WHEN SITTING ALONE at night, my thoughts often turn to dark topics. By this, I mean dark matter and dark energy. In the 30 years since I completed my PhD in physics, the world has changed a great deal, for better and for worse. On the negative front, I never would have imagined we would still be battling ignorant religious fundamentalism within my own country.
On the plus side, we have obtained more information about the cosmos in my lifetime than I would have believed possible. Our picture of reality has dramatically altered from what it was when I was a graduate student. In some cases, things we were virtually certain of turned out to be wrong; in others, the boldest and wildest extrapolations have sometimes turned out to be right on the money. In all cases, the universe has surprised us.
One of the things we don’t emphasise enough when writing about science is that most theoretical proposals about nature, made in advance of experiment, are wrong. Nature has a way of surprising us, so it’s vitally important to realise that science cannot proceed by pure thought and logic alone. Without the guidance of experiment, scientists are like those who choose to immerse themselves in sensory deprivation tanks. They inevitably tend to veer off into hallucination. So it is all the more telling when new unexpected clues about nature come from observations, or when some of our creative imaginings turn out to reflect the way nature really works.
ONE OF THE EXOTIC surprises physics has thrown at us in the past 30 years is the concept of dark matter. Dark matter was first inferred by Swiss astronomer Fritz Zwicky in 1933 when trying to figure out what stopped galaxies in massive clusters from flying apart. When I was a student, in the 1970s, the case for dark matter was suggestive, but not compelling. As a particle physicist, I became fascinated by the idea that particles could naturally be produced in the early universe with the necessary abundance and characteristics of dark matter today. But the game was wide open.
Neutrinos, which after all are known to exist, still seemed like a good bet to be dark matter particles, but it was still possible that our estimates about the amount of dark matter were wrong, and maybe it could be made up of boring things that simply don’t shine as brightly as stars or hot gas, such as planets.
Now, there is compelling evidence that cold dark matter is real; from direct measures of mass in galaxies and clusters, calculations of the abundance of light elements produced in the Big Bang, measurements of large-scale structure coming from millions of galaxies, and remarkable observations of the primordial seeds of structure observed in the cosmic microwave background (CMB) radiation from the Big Bang.
Observations of colliding galaxies suggest very convincingly not only that dark matter exists in profusion; but also that it cannot be made of normal matter. Moreover, candidates for dark matter may be on the verge of detection by direct detectors of the sort that I and others proposed more than 25 years ago, or perhaps may be produced in the coming years at the Large Hadron Collider.
Another satisfying, if initially perplexing, discovery that took me by surprise is that the universe is flat (rather than curved, or ‘open’. This rather complex idea essentially says we can follow a triangular path from point a to b to c and back to a, with the angles adding, as would be expected, to 180 degrees). I remember when I was a young professor at Yale University in Connecticut, one of my senior colleagues, an observational astronomer, told me of a theorem he was pretty certain was true: the universe would conspire to ensure that we couldn’t accurately measure any fundamental cosmological parameter.
After decades of false claims and false starts he had reason to be jaded. All of that has changed. Twenty-five years ago, observers were certain that there was not enough matter in the universe to produce a geometrically flat 3-D space – space must be ‘open’ or negatively curved. Theorists, on the other hand, were certain the universe was flat, because mathematically that was the only possibility that made sense. I wouldn’t have dreamed we would directly measure the geometry of the universe in my lifetime. But, once again thanks to new observations of the CMB we have done so, to an accuracy of 1%.
We theorists cannot pat ourselves on the back too much for our correct guess about geometry, however, because we were completely wrong about what it is that makes the universe flat. We thought it was lots of dark matter. Instead, in the biggest surprise in a century, it was discovered that empty space apparently accounts for more than 70% of all of the energy in the universe. And we don’t have the slightest idea why!
Our earlier calculations had suggested that if the energy of space wasn’t zero, it had to be 120 orders of magnitude larger than the energy of everything we see, which was so ridiculous (and observationally impossible) that we figured it must be zero. So we could sleep at night. But we were wrong.
The fact that empty space has energy has changed everything: not only our understanding of the current universe, but also its future. Nothing prepared us for this shock, and it could take us a long time before we understand the origin of this energy of nothing.
