This Week's Finds in Mathematical Physics (Week 32)
John Baez
John Baez
Well, I visited Georgia Tech last week to spread the gospel of "knots
and quantum gravity," and came across a most fascinating development.
I'm sure readers of sci.math and sci.math.research have taken note of
the New York Journal of Mathematics. This is one of the first refereed
electronic journals of mathematics. Neil Calkin at Georgia Tech is
helping to start up another one --- the Electronic Journal of
Combinatorics. Though it's unlikely, perhaps some among you are still
unaware (or unconvinced) of how essential it is that we develop fully
refereed free-of-charge electronic journals of mathematics and physics.
The first and most obvious reason is that computer-based media offer all
sorts of flexibility that print media lack --- more on this later. But
the other reason is that the monopoly of print journals *must* be
broken.
For example, U. C. Riverside does not subscribe to Communications in
Mathematical Physics, despite the fact that this is *the* crucial
journal in that subject, because this journal costs $3,505 a year! The
ridiculous price is, of course, in part precisely because this is the
crucial journal in that subject, in part because the journal uses
antiquated and expensive production methods involving paper, and in part
because, being a big operation, it is basically run by a publishing
house rather than mathematical physicists. Luckily, with the advent of
the preprint mailing lists hep-th and gr-qc, I don't *need* to read
Communications in Mathematical Physics very often! I simply get my list
of abstract each day by email from Los Alamos, and send email to get the
papers I want, in LaTeX or TeX form. The middleman has been cut out ---
at least for the moment.
One problem with preprint mailing lists, though, is that the preprints
have not gone through the scutiny of the referee process. This is,
frankly, much less of a problem for the *readers* than is commonly
imagined, because this scrutiny is less intense than people who have
never refereed papers think! Many refereed papers have errors, and I
would personally feel very uncomfortable using a result unless I either
understood the proof or knew that most experts believed it. The real
need for refereed journals, in my slightly cynical opinion, is that
academics need *refereed publications* to advance in their jobs: the
people who give tenure, promotions etc. cannot be expected to read and
understand ones papers. This is, of course, also the reason for other
strange phenomena, such as the idea of *counting* somebody's
publications to see how good they are. We need only count Alexander
Abian's publications to see the limitations of this approach.
Eventually, a few birds may be killed with one stone by means of "seals
of approval" or SOAPs, which are being widely discussed by people
interested in the "information superhighway," or --- let's call a spade
a spade --- the Internet. For more on these, check out the newsgroup
comp.interpedia, or read material about the Xanadu project. The idea
here is that eventually we will have a good system whereby people can
append comments to documents, such as "there is an error in the proof of
Lemma 1.5, which can be fixed as follows..." or simply various seals of
approval, functioning similarly to the seal of approval ones paper
obtains by being published in a journal. E.g., one could make ones
paper available by ftp or some other protocol, and "submitting it to a
journal" might amount to asking for a particular SOAP, with various
SOAPs carrying various amounts of prestige, and so on.
Of course, journals also function as a kind of information "hub" or
central access point. We all know that to find out what's the latest
trend in particle physics, it suffices to glance at Nuc. Phys. B and
certain other journals, and so on. It is not clear that the function of
"hub" and the function of SOAP need be combined into a single
institution, once the onerous task of transcribing ideas onto dead
trees and shipping them all around the world becomes (at least partially)
obsolete.
It is also not at all certain whether, in the long run, the monopolistic
power of journals to charge large fees for accessing information will be
broken by the new revolutions in technology. This is, of course, just
one small facet of the political/economic struggle for control over
information flow that is heating up these days, at least in the U.S.,
among telephone companies, cable TV stations, computer networks such as
Compuserve, etc. etc.. If mathematicians and physicists don't think
about these issues, someone else who has will wind up defining the
future for us.
Anyway, for now it seems to make good sense to start refereed journals
of mathematics and physics that are accessible electronically, free of
charge, over the Internet. Not too long ago one would commonly hear the
remark "...but of course nobody would ever want to do that, because..."
followed by some reason or other, reminscient of how CLEARLY nobody
would want to switch from horses to automobiles because then one would
have to build GAS STATIONS ALL OVER THE PLACE --- obviously too much
bother to be worthwhile. Now, however, things are changing and the new
electronic journals are getting quite respectable lists of editors, and
they seem to have a good chance of doing well. I urge everyone to
support free-of-charge electronic journals by submitting good papers!
