@avid yeah you can download a presentation for offline presenting with the free version. It has a prezi logo on it (which I think you can remove with the paid for version) but apart from that is completely free AFAIK...
And as a result ordered 'the unimaginable mathematics of the library of babel'
I remember reading something when I was young that applied the same thinking to pictures. Take a standard digital bitmap, say 1920x1080x32bit color. Now generate all possible combinations.
And you have an image depicting, perfectly, your own death. And images of landscapes from distant galaxies...etc...
heck, imagine you take any one 640x480 image - you've got 235,008,000 possible versions of it where one single pixel has had its RGB value changed to something else.
and to the naked eye most of them will be visually indistinguishable from each other.
and even doing the most rudimentary visual classification at that point becomes infeasibly cumbersome.
2x2 pixel RGB should be feasible though, right!?!?!?...
nope. 4,195,020,000 possible images
now the more fun part is when you do it with polygons. assuming each polygon can have one of 16 colours, and each vertex can sit on one point in a 10x10 grid, how many polygons can you map before it becomes infeasible?
for extra points, take into account that no two polygon vertices can be on the same point
for the same polygon, that is.
well it's not a polygon if two of its points are the same
I remember that Thomas once talked about this, but I still don't understand how clock synchronization happens between the GPS satellite and GPS receiver.
@Adnan we're not talking about triangulation, where you have a sphere, then a ring, then two points. We're talking about relative distance...it's a bit weird.
@ThomasPornin Ooooooh! Makes much more sense. Thanks!
@lynks Aha! I think the reason I thought it needed 3 was because I was thinking about it as if it's measuring the delay of the signal rather than the difference in the delay.
@Adnan When you have 3 satellites, you have two independent time differences (the third gives no extra information), which is enough to define a line on which the receiver is located.
When the receiver is on a boat, it can assume that it is at sea level, and infer the exact position as the intersection of the sea level with the line.
But that's not accurate because it happens that the sea level is not exactly at sea level
with four satellites, you have 6 pairwise time differences, but only 3 are independent of each other (you can compute the 3 others from them). 3 independent measures are sufficient to pinpoint the location in a 3D space.
Extra satellites can be used to make the position more accurate (because of measure approximations and irksome fluctuations due to refraction of signal in high atmosphere)
Bottom-line: signatures and timestamps won't help.
Because in order to fool a receiver, you don't have to forge a fake signal, you just have to delay a genuine signal by a few microseconds.
@Adnan The receiver is a machine, not a human. It cannot know if it really is on board a flying drone, or down in a lab basement and wrapped in tin foil.
@Adnan interestingly a point I noted with a wireless scanner the other day. the GPS was refusing to get a lock and after a while I realized that it was because the date was set wrong....
@ThomasPornin I'm trying to get a picture in my head. Relative distance from two points puts you on the surface of a 3D hyperbola of some kind I think.
I saw a cool talk on fooling GPS a while back the scary bits were that financial systems are using GPS not for location but for accurate time signals (which makes spoofing dangerous for other reasons) and that apparently military systems use civilian GPS to get the initial lock 'cause their stuff takes too long to get a good lock..
@Adnan In that experiment, they just need to beam a stronger signal. The satellite is far (hundreds of kilometers at least) and powered from solar panel, so it cannot be that powerful. A direct beam from a plane or another boat 10km away should have no problem overriding the genuine signals.
And one fact of the genuine signals is that they are broadcasted, so everybody receives them.
It is thus "easy" to receive the signals, and beam them immediately to the victim, but with slightly altered delays between them. If done properly, the signals as received by the victim will be late by less than a millisecond, and they would have a hard time detecting that.
@Adnan Yes. With some sort of timestamping you could detect if you are being fed signals from last year, but not if you are given signals from last millisecond. Signals cover less than 300km per millisecond (speed of light and so on) so getting "late" signals (of a few milliseconds) is normal.
@Adnan only because it is possible to incorporate a delay that is significant in terms of interpretation, while being insignificant in terms of signal propagation.
