objects closest to you rushing past, but objects on the horizon appear to move much more slowly. Now, scale that up by many orders of magnitude to interstellar distances and you'll see why the stars don't appear to move relative to each other.

There's software that simulates the night sky and you can run time backwards and forwards - if you wind it far enough you'll see the constellations change.

telescope - Equation to find distance between objective and eyepiece

1 A.U. is same as infinity. The difference in terms of eyepiece position is infinitesimal, you can't measure it. Anything beyond a few kilometers away is pretty much "at infinity".

Regardless of that - from the practice of designing and building telescopes, calculations only offer you a starting point. You do the math, and the distance is 105 cm. But in practice lenses will deviate from the ideal focal length. Even if they didn't deviate at some temperature, put them in a cold environment, and the focal length will change a fraction of mm.

So take the calculations as a starting point, and build the instrument in such a way as to allow fine adjustments of the position of the eyepiece. There's a device called focuser that allows such fine adjustments. Or simply rely on friction to move the eyepiece back and forth until the image looks best, and hold it there.

When using the instrument in practice, you'll forget the ideal distance. What you will do is adjust the position of the eyepiece until the image looks best. You will do that every time you observe, and often multiple times during the same observation.

---

If you want some math, take a look at the thin lens equation, and apply it to the objective lens.

f = focal length of the lens

o = distance from lens to object

i = distance from lens to image

Then the thin lens equation is:

1/f = 1/i + 1/o

i = 1/(1/f - 1/o)

If o = infinity, then i = f.

But what happens if o = 1 A.U.?

i = 1/(1/1 - 1/(1.5 * 10^11)) = 1.0000000000067 meters

The difference is something like 6.7 * 10^-12 meters. It's smaller than an atom.

black hole - Why is metallicity important in the death of stars?

I can't give a detailed answer; the details are buried in the depths of numerical stellar evolution models.

The thing that changes most with the metallicity of a newborn star is the radiative opacity of the gas. Higher metallicity leads to more opacity.

This has two immediate effects - it makes energy harder to get out of the stellar interior and makes it more likely that convection will take over.

Convection has the property of mixing up all the material within the convective zone. This can have knock on effects as to how long each nuclear burning phase lasts and how much material is consumed. It also mixes synthesised material from the interior outwards.

A further important effect is that mass loss from massive stars is very extensive and is due to radiatively accelerated winds. For a given luminosity, high metallicity gas is more opaque and easier to accelerate. Hence mass loss is very sensitive to metallicity and determines how massive the star is as it reaches the end of its life. This in turn has a large bearing on what the remnant will be.

There is a further feedback in that the wind metallicity is the metallicity at the surface, but this in turn can be affected by interior mixing that is in turn metallicity-dependent.

If that sounds complicated, that's because it is, and detailed numerical models are required to see how these things play out.

entomology - Do insects' muscles become stronger with exercise?

There are instances of insect muscle growth in response to increased use. The flight muscles of the tsetse fly (Glossina morsitans) have been observed to grow at a faster rate when subjected to enforced exercise (Anderson and Finlayson, 1976). Also larger mandibular adductor muscles (which power the feeding apparatus), and associated head capsule have been noted for caterpillars and grasshoppers feeding on particularly hard grasses (Bernays, 1986). However these examples occur immediately post-eclosion (i.e. after emergence as adults), and during immature stages respectively. Insect muscle typically grows during larval/nymphal (immature) stages, and often for a brief period at the start of adulthood - known as the teneral period. During immature stages, insects typically have a flexible membrane to allow for tissue growth and expansion, this can also be the case during the teneral period, before the inflexible exoskeleton has fully hardened. However at full maturity, insect growth is limited by the rigidity of their exoskeleton.

As far as excessive exercise is concerned, that some insects may be weakened permanently may be more to do with the fact that their life strategy is different to ours. Due to the vast number of offspring per adult, and subsequent low survival chance of any given individual, there could be an evolutionary advantage for individuals pushing themselves to possibly deadly extremes. This could lead to many deaths, whilst retaining a viable population and thus accelerate the emergence of a population of fitter individuals.

