Integration leads to Higher Dimension

Integration leads to Higher Dimension.

First let us look at the mathematical space. When we integrate we get the higher dimension plus an initially unknown constant.

Integrating a point gives us a line. Integrating a line gives us an plane / area / surface area. Integration again gives us the space / volume of a container (real or imaginary). Integration then leads us to a higher dimension.


Can this be applied to other disciplines / areas of our life?

Now, we come to the hitherto "unknown constant" on integration. Further analysis, application of range of interest, etc., gives us possible value(s) for the constant "c". However, we need not be afraid of this unknown.

Similary, when we try to integrate, then there is that unknown. Should we boldly go where we have not been before? We do take bold steps, repeatedly. Examples: going to a new school, forming new friends, finding your life-partner, taking up new jobs, heading to an unknown land, etc. In each of these situations, we adjust - we find out the values in that new dimension we have entered - and the value of constant is arrived at.

Corrollary: Differentiation gives us the slope of the function, which is a lower dimension. All we find out is "how slippery" the slope is - and usually it is quite definite, without any unknown constants.

Once again, by differentiating this and that, we only are leading ourselves to worry about the slopes... and unless it is a flat horizontal one, there is a downside to it in one way or other! I guess that is why birds of a feather flock together - there is no worry about the slope of differentiation.

Should we worry about machines with AI taking over?

No worries, I guess!

With the recent flurry of articles, including one by Elon Musk, stating that we should control the research work on Artificial Intelligence, we thought about the past and present as well.

I feel that we don't have to worry, because it seems to be no change from the status quo. How many of us really take intelligent decisions for ourselves, rather than let others dictate decisions for us? Are those decisions by others in our best interest or in the best interest of the decision maker? How many of us outsource the decisions? Here are some examples in this line of thought...

1. Elders in many places dictate the decisions. Seniors in places of study or work dictate the path of progress. The schools, colleges, courses we choose - or even the life partners - many have been decided by others.

2. Some of us want to shirk the "responsibility" of dealing with outcome of our moves, by letting others decide for us.

3. Many of us prefer others to take decisions for us, though it may be couched in hidden language as though we are taking others' inputs / advice.

4. If some people have become successful in our eyes, we want to take up similar paths. We want to try their methods. We even profess their methods to others, even if we don't follow them. Even if gut says it may not fit us, we have to try & sometimes also boast that we follow X or Y.

5. Parents, Community or Society have decided many things for us - from the small issues to the big moves.

6. We had given up our freedom in living our life & our emotions, in early days of 20th century, by waiting for the postman and the result of what he delivered (or did not). The modified avatars have been checking emails 20 times a day, peeking at social media very often or opening messengers/chats time-and-again every day.

7. Our moods are dictated by others expectations, the happenings, our projection of their future reactions to outcome, how we want to manipulate the outcome in order to satisfy X or Y or Z (or many), etc.

In other words, the "free will" we have seems to be still tempered by complex calculations on expectations, outcomes, reactions, repercussions, etc. Where is the freedom?

If so much of what we do has already been outsourced to other "supposedly" sentient / intelligent beings, why can't we outsource the decisions to machines as well? If it has better decision making capabilities over time, why not? What are the arguments for or
against a machine being inferior target for our outsourcing?

PS: This is not about Automation - but AI. Automation has always been there - every new tool (we invent or discover) reduces our effort and improves efficiency.

Decay of elementary particle - life predetermined?

Carbon dating is a nice scientific methodology to arrive at dates of fossils, which are found now-and-then across the globe. This depends on the Carbon-14 isotope that accumulates in living things, as well as the later decay, with a half-life of about 5730 years. A neutron in C-14 "spontaneously" decays into a proton, giving out an electron and an electron anti-neutrino (which means it turns into a stable Nitrogen 14 atom).

Let us review the C-14 decay. Statistically, the confidence level, which depends on the type of testing, etc., is pretty good. For beta radiation based testing, it is within 2% of estimate, given about 4 hours of measurement for 10 grams of fossil. This gives ratio of C-14 atoms to the C-12 atoms in the fossil, which then gives estimate of age of the same. A gram of carbon containing 1 atom of carbon-14 per 10E12 atoms will emit 2 beta particles per 5 seconds (refer Wikipedia).

Actually, if we look into Wikipedia and check the life span of various particles, there are specific estimates of lifetime of neutrons, protons and electrons as well.

