Phenomenon description may require deep mathematics as it
often does – deep theory of partial differentiation, tensor calculus and
quantum notation is required to understand deep physics and cutting edge
chemistry. It is deeper than me. Same time, I am not so stupid that events have
to be reduced to philosophy or law for me to understand them! Can I make a
scientific (observer independent, empirical) description of my level of
understanding? Pragmatically, I am looking to a level of good intermediate, not
an expert in any field, not scared of algebraic mathematics, but certainly far
more competent than most doctors, lawyers and business types.
A perfect example came by me, recently. It is discussed next.
Not only will you learn about what I want, but the fascinating subject matter –
dark matter to be precise.
Most scientists and astronomers believe that normal visible
matter is 5% of the universe, reachable and explainable by telescopes. Rest 95%
is dark matter and dark energy – responsible for galaxy formation and accelerated
universe inflation. When you try to understand why scientists so believe, one
goes into deep astronomy and galactic measurements. Two big reasons are
1.
Star rotation towards the end of galaxies (away
from center) is too fast (compared to newton law of inverse square. Dark matter
explain simply is that there is lot of it more rotating matter not visible to
us, hence the too fast rotations are simply wrong calculations from low mass
estimates! Black matter is uniform, too small to effect speeds of inner stars,
but substantial further away, hence hi speeds.
2.
Distant galaxies show up in multiple images, as
if there was intervening matter between, bending light and producing Einstein effect
of curvature of space and light lensing
It works and 99% of scientists and astronomers agree. Few do not, biggest
theoretician who does not is verlinde. This guy has an entropic gravity theory
derived from string theory. Simplest explanation, good for politicians,
lawyers, doctors etc (henceforth intellectuals) is that he considers gravity as
emergent from entanglement and entropy (hence information)! One of the
consequences is that for low mass, newton inverse square law results, while at
high masses, the variation is linear. Precisely the MOND empirical theory which
fit the data very well (measured rotation speeds of stars) but NO one could
explain why so in MOND!
Intellectuals are satisfied with this detail. Most vaguely understand inverse
square and linearly inverse law. But I am an engineer. Not so dumb, but not
capable of understanding the paper! Now what? Hence this essay. An intermediate
engineering understanding level call for, will have significant legal and
author implications. Details understood by good intermediate will not have to
be written. Explainers will typically address intellectuals and engineers, automatic
violence to junk from uncouth priests, politicians, intellectuals and stupid authors.
Where are the missing details? Why can’t they be approximated? All pseudos in
fact!
A somewhat deeper understanding comes as follows, good for all here.
Remember Kreyzig? The attractor at galactic center is a point. One can draw spherical
surfaces at various distances to measure the gravity effects there. Area varies
as r^2. Hence the intensity felt varies as inverse of that i.e. as Inverse
Square. But string theory has the holographic principle that says the effect is
as if the entire mass, far enough away, is concentrated on the surface! So far
enough away, effect is only linear! Joining the two gives Inverse Square near
center to inverse only towards circumference!
Verlinde is not that hard to model for better understanding. Another
great understanding to me came from understanding the idea of German shower that
sparked NASA interest in fix Hubble mission that changed human view f the
Cosmos and great pictures. Most of difficult sounding encryption can be
effectively so described. Here is an attempt.
Encryption is about trapdoor impossible one way functions. Trapdoor means
a small secret which allows simple calculation of inverse to a trapdoor-impossible
function. Most classic trapdoors use multiplication or exponentiation as the one
way, and if all computations are carried out in a semi-prime field, the factors
of the public modulus render the system trapdoor. The nicest thing about modulo
computations is that they follow normal rule, even as some computations are
exponentially more complex! A square root or logarithm is fairly easy in
ordinary math but trapdoor-impossible in discrete math!
So deep sir math say that certain operations are hard, why so is not the
trouble of engineers. ALL my methods are based on user-verifiable algebra or
statements to the effect ask any deep math sir!
No hard proofs are employed which makes the consumer dependent on certifications
of the examining scientist!
Classic encryption before Identitity based encryption IBE is vulnerable
to man-in-the-middle MITM attack where unknown consumers can be fooled by
giving them wrong credentials, used well, but easy abuse. Imposter gets between
Alice and Bob, pretending to be Bob to Alice, and Alice to Bob. All the while,
message exchange is copied. It is prevented some by using the name itself as
the key. But traditional IBE has a further problem – how do we know that the
name is correct for the identity! My solution to the problem is a number of
certificates to my pubic semi-primes that collectively essentially certify that
that the identity has passed my identity tests. The simplest, done just once
forever, is sending a test link to the email. Suddenly arun.arya@gmail.in@aaquantum has
a meaning! The email is delivered by Google only if arun.arya has proved to
gmail that aaquantum has verified the identity. Assuming tm.in means (trademark
india), big.bazar@gmail.com@tm.in has meaning too. This is much safer mail! The
entire rig morale of challenge-click for every new site goes away, as does plethora
of new passwords and their sorry pundits and rules (8 chars, at least one
capital and one punctuation)!
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