Nisi cognitio finitas, infinitum sit necesse est ignoratio
Tonight the Two Pointers and the Southern Cross were rising not long after sunset – have missed them in the sky. I always look wistfully at Alpha Centauri – the Brightest Pointer – and think it’s only a cosmic stone’s throw away… all 40 trillion kilometres of a throw *sigh*
Multi-bounce laser-sails
Crowlspace is chiefly about spaceflight and cosmic things, but the Tomb stuff has popped up, so I felt compelled to write. Back to the central topic now… a new idea has arisen for pushing things around with lasers – why not recycle the laser beam itself? This idea was recently discussed at Centauri Dreams and references a paper by Robert Metzger and Geoff Landis, which looks at an Earth-Mars mission using multiple-reflection.
Apparently ultra-reflective surfaces for a given frequency are now feasible – we’re talking 99.99995% of all the energy of a beam being bounced off the surface. That’s enough to allow many thousands of bounces of the beam itself, between laser and target, thus boosting the effective momentum transferred by the beam’s energy. It takes 150 MJ to give a 1 Newton impulse to a perfect mirror, but if the beam could be bounced 20,000 times, losing a bit of energy as heat each time, then the effective force multiplies about 10,000-fold. Of course the effective path-length goes up 20,000-fold, so the acceleration distance has to be pretty short too before the diffraction limit spreads the beam out too much.
In the Metzger/Landis example the boost is assumed to be 1,000-fold and the diffraction-limit gives a boost range of 210,000 km for acceleration at 0.33 m/s^2, boosting the laser-sail/payload of 20 tons to 12 km/s. That’s enough for an Earth-Mars transit in 96 days, which is pretty respectable. The energy cost works out at $240/kg, supplied by a couple of reactors at Earth and Mars. There’s no reason why nuclear reactors are required as Landis himself has posited designs for 3 GW (in-space power) Solar Power Satellites that mass a mere 1,300 tons. With 70% efficient concentrator solar cells the mass is halved, and for just a GW of power the mass drops to a mere 200 tons. Lighter than a GW reactor, unless it’s an open-cycle gas-core reactor, which by itself would make a good rocket.
A 10 ton payload may not sound like much, but it’s 1/3 what the Shuttle laboriously hauls into orbit when fully loaded. A lot of payloads launched fast would make the system worthwhile, and that’s the main point. Also payloads boosted into near-Hohmann transfer orbits requiring a mere 4 km/s could mass 90 tons over the same boost distance and that’s serious payload on an interplanetary trajectory.
Well the Tomb has sunk like a lead balloon and leading the charge has been other archaeologists – basically the people involved in the Jesus Tomb have overstated the case for its contents as the mortal remains of JC and kin. Fair enough. Do a Web-search and you’ll find plenty of arguments about the Tomb, which is interesting by itself. I think the most telling argument is the recent revelation that the James Ossuary was photographed in 1976 before the Talpiot Tomb itself was discovered in 1980. So it can’t be the putative missing ossuary, thus knocking one support out from under Jacobovici and Cameron’s case. Another problem is that the name identified as “Yeshua” could equally be “Hanun” as the inscription is hard to read. This kind of militates against their central claim, that it’s Jesus’s family – Marys and Josephs are a dime a dozen in First Century Jewish family plots.
Oh well. It was a nice prospect while it lasted – archaeological proof of a mortal Jesus. Now we’re left with two competing faith claims – that dead people don’t rise, and that God raised Jesus on the Third Day. The latter seems more an act of faith than the former, but it’s hard to refute the claim that JC was reported to have left his tomb empty by his closest friends and followers. All the textual evidence tells us that the tomb discovery was followed by apparitions of the Risen Christ – though the nature, number and location varies from Gospel to Gospel.
I’ve already said that I think the tomb was found emptied, but it took time for the Risen Christ to be believed – Mark and Matthew make this pretty clear, since both locate the apparitions squarely in Galilee. Luke and John are more problematic for my view, but both are rather at odds with the first two Gospels. Why the disparity? And why does John feature a major appearance to Peter, and his old business partners, in the Sea of Galilee when Luke doesn’t if they’re drawing on the same source events?
