Science books for 14-year-olds
18 hours ago in The Curious Wavefunction
We deliberately do not attempt any theoretical or phenomenological interpretation of the results.So let me ignore the wild theoretical implications and discussions of tachyons and just talk about the experiment and an astrophysical constraint on the velocity of neutrinos.
The beginning was heralded by an elephant's trumpet.I wrote this poem because even modern cosmology faces infinite regression paradoxes with respect to the initial impetus of the Universe. The various creation stories independently formed in different cultures create some stunning mental images for me. The funniest idea for me is that the Universe is resting on the back of a giant turtle. What is the turtle resting on? Why it is turtles all the way down. Oh, and I almost forgot the best blog posts always have a picture; here is a picture of a turtle.
The universe is carried on the back of an ancient turtle.
There were once ten suns embodied by crows. All but one crow was shot by an archer.
The moon is a decapitated head. Her face is painted with bells.
The stars are your ancestors eyes worth remembering.
In time you too will have nine tails and be older and wiser.
All the things which you do not know are vague. Drift clouds.
Having come so far is a matter of vagueness.
your brain contains 100 billion neurons and 10,000 times as many connectionsProfessor of Molecular Cellular Physiology at Stanford Stephen Smith says in a press release on brain imaging that
In a human, there are more than 125 trillion synapses just in the cerebral cortex aloneRené Marois from the Center for Integrative and Cognitive Neurosciences at Vanderbilt Vision Research Center states in a recent paper 
The human brain is heralded for its staggering complexity and processing capacity: its hundred billion neurons and several hundred trillion synaptic connections can process and exchange prodigious amounts of information over a distributed neural network in the matter of milliseconds.I have enough expert sources now to confidently say these experiments agree that the human brain has some 100 billion neurons (1011). The number of connections seems less precise, but it is at least several 100 trillion connections (1014) as judged by Marios and Smith and as much as 1015 as judged by Seung.
There are more connections in the brain than atoms in the Universe.A really clever person pointed out that
Theoretically, if we took all the atoms in the universe; wouldn't that include the atoms within the brain?People have this feeling that the number of connections between items can be much larger than the number of actual items in the collection and while this intuition is true the idea that there are more connections in the brain than there are atoms in the universe is absurd. Lets put it in perspective that a few grams of any substance, like water, is measured units of moles. A mole is standard unit of measurement corresponding to the absolute 6.02 x 1023. Thus even a drop of water contains more atoms than there are connections in the brain.
The mean total brain volumes found here (1,273.6 cc for men, and 1,131.1 cc for women) are very comparable to the results from other high-resolution MRI-volumetric studies.We can take the volume of the brain as 1000cc as a low estimate (which will only over estimate the density of connections).
|NP⊃x||'never print x'|
|PP ⊃x||'print xx'|
|NPP⊃x||'never print xx'|
Halting. The scientist claims that
Haltingcan correctly tell your own code
B(P,i)whether a program halts.
if Halting(P,i)==true then
return true // the program halts
return false // the program does not halt
X, which is any program, as an argument.
if B(X,X)==true then
while(true) //loops forever
Edoes is take
Band passes it
Xfor both arguments. Program
Ewill get back from
false. If it receives back
trueit will enter an infinite loop and if it receives back
falseit will terminate.
Band feed it
Efor both arguments. What answer will
B(E,E)give? Think about it.
E(E)which will then run the program
B(E,E). The answer to
B(E,E)will either be either true or false. If the result is
Eactually returns true and halts immediately; if the result is
Haltingthinks our program does halt, but the program
Ethrows itself into a loop upon this condition and will never halt. Either way program
Ewas written very craftily to break
Bon purpose, but nonetheless the damage is done.
Ecannot be made reliable even in principle. It matters not how clever you are and or how powerful your computer is. There is simply no reliable computer program that can determine whether another program halts on an arbitrary input. The incompleteness problem may have seemed a little bit distant and philosophical, but if you have read this far it should be evident that the halting problem has deep implications computing.