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Find Out About the Future of Science
Science magazine writer Charles Seife has written a new book, Alpha and Omega: The Search for the Beginning and End of the Universe. According to Publishers Weekly, Charles claims, "Scientists...now know how the universe will end and are on the brink of understanding its beginning. Their findings will be among the greatest triumphs of science, even towering above the deciphering of the human genome." A brave statement! Charles is happy to answer your questions about ongoing research that is busily revealing the basic nature of life, the universe, and everything in a serious (as opposed to humorous) sense, so ask away. One question per post, please. We'll post the answers as soon as we get them beck.
do you get embarassed by publishing hype such as "Scientists...now know how the universe will end"?
You're quoted as saying, "Scientists...now know how the universe will end and are on the brink of understanding its beginning. Their findings will be among the greatest triumphs of science, even towering above the deciphering of the human genome." Is it also your belief that the consequences of understanding the beginning of the universe will approach the transformation of living that we're just beginning to see from the deciphering of the genome?
the Universe will end with a cliff hanger to set things up for Universe II
Do not try to read the dupe, thats impossible. Instead, only try to realize the truth
What truth?
There is no dupe
Since we now know how the universe will end, would it be possible to set up some sort of restaurant there?
So... How will the Universe end? Big Crunch, Dark & Cold, Equilibrium, Giant Black Holes, Act of God, or... what?
And, of course, how can you be so sure of that? [Add "You, Insensitive Clod!" to this last question for the humorous touch...]
Whatever theory you build today will only be validated in, what? A dozen billion years? More? So what makes you so sure you know the ned of the Universe today?
Please note: this is really a serious question. I am interested in the End of the Universe as we know it. Thanks for your answers!
The right to offend is far more important than the right not to be offended. (Rowan Atkinson)
Thank you for that pointless comment. You have taken usefull energy and turned it into a slashdot comment, thereby bringing the universe closer to heat death.
Can we explain the expansion of the universe and why the rate is changing? Can we claim to know how the universe will end if we can't answer that?
It's a question I've had for a long time and I sometimes think about it and it freaks me out :) no really. Ok, we "know" (until someone else proves it's wrong) how the universe is going to end. We are about to "know" how it really started. Great! However, when we are talking about the universe... we are assuming that it is infinite. I just have a hard time with this Infinite Universe concept... the universe NEEDS to be contained within something... however, even if we discover the container... it will end up being a part of our definition of universe and then we'll need to search for the container's container. Anyway, any thoughts on that?
Oh god (irony), not this crap again.
Haven't you got anything better to do that to keep 'refining' Creationism whenever in response to Evolution showing it to be unnecessary.
There is NO NEED for intelligent design. It's only purpose is to allow you justify your belief in God. I don't care if it's the Bombadier Beetle, the jinking Moth, whatever, it's just as sensible to think of a way it could've evolved than to allege that there is a God. And a God is a damn big hypothesis that only serves to abstract out the thing you can't explain.
Justin.
Bored of bloody desperate religionists arguing over who's got the best imaginary friend.
You're only jealous cos the little penguins are talking to me.
IAALS.
Since it is something of an open issue, what is the current understanding of the nature of dark matter in our universe? What kinds of questions are still being investigated? What kinds of hypotheses do we have now, and what do they imply?
...only a theory.
Please, before you start arguing about science, try and understand its terminology at least a little.
Whoa there, no need to get nasty. We'll post them questions as soon as we thinks them up. What kind of name is Beck for a dog anyway.
An Indian-American Hindu committed to non-violent thought/speech/action alarmed by the global explosion of radical Islam
Although OOGG caveman, OOGG not around during Big Bang, Pre-Cambrian era, dinosaurs, etc. However, OOGG old enough remember debate on Darwinian evolution.
You mention "continually reexamined in the light of new evidence" yet mention no new evidence. OOGG hear such comments many times. OOGG know Darwin think of many objections, answer with real evidence. Many observations on human breed pigeons, dogs, agriculture, etc., substantiate Darwin argument. Many more observations since Darwin's time substantiate evolutionary ideas. "Intelligent design" provide no observation other than "I don't believe in the alternative."
Perhaps try read Darwin's book?
Theoretical physicists and astronomers don't "know" anything by definition. They guess using the best mathematical and scientific models they have at their disposal.
Science used to "know" the world was flat. They used to "know" that the sun revolved around the earth, and that the human heart worked just like a furnace.