References

• Anderson, M. & Finlayson, L.H., 1976. The effect of exercise on the growth of mitochondria and myofibrils in the flight muscles of the tsetse fly, Glossina morsitans. Journal of Morphology, 150(2), pp.321-326.


• Bernays, E.A., 1986. Diet-Induced Head Allometry among Foliage-Chewing Insects and its Importance for Graminivores. Science, 231(4737), pp.495-497.

How does a plant cutting develop roots?

Plants grow only from regions at the tips of the roots and shoots called meristems.

Within the meristem areas there are stem cells ("blank" unspecialised cells). Unlike animal stem cells, plant stem cells are totipotent - meaning that they can differentiate into any type of cell. Therefore when the cutting is taken from the end of the shoot, the stem cells can differentiate into root cells or shoot cells depending on their conditions.

Because the meristems (therefore the unspecialised stem cells) are only located at the tips of shoots, you cant grow a cutting from the middle of a branch.

extra terrestrial - How should one rationally deal with the issue of space travelling alien civilizations?

What kind of reasoning is appropriate to understand the as of today unanswered question of whether there are (other) interstellar space travelling civilizations in the Milky Way?

We have already sent probes towards the border of the Solar system. And even landed human beings on another celestial body and brought them home alive and well. If we extrapolate the 50 years of space travel, the 100 years of electronics (radio), the 400 years of physical science, to just a fraction of the biological age of humankind into the future (like a few thousands of years), interstellar travel is not out of the question for us or at least our artefacts. So I imagine two possible alternatives:

1) The Milky Way is cluttered by lots of space travelling civilizations like us and our future. Once one of them/us gets going, they'll soon be everywhere. The Sun orbits the Milky Way every 250 million years, about 2% of the age of the galaxy. Going to the nearest stars is enough to soon be everywhere. But if they are everywhere since almost always, they should be here, we should be their seed.

2) We are the only space travelling civilization in the entire galaxy, ever. But then what makes us unique? We consist of the most common elements and volatiles of the universe and our planet and star and galactic location all seem to be very typical. There's no known trace of any uniqueness here. Whatever could it be?

Are there more alternatives?

While we cannot say today which alternative is true, we should be able to at least specify the possible alternatives. But to me they all seem to be absurd! What would be a rational logical scientific approach to this apparent paradox?

light - What does the filter name I+z' mean

They must be referring to two different filters:

• the (Bessel) I filter which has a central wavelength of $lambda simeq 800,mathrm{nm}$ and a width of $Deltalambdasimeq 150,mathrm{nm}$, and


• the (Sloan) z' filter, which has $lambda,Deltalambda simeq 970,255,mathrm{nm}$.

Hence their transmission is in the near infrared ("NIR"), and they're both above 700 Å.

The exact transmission curves vary a little depending on the producer, so if you want to calculate exact magnitudes, for instance, you need to find the transmission curves for the telescope in question. From the TRAPPIST equipment website, it seems they use filters from Astrodon. Astrodon don't seem to provide filter curves for these exact filter, but if you're okay with a good approximation, you can find the curves here:
Bessel I and
Sloan z'.

genetics - What do the variants on the PolyT sequence mean?

My son has been diagnosed with Cystic Fibrosis. I am not looking for medical advice regarding his condition, but I am very interested in understanding the genetic causes of his condition.

In addition to the common CF mutation Delta F508, my son's genetic testing revealed both 6T and 9T variants of the PolyT sequence.

If I understand it correctly, it seems that the variants (I have found repeated reference to 5T, 7T, and 9T variants, but almost nothing on 6T) are tied to errors in the RNA transcription of the CFTR protein, but I don't understand how, or what the difference between these variants are.

What does "variant of the PolyT sequence" mean in this context, what are the difference between 5T, 6T, 7T, and 9T, and how do they impact the production of the CFTR protein?

physiology - What happens to a human body once a sugary snack is consumed?