Yet having said that I have my doubts about the skeptical case for a dead Christ too. Chief amongst my “doubts” is the enigma that is the Shroud of Turin – which recently has been proven somewhat older than the 1988 radiocarbon dating first implied. Apparently the samples for the dating had all been taken from a Medieval patch – the rest of the cloth itself is much older, as measured, albeit roughly, by a biochemical clock related to the aging of the fabric.
The Shroud itself proves that a dead man was in it, but why it became associated with JC is because of the unique wounds the Shroud Man bears – multiple lacerations to the forehead (i.e. Crown of Thorns) and the bleeding wound in his side. Plenty of other people had been crucified and scourged by the Romans – also seen on the Shroud Man – but the extra abuse of the victim is surely unique. But if the Shroud Man is JC then why isn’t the Shroud mentioned as an amazing sign in the Gospels?
Isn’t it?
And of course the Discovery Channel is airing the documentary. There’s some good support material provided online, so check it out. A problem for future investigation is that any bones found with the ossuaries have been reburied due to the Israeli religious laws on such issues, so a lot of data is probably gone.
The Family Tomb of Jesus
…but there was another tomb nearby, currently unexplored. What surprises will it hold?
So is it a Jewish conspiracy to trash the One True Faith (TM) or is it a statistical goof being flogged to the world for the sake of publicity?
About 1980 a bunch of archaeologists stumbled across a tomb with a bunch of old bone boxes, all with names familiar to anyone who read the New Testament – a Mary, a Joseph, and Matthew, etc etc. The find has kind of mouldered, waiting for some serious research. In recent years several have re-examined the find, and now Guerilla archaeologist Simcha Jacobovici and James Cameron ( of Terminator fame etc) have gone even further to confirm the remains are all one family, and make a documentary claiming it’s the family of Jesus, plus the remains of his son (the grandson of G_d?)
Bones of Jesus
The Jesus Family Tomb
y-Net News on the claims
Official Webpage… just a placekeeper for now
Now the find itself is over 27 years old, but when it was first exposed there was no decent forensic techniques for testing for familial relationship between bones. Now with DNA testing that’s straight-forward and someone has confirmed what could’ve been guessed from the start – the individuals are related. But how seriously can we take the main claim – that it’s the family tomb of Jesus? Imagine the problems this will cause for all those atheists who believe JC was just a myth and never existed. “Wrong! We have his bones… damn!”
Clearly it’s a problem for people who believe in a flesh-and-blood resurrection. But not every Xian does. The parent group of the Jehovah’s Witnesses is still in existence and they don’t believe he rose physically. Plenty of liberal Xians believe he rotted in some grave… but who cares what they believe anyway? The Jews might be happy with the outcome, but then again who wants to tell the Xians the bad news? On one of the News Magazines on Aussie TV this week there’s a report from Zanzibar about how thousands of Xians are converting to Judaism (!!!) This finding might only tip the balance for even more teetering believers, who’ll dump a failed Messiah for hope in a more triumphant one.
Yet, as others have already noted, the names were pretty common in Judea at that time, so the odds are that plenty of tombs had a similar bunch of names on the boxes.
Michael Prescott’s blog on the find
…that last blog-site also discusses a new book which looks at the Gospels as eye-witness material. There’s some evidence in favour of the idea, at least for “Mark” and “John”, but it by no means proves the Gospels were 100% inerrant either. Stylistic reasons influenced ancient writers as much as wanting to report facts, thus all the thinly veiled allusions to Old Testament parallels in the Gospels. Another issue is that the Gospellers were trying to fit JC into OT prophecies – with varying degrees of success. What didn’t fit probably got left out. The whole of the Passion Narrative can be related to Old Testament prophecies which has led more than one scholar to state the obvious – the whole sequence was written as if the prophecies were fulfilled. In reality JC might’ve been executed like any other anonymous agitator – but he was important enough to rate a mention by Josephus, so who knows? Maybe he did chat to Pontius Pilate – but try getting the Gospels to agree about the details.
Anyway food for thought.
When the first molecular clock studies were performed on the apes what surprised everyone was just how recently the human line had split from the apes – prior to that first study in the 1970s everyone had thought the human line went back 20 million years. Then the first result shattered that old view by dating the split to just 4.5 million years ago. In the 30 years since the dating has gradually risen to somewhere between 5 – 7 million years ago, about the same age as the oldest “definite” (in some minds, at least) human ancestors.