Then, one day, some guy sailed over the horizon and didnt fall off. A pump was invented, and the notion of a heart as a pump came to being.
Each time people had thought they'd reached the pinnacle of understanding, and had all the answers. Then paradigms shifted, and completely changed our ways of thinking, and all our previous answers and theories were null and void.
What makes you so sure that this isnt simply happening again?
I don't need no instructions to know how to rock!!!!
(I realise this work is more than jsut Lee Smolin's, but he wrote the book I read about it a few years ago.)
As I understand it, there is a serious strand of thought in cosmology that suggests that our universe may be only one of (an infinite number of) alternatives. A small finite area in a parent universe undergoes inflation and blows up like a very fast balloon; for observers within this bubble, theirs is the only universe. Smolin also talks about how this hypothesis might tie in with the six magic physical constants which, if their values were even slightly different, would cause totally different physical conditions within our universe. If the inflationary bubbles occur within singularities, they would also be unknowable to their parent universe. A universe with lots of black holes would tend to give rise to offspring that would also have lots of black holes, and vice versa. I'm badly mangling his explanation of this ! but he provides an IMHO elegant explanation for the phenomena of these numbers' values appearing to have been tuned very precisely to the values neccessary for "our" sort of universe, and hence, life, and ultimately us and any other observers out there.
What's your opinion of this? It seems to me that this hypothesis makes no testable predictions and so falls beyond the remit of the scientific method. Is it just a smart way of talking around the anthropic principle, or might this be one of the key concepts to help tie up the loose ends in the standard model?
"None are more hopelessly enslaved than those who falsely believe they are free." -- Goethe
I will pay out 10 to 1 odds upon end of the universe that it ends in a different fashion they they propose. Please send me any amount of money and if I am wrong I will immediately pay out all winners upon destruction of everything.
Worst. Sig. Ever.
Intelligent Design, a recent theory that has gained enough respect from the scientific community
Woah, stop right there.
It's proponents claim that it has respect in the scientific community. You will find scientists who like the idea. But the fact is, so far as peer review and confirming experiments and the general scientific community, it is not considered really a viable theory. It's certainly not any competition for evolution amonst the sceintific community at all.
The proponents' PR claims it is, but that's just the PR.
See, for example, http://www.phys.cwru.edu/~krauss/inteloped.html.
-Rob
It's well known that our view of the world around us was radically changed by Einstein, Heisenberg, and other scientists of their day. Einstein gave us relativity, and Heisenberg ushered in quantum mechanics (of course Einstein and his explanation of the photo-electric effect). Both of these thoeries led to radical departures from well established theories. However, there were, at the time, known physical effects that could not be explained by then current theories, i.e. the above mentioned photo-electric effect, blackbody radiation, Michelson's measurement of the speed of light, etc. etc. that make it clear in hindsight that the a profound shift in understanding was required.
My question is what, if any then, are the areas where we need similar paradigm shifts to answer current outstanding questions? It seems to me, at least, that maybe there aren't any, and today's scientists are left working harder and harder simply to add a few significant digits to existing theories. What are your thoughts?
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As we all know, market forces are omniscient and omnivident. The market suffereth long, and is kind; the market envieth not; the market vaunteth not itself, is not puffed up.
So, what we need is an online futures market in which cosmologists could put their money where their mouth is.
You say the universe will collapse in a big splat in 20 billion years? Fine, bet on it. 20 billion years if the universe hasn't collapsed, you'd better pay off. 20 billion years' worth of interest should make you think carefully before mouthing off!
You say there's a parallel universe nearby? OK, plunk down your money. If there is one, you win. (And your counterpart in the parallel universe, of course, loses. What point is there in parallel universes unless we can transfer money between them?)
An asteroid might slam into the Earth a year from now, destroying all human life, but if you manage to pick the exact day it happens, you could be rich!
"How to Do Nothing," kids activities, back in print!
I read the whitepaper presented, and it has some difficulties:
1. It suggests the variables necessary for life as we know it. While life on Earth is incredibly varied, it isn't the end-all-be-all. Perhaps fundamentally different life could exist in different conditions, ranging from the mass of a neutrino to the spectral-jibber-jabber constant.
2. It doesn't present ranges for the variables. It does give "if higher/lower/more/fewer" qualitative statements, but not quantative. What if a variable was increased by 1%? 10%? 100%? What is the range for those variables to preserve current life-abling conditions?
