tag:blogger.com,1999:blog-8587336.post7804217981076754605..comments2021-02-27T06:11:39.502-08:00Comments on CONTRARY BRIN: Next Technologies!David Brinhttp://www.blogger.com/profile/14465315130418506525noreply@blogger.comBlogger27125tag:blogger.com,1999:blog-8587336.post-25347588466867612612014-08-26T14:44:14.340-07:002014-08-26T14:44:14.340-07:00So would The Uplift War count as a prediction for ...So would <strong>The Uplift War</strong> count as a prediction for the Google Glass brainwave interface?Matt Gnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-3060061157225837022014-08-24T15:52:31.708-07:002014-08-24T15:52:31.708-07:00http://en.wikipedia.org/wiki/Hyperreal_numberhttp://en.wikipedia.org/wiki/Hyperreal_numberJumperhttps://www.blogger.com/profile/11794110173836133321noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-29381327684186560592014-08-24T15:44:15.221-07:002014-08-24T15:44:15.221-07:00Some contingent of my friends here will enjoy the ...Some contingent of my friends here will enjoy the essays here:<br />http://www.stonekettle.com/<br /><br />Warning: possible angertainmentJumperhttps://www.blogger.com/profile/11794110173836133321noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-41952760240773454882014-08-24T15:39:58.338-07:002014-08-24T15:39:58.338-07:00One does not have to count all integers to prove t...One does not have to count all integers to prove they constitute and infinity. "Countable" means there is no bonded length within which a finite number of integers cannot be counted.<br /><br />But the Hilbert-Cantor magic does not have to involve some infinity that is "out there." It can be proved there is an infinite number (uncountable) of rational numbers between each and every integer. That fact proves that there are "levels" of infinity. It is not philosophy, it is math. <br /><br />And there's an infinite amount of irrationals between each rational. Sorry, that's math again.<br /><br /><br />======<br /><br />onwardDavid Brinhttps://www.blogger.com/profile/14465315130418506525noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-6656765380062467392014-08-24T15:31:51.062-07:002014-08-24T15:31:51.062-07:00locum seems to be proposing an uber-Feynmanian mat...locum seems to be proposing an uber-Feynmanian mathematical philosophy such that, no, "countables" are not actually in the set of countables. While I tend to applaud uber-Fenmanian thought, as shortcuts to the bottom line are interesting and bear fruit in the form of time saved, I understand the nomenclature is not tied to the folk etymology of the words.Jumperhttps://www.blogger.com/profile/11794110173836133321noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-5455436214832228512014-08-24T14:08:32.813-07:002014-08-24T14:08:32.813-07:00Off on a mathematical tangent here, but talk of pi...Off on a mathematical tangent here, but talk of pi and "e" got me remembering the Golden Ratio, which I seem to recall (with a bit of irony) is itself irrational. Approximately 0.618, and its reciprical is approximately 1.618, which is not coincidence, but rather the whole point.<br /><br />What <b>is</b> coincidence, though, is that this is also the approximate ratio of a kilometer to a mile.<br /><br />Does anyone else feel like that should be significant somehow? <br /><br />LarryHartnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-74082095704712183412014-08-24T14:02:25.865-07:002014-08-24T14:02:25.865-07:00@locumranch
I think you have a lot of trouble wit...@locumranch<br /><br />I think you have a lot of trouble with colorful language. The entire disagreement here seems to be over the usage of "countable". You're using "countable" to mean "finite", and mathematicians have a different meaning for the term. You sound like you want to take issue with the use of that particular word to mean something other than "finite". <br /><br />But I don't think anyone else cares about that as an issue. The important thing is that mathematicians refer to the infinite set of integers as being different in kind from the infinite set of real numbers, and "countable" is a reasonably-understood analogy to make it a perfectly Cromulent word to use [/Simpsons].<br /><br />LarryHartnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-14751929622138741972014-08-24T10:02:02.450-07:002014-08-24T10:02:02.450-07:00Listen to Larry.