Let me briefly describe the electronic journals I mentioned above. The
New York Journal's chief editor is Mark Steinberger, at SUNY Albany,
ma...@sarah.albany.edu. The journal covers algebra, modern analysis, and
geometry/topology. Access is through anonymous ftp, gopher and
listserv, the latter being (I believe) a mailing list protocol. One can
subscribe by sending email to list...@albany.edu or
list...@albany.bitnet; if you want abstracts for all the papers, the
body of your email should read
subscribe NYJMTH-A <your full name>
but you can also subscribe to only certain topics (one of the great
things about electronic journals --- one can only begin to imagine the
possibilities inherent in this concept!), as follows:
Algebra:
subscribe NYJM-ALG <your full name>
Analysis:
subscribe NYJM-AN <your full name>
Geometry/Topology:
subscribe NYJM-TOP <your full name>
Papers are accepted in amstex and amslatex, and when you get papers you
get a .dvi file.
The Electronic Journal of Combinatorics is taking a somewhat more
ambitious approach that has me very excited. Namely, they are using
Mosaic, a hypertext interface to the WWW (World-Wide Web). This means,
to technical illiterates such as myself, that if you can ever get your
system manager to get the software running, you can see a "front page"
of the journal, with the names of the articles and other things
underlined (or in color if you're lucky). To go to any underlined item,
you simply click your mouse on it. In fact, you can use this method to
navigate throughout the whole WWW, which is a vast, sprawling network of
linked files, including --- so I hear --- "This Week's Finds"! In the
Electronic Journal of Combinatorics, when you click on an article you
will see it in postscript form, pretty equations and all. You can also
get yourself a copy and print it out. Neil showed me all this stuff and
my mouth watered! The danger of this ambitious approach is of course
that folks who haven't kept up with things like the WWW may find it
intimidating... for a while. It's actually not too complicated.
This journal will be widely announced pretty soon. The editor in chief
is Herbert S. Wilf, wi...@central.cis.upenn.edu, and the managing editor
is Neil Calkin, cal...@math.gatech.edu. It boasts an impressive slate
of editors (even to me, who knows little about combinatorics), including
Graham, Knuth, Rota and Sloane. To get browse the journal, which is
presently under construction, you just do the following if you can use
Mosaic: "Click on the button marked 'Open' and then type in
http://math34.gatech.edu:8080/Journal/journalhome.html." To *get*
Mosaic, do anonymous ftp to ftp.ncsa.uiuc.edu and cd to
Web/Mosaic_binaries --- and then you're on your own, I just tried it and
there were too many people on! --- but Neil says it's not too hard to
get going. I will try as soon as I have a free day.
"Ahem!" the reader comments. "What does this have to do with
mathematical physics?" Well, seeing how little I'm being paid, I see
nothing wrong with interpreting my mandate rather broadly, but I should
add the following. 1) There are periodic posts on sci.physics about physics
on the WWW; there's a lot out there, and to get started one always try
the following. The information below is taken from Scott Chase's
physics FAQ:
---------------------------------------------------------------------------
* How to get to the Web
If you have no clue what WWW is, you can go over the Internet with
telnet to info.cern.ch (no login required) which brings you to the WWW
Home Page at CERN. You are now using the simple line mode browser. To move
around the Web, enter the number given after an item.
* Browsing the Web
If you have a WWW browser up and running, you can move around
more easily. The by far nicest way of "browsing" through WWW uses the
X-Terminal based tool "XMosaic". Binaries for many platforms (ready for
use) and sources are available via anonymous FTP from ftp.ncsa.uiuc.edu
in directory Web/xmosaic. The general FTP repository for browser
software is info.cern.ch (including a hypertext browser/editor for
NeXTStep 3.0)
* For Further Information
For questions related to WWW, try consulting the WWW-FAQ: Its most
recent version is available via anonymous FTP on rtfm.mit.edu in
/pub/usenet/news.answers/www-faq , or on WWW at
http://www.vuw.ac.nz:80/overseas/www-faq.html
The official contact (in fact the midwife of the World Wide Web)
is Tim Berners-Lee, ti...@info.cern.ch. For general matters on WWW, try
www-r...@info.cern.ch or Robert Cailliau (responsible for the "physics"
content of the Web, cail...@cernnext.cern.ch).
