How do we know neutrinos exist

I was wondering today why should we postulate neutrinos and make life more complicated than it already is.

This article explains why neutrinos are required and in addition as a bonus explains how they are detected. Apparently it is must for accounting for conservation of energy in beta decay.

Story of the Neutrino

Income inequality of US or hail capitalism US style!

This is from wikipedia and made me fall out of my chair!

1. Top 1% owns 35% of wealth.
2. Top 5% owns 60% of wealth or 3 out of every 5 dollars.
3. Bottom 40% owns  just 0.2% of wealth.
4. Bottom 60% owns just 4% of wealth or 96% is owned by top 40%

Really hail capitalism US style - 60% is poor because they don't try and Big banks/wall street firms will get saved by government if they fail [of course with fat bonuses for their executives].

Is there an opposite of absolute zero temperature?

That is do we have a highest possible temperature in the universe?

We know we have a lowest possible temperature  [−273.15° Celsius] when all particles of the system have no kinetic energy at all.

I was wondering is there an opposite of absolute zero and looked up in the net.

These two articles discuss this. Apparently it goes to the heart of physics!

Current contender is Planck temperature at
                     32
1.4 x 10 
 
PBS - absolute hot

and

http://en.wikipedia.org/wiki/Absolute_hot

Why a digital computer is just a DFA?

Pedantically speaking of course!

A digital computer is just a Deterministic finite automaton, which of course is equivalent to the complexity [or power] of Regular expressions.

How?

A digital computer just has 2^[memory size] states it can go to. So it is equivalent to a DFA having 2^[memory size] states. So in that sense it is no more powerful than a DFA.

But given that these 2^memory size states are huge, it does approximate a universal Turing Machine!

But to reiterate pedantically speaking it is just a DFA with huge number of states!

Layman definition of P, NP and NP-complete

Here is my layman intuition for these important complexity classes:

1. P

All problems which are solvable in polynomial time.
Sorting for example.

2. NP

All problems which can be verified in polynomial time. That is given an instance of a problem and its 'solution' we can tell in polynomial time whether it is indeed a solution or not.
Integer factorization for example.

3. NP-hard

All problems which are harder than NP or at least as hard as NP. Any thing whose verification is exponential will trivially belong to this. 
For example factorial of n.  Or producing all permutations of n.
[Technical nit - problems have to be decision problems for them to be in P, NP etc. but we will ignore this for now]

4. NP-complete 

 

It is in NP - hard  as in 3) above and this can be reduced to a problem in NP. So in a sense NP-completeness brings down the complexity a notch from NP-hard to NP.
For example, subset sum problem. In general many optimization problems end up here.

 

In layman terms:

P <= NP

P+NP-Complete = NP

 

NP < NP-hard

NP-Complete < NP-hard [this follows from previous inequality]

Largest factored number

I was listening about Quantum computation in Quantum theory - lecture 15.

Suddenly I started wondering what is the biggest number [known publicly] to have been factored. As usual I turned to wikipedia.

This number known as RSA-768 is the hardest known number [having only 2 prime factors also called semiprime].

1 ]=> (* 33478071698956898786044169848212690817704794983713768568912431388982883793878002287614711652531743087737814467999489 36746043666799590428244633799627952632279158164343087642676032283815739666511279233373417143396810270092798736308917)

;Value: 1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413


If we purely go by digit size it is:

 1061

2   - 1 

it is 320 digits!

Great Perimeter institute physics videos

I found very good set of physics course videos in perimeter institute recorded seminar archive.

I am going through these 2 courses and they are very good and highly recommended.

1.  Advanced General Relativity

This course introduces general relativity at advanced level as the name implies. Prof. Sorkin is very smart and good teacher despite his soft voice!

I enjoyed the explanation of Covariant derivative and Lie derivative in particular. It gave me an intuition in to why covariant derivative is inextricably linked to metric and very intuitive explanation of Lie brackets as the "inability of the parallelograms to close".

2. Quantum Theory

It introduces quantum theory again at an advanced level. Prof. Emerson again is very good teacher and has a good voice as a bonus.

I am only half way through the course so far. I enjoyed the foundation discussions in lecture 7 and more importantly the connection between classical and quantum mechanics in lecture 8. Latter gave an intuition about why jumping of state is not so different from classical probabilistic "state update rule" and surprisingly where they differ is after the measurement we DO NOT see the outcome.
1. In Quantum mechanics coherent superposition is destroyed and it definitely is in one of the eigen states [although we didn't take a look at the actual state!]
2. In classical mechanics "coherent superposition" remains in the sense same probability density function continues to apply.

This was very interesting observation and came us a surprise to me! This point alone was the worth effort I spent in learning these videos.