I think most scientists would concur that the probability of life as we know it is almost certainly zero*. And yet, we have life, as we know it. If a variable was fudged in the past, we surely wouldn't have life as we know it, but that is not the same analysis as not having life at all.
* math for really, really, really freakin' close to zero. A finite number of instances of life given an infinite number of chances.
Support a few technologists in Washington.
Possible scenarios include:
This fell out of favour a while back, when the need for a flat universe became apparent. In this scenario, the universe's espansion halts and it re-collapses. Once it was thought that this would involve time running backwards/entropy reversal during the crunch phase, but it was later shown that scenarios with increasing entropy also existed. There was much speculation about whether the universe would "bounce" after it crunched, forming a new expanding universe.
This scenario was popular when we'd made a detailed enough survey to know that that amount of bright matter in the universe was far too low to counteract the expansion. It fell out of favour when our estimates of the amount of dark matter got better.
In this scenario, the universe keeps expanding quickly, and all matter that isn't gravitationally bound into clusters is separated by vast empty regions of space. As the universe's expansion represents the expansion of space itself, sufficiently large gravitationally bound clusters might still be disrupted, due to distances changing internally. Galaxies burn out as stars exhaust their fuel, stellar corpses eventually merge with each other and with the central black hole, which finally decays after a mind-bogglingly huge length of time.
This scenario assumes that the amount of matter - light and dark - is perfectly balanced with the expansion of the universe. There was strong circumstantial evidence for a scenario like this, due to the fact that deviations from flatness amplify over time and that our universe was still _roughly_ flat - but the linchpin was a variety of models for the early universe - and the big bang - that required the universe to be flat. More detailed measurements of the amount of dark matter in the universe seemed to be consistent with this model.
In this scenario, the rate of expansion slows, approaching zero as time goes to infinity. Distance still goes to infinity as time goes to infinity, but not as rapidly. From a local point of view this looks a lot like Whimper Version 1.
This model arose when evidence for dark energy was discovered by observations of distant parts of the universe. In this model, the universe started out as flat, but a weak repulsive effect comes into play that causes expansion to accelerate. The effect is small enough that we haven't diverged that greatly from flatness yet, but in the end, it'll be Whimper Version 1 all over again. This is one of the two currently plausible scenarios.
This model was the result of closer examination of the scalar field models used to drive inflation in the early universe. In the inflationary model - which itself was proposed to solve the problem of the universe's matter distribution being so smooth - a "scalar field" existed in the early universe that permeated space and caused vast amounts of new space to be created. In the original version of the inflationary model, this scalar field's effects died out shortly after the big bang. A later model, however, proposed that the field was not cancelled everywhere - in some regions of the universe, constructive interference would cause it to be strong enough for inflation to continue.
Thus, we have a model where the universe looks mostly like our own, except for regions where it "buds" to form new universes. This process continues forever. This is the second scenario currently considered plausible (with the scalar field taking on the role of "dark energy").
This is the model proposed by
As a layperson with an interest in cosmology and physics, I seem to hear about an increasing number of hacks to the Standard Model. By hacks I mean things like dark energy, whose value apparently fluctuates over (cosmological) timescales; there's another idea that the speed of light(I think?) ha varied over time, and that this is the only way to explain the cepheid data (supernovae of known brightness) as we get to see supernovae from further and further away (which occured further and further back in time of course.)
Isn't the use of ugly hacks to prop up an established theory in the face of contradictory observations an indicator of a theory which needs to be chucked out en masse and reformulated in the light of a more fundamental description of physics?
"None are more hopelessly enslaved than those who falsely believe they are free." -- Goethe
Do you think the evidence that the expansion of the universe is accelerating is concrete? And, what effect do you think this conclusion should/will have on humans?
There are two points to be made here, methinks: /now/ how the universe started and will end, but in a lot of the details - and possible the final outcomes - they're almost certainly wrong. A few short years ago we know exactly how Jupiter was formed; then Galileo dropped a probe into the atmosphere, and suddenly more questions arose. Now no-one knows why its atmosphere or its winds are the way they are. Science is littered with such examples; particularly cosmology. How recently is it that we didn't even know gamma ray bursts existed? There'll always be stuff we haven't accounted for, so theories will always be based on incomplete data.
