On 11/28/2015 6:42 PM, Cedron wrote:> Yes, Math is weird, but not for that. No fixing needed there, just an > expansion of your space. > > What's really weird, at least to me, is that there are just as many > integers as there are fractions. >I think what is really weird in math is that there more irrational numbers than rational ones.> Extra credit question: Is weirdness orthogonal to usefulness? > > Ced > > > --------------------------------------- > Posted through http://www.DSPRelated.com >
Math is Weird
Started by ●November 28, 2015
Reply by ●November 30, 20152015-11-30
Reply by ●November 30, 20152015-11-30
On Sun, 29 Nov 2015 23:37:11 -0600, Nasser M. Abbasi wrote:> On 11/28/2015 6:42 PM, Cedron wrote: > >> Yes, Math is weird, but not for that. No fixing needed there, just an >> expansion of your space. >> >> What's really weird, at least to me, is that there are just as many >> integers as there are fractions. >> >> > I think what is really weird in math is that there more irrational > numbers than rational ones.So, numbers mirror humanity -- what's weird about that? -- www.wescottdesign.com
Reply by ●November 30, 20152015-11-30
On Monday, November 30, 2015 at 12:37:18 AM UTC-5, Nasser M. Abbasi wrote:> On 11/28/2015 6:42 PM, Cedron wrote: > > > Yes, Math is weird, but not for that. No fixing needed there, just an > > expansion of your space. > > > > What's really weird, at least to me, is that there are just as many > > integers as there are fractions. > > > > I think what is really weird in math is that there more irrational > numbers than rational ones. > > > Extra credit question: Is weirdness orthogonal to usefulness? > > > > Ced > > > > > > --------------------------------------- > > Posted through http://www.DSPRelated.com > >Holds for people too. How else could we have the prez we have?
Reply by ●December 1, 20152015-12-01
Nasser M. Abbasi wrote:> On 11/28/2015 6:42 PM, Cedron wrote: > >> Yes, Math is weird, but not for that. No fixing needed there, just an >> expansion of your space. >> >> What's really weird, at least to me, is that there are just as many >> integers as there are fractions. >> > > I think what is really weird in math is that there more irrational > numbers than rational ones. >The rationals are like the veins in the leaf; the irrationals are the webbing between the veins.>> Extra credit question: Is weirdness orthogonal to usefulness? >> >> Ced >> >> >> --------------------------------------- >> Posted through http://www.DSPRelated.com >> >-- Les Cargill
Reply by ●December 1, 20152015-12-01
On Mon, 30 Nov 2015 23:19:26 -0600, Les Cargill wrote:> Nasser M. Abbasi wrote: >> On 11/28/2015 6:42 PM, Cedron wrote: >> >>> Yes, Math is weird, but not for that. No fixing needed there, just an >>> expansion of your space. >>> >>> What's really weird, at least to me, is that there are just as many >>> integers as there are fractions. >>> >>> >> I think what is really weird in math is that there more irrational >> numbers than rational ones. >> >> > The rationals are like the veins in the leaf; the irrationals are the > webbing between the veins.I like that metaphor. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●December 1, 20152015-12-01
On 11/30/2015 12:37 AM, Nasser M. Abbasi wrote:> On 11/28/2015 6:42 PM, Cedron wrote: > >> Yes, Math is weird, but not for that. No fixing needed there, just an >> expansion of your space. >> >> What's really weird, at least to me, is that there are just as many >> integers as there are fractions. >> > > I think what is really weird in math is that there more irrational > numbers than rational ones.I don't know why you consider this to be weird. The field of real numbers includes all. Irrationals are the default and rational numbers are a (very) special case. It feels expected to me there are a lot more irrationals than rationals. Much like there are a lot more reals than integers. -- Rick
Reply by ●December 1, 20152015-12-01
>Yes, weird! Three lines can not all be perpendicular to each other, but>signals can all be orthogonal. What's up with that? Why doesn't >someone fix geometry? > >-- > >RickEvery N point signal is an N dimensional vector. For an N dimensional space we can find orthogonal set of vectors. The number of these orthogonal sets are infinite. But we can choose a basis set of length N that is unique in N dimensional space. The lines in geometry are two dimensional objects that can be described by two dimensional vectors. Although we can find many orthogonal lines but all of them are two dimensional. therefore every two orthogonal vector form a basis it means that any line in this space can be described in terms of the basis. That's why we can not find three orthogonal lines in 2D space. We always plot the signals in time or frequency domain. It seems a two dimensional space. But when we want to measure the orthogonality we always take the dot product of two N point signals. That's why we have to consider the signal in an N dimensional space because we already have defined the dot product in this way. We can not imagine more than three dimensions that's why we feel they are different. In FFT we always map the N point signal to another N point signal. We do not loose the dimensions. But any periodic signal can be described by lower number of points in the frequency domain. We have the same idea in geometry. A line in 3D can be described by lower number of dimensions. --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●December 4, 20152015-12-04
On Tue, 1 Dec 2015 13:51:18 -0500, rickman <gnuarm@gmail.com> wrote:>On 11/30/2015 12:37 AM, Nasser M. Abbasi wrote: >> On 11/28/2015 6:42 PM, Cedron wrote: >> >>> Yes, Math is weird, but not for that. No fixing needed there, just an >>> expansion of your space. >>> >>> What's really weird, at least to me, is that there are just as many >>> integers as there are fractions. >>> >> >> I think what is really weird in math is that there more irrational >> numbers than rational ones. > >I don't know why you consider this to be weird. The field of real >numbers includes all. Irrationals are the default and rational numbers >are a (very) special case. It feels expected to me there are a lot more >irrationals than rationals. Much like there are a lot more reals than >integers."Now they know how many reals it takes to fill the Albert H-a-a-a-ll" :-) (I don't think you can count them all.) I like to hang outside on a park bench during the summer and study. One night I saw a disheveled homeless dude walking toward me with a sense of purpose. Uh-oh. Him: "So you're reading science books, eh? What is that, differential equations?" Me: "errr...yeah" Him: "You know what blows my mind? A Koch fractal can have an infinite perimeter, but a finite area. That blows my mind!" Me: "wha?" (I knew that was correct, but WTF?) Him: "And I hear that no matter which two irrational numbers you pick, there's always a rational number between them. And vice versa. That blows my mind, man!" I explained the latter to him, and he nodded his head. Then we exchanged a bunch of good drummer jokes. He was hilariously funny. No friggin' idea where that guy came from, but that was amazing. Anyway, thanks for reminding me of that!
Reply by ●December 4, 20152015-12-04
On 04.12.2015 22:13, Max wrote: (snip)> Anyway, thanks for reminding me of that! > >My most productive hours of study are while I'm riding on a train (or waiting at a railway station). For me it's the perfect environment to concentrate on something. A couple of years ago I was absorbed in reading a DSP book while riding a commuter rail line well after 1 a.m. The car was empty save for a couple strangers not far from me who had drunk some alcohol (there were empty bottles) and now were asleep, each of them lying on a row of seats. At that point some other guy went through the car, and as I imagine had mistaken us for a single company. So as he passed me and those guys he muttered in surprise: "F**k me! Students." Don't know why, but that memory caused me to smile. -- Evgeny.
