Slashdot Mirror

It's popular on Slashdot to loudly pronounce that strong AI is impossible. This is different from years past. I take the change to mean that it's coming very soon. As it seems more inevitable people who don't want change (whether out of fear, distrust, or sour grapes) will decry AI more.

Now weak AI isn't just coming. It has arrived. And Moore's law was supposed to have stopped years ago but supercomputers and video cards are still on a logarithmic slope for performance and price. The human brain is estimated to calculate between 100 petaflops and 1 exaflop. I know that's not a good metric but for this purpose it suffices. But as performance keeps doubling and doubling it becomes more evident that even the highest estimates are a question of a few more doubling periods. And the highest estimates assume direct one-to-one simulation of each neuron. Consider how many neurons are used for breathing, processing vision, and other things that either aren't needed in a machine or have already been done at a much lower computational cost on silicon.

It's true we don't know everything about how the human brain works. But recent progress is undeniable in terms of success stories. Jeopardy. Go. Commodity trading. Corporate resource balancing. Piloting. To keep shouting that strong AI is impossible is to only betray one's own insecurity. You are not special. Your brain doesn't run on quantum magic. You have no soul. Fucking deal with it.

That's what we have shielding for. All modern digital signaling cabling worth a damn is shielded end-to-end. Now not all on-board electronics in consumer products is shielded, true, but pretty much all of the electronics on board of an airplane is. The screens you see on flight decks are housed in separate grounded metal cases, and all cabling going to/from them is shielded as well. My guess is either your 1W UHF transmitter does a lot more than 1W output, or your electronics is so badly shielded, it's a wonder it's working at all. Another possibility would be interference through the power supply. Cell phones have 1-2W UHF transmitters and I just checked, yep, I can have a phone conversation while working at my computer desk.

Sand slides in an hour glass are instances of "Self Organizing Criticality"

There is a book

Looks like this format of satellite is finding a good few uses http://www.wired.com/wiredscience/2013/06/startup-skybox/ aswell as smallish satellites from Guildford University UK http://www.surrey.ac.uk/ssc/activity/phd_projects/small_satellite_sar.htm.

Markup languages are for machine consumption, not human readability

Machines have no trouble with <option checked>foo</option>. The desire to force XML compliant checked="checked" on HTML is not rooted in parsing difficulty or performance or any other machine processing rationale. The only actual problem with <option checked> is that it offends the sensibilities of XML advocates. Writing interpreters capable of handling "unclosed" tags or valueless attributes is a solved problem.

which would not be tolerated in any compiled or interpreted language.

Among the common compiled languages we have C++ which "is ambiguous, context-dependent, and potentially requires infinite lookahead to resolve ambiguities," * and which precludes the use of parsers based on formal grammers. Perl is an example of an interpreted language that can't be parsed. Here is a thousand or so words on the implications of Javascript semicolon insertion.

In short, your appeal to the rigor of compiled or interpreted languages is not credible.

http://info.ee.surrey.ac.uk/Personal/Z.Kalal/tld.html

TLD

TLD is an award-winning, real-time algorithm for tracking of unknown objects in video streams. The object of interest is defined by a bounding box in a single frame. TLD simultaneously Tracks the object, Learns its appearance and Detects it whenever it appears in the video. The result is a real-time tracking that typically improves over time.

Due to its learning abilities, TLD has been advertised under name Predator. The video to the left introduces Predator and proposes several potential applications.

TLD has been developed by Zdenek Kalal during his PhD thesis supervised by Krystian Mikolajczyk and Jiri Matas. The main contributions of TLD have been presented at international computer-vision conferences. For his work on TLD, Zdenek Kalal has been awarded the UK ICT Pioneers 2011.

Key Features

        TLD tracks currently only a single object
        Input: video stream from single monocular camera, bounding box defining the object
        Output: object location in the stream, object detector
        Implementation: Matlab + C, single thread, no GPU
        No offline training stage
        Real-time performance on QVGA video stream
        Ported to Windows, Mac OS X and Linux

Free Version

TLD can be downloaded for testing. We provide a precompiled demo (Windows) and a source code that is released under GPL version 3.0. In short, it means that any distributed project that includes or links any portion of TLD source code has to be released with the source code under the GPL version 3.0 license or later.
Commercial Version

A license has to be purchased for using TLD in closed source projects. The licencing is managed the University of Surrey. Please contact the Technology Transfer Office at the University of Surrey for further information.
More Information

        High-level description of TLD
        Components of TLD
        Learning component of TLD
        Application of TLD tracker to faces
        Detailed description is in the following papers: ICCV'09 (w), CVPR'10, ICIP'10, ICPR'10
        Many technical questions (e.g. installation) are being discussed in the following discussion group.

