Whatz prooved & Whats not :: A DEAD END SUPPLIMENT !

Hey all !

Hmm ...
Another Dead End ? Nope I'm saturated of those now. But this one's interesting enough to be brought to notice of the blog.

A seemingly remarkable proof indeed for prooving that all numbers are interesting !
But Can a subjectivity of the problem be discussed mathematically ? The answer seems to be yes !?!

Now lemme introduce you 2 a couple of DEAD ENDS :

(1)

To Proove : Every natural number N can be described within 15 words.
Assumption : Let there be a set S of number which cannot be expressed within 15 words.
Ordering the set S & pickig out the first element, say P we get P as :
P is the "the smallest natural number that cannot be unambiguously described in fifteen words or less".

:. P can be described within 15 words.
By Reductio Ad Absurdum ;
We herey proove the Statement that :
EVERY NUMBER CAN BE REPRESENTED WITHIN 15 WORDS.

(2)

I begin this one, relating to the THEOREM OF MATHEMATICAL INDUCTION as quoted by Arun in a comment to the previous post.

"

The principle of mathematical induction basically is a logical proof of extention. If you can show that:
1) The statement is true for the base case, i.e. 0 generally,
2) That if it is true for n, n-1, n-2, it IMPLIES truth for n+1.

"


Okay. Let there be a statement S(n) depending on n which can be either TRUE or FALSE.

I DEFINE S(n) as :
S(n): "In ANY group of 'n' blog-members, all have equal ages."
OR
"In a set of blog-members-ages from ANY particular blog, all values are equal."

Now proceeding on the lines of the above discussed theorem, lets discuss S(1).
: " In ANY group with 1 blog-member, All blog-members have equal ages ( Takin one member at a time since n = 1 )."
Clearly S(1) is TRUE.

Assume that S(k) is TRUE which implies that :
: " In ANY group of 'k' blog-members, all have equal ages."

Now to proove S(n) for all N belongs to (1,infinity), We must proove S(k+1).

So now we have a set of (k+1) blog-members. Of those, we can choose different combinations of 'k' blog members. In each of these combinations, all blog-members would have equal ages. Therefore, All blog-members in the (k+1) blog-member set are equal in age.
:. S(k+1) is TRUE if S(k) is TRUE.


S(1) is true. S(k+1) is TRUE When S(k) is TRUE.

:. by the THEOREM OF MATHEMATICAL INDUCTION ...

S(n) is TRUE.

Implying this for the blog KVPY2005 : Fused Bulbs... I hereby proove that all memebers in this blog are equal in age, which is conincidentally true within the limits of error. lol.



Ill leave the implications to be discussed by the blog members.

WAITING FOR COMMENTS

(desperately hehehe)

Twish

Boring Numbers?

Hey. It's been a long time since I've posted anything, so I'll make a candid proof I saw on the net somewhere.

This deals with a really fundamental theory:

There is no such thing as a uninteresting number.

As we deal with the earth-shaking proposition, one must have a deep fundamental knowledge of sets. Let us limit our theory to the infinite set of natural numbers.

On with the proof:
Let N be the set of all natural numbers, of which X represents the set of uninteresting number. First let us order this set X in numerical order. Let us now analyse the first number of this set. Our understanding of what makes a number interesting is so fragile that to produce such an example is a great step forward. Thus this number being the FIRST uninteresting number is of vital importance, bringing our interest to it. Thus it can not belong to the set, and isn't the first element. Let X' be the revised set omitting this fraud. Thus the second term of set X is the first of set X'. We can apply the same reasoning here, and easily omit this element, and continue to do so for all other numbers of the set, making it a null set. Thus it is easily proved that there is no uninteresting number.

Lovely proof isn't it? But there does exist a very important logical consideration. If one considers ONLY the negative numbers, our present ordering is befuddled, but do not panic. Suppose we order them in REVERSE order, letting greatest come first. Thus we can proceed by the same steps as above.