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And: 2) there are rumors, which I had better not elaborate on yet, about
an impending electronic journal of mathematical physics! I eagerly
await it!
Okay, just a bit about actual mathematical physics per se this time.
1) On quantum mechanics, by Carlo Rovelli, uuencoded PostScript file, 42
pages available as hep-th/9403015.
This interesting paper suggests that reason why we are constantly
arguing about the meaning of quantum mechanics, despite the fact that it
works perfectly well and is obviously correct, is that we are making a
crucial conceptual error. Rovelli very nicely compares the problem to
special relativity before Einstein did his thing: we had Lorentz
transformations, but they seemed very odd and paradoxical, because the
key notion that the space/time split was only defined *relative to a frame*
(or "observer" if we wish to anthropomorphize) was lacking. Rovelli
proposes that in quantum mechanics the problem is that we are lacking
the notion that the *state* of a system is only defined relative to an
observer. (The "Wigner's friend" puzzle is perhaps the most obvious
illustration here.) What, though, is an observer? Any subsystem of a
quantum system, says Rovelli; there is no fundamental "observer-observed
distinction." This fits in nicely with some recent work by Crane and
myself on quantum gravity, so I like it quite a bit, though it is
clearly not the last word on this issue (nor does Rovelli claim it to
be).
2) Adjointness relations as a criterion for choosing an inner product,
by Alan Rendall, gr-qc/9403001.
The inner product problem in quantum gravity is an instance of a
general, very interesting mathematics problem, namely, of determining an
inner product on a representation of a star-algebra, by demanding that
the representation be a star-representation. Rendall has proved some
very nice results on this issue.
3) Gromov-Witten classes, quantum cohomology, and enumerative geometry,
by M. Kontsevich, Yu. Manin, hep-th/9402147.
I will probably never understand this paper so I might as well mention
it right away. Kontsevich's work on knot theory, and Manin's work on
quantum groups and (earlier) instantons is extremely impressive, so I
guess they can be forgiven for their interest in algebraic geometry.
(A joke.) Let me simply quote:
"The paper is devoted to the mathematical aspects of topological
quantum field theory and its applications to enumerative problems
of algebraic geometry. In particular, it contains an axiomatic
treatment of Gromov-Witten classes, and a discussion of their
properties for Fano varieties. Cohomological Field Theories
are defined, and it is proved that tree level theories
are determined by their correlation functions. Applications
to counting rational curves on del Pezzo surfaces and projective
spaces are given."
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Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics (as well as some of my research papers) can be
obtained by anonymous ftp from ucrmath.ucr.edu; they are in the
directory "baez." The README file lists the contents of all the papers.
Please do not ask me how to use hep-th or gr-qc; instead, read the file
preprint.info.
Archimedes Plutonium
I never liked the Kirchhoff laws when doing them in college physics. My impression was-- who needs them, but now they come in critical importance. They fill out some of the True Physics. I am guessing no-one asked the question in Old Physics, which of the Maxwell Equations is Kirchhoff laws? Pretty sure no-one asked that question. Even Halliday and Resnick have it on page 677 before they begin to discuss the Maxwell Equations with Ampere's law on page 714. Old Physics treated the Kirchhoff's laws as some sort of periphery item, an item particular to circuits but not Maxwell theory, an item before Maxwell's Equation but not actually within Maxwell's Equation.
AP suspects though that the Kirchoff's laws, not sure yet, but only a hunch, that the Kirchhoff's laws once well understood demand that Ohm's law of Old Physics as V = CR, that it is truly V = CBE where R, Resistance = Magnetic Field x Electric Field. It is my hunch but not yet proven that the bizarre case of adding more resistors actually decreases the overall resistance of a parallel circuit is explained by V= CBE. Such totally counterintuitive result should be easily explained with a V = CBE but not with a V= CR. That is, because of R=BE we have another factor than simply R alone.
And in my textbook I dismiss the total Maxwell Equations as either in full error such as Gauss's law of no magnetic monopoles, when monopoles are the foundation of EM theory. Or the other laws in Maxwell Equations for they are missing many rules and laws, such as Lenz's law such as Kirchoff's laws.
