"My own suspicion is that the universe is not only queerer than we suppose, but queerer than we *can* suppose." -J.B.S. Haldane

What is physics?  For some, it's a college course with a figurative inverted pentagram hovering over it; a place of headaches and scary concepts better reserved for the gifted and "special" among us.  Other, more traditional types, may see physics as a more literal representation of the inverted pentagram; in their eyes a discipline reserved for God alone to know, not for us mortals better served living out our years in fear of God and God's infinite wisdom.  For them, passionate belief alone ought to do.  In contrast, a physicist might look at an inverted pentagram with an interest in learning the shape, it's sides, and it's angles.  They might ask: Where else do we see this shape?  Do we see it in the platonic solids, the fundamental shapes in the universe?  How does the physical world relate and interact with shapes like these?  Is there a way to describe it with math?  Physics is about ratios, patterns, and abstractions.
 
If evolution has brought us anything, it's our ability to abstract.  Abstraction is a phenomenon of imagination.  Every time we plan for the future or review past events we are abstracting time.  In doing s0 we garner value in the form of increased adaptability.  We abstract not only our past and future, but objects all around us too.  Language is a tool that allows us to abstract an object into a sound.  A "chair" is an object that we sit on.  When we say or think of chair, we imagine the concept of "chair" which encompasses every other "object for sitting".  We went from one object in front of us, to every chair imaginable, with a single word, or a single thought.  
 
Physics takes this ability further and pushes our ability to abstract to its very limits.  For example:  V = IR.  This is the fundamental electrical circuit ratio equation.  Now we are abstracting a dynamic system.  This is an equation that states, Voltage (V) is equal to Current (I) multiplied by Resistance (R).  In other words, the voltage of an electrical system is proportional to the current flow multiplied by the resistance of the circuit.  As an analogy, imagine a closed loop hose with a pump attached and a single nozzle that's closed, also attached.  The voltage is the pressure inside the hose, the current is the flow rate of the air once the nozzle is opened, and the resistance is the bottleneck created at the nozzle opening that only let's out so much air per-unit-time.   
 
The ratio described above has analogous relationships in every engineering discipline.  With a fluid system we have pressure, flow, and resistance; with a translational mechanical system we have velocity, force, and damping; with a rotational mechanical system we have rotational velocity, torque, and damping; and with a thermal system we have temperature, heat flow, and resistance, (there are others too).  All of these trinary groups are analogous to one another.  The difference is the form of energy and the materials used. 
 
The equations we use today to design systems, first abstracted from real world phenomena, have done nothing short of transform our world.  Technology, increased standards of living, and the overall mitigation of suffering are owed in significant part to the application of these, and other physics equations.  Abstraction is a wonderful faculty we humans possess, (some more than others of course).

Our minds are unique.  Some of us can grasp these concepts with relative ease, whereas others are more effective in different areas of knowledge.  However, even the relatively math literate of us reach an upper bound of physics understanding - as with any field.  The extreme fringes of any highly abstract discipline are always ripe with the rarest and brightest, and often the most eccentric.  Stephen Hawking's A Brief History of Time is an attempt by one of the rarest and brightest to reign in some of the most challenging physics concepts into near Earth orbit, and present them to the non-math literate general public.  This is both the bane and the triumph of the book.

On the one hand, some of the book concepts are rather mind-warping.  I wonder how many pages or books the equations would take up, if shown.  Would it really add any benefit for the common reader to see a series of integrals, partial derivatives, or vector equations?  I haven't looked much into some of the more complex physics equations, but no do doubt they include a learning curve. 
 
On the other hand, I would have liked to see some math equations partnered with a summary breakdown of the symbols and meanings of key variables.  A cursory presentation of some equations opens up the more elaborate ideas to broader understanding.  Most readers, I'm sure, have been introduced to math on some level, even if basic arithmetic.  An introduction to basic algebra, and may even a little calculus and statistics, and how they work with some of the concepts, not only give readers a deeper understanding of physics, but also the opportunity for those afraid of math and physics the chance to be inspired, and dive deeper.  You never know when the next Niels Bohr, Richard Feyman, or Grigori Perelman will come alone.  Sometimes all they need for inspiration is a new idea revealed in a particular way.  Why leave out the math basics? 

