Starts With A Bang! » Scientific papers Ethan Siegel's blog/video blog about Cosmology, the Universe, and everything else Sat, 04 Apr 2009 20:12:38 +0000 en A Rule of Thumb for Scientific Papers? Mon, 16 Mar 2009 18:32:44 +0000 ethan There have been a number of readers who have pointed me to scientific papers, many of which make outrageous claims. There are many different levels of outrageous, ranging from least to most outlandish:

  1. Plausible — explaining a newly observed phenomenon based on a theory with lots of supporting evidence.
  2. Speculative — based on an untested theory with marginal but inconclusive evidence.
  3. Hopeful — based on an untested theory with no real supporting experimental or observational evidence.
  4. Stabbing in the dark — simply adding X new parameters (or wiggle-room) to a theory in order to possibly explain X or fewer new results.
  5. Stabbing in the dark without a knife — advancing a theory that is known to conflict with experiments on many fronts in order to explain one new observation.

Those that fall into the first category make me very happy as a scientist, and are the papers I strive to write when I do my research work. Why? Because the laws of nature tend to be very simple, and most things can be understood without having to resort to new physics. This interacting pair of galaxies (a.k.a. the antennae galaxy) is an excellent example:

Many of the scientific papers I see today (and most of the ones I get sent) fall into the third category. But they upset me greatly, because the authors treat it like it’s in the second category. One of the big things you may have heard about is the PAMELA data:

People have been publishing papers left and right trying to explain the “observed excess” in terms of dark matter that annihilates with itself. Could dark matter annihilate with itself? Sure! We don’t see any evidence of this, yet, but it could, in principle. If you look at the PAMELA data above, there are extra high-energy positrons, to be sure. But, and this is very important, we know that most of it is not caused by annihilating dark matter. There is some astrophysical phenomenon making anti-electrons (i.e., positrons) that we do not understand, but the observed amount is too great to fit in with what we know about dark matter. We also have seen this for many years; the PAMELA data is nothing new.

But the big problem with these explanations is that there is no observed excess of anti-protons! That would be compelling evidence, but we don’t see any evidence for it at all. Yes, I think anyone can write a bunch of papers explaining phenomena that doesn’t happen, but why would you, and how would that possibly qualify as interesting science?

But there is a surefire way to identify a scientific paper that falls into the worst two categories up there. You don’t even need to get past the title of the scientific paper to do it:

Does the paper you’re reading end in a question mark? If so, the answer is almost always “No!” But they make interesting, imagination-capturing claims, and so they get media attention, even though they’re mostly scientifically baseless. Let’s take a look at some of the astrophysics papers that come up (my comments in parentheses):

  • Could some black holes have evolved from wormholes? (Could a wormhole ever even — realistically — exist in our Universe? The current evidence says no.)
  • Could the Pioneer anomaly have a gravitational origin? (Let’s see, did gravity just randomly decide to turn the volume up in the 1980s? No? Surprise, surprise!)
  • Do We Live in the Center of the World? (Oh my, Copernicus! Do you think the answer to this one might be “No?” Just maybe? Would this paper ever have garnered anything other than laughs if Andrei Linde weren’t one of the authors?)

You get the point. Seems like an easy lesson to learn, yes? Well, apparently, not for many scientists, because today, this paper came out:

Do we live in a “Dirac-Milne” universe?

For a little more information on what a Dirac-Milne Universe is, take a look at this, from the abstract:

…an unconventional cosmology, the Dirac-Milne universe [is] a matter-antimatter symmetric cosmology, in which antimatter is supposed to present a negative active gravitational mass.

How simple. Except for one little thing: we’ve observed antimatter! And it has a positive mass! That’s been measured! So what this paper says is, if the laws of physics were entirely different, which they aren’t, we could imagine a Universe where some of the more complicated things we see were explained, even though it jettisons simple, valid, and accepted explanations for many other things.

How is this acceptable science? How is this deemed interesting? How am I the only one grossly outraged by this? I thought the whole point of science was to investigate and understand what occurs naturally in the Universe, not to invent rules that we know are incorrect and ask, “What if…?” I mean seriously, you may as well write a “scientific paper” about time machines:

And I would be fine with this if the authors would just own up to the fact that this falls into category 5, but they don’t. If you’re going to go off into fairy-land, don’t try to convince us that it’s reality, or that it’s even plausible as reality. This is a lesson that I wish scientists would learn, but that it’s absolutely vital that science journalists learn. I can spot it for astronomy/astrophysics/physics, but who’ll do it for health, for biology, and for the environment?