FAQ

        How do you manage the number of templates in TLD?
        For the moment, we do not put any constraints on the number of templates in memory. The number of templates typically stabilizes around 100, depending on the appearance variability of the object and background.
        What kind of hardware is TLD running on?
        TLD has been tested using standard hardware: webcam, Intel Core 2 Duo CPU 2.4 GHz, 2 GB RAM, no GPU processing is used and runs in a single thread. The demands of the algorithm depend on required accuracy of the algorithm.
        To what degree is TLD invariant to light levels?
        We use illumination-invariant features for detection. So as long as the changes in illumination are global, the performance does not change. If there is a strong local illumination change, the system is learning the appearance changes thus created.

This is pretty much a tracking problem, I would use the open source Predator Tracking algorithm to track each of the car simultaneously. The problem I see is if it is going to be fast enough for 100 cars, but it is worth to investigate it. http://info.ee.surrey.ac.uk/Personal/Z.Kalal/ Alternatively, thinking about using open source-hardware as a solution, use the open source Arduino Micro-controller Piece the sensor you need, and you will have your system at a much lower price ! http://www.arduino.cc/

A bullet that, when fired, acquires an image of the target and pursues it. Kind of like the Predator Object Tracking System(POTS) that got so much press here three weeks ago. POTS would be excellent for riflery, since the object image need be consistent for, at most, two seconds.

A license has to be purchased for using TLD in a commercial project. The licencing is managed by the IP owner, the University of Surrey and the fee is subject to negotiation.

It doesn't sound like it's meant to bring down some random spacejunk with which it collides (which would mostly pass through it after all, at best / if impacts won't produce more debris), just to bring down a satellite to which it is attached. Not the only effort of such kind

"CubeSail" for example; soon available for deployment - http://www2.surrey.ac.uk/mediacentre/press/2010/26099_a_mission_to_clear_dangerous_debris_from_space.htm

Should make some nicely visible light show from time to time...

Plus what would mostly suffice is...knocking out the solar panels of G15.

The problem is - I don't think GEO satellites have all that great close rendezvous capability, there was no need. Not a showstopper, but hitting G15 in the desirable way might be...hard. And risky

Even more desirable, probably, would be positioning the second satellite very close to G15, in a way that will starve it from power (by shadowing G15 solar pannels). Still has the problem with precision rendezvous...

Too bad the mission of a large, deployable aerodynamic sail, meant for deorbiting satellites on which it is attached, is not nearly ready. If it were - it could be perhaps feasible to repurpose the sail test satellite (plus give it better rendezvous capability / visual system; since the satellite is apparently very small, you won't even require large and expensive rocket to put it in GEO) for "let there be darkness" mission...

I am using Fedora Core 8 on a laptop with a Atheros AR5212/AR5213 Multiprotocol MAC/baseband processor. The drivers wrk perfectly.

First of all, the broadband router was not configured to enable wifi - that required some grokking of the installation manual to get the IP address, username and password to access the configuration menu, all on the same channel/frequency.

Then there was the configuration to follow various Security Tips.
Regardless of my location, six or seven different wi-fi networks will show up on the configuration manager.

The default setting for the wifi configuration menu was "ad-hoc", but nothing would happen until "managed" mode was selected.

Ad-hoc vs Managed mode

Then there was the problem of getting the wifi driver to be automatically seleted upon startup (there are two possible communications modes: Ethernet RJ45 vs. wi-fi).

Until thes security key was set using iwconfig, nothing would work.

Setting up a WPA pass phrase

And cracking a WPA passphrase, which makes the above seem a bit pointless.

In all probability, the need for all of this has probably gone away with more recent distro's - I had similar problems in the past with various other drivers.

I don't know if it would be considered a "scientific" theory or not, but consciousness is often considered to be simply an emergent property of the complexity of the brain.

This might some dumb, but does this really say anything? Isn't it just adding the geek buzzword "emergent" to the idea that the mind is in the brain? Just a Web 2.0 saying that the brain creates mind? Like, is anyone really still considering that the mind is a soul, a ghost, or some being from another dimension that interfaces with the body?

Personally, I'm in favor of the cemi theory of consciousness. It holds that consciousness is the EM interference field generated by nervous systems.

