In my prior post, I commented on Taylor's guest post on Pharyngula. Taylor is a Christian, and he made some excellent points. P.Z. Myers responded to them, and I'll comment here on Myers' responses.
Here's Myers' response to Taylor's post, with my commentary.
Myers:
The cosmological proofs are based on the impossibility of infinite regress in an essentially ordered series of causes (I discuss Aquinas' First Way in some detail here.) The agency of the First Cause is demonstrated by the cosmological arguments. The Intelligence that grounds existence is demonstrated by Aquinas' Fifth Way, which proves the existence of a Final Cause for the universe.
Myers of course understands none of this, and cares about none of it. He's an atheist, and, despite the hype, reason has nothing to do with his opinions.
In fact, classical and modern philosophers and theologians have observed that secondary causes can't exist without a Primary Cause.
Myers understands none of this.
I believe Christianity is true because I have that personal relationship (as do millions of Christians). I am a very imperfect vessel for God's fellowship, but He deigns to associate with me, which is striking evidence of His mercy. The uniqueness of Christianity is this relationship, and I believe that is much of what Taylor means.
Myers:
Taylor's essay is wise and truthful. The atheists' entries are various expressions of juvenilia and narcissism.
New Atheism is an amalgam of those traits, held together by vincible ignorance.
First, Taylor's post:
Why I am a Christian – Taylor
December 1, 2011 at 8:50 am PZ Myers
Hi PZ, I know this isn’t exactly what you called for, and you probably won’t post this on your famous blog (understandably), but I feel quite strongly that I have two very good reasons for being a Christian:
1) Existence
2) The Uniqueness of Christianity
Now I’ll elaborate a little:
1) The universe exists. Disregarding modern philosophy for a minute, I think this one is fairly obvious. As far as I can know anything, I know that the universe exists. That means it had to have a beginning. Now, the existence and order of the universe may or may not be explained by the Big Bang (I’m no theoretical physicist), but it seems to me that the Big Bang still needs a Big Banger. Someone or something to start the whole thing off. Multiverse theory? I think it still needs some work. And evidence. An eternal Universe? Ok, but I think there are some problems with assigning non-material properties (namely eternal existence) to material things (namely matter). I’ll come back to that. But for now, I’m at the point where I admit that there has to be a beginning, an “uncaused cause” as the philosopher’s put it.
2) That “uncaused cause,” that “Big Banger,” the being that caused everything else to exist, must be the God of the Christian Bible. Why? Because of Christianity’s uniqueness. Say what you will, but after years of studying world religions, Christianity is entirely unique. To oversimplify my case: Every other religion requires an action (service, certain words or actions, good works, etc.), in return for a reward. Christianity is the exact opposite. You are called by Christ first, saved from yourself (that’s the reward), and then the good works flow out of gratitude, or a desire to be more like God. You don’t have to do good works to be saved. Can you see how this is unique?
Now, as to the point about assigning eternal properties to material objects, I don’t see how this is beneficial. Christianity says God created the universe, and He is eternal, intelligent, and caring. Atheism says that the universe created itself, and it is eternal, unintelligent, and uncaring. Is that really better? Personally, I can’t believe that this universe is unintelligent, nor that all of the pain and suffering I see is purposeless.
It seems pretty straightforward to me, but I look forward to hearing your thoughts.
God bless, and stay warm up there,
Taylor
United States
Here's Myers' response to Taylor's post, with my commentary.
Myers:
...#1 is meaningless. Physics has evidence that our universe had a beginning, but there is absolutely no reason to suppose a cosmic benign intelligence was behind it.The classical proofs of God's existence have nothing to do with a temporal beginning of the universe. They are valid even if the universe is eternal in the past.
The cosmological proofs are based on the impossibility of infinite regress in an essentially ordered series of causes (I discuss Aquinas' First Way in some detail here.) The agency of the First Cause is demonstrated by the cosmological arguments. The Intelligence that grounds existence is demonstrated by Aquinas' Fifth Way, which proves the existence of a Final Cause for the universe.
Myers of course understands none of this, and cares about none of it. He's an atheist, and, despite the hype, reason has nothing to do with his opinions.
An avalanche also has a beginning, but we don’t assume it was a little man triggering it by intent.Myers confuses primary and secondary causes. Avalanches can be investigated and explained using natural laws, which are secondary causes. The existence of a primary cause is independent of demonstration of secondary causes. To demonstrate secondary causes is not to disprove primary cause.
In fact, classical and modern philosophers and theologians have observed that secondary causes can't exist without a Primary Cause.
Myers understands none of this.