Keep that in mind whenever you read about science, including at the latest Carnival of Space, where someone thinks I should write about Venus all the time!

There isn’t enough punishment for this Mon, 09 Feb 2009 22:25:22 +0000 ethan I normally try to keep my nose out of areas where I’m in over my head. In other words, there are areas where I’m an expert, and there are areas where I keep myself as informed as I can, but I have to rely on experts for their information. For instance, if you wanted to know about dark matter in our own galaxy, you should definitely come to me:

I’ve got expert knowledge on this, I’m familiar with what makes my findings scientifically rigorous and valid, and I know how to draw responsible conclusions based on the data in front of me. It is completely unreasonable to expect someone who isn’t an active researcher in theoretical astrophysics and cosmology to be an expert in the same way I am.

And by the same token, there are areas where I’m not an expert, such as what the incidences, symptoms, and causes of autism in children are:

So, to be informed, it should be reasonable for me to rely on the scientific findings of experts in that particular field of medical research. Now, I’ve talked before about the importance of being a good scientist, especially when your research can affect the health and well-being of others. So without further ado, I’d like to introduce you to someone you may not have heard of (unless you’re a huge fan of Bad Astronomy), Andrew Wakefield.

To give you the extremely quick version: in 1998, Dr. Andrew Wakefield published a very controversial paper following 12 children’s conditions at a clinic. His conclusion was that eight out of the twelve developed symptoms of autism after receiving their Measles, Mumps, and Rubella (MMR) inoculation. Since that piece of research, many millions of dollars have gone into researching the possibility of a link between vaccines and autism. Thousands of children have not been inoculated out of a fear of developing autism, and a few of those children have died as a result of contracting a disease for which a simple vaccine exists. There has been a huge grassroots movement that has sprung up among parents of autistic children, blaming the vaccine for their woes:

Now, over the last 11 years, overwhelming evidence has shown up that there is no link, not even a correlation (much less a causation) between vaccines and autism. But this past Sunday, an article came out in Wakefield’s home country of the UK, declaring the following:

MMR doctor Andrew Wakefield fixed data on autism

What? We have not just a scientist, but a medical doctor dealing with one of the fastest growing epidemics in medicine, falsifying results? And publishing them in a medical journal (the Lancet)? Remember that “eight out of twelve” statistic I quoted you earlier? Here’s what we get, upon further review:

Our investigation, confirmed by evidence presented to the General Medical Council (GMC), reveals that: In most of the 12 cases, the children’s ailments as described in The Lancet were different from their hospital and GP records. Although the research paper claimed that problems came on within days of the jab, in only one case did medical records suggest this was true, and in many of the cases medical concerns had been raised before the children were vaccinated.

The details are even worse. It turns out that after Wakefield’s “suggestion” that MMR, bowel disease/inflammation and autism were linked, the children were re-examined and diagnosed with these new bowel problems. I was unable to find US data, but in the UK, the number of confirmed measles cases in 2008 was 1,346. Want to know what the number of cases was in 1998, the year Wakefield’s paper was published? 56. One scientist’s false data has led to the resurgence of a disease that should be eradicated by this point. Nice move, Andrew, seriously.

That said, autism is a serious problem. We don’t know what causes it, we don’t know why the incidence of autism is so much higher than it’s ever been in the past, and these are things that need further investigation, absolutely. But not on a foundation of lies. And not by searching for a link that doesn’t exist with vaccines. Let’s do everyone justice, and have some sort of accountability for doctors and scientists who, through their actions (whether through ethical incompetence or unethical falsification), cause unnecessary death and disease among the general populace.

If you’re going to accept being lauded as an expert, you have to accept the responsibility of being an expert. Be honest. Be ethical. Or go do something else.

Bad Science Makes Me Angry! Mon, 03 Nov 2008 19:01:53 +0000 ethan Okay, folks, I have two words I’d like you to think about: correlation and causation. When we say two things are correlated, we mean that somehow, when one of them shows a change, the other one changes, too. But it’s a big leap to say that one is causing the other.

