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.
I find it comforting. You look at that photo and all of a sudden your stupid problems and worries seem laughingly insignificant. It's better than religion.
It's like the total perspective vortex but some how completely backward. I remember explaining it as much as possible to my brother; he looked at it for a bit stopped and said
When I was nine I was playing with BASIC and wrote a simple program that would enumerate all colors of all pixels on the screen. I wanted to see all possible images "fly by" so to speak. First I got frustrated because it was running so slowly, only then I started to think...
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.
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.
Damn. I watched a short film very similar to this where a mathematician woman made a super computer in her home to do the same thing. It pissed off her husband who finally takes off and she's left with her obsession. Can't remember the name.
The top for me would be boltzmann brains - http://en.wikipedia.org/wiki/Boltzmann_brain
Better to read the wiki article, since I might not do it justice. A self conscious being might pop into existence based on random fluctuation.
besides "you and everyone you know are going to die" at age 3, or "there is no santa claus" which logically led to "God is an imaginary friend for grown ups" at age 10.
The fact that we're all akin to lumbering flesh robots designed to help our genetic material persist. That was kind of humbling.
I considered the stories of Santa Clause and God to be pretty mind-blowing when they were presented as fact. So the realization that both were made up was kind of a return to sanity.
the santa claus/god realization could have been like 12 or 13, I don't remember exactly when I was told there was no santa, I'm estimating. I know I was three with the death thing, my parents remember me crying myself to sleep repeatedly moaning about it. of course they could be mistaken.
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.
"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.
I remember clearly in elementary school when I suddenly understood that gravity is just a constant acceleration; if I were in a box in space accelerating at 9.8 m/s^2, it would feel exactly the same. For some reason, I found that absolutely mindblowing at the time. I spent all day trying to explain it to everyone else, and I don't think I've ever been so excited about knowing something again.
Do you also find it weird to think about how without gravity we couldn't walk? That one gets me especially hard because it's a such a tangible example of how we've evolved to take advantage of laws of the laws of physics, and how if these laws were even slightly different then we wouldn't be here, or at least not the same as we're here now.
The first day of a robotics class, my teacher explained that we don't really walk. Each step is graceful falling. Place one foot forward, tilt and fall till the foot hits and repeat.
I hate to be the one to break to this to you, but your robotics teacher was off his or her rocker or was trying to make a much larger point with a bad example.
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.
I'm not sure if this is the most, but Cantor's Diagonal Argument[1] is the first that comes to mind, probably even more as an example of a creative approach than for its implications (although those are pretty huge too).
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.
Everything that makes up my physical body has existed and always will exist, in some form or another. Whoa!
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
"Everything that makes up my physical body has existed and always will exist, in some form or another." The physicist richard feynman in the first lecture of "the feynman lectures on physics" says that the most important fact, that would convey the most information would be the atom hypothesis or fact. Which is essentially what you said except with the additional bit of information that "... all matter is made of indivisible particles that both repel and attract each other depending on the distance between them"
The point when I realized that most things I hear are probably bs and I need to think for myself, regardless of the source.
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.
You can represent any book, any image or any sound with a large number.
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.
Cantor's diagonal argument -- proof that the Real numbers are more infinite than the Integers (or Naturals). Slightly more mind-blowing than the algebraics are no bigger than the naturals.
The second time I read Cryptonomicon, the implications of evolution finally dawned on me -- I have an unbroken line of ancestry stretching back 4 billion years. Most of my ancestors weren't even human...
I'm Italian, born and raise there. I moved here in Florida 5 years ago.
My ex-girlfriend is American, born and raise here.
One day I met her best friend from college (he lives here in Florida as well), and he told me that his father was Italian. When he told me his lastname, I told him that I know people with the same last name from my grandfather's hometown, so I asked him to ask his father where he is from. We ended up finding out that he was from the same place and that he was friend with the only family member (a very far one, my grandfather's cousin) I have here in the States, in Connecticut.
* 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.
I accidentally alt tabbed to a tail of a kernel log where a packet hit the wire at the exact moment that I accidentally alt tabbed. The IP address looked weird to me for some reason so I reverse resolved it and traced it, it belonged to the first ISP I'd ever used, I ran an nmblookup on the machine name and it was my first girlfriend's computer name.
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.
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.
The one that I just read ten minutes ago, that my childhood hero Wade Boggs once drank 64 Miller Lites on a cross-country flight (without dying) has to be up there.
There is the classic story of David Boon (Australian cricketer) logging 52 beers on a flight. I don't think he would've touched anything but full strength:
Parallel Universes, I literally fell of my chair when I heard a scientist telling, "There are infinite versions of our universe, all slightly different".
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.