The trouble with Maxwell Equations, is they are not built from a sound foundation but rather Maxwell built them from "modeling experiments". When you build Physics from modeling, you capture some features of Nature, but bound to miss many. The firm sound foundation I speak of is to take New Ohm's Law Voltage = Coulomb x Magnetic Field x Electric Field take that as primal equation V= CBE and then differentiate all the permutations of V= CBE to gain all the laws of EM theory. James Clerk Maxwell should have looked to Mathematics for a foundation of EM Equations, especially to the idea that Volume in geometry encompasses all within its domain. So transfering that idea of Volume in Geometry is a completeness, then Voltage must be a volume type of formula such as V= CBE.
There are 6 laws to complete EM theory, and not what Maxwell theorized to become just his 4 equations, but 6 equations.
Those 6 can be written as this.
1) Magnetic Monopole has units: Magnetic Field B = kg/ A*s^2 = kg/ C*s
Electric Field is E = kg*m^2/ A*s^2 = kg*m^2/ C*s
2) New Ohm's law V=CBE
3) C' = (V/(BE))' = V'BE/(BE)^2 - VB'E/(BE)^2 - VBE'/(BE)^2 which is Faraday's law.
1st term as current production -- 2nd term as Lenz law -- 3rd term as DC, AC direction
4) B' = (V/(CE))' = V'CE/(CE)^2 - VC'E/(CE)^2 - VCE')/(CE)^2 which is Ampere-Maxwell law.
1st term as B production -- 2nd term as Displacement current -- 3rd term as parallel attract
5) E' = (V/(CB))' = V'CB/(CB)^2 - VC'B/(CB)^2 - VCB'/(CB)^2 which is Coulomb-gravity law.
1st term as E production -- 2nd term as inverse square of distance -- 3rd term as synchronicity
6) V' = (CBE)' = C'BE + CB'E + CBE' which is electric generator law
1st term as V production -- 2nd term as DC generator -- 3rd term as AC generator
Now Kirchhoff's laws one involves the Series circuit and the other involves the Parallel circuit where Voltage is constant but the resistance and current varies. So what I am looking for is one of the three terms in either V', E', B', C' looking for a term such as V/C'B or V/C'E to find Kirchoff's law for Parallel circuit. For Series circuit we have the current is constant, the Coulomb is constant and that means the V and R varies, and in AP equations R= BE. So I am looking for a term in V', E', B', C' that is this Kirchoff's law for Series in a term such as V'/CB' or V'/CE' to find Kirchhoff's law for Series circuit.
TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
by Archimedes Plutonium
Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. Good luck.
Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.
The world needs a new standard in physics education since Feynman set the standard in 1960s with his "Lectures on Physics" that lasted until about 1990 and then AP's Atom Totality theory caused Feynman's Lectures to be completely outdated. And so much has changed in physics since 1960s that AP now sets the new world standard in physics education with this series of textbooks.
To be a Master of physics or Calculus or Mathematics, has to be seen in "signs and signals". Can you correct the mistakes and errors of Old Physics, of Old Calculus, of Old Math? If you cannot clean up the fakery of Old Physics, of Old Calculus, of Old Math, you have no business, no reason to write a physics, calculus or math textbook. There is an old legend in England about King Arthur, and the legend goes, that the King is the one who pulls Excalibur out of the iron anvil. Pulling the sword out of the anvil is a metaphor for Cleaning up all the mistakes and errors of Old Physics, of Old Calculus, of Old Math.
Should you write a textbook on Calculus, if you cannot see that the slant cut in a cone is a oval, never the ellipse? Of course not. Should you write a Calculus textbook if you cannot do a geometry proof of Fundamental Theorem of Calculus? Of course not. Should you write a physics textbook if you cannot ask the question, which is the atom's real true electron, is it the muon or the 0.5MeV particle that AP says is the Dirac magnetic monopole.
