tag:blogger.com,1999:blog-3555199390227912207.post4732432047299195687..comments2022-12-01T05:51:34.273-05:00Comments on Egnorance: My comments on P.Z. Myers' reply to Taylormregnorhttp://www.blogger.com/profile/11431770851694587832noreply@blogger.comBlogger53125tag:blogger.com,1999:blog-3555199390227912207.post-75569911463611963242012-01-06T19:06:29.511-05:002012-01-06T19:06:29.511-05:00Cat,
You don't understand these things well ...Cat, <br /><br />You don't understand these things well enough to explain them using Mickey Mouse cartoons. So stay with the example you have suggested yourself. Can you reproduce my calculations? I can walk you through them if they seem hard.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-48847714734368435532012-01-06T16:17:41.482-05:002012-01-06T16:17:41.482-05:00Oleg, one more try. Sine and cosines describe a c...Oleg, one more try. Sine and cosines describe a circle in xy space. Some friends at work had this analogy: <br /><br />Frequency tells you how fast the hamster is turning the wheel and phase tells you where the wheel is in the circle. None of it tells you how many times the hamster has already gone around. At least until the bearing wears through, and the you know its been "enough".<br /><br />:-)K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-22083022892230590662012-01-06T10:04:19.827-05:002012-01-06T10:04:19.827-05:00Oleg, you can't take a frequency spectrum and ...Oleg, you can't take a frequency spectrum and figure out what year it came from. I'm sorry, but absolute time is lost.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-86077017944368688032012-01-06T07:47:02.207-05:002012-01-06T07:47:02.207-05:00As you wish, Cat.
We take two signals. f_1(t) = ...As you wish, Cat. <br /><br />We take two signals. f_1(t) = \cos{t} between t=0 and 2\pi (and zero otherwise) and f_2(t) = \cos{t} between t=8\pi and 10\pi (and zero otherwise). <br /><br />The Fourier transforms for the first signal is <br />F_1(\omega) = \int_0^{2\pi} \cos{t} e^{i\omega t} dt = \frac{e^{2\pi i(\omega+1)}}{i(\omega+1)} + \frac{e^{2\pi i(\omega-1)}}{i(\omega-1)}. F_2(\omega) equals F_1(\omega) times the phase factor c(\omega) = e^{8\pi i\omega} generated by the delay of 8\pi. It is this phase factor that allows one to distinguish between the two Fourier transforms. <br /><br />I can see where the error likely creeps into your thinking. You seem to think that since the signals are periodic, their Fourier transforms exist only at frequencies \omega=+1 and −1. If that <i>were</i> the case then the phase factor c would be 1 and you would not be able to distinguish F_1(\omega) from F_2(\omega). But the signals are <i>not</i> periodic, for they are not repeated indefinitely. As a result, their Fourier transforms are peaked near \omega=+1 and −1, but they do not vanish at nearby frequencies. <br /><br />If you wish to think physically about this, think Heisenberg uncertainty relation. A wave that has a finite extent \Delta t in time has a finite width \Delta \omega \approx 1/\Delta t in Fourier space. In this case, the frequency width is 1/(2\pi). <br /><br />Before you reply, Cat, read carefully through my comment and do the math. That should have a sobering effect.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-84601092151563058962012-01-06T07:41:42.398-05:002012-01-06T07:41:42.398-05:00PS.