#2 is absolutely the dumbest reason I’ve ever heard (and I’ve heard it many times) for believing Christianity is true. Here, I’ve just invented a religion: you achieve salvation by hopping precisely three times on one leg every morning. If you forget and die unhopped, you go to hell; so long as you have hopped, you are forgiven and go to heaven. That’s entirely unique, but it doesn’t make it true — in this case, and in Christianity’s case, it’s just stupid.Christianity is certainly unique, in that it posits the necessity of a personal relationship with God as the basis for salvation.
I believe Christianity is true because I have that personal relationship (as do millions of Christians). I am a very imperfect vessel for God's fellowship, but He deigns to associate with me, which is striking evidence of His mercy. The uniqueness of Christianity is this relationship, and I believe that is much of what Taylor means.
Myers:
Now compare this Christian entry, selected as the best of the religious submissions so far, to the atheist submissions, which were chosen entirely at random.
Taylor's essay is wise and truthful. The atheists' entries are various expressions of juvenilia and narcissism.
New Atheism is an amalgam of those traits, held together by vincible ignorance.
"which were chosen entirely at random."
ReplyDelete'Random'? Really now, Peezle. A lie on top of the distortions... classy.
A) He is lying and picked the 'best' ones - ones that imitate his own opinions. A read of that post will instantly back this point.
B)Randomness is not something that can be achieved by such methods as arbitrary judgements (like his selection method).
From these two very simple lines, the tactical mind can make several EZ deductions about PZ.
First he is a liar - and not a good one. He misrepresents the data DELIBERATELY, then tries to make a comparison with that distortion.
A deliberate distorter of truth? Not a good start. If PZ were a mooj and this were a meet up with field command, the next visit would be with his successor.
Secondly, his use of the term 'random' is obviously both for purposes of appeal to the youth and children his 'blog' appeals to. He is desperately trying to be 'cool' for the kids. Fatal for a nerd like him.
Third the use of term 'random' illustrates just how illiterate he is on the VERY subject he claims a gnosis (origins, physics, cosmology)
So.... is he just a an ignorant,lazy conformist, or a LYING ignorant and lazy conformist?
The latter seems quite obvious to me.
In religion when someone deliberately distorts the truth to push an agenda or new creed it is called a heresy and seen as a violation by the faithful.
What do positivists call it when someone does the same to science? THAT is what PeeZee is.
Maybe an old term would fit best: "Snake oil Salesman"
CrusadeRex,
ReplyDeleteHow would you define 'random'? It's actually difficult to define and even to achieve.
Apple, when it was introducing its random play on the iPod, had to introduce a pseudorandom function to prevent the same song being repeated immediately.
I'd imagine that PZ just had a list of replies and just picked them randomly without reading them. Perhaps not the best method of doing it, but not lying.
Your definition of 'heresy' is ahistorical too. Heresies are defined on the basis of the winning dogma. Luther was regarded as a heretic by the Catholic Church, but when Lutherism won, at least in part of Europe, it stopped being a heresy and became accepted dogma, at least in part of Europe anyway.
Michael,
ReplyDeleteIt's illogical to attempt to prove the existence of god by insisting that there's a primary cause, which is defined as being caused by a god. It's a circular argument, even worse than your mischaracterisation of natural selection as 'survivors survive'. God created the Universe, therefore god exists is not a logical argument. The conclusion is just restating the premise, which isn't proved in the first place.
Rex,
ReplyDeletethats a LOT of typing just to argue over the term 'random.' Talk about a quibble..
@bach:
ReplyDelete[It's illogical to attempt to prove the existence of god by insisting that there's a primary cause, which is defined as being caused by a god. It's a circular argument,...]
We deduce the existence of God by logical demonstration. We don't "insist". It's a deductive argument (the cosmological argument), and it's not circular reasoning.
You need to know at least a little bit about the arguments you claim to refute, in order to be taken seriously.
@bachfiend
ReplyDelete...a primary cause, which is defined as being caused by a god.
No, the primary cause IS God.
God (the primary cause) created the Universe, therefore God exists, is as a logical as 2+2=4.
The more I read atheist arguments, the more disappointed I become. There's just nothing there at all. Myers is dismissive where he has no right to be. I can certainly understand his position, even sympathize with it as I have experienced science-based doubts in my own life. However, it's clear from his response that the comprehension does not go both ways.
ReplyDeleteAddendum: Worse still, Myers isn't even trying to understand.
ReplyDeleteThe classical proofs of God's existence have nothing to do with a temporal beginning of the universe.
ReplyDeleteYour criticism of Myers' response on this point is moronic. Meyers was responding to the claim that the temporal beginning of the universe was evidence for God (or as the claim put it, a "Big Banger").