An interesting illustration of the idea is presented in Verner Vinge's A Fire Upon the Deep. In it, some dog-like creatures are individually incapable of coherent thought, but can join together in packs, and self-awareness and human-level intelligence emerges. Very interesting treatment.

This strikes me as modern-day homunculism. Instead of a homunculus that can do everything a person can do, it's a slightly dumber homunculus, and a whole group of them at that.

Yes, I'm aware that we've identified emergent behavior in certain flocking phenomena, like an ant colony, but for me, it's going to take more experimentation to show that the mind is simple emergence from a flock of nerves.

http://www.cs.surrey.ac.uk/FMS/evoting/bibliography.php

You should do it, then, and make a name for yourself. The maximum range that anyone has been able to communicate with these chips is about three meters, and that in a carefully-controlled, RF-damped lab environment[*].

Part of the thing that makes it so difficult is that the card is powered by inductance from the reader's field. Since power delivered to the card decreases with the cube of distance, this means that as range increases the power requirements go up dramatically. Another part of the problem is that the signal transmitted by the card is very weak and omnidirectional. While the reader can use a directional antenna to increase the effective range at which it can deliver sufficient power and a strong signal, the card does no such thing, meaning its signal rapidly falls below the noise floor as the distance increases.

[*] There are some papers floating around that demonstrate ability to communicate with a contactless smart card from arbitrary distances, but they do it by putting a powered repeater right next to the card.

Microwatt transmitters are routinely read at distances of dozens or hundreds of kilometres 1, 2. I don't see why a quarter milliwatt RFID chip couldn't be read from similar distances.

RFID range is largely a matter of how sensitive your receiver and antenna are. RFIDS put out approximately 250 microwatts of power. According to this, a 1 microwatt transmitter has a range of 45km. So with a good antenna and receiver, I don't see reading RFIDS from a hundred metres away to be much of a problem.

This one is better, in my opinion, it displays the stone clac^H^H^H^Hsemaphore tower and the wooden part on top structure to relay the messages.

I'm not a specialist when it comes to transmitters and receivers, but I found a few more bits of information that you might find interesting:

"After launch, Pioneer 10 was capable of transmitting data at a maximum data rate of 2408 bits per second. Now the data rate is 16 bits per second. Reducing the bit rate compensates for the reduced signal strength; it is like speaking more slowly to enunciate more clearly. The signal strength from the craft's main transmitter is now about 7.8 watts; by the time it reaches the DSN antennas, the signal has diminished to less than a billionth of a trillionth (10-21) of a watt."

http://www.newscientist.com/article/mg13318105.500 -pioneer-the-persistent-probe-pioneer-10-the-first spacecraft-to-head-for-jupiter-proved-that-probes- could-reach-the-outerplanets-of-our-solar-system-t wenty-years-on-it-is-sending-us-messagesfrominters tellar-space.html

Deep space tracking station - http://personal.ee.surrey.ac.uk/Personal/D.Jefferi es/tidbin.html

"Successfully sending a DSN signal into Voyager-2's receiver is like throwing a baseball across thousands of miles of ocean into a porthole of a moving cruise ship."

http://www.spacetoday.org/SolSys/DeepSpaceNetwork/ DeepSpaceNetwork.html

I just cannot praise the people who made and make this project possible enough. The facts are jaw dropping!

Well, I just looked up the Surrey Computing BSc brochure (warning: PDF) and to be brutally honest, I'm not that impressed.

Perhaps their presentation in the brochure is bad or their courses are unfortunately named, but when two of the five "core" modules in the first year are given as "web publishing" and "professional studies", while the first course in data structures and algorithms features in the second year alongside "usability engineering", alarm bells are ringing pretty loudly.

Where are the courses on different programming styles and languages? Operating systems? Applications like databases, graphics and image processing, natural language processing? Numerical analysis? Programming language design and compiler construction? There do seem to be some interesting courses among the optional modules, particularly by the final year, so perhaps these things really are covered and the advertising is poor.

I suggest you seek a more detailed syllabus, and compare it with alternatives offered at other universities, before committing to this course. Looking at a few other places (I tried Cambridge, Warwick, Brunel, Imperial) there is considerable variation in what's offered, and at first glance, I'd suggest the Imperial or Cambridge syllabuses as guidelines for the sort of things to look for.

(from http://www.etymonline.com/index.php?term=hear)
"...Hear, hear! (1689) was originally imperative, used as an exclamation to call attention to a speaker's words; now a general cheer of approval..."

