Back in the 1920s Hubble did photographic surveys of the sky with long exposures. Here is what he found. Pick a random spot in the sky. Take a long exposure. Count the stars you can see. Take a magnifying glass. Count the galaxies you can find. With a few obvious exceptions, there will be more galaxies than stars. A lot more. (Obvious exceptions would include things like nebulae that you can't see through to see galaxies behind them.)
Every light there is a galaxy (okay Like and 7 stars).
I remember seeing that photo when it came out and sort of brushing it off because it wasn't some sweeping nebula. Four years of an astrophysics degree later it nearly brought me to tears just thinking about looking at 10000 galaxies and the full weight of that sight. It's one of those things thats more powerful the more you understand it.
Yeah... it kind of blows my mind.
"Well, I have to live forever now."
If I can display a picture of a car on this monitor, then that picture would eventually also show up 'by chance' with my program! Mind blown. Then I realized it would have to show every picture in the world eventually, because every picture in the world could be displayed on my monitor. Mind blown again. Then I realized it would display every book in the world also, because a picture of a page of text is just another picture. Whoa. Then I realized the monitor would also eventually display all things that happened in the past that we had no records of and everything that was going to happen in the future!
Of course I couldn't grasp exactly how long the program was going to take, but I realized that if it had to go through infinitely many pictures it would have to take infinitely long to run.
But now I can do the real math. Should be fun:
Display 60 frames per second. 3600 seconds in an hour, 85000 in a day, 31 million seconds in a year. So 1860 million images per year.
How many possible pictures are there?
640 x 480 x 16 bits = 0.5 MB frame buffer. Kilobyte is 10 bits, megabyte is 20 bits. So there are 2 ^ 20 bits and each bit we have to toggle so there are 2 ^ (2 ^ 20) combinations.
1860 million combinations ~ 30 bits. Since we have 2 ^ 20 bits worth of statespace those 30 bits are completely insignificant. So let's assume there are a billion people with a billion computers each who work on the problem in parallel. Then there are 2 ^ (30 * 3) = 2 ^ 100 images processed each year. This still doesn't make any difference! 2 ^ 30 - 100 bits = 2 ^ 30 bits.
It would take over 10 ^ 300000 years for a billion people with a billion computers each that process 60 frames per second to enumerate the different values of a 640 x 480 monitor.
And that's just for a single megabyte. Mind blown.
Other implications:
1. Knowledge is finite(a big number but finite, only 10^100 atoms in the universe so even if your screen was big as the universe there is only so much it could show)
2. Solving a problem can be interpreted as a search through linear space of all possible permutation. So, lets say that the drug to cure cancer could be in the form of an equation, it would show up on the screen eventually.
3. Oh, if there is a God, his pic will eventually come up on your computer.
Other Top contenders for me are: 1. Zeno's Paradox - http://en.wikipedia.org/wiki/Zeno%27s_paradoxes
2. Birthday Paradox - http://en.wikipedia.org/wiki/Birthday_Paradox
3. Twin's Paradox- http://en.wikipedia.org/wiki/Twin_paradox
4. Monty Hall Problem - http://en.wikipedia.org/wiki/Monty_hall_problem
5. Stanford Prison Experiment - http://en.wikipedia.org/wiki/Stanford_prison
6. Asch Conformity Experiment - http://en.wikipedia.org/wiki/Asch_conformity_experiments
7. Milgram Experiment on obedience to authority figures - http://en.wikipedia.org/wiki/Milgram_experiment
8. Placebo and Nocebo - http://en.wikipedia.org/wiki/Nocebo
9. Godel's Incompleteness Theorems - http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...
It may not be the most mind-blowing fact I've heard in my life, but it's one of my favorites. It shows how much a good story can change perceptions.
(Yes it takes much longer for a new tree to grow to replace a chopped down one, but still. It's much more renewable than gold.)
The fact that we're all akin to lumbering flesh robots designed to help our genetic material persist. That was kind of humbling.
http://www.amazon.com/Selfish-Gene-Anniversary----Introducti...
anyway, the ages were only there because I hadn't seen anyone referencing anything other than facts they heard recently. in reality nothing you've heard recently could be as earth shattering as the facts you learn when you're a kid that pull the veneer off your rosy fantasy world.