Can't quite the Egnorance. Worse than smo...PS. <br />Can't quite the Egnorance. Worse than smoking!Anonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-75574833199619747182012-01-06T07:41:05.100-05:002012-01-06T07:41:05.100-05:00KT,
I ask this honestly, to see if I get the drift...KT,<br />I ask this honestly, to see if I get the drift of what your arguing with Oleg...<br />Are you suggesting that the 'time-stamp' of the Fourier Transform is one of DURATION, not a coordinate in time. For example it may express the signal projection/broadcast (not sure of correct term) will last 10 minutes, but does not tell us WHEN the signal was broadcast?<br />Or am I totally lost here?Anonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-63776447409728171102012-01-05T23:39:11.947-05:002012-01-05T23:39:11.947-05:00Wrongo, my lad. Phase only resolves to the period...Wrongo, my lad. Phase only resolves to the periodicity of the signal. After that, it's all the same. That is, if I have a signal with period of 1 second and I capture it from 0.5 to 1.5, the Fourier transform will indeed be different than if I took from 0 to 1. However, if I take it from 1.5 to 2.5 it looks the same as it does from 2.5 to 3.5 or 143.5 to 144.5.<br /><br />Think about it. If the signal is continuously repeating for the period of observation and you capture a period of it, you can't tell where in time the thing came from. Absolute time is lost, but time relative to the periodicity of the signal is retained.<br /><br />Try it for yourself. Take the Fourier transform of Cos (theta) from 0<theta<=2Pi and compare it to the Fourier representation of the same signal from 8Pi<theta<=10Pi. Since the two signals are indistinguishable, their Fourier transforms are indistinguishable. Otherwise, as time went on, the Fourier transforms of identical signals would diverge.<br /><br />Frequency representations, whether they are continuous or discrete, always have at least an implied time stamp even if it is "March 3, 2009". Otherwise phase would have to resolve along an infinite axis of time and it doesn't, it only resolves to the period of the signal.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-36726889439297193752012-01-05T23:17:24.064-05:002012-01-05T23:17:24.064-05:00Cat: Oleg, no signals are constant in time. "...Cat: <i>Oleg, no signals are constant in time. "Continuous Fourier transforms" still assume a start and end time which are not part of the frequency representation itself.</i><br /><br />Sorry, Cat, but you're wrong. The start and end time (and everything else) are fully encoded in the Fourier transform of a signal. As a complex phase. <br /><br />For example, we can take the Fourier transform of a rectangular pulse that begins at time −T/2 and ends at time +T/2. The result is 2 \sin{\omega T/2}/\omega. Are you with me, Cat? <br /><br />Assume you are. Now take the same signal and shift it in time so that it begins at 0 and ends at T. The Fourier transform is (e^{i\omega T}-1)/i\omega, or the previous result times a pure phase factor e^{i\omega T/2}. <br /><br />Even more generally, give me the complex Fourier transform of a signal and I will give you the original. With start and end times.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-71416584133279696162012-01-05T22:56:24.398-05:002012-01-05T22:56:24.398-05:00OK, I can't resist.
Oleg, no signals are cons...OK, I can't resist.<br /><br />Oleg, no signals are constant in time. "Continuous Fourier transforms" still assume a start and end time which are not part of the frequency representation itself. For example, if I claimed my frequency representation of the atmospheric noise in the VLF frequency band in the region of Miami as continuous and required no start time to be specified, then I would be hooted out of the lab in derision as someone would point out that the frequency representation of the newly-cooled Earth would not be captured in the same equations as the frequency representation of the noise-rich summer thunderstorms of 2011. Prior to that, the deep, empty space of pre-Earth would be similarly unrepresented. You <i>have</i> to specify (or at least imply) a start time outside of the frequency representation otherwise it's total nonsense.<br /><br />You know, this is all very rude of me. You've got an image of me as a total dunce. You want to mock me. I'll help.<br /><br />I actually think the Chargers' decision to keep Norv Turner wasn't all that bad. The injuries to the receiver corps at the beginning of the season might have been enough to scuttle everything even if you'd had Don Shula as coach.<br /><br />There. Now you can make fun of me. Almost everyone else in San Diego probably would if they'd read that.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-76509049630199393272012-01-05T22:51:34.813-05:002012-01-05T22:51:34.813-05:00That's OK, Cat. Who needs calculus anyway? It&...That's OK, Cat. Who needs calculus anyway? It's not in MCAT anymore.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-54749475034434397142012-01-05T22:45:14.245-05:002012-01-05T22:45:14.245-05:00Yeah, oleg, it stopped at integers. I'm an id...Yeah, oleg, it stopped at integers. I'm an idiot. Duhhh.<br /><br />You found me out.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-77444788740718827102012-01-05T19:53:23.500-05:002012-01-05T19:53:23.500-05:00Cat: The continuum? Sounds metaphysical.
