Νόμιζα ότι έγινε με αυτή τη σειρά αθεϊσμό. Ωστόσο,, Ήρθα σε αυτό το απόσπασμα από το βιβλίο του Wayne Βαφεία, Ιερή ζωή σας. Ένας φίλος μου ό, τι θα έμενε ως ένα είδος νουθεσία για όσους από εμάς δεν πιστεύουν.
I want to wrap up this series on atheism with a personal story about the point in time where I started diverging from the concept of God. I was very young then, about five years old. I had lost a pencil. It had just slipped out of my schoolbag, which was nothing more than a plastic basket with open weaves and a handle. When I realized that I had lost the pencil, I was quite upset. I think I was worried that I would get a scolding for my carelessness. Μπορείτε να δείτε, my family wasn’t rich. We were slightly better off than the households in our neighborhood, but quite poor by any global standards. The new pencil was, για μένα, a prized possession.
The atheist-theist debate boils down to a simple question — Did humans discover God? Ή, did we invent Him? The difference between discovering and inventing is the similar to the one between believing and knowing. Theist believe that there was a God to be discovered. Atheists “ξέρετε” that we humans invented the concept of God. Belief and knowledge differ only slightly — knowledge is merely a very very strong belief. A belief is considered knowledge when it fits in nicely with a larger worldview, which is very much like how a hypothesis in physics becomes a theory. While a theory (such as Quantum Mechanics, για παράδειγμα) is considered to be knowledge (or the way the physical world really is), it is best not to forget the its lowly origin as a mere hypothesis. My focus in this post is the possible origin of the God hypothesis.
The only recourse an atheist can have against this argument based on personal experience is that the believer is either is misrepresenting his experience or is mistaken about it. I am not willing to pursue that line of argument. I know that I am undermining my own stance here, but I would like to give the theist camp some more ammunition for this particular argument, and make it more formal.
I have a reason for delaying this post on the fifth and last argument for God by Dr. William Lane Craig. It holds more potency than immediately obvious. While it is easy to write it off because it is a subjective, experiential argument, the lack of credence we attribute to subjectivity is in itself a result of our similarly subjective acceptance of what we consider objective reason and rationality. I hope that this point will become clearer as you read this post and the next one.
In the previous post, we considered the cosmological argument (that the Big Bang theory is an affirmation of a God) and a teleological argument (that the highly improbable fine-tuning of the universe proves the existence of intelligent creation). We saw that the cosmological argument is nothing more than an admission of our ignorance, although it may be presented in any number of fancy forms (such as the cause of the universe is an uncaused cause, which is God, για παράδειγμα). The teleological argument comes from a potentially wilful distortion of the anthropic principle. The next one that Dr. Craig puts forward is the origin of morality, which has no grounding if you assume that atheism is true.
Καθ. William Lane Craig is way more than a deist; he is certainly a theist. Όντως, he is more than that; he believes that God is as described in the scriptures of his flavor of Christianity. I am not an expert in that field, so I don’t know exactly what that flavor is. But the arguments he gave do not go much farther than the deism. He gave five arguments to prove that God exists, and he invited Hitchens to refute them. Hitchens did not; τουλάχιστον, not in an enumerated and sequential fashion I plan to do here.
This post is an edited version of my responses in a Webinar panel-discussion organized by Wiley-Finance and FinCAD. The freely available Webcast is linked in the post, and contains responses from the other participants — Paul Wilmott and Espen Huag. An expanded version of this post may later appear as an article in the Wilmott Magazine.
What is Risk?
When we use the word Risk in normal conversation, it has a negative connotation — risk of getting hit by a car, για παράδειγμα; but not the risk of winning a lottery. In finance, risk is both positive and negative. Μερικές φορές, you want the exposure to a certain kind of risk to counterbalance some other exposure; κατά καιρούς, you are looking for the returns associated with a certain risk. Risk, in this context, is almost identical to the mathematical concept of probability.
But even in finance, you have one kind of risk that is always negative — it is Operational Risk. My professional interest right now is in minimizing the operational risk associated with trading and computational platforms.