A new study has thrown a monkey-wrench into the works. The Open Access Journal, the Public Library of Science – Genetics, has just published this paper:
Article:
Genomic Relationships and Speciation Times of Human, Chimpanzee, and Gorilla Inferred from a Coalescent Hidden Markov Model Hobolth A, Christensen OF, Mailund T, Schierup MH PLoS Genetics Vol. 3, No. 2, e7 doi:10.1371/journal.pgen.0030007
…a hidden Markov model tries to account for all the different ways a particular gene lineage can differ from a species lineage. Through the vagaries of inheritance two members of the same species can have genes with lineages that date back before the species split from its sister species. You and I could have genes that diverged before our ancestors became bipedal apes, if not further back. Because the genome of a species is represented by at least thousands of individuals there’s a finite chance this can happen. Only if the original population crashes to just a handful of members can gene lineages be forced into a single common time of origin – and this leaves a distinctive genetic signature in the population. Cheetahs, for example, show signs of being reduced to a single litter at a point about 13,000 years ago. As a population their genetic variation is very, very low.
Humans are more varied, but less so than chimps, so we’ve come closer to extinction than they have at some point in the past. The eruption of the super-volcano, Toba, about 72,000 years ago is considered a likely suspect in causing that population bottle-neck, and just possibly causing our species to have its current genetic make-up. Our ancestors might have come from a group of about 10,000 at that point, preserving some old gene lines and eliminating many others.
Once all the weird and wonderful genetic trails have been accounted for the new study indicates that chimps and humans diverged a mere 4 million years ago (mya). If so then all the Australopithecine species before 4 mya are actually possible ancestors of both chimps and humans. The recent tool use – hammer stones and now spears for hunting monkeys – seen in chimps could mean our common ancestors had similar capabilities.
That very late date for the human-chimp split means chimps once walked upright like humans, then became specialised knuckle-walkers. Knuckle-walking is as odd as bipedalism, and isn’t seen in any apes other than gorillas and chimps. Could gorillas have come from an upright ancestor too? The dates might be just right, especially if Ororrin (6 mya) and Sahelanthropus (6-7 mya) are both confirmed as bipedal. Interestingly one specialist who examined Sahelanthropus was of the opinion that that hominid was most like a young gorilla.
So could Ardipithecus, Australopithecus anamensis and the other hominids just mentioned really be ancestors to both chimps and humans?
In the previous section I noted the apparent non-Orthodox burial tradition that Jesus was buried by his enemies, not his friends as the Gospels would lead us to believe. The Gospel of Peter states:
And then they plucked the nails from the hands of the Lord and laid him upon the earth: and the whole earth was shaken, and there came a great fear on all.
…yet oddly enough the Apostle Paul is quoted as saying (Acts13:29):
When they had carried out all that was written about him, they took him down from the tree and laid him in a tomb.
…[they being the rulers and people of Jerusalem.] This fragment seems even more unlike the tale about Joseph of Arimathea – whom Paul doesn’t mention – and more like an early tradition that avoided the Great Gospel Edit. All the Gospels have been subtly “retouched” by scribal copying over time, harmonising in ways that might cover-up conflicting points-of-view. Some conflicts did escape – John pointedly says Jesus carried his own cross, flatly denying a role to Simon of Cyrene. Also John’s Jesus dies almost serenely, without any great heart-rending cry, nor fantastic signs in the Temple or tombs of Jerusalem. And Mary heads to the tomb on Easter morning without any materials for preparing Jesus’ body, probably because Joseph and Nicodemus had already covered the corpse in “75 pounds” of myrrh and aloes. Again utterly unlike the Synoptics. And there’s no mention of Mary and the other women watching where Jesus was buried, perhaps again because Joseph & Nicodemus are in charge of that too.
Noted Bible Scholar Raymond Brown notes:
A sermon in Acts 13:27-29 reports: “Those who lived in Jerusalem and their rulers…requested Pilate to have him killed; and when they had fulfilled all that was written of him they took him down from the tree and placed him in a tomb.” John 19:31 tells us that the Jews asked Pilate that the legs of the crucified be broken and they be taken away. A variant reading at the end of John 19:38 continues the story: “So they came and took away his body.” Similarly in Gpet 6:21 we read, “And then they [the Jews] drew out the nails from the hands of the Lord and placed him on the earth.” Justin (Dialogue 97.1) phrases the burial thus: “For the Lord too remained on the tree almost until evening [hespera], and towards evening they buried him” – in a chapter where the context suggests that “they” may be the Jewish opponents of Jesus rather than his disciples.