Here are some figures of "Mean Lifetime" from Wikipedia:
Proton	More than 2.1×10E29 years
Electron	More than 6.6×10E28 years
Free Neutrons	881.5±1.5 s (more than 14 minutes)
Muon	2.197×10E−6 seconds (2.197 millionth of a second)
Tau particle	2.9×10E−13 seconds (0.29 trillionth of a second)
W and Z Bosons	Halflife of 3×10E−25 seconds (0.3 trillionth trillionth of a second)

Given the half-life of C-14 being 5730 years, it is estimated that about 50% of them decay in that time period. In a fossil preserved for 5730 years, which has, say, 1x10E10 atoms of C-14, we can assume that it would have had 2x10E10 atoms 5730 years ago. When we dig deeper into the quantum level, the question then arises on "which" of the atoms decay, while which "live" longer? Of the 2x10E10, there is a regular decay of atoms, which seems to be quite consistent too, as claimed by Carbon dating process.

The rate of decay, being consistent, would also mean that within, say 575 years, some atoms would have decayed, the counts for which must be within the expected range of errors. After 1150 years some more. After 5730 years, we find that 1x10E10 have decayed. Some C-14 may decay after 57,300 years too.

(1) However, which atom(s) get to decay earlier and which atom(s) get to "live" as long as 53,000 years? Is there any coordination? What other factors are involved?

(2) How would the consistency of rate of decay be explained, while at same time the atoms are assumed to have no "intelligence, information, data-exchange", etc. (unless I have read wrong)? How could one atom decay after 575 years, while another lives for 57300 years (or longer) - and on what basis? If it is purely by chance, then consistency cannot be easily explained. If it is not by chance, what is the scientific process?

(3) If a scientific process cannot be attributed, then is there "coordination" of activities? Do atoms have "life" defined within it? Or is that controlled by an "elusive God"?

(4) If these are not acceptable, then is there a collective "consciousness"? Can there be individual consciousness, even at atomic level (which is the smallest level we observe, due to our own limitations and limitations of instruments we have developed)?

Diverging a bit, I would like to recall here a nice view of "dark times", in a speech by a descendant of a Punjabi immigrant in the USA. She said "the darkness may not be the darkness of death, but it could also be the darkness of the womb - before birth, before a new beginning".

(5) In the same line of thinking, should we consider the decay of the Neutron as its death? Or should we think of the birth of the proton and electron by division of the Neutron?

Some experts, with more knowledge on the science of decay, half-life, life of particles, may throw light to us common folks, who are stumped by basic questions when we look at the quantum level.

Refraction - a surface awareness

Refraction is defined as a surface phenomenon. When a ray of light passes at an angle other than normal to a surface, the phase velocity of the light reduces, if entering a denser medium (higher refractive index), and increases if it moves to a rarer medium. Moreover, the direction of the light wave is changed a bit based on the sine rule (Snell's law). Further explanation of conservation of energy is also outlined by Fresnel's equations, where part of the light is reflected and part refracted.

The above is just a short summary of refraction as we are taught in school. A bit further of explanations are required, to ensure we have covered all aspects. Both medium are considered transparent for these experiments. Translucent materials would absorb part of light and reflect some of the light as well. Moreover, we are considering homogeneous medium for simplicity sake. In heterogeneous / non-uniform medium, there will be more collisions of the photons, absorption, reflection, etc.

The overall concept however does raise some questions at a quantum level. At quantum level, we all are told that there is lot of empty space between the nucleus and electrons. There is lot of empty space between atoms that form a molecule (say glass molecules). There is very higher order of empty space in case of air and we have very highly mobile atoms/molecules. In case of water, even though there is Brownian movement, there is still quite a bit of empty space.

We have usually simplified understanding of refraction into 2-dimensional ray-theories. We are all told of the rays being on the same plane. However, a "surface" / boundary between two medium is usually 3-dimensional. What really happens to the angles of incidence and refraction? 

Other than that, we have many more questions.

(a) As the photon approaches the line of boundary between the two mediums what influences the change in direction of light? Are there different kinds of fields in the two mediums? Does Glass or Water have a different field, that affects the path of light (or path of photon)?

(b) Do the atoms/molecules exert any electro-magnetic field affecting the electro-magnetic waves? Is there a regular field that exists around every atom/molecule? If yes, what is its effect - if not, how does the surface, its angle with respect to the approaching photon, etc., cause the consistent effect?

(c) How is the change of direction different for different angles of approach to the surface separating the two mediums? Does the light sense the alignment of the series of atoms/ molecules of the medium? Or is this also a function of "alignment of the field and its effect"?

(d) At what point does the change in direction happen - as soon as it is within X distance of the field near the boundary? What is value of X that we can reasonably surmise, for a significant effect of change in path?

(e) If there is a very thin film of the medium (hence light emerges back into first medium), then how is the change in path perfectly in opposite direction while going through all that empty space between electrons, nucleus, atoms and molecules? A question similar to (c) above, but now the light diverges from normal (assuming the film has higher refractive index).

(f) So, is refractive index a function of this "field" and is the field same as the electromagnetic field? Or is it a function of the electromagnetic field? Or is it possible that the field is something entirely different? When we think of concept of heat, temperature, etc., along with the refraction concept, and then electromagnetic fields - where do they all fit in, in the quantum level?