An infinite set of integers can ...Listen to Larry.<br /><br />An infinite set of integers can only be considered 'countable' if it is bounded by zero & any particular integer, meaning that a 'countable infinity set' assumes finite (as in non-infinite) limits which, if accepted, beg the existence of transfinite numbers, much in the same manner that Zeno argues his Paradoxes of Motion.<br /><br />In this way, Cantor betrays himself as a philosopher rather than a mathematician, and further study reveals that many of his mathematical proofs are (in actuality) recursive metaphysical argument masquerading as mathematics:<br /><br />https://www.math.dartmouth.edu/~matc/Readers/HowManyAngels/Cantor/Cantor.html<br /><br /><br />Bestlocumranchnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-10627319874653212722014-08-24T08:53:03.080-07:002014-08-24T08:53:03.080-07:00locumranch:
and it is this real lack of numerical...locumranch:<br /><i><br />and it is this real lack of numerical malleability which (first) denies us the assumption of multiplicity and (then)forces us to conclude that an infinity based on real numbers is by definition 'uncountable'.<br /></i><br /><br />"Countable" has a more specific meaning in the mathematical world.<br /><br />Of course, you can't count to infinity, so you can't count all of the integers. But you <b>can</b> count all of the integers between zero and any particular integer.<br /><br />The same statement does not hold for real numbers.<br /><br />That's why the infinite set of integers is considered "countable" and the infinite set of real numbers is not.<br /><br />(I do remember that much from my college days)LarryHartnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-22967356249529837412014-08-24T07:19:11.008-07:002014-08-24T07:19:11.008-07:00Tony Fisk:
Just to add to the fun, there are also...Tony Fisk:<br /><i><br />Just to add to the fun, there are also an infinite number of transcendental numbers (inexpressible as a logarithm) between every irrational number.<br /><br />As far as I am aware, we only know two of them: 'π' and 'e'<br /></i><br /><br />This is embarrassing to admit, because 35 years ago, I <b>was</b> a math major, but the skills have rusted.<br /><br />Wasn't the very definition of 'e' tied in with a concept of 'natural logarithms'?LarryHartnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-83180507545613245882014-08-24T07:10:48.654-07:002014-08-24T07:10:48.654-07:00Mark:
Of course computers can theoretically drive...Mark:<br /><i><br />Of course computers can theoretically drive both faster and safer than humans. Sure, there is that "theoretically" in the sentence, it still needs to be proved...<br /></i><br /><br />A favorite line of mine, attributed to Yogi Berra:<br /><br />"In theory, there is no difference between theory and practice, but in practice, there <b>is</b>."LarryHartnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-16060312709981210432014-08-24T07:03:56.971-07:002014-08-24T07:03:56.971-07:00David,
Quake?David,<br />Quake?Paul451https://www.blogger.com/profile/12119086761190994938noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-78987636263068844232014-08-24T03:59:56.579-07:002014-08-24T03:59:56.579-07:00Hi Locum
Better read all that again,
You obviousl...Hi Locum<br /><br />Better read all that again,<br />You obviously have not got it the first time<br /><br />Incidentally we are talking "real" numbers here - even the irrational and transendentalDuncan Cairncrossnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-80356216862266797532014-08-24T02:27:52.215-07:002014-08-24T02:27:52.215-07:00What Duncan and Jonathon describe as the 'math...What Duncan and Jonathon describe as the 'mathematics' of infinity is not mathematics but an unsupported and unsupportable non-empiric (a priori) philosophy.<br /><br />Cantor's 'Levels of Infinity' and Hibert's (Infinity) Hotel paradox both rely on the exploitation of negative and imaginary numbers to suggest that something called a 'Countable Infinity Set' can exist even though such an 'infinite set' would be 'uncountable' in the realm of real numbers.<br /><br />In effect, Cantor's transfinite argument is a circular one which 'begs the question' by (first) positing that infinity is 'countable' and (then)concludes that the mere act of plus-one counting confirms a multiplicity of infinities.<br /><br />Unfortunately for Cantor, real numbers are much less malleable than imaginary ones, and it is this real lack of numerical malleability which (first) denies us the assumption of multiplicity and (then)forces us to conclude that an infinity based on real numbers is by definition 'uncountable'.<br /><br />I, too, can 'conceive' of seven multiple infinities & many other impossibilities before breakfast but, unlike some of you, I know that 'conceiving' of something does not necessarily make it true.<br /><br /><br />Bestlocumranchnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-83900386267432557062014-08-23T22:31:06.042-07:002014-08-23T22:31:06.042-07:00Quick comment on driverless car discussion: the te...Quick comment on driverless car discussion: the tendency has been for drivers to drive more recklessly as more safety features are added. This isn't to say drivers are turning into hoons, but I doubt the same psychology will apply to AI drivers.