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.

Top 10 innovations of 20th century

10. Digital camera

9. ATM

8. Man made satellites and GPS

7. GUI (Graphical User Interface)

6. Refrigerator

5.  Television

 4. Internet

3. Cell Phone

2. Air planes

1. Computer

Honourable mentions:

X-rays, MRI and Ultra sound scans

Credit cards:

How to know if you are educated

How to know if you are educated - that is well-educated. It simply doesn't mean you have a degree in something.

1. You know earth is round. 

It is so simple and obvious, but I don't think many people feel it in their bones. For example, How would you tell a kid that earth is round?

I was taught the example of approaching ship. When it approaches we would see its  bottom part first instead of mast. As I hadn't seen a ship approaching, I had no way of knowing whether it is true. I  could simply accept either statement as true!

One illustration I can think of is you can fly to USA from India in two different directions say through Tokyo or through London. It will be possible only if earth is around.

Another is when it is day in say India it is night in USA. It can't happen if earth is flat. All the earth will get sunlight at same time.

Another is all the satellites rotate the earth and in particular some as geo-synchronous. This makes sense only if earth is round and rotating in its axis.

2. You know earth orbits sun and not the other way around.

It is very hard to get an intuitive feel of this. Particularly because earth hardly seems to be moving [except when there are earthquakes!]. Here you need a good education to help you.

Many people would think that seasons occur because of earth's orbit. No - it is actually because of earth's tilt of 23 degrees. In fact most of the northern hemisphere is farthest from sun in summer.

One way to see this is [if we assume earth is moving] if we were not rotating we will fly away [or towards] from sun and it should get colder over years. So only option left is to orbit. Of course we could be standing still. Why that is not an option with sun around is our point 3)

3. You know Newton's theory of Gravity.

That every thing attracts every thing else [not just girls attract boys or vice versa]. It is the reason we feel pressure on us when sit or stand. That's the reason it hurts when we fall. In fact it is the reason we fall at all.
If earth were to stand still sun would simply attract it and earth would have collided with sun.
Once we understand gravity it is the easiest of all to grasp as we feel it all the time.

4. You know Darwin's theory of evolution by natural selection.

You understand all species once shared a common ancestor and evolved into different species due to natural selection.
This one is hard to swallow because it hurts our pride. We have to come to the realization that we are only special to the extend every other species are special as far as earth is concerned.
But all that shared DNA code, chimpanzee and kangaroo loudly proclaims its truth. We are not well-educated we don't understand evolution.

5. Common courtesy

If we don't have basic respect for people then all our education hasn't really done anything for us after all. It simply didn't have the intended effect - to make us civilized.