Maths is about understanding something the right way. And I'm guessing this kid did not take the seven seconds to do anything complicated. He just factored 32. i.e. 2^5. Then noticed that 999,999,999 + 1 = 1,000,000,000 = 10^10 = 2^10 * 5*10 which clearly contains a factor of 2^5. So 32 goes into 1,000,000,000. So the remainder after division of 999,999,999 by 32 is 31.
I think you need about 2 seconds for that once you realise the correct way to think about it. So he took 5 seconds to work out what he should do. Quick kid!
Good point, but sadly faster than light communication allows messages to be sent back in time (due to special relativity). So once we invent FTL communication were going to be more worried about some severe problems with causality than about aliens many light years away.
Why celebrate according to the decimal system?
on
Today Is EPOCH Day 15000
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· Score: 3, Informative
I'll be saving my champagne for Epoch day 16,384 (otherwise known as 2^14). A little under 4 years to go...
Excuse me for replying to my own post. I should also mention that Poincaré's conjecture was not about 'a method for determining whether a three-dimensional manifold is a spherical'. It is simply the question of whether there are non-spheres in 3d which have all loops contractible (for a more accurate description, see the parent). The question about methods/algorithms for determining whether or not something is a 3-sphere is in itself very interesting though.
As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places. The Poincare conjecture states (in simple terms) that:
Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).
The words "homologous" and "boundless" have little/nothing to do with it.
So here I am at home on a Sunday morning reading the news and I find you guys embroiled in a huge argument about my area of research. Quite a pleasant surprise actually. So in response, here's a short list of uses of knot theory:
1) Tying your shoelaces (but of course no one cares)
2) Studying supercoiling of DNA (how it wraps itself up into a small space yet still wriggles enough to present all of it's length at short notice for interactions with cells' other mechanisms)
3) The geometry of three dimensional space (all closed oriented three dimensional spaces can be constructed from knots and the three dimensional sphere! So knot theory has major applications to 3D geometry)
4) The geometry of four dimensional space (for example, surfaces in 4D spanning between knots can be used to specify exotic smooth structures. The existence of such shocked the world of geometry in the 80's)
5) TQFT, Mirror Symmetry, Quantum Gravity etc (the tools developed in and around knot theory are one facet of a huge push in mathematics to forge a better understanding of some of the deepest ideas in modern theoretical physics)
...and I'm sure I have missed out plenty. My point is that mathematics is full of weird abstract nonsense, which is not actually nonsense when you look deep enough. There is after all a reason why we study it.
Yet another plausible explanation is that they are concerned that someone else may soon have one (possibly even already) and they would like very much to know what things it renders insecure.
I am a mathematician and you sir are insulting the abilities of drunk lemurs. I personally worry that I would never send any e-mail if I had to answer arithmetic or sports questions.
What they should do for us is to add the option of deep philosophical questions. I would happily give a brief answer while sober, but if I were drunk I would be so distracted that I would be sober by the time I finished formulating my answer.
the current symbolic form it takes, can be expressed in many different ways.
I heartily agree with this. Different forms serve different purposes.
What I was worried about was your previous suggestion that physics and mathematics be unified. Definitely too much mathematics has been removed from school physics and this ruins it. Moreover physical applications would show kids why they should care about mathematics. What they should begin to notice though is that the things they are learning are useful outside of physics. And they should also learn some things which they will be hard pressed to find direct physical applications for at their level (elementary number theory, probability theory).
I propose instead that the application of mathematical ideas in Physics, Biology, Chemistry, Geography,... (heck, everything) be emphasized more in school. And that mathematics lessons teach enough to make this possible.
Mathematics in necessarily abstract. It is the science in which one disconnects interesting patterns from their context and studies them in their own right. A great deal of effort also goes in to applying general mathematical knowledge in a particular context.
If we never used the mathematics out of context a lot of ideas developed in physics would still be just that. Statistics (used for example in the study of cancer) would lose out greatly if Newton's theory of infinitesimals had not been developed out of its physical context context into 'calculus' and then applied to probability density functions.
Wikipedia is great for maths. I use it a lot. When I look something up I don't necessarily understand all the terms used to explain it, so I click on some of the links to explain those terms,... etc.
Hey. A lot of people devote a lot of their time in explaining their areas of mathematics to the general public (including myself). And as for your distaste for abstraction. That's what maths is!
There is a reason the general public do not follow much in the way of mathematical developments and that is because research level mathematics is actually really hard and takes a lot of dedication to understand well.
There is also no elitist clique. We love it when people show interest in our work and want to understand it.