ONE OF THE MOST FUNDAMENTAL questions in cosmology is: where do the primordial lumps that form galaxies, stars, planets, and eventually us, come from? Thirty years ago, there wasn’t any theoretical clue, and observationally we were also in the dark, at least metaphorically. In the intervening period, a fundamental idea called inflation not only allowed a possible explanation of a flat universe, but also predicted that quantum mechanics in the early universe could have resulted in all the structures we now observe.
Then, in 1992, we discovered that nature had been unexpectedly kind to us. Against all odds, the CMB radiation turned out to be unpolluted by other astrophysical sources so that we could observe its fine structure and get direct information about the early universe. These observations have confirmed our ideas about dark matter, dark energy and the formation of structure. Additionally, the primordial hot and cold spots we see have precisely the distribution that inflationary models predicted. Have we proved inflation yet? No, but things are looking very good.
Things look good also for the belated appearance of the Higgs boson, predicted by several theorists, including British physicist Peter Higgs, in 1964. I admit I was betting against this. The idea that an otherwise invisible background field exists throughout space, whose interactions with most elementary particles moving through the field gives them their observed masses, just seemed too slippery, and too simple to be true.
But, if you slap space hard enough at one point, quantum mechanics says you should produce particles associated with the Higgs field, and that is apparently what has happened at the Large Hadron Collider at CERN. If this is confirmed, it will not only cap the greatest intellectual adventure humans have ever undertaken, but also confirm another fascinating feature of the universe: our existence is essentially an accidental by-product of the state the universe cooled into, and the key determinants of our present and future reside in what otherwise appears to be empty space.
Science fiction writers couldn’t imagine a universe more remarkable than the one we live in. What surprises await in the next 30 years? If I knew, they wouldn’t be surprises.
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Insightful and interesting piece of writing. We are still in the kindergarten when it comes to knowing our Universe fully but we are taking giant leaps too.
“Now, there is compelling evidence that cold dark matter is real; from direct measures of mass in galaxies and clusters, calculations of the abundance of light elements produced in the Big Bang, measurements of large-scale structure coming from millions of galaxies, and remarkable observations of the primordial seeds of structure observed in the cosmic microwave background (CMB) radiation from the Big Bang.”
The above is a prime example what scared the bejesus out of some people. That amount of knowledge and calculations this sentence combines really is tells people generally that they do not count, they are nothing special, and that they will never understand how other people can make such statements.
But we must not seek to dumb down our answers to them, but force them to raise up to a higher level where they can understand the ideas behind the quoted sentence.
With regards to religious belief, that can and should be ignored, if only for the fact that we have examined everything that the religious has offered as evidence and our time is limited, so we should not waste any more of it.
Is it possible to squeeze the constituents of dark matter out of the present body of theories. If the Higgs left super symmetry in the dark and all known particles are ruled out, do we need a fundamentally new way of thinking?
In my experience, students don’t have fear of science. It’s all cool stuff. But some have fear of math. Fear of math for most is due to fear of failure. If one adds three plus four, and is off by one, it’s not close – it’s wrong. The way arithmetic is often taught, the rememdy for failure is more practice. It feels like punishment. One of God’s little jokes is that any fear inhibits the higher brain functions one needs to do math. So fear of failure tends to be self-fulfilling. The cure for math anxiety should have a first step that teaches arithmetic in a way that ensures understanding and reliability. The Japanese abacus (the soroban) is among the better teaching techniques that does this. Arithmetic steps become mechanical sequences. Carries and borrows are handled immediately, and don’t need to be remembered. In long division, there’s no penalty for guessing if one always guesses low. The technique makes good use of mechanical memory and the visual brain systems. With a solid base in arithmetic, symbolic math becomes easier. Science requires the two great skills – language and math. And skepticism. In science, one assumes that guesses are wrong, and tests them with experiments.
“The Standard Model still rules OK, but the main test will come when the gamma rates are updated.”
If we could manipulate the Higgs Boson, to simulate large amounts off mass; wouldn’t gravity come right along with it?
Gravity means, artificial gravity, I’m speaking of the sci-fi variety. (Gravity plating).
That’s not really “artificial gravity”, that’s “artificial mass”. Horse of a different color.
Sure if we had unlimited energy maybe. The LHC uses 92 megawatts per hour to run according to this page:
http://science.howstuffworks.com/sci…-collider3.htm
….and according to wiki it will produce “a single higgs boson every few hours”.
http://en.wikipedia.org/wiki/Large_Hadron_Collider
You’d need the energy output of a star to manipulate gravity in any meaningful way.