If a receiver has an embedded clock with nanosecond precision and accuracy, maintained synchronized with the GPS clock through some unspecified means, then the receiver could measure absolute distances with satellites and thus detect some kinds of fool play (assuming that the signals are timestamped and signed, which they are not at the moment).
@Polynomial That one is an open problem. We don't really know, although we suspect that it is true (i.e. every possible sequence of bits appears somewhere in the binary representation of Pi).
I came across the following image, which states:
$\pi$ Pi
Pi is an infinite, nonrepeating (sic) decimal - meaning that
every possible number combination exists somewhere in pi. Converted
into ASCII text, somewhere in that infinite string if digits is the
name of every person you w...
@Polynomial There is a lot of published work which basically amounts to: "We looked real hard for biases or other fast means of computing the digits, but we found none. We don't really know why."
@Adnan Technically, everything that we write on a public medium, including the DMZ, can constitute a "publication" for purposes of researching precedents in patent litigation.
@lynks The interesting thing is that while no bijection exists between the two sets, there is a rational number between two irrational numbers and vice versa
@TerryChia Rational numbers are countable, meaning you can define a process which goes through each number, one after the other, and such that every rational will be reached at some point.
Irrational numbers are not countable; they are a "bigger" infinity.
Actually Transcendental numbers are not countable, but non-transcendental numbers (aka "algebraic") are countable (they include rationals and a lot of irrationals)
Think about encoding an arbitrary polynomials with rational coefficients (think of rationals as p/q, not recurring decimals) as a single number. It's a computer problem.
@ManishEarth well if you're encoding a polynomial as an integer, that integer is just re-encoded as a set of "on" or "off" gates... what's to say you can't just encode each coefficient as a different base.
@ThomasPornin If I use the degree as a dimension the number of total dimensions becomes infinite, because I have to allow for the remaining dimensions to be accomodated
@ManishEarth Well, yes, you cheat. The point is really that a polynomial has only a finite number of non-zero coefficient (which explains why a polynomial can have a well-defined degree).
The usual proof of non-countability of R implies defining a number with an infinity of non-zero digits, and that's a crucial part of the argument.
(Not that having an infinity of digits is really a problem for countability, but having an infinity of independent choices for digits does it.)
Is anyone good at charsets and all that junk? In the header of a page, data from a database is fetched and displayed properly with accents. However in the body, data is fetched but invisible if there is an accent in the word.
It is not the same table but the collation is exactly the same. I'm confused as hell.
@Simon The golden rule is: Charset in the dataase should be UTF-8, fetch using UTF-8, send the HTTP headers as UTF-8, set meta to UTF-8, and set your IED to UTF-8
@Polynomial Well, yes: if HTTP header and HTML contents (BOM, meta tags) don't agree, hilarity can ensue. But with dynamically generated content, the Web server cannot necessarily adjust the header to match the HTML (Apache will do the match for static files, though).
I still don't get why in the header the accent is displayed but not in the body.
Also, if I add a static value with an accent in the body, it is displayed. It's a DB issue but still, I don't get it because the first value came from the DB too.
I used Tor, but I didn't like it what I found there... you know what I'm talking about...so there's no Secure VPN? it doesn't matter if you pay or not? — jcho36014 mins ago
one of the worst ones I've seen... picture of Misty from Pokemon, cut in half, her bottom half being raped by Blastoise, her top half impaled on a wooden spike.
at that point you really question who got up in the morning and thought "yup, that's what imma draw today."
@ThomasPornin Well physics is weird in its own way. A typical case: "We assume x, which is wrong, but that doesn't matter. It'll work out anyways."
somewhat similar to the random oracle issue in crypto
another fun part of physics is notation. Each corner is using completely different notation, often in ways that ca only be parsed with sufficient contextual knowledge.
I came across the following image, which states:
$\pi$ Pi
Pi is an infinite, nonrepeating (sic) decimal - meaning that
every possible number combination exists somewhere in pi. Converted
into ASCII text, somewhere in that infinite string if digits is the
name of every person you w...