Now, we come to a very important juncture. If we combine these two sets, and look at ALL integers, we're stuck. For sure the negativity is an important difference between '+' and '-' numbers, and we can't ignore it. A set of Z has no beginning or end, so we CAN'T order it, and use this lovely proof for it. So it seems that the interesting-ness of certain '+' or '-' numbers makes other numbers loose there interesting-ness. But I thought interesting-ness was an intrisic property of a number. I.E. that a number can be called interesting because of a property that it exhibits, i.e. primality (it being prime) or it's square-ness/cube-ness/n-power-ness, or a pattern exhibited by its digits (like 12321).
Appealing to this logic, we could either conclude two things: That there exist no uninteresting numbers, or that the interesting-ness of a number does infact depend extrisicly as well as intrisicaly, and that it depends on a negative counterpart (whether that is the negative of the same number or not can not be concluded though).
As much as I'd like to take the latter, for it's more complicated, and that it IS earth-shaking in its statement, I'll abuse Occam's Razor and say that the former is obviously true.
Occam's Razor is: All explanations are simple, and the more complex one is more probably wrong. Note the keyword: Probably. It's generally quoted with overexagerrations like:
When you see a reflection:
1) Light is getting reflected
2) There is an alternate reality, which can be entered through the window, and which is inhabited by people who look EXACTLY like you, and happen to do EXACTLY what you are in front of the mirror.
Sometimes I think that life would be a lot more fun if it weren't so obviously 1.
That's all for now. I hope to be back this weekend with a post on the brain.
Signing off and Id Mubarak,
Arun

BEFORE THE BEGINNING AND BEYOND THE END (PART 2)

Hello again all of you. I am back, with a spicy second part of my article. The contents of this article as well as the one it follows is a collection of well laid facts cemented with the author's own ideas. Thanx 4 reading guys, enjoy. Please refer to the previous section wjenever in doubt.


Let us now extend our view of the symmetry about the big bang, we can go forth to say that the previous universe too must have originated from another big bang. Therefore, this brings us back to the concept of oscillating universe theory. However, the problem with oscillating universe is Entropic considerations. The problem is the following:

The oscillating universe theory says the entropy of all the singularity states of the universe have same entropy. Now let us assume the whole of the universe as one system. Suppose right here right now, I drop an egg and break it. I have thus increased the entropy of the universe. However, when our universe reaches its next big crunch, the entropy has to be same as that of the last singularity. There is the problem, entropy remaining constant although the system is experiencing an irreversible process. I will try to provide an explanation for it.

All of us know about supernovae explosions. Some parts of a dying star blows off as a huge explosion into the realms of the vast universe, and the remaining collapse into a tiny dwarf star. Let’s apply this logic to the entire universe.

Let S1 and S2 be two singularity states. A big bang at S1, expansion, and then contraction and finally a big crunch at S2 are the sequence of events. The change in Entropy is ΔE. According to Boltzmann postulate or the definition of Entropy,
ΔE = kb (ln Ω1 - ln Ω2) where, the sigma are the no of ways in which the same microscopic arrangements can be restored from a starting state.
So what we do now is very simple. We ‘transfer’ all the disorder in the whole of the universe to say a few moles of gas molecules. We outcast there molecules and allow the rest of the universe to move into singularity 2.

Let me make this more lucid. While playing billiards (or pool or snookers ... whatever), on a perfectly friction less table, we first break the triangular arrangement in the middle by a slow strike, the balls go a little haywire and keep moving and colliding with each other. As these collusions continue, the entropy is constantly increasing with time. But there is a remote possibility that say seven of these balls will again come back and form a tight arrangement. The remaining two will remain in a state of even increased randomness. Thus we can say that the entropy got localized to the two balls or got transferred from the other seven balls to the two.

This is one way in which we can satisfy both the oscillating universe theory and the second law of thermodynamics. But this too has a lot of problems of its own. First and the most important is that it is unable to explain the birth of the universe (I am talking about the real birth – the first big bang) and it too says that there has to be some thing beyond our universe.