1. Scientists may know
Which brings me nicely to point two: supposing our Brainiacs are right? That's hardly the mystery taken out of everything; questions abound, and always will. Maybe when we're all in our Vorlon-like encounter suits we'll have a decent understanding of the part of the universe that we can see; before then, there'll always be questions.
Is this universe actually capable of creating true near-infinite randomness, or are all the sources fundamentally affected by characteristics relating to the beginning (and/or end) and basic properties underlying them?
ObDisclosure: yes, I am a Christian. No, I am not an Intelligent Design or Creation Science advocate. I object to both ID and CS on theological grounds rather than scientific ones, for reasons I hope will be clear.
There is NO NEED for intelligent design.
On the contrary: if there was no need for the idea of intelligent design (note that I didn't call it a theory), nobody would've come up with it. It's pretty well-understood that there are a large number of fundamental constants which are balanced just perfectly to allow complex systems to arise in the Universe. This creates a question: how did this perfect balance come to be? Some people feel the need to have an answer, and for these people, ID fills a genuine need.
On the other hand, ID isn't science. Science is concerned with empirical observations and testable hypotheses. You can't empirically test God. Theologically speaking, we can't test God because he exists on such a level beyond us that we can't conceive of a test. (There are many other theological problems with testing God, but leave those alone for now.) And scientifically speaking, God defies all attempts at making testable hypotheses. So either way, you're screwed by introducing ID into a scientific curriculum. If you want to believe in ID, great; just please don't call it science.
Interestingly, the Catholic Church doesn't believe in ID except in a very abstract way. The Catholic Church has, amazingly enough, learned from Galileo and Copernicus and all the rest. Many times in the past the Church said such-and-such a physical phenomenon is the direct handiwork of God, only to have it shown that it's not God's direct handiwork anyway. At that point, what do you do? Redefine God so that "well, God's still directly handling the other things, just not that"? And what happens when natural processes are discovered for the other things?
The Catholic Church has become so cognizant of this that they've assigned it a name: the God Of The Gaps. If every unexplainable instance is attributed to God, the Catholic theology goes, then whenever a previously unexplainable instance is discovered to have an explanation, God's glory is diminished by the explaining.
ID is a God Of The Gaps argument. We don't understand how the finely-balanced nature of the cosmos is possible, therefore God must have done it... well, what happens if/when we discover there's a natural phenomenon behind it?
Re: why I object to ID and CS on theological grounds instead of scientific ones... ID and CS are both theological models of the world. As such, they can't be refuted with science. They stand entirely apart from it.
The existence of God cannot be disproven scientifically. As long as something cannot be disproven, it is a valid theory.
Err... if a theory is not falsifiable, it is certainly not a useful theory, scientifically speaking.
And if, as you assert, the existence of God cannot be disproven scientifically, then God is not a topic of science. So....
What I am trying to say is that you can believe what you want, but don't force it on others. Eliminating Intelligent Design, or whatever you want to call it, from school curriculum amounts to nothing more than censorship, just like eliminating evolution.
You can keep intelligent design in your curriculum. But it should be a part of a religion or comparative world faiths class, not a part of a science class, because it is not science. It is wrong to claim that it is, and it is dogmatic interference to insist that it be taught as such.
-Rob
I read last week that it IS possible for this really be a two-dimensional "holographic" universe with time added. Then, just a couple of days ago, I read of Mr Lynd, the young Australian thinker(maybe Einstein calibre?) who now proposes there is no basis for time being a physical fact. This leads me to envision, and PLEASE correct me if I'm wrong, a simple two dimensional universe, WITHOUT time, "holographically" projected as our universe. That brings us to the proposition we MAY actually be "shadows in the mind of God"? Was the beginning of the universe possible given such parameters, and once "GOD" stops thinking about us will we just disappear(the END of the Cosmic Movie?). Or is this line of reasoning COMPLETELY out of line? Thanks for any comments in advance? Bruce
Bruce
Assuming that scientists do answer the questions "How did the universe begin?" and "How will it end?", what are the implications for your life personally, and in your judgement for society as a whole? Final proof of such answers could have profound moral and sociological effect. For example, much of science is dedicated to these topics today- once the answers are set, what is tommorrow's "next big question"? On a personal level, how would you change if you knew for sure the answer to these questions? Would you see other people differently?
There have been some recent experiments, mostly spearheaded by Roger Nelson of the Princeton Global Consciousness Project, that show a correlation between human consciousness and quantum events. Some have speculated that consciousness may lay outside of what we know about physics.