Sometimes they do. Let’s say the rabbit population is exploding out of control. What do you do? Bring in a few foxes. Within a short time, because of all the food, the fox population will explode, and the rabbit population goes down. The population of rabbits and foxes are not only correlated, there is a causal relationship between them.

But sometimes two things coincide with each other, yet aren’t related. For example, the last Glacial Period reached its maximum extent 18,000 years ago, and then after a few thousand years, the ice retreated and the sea levels rose. Coincidentally, a very nearby, powerful supernova went off about 12,000 years ago.

Are these two events correlated? Yes, of course. They happened close to one another in time. But did one cause the other? Probably not; we know what causes supernovae (it isn’t anything on Earth) and we think other things caused the end of the last glacial period.

So today, there’s been a report all over the news:

Sexual content on TV is linked to teen pregnancy.

When I saw this, I thought that this was a highly interesting finding. Until I actually read the study. The science here is horrible. Let me summarize what the RAND corporation did, and why you should never trust a study like this.

  1. They followed the television viewing habits of 12-17 year olds for 3 years.
  2. They looked for a correlation between televised sexual content and pregancy (for girls) or responsibility for pregnancy (for boys).

And that’s all they did. And lo and behold, look at what they found!

Teens who were exposed to high levels of television sexual content (90th percentile) were twice as likely to experience a pregnancy in the subsequent 3 years, compared with those with lower levels of exposure (10th percentile).

Are you kidding me? That’s it? You found that teenagers who spend more time doing things associated with sex and show a higher interest in sex are more likely to be having unprotected sex? (Excuse me while I act half my age.) DUH! (Thank you.) Why is this not exactly what you’d expect? Of course they’re correlated! But why would you come to the illogical (and unsupported by any evidence) conclusion that watching sex on TV causes teenage pregnancy? Wouldn’t it be far more likely that the teenagers who pursue sexual content are the ones who are having more sex, or at least more unsafe sex? It’s not a good scientific technique: correlation does not imply causation!

Further research led me to uncover that this isn’t the first time they’ve published a report that has this abhorrent technique. Remember all the hoopla about teen violence and violent content on TV, the web, and video games? Same thing. They surveyed violent and nonviolent kids, surveyed their searches for violence, and (surprise, surprise) the ones who commit violent crimes are more likely to have searched for violence. Again, clearly, there’s a correlation. But it seems way more likely that the violent kids searched for violence, not that the kids who saw violence were more likely to go out and commit it.

The lesson? If you want to draw a conclusion about this, you have to test for it! They haven’t even devised a method for testing this. All they showed is that these things are correlated. You know, like global average temperature and pirates.

Give me a break.

If you miss the astronomy, the new Carnival of Space is up; I recommend you check it out!

How “Quantum” is the Big Bang? Tue, 13 May 2008 18:36:53 +0000 ethan There is a very techincal paper this morning by Martin Bojowald that asks the question, How Quantum Is The Big Bang? Let me break it down for you.

If you took a look at empty space and zoomed in on it, looking at spaces so small that they made a proton look like a basketball, you’d find that space wasn’t so empty after all, but was filled with stuff like this:

What are these? They’re little pairs of matter particles and anti-matter particles. They spontaneously get created, live for a brief fraction of a second, and then run into each other and disappear. That’s what happens on very small scales, in the quantum world. (This is known as the Heisenberg Uncertainty Principle, and it actually happens!)

Well, the Universe today is huge. But it wasn’t always; back when the Big Bang was happening, all the matter and energy in the Universe was concentrated into a volume so small that these quantum effects were important!

So now, we can ask the question: how important were these quantum effects at the time of the Big Bang? (FYI: this is talking about what happens at a singularity, so this is even before inflation!) And what he basically found is that at these super-high densities, you start to run into something very interesting. Remember the Pauli Exclusion Principle? It says that no two fermions (e.g., protons, neutrons, or electrons) can occupy the same quantum state. You put all the matter in the Universe into a small enough volume, and you wind up “squeezing” everything together!

And what he found, as best as I understand it, is that the quantum state of whatever’s in the Universe determines what type of Big Bang you get! Is it the same in all directions? Well, that depends on what the quantum state of the Universe is. Will it start expanding, contracting, or oscillating? Again, depends on the quantum state. We don’t know what that state is, especially in the context of inflation (which might wipe out all of that information), but this is what they’re trying to figure out! No definitive answers yet, but at least the quantum gravity people have gotten to the point where they can start to ask this question!