The human/animal digestive tract breaks down food chemically (with low pH/acid), enzymatically (like proteases and glycolytic enaymes which break down protein and sugars respectively), as well as symbiotically (bacteria participates in the breakdown of some compounds in the gut). The results are released into the blood stream for the most of the body to assimilate.

With foods with complex carbohydrates (scenario 1), the results can be only a modest change in the glucose level in the serum. This depends upon the specific food which you can understand better by researching the 'glycemic index'. Highly glycemic foods result in rather short term release of simple carbohydrates glucose/sucrose into the blood. Lower glycimic food contain complex carbohydrates (which are elaborate chains of sugars) which need to be broken up into simple carbohydrates before they are metabolized the the cells.

Foods which contain a lot of simple carbohydrates change the sugar levels in the blood nearly immediately and it can go quite high. simple carbohydrates are monomers or dimers of sugars. BTW complex carbohydrates have few pictures on the web, but you can imagine them as chains and networks of many many simple carbohydrates linked together.

Not all simple carbohydrates are used by human beings for energy. For instance the glycosamine in 'joint juice' is the sort that makes cartilidge, which just to show you how different some complex carbohydrates can be. BTW i don't recommend joint juice, just trying to give a familiar example. Its unlikely that the glucosamine you drink will be directly used for your joints!

So glucose is the energy currency in the blood. when the glucose level goes up insulin is secreted by the pancreas which tells the cells to take up the glucose for glycogen (internal cell energy storage in a complex carbohydrate) or to be metabolized directly. Diabetes results when insulin is not produced (type I) or when the cells stop responding to insulin (type II).

Human tolerance to glucose in the blood is estimated to be up to about 100 mg/dl long term. higher than this on the average is not healthy and can go up to several hundreds and cause lots of degeneration in the kidney, liver, and eyes, and more. Exercise and fasting increase insulin sensitivity and athletes have blood glucose that is quite low even if they have a sugary beverage.

hope this helps - many keywords embedded within...

One last note. Fructose, which is about 45-60% of high fructose corn syrup (the rest is sucrose) is almost entirely metabolized in the liver. This is why fructose can be harmful to people who drink too much sweetened beverages. With the liver taking in the vast majority of fructose, it tends to make fat out of it, sort of overdosing it to make it fatter than the rest of you relatively quickly. Fatty liver is a marginally disfunctional liver and can cause health problems down the way. Abdominal body fat (not on your love handles, but amongst your chest cavity and internal organs) is particularly harmful as it interferes with all sorts of organ function. Probably something everyone should be aware of.

endocrinology - What is the mIU unit as used in hCG hormone levels?

IU stands for "International Units" and it is an arbitrarily chosen unit of measure used mostly to quantify hormones, vitamins or various substances found in the blood.

The idea is well explained by the Wikipedia article on international units)

Many biological agents exist in different forms or preparations (e.g. vitamin A in the form of retinol or beta-carotene). The goal of the IU is to be able to compare these, so that different forms or preparations with the same biological effect will contain the same number of IUs. To do so, the WHO Expert Committee on Biological Standardization provides a reference preparation of the agent, arbitrarily sets the number of IUs contained in that preparation, and specifies a biological procedure to compare other preparations of the same agent to the reference preparation. Since the number of IUs contained in a new substance is arbitrarily set, there is no equivalence between IU measurements of different biological agents. For instance, one IU of vitamin E cannot be equated with one IU of vitamin A in any way, including mass or efficacy.