It says our universe is constantly losing its mass into darkness (dark energy?). It predicts a very gruesome death to our lovely universe. A heat death scenario – a situation when there will be no energy gradients and hence there will be no process. (All processes require flow of energy.) But certainly it has done one good thing for sure, it has increased the life span of our universe to much beyond of what Big bang theory had proposed. It never says that the Big bang theory is wrong but it says that the big bang was not the beginning but only a phase change in the history of our universe.

I will not end this article with a conclusion as conclusions are for the readers to devise. It is a philosophical question and until we find a proof we can only speculate. We are like a child who presses its nose on a mirror, accepting it to be window. He knows it is not the reality. It is only the preconception in his mind. Reality lies beyond the glass- break it open. But he is afraid that in the process of breaking open the mirror and discovering the reality, he will destroy his well constructed sand castle.

Saurya Time Mishra

PS: Sorry if u couldn't c the comments before. Dunno y, but still, u can add them now!

~Gr81~

Diwali

Hello Everybody!!

Well, my Exams are over and I'm enjoying this festive season. Hopefully u ppl are enjoying too!

So ppl:

दीपावली की ढेर सारी शुभकामनाएँ!!

____________0____00___0____________
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_____________000000000000__________
________0______000000000___________
____000000000_____00!______________
_____000000000___________000000____
_____00______00_________000000000__
______________00_______0000__00000_
______________00_______0!______000_
_____________000___00000________00_
____________000__00000000________0_
0________0000000000000000________0_
0________00000_0000____00________0_
00________00____00_____00________0_
00_______________00____00_______00_
_00______________000___00_______00_
_00_______________00___00______000_
__00______________000__0000000000__
___00____________0000___00000000___
____000__________0000____00000_____
_____0000______00000_______________
______00000000000000_______________
________0000000000_________________

We all know that busrting crackers pollutes our environment. But who cares about the "E"-nvironment?

So blast as many "E"-crackers as you want, and "E"njoy this "E"-Diwali!!

E-Diwali!


And yeah, more important stuff HERE:

Now I have a few days time, so tell me what all do you want to change in the blog....
Like:
- Add Intro
- Decrease no. of Posts visible
- Change theme (to what?? plz suggest...)

Write any kind of suggestion (ANYTHING... even something like flashy links...)

So waiting for ur suggestions!

PS:
Are u busy? If not, mayb u should see this:

• LOGAN's Mystery Of Time And Space Adventure [Mystery Game]
• Pencilmation [Cool Stick Figure Animation :D]

--

रसज्ञ शर्मा
* Rash thegr81!! *

Modern physics and Vedanta.

Ok, I agree the topic seems to be a turn-off but the ensuing article might just not be one. Actually I read a book of the same name by swami jitatmananda (a gem by all accounts –google him if u like). That along with a few observations of mine constitutes this post. So, back to the topic .Vedanta defines maya as sthana-kala-nimitta (ie space time causation). Without either one of these the other one has no meaning – nor does maya. Rings a bell –einstein’s space time continuum et all?-it should.
There is also the question of consciousness. It has already been mentioned in the Upanishads (or vedantas for that matter they are the same), that consciousness/awareness/opinion, whatever one may call it, affects the surroundings. And it has only recently been proved that the outcome of an elementary experiment (which can have only 2 outcomes) can be affected if the scientist conducting it has a biased opinion –all this is actually much more complicated than it sounds- but that’s that. There are similar mergers in oriental philosophy and occidental science that are increasingly evident even as we speak. Scientists like john a. wheeler have coined mouthful names for the phenomenon but I left the book at my hostel so I cannot quote. But this still might open avenues of thought open to many of u. and if u ask me, gita seems lifeless to me- Vedanta packs in much more excitement & cloudy aura. Issue a translation from ur library and go through it. Gita, on the hand was a part of Mahabharata which was purely a literary creation. Gita, once translated seems bland but yeah it uses devices and metaphors well. I don’t know that much Sanskrit but ppl seem to go gaga over gita – its just common sense! Or thus I think,well then each to his own.
How do u ppl like resonance though? For me some articles drive well, while most yield a tangent (vidyapith colliloquy for did-not-quite-get-that).
Now look here I am absolutely greedy on feedback so do comment.

latest intro

My pic!