That is awesome. I want one! The processing for 3D environments in games already includes a moving perspective, so this should take very little extra processing to produce awesome effects.
...there's usually going to be some prior art if your work has any value at all...As long as your work builds upon what's been done in a meaningful way, your ideas should be patentable.
I'm sorry. You appear to be advocating the right to patent ideas which you were not the originator of. I find this objectionable. Your patents should only cover those precise parts which are novel. And even then only if they pass the conditions of originality and non-triviality.
Americans alone 'waste' around 325,000 lifetimes a year watching TV. Sure some chunk of it counts as education and healthy relaxation, but I'm not prepared to believe that even makes up half of it.
I think of the projects the article mentions as more like 'SETI at home'. Getting people to use unused cycles to do something potentially productive and pretty much guaranteed to be better for them. It's a shame my computer's CPU doesn't benefit from the experience of running some 'SETI at home' calculations.
It's a good philosophical question though. When is a collection of things (say atoms, bricks and mortar, etc.) a thing and when is it just lots of things? Deep down atoms don't come anywhere near touching each other to make molecules and larger structures. I myself am just a collection of tiny dots floating in space a long way from each other.
So we are to understand that dark matter, acted on only by gravity, forms sheets and filaments? We know very well what shapes distributions of particles form over time with only gravity acting on them and they look a lot like galaxies and very little like sheets and filaments. Can anyone clear this up for me?
The colour of the balloons is just an artefact of the translation from the song's original German where they were just "99 Luftballons" (actually the German lyrics tell a much better story as the translation changes a lot). So the world is over whatever colour they make them.
It generates energy as the knee is using energy to slow your downward motion, hence the statement "less than one watt of EXTRA metabolic power for each watt of electricity".
Yes. Parent is weirdly correct, yet totally misses the point. We (by which I mean people who want to live in a nice world) really do wish to endow people with certain basic rights. Something along the lines of "Do unto others as you would have them do unto you". It makes me feel rather more secure and happy feeling I can trust most people not to abuse me or people I care about in certain ways.
So your creator had the same suggestions. Brilliant. Sounds like someone who cared about our wellbeing. But wouldn't it be a shame if we could not understand that the need for human rights arises independently of (our knowledge of) his existence?
Really? And even if this is 'true', the 248 dimensions of E_8 are used to explain the symmetries of fields in the universe, not as a model for the universe itself. A simple example of what I mean is the following. The surface of a sphere is two dimensional, but the group of rotations you can perform on it is three dimensional. If I really wanted to I could create an E_8 principle bundle on the sphere (representing some kind of generalised fields) which would trivially have at least E_8 symmetry group.
I second the sibling's motion. Curiously this is exactly what we need to introduce an element of competition into the markets and hopefully get M$ to improve their product (and/or reduce it's price). I welcome any arguments against this idea.
Slashdot Mirror
Maths is about understanding something the right way. And I'm guessing this kid did not take the seven seconds to do anything complicated. He just factored 32. i.e. 2^5. Then noticed that 999,999,999 + 1 = 1,000,000,000 = 10^10 = 2^10 * 5*10 which clearly contains a factor of 2^5. So 32 goes into 1,000,000,000. So the remainder after division of 999,999,999 by 32 is 31. I think you need about 2 seconds for that once you realise the correct way to think about it. So he took 5 seconds to work out what he should do. Quick kid!
Good point, but sadly faster than light communication allows messages to be sent back in time (due to special relativity). So once we invent FTL communication were going to be more worried about some severe problems with causality than about aliens many light years away.
I'll be saving my champagne for Epoch day 16,384 (otherwise known as 2^14). A little under 4 years to go...
Excuse me for replying to my own post. I should also mention that Poincaré's conjecture was not about 'a method for determining whether a three-dimensional manifold is a spherical'. It is simply the question of whether there are non-spheres in 3d which have all loops contractible (for a more accurate description, see the parent). The question about methods/algorithms for determining whether or not something is a 3-sphere is in itself very interesting though.
Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).
The words "homologous" and "boundless" have little/nothing to do with it.
Hey. With enough rockets to get there the Sun is already the ultimate crematorium. It might be a little tricky to recover the ashes though.
1) Tying your shoelaces (but of course no one cares)
2) Studying supercoiling of DNA (how it wraps itself up into a small space yet still wriggles enough to present all of it's length at short notice for interactions with cells' other mechanisms)
3) The geometry of three dimensional space (all closed oriented three dimensional spaces can be constructed from knots and the three dimensional sphere! So knot theory has major applications to 3D geometry)
4) The geometry of four dimensional space (for example, surfaces in 4D spanning between knots can be used to specify exotic smooth structures. The existence of such shocked the world of geometry in the 80's)
5) TQFT, Mirror Symmetry, Quantum Gravity etc (the tools developed in and around knot theory are one facet of a huge push in mathematics to forge a better understanding of some of the deepest ideas in modern theoretical physics)
It's not all just "brain-wanking".