But, it IS a good show and I've managed to, at one time or another, see all but the (traditionally) "missing episodes" and the rest of "season two" (in reality the twenty-eighth season - http://www.ee.surrey.ac.uk/Contrib/SciFi/DrWho/epi sodes.html)

I've used both eBay and Craigslist extensively (eBay more), both buying and selling (about 50%/50%). Because both those sites reach such a large audience, the range of users is really too great to summarize in any detail. The user groups get more homogenous when dealing in specific items, but even then there is a wide variety. One point I'd like to make is that in at least 600 transactions, I have not seen any bona fide altruism. I have never had any buyer pay more than was necessary and have never had a seller send me an item that was vastly better than what was shown in the auction (although every now and then they'll include something small that wasn't mentioned). If sellers included something small extra, it was often a way to vye for repeat business (and hence, they were probably more experienced salespeople). People do things for a reason (even the Dadaists ran into trouble there).

In judging on the amount of time it takes to list an item on eBay as compared to Craigslist, it's clear that Craigslist takes far less time to list an item on. It's also free to list most items/services. Because they have very little to lose, it's easy for anyone to throw a five-word ad up on Craigslist. Therefore it's reasonable to assume that because they have so little to lose, people will try to "reach" for the best deal they can. Craigslist does fill a need, though, for those of us who don't read newspapers at all....

FreeBSD 6.1-PRERELEASE (SE7210TP1E) #0: Tue Mar 14 12:15:56 CST 2006

Welcome to FreeBSD and the wonderful world of UNIX!
                Abandon all Hope, ye who Enter Here...

If you need help, the commands; man, whatis, and whereis will help you.
For an introduction to UNIX head on over to:
                http://wks.uts.ohio-state.edu/unix_course/unix.htm l
                http://www.ee.surrey.ac.uk/Teaching/Unix/
                http://www.mcsr.olemiss.edu/unixhelp/

Throughout the ages many composers (J.S. Bach/Schubert/Bartok), have used the fibonacci numbers in their works: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibon acci/fibInArt.html#music Many contemporary composers like Ligeti and Chowning use mathmatical formulas like the fibonacci number as well. So, how is this news... most students in music are supposed to have remembered this from their classes ;)

This is rather puzzling. A quantum mechanism has been proposed. I should point out the the author's (McFadden) book is where I learned of these surprising mutations.

My mistake; twice a day (plus 1/365ths of an orbit). It would also be a huge menace since it would be plowing through the geosync belt, crashing into the world's most densely packed satellite constalations. Once it hit one unlucky bird, the debris from the collision would polute the entire belt with high speed projectiles, causing further destruction. Potentially ending in a chain reaction which leaves the entire orbit unusable for thousands of years. Please don't do this.

http://www.ee.surrey.ac.uk/Contrib/SciFi/Blakes7/e pisodes.html

I believe actor Gareth Thomas (Blake himself) went AWOL for (at least) the second series due to Royal Shakesperae Company commitments.

And Jacqueline Pearce as Servelan has to be the horniest Sci-Fi woman in the whole of SF TV and cinema history!

I call for an open source tea standard. BS 6008 and ISO 3103 restrict my acess to tea. (Yes. They actually exsist.) Here is a pdf of the actually standard http://ftp.ee.surrey.ac.uk/papers/AI/L.Gillam/bs_t ea.pdf#search='BS6008' and a place where you can buy it. http://www.iso.ch/iso/en/CatalogueDetailPage.Catal ogueDetail?CSNUMBER=8250

Phase velocities > c have been known for years. In fact, it used to be standard content in electronics courses related to waveguide technologies. Probably for its woooo-factor.

A quick google reveals a nice discussion at http://www.ee.surrey.ac.uk/Personal/D.Jefferies/wg uide.html

The relevant bits:

Group and phase velocity.
The energy and the modulations on the microwave signal going down the waveguide both travel at the "group velocity" c*cos(alpha) which is necessarily less than the velocity of light c. The pattern however travels at the "phase velocity" c/cos(alpha) which is necessarily greater than the velocity of light. The product of (group velocity)*(phase velocity) = c^2.

Look at the website posted in the parent...

Now look at this:

http://www.ee.surrey.ac.uk/Personal/C.Poa/index.ht m

so who stole the code?

The Iridium network covers the entire globe. Coverage map would look like this. I'm not sure where you got your coverage map from, Iridium's site doesn't even display a map on their site that I could find. But the Iridium satellites are not in geocentric orbit, they contiunally sweep across the globe, so they in effect have to cover the entire globe or there would be a moving non coverage area.