Further, Aquinas' "First Way" is nothing more than gobbledegook. It assumes a whole host of undemonstrated things: the reality of "potency", that "potency" must be actualized by "another", that there cannot be infinite regress, and so on. It is a pile of unwarranted assumptions stacked upon unwarranted assumptions that make you feel good, but have no meaning and cannot be used to prove anything at all, despite your whining and bleating.
Egnor,
ReplyDeleteI think the only reason you accept Aquinas' arguments as valid proof of God's existence is that you want to believe the conclusion. Plenty of professional philosophers (most for all I know) do not accept the proofs as valid. Given your, [cough], limited reasoning skills, your opinion is about as valuable as your opinion on the validity of the proof of Fermat's last theorem.
For me, the problem with the cosmological argument is that in order to support the notion of the Christian God it’s argued that this First Cause must be complex in nature, when if fact the entire history of science has demonstrated over and over again that complex systems can come about by the action of simple laws on simple constituents. Whatever the fundamental principle that allows there to be something rather than nothing, there really is no logical reason to suppose it has to be any more complex than any of the other simple laws that give rise to complex phenomena. What is more likely, that the principle that allows for something would produce a plank sized region of inflation field, or that it would necessitate an omnipotent and omniscient being just kind of sitting there longing to be worshiped.
ReplyDeleteOf course the great magic man in the sky may always find refuge in the cosmological argument because we are talking about things that may never be unobservable. From now until eternity we may be stuck choosing between magic man and the multiverse, but keep in mind that in the history of the world, the solution to every problem ever solved has turned out to be not magic.
Another thing, nobody says “the universe created itself” except for theists mischaracterizing atheists. It’s a straw man based on theist’s utter lack of knowledge and imagination.
-KW
Your criticism of Myers' response on this point is moronic.
ReplyDeleteGiven your, [cough], limited reasoning skills
And so it goes. Since none of the atheists in this particular thread want to break the ice, I'll do it.
You, Egnor, believe in the Easter Bunny. Neener neener neener.
(Every atheism thread needs a reference to the Easter Bunny.)
In the end, however, everyone believes in some variety of Easter Bunny. Scientific atheists fall back on preposterous constructs such as the multiverse, the Landscape or equally fantastic structures to explain the values of universal constants. They love to prove they can understand the Universe through science, but neglect to mention that consciousness is a miniscule subset of the Universe and explaining one away must explain the other away as well. Poof! No point to conversation, but they continue to blather on anyway.
And that is why these atheists bore me. it's all yelling and chest thumping and no apparent comprehension of other points of view or even the implications of their own viewpoint at all.
Sigh.
@anon:
ReplyDelete[the problem with the cosmological argument is that in order to support the notion of the Christian God it’s argued that this First Cause must be complex in nature...]
The classical arguments are that God is utterly simple, because complexity, if it were part of God's nature, would be itself in need of explanation that would presume cause prior to God Himself.
The argument that God must be complex, in the sense of a complexity of relations between parts, is not a classical theological argument. The argument in fact has always been the opposite. Aquinas, among many other theologians,devotes many pages to demonstration of God's utter simplicity.
The only wrench in the simplicity argument is the doctrine of the Trinity, which is of course a relation within God. I'm not a theologian, and the Trinity has always been a mystery, but my understanding is that the Trinity is God's understanding and love within Himself-- the Son is the Father's knowledge of Himself, and the Holy Spirit is the Love between the Father and Son.
C.S. Lewis explained nicely in a way that I found helpful. He wrote that God is a spirit so powerful and transcendent that his knowledge and love are Persons in themselves. Me, myself and I, in a sense. In human beings these relations are within each person. In God these relations are Persons Themselves.
I find the Trinity utterly fascinating.
The argument that God must be more complex than His creation is not an argument that theologians make. It is a caricature.
@K T Cat
ReplyDelete...these atheists bore me. it's all yelling and chest thumping and no apparent comprehension...
Right on! I call this the primate syndrome...
Dr. Egnor,
ReplyDeleteI thought you might be interested in this. It's about atheists teaching courses on scripture.
http://newsbusters.org/blogs/david-limbaugh/2012/01/03/why-are-liberals-blind-their-bias
Joey
"The argument that God must be complex, in the sense of a complexity of relations between parts, is not a classical theological argument. The argument in fact has always been the opposite. Aquinas, among many other theologians,devotes many pages to demonstration of God's utter simplicity."
ReplyDeleteWith all due respect to Aquinas, but he didn't have access to the knowledge and mathematical tools that we have, such as information theory and concepts like Kolmogorov complexity. God cannot be omniscient and simple at the same time, at least not in terms of modern information theoretical concepts.