My uncle was smoking a cigarette and drinking a cup of coffee at the kitchen table near the cookie jar at Grandma's house during Thanksgiving.
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.
For me it is the fact that all life appears to have originated from one common ancestor and that life appeared fairly quickly after the earth formed and that there is an unbroken chain of life between me and that first molecule that replicated and transformed itself using energy from its environment.
A computer and an innovative mind were the only tools necessary to sustain myself economically and make the world a better place. I'm still working on the mind, but the MBP was a good investment towards that end :)
It was pointed out [1] that this thread was the source of a controversy that lead to a Florida law student and political candidate losing his position writing for the student paper:
Hmmm, "heard/read" limits it a bit, as "self realization" is more memorable.
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.
2nd Law of Thermodynamics... Things flow from hot to cold, from simplicity to complexity. It is the only asymmetrical physical law! Does it have anything to do with time? We don't know!
Oh, I must say, someone mentioned Godels Incompleteness Theorem, and this comes pretty close. But I think the 2nd law if you think about it, can explain so much.
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:
That we have all evolved from some very simple single-cellular ancestor that lived billions years ago and everything that happens to us on a biological level is encoded in the DNA.
(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:
Logic paradoxes always did (and still do) blow my mind:
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.
I believe the idea is that the problem of moving is atomic. To move, you must know how to move (assuming the world is not discrete).
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.
What blew my mind was realizing that the amount of energy people put into arguments about "belief in evolution" is far more than the amount of energy put into actual research. (Similar for "belief in creationism" vs actually studying the Bible.) It's apparently very important for everyone to have a strong opinion on a topic that doesn't really matter that much if you're not doing medical or biological research.
It depends how you define "don't believe". They might say they don't believe in evolution, but that doesn't mean they act in ways that are logically congruent with evolution being false.
"Most people don't act in ways that are logically congruent with all their beliefs."
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.
I'm sure there's a word you can define as something that you act logically consistent with, but I think it's closer to the word "motivation" than the word "belief".
If somebody says "evolution is a lie, and it shouldn't be taught to children", the fact that they don't actually live their life according to that credo is sort of irrelevant.
I've no idea if this is true or not (probably not due to where i heard it) but a poll was taken in the US about foreign aid.
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.
I couldn't see how anything could possibly stay in orbit when gravity pulled everything together until I wrote a computer program to simulate orbits in 2d: http://ln-s.net/7oFZ
It was really enlightening to fiddle with the constants and to create events that show how kinetic and potential energy interact in space.
When a primary school teacher told me that planes fly because the faster moving air on top of the wing creates a low pressure zone and sucks up the wing.
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.
1. That humans kill each other because of differing opinions.
2. That I see only my own point of view till I live - at every moment, there are billions of folks who are living a different life and experience.
3. When we gaze at a star, we are gazing into the past.
Most recently I found out that the Russian Salyut 3 space station (whos missions were to take 3" resolution pictures of the US) had a cannon mounted on the bottom of it. Not only was there a machine gun in space, but it was fired too.
For me, when I finally grasped Einstein's theory of special relativity, that was a pretty mind blowing experience. It's not as easy to fully get as you might think but when you do it's an almost zen-like experience.
The almost casual mention in Umberto Eco's 'Foucault's Pendulum' that ancient civilisations had electric lights and batteries. Not sure how well this theory holds up nowadays, but I was pretty amazed...
This doesn't answer you're question, but I'm really impressed that someone was clever enough to invent hash tables. Lagrange interpolation is also something I'm not sure I could have invented.
that fast food hamburgers are only 2.1% to 14.8% Meat (B. Prayson et al. Fast food hamburgers: what are we really eating?, Annals of Diagnostic Pathology 12 (2008) 406–409
about 90% of my misery, unhappiness, frustration in life are due to one word: expectation. Once I understood that my sufferings are caused by unmet expectation of myself and/or others, my sufferings ease.
ps. still have high expectations, just not suffering.
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.
(1) All life on Earth is based on DNA. There is no alternative, no second choice, no runner up.
(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.
While it's debatable whether viruses count as a form of life, RNA viruses do exist. It's also generally believed that there were RNA-based forms of life before the advent of DNA.
You are spot on about #4. The more we learn about our world, the more creative ways we come up with to destroy it.
That 50% of step daughters will have some sort of unwanted sexual relationship with their step fathers. I don't know if this means actual sex or just unwanted advances. Either way is just mind boggling.
It's so gross on so many levels. I don't recall where I read it, and I hope it's false.
That in 1933 the United States declared bankruptcy and has been so ever since. Also, the original 13th amendment of the Constitution was simply deleted and replaced. And the 16th amendment was never ratified.
The Congress shall have power to lay and collect taxes on
incomes, from whatever source derived, without apportionment
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.
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.)