For hCG, in the 55th report for of the WHO Expert Commitee on Biological Standardization, you could find:

The Expert Committee on Biological Standardization, after consideration of this issue (11), concluded that the choice of unit should be made on a case-by-case basis and reflect, and be based on, the biological and medical as well as the physicochemical information available.
Many biologicals exist in both active and inactive states, and the clinically relevant form of the analyte may depend on the diagnostic aim. For example, the active state of the placental hormone chorionic gonadotrophin (hCG) is the relevant molecule to measure in the diagnosis of pregnancy, whereas the biologically inactive free beta subunit (hCG-beta) is measured to diagnose choriocarcinoma. Generally, a measurement of biological activity is expressed in IU, whereas measurement of the amount of a protein or of a specific protein structure is expressed in SI. In this case there would be a compelling reason to relate the measurement of hCG to a unit of biological activity, and the measurement of hCG-beta to an SI unit of quantity. Accordingly WHO has established a reference preparation for hCG (currently the fourth International Standard, with an assigned content of 650 IU/ampoule) (7) and a reference preparation for hCG-beta (currently the first WHO Reference Reagent for immunoassay of hCG beta subunit, with an assigned content of 0.88nmol/ampoule) (18). The former preparation was assigned a value based on bioassay, whereas the latter preparation had been extensively characterized by physicochemical and
immunological methods and calibrated in nanomol by amino acid analysis. Applying these considerations of the properties of biological analytes, and their measurement in the clinical situation allowed the WHO biological reference standard for hepatitis B surface antigen, assigned a value in arbitrary IU rather than in SI units, to be adopted by the medical devices sector of the European Commission as the standard required for the fulfilment of the so-called Common Technical Specifications (CTS) for in vitro diagnostic devices. The Common Technical Specification document supporting the European (IVD) Medical Devices Directive 98/79 EC is a legally binding document within the 25 countries of the European Union.
Where it is appropriate for a WHO biological reference standard to be calibrated in SI units, the principles outlined in ISO 17511 (8) should be followed. This will necessitate the existence and use of an appropriate single reference method and an assignment of uncertainty, derived from calibration data. Such a reference method should not be a biological assay because the factors that affect the results of such assays are not fully understood. Where they are used, SI units assigned to biological reference standards should be derived from, and traceable to, physicochemical procedures.

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Note that IU are not the same as enzyme units (U) which is a measure of enzymatic activity

galaxy - Galactic extinction as a function of distance

You might want to have a look to the GALExtin models. The official site is still not finished (not even sure if it's still being developed), but you can access the original article here, and download the models here.

Here's a poster that provides a quick introduction.

Basically this is composed of two models of the Galaxy (one with spiral arms and one without) to which you give a (l, b) direction and a distance, and it gives you back the extinction.

It's a little bit old but perhaps it can be useful to you.

Also, the advice given by Rob is a good one: for such small distances perhaps the best thing to do is to assume zero extinction.

Magnetic fields of peculiar HgMn A type stars

One thing that seems to be clear is that HgMn stars have only an extremely weak net longitudinal magnetic field component, if any. Shorlin et al. (2002) did an early survey of HgMn, Am, and Ap stars, and detected no longitudinal magnetic fields in the former, with a median 1$sigma$ uncertainty of 39 Gauss. Makaganiuk et al. (2010) also found $B_z$ values of 0 in the stars they surveyed, with a higher precision - a 1$sigma$ uncertainty of 0.81-10 Gauss, varying between stars. Other studies also yielded precisions of less than a few Gauss for some stars (see mentions by Makaguniak (2011)).

Some reports have found longitudinal values in the 10s to 100s of Gauss, but as Kochukhov notes, subsequent inveistigations have failed to confirm these findings, which have had extremely high uncertainties. One example is Hubrig et al. (2012), the paper you cite, which claimed to have found weak longitudinal and quadratic fields in several stars, including HD 65949. Kochukhov et al. (2013) then found no longitudinal fields on the star, to within a few Gauss, and Bagnulo et al. (2013) attributed to 2012 findings to instrument error, leading to flawed data.

Non-longitudinal magnetic fields have not been observed in much detail (small-scale longitudinal fields have not yet been ruled out, either, by large-scale global ones appear to be nonexistent), and complicated ones could still exist. Kochukhov et al. (2013) do say that they have ruled out large so-called tangled magnetic fields, but small-scaled ones are still possible, according to Hubrig.