So please explain (in your own words) how God can know everything and be utterly simple at the same time.
@troy
ReplyDelete...Kolmogorov complexity...
That's kid stuff compared to the semiotics of life!
Egnor: The classical arguments are that God is utterly simple, because complexity, if it were part of God's nature, would be itself in need of explanation that would presume cause prior to God Himself.
ReplyDeleteThat's a great way to solve complex problems. Just declare them solved! I wonder why this "learning strategy" hasn't been widely adopted in the sciences. Makes one's life so much easier!
@Troy:
ReplyDeleteYour question is a good one, and warrants a post, which I'll try to do shortly.
Briefly, simplicity in the sense meant here means not composed of parts. All material things are not simple, because all material things have parts.
God is immaterial-- a Spirit-- and some spirits have metaphysical parts-- essence and existence, for example. In God, essence (what God is) existence (that God is), so God lacks metaphysical parts as well.
Parts are not simple because the relation between parts involves potentialities. God is pure act, with no potency, so He does not have parts of any sort, including metaphysical.
Metaphysical simplicity does not mean that God is dumb, or weak, etc. It means that me is pure act-- being itself. His essence is not really comprehensible to us in itself. We can only understand Him very incompletely-- by analogy.
I'll post in more detail soon.
"It means that He (not me) is pure act..."
ReplyDeleteA Freudian slip?
@oleg:
ReplyDelete[That's a great way to solve complex problems. Just declare them solved!]
The necessary lack of potency in God (God cannot have parts, because parts imply potency because there are always potential relations between parts) is deduced from the Prime Mover argument. It is not a declaration, it is a deduction. A deduction you don't understand, I should add.
[I wonder why this "learning strategy" hasn't been widely adopted in the sciences. Makes one's life so much easier!]
There's plenty of deductive knowledge in the science, especially in applied mathematics. But of course much science is empirical and inductive.
It's humorous that you would assume that the method most appropriate to understanding the supernatural (deduction) must be the same as the method most appropriate to understanding nature.
You really need to get help for this scientism. It's intellectually disabling.
@Troy:
ReplyDelete[With all due respect to Aquinas, but he didn't have access to the knowledge and mathematical tools that we have, such as information theory and concepts like Kolmogorov complexity. God cannot be omniscient and simple at the same time, at least not in terms of modern information theoretical concepts.]
Metaphysical simplicity does not mean stupidity. It means purity-- pure actuality-- lack of admixture.
Kolmogorov complexity and other concepts of information theory have nothing to do with the cosmological arguments, which depend on the potency/act distinction, on causation in an essential series of causes, and the concept of necessary existence.
Kolmogorov complexity is of great practical use in signal processing, etc. It has no obvious application to questions of God's existence, that I can see.
God is a Spirit, not a signal.
God is a Spirit, not a signal.
ReplyDeleteCan God make a Fourier representation so complex that even He can't invert it back into the time domain?
@KT Cat:
ReplyDeleteI find the correspondence between the frequency domain and the time domain almost mystical.(I use it quite a bit in my research)
I realize that it's a clever and useful but mundane mathematical method. But I have long been fascinated by the ability to describe reality with no reference to the passage of time.
It's almost like an analogy to eternity-- a glimpse of the other world.
Egnor: There's plenty of deductive knowledge in the science, especially in applied mathematics. But of course much science is empirical and inductive.
ReplyDeleteIt's humorous that you would assume that the method most appropriate to understanding the supernatural (deduction) must be the same as the method most appropriate to understanding nature.
Mathematics and scholastics are both old branches of knowledge. However, one of them died a long time ago. The other is still alive.
Egnor: I realize that it's a clever and useful but mundane mathematical method. But I have long been fascinated by the ability to describe reality with no reference to the passage of time.
ReplyDeleteThat's because they did not teach you physics well enough.
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.
"Metaphysical simplicity does not mean stupidity. It means purity-- pure actuality-- lack of admixture."
ReplyDeleteWhat I was trying to get at is that God must somehow contain or store huge quantities of information about our universe - past, present and future. It seems weird to call such a being simple.
Are we now saying God applied a God-transform to the data? The ultimate data-compression technique?
@oleg:
ReplyDeletePretty sloppy definition of a Fourier transform.
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.
@troy:
ReplyDeleteThe 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.
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.
God has no body, is pure spirit, and His essence (what He is) is identical to His existence (that He is).
We have difficulty with the concept of omniscience and omnipotence in a simple Being because we apply natural categories to a supernatural Being.
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.
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.
Egnor: Pretty sloppy definition of a Fourier transform.