[Reference… Raymond Edward Brown, The Death of the Messiah: From Gethsemane to the Grave: a Commentary on the Passion Narratives in the Four Gospels (New York: Doubleday, 1994), pp. 1218-1219. From Pete Kirby’s Internet essay on the Empty Tomb, conclusions my own.]
In the end what we might be seeing is how successive Gospels have “written in” Joseph into the fold of believers in JC. In Mark Joseph was one of the “bad guys”, the Sanhedrin, who buried JC out of pious commitment to a Deuteronomic command. He becomes more ambiguous in Matthew and Luke, and is made a secret disciple in John. Why? Notice also that John studiously avoids making Mary, and the other women, witnesses and burial attendants at the tomb – the men give JC a royal burial (75 pounds of aromatics remember.) Perhaps in the original version the first burial is a hurried emergency burial because the end of the day is approaching and to not break Deuteronomy‘s command (no bodies on trees overnight) Joseph, and the burial team (implied because the dead thieves were being interred too), had to commandeer an empty tomb to store the bodies for later disposal, perhaps the next day in a mass grave with a bucket of lime to sanitise the decaying remains.
If Mary had seen the burial, and not the next-day removal, she may well have come back to the other disciples with news of an empty tomb – and no one would ever know any different. In Mark and Matthew the disciples run off and are “told” via angelic vision to go to Galilee. In Peter and, perhaps, John 20, the disciples retreat to Galilee in fear for their lives. There, after an indeterminate time, they experience the Risen Jesus on a hill-top (Matthew 28: 16,17) – at least some of them do – and return to Jerusalem with an “infectious vision” convincing Jesus’ Brother James and eventually Saul/Paul.
To me, on my agnostic days, that seems like enough of a trigger, at least a decent throw-away line when arguing with Believers, that by the time anyone, enemy or friend, thought to check for an Empty Tomb or find JC’s body there was nothing to be found. However that might not be enough to explain how that Resurrection Belief kicked off. But what kind of Resurrection is it that gets this reaction:
Then the eleven disciples went to Galilee, to the mountain where Jesus had told them to go. When they saw him, they worshipped him; but some doubted.
How was JC buried? And by who? Friend or foe?
All four canonical Gospels tell us that Joseph of Arimathea buried Jesus out of personal piety and secret discipleship. Evangelists of the present day use the Empty Tomb as proof of a bodily resurrection of Jesus – but what if the Tomb burial tradition is wrong? Other traditions exist – here they are…
The Gospel of Mark 15:42-47. It was Preparation Day (that is, the day before the Sabbath). So as evening approached, Joseph of Arimathea, a prominent member of the Council, who was himself waiting for the kingdom of God, went boldly to Pilate and asked for Jesus’ body. Pilate was surprised to hear that he was already dead. Summoning the centurion, he asked him if Jesus had already died. When he learned from the centurion that it was so, he gave the body to Joseph. So Joseph bought some linen cloth, took down the body, wrapped it in the linen, and placed it in a tomb cut out of rock. Then he rolled a stone against the entrance of the tomb. Mary Magdalene and Mary the mother of Joses saw where he was laid.
The Gospel of Peter 21-34. And then they plucked the nails from the hands of the Lord and laid him upon the earth: and the whole earth was shaken, and there came a great fear on all. Then the sun shone forth, and it was found to be the ninth hour. And the Jews rejoiced, and gave his body unto Joseph to bury it, because he had beheld all the good things which he did. And he took the Lord and washed him and wrapped him in linen and brought him unto his own sepulchre, which is called the Garden of Joseph. Then the Jews and the elders and the priests, when they perceived how great evil they had done themselves, began to lament and to say: Woe unto our sins: the judgement and the end of Jerusalem is drawn nigh. But I with my fellows was in grief, and we were wounded in our minds and would have hid ourselves; for we were sought after by them as malefactors, and as thinking to set the temple on fire. And beside all these things we were fasting, and we sat mourning and weeping night and day until the Sabbath. But the scribes and Pharisees and elders gathered one with another, for they had heard that all the people were murmuring and beating their breasts, saying: If these very great signs have come to pass at his death, behold righteous he was. And the elders were afraid and came unto Pilate, entreating him and saying: Give us soldiers that we (or they) may watch his sepulchre for three days, lest his disciples come and steal him away and the people suppose that he is risen from the dead, and do us hurt. And Pilate gave them Petronius the centurion with soldiers to watch the sepulchre; and the elders and scribes came with them unto the tomb, and when they had rolled a great stone to keep out (al. together with) the centurion and the soldiers, then all that were there together set it upon the door of the tomb; and plastered thereon seven seals; and they pitched a tent there and kept watch. And early in the morning as the Sabbath dawned, there came a multitude from Jerusalem and the region roundabout to see the sepulchre that had been sealed.