Do you think there will be any fruitful (i.e., predictive) experimentation in this matter? Could we someday develop a theory that will unite physics and consciousness?
Genocide Man -- Life is funny. Death is funnier. Mass murder can be hilarious.
I am a physics graduate student in theoretical cosmology and these types of claims irritate me. Sure, after WMAP measurements of the CMB combined with Lyman break galaxy data we have determined the cosmological parameters today such as lamda, omega_matter, sigma8, but we are far from understanding how the universe will end. For example, the dark energy (lambda) is what is forcing the expansion of the universe at present, but we don't know what the nature of the field driving the expansion is or even if it is constant or accelerating (quintessence theory).
Even when we understand the dark energy it can not be hailed as a triumph above all other discoveries, because we don't know how galaxies form? How massive (primordial?) black holes at the centers of galaxies form? What re-ionized the universe? How even a single star forms?
Unfortunately, this is also a view held by many older astronomers and physicists in academia, because they have pushed so hard for so long for the values of these fundamental parameters.
None the less, the book looks interesting. I always enjoy books about science and scientists. My question for Chris Seife, which is related to his phenomenal statement, is: As a science writer, do you attempt to explain the hard science to people and if so do you feel it is important for scientist to try and explain their work to the public, or is it better to skip the details and just show them pretty pictures and cool stories? We all know that's what gets science funded.
Censorship rests on the child's delusion that "If I shut my eyes so I can't see it, it isn't there".
From the HyperDictionary: scientific theory - a theory that explains scientific observations; "scientific theories must be falsifiable"
Proponents of ID and other some such notions love to brutally abuse the term theory to confuse the issues. For something to rise to the accepted level of theory, it must be based on scientific observations. It must have passed through the hypothesis stage of initial concept deliniation. It must be tested repeatedly, succeeding each time (or the initial hypothesis must be reworked). It has to pass peer review.
ID and other notions don't even rise to the level of hypothesis.
> Intelligent Design, a recent theory that has gained enough respect from the scientific community
ID has no respect in the scientific community whatsoever. (If it did, Dembski wouldn't be making up paranoid conspiracy theories to explain why it doesn't.)
> that it is being taught alongside evolution in many schools and colleges
A number of creationist pressure groups have tried to get it adopted by state school boards, but AFAIK they haven't actually succeeded anywhere.
Which is all for the best, since if you ask an ID advocate what should go in their lesson plan all you'll get is a blank look. All the political noise the ID movement has stirred up over the past few years is based on nothing more than a couple of easily refuted arguments that evolution must have had some help somewhere along the way.
> explains that to even reach the stage at which we exist there are no fewer than twenty-six variables necessary for our universe to even consider permitting life and a further sixty-six within our galaxy and Earth itself that allowed the multitude of living beings not only to come into being but to flourish
Those aren't findings of the ID movement; they're arguments that the ID movement appeals to. (Showing, in passing, that ID is nothing more than the old fine-tuning argument painted up with a fresh layer of pseudo-science.)
> (this whitepaper that was in My Favorites breaks these criteria into probabilities -- great read if you prefer to see the evidence of this hypothesis)
Probability arguments are what creationists use to deny that something has happened. (Scientists also acknowledge that the universe is a very improbable place, or would be if all configurations of matter and energy were equally probable, but from that recognition they part with creationists by investigating the causes of the observed non-randomness rather than invoking armchair arguments to deny causes.)
> Some perhaps are content with chaos theory, but I'm glad there's another scientific viewpoint that can rationalize the concept that free will is the only variable that yet seems unaccounted for
The existence of free will hasn't even been demonstrated; it's small wonder that it hasn't been accounted for.
>
No, it isn't even a theory. It's speculation unconstrained by any evidence.
> So I'm glad that there are still some minds out there, like Copernicus and Einstein, that are not satisfied with science by rote, and I think that if we allow ourselves break out of the current dominant paradigms for just a little bit the change in perspective can open many new insights.
Hope you were just trolling. That would be a good trollpost, but a pathetic serious post.
Sheesh, evil *and* a jerk. -- Jade
> Yes, so-called "Intelligent Design" is inherently a religious concept. So what? How does that invalidate it? The existence of God cannot be disproven scientifically. As long as something cannot be disproven, it is a valid theory.