ReplyDeleteDo you know what "in a nutshell" means? It is nonetheless enough for someone who understands enough of the physics.
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.
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.
Egnor: 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.
ReplyDeleteIt cracks me up how theologists dream up definitions that make no sense whatsoever and present them as profound.
This comment has been removed by the author.
ReplyDeleteDelete Comment From: Egnorance
ReplyDeletecrusadeREX said...
@Bach,
I am sure you're right. I am sure he misusing the word intentionally.
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.
"Your definition of 'heresy' is ahistorical too. "
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.
" but when Lutherism won,"
Won what?
"...it stopped being a heresy and became accepted dogma, at least in part of Europe anyway."
Even if I accept your Superbowl version of history, you make my point for me.
@Mulder,
"thats a LOT of typing just to argue over the term 'random.' Talk about a quibble.."
Lot of typing? Really? Maybe you were looking for the leapfrog blog? The Sesame Street forum?
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).
Hope that is not too many words for you, Mulder.
@KT,
"Worse still, Myers isn't even trying to understand."
My point entirely. Myers is all about enforcing a dogma, not searching for a truth. His sophomoric response smacks of intellectual dishonesty and intolerance.
"Can God make a Fourier representation so complex that even He can't invert it back into the time domain?"
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
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.
'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?
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.
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.
@Pépé
"That's kid stuff compared to the semiotics of life!"
Too true. Another level entirely.
@Oleg,
ReplyDelete"It cracks me up how theologists dream up definitions that make no sense whatsoever and present them as profound."
Your lack of understanding is not evidence for (or for the lack of) profundity of various theological positions.
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.
Oh well, you keep on laughing Oleg.
They say it's good for the soul.
CrusadeREX, I was kidding. I'm a confirmed Papist.
ReplyDelete:-)
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!
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.
ReplyDeleteGeeze, oleg, get a humor infusion, would you?
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.
I hold several patents in this area. You may leave quietly. Thank you.
Oops! I had that backwards. It's going from time to frequency you lose start and end times.
ReplyDeleteNow I will leave quietly! :-)
Cat, relax. We're talking about continuous, not discrete Fourier transforms. A point or two in the continuum makes no difference.
ReplyDeleteBesides, a properly defined discrete Fourier transform is a unitary transformation. No points are lost. Your engineering implementations might not do that, but that's not my problem.
@KT,
ReplyDeleteI am afraid your humour had transmitted above my frequency. I did not even receive, let alone map your signal. :P
"Captcha word: bleresy. I kid you not....I watch the replay of Newcastle's 3-0 win over Manchester United. Howay the lads!"
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.
Anyway, three cheers for the giant killers.
@All,
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.
God bless and stay well all of you.
Keep up the good work, Dr Egnor.
CrusadeRex
We're talking about continuous, not discrete Fourier transforms. A point or two in the continuum makes no difference.
ReplyDeleteThe 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.
:-)
Rex, here are the highlights. Dig Demba Ba's goal and then the own goal off of Phil Jones at the end. Awesomeness squared!
ReplyDeleteCat: The continuum? Sounds metaphysical.
ReplyDeleteDid your math education stop at integers and fractions? Live and learn.
Yeah, oleg, it stopped at integers. I'm an idiot. Duhhh.
ReplyDeleteYou found me out.
That's OK, Cat. Who needs calculus anyway? It's not in MCAT anymore.
ReplyDeleteOK, I can't resist.
ReplyDeleteOleg, 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 have to specify (or at least imply) a start time outside of the frequency representation otherwise it's total nonsense.
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.
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.
There. Now you can make fun of me. Almost everyone else in San Diego probably would if they'd read that.
Cat: 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.
ReplyDeleteSorry, 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.
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?
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}.
Even more generally, give me the complex Fourier transform of a signal and I will give you the original. With start and end times.
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.
ReplyDeleteThink 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.
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.
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.
KT,
ReplyDeleteI ask this honestly, to see if I get the drift of what your arguing with Oleg...
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?
Or am I totally lost here?
PS.
ReplyDeleteCan't quite the Egnorance. Worse than smoking!
As you wish, Cat.
ReplyDeleteWe 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).
The Fourier transforms for the first signal is
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.
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 were 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 not 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.
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).
Before you reply, Cat, read carefully through my comment and do the math. That should have a sobering effect.
Oleg, you can't take a frequency spectrum and figure out what year it came from. I'm sorry, but absolute time is lost.
ReplyDeleteOleg, one more try. Sine and cosines describe a circle in xy space. Some friends at work had this analogy:
ReplyDeleteFrequency 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".
:-)
Cat,
ReplyDeleteYou 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.