More mass means more force needed to accelerate. That would make it a fairly useless technology for travel.
What if it were less mass? Then we’d have something approaching an inertialess drive. Assuming, of course, that this discovery leads to some practical way to (1) extract the mass from matter (2) without destroying it. Don’t look for that this century if ever.
So now you’re talking about not “adding” Higgs bosons to objects to create extra mass and therefore artificial gravity, but taking them away to create a craft with almost zero mass that requires only a tiny amount of force to accelerate?
The Higgs Boson is an artifact of the Higgs Field.
It is the Higgs Field that gives things mass. The Higgs Boson is merely a byproduct that tells us the Higgs Field is there (which we cannot measure directly).
Thus manufacturing Higgs Bosons gets you nothing. Hell, the LHC did not even see a Higgs Boson. They decay far too rapidly to be observed. What they see is a teeny (and I am talking factions of a fraction of a percent) variation in the stuff it decays into to deduce it was even there in the first place.
In short, we cannot make any use of the Higgs Boson directly. Even if we could hang on to one for any length of time beyond micro-fractions of a second I am not sure you could make any use of them.
Mass (of elementary fermions, i.e. matter particles) is given by the coupling of the fermion to the Higgs field, so we’d need to figure out a way of ‘tuning’ this coupling in order to produce any effect.
If you’ve got a bit of a background in physics/are willing to overlook a few equations, Frank Wilczek’s article ‘Origins of Mass’ gives a good overview.
better still, antigravity — then, we don’t need to decouple matter from mass; we need to decouple mass from gravity. Is that theoretically possible? There are hypothetical “gravitons,” and maybe identifying the Higgs boson could give us a handle on gravitons, which are presumably another type of boson. But, as I very imperfectly understand it, gravitons, if they exist, mediate gravity only at subatomic distances; gravity at any greater distance or scale is purely a matter of spacetime-curvature induced by the presence of fermion-mass-in-the-aggregate — therefore, manipulating gravitons would not allow us to, say, cancel out or reverse a planet’s gravitational field at the level necessary to launch a spaceship, or even to keep Luke Skywalker’s landspeeder hovering above the ground. Am I wrong?
Artificial gravity(as distinct from antigravity) is something we easily can make already, just by spinning the spaceship like a tilt-a-whirl.
There may or may not be gravitons, gravity may or may not actually exist, and if it does we probably can’t generate or destroy it. The problem is that our means of testing is rather limited. We know less about gravity than any of the other forces (which are probably a single force). Gravity exists – we can measure and predict it. But we don’t know why it exists at all.
Of the four fundamental forces gravity is the holdout. Quantum Mechanics is perhaps the most successful theory ever put forward by man. It has been tested repeatedly to insane levels of precision and so far it has never failed.
Never failed that is till you mix gravity into the equation then it all goes to hell in a big way. Relativity, which deals with gravity, is likewise a hugely successful theory and been proven over and over again.
But the two do not play nice together at all. The theory of the very large and the theory of the very small are anathema to each other.
Gravitational mass and inertial mass are not the same thing. In the equivalence principle states that inertial and gravitational mass are equivalent, but they’re not the same thing. One is a result of the Higg’s field and binding energy, the other comes from gravity. Dropping a block of wood on your toe hurts like hell, so does stubbing your toe on it. Same injury, same result, but differing sources of pain: gravity and inertial mass.
The Higgs Boson is what gives things mass. Mass in turn creates gravity. But the Higgs Field is not gravity.
In zero g you still have the same mass.
In a weightless environment, water still has the same amount of inertial mass. So does everything else in your body. Water (H2O) in space is just as good for you as water on earth. However, as the article cites, heavy water(HDO, D2O, TDO, THO, T2O ) is bad for you even on earth.
General relativity follows essentially from two postulates, the general principle of relativity (which says that physics does not depend on the choice of coordinates) and the equivalence principle (you can’t locally tell the difference between acceleration and the effect of a gravitational field). Both are, of course, not proven — they’re postulates, and the other forces depend on postulates of their own — but it would just be a weird universe in which it made a physical difference what numbers we use to coordinatize a manifold, for example. And the understanding of gravity that follows from these assumptions is just as complete (or incomplete) as we have for the other forces, and just as much in account with experiment.