How do you measure Risk?
Measuring risk ultimately boils down to estimating the probability of a loss as a function of something — typically the intensity of the loss and time. So it’s like asking — What’s the probability of losing a million dollars or two million dollars tomorrow or the day after?
The question whether we can measure risk is another way of asking whether we can figure out this probability function. In certain cases, we believe we can — in Market Risk, για παράδειγμα, we have very good models for this function. Credit Risk is different story — although we thought we could measure it, we learned the hard way that we probably could not.
The question how effective the measure is, είναι, κατά την άποψή μου,, like asking ourselves, “What do we do with a probability number?” If I do a fancy calculation and tell you that you have 27.3% probability of losing one million tomorrow, what do you do with that piece of information? Probability has a reasonable meaning only a statistical sense, in high-frequency events or large ensembles. Risk events, almost by definition, are low-frequency events and a probability number may have only limited practical use. But as a pricing tool, accurate probability is great, especially when you price instruments with deep market liquidity.
Innovation in Risk Management.
Innovation in Risk comes in two flavors — one is on the risk taking side, which is in pricing, warehousing risk and so on. On this front, we do it well, or at least we think we are doing it well, and innovation in pricing and modeling is active. The flip side of it is, φυσικά, risk management. Εδώ, I think innovation lags actually behind catastrophic events. Once we have a financial crisis, για παράδειγμα, we do a post-mortem, figure out what went wrong and try to implement safety guards. But the next failure, φυσικά, is going to come from some other, totally, unexpected angle.
What is the role of Risk Management in a bank?
Risk taking and risk management are two aspects of a bank’s day-to-day business. These two aspects seem in conflict with each other, but the conflict is no accident. It is through fine-tuning this conflict that a bank implements its risk appetite. It is like a dynamic equilibrium that can be tweaked as desired.
What is the role of vendors?
Σύμφωνα με την εμπειρία μου, vendors seem to influence the processes rather than the methodologies of risk management, and indeed of modeling. A vended system, however customizable it may be, comes with its own assumptions about the workflow, lifecycle management etc. The processes built around the system will have to adapt to these assumptions. This is not a bad thing. At the very least, popular vended systems serve to standardize risk management practices.
After reading a paper by Ashtekar on quantum gravity and thinking about it, I realized what my trouble with the Big Bang theory was. It is more on the fundamental assumptions than the details. I thought I would summarize my thoughts here, περισσότερο για δικό μου όφελος από οποιονδήποτε άλλο,,en,Κλασικές θεωρίες,,en,συμπεριλαμβανομένων SR και QM,,en,να αντιμετωπίζετε το διάστημα ως συνεχές τίποτα,,en,οπότε ο όρος διαστημικό χρόνο,,en,Τα αντικείμενα υπάρχουν σε συνεχή χώρο και αλληλεπιδρούν μεταξύ τους σε συνεχή χρόνο,,en,Αν και αυτή η έννοια του διαστήματος διαστημικού χρόνου είναι διαισθητικά ελκυστική,,en,ατελής,,en,Σκεφτείτε,,en,ένα περιστρεφόμενο σώμα σε κενό χώρο,,en,Αναμένεται να παρουσιάσει φυγοκεντρική δύναμη,,en,Τώρα φανταστείτε ότι το σώμα είναι ακίνητο και ολόκληρος ο χώρος περιστρέφεται γύρω από αυτό,,en,Θα βιώσει οποιαδήποτε φυγόκεντρη δύναμη,,en,Είναι δύσκολο να καταλάβουμε γιατί θα υπάρξει κάποια φυγόκεντρη δύναμη εάν ο χώρος είναι κενός τίποτα,,en,Η GR εισήγαγε μια μετατόπιση παραδείγματος, κωδικοποιώντας τη βαρύτητα σε χωροχρόνο καθιστώντας έτσι δυναμική στη φύση,,en,αντί για κενό τίποτα,,en,η μάζα ζωντανεύεται στο διάστημα,,en.