I also recommend "Quantum Evolution" by Johnjoe McFadden. It too makes the case that consciousness is a product of quantum phenomena.

Maybe Dr Who didn't get a big run in the USA. It ran every week day for most of my childhood in Australia in the 70s-80s. There were only two channels, so if you weren't watching the news, you were watching Dr Who. In the same time slot they also used to run The Goodies, The Kenny Everett Video Show and Monkey. Growing up in Australia or England you would certainly have been exposed to all four of these shows as a kid.

If you don't believe me, ask Zeldman, or read here.

It would be around 270ms for a satellite in geosynchronous orbit. It would be a bit more for a router on the moon. :)

That's a one-way trip. Meaning that traffic only goes to the satellite and back to earth once. That's great if you've got some sort of instrumented satellite up there and you're trying to query it for data, or if you're broadcasting (one way). But because this thing's a router, that implies that traffic will be two-way.

This means you're going to have that minimum 270ms lag on the outbound leg, but you've got to take into account the return trip, which doubles the minimum latency to 540ms (that's a half-second to you and me). If there's even typical latency on the terrestrial side (at both ends), you're probably talking another 50-60ms, so a typical ping time will most likely be 600ms or more.

Of course, this assumes that the space router satellite will be placed in geosynchronous orbit., but there's nothing in TFA to indicate that's how it'll be used. It might be placed in a lower orbit, as part of a constellation of satellites, the way Teledesic had planned to do, in which case, the latency would be much lower.

Ok guys this really stinks of a practical joke, hidden camera style?

Anything that involves a 'youth-driven ceremony' is a waste of time by someone who has absolutely no idea whats going on. Just listen to this song Einstein (not enough time) (im sorry for the bandwidth you're about to get surry uni) if you think im wrong. its definately in the C rap MC category.

"We want to show that physics is not about the stereotype of the mad scientist. Physicists are normal people doing normal things."

But thats exactly what appeals to people! no-one wants to be doing a boring normal job, people wan't blade-switches.

The reason physics has declined in this country, and I know, i've just been through uni, its because when people leave school they are shit scared that they are going to do a worthless degree where all the jobs are taken. If you want people to take up physics you have to proove to them that there are jobs out there that pay well and are worth atleast £10,000 debts at 21.

At the 65K foot hieght they are talking about They are well above even the highest of storm clouds (50K feet is the top height I was able to find listed by the national weather service.) Also high enough to be above commercial and military flight paths. So weather is not a problem.

The other thought I've seen expressed concerns lag time With only 65K feet to transgress the lag shouldn't be any greater than wired communications in any single band. Point being that 13 miles isn't that great a distance for radio wave propogation ( 3,00000 km per second in vacuum ) So unlike SatCom where You have to calculate in Phase delay etc there is none of that affecting something at such a low height. Granted in it's initial phase it may not be the ideal gaming platform for some really lag sensitive games for most situations it won't be a concern.

What does have potential affects can be things like ground clutter (Extreme example turn on your microwave while using 802.11b in a small apartment.) Radio shadow. (tall buildings) etc. However these are things that affect a number of current radio communications systems and the 13M hieght will help. (Thats why the roof of the tallest building in a city is such valuable real estate)

The other neat thing is that you have a much lower horizon affect (the horizon is farther away from the top of a mountain than at sea level.) etc. I wouldn't expect it to be reliable for symetric communications links (The power down will be easier to create than the power up from a small device like a handheld. So give the db loss over the distance you won't find yourself serving a slashdotable server off of the connection. But for e-mail, blackberry, web surfing or sending off a modified spread sheet to the boss I would expect it would equal normal home DSL without a problem.

Strange too that no one ever talks about the lag in wired communications even though it is there. I remember as a child talking with my Aunt and Uncle living in Europe at the time on the phone. You really had a problem with knowing when the other person was speaking because of the lag.

Some useful links
http://www.cosmic.ucar.edu/related_papers/2002_wu_ cedar_sporadic_e.pdf

http://www.ee.surrey.ac.uk/SSC/CSER/UOSAT/IJSSE/is sue1/seumahu/seumahu.html

URL:http://www.vigyanprasar.com/ham/IONOS.htm

TV runs at 30 fps (actually it's something like 29.97), not 25.