Feynman wrote the last textbook in 1960s to guide physics forward, and although Feynman did not clean up much of Old Physics, he did direct the way forward in that Electricity and Magnetism in his Quantum Electrodynamics was the way forward. It would have been nice for Feynman to have found that it is impossible for a 0.5MeV particle to be the atom's electron moving near the speed of light outside the proton of hydrogen and still remain an atom, thus all atoms collapse. It would have been nice for Feynman to say the muon is the real atom's electron and that the 0.5MeV particle was Dirac's magnetic monopole. But it just was not in the fated cards of Feynman's physics. Yet, his textbook served the leadership of physics from 1960 to 1990. Time we have the new replacement of physics textbook.
Now, in 2021, we need a new textbook that carries all of physics forward into the future for the next 100 years, and that is what this textbook is.
I will use Halliday and Resnick textbook as template to garner work exercise problems for 1st year and 2nd year college. For 3rd and senior year college physics I will directly use Feynman's Lectures and QED, quantum electrodynamics. Correcting Feynman and setting the stage that all of physics is-- All is Atom and Atoms are nothing but Electricity and Magnetism.
Much and most of 20th century physics was error filled and illogical physics, dead end , stupid paths such as General Relativity, Big Bang, Black holes, gravity waves, etc etc. Dead end stupidity is much of Old Physics of the 20th century. What distinguishes Feynman, is he kept his head above the water by concentrating almost exclusively on Electrodynamics. He remarked words to the effect== "QED is the most precise, most accurate theory in all of physics". And, that is true, given All is Atom, and Atoms are nothing but Electricity and Magnetism.
This textbook is going to set the world standard on college physics education. Because I have reduced the burden of mathematics, reduced it to be almost what I call -- difficult-free-math. I mean, easy-math. Meaning that all functions and equations of math and physics are just polynomials. All functions of math and physics are polynomials. Making calculus super super easy because all you ever do is plug in the Power rules for derivative and integral, so that physics math is able to be taught in High School. In other words, physics with almost no math at all-- so to speak, or what can be called as easy as learning add, subtract, multiply, divide.
What makes both math and physics extremely hard to learn and understand is when mathematics never cleans itself up, and never tries to make itself easy. If all of math can be made as easy as add, subtract, multiply, divide, no one would really complain about math or physics. But because math is overrun by kooks (definition of kook: is a person who cares more about fame and fortune than about truth in science), that math has become a incomprehensible trash pile and the worst of all the sciences, and because the math is so difficult, it carried over into physics, making physics difficult.
You see, one of the greatest omissions of science in the 20th and 21st century was the idea that math can be reduced to a Simplicity of education. That math need not be hard and difficult. Yet no-one in the 20th and 21st century ever had that idea of simplicity, (with the possible exception of Harold Jacobs) that math had run out-of-bounds as a science and was more of a science fiction subject for kook mathematicians. Had become absurdly difficult because of the reason that kooks gain fame and fortune on making math difficult. Mathematicians never thought their job was to make math simple and easy, instead, the kooks of math piled on more trash and garbage to make math a twilight zone of science.
When you make all of math be just polynomial equations and functions, you make math the easiest of the major sciences, which then follows up by making physics easy as possible.
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Table of Contents
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Part I, Introduction, and about physics.
a) About this textbook and series of Physics textbooks.
b) Brief history lesson of 20th century physics.
c) How we make the mathematics super easy.
d) Horrible concept of "charge" in Old Physics, and thrown out of New Physics.
e) How I have to use Biology DNA knowledge to unravel the physics light wave.
Part II, 6 Laws of EM theory.
f) The 6 laws of ElectroMagnetic theory and their Units, EM theory.
g) The four differential equations laws of EM theory.
h) Defining the units of Coulomb and Ampere as C = A*seconds; and the Elementary-Coulomb.
i) Faraday Constant Experiment in classroom.
j) Matching the physics Algebra of units with the physics Geometry of units.
k) The EM Spectrum, Electromagnetic Spectrum.
Part III, 1st Law of EM theory.
l) 1st Law of EM theory; law of Magnetic Monopole and units are B = kg/ C*s = kg/ A*s^2.
m) Series versus parallel connection of closed loop.
Part IV, 2nd Law of EM theory.
n) 2nd Law of EM theory; New Ohm's Law V = CBE, the Capacitor-battery law.
o) Review of Geometry volume in 3D and path in 2D.