The fact that it can't be disproven shows its worthlessness as a theory. There is no conceivable observation that isn't compatible with 'goddidit', which makes 'goddidit' completely useless as an explanation for anything.
[Snip fantasia on Genesis I]
> For having been written thousands of years ago by a man (Moses) who knew nothing about science, it seems pretty close to me.
Regardless who wrote it and when, it sounds pretty wrong to me.
> I understand why some people refuse to believe in a God. It takes a very open mind to believe in something you have no evidence of.
Alas, it takes an open mind to believe in things we do have evidence of, such as the big bang and biological evolution.
And if you're so keen on believing stuff without any supporting evidence, why don't you believe in all the other gods and unicorns that people have professed throughout the ages? You're merely engaging in special pleading.
> Eliminating Intelligent Design, or whatever you want to call it, from school curriculum amounts to nothing more than censorship, just like eliminating evolution.
No, omitting ID is just like omitting other pseudosciences based on bad arguments.
Sheesh, evil *and* a jerk. -- Jade
Like, what made the big bang happen?
God?
Oh, who made God?
SuperGod?
Who made SuperGod?
SuperDuperGod?
Who made SuperDuperGod?
Meanwhile, 500 billion light years away, another universe is big banging its way in our own universe but past the edge of our own big bang. Aliens from that universe will never see us and we will never see them, even though we are arranged in a convenient diagnonal, if viewed 20 trillion light years from above.
This is my sig.
No one can disprove God's existence.
I can't disprove the existence of Leprechauns either, but that doesn't mean I go looking for gold at the end of a rainbow.
The unending search for truth through science is a humanistic attempt to place one's self above God and finally be "free" from Him.
That's an awfully general statment there. If what you mean is that revealed religion is the only access to "God", then which one are you talking about.
In order for someone to disprove God's existence they would have to be omniscient and omnipresent.
Why ? Deists have produced some interesting "proofs" of a "Greatest Conceivable Being" (google it yourself) but these have nothing to do with disproof. BTW the GCB may have nothing to do with the "God" of the 1611 KJV.
It sounds like you resent science. Scientists typically are not trying to prove, or disprove the existence of god, God or the GCB. They work only by what can be observed. And you are correct, scientists are neither omniscient, omnipotent, nor omnipresent; if those qualities are required you must go to someone who claims to have a revelation from a being that is. Who would that be Moses ? Mohammed ? Jesus ? Siddhartha ? Zarathushtra ?
-- Rich
Free your mind and your Ass will follow -- George Clinton
A few quick replies... overall, I'd urge you to try moving towards the attitude of the parent post to yours a bit more. I'm personally an atheist, but I'm very comfortable dealing with "believers" who know what it is they're choosing, and how it relates to science.
I defy anyone to explain to me how one species ever evolves into a completely different species.
What do you mean by "completely different species"? All it means when a different species appears is that members of the new group are different enough that they can't reproduce with the original species anymore. We still have something like 98% of our DNA exactly like that of a chimp... but our reproductive details are different enough that we can't produce a natural hybrid. It's silly to say we're completely different.
Now, suppose I'm right... The Bible talks about a time when everyone answers to God for what they've done.
Where do you fit in the atheist who volunteers for public services, gives to charities, etc.? There are plenty of people out there who don't believe in God but who follow the same ethical rules as you do, for different reasons.
And where do you fit in people who lived before monotheistic religions were even an option? Are they all still in hell? Poor suckers.
Just my thoughts on this... I think you'll find that the average atheist didn't choose that path to "permit" them to break the rules. For me, at least, all of the human religions that I know about just seem... well, really unlikely. The only idea that comes close is the suggestion that there's some force that started the whole ball rolling... but we know nothing about it, and praying to it or worshipping it as about as useful as praying to my own foot.
I'd probably sleep better if I believed that I would move on to some kind of pleasant afterlife after I die, but I'd rather live my life based on the best assumptions I can come up with -- not the most comfortable ones.
There are only 10 types of people: those who understand decimal, those who don't, and, uh, 8 other types I forget.
You know, I flipped a coin 30 times the other day and came out with the following result: HTHHTTTHHTHHTHTTHHTHHTTTHHTHTT
Now I ask you: what is the likelihood of my getting exactly this sequence of heads and tails? And to think I got exactly this, without a single mistake! I can't believe my luck! Clearly the result of divine intervention!
(Message: Be careful trying to apply probability theory when the result is a priori known.)