Gravitational Waves: Inflation or not? Thu, 17 Apr 2008 19:23:38 +0000 ethan Nothing gets past you, does it? A scientific paper came out earlier this week, and I took a look at it, sighed, and Jamie asked me, “What?” And I said to her, “When I see bad science, it just makes me a little bit frustrated and sad.” Of course, I had no intention to write about it.

But then Starts With A Bang reader Matt emailed me, and writes the following about this press release that he had seen:

You have two explanations for these gravitational waves now and that much I understand. But they make it sound as if symmetry breaking and inflation are competing theories. They aren’t, right? Do phase transitions influence inflation (it would make sense)? How are those two related? The inflation rate depends on the energy density of the universe (-> scalar fields), right?

And the point is: Even if we attribute the gravitational waves to the process of symmetry breaking, we’d still need to explain the uniformity of the universe because symmetry breaking only explains the origin of the fundamental forces.

So the paper is by Lawrence Krauss, whom I met once back in 2006, when I was giving a talk at Vanderbilt. Lawrence shows up about 40 minutes late (to my one hour talk), makes a scene when he walks in, and demands, “What did I miss?” Feeling indulgent, I gave him a 15 second synopsis of the last 40 minutes, and he goes, with a satisfied smile, “Oh, not much then.” Way to make a good impression on me, Lawrence.

Anyway, his scientific paper doesn’t have anything wrong with it. He basically talks about how a global phase transition can generate gravitational waves, which is 16 year-old news, and those waves might be strong enough to show up in the CMB, just like those from inflation. Is this big news? Come on, anyone can write a paper where you make gravitational waves (the link is to a paper I wrote in 2005).

Here is the important difference, however:

  • Inflation predicts a scale-invariant spectrum.
  • Other mechanisms to make gravitational waves don’t.

A “scale-invariant” spectrum means that energy is evenly distributed in waves of different sizes. Let’s compare the spectrum of inflation (green curve):

to the spectrum in Lawrence’s paper (figure from the paper; he plots things in different units):

and just for fun, let’s throw in the spectrum that my old paper predicts (it’s very different from inflation):

Now, here’s the thing missing from Lawrence’s paper (and admittedly, my paper, too). What is this going to look like in the Cosmic Microwave Background? People have computed it for inflationary models, and know that the shape of the curve should look just like this (the blue curves are for different amplitudes of inflationary models),

so people can go out and try to measure it. Specifically, for those of you who want details, this is looking at the B-mode spectrum of the microwave background, which is one of the things that Planck is designed to measure. What does this new paper predict for their data? Well, they conveniently don’t publish it. Why not? Because it would decidedly be very different from anything resulting from inflation.

Lawrence’s paper talks about something that happens way after the end of inflation, and doesn’t affect the spectrum from inflation or anything related to inflation at all. The paper just gives an extra way to generate gravitational waves of large-enough amplitude that they might show up in the CMB. And they might, if the new physics which he made up is correct. Which, who knows, it might be, and at least we have something new to look for. But this research does nothing to eliminate the need for inflation or change the predictions of inflation, and the press release is indeed wrong for implying that. Thanks, Matt, for forcing me to clear that up.

It’s getting near the end of the week again, so check out this week’s Carnival of Space over at KYsat. Is the KY for the state or the… other thing?

A Discovery of Gravitational Waves? Fri, 04 Apr 2008 09:05:43 +0000 ethan Two summers ago, I was in Les Houches, France, for a summer school that turned out to be one of the best experiences of my life. Seriously, we’d wake up every day and this was the view from the school:

Well, the University/Institution that ran the school sends periodic updates to me. And they linked me to this release. Here’s the interesting and (if it’s true) sensational claim that the release makes:

Recently, a team of theorists … performed a new analysis of all available CMB and LSS data including the WMAP and Sloan data and favor an inflation model where exist primordial gravitational waves: the amount of the ratio r between these waves and the density fluctuations is non zero in their model. … In the frame of their model, the team obtains the inflaton potential which best fits the data together with the most probable value for the primordial gravity wave ratio r ~ 0.055. This value is within the reach of forthcoming CMB observations.