Classical theories (including SR and QM) treat space as continuous nothingness; hence the term space-time continuum. Κατά την άποψη αυτή, objects exist in continuous space and interact with each other in continuous time.
Although this notion of space time continuum is intuitively appealing, it is, at best, incomplete. Consider, για παράδειγμα, a spinning body in empty space. It is expected to experience centrifugal force. Now imagine that the body is stationary and the whole space is rotating around it. Will it experience any centrifugal force?
It is hard to see why there would be any centrifugal force if space is empty nothingness.
GR introduced a paradigm shift by encoding gravity into space-time thereby making it dynamic in nature, rather than empty nothingness. Έτσι, mass gets enmeshed in space (και χρόνος), ο χώρος γίνεται συνώνυμος με το σύμπαν,,en,και η ερώτηση περιστρεφόμενου σώματος γίνεται εύκολη απάντηση,,en,θα δοκιμάσει την φυγόκεντρη δύναμη αν είναι το σύμπαν που περιστρέφεται γύρω από αυτό επειδή είναι ισοδύναμο με το κλονισμό του σώματος,,en,δεν θα το κάνει,,en,αν είναι σε κενό χώρο,,en,κενο διαστημα,,en,δεν υπάρχει,,en,Ελλείψει μάζας,,en,δεν υπάρχει γεωμετρία χωροχρόνου,,en,πριν από τη Μεγάλη Έκρηξη,,en,αν υπήρχε ένα,,en,δεν θα μπορούσε να υπάρξει χώρος,,en,ούτε θα μπορούσε να υπάρξει κάτι τέτοιο,,en,πριν.,,en,ότι το χαρτί Ashtekar δεν δηλώνει ξεκάθαρα γιατί έπρεπε να υπάρξει μεγάλη έκρηξη,,en,Το πλησιέστερο που παίρνει είναι ότι η αναγκαιότητα του ΒΒ προκύπτει από την κωδικοποίηση της βαρύτητας στον χωροχρόνο στο GR,,en,Παρά την κωδικοποίηση της βαρύτητας και καθιστώντας έτσι τη δυναμική χωροχρόνου,,en,Το GR εξακολουθεί να αντιμετωπίζει το χωροχρόνο ως ομαλό συνεχές,,en,ένα ελάττωμα,,en, and the spinning body question becomes easy to answer. Ναι, it will experience centrifugal force if it is the universe that is rotating around it because it is equivalent to the body spinning. Και, δεν, it won’t, if it is in just empty space. Αλλά “empty space” doesn’t exist. In the absence of mass, there is no space-time geometry.
Έτσι, φυσικά, before the Big Bang (if there was one), there couldn’t be any space, nor indeed could there be any “before.” Note, Ωστόσο,, that the Ashtekar paper doesn’t clearly state why there had to be a big bang. The closest it gets is that the necessity of BB arises from the encoding of gravity in space-time in GR. Despite this encoding of gravity and thereby rendering space-time dynamic, GR still treats space-time as a smooth continuum — a flaw, σύμφωνα με τον Ashtekar,,en,ότι η QG θα διορθώσει,,en,αν δεχτούμε ότι το σύμπαν ξεκίνησε με ένα μεγάλο κτύπημα,,en,και από μια μικρή περιοχή,,en,πρέπει να υπολογίσουμε τα κβαντικά αποτελέσματα,,en,Ο χώρος-χρόνος πρέπει να κβαντιστεί και ο μόνος σωστός τρόπος για να γίνει αυτό θα ήταν η κβαντική βαρύτητα,,en,Μέσω QG,,en,αναμένουμε να αποφύγουμε την ιδιαιτερότητα του Big Bang της GR,,en,με τον ίδιο τρόπο ο QM λύνει το απεριόριστο ενεργειακό πρόβλημα εδάφους στο άτομο του υδρογόνου,,en,Αυτό που περιέγραψα παραπάνω είναι αυτό που καταλαβαίνω ότι είναι τα φυσικά επιχειρήματα πίσω από τη σύγχρονη κοσμολογία,,en,Το υπόλοιπο είναι ένα μαθηματικό οικοδόμημα χτισμένο πάνω από αυτό το φυσικό,,en,ή μάλιστα φιλοσοφικό,,en,Αν δεν έχετε ισχυρές απόψεις για το φιλοσοφικό ίδρυμα,,en,ή αν οι απόψεις σας είναι συνεπείς με αυτό,,en,μπορείτε να δεχτείτε το BB χωρίς καμία δυσκολία,,en,Έχω διαφορετικές απόψεις,,en, that QG will rectify.