<br /><br />What driverless cars *will* be useful for is to move share vehicles between pick-up and drop-off points. Someone a while back estimated that such a system is extremely fuel efficient (even beating bicycles.. there was a bit of a discussion about that one)Tony Fiskhttps://www.blogger.com/profile/14578160528746657971noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-8650184344027866822014-08-23T21:57:15.196-07:002014-08-23T21:57:15.196-07:00Guys I already tried. He IS getting better! And ...Guys I already tried. He IS getting better! And occasionally is cogently worth the effort.<br /><br />David Brinhttps://www.blogger.com/profile/14465315130418506525noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-49137013748295373432014-08-23T21:50:25.123-07:002014-08-23T21:50:25.123-07:00(... lies in wait for someone to pounce triumphant...(... lies in wait for someone to pounce triumphantly with more.)Tony Fiskhttps://www.blogger.com/profile/14578160528746657971noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-33220798752325099842014-08-23T21:48:47.054-07:002014-08-23T21:48:47.054-07:00Just to add to the fun, there are also an infinite...Just to add to the fun, there are also an infinite number of <i>transcendental</i> numbers (inexpressible as a logarithm) between every irrational number.<br /><br />As far as I am aware, we only know two of them: 'π' and 'e'Tony Fiskhttps://www.blogger.com/profile/14578160528746657971noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-55122115359866192282014-08-23T21:43:23.138-07:002014-08-23T21:43:23.138-07:00Mark,
"Of course computers can theoretically ...Mark,<br /><i>"Of course computers can theoretically drive both faster and safer than humans. Sure, <b>there is that "theoretically"</b> "</i><br /><br />And that was my point. Saying that driverless cars will allow faster roads ignores actual history. As we've made cars safer, authorities also often cut speed limits (and enforced those limits more pedantically.) There is no way in hell authorities will raise the speed limit for driverless cars.<br /><br />Google is already getting grief because they programmed their driverless vehicles to travel up to 10kmh over the local limits in order to keep up with traffic flow as they believed that if traffic was flowing 5-10kmh above the limit it would be more dangerous to stick to the limit and become a moving obstacle. Authorities disagreed... loudly. Likewise, Google's vehicles weren't to have manual controls, just a go-button. Californian authorities insisted on having a full manual control, even though there's been plenty of research suggesting that "taking over" from an autopilot <i>during</i> an emergency actually increases the risk. For cars, a big red Stop button which cuts the engine power, and signals the autopilot to stop as safely as it can, is better.<br /><br />I'm willing to bet that in many jurisdictions, the first generation of autonomous cars will be required to travel <i>below</i> the speed limit, and with greater than normal inter-vehicle gaps. And those restrictions will remain even if they later ban drivers from freeways and other high speed roads.<br /><br />[Two local examples. A local rural road had a 110kmh limit for at least the 30 years that I've been using it, in spite of broken edges and no outer lane markings. Council widened the lanes, added proper outside lane markings (which made the road much safer at night), and, having improved the safety of the road dramatically, <i>lowered</i> the speed limit. Just this last week, a truck lost its brakes on a down-hill stretch of a different freeway, crashing and killing someone in a car. The speed limit was 110kmh, the truck was going just 70kmh when it lost its brakes (and 150kmh when it crashed), and instead of installing another arrestor-bed (sand/gravel pit) at the bottom of the hill (as its own advisers had recommended several years ago), they are reducing the limit for all vehicles on that major freeway to 60kmh. In the last decade, I can't recall <i>ever</i> seeing a speed limit raised because, say, a problem road was made safer, no matter how many people complain.]<br /><br />[3-6mph (5-10kmh), 68mph (110kmh), 93mph (150kmh), 43mph (70kmh), 37mph (60kmh) for US readers.]<br /><br />tl;dr - If robo-cars are allowed to travel faster than regular cars, I will eat my hat.Paul451https://www.blogger.com/profile/12119086761190994938noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-79824637350121367072014-08-23T20:22:58.660-07:002014-08-23T20:22:58.660-07:00Hi Locum
You need to read some basic mathematics