Close runner-up: There are zillions of slightly different versions of me. http://arxiv.org/PS_cache/astro-ph/pdf/0302/0302131v1.pdf
Third place: There are only around one and a half thousand people signed up for cryonics worldwide.
This is a lot more surprising once you learn that because you can pay for cryonics with your life insurance, it literally costs only a few bucks a month.
If walking was simply graceful falling, it would imply that once we begin the process of "falling" onto the next foot, we couldn't significantly affect the outcome. However, because I can start walking and then stop with a single leg half way between it's highest point and the ground, this explanation of walking as falling becomes very problematic.
Now it appears to be a [self] post.
Charles Petzold's "Annotated Turing" has a great run down of this and a bunch of the other mind-blowing things that came out of math in the late 19th/early 20th centuries.
OK how about the Axiom of Choice?
Another one: Assuming peak efficiency, the turbines in the Grand Coulee Dam generates 1 gram of heat and light every 3.7 hours. All that water for one measly gram of something! Source: http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
What naturally followed was the realization that there are an infinite amount of things not yet solved or understood and I have the power to try to discover any bit of it.
It seems a pretty obvious statement, but it took me 24 years to really became aware. Now I know how important is to meditate on a daily basis.
You can set up a cipher where anyone can write you messages using publicly available information, but only you can read them.
Human DNA is essentially a digital code, has a finite number of bits, and is smaller than data sets which we routinely manipulate today.
Every known way of making meaningful computations can be represented in a formal system which you can write down on the palm of your hand.
You can also write a recipe for producing the entirety of an infinitely detailed image, that keeps being visually interesting as you zoom in, on the palm of your hand.
Instead, it can be said that human genome can be represented by a digital code, which has finite number of bits.
e^iπ + 1 = 0
* the ratio between the a circle's circumference and diameter
* the number such that the derivative of e^x = e^x
* the square root of negative 1
Have anything to relate them to one another?? That last one isn't even a number!Mind. Blown. The universe is one crazy place.
o, and another cool one is (1/2)! = sqrt(pi)
(http://www.sffworld.com/authors/s/stephenson_neal/excerpts/c..., bottom of page)
1) Cleopatra lived closer in time to the moon landings, than the building of the pyramids.
2) The Comparison of Moores Law to A Series paper at the start of this talk: http://www.w3.org/2005/Talks/11-steven-ac-declarative/
1. Benford's Law - http://en.wikipedia.org/wiki/Benfords_law
2. Two envelopes problem - http://en.wikipedia.org/wiki/Two_envelopes_problem
* I bumped into a girl that I went to South Eugene High School with at the train station here in Padova, Italy. We were even on the same train. I was quite literally speechless for a moment or two.
* I worked with a person in San Francisco whose dad had known my dad and uncle in the same small town in Montana.
Utterly freaked out I contacted her via IM, not having actually known how to do that and not having spoken to her for a very long time and verified that it was indeed her ip address and she was indeed at that computer, but she had absolutely no idea how I had managed to ascertain that fact and was about as freaked out as I was by the episode.
We talked for many hours before it finally dawned on me exactly what had happened.
On the exact day that I had been checking firewall rules on my laptop with kernel packet logging enabled, at the exact second that I had accidentally alt tabbed to a terminal window that was tailing said packet log, she had done a search on napster for a song that I happened to have.
This is very much the weirdest coincidence I've ever experienced in my life thus far.
http://www.almaden.ibm.com/vis/stm/images/stm15.jpg
Watching an Open University TV programme about James Lovelock and the Gaia Hypothesis-
http://www.youtube.com/watch?v=5yvQVD7sgn0
Stumbling upon cybernetics and Metasystem Transition theory-
http://pespmc1.vub.ac.be/mstt.html
The first time watching each of The Matrix films and picking it apart in realtime, and yes, the ending of Revolutions is a Metasystem transition.
Lots of synchronicity in my life, a few examples, when I first heard about tuple spaces and Linda, and pulling out Mirror Worlds by Gelernter from my bookshelf as I had bought it a couple of years before and not read it yet, then again that has happened a few times since, the last time was when I was getting interested in classification and found I had Sorting Things Out by Bowker and Star, I keep buying books I don't know I'll need, until that time in the future that I do. Someone else mentioned the Asch conformity experiments, which I came across on YouTube and then within the week I was reading the book Poker Without Cards and the experiments were mentioned in the book, even though I hade no idea before hand, there were other instances of synchronicity with that book, but I don't want this post to end up as tr;dr.
http://www.thefanatics.com/content.php?id=330
And, of course, ex-Prime Minister Bob Hawke made it into the Guinness Book of World Records for drinking 1.7 L of beer in 11 seconds in 1953:
This really blew my mind when I was six.