Yet another plausible explanation is that they are concerned that someone else may soon have one (possibly even already) and they would like very much to know what things it renders insecure.
You can happily use a 2D (Hausdorf) measure on a 3D set. No problem. But the result would be infinite. I imagine they plan to be quite expensive.
I am a mathematician and you sir are insulting the abilities of drunk lemurs. I personally worry that I would never send any e-mail if I had to answer arithmetic or sports questions.
What they should do for us is to add the option of deep philosophical questions. I would happily give a brief answer while sober, but if I were drunk I would be so distracted that I would be sober by the time I finished formulating my answer.
the current symbolic form it takes, can be expressed in many different ways.
I heartily agree with this. Different forms serve different purposes.
What I was worried about was your previous suggestion that physics and mathematics be unified. Definitely too much mathematics has been removed from school physics and this ruins it. Moreover physical applications would show kids why they should care about mathematics. What they should begin to notice though is that the things they are learning are useful outside of physics. And they should also learn some things which they will be hard pressed to find direct physical applications for at their level (elementary number theory, probability theory).
I propose instead that the application of mathematical ideas in Physics, Biology, Chemistry, Geography,... (heck, everything) be emphasized more in school. And that mathematics lessons teach enough to make this possible.
If we never used the mathematics out of context a lot of ideas developed in physics would still be just that. Statistics (used for example in the study of cancer) would lose out greatly if Newton's theory of infinitesimals had not been developed out of its physical context context into 'calculus' and then applied to probability density functions.
Wikipedia is great for maths. I use it a lot. When I look something up I don't necessarily understand all the terms used to explain it, so I click on some of the links to explain those terms,... etc.
Hey. A lot of people devote a lot of their time in explaining their areas of mathematics to the general public (including myself). And as for your distaste for abstraction. That's what maths is! There is a reason the general public do not follow much in the way of mathematical developments and that is because research level mathematics is actually really hard and takes a lot of dedication to understand well. There is also no elitist clique. We love it when people show interest in our work and want to understand it.
Thanks again for the link.
...there's usually going to be some prior art if your work has any value at all...As long as your work builds upon what's been done in a meaningful way, your ideas should be patentable.
I'm sorry. You appear to be advocating the right to patent ideas which you were not the originator of. I find this objectionable. Your patents should only cover those precise parts which are novel. And even then only if they pass the conditions of originality and non-triviality.
I think of the projects the article mentions as more like 'SETI at home'. Getting people to use unused cycles to do something potentially productive and pretty much guaranteed to be better for them. It's a shame my computer's CPU doesn't benefit from the experience of running some 'SETI at home' calculations.
It's a good philosophical question though. When is a collection of things (say atoms, bricks and mortar, etc.) a thing and when is it just lots of things? Deep down atoms don't come anywhere near touching each other to make molecules and larger structures. I myself am just a collection of tiny dots floating in space a long way from each other.
So we are to understand that dark matter, acted on only by gravity, forms sheets and filaments? We know very well what shapes distributions of particles form over time with only gravity acting on them and they look a lot like galaxies and very little like sheets and filaments. Can anyone clear this up for me?
The colour of the balloons is just an artefact of the translation from the song's original German where they were just "99 Luftballons" (actually the German lyrics tell a much better story as the translation changes a lot). So the world is over whatever colour they make them.
It generates energy as the knee is using energy to slow your downward motion, hence the statement "less than one watt of EXTRA metabolic power for each watt of electricity".
So your creator had the same suggestions. Brilliant. Sounds like someone who cared about our wellbeing. But wouldn't it be a shame if we could not understand that the need for human rights arises independently of (our knowledge of) his existence?
Really? And even if this is 'true', the 248 dimensions of E_8 are used to explain the symmetries of fields in the universe, not as a model for the universe itself. A simple example of what I mean is the following. The surface of a sphere is two dimensional, but the group of rotations you can perform on it is three dimensional. If I really wanted to I could create an E_8 principle bundle on the sphere (representing some kind of generalised fields) which would trivially have at least E_8 symmetry group.
Actually, in my experience the NPC AI leaves a lot to be desired and the monthly fees are pretty huge!
I second the sibling's motion. Curiously this is exactly what we need to introduce an element of competition into the markets and hopefully get M$ to improve their product (and/or reduce it's price). I welcome any arguments against this idea.