Hawking ultimately went with only one equation in the book, Einstein's theory of relativity:  E = MC^2.  In scoping the book, he debated what equations to show, and on the suggestion of "someone" that each equation in the book would halve the sales, he chose to avoid them almost completely.  I don't think I agree with this.  I think more math would have added value.  
 
Nonetheless, plenty of brain candy is offered up throughout.  How about this one:  "A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but neither does space have any boundary.  Gravity is so strong that space is bent round onto itself, making it rather like the surface of the earth...We shall see later that when one combines general relativity with the uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without any edges or boundaries."  In other words, no matter how far you go in any direction, you'll never reach the end of the universe.  We are forever trapped in a bubble.  At least we have a little room to roam around. 

Similarly, there is an absolute limit to measurement.  In Heisenberg uncertainty, to measure something very small, "...one cannot use an arbitrary small amount of light; one has to use at least one quantum.  This quantum will disturb the particle and change its velocity in a way that cannot be predicted.  Moreover, the more accurately one measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single quantum.  So the velocity of the particle will be disturbed by a larger amount.  In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa.  Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particles can never be smaller than a certain quantity, which is known as Planck's constant."  Particles at smaller and smaller quantum levels become more and more fuzzy and unpredictable until we reach a limit to understanding.
 
So, we have the possibility of never leaving the universe and knowing what's beyond, and Planck's constant and the limits of measurement.  Can Hawking at least clear up the strange nature of black holes for us?  He describes the phenomenon from the view of an astronaut, "Suppose an intrepid astronaut on the surface of the collapsing star, collapsing inward with it, sent a signal every second, according to his watch, to his spaceship orbiting about the star.  At some time on his watch, say 11:00, the star would shrink below the critical radius at which the gravitational field becomes so strong nothing can escape, and his signals would no longer reach the spaceship.  As 11:00 approached, his companions watching from the spaceship would find the intervals between successive signals from the astronaut getting longer and longer, but this effect would be very small before 10:59:59.  They would have to wait only very slightly more than a second between the astronaut's 10:59:58 signal and the one that he sent when his watch read 10:59:59, but they would have to wait forever for the 11:00 signal.  The light waves emitted from the surface of the star between 10:59:59 and 11:00, by the astronaut's watch, would be spread out over an infinite period of time, as seen from the spaceship."  Another way to understand, that helps me visualize this concept, is to imagine viewing an astronaut moving toward a black hole.  As they reach the event horizon, you would see the astronaut pause, then remain on the edge of the horizon, for infinity.  From the astronauts point of view, they would see all points of light (stars) moving away, slow at first, and then faster and faster until they collapse into nothing.
 
Upon completion of Hawking's historic work, is my understanding of astrophysics any clearer?  Maybe a little, but if anything, I appreciate it more.  There is still so much we don't know about the dynamics and intricacies of our cosmos.  CERN, gravity-wave observatories, and the James Webb telescope (launching in 2021) are a few of the tools that will continue to open the curtains on some of the universe's great mysteries. 
 
Our species is, in part, one of exploration and discovery.  With every rock turned over, great reward awaits, along with some risk.  Beyond the geopolitical turmoil beset on every country on some level, with the internet, new technologies, and the world's greatest minds - and their uncanny ability to abstract  - the future of physics right now is in a better place than it's every been.  The countries of the world can only benefit from the technology to come, after further inquiry into the unknown. 
 
R.I.P. Dr. Hawking, and thanks for bringing modern physics to the masses.
 



Summary:  A mind-twisting introduction to the bizarre world of astrophysics.  Some equations would have complemented the descriptions.   
 
Rating:  7.0

-E.B.
 2018-07-17