Τώρα, if we accept that the universe started out with a big bang (and from a small region), we have to account for quantum effects. Space-time has to be quantized and the only right way to do it would be through quantum gravity. Through QG, we expect to avoid the Big Bang singularity of GR, the same way QM solved the unbounded ground state energy problem in the hydrogen atom.
What I described above is what I understand to be the physical arguments behind modern cosmology. The rest is a mathematical edifice built on top of this physical (or indeed philosophical) foundation. If you have no strong views on the philosophical foundation (or if your views are consistent with it), you can accept BB with no difficulty. Unfortunately, I do have differing views.
Οι απόψεις μου περιστρέφονται γύρω από τις ακόλουθες ερωτήσεις,,en,Γιατί η ταχύτητα του φωτός είναι σημαντική σε αυτό,,en,Πού λειτουργεί το,,en,Αρχή αβεβαιότητας του Heisenberg,,en,προέρχομαι,,en,Οι θέσεις αυτές μπορεί να ακούγονται σαν άχρηστες φιλοσοφικές σκέψεις,,en,αλλά έχω κάποια συγκεκριμένα στοιχεία,,en,και κατά τη γνώμη μου,,en,σπουδαίος,,en,Αποτελέσματα,,en,παρατίθενται παρακάτω,,en,Είναι οι GRBs και οι ραδιοφωνικές πηγές Luminal Booms,,en,Ένα άρθρο που δημοσιεύτηκε στο IJMP-D,,en,που έγινε ένα από τα,,en,Κορυφαία άρθρα,,en,του περιοδικού,,en,Προσπαθώντας να το δημοσιεύσετε.,,en,Υπάρχει πολύ περισσότερη δουλειά σε αυτό το μέτωπο,,en,Αλλά για τα επόμενα δύο χρόνια,,en,με το νέο μου βιβλίο και τις πιέσεις από τη σταδιοδρομία μου,,en,Δεν θα έχω αρκετό χρόνο για να σπουδάσω GR και κοσμολογία με τη σοβαρότητα που αξίζουν,,en,Ελπίζω να τους επιστρέψω μόλις περάσει η τρέχουσα φάση της εξάπλωσής μου,,en,Ashtekar,,kn,θεωρία της Μεγάλης Έκρηξης,,en,κοσμολογία,,en.
- Τι είναι το διάστημα?
- Why is the speed of light important in it?
- Where does the Heisenberg Uncertainty Principle come from?
These posts may sound like useless philosophical musings, but I do have some concrete (and in my opinion, important) results, listed below.
- Are GRBs and Radio Sources Luminal Booms? (An article published in IJMP-D, which became one of the “Top Accessed Articles” of the journal. :-))
- Light Travel Time Effects and Cosmological Features (Trying to get this one published.)
There is much more work to be done on this front. But for the next couple of years, with my new book contract and pressures from my quant career, I will not have enough time to study GR and cosmology with the seriousness they deserve. I hope to get back to them once the current phase of spreading myself too thin passes.
This sounds like a strange question. We all know what space is, it is all around us. When we open our eyes, we see it. Αν βλέπουμε είναι πιστεύοντας, then the question “Τι είναι το διάστημα?” indeed is a strange one.