We know there’s something that behaves very much like anti-gravity, known as dark energy. This can be, for instance, sourced by a fluid with negative pressure, and there’s no a priori reason such a thing can’t exist.
Of the four fundamental forces gravity is the holdout. Quantum Mechanics is perhaps the most successful theory ever put forward by man. It has been tested repeatedly to insane levels of precision and so far it has never failed.
Never failed that is till you mix gravity into the equation then it all goes to hell in a big way. Relativity, which deals with gravity, is likewise a hugely successful theory and been proven over and over again.
But the two do not play nice together at all. The theory of the very large and the theory of the very small are anathema to each other.
So, in a sense we do not know what to make of gravity. It is the only one of the four fundamental forces you cannot shield yourself against. It is by FAR the weakest of the forces (by orders of magnitude) yet in some cases it can overwhelm everything else (think black holes).
Relativity says gravity is essentially the curvature of space. Mass curves space and we follow that curve akin to a marble rolling across a sheet with a bowling ball in the middle. In order to “make” gravity you need mass. Want 1g of gravity on your spaceship? Then you need the mass of the earth to generate it.
Anti gravity would be reversing the curvature which would need negative matter (not antimatter…antimatter is real). We’ve never seen negative matter though and haven’t a clue how to make it and it probably isn’t even possible.
So, in short, gravity is the fly in the ointment. The Higgs Boson discovery is cool and a step forward but we have a long way to go yet.
Why be so hasty as to consider the Being of Human to be accidental? It could be argued, and argued reasonably well without any religious thought attached, that the Being of Human must be considered within a fundamental force for Being existing. What could such fundamental force for Being be?
Consider this:
– there need be a fundamental force for Being
– that all Being is subjected to such fundamental force
– that such fundamental force for Being must be self enforcing
– that such self enforcing is by Being
The problem arises when trying to come to terms with the origin of such a fundamental force. Here we take a leap in logical understanding and set forth as follows:
– everything as many is by Being some thing
– everything as one is no thing
– nothing does exist
– out of nothing arose/arises Being by division of nothing
It must be understood here that by Being I refer to all Being, including the Being of Human,the Being of Sun, the Being of Atom, the Being of Galaxy, the Being of Tree and so forth.
All Being is as incompleteness by necessity. The process of Being unfolding is by being – continuously.
Now, let’s suppose that the ‘energy of nothing’ is the state of possibility of everything as one, which would be nothing. Being is as incompleteness by necessity for if Being were to be as everything as one, it would be nothing, and Being would thereby disappear.
But Being, all Being, is by being in direction toward, thereby going forward. The toward direction would be by Being being in contact with the possibility of there being everything as one, but Being can never attain such completed Being as everything as one because Being would thereby come to a halt. In other words, Being, as incompleteness, is always moving towards or in direction of ‘the energy of nothing’, tapping out of such energy the continued Being as ‘the energy from nothing’, thereby going forward.
All Being moves towards a form of completing. And since the ‘energy of nothing’ would hold the possibility of everything, such ‘energy of nothing’ would be most primal and would be most abundant.
The fundamental force for Being would therefore have to be a force of unite/divide simultaneously. A uniting with the ‘energy of nothing’ forms the Being into a state of some thing, which is as division simultaneously. Always.
Richard Dawkins,and others, are therefore wrong in believing that the Being of Human is merely a vehicle of transport for genetic material, and furthermore within such understanding, that the reproduction aspect plays therein the driving force. However, it is the incompleteness of Being by necessity and the reproduction aspect as inevitability which makes up the fundamental force for Being, the unite/divide being simultaneous.
The ‘energy of nothing’ is the state of all possibilities out of which the incompleteness of Being taps into for Being. The ‘energy of nothing’ securing that Being can be the ‘energy from nothing’ as some thing.
Francien Verhoeven
http://www.letteredonline.com under ‘the big picture’
Why be so hasty as to consider the Being of Human to be accidental? It could be argued, and argued reasonably well without any religious thought attached, that the Being of Human must be considered within a fundamental force for Being existing. What could such fundamental force for Being be?
Consider this:
– there need be a fundamental force for Being
– that all Being is subjected to such fundamental force
– that such fundamental force for Being must be self enforcing
– that such self enforcing is by Being
The problem arises when trying to come to terms with the origin of such a fundamental force. Here we take a leap in logical understanding and set forth as follows:
– everything as many is by Being some thing
– everything as one is no thing
– nothing does exist
– out of nothing arose/arises Being by division of nothing
It must be understood here that by Being I refer to all Being, including the Being of Human,the Being of Sun, the Being of Atom, the Being of Galaxy, the Being of Tree and so forth.