Did you...Cat: <i>The continuum? Sounds metaphysical.</i> <br /><br />Did your math education stop at integers and fractions? <a href="http://mathworld.wolfram.com/Continuum.html" rel="nofollow">Live and learn</a>.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-84012546179258589692012-01-05T17:21:32.161-05:002012-01-05T17:21:32.161-05:00Rex, here are the highlights. Dig Demba Ba's ...Rex, <a href="http://www.foxsoccer.tv/watch/type/vod/video/1894938/title/newcastle-v-man-utd" rel="nofollow">here are the highlights</a>. Dig Demba Ba's goal and then the own goal off of Phil Jones at the end. Awesomeness squared!K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-43492466539827474812012-01-05T17:19:28.321-05:002012-01-05T17:19:28.321-05:00We're talking about continuous, not discrete F...<i>We're talking about continuous, not discrete Fourier transforms. A point or two in the continuum makes no difference.</i><br /><br />The continuum? Sounds metaphysical. A good scientific atheist would never sully his hands with something that can't actually exist. I call Easter Bunny on your argument.<br /><br />:-)K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-3348048638703546452012-01-05T05:48:11.780-05:002012-01-05T05:48:11.780-05:00@KT,
I am afraid your humour had transmitted above...@KT,<br />I am afraid your humour had transmitted above my frequency. I did not even receive, let alone map your signal. :P<br /><br />"Captcha word: bleresy. I kid you not....I watch the replay of Newcastle's 3-0 win over Manchester United. Howay the lads!"<br /><br />Congrats! I am always glad to see anyone beat united. Been a Reds (LFC) fan since I can remember. Not been following the premiership, or anything but local league hockey (CHL like 1st div) for a couple of years....too much going on. But my wife gives me the updates. <br />Anyway, three cheers for the giant killers. <br /><br />@All,<br />It seems I am on ignore / insult these days here folks and I am becoming increasingly busy at my post and with my rediscovered early fatherhood duties...so I will bid you adieu and check in later this month. <br />God bless and stay well all of you.<br /><br />Keep up the good work, Dr Egnor. <br />CrusadeRexAnonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-44526746990644040952012-01-04T21:54:33.068-05:002012-01-04T21:54:33.068-05:00Cat, relax. We're talking about continuous, no...Cat, relax. We're talking about continuous, not discrete Fourier transforms. A point or two in the continuum makes no difference. <br /><br />Besides, a properly defined <a href="http://mathworld.wolfram.com/DiscreteFourierTransform.html" rel="nofollow">discrete Fourier transform</a> is a unitary transformation. No points are lost. Your engineering implementations might not do that, but that's not my problem.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-68122280988241694452012-01-04T20:42:08.746-05:002012-01-04T20:42:08.746-05:00Oops! I had that backwards. It's going from ...Oops! I had that backwards. It's going from time to frequency you lose start and end times.<br /><br />Now <i>I</i> will leave quietly! :-)K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-76673258610352053662012-01-04T20:40:45.732-05:002012-01-04T20:40:45.732-05:00In a nutshell, the Fourier transform of a signal i...<i>In a nutshell, the Fourier transform of a signal is the response of a harmonic oscillator with a given natural frequency to that signal (amplitude and phase of its oscillations). If you know how oscillators of all frequencies respond to a signal, you can reconstruct the signal itself. That's it.</i><br /><br />Geeze, oleg, get a humor infusion, would you?<br /><br />And by the way, you're not entirely correct. Going from the frequency domain to the time domain, you lose t0 and t1, the start and end times of the signals. That means you lose track of when they occurred, unless you stored a time stamp along with your frequency representations, something that does not happen by itself in a Fourier transform.<br /><br />I hold several patents in this area. You may leave quietly. Thank you.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-35053158299437371732012-01-04T20:35:36.897-05:002012-01-04T20:35:36.897-05:00CrusadeREX, I was kidding. I'm a confirmed Pa...CrusadeREX, I was kidding. I'm a confirmed Papist.<br /><br />:-)<br /><br />Captcha word: bleresy. I kid you not. That's what I'll be charged with after my drunken shouts tonight as I watch the replay of Newcastle's 3-0 win over Manchester United. Howay the lads!K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-29443149440401527472012-01-04T08:03:41.492-05:002012-01-04T08:03:41.492-05:00@Oleg,
"It cracks me up how theologists dream...@Oleg,<br />"It cracks me up how theologists dream up definitions that make no sense whatsoever and present them as profound."<br /><br />Your lack of understanding is not evidence for (or for the lack of) profundity of various theological positions. <br />Maybe the comedy truly lies with the reductionist attempting to address real and unavoidable complexities BEYOND the grasp of their dogmatic materialism? No. That's really rather sad...not funny. <br />Oh well, you keep on laughing Oleg. <br />They say it's good for the soul.Anonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-92062200950196531022012-01-04T07:54:18.291-05:002012-01-04T07:54:18.291-05:00Delete Comment From: Egnorance