L...Hi Locum<br />You need to read some basic mathematics<br />Look up<br />Rational numbers<br />Irrational numbers<br />Levels of infinity<br />Hilbert's Hotel<br /><br />It will open your eyes - its fun<br />Weird - but fun<br /><br />http://www.scientificamerican.com/article/strange-but-true-infinity-comes-in-different-sizes/<br /><br />http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_HotelDuncan Cairncrossnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-62617017542956107862014-08-23T19:44:50.335-07:002014-08-23T19:44:50.335-07:00locum, perhaps you should actually study mathemati...locum, perhaps you should actually study mathematics before saying what's "impossible". Mathematicians contemplate seven multiple infinities before breakfast.Jonathan S.noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-76845908870436385992014-08-23T18:58:40.723-07:002014-08-23T18:58:40.723-07:00It's nice to read a post with an empiric and/o...It's nice to read a post with an empiric and/or scientific basis, especially after the last one violated basic mathematical principles by its attempt to add to or multiply by an immeasurable like infinity, giving us yet another definition for an Optimist:<br /><br />One who expects an integer after multiplying and/or dividing by either infinity or zero.<br /><br />I also apologise, btw, for accidently giving away the plot for 'The Practice Effect' (above).<br /><br /><br />Bestlocumranchnoreply@blogger.comtag:blogger.com,1999:blog-8587336.post-41097478143084585042014-08-23T14:00:54.719-07:002014-08-23T14:00:54.719-07:00Paul,
I don't understand your complaint about...Paul,<br /><br />I don't understand your complaint about "fast roads" at all. <i>Of course</i> computers can theoretically drive both faster and safer than humans. Sure, there is that "theoretically" in the sentence, it still needs to be proved, but using seatbelts as a counter example makes no sense at all.Markhttps://www.blogger.com/profile/08254344563346437079noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-49372647171099561052014-08-23T06:43:14.493-07:002014-08-23T06:43:14.493-07:00From: 2050 and the Future of Infrastructure
"...From: 2050 and the Future of Infrastructure<br /><i>" 'Smart roads are fast roads. Travel speed will be increased at the same time safety is improved.' "</i><br /><br />Errr, no. We've added crumple-zones, seatbelts, airbags, ABS, and increasingly ESC, seen the corresponding drop in road deaths per driven mile, and yet speed limits have dropped over and over.<br /><br />Re: Space-based solar power<br />Always thought that an ideal first market would be for a lunar facility, to deal with that 2-week night, in a location where the customer is willing to pay a lot more than usual.<br /><br />Re: Mass energy storage<br />In 15-20 years, Tesla is going to have a <i>lot</i> of battery packs being traded/upgraded from early model electric cars, where they've lost enough range to be annoying to drivers, but are still holding, say, 50-75% of their original capacity. Before they are stripped and recycled for lithium, there may be a secondary market for home storage... If only there was a way for Musk to leverage that... Oh wait, he also owns Solar City, whose business model is you let them install free panels and they sell you cheaper power. So they'll be able to add storage options for their customers, via a simple plug'n'play battery pack, and not only store daytime solar for off-peak, but also buy cheap off-peak power and sell it back to the grid on-peak, being able to control the distributed array of battery packs installed in customer's homes to maximise profits, giving the customers yet cheaper power as a side-effect.<br /><br />Regular utilities wouldn't be able to convince enough people to let them install remotely controlled battery packs in their homes, but Solar City can.<br /><br />And with sufficient storage, electricity becomes a commodity rather than a service. It's a total game changer. (Also a nice back up for that little Carrington problem.)Paul451https://www.blogger.com/profile/12119086761190994938noreply@blogger.comtag:blogger.com,1999:blog-8587336.post-41306645124091498062014-08-23T05:57:52.160-07:002014-08-23T05:57:52.160-07:00re: fast trains. The motion sickness prblem is e...re: fast trains. The motion sickness prblem is easily fixed. Make trains more like aircraft - use small windows. Display motion stabilized video of the surroundings instead. <br /><br />Hyperloop would be impractically expensive if underground as the BBC article atates. It is meant to be suspended pipes that have a small footprint. <br /><br />Re: DARPA PNT. Isn't that just inertial navigation? What is old is new.<br /><br />re: CO2 to methanol catalysis. I'll be impressed when they can do this more efficiently than micro organisms, at industrial scale to make a difference in the use of CO2 sources and more cheaply than natural systems.<br /><br />re: 3D printing of different metals together. I had assumed this was the key technology behind the 3D printed rocket engines at Aerojet and Tesla. Clearly this is an important technique to make complex machines and machine parts. Some threads ago, there was an item about controlling crystal sizes, which really just emulated some traditional metal working techniques. This blows way past those techniques to allow creation of truly interesting structures.<br /><br />Alex Tolleyhttps://www.blogger.com/profile/01556422553154817988noreply@blogger.com