One thing worth noting is that the vast majority of these studies, including the one you referenced, which has been disputed, are focused on B-type HgMn stars, in part because fewer A-type HgMn stars have been discovered.

Since the Universe is expanding, is it accurate to say that a galaxy is 5 billion light years away?

I'm not 100% sure if I'm understanding what your asking, but if your question could be rephrased as "how do we measure distances in an expanding universe?", then I can try to answer that.

Depending on what astronomers measure they use different distance measurements. For example the comoving distance between two objects takes into account the expansion, and so does not change with time. If you know the redshift of the galaxy, for example by measuring the spectrum, and have a cosmological model, then you can calculate the comoving distance. Here cosmological model means constraints on the amount of dark energy, matter (both dark and regular) and radiation. The current accepted model is that the universe is around 70% dark energy and 30% matter, most of which is dark (with negligible radiation). The percent here refers to the fraction of energy density. Note that these values change over time, mostly since dark energy is like a property of space and so increases as the universe expands.

For some more info see:
https://en.m.wikipedia.org/wiki/Distance_measures_(cosmology)

Note that light years is a definite measurement, and so we can use it a valid unit for all distance measures.

black hole - How can a naked singularity be possible?

Nobody likes the idea of naked singularities, as they would have a toxic effect on causality. If a singularity existed that was not separated from us by an event horizon, then not only would the future not be predictable, but the past would not be fixed. Like the grandfather paradox, it wouldn't make sense, so it cant exist. The trouble is that GR doesn't implicitly rule them out.

If a black hole is spinning fast enough, or has enough charge then it seems a naked singularity could form. Naively you may think that the centrifugal force in the first case, and the electromagnetic force in the second are sufficient to overcome gravity.

I particular if $G^2M^4/c^2 < J^2$, where J is angular momentum, M is the mass, G is the gravitation constant, and c is the speed of light. The there will be a naked singularity. For a small, stellar mass black hole would need an angular momentum of $10^{42} mathrm{kg m^2 s^{-1}}$ to lose its event horizon

human biology - Fetal development, gastrulation and embryonic disc

I am completely confused by the images circulating on the internet of human gastrulation.

First, lets see how it happens in deuterostomes. This image depicts the process:

(image is from Wikipedia)

From here we can conclude that blastula becomes gastrula when some of the ectoderm beecomes endoderm, the place where it goes inside becomes anus and then mesoderm is formed.

Ectoderm here is the outermost level and gastrula already has anus.

However, in this image of human gastrulatuion we see completely different things:

(image source)

The mesoderm here is the outermost layer, ectoderm is inside and the gut cavity is formed by the separation of a part of the yolk sac. There is no anus and the posterior end of the gut is blind. Also other similar images suggest that a twins may be separated already after the mesoderm was formed (thus uniplacental twins).

The lack of agreement between the images disturbs me.

Just to point out some of the differences in the depicted processes:

• In first image mesoderm forms after gastrulation, on the second it forms far before gastrulation


• In the first image anus forms in the process of gastrulation, in the second image anus remains blind


• In the first image ectoderm is the outermost layer, while in the second picture mesodem is the outermost level that encloses all, including ectoderm.

evolution - Can two humans with 44 chromosomes produce viable offspring?

Interesting question. You refer to aneuploidy.

I don't have idea, but I loved to make some calculations. Feel free to edit because there are some very approximative assumptions.

Aneuploidy, the loss or gain of a chromosome, is estimated to occur in 13-25% of oocytes, 1-4% of sperm, 20% conceptuses and 0.3% of newborns. (reference)

The 46 chromosomes are made of 23 pairs, if the chromosome loss is evenly distributed, we have 0.3% / 23 newborns with the same chromosome loss (0.013 %).

Now, consider that the lost chromosome is likely not really lost, but just translocated on another of the 22 chromosomes. For instance, the individual you refer was having two chromosomes (the 14 and the 15) fused together.