The first hi-mates. I know I am the last un, but cant help with being in skool can I?So here is my intro.
Name: debanjan basu
Nick: my classmates call me basu (with that inimitable undertone of contempt-u know the sort)- n I am fine with that.
Identification: Kept me thinking actually coz I did not do anything special(read stupid) over there but the pic may help. Oh yes......I am from Ramakrishna mission vidyapith, deoghar .that'll do, wont it?
So that's all , as twish correctly pointed out, we shall all get together nxt summer.

BEFORE THE BEGINNING AND BEYOND THE END

Part 1

There was nothing at all, no space no time (not even me), then all of a sudden it all happened - The Big Bang. A theory we all have believed so blindfolded. A Theory that created a bigger bang in the world of science than the Big Bang itself. A theory that certainly could explain cosmic background wave and the red shift of the expanding universe, and even satisfies religious claims of things like God making everything. Everything is completely all right until we step beyond the beginning. People have asked numerous questions, “What was there before Big Bang?” The scientific community with a Godly authority turned all of these questions down. I will not repeat them.

But this was not all. This theory at last seems to be breathing it’s last (and thank God). The theory, which was once rejected, is now betting a rebirth – The Oscillating Universe theory. The General Theory of relativity, which so well explains everything regarding gravity, fails miserably in what we call Singularity – space and time condensing to one point – densities touching incredible values and distances reducing to about 10^-39 - the plank scale. And the reason? The same thing, which my dear blogmate Arun and I have been arguing upon – Calculus. We all know that charge is quantized, so is angular momentum of electrons, even mass. Let us take a step forward and extend quantization to time and space. Space is nothing but a fabric woven out of individual fibres. Calculus cannot be directly applied over discontinuous space. However applying it with a little modification allows us to end all problems. This theory is popularly known as the Loop Gravity Theory and interestingly but as expected originated in India.

The Theory was aimed at explaining the physics at plank scale which it did successfully. However, it led to another implication and directly counters the concept of the Big bang.. When all matter in the universe approach singularity, the theory says, there comes into play a force – one of tremendous magnitude, manifold greater than gravity itself and repulsive in nature. The situation is similar to a ball hitting a spring and bouncing back.

Certainly with this knowledge we can answer the most controversial question, “What was there before the big bang?” The answer is there was the countdown to a big crunch. We now have a universe that does not begin at the big bang, but only is symmetric about it.

What I want to say is here – Wasn’t it Obvious? We should have guessed it earlier. Let me explain why and how.

I would like to repeat the philosophy of a 2^nd century Chinese philosopher. Every event is preceded by another event. (The former is the cause of the later) Hence, the implication follows that there has to be some thing before the Big bang the cause of the Big bang, more specifically. (Speaking further, we can say that there should be no beginning to the universe, but we will see to that later) To further justify the statement, and denounce the creation of space-time at t=zero (and with it the Big bang theory), I will give the following argument.

Let us say there was a primeval atom, which exploded to create the universe, space and time. The question is why at all did it explode? This can be answered in two ways. Firstly there was some thing (or someone …say God) outside it who/which caused the Big bang to happen. That means, there was something – matter, energy or say a consciousness excluded from the Primeval atom. But this is against our Big bang theory. The second way is to use probabilistic mechanics. The primeval atom just like a radioactive atom had a probability of disintegration at any given time. (I am sorry, but using probability without the concept of time is just impossible.) So there has to be Time before Big Bang. This again violates the Big Bang theory.

I would love to write more but its not possible in a single blog. I will put it all in the second part very soon. So stay tuned, the sting is in the end, I assure you.

Saurya "Time" Mishra