Για να είμαστε δίκαιοι, we don’t actually see space. We see only objects which we assume are in space. Rather, we define space as whatever it is that holds or contains the objects. It is the arena where objects do their thing, the backdrop of our experience. Με άλλα λόγια, experience presupposes space and time, and provides the basis for the worldview behind the currently popular interpretations of scientific theories.
Although not obvious, this definition (or assumption or understanding) of space comes with a philosophical baggage — that of realism. The realist’s view is predominant in the current understanding of Einstien’s theories as well. But Einstein himself may not have embraced realism blindly. Why else would he say:
In order to break away from the grip of realism, we have to approach the question tangentially. One way to do it is by studying the neuroscience and cognitive basis of sight, which after all provides the strongest evidence to the realness of space. Space, και με μεγάλο, is the experience associated with sight. Another way is to examine experiential correlates of other senses: What is sound?
When we hear something, what we hear is, φυσικά, ήχο. We experience a tone, an intensity and a time variation that tell us a lot about who is talking, what is breaking and so on. But even after stripping off all the extra richness added to the experience by our brain, the most basic experience is still a “sound.” We all know what it is, but we cannot explain it in terms more basic than that.
Now let’s look at the sensory signal responsible for hearing. As we know, these are pressure waves in the air that are created by a vibrating body making compressions and depressions in the air around it. Much like the ripples in a pond, these pressure waves propagate in almost all directions. They are picked up by our ears. By a clever mechanism, the ears perform a spectral analysis and send electric signals, which roughly correspond to the frequency spectrum of the waves, to our brain. Σημειώστε ότι, so far, we have a vibrating body, bunching and spreading of air molecules, and an electric signal that contains information about the pattern of the air molecules. We do not have sound yet.
The experience of sound is the magic our brain performs. It translates the electrical signal encoding the air pressure wave patterns to a representation of tonality and richness of sound. Sound is not the intrinsic property of a vibrating body or a falling tree, it is the way our brain chooses to represent the vibrations or, more precisely, the electrical signal encoding the spectrum of the pressure waves.
Doesn’t it make sense to call sound an internal cognitive representation of our auditory sensory inputs? If you agree, then reality itself is our internal representation of our sensory inputs. This notion is actually much more profound that it first appears. If sound is representation, so is smell. So is space.
|Εικόνα: Illustration of the process of brain’s representation of sensory inputs. Odors are a representation of the chemical compositions and concentration levels our nose senses. Sounds are a mapping of the air pressure waves produced by a vibrating object. In sight, our representation is space, and possibly time. Ωστόσο,, we do not know what it is the representation of.|
We can examine it and fully understand sound because of one remarkable fact — we have a more powerful sense, namely our sight. Sight enables us to understand the sensory signals of hearing and compare them to our sensory experience. Στην πραγματικότητα,, sight enables us to make a model describing what sound is.
Why is it that we do not know the physical cause behind space? Μετά από όλα, we know of the causes behind the experiences of smell, ήχο, κλπ. The reason for our inability to see beyond the visual reality is in the hierarchy of senses, best illustrated using an example. Let’s consider a small explosion, like a firecracker going off. When we experience this explosion, we will see the flash, hear the report, smell the burning chemicals and feel the heat, if we are close enough.
The qualia of these experiences are attributed to the same physical event — the explosion, the physics of which is well understood. Τώρα, let’s see if we can fool the senses into having the same experiences, in the absence of a real explosion. The heat and the smell are fairly easy to reproduce. The experience of the sound can also be created using, για παράδειγμα, a high-end home theater system. How do we recreate the experience of the sight of the explosion? A home theater experience is a poor reproduction of the real thing.
In principle at least, we can think of futuristic scenarios such as the holideck in Star Trek, where the experience of the sight can be recreated. But at the point where sight is also recreated, is there a difference between the real experience of the explosion and the holideck simulation? The blurring of the sense of reality when the sight experience is simulated indicates that sight is our most powerful sense, and we have no access to causes beyond our visual reality.
Visual perception is the basis of our sense of reality. All other senses provide corroborating or complementing perceptions to the visual reality.
[This post has borrowed quite a bit from my book.]