TV in the US (NTSC) is at 59.94 fields per second interlaced, so it is equivalent to 29.97 frames per second. However, in Europe TV (PAL) is 50 fields per second interlaced, or 25 frames per second. The reason for the difference is the difference in the mains AC frequency on opposite sides of the pond. (The 60/59.94 disparity is due to a complication of colour TV). This has annoying consequences when transferring video, as conversion is required (also in terms of number of lines). Cinema film tends to run at 24 full frames per second, just to make things a little more complicated. Here is a comparison of TV formats.

I've recently heard about a new technique about nuclear waste disposal. Too bad I only can find the following:

A new technique has been discovered that will allow much easier cheaper disposal of nuclear waste. Instead of storing the waste in special, very expensive, underground areas, it can now be transformed into different non-radioactive and harmless material.

LunarEclipse.mp4 can now be downloaded (2.5Mb). Original WMV converted to Apple Quicktime MP4 format via AVI. Academic hosted server, so bandwidth should be okay. Will have to remove tomorrow (Monday 1st Nov, 1600GMT).

Other favorite is the pseudoscience behind marketing industry equations like
opportunities to see (OTS). I can never remember these offhand because they are so meaningless, but it is fascinating to think of the millions of dollars spent on ie outdoor billboards, where the advert is sold on the basis of these "opportunities to see." See also A Test of the Direct/Indirect BBD and Other Exposure Distribution Models.

I think that is mainly true of the NTSC signal since it was developed before color televion came around. You'll notice that NTSC sets have adjustments for color. PAL and Secam reproduce colo(u)rs more acurately by better correcting for the loss during transmission so those sets tend not to need colour adjustment knobs. http://www.ee.surrey.ac.uk/Contrib/WorldTV/

Actually, it doesn't take much power at all to get to a satellite -- it depends on how much data you want to transmit. Sure, voice will take a hefty rig like an irridium phone, but small amounts, such as GPS coordinates, require very little power and can use a short whip antenna. For example, take a look at orbcomm -- Garmin already has a unit that combines this satellite with GPS.

And all normal cell phones do reach satellites... spy satellites, that is :-)

I agee on your second point ... I was disappointed to find out that the only GPS on my "gps phone" was that the base stations' positions had been determined with GPS. Yeah, I've got a GPS-enabled ham sandwich because it's in my house and I know the GPS lat/lon of my house...

Actually, they may also be referring to "Major Tom - Coming Home" by Peter Schilling, which was featured in an amateur video of a satellite launch.
In fact, I'd put money on it.
See it here

Not true that Apple don't care about developers. Remember the whole deal with Apple's Theme Converter for Mac OS 8.5 and how they after much press skipped it?

It should also be noted that while the university gets almost all of these journals online any way we still pay an awful lot for the privilege of using our own paper to print them out.

Ian

Most people don't seem to be aware of the fact that coal power plants are more radioactive than nuclear power plants.

It is also now possible to design nuclear power plants so that they fail safe, unlike the poorly designed plant at Chernobyl.

Safety-driven memes are difficult to counter, but once we run out of options perhaps we'll do what we must.

While it seems strange, it almost seems to make sense. The Fibonacci sequence is found in nature all the time, and as you can see in shells, a spiral fits it perfectly. As old as the universe may be, isn't it possible that it's only the beginning of this spiral, shaping it like a horn?

At one time, there were only integer numbers from 1 to infinity. Then came zero. Back then, people thought that nothing could be smaller than 1, but then zero arrived. So we had a lot of integer numbers, usually refered to as "natural numbers", or N. Then we found out that there were also negative numbers, and we had Z.

At that time, we thought that right after 1 came 2, but then we found that 1.5 was also there... we got the ratios... Granted that A and B are integers, then A/B is also a number, a "rational" number, Q. We then thought that every number could be represented as either an integer, or a ratio of integers A/B, but then came the square root of 2. So we have irrationnal numbers, which, with the rational numbers, make up the real numbers.

We then thought that with the real numbers, we had all we needed to make maths work. Then came along the square root of minus one. That then gave the imaginary numbers, which, with the real numbers, make up the complex numbers.

So, all those time, we believed something to be true, but then another mathematician proved us wrong.

Most interresting things in math are related to something in either physics or chemistry. Pi is the ratio of the circumpherence of a circle to its diameter, the exponential function describes the nuclear desintegration of unstable elements and so on.

When Fibonacci "discovered" his series, it was merely a slight mathematical amusement, but when we discovered that nature actually used the mathematical function of the Fibonacci series, then it became interresting.

At the current time, infinity is merely a mathematical amusement, and if we can never find a way to concretly apply the notion of infinity in science, then mathematical infinity might be a concept that doesn't really exist.