Too many questions raised when we dig deeper, and still searching for answers.

Maybe a kind reader will point us to some good information that can set right the simple doubts of a common man.

Observable Universe - two Titanics

We are fascinated at the vastness of the observable universe. If we wish to apply a model of the universe using smaller entities from our regular life, it can give us a simpler perspective to the size of the cosmos we perceive.

Let us take our sun and equate it to the nucleus of a Hydrogen atom - yes, a proton. If we take the diameter of the sun to be the diameter of the nucleus of the atom, then the electron orbiting the sun is actually at 20 times the distance of Pluto! Rather, Pluto is orbiting the nucleus at 1/20th of the distance of the first electron at the highest energy level (1s orbital). Earth is much closer - just 1/1000th of the distance the electron would be held at!

Now, how does the currently perceivable limits of the universe scale when the sun is the size of the proton? With simple, back of the envelope calculations, we can find that the approximate size that humans can observe with current instruments is about twice the length of the Titanic. Yes, that is about it. Approximately 535 metres in each direction - so the entire observable universe from end-to-end would be a bit more than a kilometer.

Where do we fit in, in this model? We are obviously the size of a minute dot in this Hydrogen atom. Each person would be the size of a dot 3 billionths of the size of that nucleus, orbiting at a distance of 215 times the size of the nucleus. The earth is approx 1/100th the size of this nucleus (approximately 109 per Wikipedia article on Sun).

What is the size of the Milky Way in that case? The milky way will fit into a small ball-bearing - yes, approximately 2 mm diameter on the elongated side of the spiral galaxy. That is, it is a spiral between 1.1mm - 2mm in size.

That is all? That is it? Yes, that is the limits of our abilities, science and scientific instruments we have constructed till date.

Here is a tid-bit: How many molecules of gaseous Hydrogen will fit into that Milky way galaxy in this comparison? If we would like to compare the number of hydrogen atoms in 1.1mm to 2mm size Milky way, with the number of stars that are estimated to exist in this galaxy, we have about 250,000 hydrogen atoms for each star in the galaxy. This shows how sparsely Milky way is populated by stars, compared to standard 1 atomospheric pressure Hydrogen atoms (solar systems) in similar scale.

Open question that we will discuss later: Is there a possibility that the universe is much larger? Yes, it is very much possible. One has to read up on Cosmic microwave radiation to look for one example of unexplained uniformity from currently observed lumped galaxies and vast empty space.

Outcome of Rigorous Steps - Beautiful Science

Firstly of all, hope you all followed your own individual rigorous scientific steps on evening of Dec 31st, with very measured downing of spirits (where applicable) to uplift the spirits and herald in the New Year in one of the best of yearly rituals. Wish you all a prosperous 2017, when we reach higher towards our goals.

• We seem to follow never ending repeat steps day-in and day-out, from morning till evening, with a nice end-goal in mind - for 5 days a week (sometimes 6 or even 7). Some strict schedules are followed in these rituals with simple regular expectation of returns - compensation. It does not stop there, as we also expect something more, for having done the processes in meticulous manner - a promotion and / or big increment. However, this is not guaranteed, as that depends on the specific procedures that have been followed in the previous 365 days in direct relationship with boss(es). Unless boss(es)' wishes had been carried out explicitly or subtly, like laughing at their mundane jokes in measured manner, taking up their work & giving them the credit for job well done by us, and some favors done which are not so easily expressed in this civil forum, the efforts at work don't yield the expected bonus fruit. Yet, these are the rituals we repeat week after week, month after month and year after year. In search of something - compensation, status, assets, happiness in future?

  

  Our Modern Rituals

• Belief that modern technological steps like checking emails many times a day, being available for conference calls at god forbidden hours (small g) are the super methods provided to us by science for our growth.

• If we do not follow simple procedures when we start the vehicle and begin driving, then additional steps need to be performed to correct the same. If one has not switched on the blue-tooth, then either pull over to do the same - or check the road, mirrors, etc., before switching them on, on-the-go. Prayaschittham is always there, dictated by science to ensure accident free remedy. If the wires and ear plugs were not put in place before the drive, then shoving the mobile phone inside the helmet can be achieved, by following 1 or 2 different methods as alternative - of course, following strict methodology to avoid accidents. We love to follow these simple logical steps again and again - every day (and alternatives at times), in order to get the benefits of science's donations to our lives. Science however has prescribed all the steps & alternatives. Each one follows a strict procedure for every ride, every day, every week... However, for every missed sub-task, there is a set of operations to set things right (though the fact that these are predefined operating procedures is easily overlooked).