Many-worlds interpretation:
Many-worlds is a postulate of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the reality of wavefunction collapse, which implies that all possible alternative histories and futures are real —each representing an actual "world" (or "universe"). It is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many worlds.
Many-worlds claims to reconcile how we can perceive non-deterministic events, such as the random decay of a radioactive atom, with the deterministic equations of quantum physics. Prior to many-worlds, reality had been viewed as a single unfolding history. Many-worlds, rather, views reality as a many-branched tree, wherein every possible quantum outcome is realised.
It is Anathem by Neal Stephenson.
Great book. Like most Stephenson books it gets a little weird at the end but is nonetheless well worth reading.
He showed me how small our sun is by showing me the tip of his cigarette and comparing it to the top of his coffee cup i.e. the size of larger stars in the universe.
I was about six years old and the universe suddenly became a drastically larger place.
http://chalkboard.blogs.gainesville.com/2010/10/candidate-lo...
[1]http://www.reddit.com/r/AskReddit/comments/dlrjs/whats_the_m...
However, in the 7th grade (age 13-14), my math teacher explained to me that education was a "privilege, not a punishment". I don't remember how it changed my thought processes, but I remember the moment. Previously, I was what you might call a "slacker". After that, I was "nerd slacker" - at least I paid attention, even if I was still lazy.
A decade late, I graduated university with a degree in Mathematics and went into software engineering. Smart + lazy = good software.
1. The volume of water and air on Earth, compared to the Earth:
http://www.sciencephoto.com/images/download_lo_res.html?id=6...
2. The relative sizes of Earth, Sun and the biggest known stars, and the fact that a passenger airplane would take 11,000 years to circle the biggest known star:
"study of inherited changes in phenotype (appearance) or gene expression caused by mechanisms other than changes in the underlying DNA sequence"
http://en.wikipedia.org/wiki/Bells_Theorem
(This article is quite complex; there was a superb article in Scientific American that described Bell's experiments and conclusions simply and clearly; it's here:
http://www.scientificamerican.com/article.cfm?id=was-einstei...
but unfortunately it's behind a paywall).
*Hydrogen, helium and a bit of lithium aside.
1: The farther out in space you look, the farther back in time you are seeing. If you could look back all the way to the big bang, you would be looking (billions of miles away) at the inside of a universe about the size of a grape fruit (or whenever super-inflation was supposed to start).
2. You cannot move. In order to move between A and B, you must first move half way between the two. etc.
3. Some people "invest" in the lotto.
It is the same as "you cannot arrive", except in reverse. Or that "you cannot rotate one of two parallel lines", because the jump from parallel to intersecting is elusive.
Do they really believe them then? Is there any reason not to say that a belief, by definition, is something (among other things) that you act logically consistently with.
ie. You can make statistics say almost anything you want.
68% said that too much was spent on foreign aid, 59% said they thought it should be cut.
Thus 9% think foreign aid is too high but shouldn't be cut. It isnt so much this specific example, but i bet pollsters get this kind of thing all the time, which i find fascinating.
Bonus points if you know where its from.
I think the issue with your presentation is that 'cut' can mean either 'reduced' or 'eliminated'.
http://www.tvloop.com/the-west-wing/show/quotes/joshua-lyman...
It was really enlightening to fiddle with the constants and to create events that show how kinetic and potential energy interact in space.
It was obviously wrong, because some planes can fly upside down, and that was when I realized that just because an adult speaks with authority about something they believe to be true doesn't mean it is true.
- E=mc2
- Genocide in Darfur http://en.wikipedia.org/wiki/War_in_Darfur and
- Wealth controlled by top 1 percent of population in US http://www.slate.com/id/2268872/
http://www.tvkim.com/watch/357/kims-picks-mute-autistic-girl...
Oh also that "Monopoly" is an American invention (I assumed it was as British as the Queen).
ps. still have high expectations, just not suffering.