So now in English: based on the most recent data from the microwave background and from galaxy surveys, we can figure out some of the parameters of the theory (inflation) that set up the big bang. There are fluctuations in the energy density (corresponding to places where galaxies will and won’t form), and we see those; those are the hot and cold spots in the microwave background. But what we haven’t yet seen are fluctuations that are characteristic of gravitational waves left over from inflation/the big bang. Inflation has a very different prediction for gravitational waves than the big bang without inflation, so this could be very strong evidence for inflation if they find it. They can’t measure the waves outright, but they can measure how strong the gravitational wave fluctuations are compared to the matter/energy fluctuations. They cleverly name this r, for ratio.

Now, in most simple models of inflation, r is teeny-tiny, and we’ll never see it. But what they claim is to have evidence for r being at least 0.016 (at the 95% confidence level). Here’s the graph of their results overlayed over the constraints from the microwave background:

Everything above the line that says “h=-0.99″ is the stuff that’s allowed at 95% confidence level; this means there’s only a 5% chance, all things being equal in their analysis, that r is below that line. (ns is measured, by the way, and is about 0.97 +/- 0.02.) The scientific paper is available here, however, they do make an assumption here, that if it’s false, invalidates their conclusions. Their assumption? That the potential that gives rise to inflation is a polynomial of the form:

V(x) = A + Bx + Cx2 + Dx3 + Ex4.

Is this a good assumption? No. It’s a shame that you have to be not just a scientist, but a scientist well-versed in inflation theory to realize that a big sweeping claim like this is probably wrongheaded. But now you know something that probably only a few thousand people in the world know! Happy Friday!

Cosmic Conspiracies! Tue, 01 Apr 2008 20:06:24 +0000 ethan There are a number of parameters that we deal with in cosmology that have no dimensions; that is, they’re just numbers. And yet, there are a remarkable number of coincidences that just “happen to be that way” in our Universe.

Douglas Scott, in this paper, points out some of the more puzzling ones, including:

  • The age of the Universe (13.7 billion years) is exactly three times the age of the Solar System (4.5 to 4.6 billion years).
  • The dark matter fraction of the Universe (OmegaDM=0.23 +/- 0.02) is equal to the Helium mass fraction (Yp=0.238 +/- 0.010) of the baryons.
  • The Hubble constant (H0) times the age of the Universe (t0) is exactly 1 (H0t0=1.03 +/- 0.04).
  • T0, the temperature of the cosmic microwave background, is exactly the triple point of water temperature divided by 100.

What does this mean? Let’s ask Douglas Scott:

Which of these turn out to be complete coincidence
remains to be seen. But perhaps one of them will be
the ‘smoking grail’ that cosmologists have been looking
for to lead us beyond vanilla ΛCDM into a whole new
ice-cream parlour of models.

In the absence of ice cream, then, this means absolutely nothing! (Although the coincidences are real, and feel free to quote me on them.) Happy April Fools’ Day!

The Science of the Brightest GRB Wed, 26 Mar 2008 20:21:29 +0000 ethan Last week, the brightest gamma-ray burst ever was observed. (See here.) I wanted to know what it was that caused this bright explosion that, despite it being at redshift z=0.94 (or about 7.5 billion light years away), it was visible on Earth with the naked eye!

Well, a scientific paper was written on the observations of this burst, named GRB 080319B, or the second GRB observed on 03/19/08. Let me take you through the highlights. First off, here’s what it looked like, in gamma-rays (left) and the afterglow in the optical/UV (right):

When we look from Earth, the faintest objects we can see with the naked eye are around magnitude 6, with smaller numbers being brighter. Well, the graph below (stolen from the linked paper above) shows how bright this is:

It weighs in, at its brightest, at magnitude 5.5 in the V-band (V is in the visible part of the spectrum). It’s much brighter in gamma rays, but we can’t see those with the naked eye. Now, that light-curve, fading over time, looks familiar to me. Why? Because I’m an astrophysicist and look at junk like that all the time. You know what it looks like? A supernova light curve. Let’s dig one up and compare…

Well, don’t those look similar? The major difference? The scale: this gamma-ray burst fades out much more quickly (about 10x as fast) as your typical supernova. Does this mean it is or isn’t a supernova? Well, the conclusion they reach in the paper is that it isn’t just a supernova. It’s most likely a very massive supernova that has very powerful, unusually collimated jets, one of which happens to be pointing right at us (see the image at right). The jet blast remains highly collimated for only a very short time, and that’s why it appears to fade so quickly. This simulation shows what a supernova that creates a gamma-ray burst might look like.