• Science has enhanced our lives' main ambitions - to gossip, complain, boast, talk (and ignore/ not listen) - by providing new technologies that fast forward the same. We love the rituals and the goals too - in this case... Nothing like complaining (without looking for solutions), sugar-coating of achievements, shoving problems under the rug, etc.

Tracking - CAG

• The CAG (Comptroller Auditor General a.k.a. ChitrA Gupta) keeps track of your adherence to scientific processes - like hours spent at work, hours spent on social media, official mails processed outside work hours, appropriate social behaviour in presence of bosses & management, etc., in order to allocate appropriate resources to you. Accumulating the necessary resources through-out life is the supreme mantra for our enlightenment. (BTW, after cyclone Vardah, there is more Gayab-tree rather than Gayathri)

• Oh, how did we miss the rigorous process we start at age 3 (or earlier) and continue till we are 21, 22, 24, 25 or 28? Yes, that nice Basic Scientific process called "education" - we so amazingly devote so much of time in getting many things close to perfection during the short couple of decades. Every person wants their ward(s) to follow this ritual without fail with different goals in mind (their goals and/or ward's goals). Some plan for first year result, medium term expectations or long-term life goals. Some have 2-year expectation, 5-year plan or 10-year vision of future. We work through science-prescribed rigorous steps of waking up early in morning and rushing through, packed like sardines with similar aged folks, returning home after lot of studies, bit of play and some general learning - all towards the end-goals. Is there any guarantee that a person skilled in Mathematics will not end up a clinical assistant (where counting the pulse is maximum Maths one may do - or may compare the lab result numbers to the range of numbers given in the guideline charts), or a person interested in healing & human body does not end up as a teller in a bank counting notes? No - but we still follow the scientific process outlined by generations (oh sorry, only past 6 to 15 generations) in search of our varied goals. Is that better - or some other rituals (oh, I thought those were scientific too) prescribed for many millenia will be the best to take us through the travails of our insignificant life in this enormous cosmos?

• Only 2 or 3 or 4 people need to follow procedures in order to perform a complex task of transporting hundreds / thousands of people in one go. The pilot / driver, the co-pilot / conductor / guard, the ATC / station masters - if they follow their scientific rituals can ensure people reaching their goals. However, the same concept cannot be and should not be applied to any processes/ procedures followed over millenia, because there is no proof that they are for "Yogak-shemam vahamyaham". So, I guess scientific methods are really important - but...

• Oil made in India is bad, but those made based on recent science are so great that we are being delivered from near extinction. No, it is not economics - it is pure scientific research without any ulterior motives. Really? Coconut oil, Sesame oil & Groundnut oil are bad for us in India? Come on...

  

  Modern Science???

• Social media is an excellent scientific tool to spread 9% lies and 90% exaggerations. That is so awesome that we come together and live closer together (in 'apart'ments), but behave like zombies in front of our neighbours, not knowing from which planet they have landed.

• We should not reduce salt intake when you have high-BP, because it is not proven scientifically with recorded statistics (up to end of 20th century)... and now that it has been proven scientifically, it is the science community that must be awarded encomiums to having amazingly introduced this great concept to humanity. Something which has been followed for some generations in India, without any other prescription of diet or medicines.

• We get super-excited watching shouting wars in the middle of our living rooms, staged miles away, through a rectangular portal, thinking the methodical feed of data will somehow enhance our life - either towards our goals, or just destressing from our other exciting daily rituals.

• No imports of your stuff without DDT treatment... then, after you destroy your lands - DDT is bad for food and hence we will not import your food stuff. That is top-class scientific research of the 20th century.

• Ghee is the evil invented in Bharatha kanda, in order to subjugate all humans. Thank God science has come to deliver us. Tamarind, Neem, Turmeric, anti-bacterial treatment of homes, streets, self, - all are evil - per research, until it is given up - and then re-introduced from the scientific community as outstanding findings of the entire 14 billion years. Oh, I love my cow produce like milk, butter, ghee, etc. (oops, I should not discriminate on sex - bull produce too)

• ENJOY - Still we all should enjoy our own individual methodologies, procedures & processes developed carefully since the age of 1 upto age of 18 (or whichever age is attributed to Albert Einstein's quotes), and then polished - so that we excel & succeed in our lives. We should leave behind the mundane rituals developed over millenia, because the end-goals are not guaranteed - while our scientific tools & technologies guarantee the greatest of achievements in our lives, time & time again, in such a repeatable fashion that in last 200 years humans have never ever been sooooo happy.

PS: This is what a cyclone, followed by eager folks who want to saw off cut trees to smaller pieces, at 1:30 AM using a chain-saw, does to people. Especially when it was supposed to be a "Silent Night, Holy night" (night of 24th December).

PPS: I retain the right to rescind some or all of above statements, as and when I get enlightened & move from my small sandbox, to reach out towards TBS (not Turner Broadcasting system, but Totally Bureaucratic Sanity).