It still blows my mind.
d/dx (e^x) = e^x
lame.
With the link we're ostensibly talking about them, without it we're reduced to their level, and just having the same adolescent discussion again. Editing out the link makes HN more like reddit.
(2) While there are millions of species on Earth that have long been stable and successful and still are, humans have by some astronomically wide margin the most powerful capabilities with, again, no alternative, no second choice, no runner up.
(3) For all we have done with working with information, computing, human physiology and psychology, we still have hardly a weak little hollow hint of a tiny clue how to program a computer to be as smart as a human, dog, kitty cat, dolphin, or ... many more.
(4) On the one hand, humans, both individually and collectively, commonly make serious, disastrous mistakes for even just silly reasons. On the other hand, humans have made shockingly good progress even at understanding the universe. How could the same species have both such big disasters and bit successes?
(5) As we try to understand the universe in greater detail, we get in effect 'throttled': We can't go faster than the speed of light; we can't look in detail at a scale much smaller than an atom; we can't have energy enough to explore all the possible particles. In each case, we are throttled, and essentially blocked, not by hard barriers but just by increasing costs.
(6) As mentioned by others, the Einstein, Podolsky, Rosen (EPR) spooky action at a distance paradox.
(7) There is a naughty boy in his room with his relatively large computer. He types in candidate laws of physics and then clicks on the button Big Bang. Mostly all he gets is a fast poof but occasionally he gets something interesting. How do we tell our universe from something in this boy's computer? More generally, how are the laws of physics enforced?
(7) Suppose n is a positive integer, R is the set of real numbers, R^n is Euclidean n-dimensional space, and C is a closed subset of R^n. Then there exists a function f: R^n --> R so that f is zero on C, positive otherwise, and infinitely differentiable.
It is fair to say that the Mandelbrot set is bizarre, but it is a closed subset of R^2. So, the Mandelbrot set is the level set of an infinitely differentiable function. So, a very smooth function can have a bizarre level set.
Also, the graph in the plane of one dimensional Brownian motion is closed and almost surely differentiable nowhere. So, a curve differentiable nowhere can be the level set of an infinitely differentiable function.
So, could have a landscape given by an infinitely differentiable function, in a valley pour in water, form a lake, and, as in Mandelbrot, have the boundary of the lake be as irregular as the Mandelbrot set or Brownian motion. So, a very smooth landscape can have lakes with very irregular boundaries.
You are spot on about #4. The more we learn about our world, the more creative ways we come up with to destroy it.
It's so gross on so many levels. I don't recall where I read it, and I hope it's false.
The several state legislatures ratified the Sixteenth Amendment on the following dates: Alabama, August 10, 1909; Kentucky, February 8, 1910; South Carolina, February 19, 1910; Illinois, March 1, 1910; Mississippi, March 7, 1910; Oklahoma, March 10, 1910; Maryland, April 8, 1910; Georgia, August 3, 1910; Texas, August 16, 1910; Ohio, January 19, 1911; Idaho, January 20, 1911; Oregon, January 23, 1911; Washington, January 26, 1911; Montana, January 27, 1911; Indiana, January 30, 1911; California, January 31, 1911; Nevada, January 31, 1911; South Dakota, February 1, 1911; Nebraska, February 9, 1911; North Carolina, February 11, 1911; Colorado, February 15, 1911; North Dakota, February 17, 1911; Michigan, February 23, 1911; Iowa, February 24, 1911; Kansas, March 2, 1911; Missouri, March 16, 1911; Maine, March 31, 1911; Tennessee, April 7, 1911; Arkansas, April 22, 1911 (after having rejected the amendment at the session begun January 9, 1911); Wisconsin, May 16, 1911; New York, July 12, 1911; Arizona, April 3, 1912; Minnesota, June 11, 1912; Louisiana, June 28, 1912; West Virginia, January 31, 1913; Delaware, February 3, 1913; Wyoming, February 3, 1913; New Mexico, February 3, 1913; New Jersey, February 4, 1913; Vermont, February 19, 1913; Massachusetts, March 4, 1913; New Hampshire, March 7, 1913 (after having rejected the amendment on March 2, 1911). The amendment was rejected (and not subsequently ratified) by Connecticut, Rhode Island, and Utah.