All Being is as incompleteness by necessity. The process of Being unfolding is by being – continuously.
Now, let’s suppose that the ‘energy of nothing’ is the state of possibility of everything as one, which would be nothing. Being is as incompleteness by necessity for if Being were to be as everything as one, it would be nothing, and Being would thereby disappear.
But Being, all Being, is by being in direction toward, thereby going forward. The toward direction would be by Being being in contact with the possibility of there being everything as one, but Being can never attain such completed Being as everything as one because Being would thereby come to a halt. In other words, Being, as incompleteness, is always moving towards or in direction of ‘the energy of nothing’, tapping out of such energy the continued Being as ‘the energy from nothing’, thereby going forward.
All Being moves towards a form of completing. And since the ‘energy of nothing’ would hold the possibility of everything, such ‘energy of nothing’ would be most primal and would be most abundant.
The fundamental force for Being would therefore have to be a force of unite/divide simultaneously. A uniting with the ‘energy of nothing’ forms the Being into a state of some thing, which is as division simultaneously. Always.
Richard Dawkins,and others, are therefore wrong in believing that the Being of Human is merely a vehicle of transport for genetic material, and furthermore within such understanding, that the reproduction aspect plays therein the driving force. However, it is the incompleteness of Being by necessity and the reproduction aspect as inevitability which makes up the fundamental force for Being, the unite/divide being simultaneous.
The ‘energy of nothing’ is the state of all possibilities out of which the incompleteness of Being taps into for Being. The ‘energy of nothing’ securing that Being can be the ‘energy from nothing’ as some thing.
Francien Verhoeven
Theory predicts the existence of two bosons whose s differs from 1. The force carrier for gravity is the hypothetical graviton; theory suggests that it has s = 2. The Higgs mechanism predicts that elementary particles acquire nonzero rest mass by exchanging Higgs bosons with an all-pervasive Higgs field. Theory predicts that the Higgs boson has s = 0. If so, it would be the only elementary particle for which this is the case.
If there is a physical situation in which it is impossible to tell which way it happened, it always interferes; it never fails. The word “interferes” in this context is a quick way of saying that such objects fall under the rules of quantum mechanics, in which they behave more like waves that interfere than like everyday large objects.
A tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space. For example a vector space of one dimension depending on an angle could look like a Möbius strip as well as a cylinder. Raising and lowering indices: One does this by multiplying by the covariant or contravariant metric tensor and then contracting indices, meaning two indices are set equal and then summing over the repeated indices. One can raise or lower indices to change a type (a, b) tensor to a (a + 1, b − 1) tensor (raise index) or to a (a − 1, b + 1) tensor (lower index), where the notation (a, b) has been used to denote the tensor order a + b with a upper indices and b lower indices.
By this in LHC(Large Hadron Collide, European Organization for Nuclear Research (CERN), 175 metres beneath theFranco-Swiss border near Geneva, Switzerland), one can only measure the total spin because… We can never measure the spin of a particle exactly, and the best we can do is measure its total spin, and its projection along a certain axis. The spin along the other two axes remains a mystery, because as soon as we measure its spin along one axis, the other two components of spin become indeterminate- why?
Measuring the total spin of fermions and bosons is consistent, but why not with Higgs boson?. If it is 0 spin, there is no decay into other particles to measure the spin?. A component of spin can be increased or decreased with “raising” and “lowering” operators, and the change is always in natural units of 1- means, the existence of two bosons whose s differs from 1- between gravitational field and Higgs field.
All massive particles interact with a universal Higgs field in proportion to their bound energy content, and it is this interaction or “Higgs ether drag” which causes the inertial resistance to acceleration we characterize as mass.In this point The Higgs vev is the order parameter for electroweak symmetry breaking. It behave like photon’s electromagnectic field but with mass like “brothers(goldstone bosons) impregnated” W and Z bosons(weak forces).
Uniting “massless” photons(field) can create rest mass.In above case, the rest mass is given by “gold stone bosons” and ” inertial mass” is given by “Higgs boson”. Thus uniting gravitational and electroweak forces?