crusadeREX said....Delete Comment From: Egnorance<br /><br /><br /> crusadeREX said...<br />@Bach,<br />I am sure you're right. I am sure he misusing the word intentionally.<br />Still, that makes him a lying AND lazy, conformist who twists language with popular terms in order to bullshit young people into thinking his 'oil' is THE curative.<br /><br />"Your definition of 'heresy' is ahistorical too. "<br />Sure, Bach. Your super-secular lefty views are the accepted ones...by you. But for the rest of us the term heretic and heresy are not synonymous with reformation or change. They are words with their own meanings used in context, as I have done. <br /><br />" but when Lutherism won,"<br />Won what?<br /><br />"...it stopped being a heresy and became accepted dogma, at least in part of Europe anyway."<br />Even if I accept your Superbowl version of history, you make my point for me. <br /><br /><br />@Mulder,<br />"thats a LOT of typing just to argue over the term 'random.' Talk about a quibble.."<br />Lot of typing? Really? Maybe you were looking for the leapfrog blog? The Sesame Street forum? <br />As for being a quibble, perhaps you would enlighten us as to exactly WHERE the subject is I am avoiding? ALL I see in PZ's response is misrepresentations and a childishly simple regression argument that was previously and adequately addressed by the blogger himself (Mike). <br />Hope that is not too many words for you, Mulder. <br /><br /><br />@KT, <br />"Worse still, Myers isn't even trying to understand."<br />My point entirely. Myers is all about enforcing a dogma, not searching for a truth. His sophomoric response smacks of intellectual dishonesty and intolerance. <br /><br />"Can God make a Fourier representation so complex that even He can't invert it back into the time domain?"<br />Now THAT is a fascinating knot. I must say I really enjoy your posts, KT - so try to be kind when assessing my response to this, would you? :P <br />Here it is: God IS. Therefore there is nothing he makes that cannot be undone - no matter how complex. If this expression is 'too complex' it would be His will that is was so, and His will would be what makes it so. <br />'Too complex'? Perhaps too complex for the time domain. That I could perceive. But in such an event, could God not 'revise' or 'upgrade' time as needed?<br />Perhaps this is a window into eternity you peep through with your question, KT? Perhaps such an expression COULD exist for purposes OUTSIDE of time, or in a different stream/nature of that measure. Perhaps such a mathematical expression of such vast complexity could perform a function in a 'higher' or external existence OUTSIDE of the time stream. <br />The question in my mind eventually becomes: Can God's will change, and does our reality change with it accordingly? That reality includes time and our perception of it. <br /><br />@Pépé <br />"That's kid stuff compared to the semiotics of life!"<br />Too true. Another level entirely.Anonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-2685440975258678182012-01-04T07:48:55.842-05:002012-01-04T07:48:55.842-05:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/14739783974158130525noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-8256034685955947702012-01-04T07:27:58.480-05:002012-01-04T07:27:58.480-05:00Egnor: God is pure knowledge, which is 1) unlimite...Egnor: <i>God is pure knowledge, which is 1) unlimited 2) not composed of parts. God doesn't "forget" one particular datum, or come to know something that He didn't previously know. </i> <br /><br />It cracks me up how theologists dream up definitions that make no sense whatsoever and present them as profound.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-43911720057837097992012-01-04T07:25:52.958-05:002012-01-04T07:25:52.958-05:00Egnor: Pretty sloppy definition of a Fourier trans...Egnor: <i>Pretty sloppy definition of a Fourier transform.</i><br /><br />Do you know what "in a nutshell" means? It is nonetheless enough for someone who understands enough of the physics. <br /><br /><i>What you're referring to is the frequency response of a system, which is not generally the Fourier transform of the input signal, but rather the convolution of the Fourier transform of the signal with the transfer function of the system. </i> <br /><br />You have to take the limit of zero linewidth for the oscillators. Then (the imaginary part of) the response function becomes the delta-function and you get the desired result.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-3555199390227912207.post-39321960542970450012012-01-04T06:09:37.809-05:002012-01-04T06:09:37.809-05:00@troy:
The issue is what God is, not what God doe...@troy:<br /><br />The issue is what God is, not what God does. God doesn't "contain" things. He's not a vessel. God is pure actuality, pure existence. He is metaphysically simple, in the sense that He is not a composite of things. <br /><br />I am a composite of all of my body parts, down to my subatomic particles, as well as my soul, my spirit, and my act of existence.<br /><br />God has no body, is pure spirit, and His essence (what He is) is identical to His existence (that He is).<br /><br />We have difficulty with the concept of omniscience and omnipotence in a simple Being because we apply natural categories to a supernatural Being. <br /><br />God is pure knowledge, which is 1) unlimited 2) not composed of parts. God doesn't "forget" one particular datum, or come to know something that He didn't previously know. <br /><br />The classical philosophers made very strong arguments about God's nature, based on meticulous deductive logic. The argument to God's lack of parts is based on the Prime Mover argument, from Aristotle, which demonstrates that God has no potentiality, only actuality. Parts can have various relations, which are potentialities, which God can't have.mregnorhttps://www.blogger.com/profile/11431770851694587832noreply@blogger.com