Part V, 3rd Law of EM theory.
p) 3rd law of EM theory, Faraday's law, C' = (V/(BE))'.
q) Short history lesson of Old Physics, 1860s Maxwell Equations.
r) New Rutherford-Geiger-Marsden Experiment observing Faraday Law.
s) Math Algebra for making one physical concept be perpendicular to another physical concept.
t) EM laws derive the Fundamental Theorem of Calculus.
u) Principle of Maximum Electricity and Torus geometry so essential in Atomic Physics.
Part VI
v) 4th law of EM theory; Ampere-Maxwell law B' = (V/(CE))'.
Part VII
w) 5th law of EM theory; Coulomb-gravity law; E' = (V/(CB))'.
x) Centripetal versus Centrifugal force explained.
Part VIII
y) 6th Law of EM theory, electric generator law; differential equation of New Ohm's Law V' = (CBE)'.
z) Reinventing the Multivariable Calculus.
aa) Short Circuit.
bb) Atomic bomb physics.
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Text
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Part I, Introduction, and about physics.
AP, King of Science, especially Physics
Archimedes Plutonium
Alright I am looking for the terms in AP-EM Equations (replacement of the error filled Maxwell Equations), I am looking for the terms that are the two Kirchhoff's laws. And the best way to proceed is a numbers problem. Yet, usually AP finds geometry sample problems to help understand but in this case of Kirchhoff's law and series or parallel circuits, AP finds, it strange that a numbers algebra problem sample would be best to employ.
Parallel Circuit Sample Problem:
Voltage is 120 V
Resistors 3 of them: 10 ohms, 20 ohms, 30 ohms
What is the current in each resistor?
120/10 = 12 A
120/20 = 6 A
120/30 = 4 A
The total current would be 12+6+4 = 22 A
What is the overall Resistance in Old Physics of this parallel circuit?
R= V/i = 120/22 = 5.45 ohms and considerably smaller than any of the three resistors.
So AP has to make clear what is going on here in this counterintuitive physics.
I am going to have to get a Series circuit problem sample to compare with parallel circuit.
Looking for the terms in AP-EM Equations where the two Kirchhoff laws lie. For parallel circuit it would be a constant V with varying C, B, or E. In Series circuit it would be a constant C with varying V, B, E.
V'BE/(BE)^2 - VB'E/(BE)^2 - VBE'/(BE)^2
V'CE/(CE)^2 - VC'E/(CE)^2 - VCE')/(CE)^2
V'CB/(CB)^2 - VC'B/(CB)^2 - VCB'/(CB)^2
C'BE + CB'E + CBE'
What I called synchronicity and the push versus pull in the Coulomb-gravity law above, looks to me that the force of gravity has to be a connection of the Planets to the Sun as a Parallel Circuit board of astronomy. This is probably the first time any scientist ever compared the Sun and its planets to an electric circuit board, but ladies and gentlemen, that is what gravity really is-- a form of EM.
Archimedes Plutonium
Alright, earlier today I gave a example of Parallel Circuit using Kirchhoff law, now I need the contrast with Series Circuit.
Battery of 12 Volts
Three resistors R_1 = 1 ohm , R_2 = 2 ohm , R_3 = 3 ohm of bulbs
Current in circuit is V/R_summed = 12/6 = 2 A
Current is a constant while voltage and resistance vary. In Parallel circuit the Voltage is constant while current and resistance vary.
Voltage drop across R_1 is V_1 = iR_1 , and so 2 A x 1ohms = 2 V
Voltage drop across R_2 is V_2 = iR_2 , and so 2A x 2ohms= 4 V
Voltage drop across R_3 is V_3 = iR_3 , and so 2A x 3ohms= 6 V
In a series connection you have a Voltage drop across the circuit, whereas in parallel the voltage is a constant.
From H&R, page 677
Kirchhoff's 1st law (Junction Rule) : The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction. (Conservation of electric monopoles)
Kirchhoff's 2nd law (Loop Rule) : The algebraic sum of the changes in potential encountered in a complete traversal of any closed circuit must be zero. (Conservation of energy)
So why did not the Kirchhoff laws appear in Maxwell Equations? Why are they periphery to the Maxwell Equations in Old Physics? The answer lies in the fact that Old Physics had no magnetic monopole and had their Maxwell Equations based upon modeling, rather than based on the calculus permutations of V= CBE.