The Secret Book of James. The Lord answered and said: “What is your merit when you do the will of the Father if it is not given to you by him as a gift, while you are tempted by Satan? But if you are oppressed by Satan and are persecuted and you do the Father’s will, I say that he will love you and will make you equal with me and will consider that you have become beloved through his providence according to your free choice. Will you not cease, then, being lovers of the flesh and being afraid of sufferings? Or do you not know that you have not yet been mistreated and have not yet been accused unjustly, nor have you yet been shut up in prison, nor have you yet been condemned lawlessly, nor have you yet been crucified without reason, nor have you yet been buried in the sand, as was I myself, by the evil one? Do you dare to spare the flesh, you for whom the spirit is an encircling wall? If you contemplate the world, how long it is before you and also how long it is after you, you will find that your life is one single day and your sufferings, one single hour. For the good will not enter the world. Scorn death, therefore, and take concern for life. Remember my cross and my death and you will live.”Epistula Apostolorum (Ethiopic). He of whom we are witnesses we know as the one crucified in the days of Pontius Pilate and of the prince Archelaus, who was crucified between two thieves and was taken down from the wood of the cross together with them, and was buried in the place called [the place of the skull], to which three women came, Sarah, Martha, and Mary Magdalene. They carried ointment to pour out upon his body, weeping and mourning over what had happened. And the approached the tomb and found the stone where it had been rolled away from the tomb, and they opened the door and did not find his body.
The main things to notice:
In the Gospel of Peter Jesus’ enemies took him down from the Cross, not Joseph. In fact the highlighted Joseph segment seems to interrupt the story and is possibly an interpolation by an Orthodox scribe.
In The Secret Book of James Jesus is said to have been buried in sand, contradicting the honorable tomb burial in Mark.
In the Epistula Jesus is taken off the Cross with the thieves and by implication buried with them. This would grossly contradict the Orthodox version of events.
There’s two more versions of the tradition, but they’re in some surprising places. More next time.
Mag-sails acting as interstellar brakes follow the equation:
V = Vo/(1 + k.Vo^(1/3).t)^3
…and as we discovered the distance the mag-sail travels while deccelerating from Vo to V during a fixed time, t, is:
s = Vo.t/2 * [ (V/Vo)^(1/3).(1 + (V/Vo)^(1/3)) ]
But the behaviour of a starship isn’t obvious from an equation alone. So here’s a table. What you’re seeing is the velocity broken down into short steps of 0.05 c, except the last, and the time taken for each step, plus the cumulative total. As you can see the decceleration is high – 5.6 gee at the start – and rapidly declining. The final skid from 0.05 c to just 0.0054 c takes a whopping 522 days, while the whole 0.9 c delta-vee prior takes a mere 297 days.
| V1 | V2 | factor | time (days) | time (cumulative) |
| 0.95 | 0.9 | 0.0184994 | 3.239800003 | 3.239800003 |
| 0.9 | 0.85 | 0.019923023 | 3.489119075 | 6.728919078 |
| 0.85 | 0.8 | 0.021550153 | 3.774078302 | 10.50299738 |
| 0.8 | 0.75 | 0.023425071 | 4.102432734 | 14.60543011 |
| 0.75 | 0.7 | 0.025605464 | 4.484284936 | 19.08971505 |
| 0.7 | 0.65 | 0.028167793 | 4.933025557 | 24.02274061 |
| 0.65 | 0.6 | 0.031215428 | 5.466757946 | 29.48949855 |
| 0.6 | 0.55 | 0.034891343 | 6.110520895 | 35.60001945 |
| 0.55 | 0.5 | 0.039398605 | 6.899877768 | 42.49989721 |
| 0.5 | 0.45 | 0.04503483 | 7.886949865 | 50.38684708 |
| 0.45 | 0.4 | 0.052252928 | 9.151055264 | 59.53790234 |
| 0.4 | 0.35 | 0.061774604 | 10.81858634 | 70.35648869 |
| 0.35 | 0.3 | 0.07481817 | 13.10290615 | 83.45939483 |
| 0.3 | 0.25 | 0.09359947 | 16.39207514 | 99.85146998 |
| 0.25 | 0.2 | 0.122574895 | 21.46654131 | 121.3180113 |
| 0.2 | 0.15 | 0.172096111 | 30.13919193 | 151.4572032 |
| 0.15 | 0.1 | 0.272362632 | 47.69886779 | 199.156071 |
| 0.1 | 0.05 | 0.559982927 | 98.06980993 | 297.2258809 |
| 0.05 | 0.0054 | 2.985502206 | 522.8510013 | 820.0768822 |
If you switched to rockets at 0.1 c then the mag-sail braking would last a mere 200 days. But on interstellar flights what matters is fuel expenditure and so with multiyear trip-times, a few hundred days isn’t a big reason for wasting reaction mass. But the above assumes that the mass density of the Inter-Stellar Medium (ISM) is a constant for the whole trip. This isn’t necessarily so. Larry Niven’s classic description of a ramjet in flight (in A Gift From Earth) uses the increased density of the ISM around the UV Ceti star system to provide extra braking for a rapid flight to Tau Ceti. Maps of the ISM will prove vital to future starship captains, for many reasons.
No-fuel decceleration
Robert Zubrin and Dana Andrews invented the concept of the Magnetic Sail, or Mag-Sail, which is basically a large superconducting ring which generates a large magnetic field, which mimics a planet’s magnetosphere and interacts with the Sun’s plasma-wind. Within a solar system a Mag-Sail provides unlimited range, so long as coolant lasts for the superconductors. But the most interesting use for a Mag-Sail is providing a reaction-mass free way of slowing an interstellar space vehicle. According to a NIAC study by Zubrin et. al. a Mag-Sail can potentially slow a vehicle from 0.95c to just 0.0054c in just 820 days – with no reaction mass required.
To the mathematically inclined quoting a few figures doesn’t tell one much, and so I went a little further in my reading of Zubrin and developed his equations further. His various works state that the final velocity, V, for a deccelerating vehicle goes like so…
V = Vo / (1 + k.Vo^(1/3).t)^3, where Vo is the initial velocity, k the decceleration constant, and t the decceleration time.
…with a bit of rearrangement the time can be worked out from the velocities…
t = (1/k).[ V^(-1/3) – Vo^(-1/3) ]
…i.e. inverse of the decceleration constant times the difference of the inverse of the cube-root of the final velocity and the inverse of the cube-root of the initial velocity. Which is easier to understand in symbols, if you ask me.
Let’s take a step back to the first equation. Call (1+ k.Vo^(1/3).t) a separate name, B, thus we get…
V = Vo/B^3
…and the acceleration, dV/dt, is now…
a = -3k.Vo^(4/3)/B^4
…and the initial acceleration, a(0), is -3.k.Vo^(4/3). The minus sign indicates the vehicle is slowing down.
How far does the vehicle travel while deccelerating from Vo to V? It’s a straightforward integration – much to my surprise – and boils down to…
s = Vo/(2k.Vo^(1/3))*[(B^2 – 1)/B^2]
…which, after some algebra, becomes…
s = Vo.t/2*[(1 + B)/B^2]
…which isn’t so intimidating. Alternatively we can express the decceleration constant, k, as an expression…
k = 1/t * [V^(-1/3) – Vo^(-1/3)]
and substitute into our equation for the displacement to get…
s = Vo.t/2 * [(V/Vo)^(1/3).(1 + (V/Vo)^(1/3))]
which may seem a bit strange, but even the regular equation for displacement under constant acceleration can be rearranged into a similar form…
s = Vo.t/2 * [1 + (V/Vo)]
but what does that all mean? Part II coming soon.