The interaction of a massive particle’s gravitational field with the spacetime metric is an interaction with the same spacetime metric that originally established the weak force. So “Higgs boson” intracts and interfers with the metric field of spacetime.The forced interaction between these two metric fields, one asymmetric and the other symmetric, also produces the anomalous results of relativistic motion in the spatial, temporal, and mass parameters of the moving or accelerated system- which is not in the case of masless photons or tiny neutrinos which does react with weak foeces but not like “gold stone bosons(brothers)” -Higgs boson bond.
The spacetime metric didn’t interfere with symmetry breaking of goldstone bosons, but interfers with “spontaneous symmetry breaking” of Higgs boson. So there is a flip in its quantum conservation.
At the time of big bang, all particles are moving so fast they are essentially the same as photons moving at velocity c. When space expands, further cooled energy level, there are no large, empty dimensions: instead, the metric is densely occupied with particles (quarks and leptons); photons cannot move freely under these conditions in any case. Symmetry is expressed through a “particle metric” rather than a dimensional metric. Symmetry-breaking occurs as these particles are released into the large spacetime dimensions of present space.Futher expansion will create more space but dimensions..????
Loved your latest book Lawrence – “A Universe Out of Nothing”, but something that has always makes me smile about “empty space containing something” is remembering how the earliest Greek philosophers/scientists reasoned the 4 elements and thereon the idea of the atom. Unable to measure directly what “air” contained or that “earth” was eventually indivisible at a certain point, they were able to imagine and theorize what would eventually be measured some 2000 years later. It seems to me that the “emptiness of space” is simply just an order of magnitude below our current capabilities of measurement – where that which we measure is too small to be captured by devices that are constructed of materials a magnitude larger. Thus we, like the Greek scholars, use that amazing piece of natural computing power within our heads to reason what must be true. I just wonder how long we have to wait before that next leap in magnitude is possible …
Sir, enjoyable read and well written. Any luck with resolving that Dawkins cameraman dispute re the 2009 video?
@JayGeraghty
I cam’t not believe i chose to study business communiaction rater than physics. Then again, I have heard that you have to be pretty smart
Physics is truly the superstar academic field of our time… Cannot wait for what the future brings.
Try applying this theory.
http://www.aclepd.com/universe
Thank you,
Robert Evan Howard
aclepd.com
aclepd@aclepd.com
1-801-856-3200 / U.S.A.
I don’t think the qualities required for The Higgs particle to explain the standard model is there, and I don’t think they will be found.
Neither do I think, that supersymmetry will be recognized in futuristic science.
I know I am a pain in the butt, but I believe in a complete different approach to high energy physics in the future. My vision is that future science will engulf consciousness. The mind and the spirit will be explainable through physics.
I have been a fan of Sir Roger Penrose for many years. He was the first scientist to say that consciousness should be found in the quantum field rather than in the brain. I am so much a fan, that I made my own theory out of the idea that consciousness might be explained through a better understanding of antimatter and multiverse dimensions.
My idea is that antimatter is the mirror of this universe, and that antimatter might be where memory is located.
I think that the subconscious mind and consciousness are located in multiverse dimensions in the form of antimatter.
The original standard model predicted no mass at all. That made no sence to scientists, so Peter Higgs predicted The Higgs Boson, purely from mathematics. I think the original standard model was right, particles does not exist. The physical universe is a flow of energy from minus infinite energy to plus infinite energy.
If you would like to know more, then you can watch a full videopresentation of my theory on my blog:
http://www.crestroy.com
Dark matter and dark energy remain mysterious. One thing for sure, physics has become an extraordinary expensive discipline stuffed with new wild conjectures beyond imagination. What next? (btt1943)
I hope Dr. Krauss will discover what dark energy is.
It looks like an intrinsic characteristic of the space-time fabric.
I’m a fan, Dr, Krauss (if “fan” is the right word); I find your work fascinating. That said, I tried to read this article and got so distracted with the misuse of semicolons that I couldn’t finish. But that isn’t going to stop me from tuning in; I follow you on Twitter, have heard some of your radio interviews, and have read parts of A UNIVERSE FROM NOTHING. Please keep up the outstanding work you do. And, by all means, share it with the rest of us.
P.S. On a different note–and one just for some levity, really–I would have thought the math question I had to answer to prove I was a human and not an automated spammer in order to leave this comment would have been a differential equation of some kind.
Got my just deserts. Alas, the comma is right next to the period. Without proofreaders we’re all at risk.
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