So individuals with the same chromosome loss (0.013%) should have also the same translocation on one of the remaining 22 chromosomes (0.013% / 22 = 0.00059%).**

Chances are now that two of the 0.00059% newborns with exactly the same chromosome loss, will mate together.

Assuming random mating between humans, we have 0.00059% x 0.00059% = 0.0000003 % of possibilities, which is 1 possibility every 333,333,333 human beings.

We are now 7 billions on the Earth, so assume 3.5 billion couples all fertile despite of the age. If we assume also no spatial constraints, so that everyone could mate with every else one on the Earth, there could be no more than 10 couples with the same aneuploid mutation.

Provided the mutation does not affect genes important for reproduction, for instance genes between the two chromosome junctions that get interrupted, this couple could reproduce I guess.

To find that child, chances are now that he/she will have a kariotype done. Quite difficult to find isn'it?

protostar - Is the conversion from proto-star to main sequence an event or a process?

Astronomers distinguish a prototstar from a star based on whether the object is visible. A protostar is hidden by the gas cloud that surrounds it. Protostars aren't visible. At some point in their evolution (and where this occurs depends on mass and metallicity), a protostar will start clearing the surrounding cloud of gas. This process happens very quickly from an astronomical point of view. (Aside: From a human point of view, this is anything but quickly.)

In the case of very massive stars, the newly emerged star is already on the main sequence. Very massive stars are "stars" (objects with a stable mass, stable size, and fusing hydrogen into helium) well before astronomers can see them. In contrast, very small stars spend hundreds of millions of years of evolution between being a "star" (visible to astronomers) and being on the main sequence. The star is a pre-main sequence star during this long span of time.

Intermediate mass stars also spend some time as a pre-main sequence star. How much time depends on mass and metallicity. In the case of a star with a mass of ~1 solar mass and metallicity comparable to that of the Sun, the time spent as a pre-main sequence star is on the order of tens of millions of years. In contrast, the time spent as a protostar is very short, tens of thousands of years. The time taken to clear the star system of gas (the transition from protostar to PMS star) is shorter yet, hundreds to a few thousand of years.

There is no point at which one can say fusion starts. It's a probabilistic thing, with probability increasing sharply with density and temperature. What about objects at the low end of density and temperature? This is the boundary that separates red dwarfs from brown dwarfs.

There is very little difference between the smallest red dwarfs and the largest brown dwarfs. The smallest red dwarfs are quite cool. They fuse hydrogen into helium via the p-p chain, but rather infrequently. The largest brown dwarfs also fuse hydrogen into helium via the p-p chain, but here the fusion reactions are so very infrequent that the brown dwarf gets cooler and cooler. In a trillion years, we might be able to point to a marked boundary between old red dwarfs and old brown dwarfs. Right now, that boundary is rather arbitrary.

evolution - How many times did endosymbiosis occur?

Well, it seems quite obvious that it was not a single I-eat-you-but-you-survived act but rather a convergence of endosymbiotic and host species into a greater and greater cooperation.
Of course this leaves a question if there was one or more species of endosymbionts involved.

Mitochondria are a very primeval story forced by the oxygen catastrophe, so it is hard to say, although great majority of mitochondria seems to have a single origin.

Plastids are much more divergent, however it seems that they did originated from a single source, diverged into chloroplasts, cyanelles and rhodoplasts and were later mixed up by numerous acts of secondary and even tertiary endosymbiosis (plus a further evolution); this variety can be especially seen within Euglenas, and they are the main group investigated in this manner.

Under what circumstances and why is terrific broth preferred to LB broth for E.coli growth?

I have used terrific broth to grow up transformed E. coli so they grow faster. Often people will conduct a transformation, screen the cells, and grow them up in broth for plasmid extraction. This growth would be for 12-16 hours. Instead a person could use terrific broth to grow up the cells and it would take may 6-8 hours for adequate cell density for plasmid extraction. If you are trying to express a protein then I would go with LB.

Also, I learned recently that terrific broth is also preferred over LB when needing to express proteins after transformation.