Furthermore, this is a pretty typical gamma-ray burst in every way, except it looks like it’s a little bit brighter than normal at the beginning. Here’s a graph (also from the paper) that shows you what a number of gamma-ray bursts of the same type look like:

Sure, it’s a little brighter at the peak, but overall it looks very comparable. That’s why the theory is that the jet is just unusually tightly collimated. Now, why do I care? Or, rather, how is this relevant for cosmology? As a cosmologist, one of the most important things we’re trying to figure out is the expansion history of the Universe. One way to do this is to measure an object’s redshift and its distance. Redshift is easy, but distance is hard. The two ways of doing this are to either know the intrinsic brightness and measure the apparent brightness, calculating distance that way, or measuring the apparent size knowing the intrinsic size, and calculating distance that way. The first one is potentially useful for gamma-ray bursts, if we can figure out their intrinsic brightnesses. Why is this useful? Because gamma-ray bursts are brighter than the other things we know at high redshifts, namely, quasars and supernova. They have a graph about this in the paper, too:

The farthest things we’ve ever seen are at a redshift of around 7. How much better can gamma-ray bursts potentially do? Let’s go to the article:

Finally, we examine the detectability of such events with current and future
facilities and find that such an event could be detected in gamma-rays by BAT out to z=4.9 (8σ), while the nominal EXIST sensitivity would allow detection to z=12.2. At K-band this source would have been easily detected with meter-class telescopes to z=17.

Holy crap, man. Redshift of 17? Are you kidding me? That’s back when the very first stars were forming, before (we think) there were even galaxies. Keep working on figuring out how to determine their intrinsic brightness, because if we get it, this could be the most powerful tool for cosmology ever, and could measure dark energy far better than either supernova or baryon acoustic oscillations, which are currently our two best bets.

WMAP results: Cosmology from the CMB Thu, 06 Mar 2008 22:37:19 +0000 ethan The cosmic microwave background is the radiation left over from the big bang. It’s very uniform, 2.725 Kelvin everywhere. We’re moving with respect to it, so there’s a doppler shift, and we see that as a dipole moment in the Temperature. When we subtract that out, we see variations on the order of 30 microKelvins! WMAP is a satellite (Wilkinson Microwave Anisotropy Probe) that measured these anisotropies, and they just released its year 5 data. First off, with the uniform and dipole parts subtracted out, and with the foreground from the galaxy also taken out, here’s the map of the microwave sky (a baby picture of the Universe, when it was only 380,149 years old), compared with what we used to know from the previous satellite, COBE:

As you can see, the WMAP data is far better. COBE’s angular resolution was about 7 degrees; by comparison, WMAP’s resolution is less than half of one degree. We can learn a lot about the Universe from this baby picture. Let me tell you, though, why some parts are slightly hotter and why some parts are slightly colder.

The Universe has an average density, and always did. Some places are slightly more dense; they have more energy. Other places are less dense; they have less energy. Since mass=energy, imagine it like this: to escape from the planet Earth, I need a certain amount of energy. If I move with a velocity of 11 kilometers per second, that will do it. But what if the Earth were more dense? Well, I’d need to expend more energy to escape. If it were less dense, I’d need less energy to escape. Earth is the densest planet; on the Moon, for example, escape velocity is only 2.4 kilometers per second.

Now, imagine that instead of a person, you’re a beam of light at the surface of our planet. You’re going to escape because you’re moving at the speed of light, but you have to lose energy to get out of that gravitational field.

If you’re on a denser planet, I lose more energy, and so my light gets colder than normal. If I’m on a less dense planet, I lose less energy, and the light is warmer than light that left a normal planet. Well, the light from the Cosmic Microwave Background is doing the same exact thing, except it’s leaving different regions of space instead of planets. Those blue spots are where there are overdense regions and the light we see is colder, and the red spots are underdense regions, hence that light appears warmer. And that’s why we see those patterns in the sky that we do.

But that’s not the end of the story. There’s a lot of information that we learn from looking at those patterns caused by different density regions. The whole bunch of details that we’ve learned (caution that it may get technical to those who read further) are below: