A possibly interesting tidal effect

I don’t really have the energy to talk about climate change at the moment, but did come across a paper that I thought some might find interesting. It’s by Steven Balbus and is called Dynamical, biological, and anthropic consequences of equal lunar and solar angular radii. As the title indicates, the Moon and the Sun have about the same angular size and people have often pondered if this was simply a coincidence or not. Could it be that having the same angular size has played a role in the evolution of a – supposedly – intelligent species?

A consequence of this similar angular size is that the tidal influence of the Moon and the Sun are about the same. This means that when you combine their influence, you get a beat pattern in the tidal height: over a period of many days, the height of the tide can vary quite substantially. This wouldn’t happen if there were only a single body producing the tides, or if one body were very dominant. This is illustrated in the Figure below which, you may notice, is for the Devonian period (420 – 360 Million years ago).

Figure 1 from Balbus (2014) showing how the height of the tide varies with time.

So, why is this interesting for the Devonian? This is where I get well outside my comfort zone, but my understanding is that the Devonian is the only period during which vertebrates moved from the oceans to the land. Also, if you look at the figure below, which is for the early Devonian, this happened mainly on the coastline on either side of the narrowing channel between the continents.

Credit : Ron Blakey, NAU Geology

The basic idea in the Balbus (2014) paper is that this narrowing channel meant that the tidal height would increase as the tide moved into this channel (the tidal height figure above is only for the equilibrium tide). When the tide was very high, it would wash quite far inland. However, when the tide height started dropping, it would do so rapidly and would leave behind many now isolated tidal pools. The consequence of this is that those vertebrates that could maneuver on land, would have an advantage. They could both escape from the isolated pools if trapped, but could also feed on other animals trapped in these pools. The basic idea is therefore that a combination of the combined tidal influence of the Moon and Sun, the configuration of the continents during the Devonian, and Natural Selection is what lead to the movement of some vertebrates from the oceans to the land.

One can also consider the relevance of this with respect to the anthropic principle. The anthropic principle (in its weak form at least) is that the reason our planet and the Solar system look the way they do is because if they didn’t, we wouldn’t be here to ask that question. Of course, we don’t actually know if the conditions for the development of complex, intelligent life are rare or not. However, the more we encounter rather unlikely scenarios that seem to have been required for our development (such as that presented in Balbus 2014), the more we might start concluding that complex, intelligent life in our galaxy is more likely to be rare, than common. Maybe we really are alone.

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90 Responses to A possibly interesting tidal effect

1. Pierre-Normand says:

This is somewhat related to another argument regarding the Moon and the anthropic principle. A large natural satellite has the effect of stabilizing the tilt of the terrestrial axis and hence also the climate. This new idea, in the OP, seem somewhat less explanatory useful since, it seems to me, as long as there are emerged land masses with plenty of flora and insect like creatures, lakes estuaries and marshes, there will occur selection pressures that favor migration of aquatic life forms to the lands just because of the abundance of food there, and the initial security from aquatic predators. Maybe the proposed tidal effect sped things up, though.

http://www.astrobio.net/news-exclusive/the-odds-for-life-on-a-moonless-earth/

2. P-M,
Yes, you’re right about the stabilising effect on the Moon on our rotation axis. You make a fair point about it happening anyway, but I think there are couple of factors to consider. One is – I think – that the movement of vertebrates from the ocean to the land happened only once, happened during the Devonian, and happened where you’d expect this tidal effect to play a role. This applies, I think, only to vertebrates. Invertebrates moved from the ocean to the land many times (I think), so maybe we would have evolved into intelligent crabs if it wasn’t for the similarity in the angular size of the Moon and the Sun 🙂

You’ll notice I used the term “I think” many times above, because I really don’t know much about this topic and so could be completely wrong.

3. Doesn’t the argument presented for the transition from sea to land only depend on the magnitude of the tides? Is there any advantage for the complex tidal variability due to two bodies influencing the tides?

4. Victor,
Okay, well outside my comfort zone, but I think there were two factors. One was the large variation in the tidal height. The other was how quickly it reduces once passed the maximum. If it varied slowly, then animals may not be so easily trapped and hence the effect would be less significant – at least, that is I think the argument. I think this is all very new and still quite simple, so I don’t think the argument has extended much beyond that. My understanding, though, is that this idea is being positively received by some who work in this area.

5. This is exactly the sort of question I’d like to while away my downtime pondering and discussing, if it wasn’t for the distraction of climate change and the necessity to raise awareness of its approaching dangers.

At least this is a thread which won’t require moderation. 🙂

6. Pierre-Normand says:

ATTP wrote: “One is – I think – that the movement of vertebrates from the ocean to the land happened only once, happened during the Devonian, and happened where you’d expect this tidal effect to play a role.”

Only once! That’s a good point, if true. Because of contemporary amphibious fish, salamanders, etc., I would have though such occurrences to be somewhat more common.

“Invertebrates moved from the ocean to the land many times (I think), so maybe we would have evolved into intelligent crabs […]”

If we had evolved into intelligent crabs, then we would be speculating about the brachyuric principle.

7. P-M,
I don’t know if it really was only once for vertebrates, and more than once for invertebrates. I’ve done some quite searching and the Devonian does indeed seem to be the period when it happened first, but I can’t find evidence that it happened since.

8. Okay, I’ve just found this which suggests that it did indeed only happen once and that it happened during the Devonian. Never trust the internet, though!

9. Pierre-Normand says:

Maybe vertebrates have been unable to repeat the exploit after the first wave of land migrations because land predators thereafter have had too much of a head start. Would be second comers became easy snacks before they could adapt well enough to terrestrial niches.

10. dikranmarsupial says:

11. Dikran,
Thanks, that was the intent.

12. Rachel M says:

Yes, it is a really interesting post, thanks.

I’m glad we’re not crabs as I’d never be able to manage my iPhone with claws.

13. BBD says:

ATTP

Fascinating article, thanks for posting it up. Persuasive hypothesis, too. Your closing sentence made me think, though:

However, the more we encounter rather unlikely scenarios that seem to have been required for our development (such as that presented in Balbus 2014), the more we might start concluding that complex, intelligent life in our galaxy is more likely to be rare, than common. Maybe we really are alone.

This conflates the conditions that eventually gave rise to the evolution of human intelligence with the possible evolution of extrasolar intelligence. Why should extrasolar intelligence not be, eg, medusoid and aquatic? Or a cloud of interstellar gas (I wave wildly, obvs)?

Years ago I read a rather fun book which made exactly the point that alien means alien and we mustn’t anthropomorphise.

14. BBD,

Why should extrasolar intelligence not be, eg, medusoid and aquatic? Or a cloud of interstellar gas (I wave wildly, obvs)?

Sure, that’s always possible. The point, though, (assuming I can express myself clearly) is that the if we continue to discover that our own evolution was largely a consequence of a sequence of unlikely events the more we might conclude that intelligent life is rare. We will, probably never actually know for sure. It’s possible that we may not – within our lifetimes at least – be able to definitively show that life exists on other planets even if we could find ones that were capable of hosting life.

15. BBD says:

To be clear, I suspect that while life might be fairly widespread throughout the galaxy, intelligent life may well be very rare. So rare that intelligent species rarely evolve simultaneously within galactic-scale hailing distance of each other.

16. BBD,
Yes, that’s largely why I focused in intelligent life. Life itself may be common, with intelligent life being rare. Since being engaged in the climate debate, I’m starting to doubt that it actually exists anywhere 🙂

17. BBD says:

ATTP

We crossed 🙂

if we continue to discover that our own evolution was largely a consequence of a sequence of unlikely events the more we might conclude that intelligent life is rare.

Yes. But perhaps what I’m trying to say is that intelligence is no more unlikely to have arisen elsewhere in the galaxy through some other equally random and improbable sequence of chance events.

18. If we were intelligent crabs and we’d developed along a similar path, then perhaps climate change would now be ocean acidification’s ‘evil twin’ rather than the other way round?

19. BBD says:

Since being engaged in the climate debate, I’m starting to doubt that it actually exists anywhere

Few things have shaken my (only modest) faith in human nature as much as the contrarian mindset 😉

20. BBD,

But perhaps what I’m trying to say is that intelligence is no more unlikely to have arisen elsewhere in the galaxy through some other equally random and improbable sequence of chance events.

Sure, but if it requires a sequence of unlikely events then it becomes less likely than if it does not require a sequence of unlikely events (I think that makes sense, but am no longer sure).

21. BBD says:

John
Yes 😉 But how would we have got a FF-based economy going underwater?

22. BBD says:

ATTP

I think we probably agree with each other that intelligent life is likely to be very rare 😉

My brain is on a work-to-rule this afternoon I’m afraid…

23. Surely anything that’s happened once via natural processes and pure chance can happen again? However the distances of space are so vast that I would think that we are, for all intents and purposes, alone.

And again there’s also the possibility that any intelligent species that evolve are almost bound to be so successful that they become conceited, self-centred, greedy and end up destroying the environment that enabled their existence. This might mean that intelligences in other solar systems have been and gone and others have yet to evolve into sentience.

In other words is this our brief moment and its duration is up to us?

24. Come on, BBD, surely every species likes a hot bath?

25. Rachel M says:

It’s hard to regard a species that knowingly changes the climate to the detriment of future generations of the same species as intelligent. But perhaps it’s just that we’re irrational. I’ve always liked this Bertrand Russell quote –

It has been said that man is a rational animal. All my life I have been searching for evidence which could support this.

26. john,

Surely anything that’s happened once via natural processes and pure chance can happen again?

Indeed, but given ~1010 stars in the galaxy, how likely is it that it could happen twice or more in a single galaxy.

And again there’s also the possibility that any intelligent species that evolve are almost bound to be so successful that they become conceited, self-centred, greedy and end up destroying the environment that enabled their existence. This might mean that intelligences in other solar systems have been and gone and others have yet to evolve into sentience.

Indeed, and I think that is one of the possible solutions to the Fermi paradox.

27. Rachel M says:

BBD,

Yes 😉 But how would we have got a FF-based economy going underwater?

An underwater crab-mobile??

28. Willard says:

Watch AT’s hits explode with all the science lulz.

29. EFS_Junior says:

Food for thought?

The Misanthropic Principle
http://insti.physics.sunysb.edu/~siegel/parodies/misanthrope.html

30. Tom Curtis says:

Anders, in order:

1) The solar tidal influence is only 46% of that of the moon. Where they of the same magnitude, once a month there would be not tide at all, which is never the case.

2) That the solar and lunar tidal influences are within a factor of two of each other is largely coincidental. Had the moon been as dense as the Earth, for example, solar tidal influence would have been approximately a quarter of lunar tidal influence.

3) The Moon is retreating from the Earth due to the slow transfer of angular momentum from the Earth to the Moon by the tides. This also has the effect of slowing the Earth’s day. As a consequence Earth’s day was just 22 hours long in the Devonian. I have been unable to get reliable data for the Devonian, but 620 million years ago, that means the angular radius of the moon was 7.5% larger than that of the Sun, and the lunar tidal influence 2.34 times that of the Sun (and 1.075 times larger than today). Interpolating, that indicates the Devonian angular radius to be approximately 5% greater than that of the Sun, and the lunar tidal influence to be 2.3 times that of the Sun (5% greater than at present).

Finally, it is not true that the Devonian is the only period when fish have evolved the ability to walk on land. In fact, four modern fishes have that ability. That they or their descendants have not evolved into full fledged amphibians probably has more to do with biological competition (reptiles and mammals are too efficient competitors on land) than with any other limitation.

31. Tom,
Yes, I knew the effect wasn’t exactly the same.

That the solar and lunar tidal influences are within a factor of two of each other is largely coincidental.

Yes, but the argument here is that it’s not coincidental that we happen to live on a planet where this is the case.

Finally, it is not true that the Devonian is the only period when fish have evolved the ability to walk on land.

If that is true, it would rather blow a hole in this idea.

32. Maybe the walking fish aren’t quite as much of a killer as I first thought. The issue here is more to do with an actual evolution to land-dwelling, rather than simply the ability to walk on land. The Devonian might be the only period where there was a significant benefit to this adaptation. Of course, as I said, this is well outside my comfort zone.

33. dikranmarsupial says:

While walking fish have evolved more than once, the Wikipedia article suggests that all tetrapods are descended from a single evolution of walking fish.

34. dikranmarsupial says:

which means that the evolutionary pressures that cause walking fish to turn into land animals only ocurred once.

35. It’s a nice observation that the strength of tidal influence is linked to the apparent size of the celestial body, but the density must be the same to make equal sizes result to equal tidal effects.

If the tidal influences would be equal, the variability in the tides would be larger, but the effects would not fully cancel at any time. The minimum occurs twice in a month at half moon. The tides are due to the higher derivatives of the gravitational field than the total gravitational force that affects Earth. Those derivatives do not disappear for any relative strength of the tidal influences of the Sun and the Moon.

36. Balbus’s introduction also notes that lunar tides are stronger than solar tides. As Pekka notes, that’s because the tidal forcing potential is proportional to the densities of astronomical bodies. See page 9 here: plugging in values for the Sun and Moon into equation 1.21 shows that the largest (spherical harmonic degree 2) solar tides are roughly 45.9% as large as the largest lunar tides, which matches Tom Curtis’s reference.

As Tom notes, this difference was even bigger than it is today during the Devonian. Here’s a very rough estimate. The Moon is currently moving away from the Earth at ~3.8 cm per year, because ocean tides convert Earth’s rotational momentum to the Moon’s orbital momentum. If we very roughly extrapolate this recession back 400 million years, the Moon was probably ~15,000 km closer to Earth. Because the largest lunar tides are inversely proportional to the inverse cube of the Earth-Moon distance, that means lunar tides were ~12% stronger during the Devonian.

Balbus cites papers (almost certainly more nuanced than my very rough linear extrapolation) saying the Moon was ~20,000 km closer to Earth during the Devonian, so in his model lunar tides would be even stronger while solar tides remain unchanged.

However, all that just calculates the tidal forcing potential. The shapes of the ocean floor and coastlines amplify ocean tides with periods close to a resonant period for that ocean basin, like the Bay of Fundy. It seems like Devonian continents formed a huge “Bay of Fundy” which created unprecedented numbers of tidal pools.

I’m also not (yet) convinced that lunar and solar angular radii being close to each other is really that important. As Pierre-Normand noted, stabilizing the Earth’s rotational axis seems like the Moon’s more important role in the development of life. It’s hard to imagine how complex life could evolve on a world where the axis of rotation wobbles so much that it sometimes points at the Sun, yielding (constantly changing) hemispheres of fire and ice.

Regarding other comments, I’ve often speculated that the Dunning-Kruger effect might explain the Fermi paradox. However, it seems unlikely that a civilization that has established self-sufficient interstellar colonies could vanish entirely, because the vast distances between stars act as effective quarantines. In fact, such a civilization could colonize the entire galaxy in just a few million years.

So it seems unlikely that any Milky Way civilizations have developed interstellar colonies, because they’d probably have arrived on Earth before we evolved. Maybe some species have much more self control than us, or a much lower reproductive rate so they wouldn’t be driven to colonize all the stars in the Milky Way. But that restrained species would also have to be remarkably uniform, because even the slightest tendency towards aggressive expansion would be selected for. After all, that’s why our biosphere is filled with the descendants of creatures who reproduced more often/effectively than their competitors.

Therefore, the Fermi paradox makes me think that interstellar colonization is really difficult, and/or that preventing civilizations from self-destructing long enough to cobble together a (ramscoop?) starship is really difficult. After watching Sen. Inhofe elected as the chair of the U.S. Senate Committee on the Environment, I’m starting to lean towards the latter.

By the way, David Brin’s book Existence has some fascinating speculation about the Fermi paradox. Highly recommended.

37. You’re all mis-calibrating my use of the word “about” 🙂

38. ATTP: actually, I figured you’d read Balbus’s introduction or my previous comment, so I figured you already knew that lunar tides were larger than solar tides. My gratuitous explanation and citations were provided for purposes of shameless self-promotion and as a temporary cure for boredom.

39. Tom Curtis says:

Anders, I was suggesting that the approximate equivalence of magnitude between angular radii and tidal influence was coincidental. The average* angular diameter of the Moon is approximately 31.7 minutes, while that of the Sun is 32.15 minutes, making the Sun 1.4% bigger. The Sun has 42.1% of the density of the Moon. If tidal influence correlated with angular radius, we would then expect the Sun to have a tidal influence of 42.3% of the Moon’s rather than the actual 46%. Put another way, the average angular radius of Venus is 3.47% of that of the Moon. It’s density is 154.6% of the Moon’s. If angular radius determined tidal influence, we would therefore expect Venus’s tidal influence to be greater than 3.47% of the Moon’s. In fact it is “…0.000113 times the solar effect” (Wikipedia).

Obviously there is going to be some correlation between similarity of angular radii and tidal influence but it is not linear, and the correlation is not sufficient that the similarity in angular radii of the Moon and the Sun explains their similarity of tidal influence.

(* I took the average of the maximum and minimum values, which is incorrect if weighted for duration due to orbital motion being faster at perihelion, but should be a reasonable approximation.)

For what it is worth, I am a firm believer in the weak anthropic principle and think it is no coincidence that Earth both has life, and has a large Moon. That, however, is partly based on a belief that life evolved in tidal pools, with evaporation in tide pools forming conditions to experiment in different chemical combinations or organic material, and tides distributing the the results among the different pools allowing for a primitive form of Darwinian selection. So, as a highly speculative conjecture, no tides equals no life and small tides equals greatly reduced chance of the evolution of life.

I can also well believe the existence of tides increased the potential for marine life to become land dwelling (which has occurred at least four times, though only once for vertebrates) and for the reverse process (which has occurred at least four times among vertebrates, including at least twice for mammals). It is worthy of note that of the at least four terrestial invasions, three took place prior to the Devonian (plants, and two lineages of arthropods leading to spiders and insects respectively). I should probably add velvet worms to the list of terrestial invaders as well, and there are probably a number of other obscure examples.

However, the influence of tides is not the same as the influence of a solar/lunar tidal beat.

40. Tom,

Obviously there is going to be some correlation between similarity of angular radii and tidal influence but it is not linear, and the correlation is not sufficient that the similarity in angular radii of the Moon and the Sun explains their similarity of tidal influence.

It goes as angular size cubed. I think I see what you’re saying. Depending on the composition of the Moon, for example, it would be possible to have a system where the tidal influence of the Moon and Sun were similar (within a factor of 2 for example) but in which their angular sizes did not appear all that similar.

41. Tom,
I should probably wait till morning to check this, but given that the radius of an object depends only weakly on density and if we assume that being at about 1 AU around a Sun-like star is preferred, then it may be that any Moon-like body that produced a tidal effect similar to that of the Sun would have a similar angular size. Of course, I don’t really know how much of a difference there would need to be for it to be noticeable to us.

42. Tom Curtis says:

Pekka, the strength of the tide is due to the difference in gravitational attraction between near side and far sides of the planet relative to the astronomical body causing the tides. If that difference is equal for two bodies, the derivatives are also equal for two bodies. I will grant that there would be some residual difference in a given 24 hour period due to different periods of the solar and lunar tides, but the difference would be negligible and not distinguishable from wave action.

43. Tom Curtis says:

Anders, density of the distant body is only part of the equation. The strength of the tide is due to the difference in gravitational attraction between near side and far sides of the planet. Ergo, a larger planetary diameter for the body on which the tides are raised would result in a larger tide, all else being equal. Therefore if the Earth was less dense, but had the same mass, it would have stronger tides, an effect that (I think) would increase lunar tides more than solar tides due to the proximity of the Moon. More importantly, relative distance is far more important given that difference gravitational force between two close locations will rise with greater proximity. That is why the lunar tide is over twice that of the Sun even though the Solar gravitational force on Earth is 179 times stronger than Moon (wikipedia).

So, yes, for a planet at 1 AU with a sun of approximately Solar mass, a moon of approximately the same angular radii as the that sun will have a tidal influence close to that of the sun. But given that the goldilocks zone for the sun is approx 0.5 to 2 AU, and given that stellar masses compatible solar luminosity consistent with life varies from 0.6 to 1.5 times the Sun’s (at minimum) with consequent alteration of the goldilocks range, and concurrently the mass of the sun, I doubt that in general for habitable planets the ratio of lunar to solar tidal influence is constrained to be even in the same magnitude as the ration of lunar to solar angular radii. Certainly Balbus has not shown it to be the case. He has merely assumed Earth like conditions on all relevant factors other than relative angular radii. The formula works in that very restricted circumstance but that is merely coincidental.

44. Tom Curtis says:

Dikran, I agree that the evolutionary circumstances suitable for the evolution of terrestial vertebrates occurred only once. Those circumstances, however, include such factors as the relative biodiversity of (and hence competition among) marine vertebrates, atmospheric levels of CO2 (which being high, imply a low O2 content which restricts the potential size of invertebrate land dwelling competitors), and above all the lack of vertebrate competitors on land. A modern lungfish attempting to evolve a full terrestial habit would be simply lunch for a hungry dingo, goanna or emu (or kookaburra or …). The argument that special geographical conditions come into play is not definitively wrong, and is worth exploring, but given that all the geography for the reverse transition by the ancestors of whales was the Indus River delta, the supposition that very special geographical conditions were needed does not look strong to me.

45. Oops, “inversely proportional to the inverse cube” was redundantly redundant…

46. BBD says:

Eh, heavy.

Does the evolution of intelligent life require:

M-class star

Goldilocks planetary orbital radius with liquid water etc

Does ‘intelligent’ necessarily mean a technological society?

It’s late and I have just got back from a party, so don’t take this too seriously.

47. Pierre-Normand says:

“Come on, BBD, surely every species likes a hot bath?”

Crabs and lobsters positively hate a hot bath.

48. Pierre-Normand says:

Very interesting point, Tom Curtis, about abiogenesis, the weak anthropic principle, and tides.

49. EFS_Junior says:

“If the Sun were somehow compressed enough to become a black hole, it would be less than 6 kilometers (well under 4 miles) across. It would exert no more gravitational force on Earth or the other planets in the solar system than it does now. Why? Because it would contain no more matter than it does now and it would be no closer to the planets than it is now.”

See this figure for density of the Sun

See this dataset for a model of the Sun

http://users-phys.au.dk/jcd/solar_models/

Hint: the Sun != uniform density as Balbus assumes the Sun to be in equations 1.2/1.4, thus both of these equations are invalid.

Basically, mean density is a meaningless concept for the Sun, and only somewhat less so for the Moon (as it too is not of uniform density, meaning to a 1st approximation the size of the Moon matters <<< the mass of the Moon)

Please wake me up if you all need a (rather insignificant) coastal engineer to explain M2/O2 tides in the coastal zone, who also happens to have a vast theoretical/laboratory/prototype background in harbor resonance.

Or better yet go ask someone over here (where you all will find all the hundreds of tidal constituents necessary to define the idealized tide up through the annual yearly mode for various locations in the USA):

http://tidesandcurrents.noaa.gov/

or here even

http://www.psmsl.org/

50. Eli Rabett says:

Why can intelligent life not evolve in the sea?

Is this an argument for creation?

51. Tom Curtis says:

Eli:

“Is this an argument for creation?”

No. Even applying the weak anthropic principle to the universe as a whole is not an argument for creation.

52. EFS_Junior says:

Hello,

I have a post in moderation (possibly too many hyperlinks or an inline image).

TIA

53. I don’t doubt that intelligent life like cetaceans and cephalopods can evolve in the sea. But fire played an important role in our evolution as a species which uses technology. In fact, some anthropologists say that fire makes us human. Cooked food yields more calories, which can support a larger brain. It also requires less chewing, so we don’t have to waste four to seven hours each day chewing like apes do. Controlling fire yields an immediate and intimidating technological advantage, which probably helps select for curiosity and the same general planning skills required to build telescopes.

If there’s something analogous to fire that could prompt aquatic species to develop technology, I don’t see it.

54. Pierre-Normand says:

The anthopic principle usually is put forth as an alternative to intelligent creation as an explanation of our existence in light of the putative intrinsic implausibility of the emergence (abiogenesis + evoluton) of intelligence in a physical universe that wouldn’t have its constants fine tuned in order to favor such emergence. Hence, such an implausibility is a shared assumption without which the principle wouldn’t have much of a point.

55. Mean density is a very meaningful concept for the Sun. This point is actually driven home by that NASA quote saying that the Sun’s gravity wouldn’t change significantly if it became a black hole. This actually means the radial density function is completely irrelevant to gravity outside the Sun’s surface. This can be confirmed by solving the standard freshman-level physics problem showing that the external gravity of a uniform sphere equals that of a point mass.

Unfortunately, this also causes gravity missions like GRACE to be unable to recover anything other than the radial integral of mass over the Earth’s surface, because all spherically symmetric radial densities produce the same external gravity field. This is a fundamental limitation of gravity sensing methods, but it also means that GRACE “sees” all contributions to mass change at any latitude/longitude regardless of depth. Like underground aquifer depletion, for example.

The only deviation that could even possibly affect the Sun’s tidal forcing potential is the fact that the Sun isn’t spherically symmetric- it’s actually a flattened oblate ellipsoid because of its rotation. However, these small deviations only cause gravity variations close to the Sun. Far from the Sun, its gravity is very well approximated by pretending it’s a point mass.

Balbus’s equations 1.2 and 1.4 are perfectly valid approximations.

56. EFS_Junior says:

OK, so humble apology, I was wrong, equations 1.2/1.4 or just fine.

I too get a constant forcing ratio of 0.459 for the Sun/Moon no matter the size of the Sun (mass held constant for the Sun).

“The idea is that the near match of angular sizes is a mathematical, but incidental, by-product of
the presence of a strongly modulated tidal forcing by the Sun and Moon.”

Hmm, I thought this was rather well known and for a very long time now (the “strongly.modulated tidal forcing”).

Also, the equilibrium tide is also well known, that’s how regional numerical tidal models work (or use to work) with the equilibrium tide at the outer boundary abysmal ocean.

So could someone tell me what is really new in this paper?

57. Much respect, EFS_Junior. I’m also not convinced there’s anything really new in this paper.

58. EFS_Junior says:

DS,

I was doing a spreadsheet on this (using the density data as linked above), rewrote equation 1.4, solved for f, the whole column was the same constant 0.459, so oops, time to post and eat some humble pie.

59. EFS_Junior,

So could someone tell me what is really new in this paper?

I don’t think there’s anything new in a physics sense. My understanding, which could be wrong, is that it’s the first time someone has associated this with the development of land-dwelling vertebrates.

Tom,

So, yes, for a planet at 1 AU with a sun of approximately Solar mass, a moon of approximately the same angular radii as the that sun will have a tidal influence close to that of the sun. But given that the goldilocks zone for the sun is approx 0.5 to 2 AU, and given that stellar masses compatible solar luminosity consistent with life varies from 0.6 to 1.5 times the Sun’s (at minimum) with consequent alteration of the goldilocks range, and concurrently the mass of the sun,

You can certainly out-philosophize me, but the issue is possibly whether or not what you say above is actually correct. If you reduce the mass of the host star, the peak wavelength gets longer and the energy of the photons that might be used for photosynthesis gets lower (3 photon rather than 2 photon process maybe). Also a planet in the habitable zone of a star with a mass less than 0.9 Msun would be tidally locked (just as the Moon is to the Earth). Do we need a Jupiter to clear the inner system of dangerous asteroid. Do we need a Moon to stabilise our axis and do we need a Moon so as to produce (together with the Sun) a tidal pattern with beating, etc. So, is it just coincidental that we happen to be in the system we’re in, or is it telling us something that is actually required?

I doubt that in general for habitable planets the ratio of lunar to solar tidal influence is constrained to be even in the same magnitude as the ration of lunar to solar angular radii. Certainly Balbus has not shown it to be the case. He has merely assumed Earth like conditions on all relevant factors other than relative angular radii. The formula works in that very restricted circumstance but that is merely coincidental.

I’m not sure I follow the first part of this. The tidal influence goes as something like $\rho \theta^3$, where $\rho$ is the density, and $\theta$ is the angular size. So, if the tidal influence of two bodies is similar, then the angular size is going to be similar (with a few tens of percent, at least), unless the density is hugely different (which is probably unlikely).

I also don’t think Balbus was trying to solve the problem in a general sense. He was simply illustrating that the configuration produces a system where the Sun and Moon produce a similar tidal effect and could have played a crucial role in the evolution of land-dwelling vertebrates.

60. Tom,

What I write here is irrelevant for the main point of the post, and intended only to clarify physics of tides. For me these issues came up earlier, when I was arguing against “theories multidecadal variability” based on irregularities in the motion of the Sun with respect to the center of mass of the solar system.

It’s perhaps more illuminating to say that the tides are due to the difference of the gravitational pull of the other celestial bodies at the center of mass of the Earth and at the surface, because that’s the best way of understanding why the high tide occurs twice a day rather than once. The force that causes the tide is determined by subtracting from the local gravitational pull the influence of the acceleration of the Earth as whole. That leads to zero net force at the center of the Earth and an outwards force on both sides along the line that connects the Earth to the other body. The resulting force can be studied in more detail using an expansion based on spherical harmonics as described in the thesis of Killett (link in a post of DS).

The leading term of the gravitational force is given by the second spherical harmonic. The strength of this term is proportional to M/R^3, where M is the mass of the body and R its distance from the Earth. If this term were of equal size for the Sun and for the Moon the terms would cancel at half moon. The next terms add, but they are also of very different strength, because R appears in fourth power. This term has the strength of 1.65% of the leading term according to Killett. (I hadn’t seen such an estimate before, and thought that the term could be somewhat stronger.)

61. EFS_Junior says:

ATTP,

Not so, see here:

“A woodland hypothesis of tetrapod evolution is presented here: limbs and necks were selected for by scavenging and hunting in shallow-flooded woodlands and oxbow lakes during a unique period in Earth history, after evolution of flood-ponding trees and before effective terrestrial predator resistance.” (2011)

“Their occurrence in the Zachełmie succession significantly changes our views on early tetrapod habitats, which apparently included permanently elevated and sparsely vegetated areas adjacent to shallow marine lagoons.” (2014)

In one of those “Ah ha, we have the fossils kind of way” if you know what I mean.

Kind of looks like an active area of (empirical) research. Next up, finding empirical evidence in ancient tidally dominated areas that geologically predates the above hypothesis.

Disclaimer: No, I didn’t know about/of this stuff until I went looking.

62. EFS_Junior,
Interesting, thanks. I haven’t read your links in much detail, but they seem to suggest that there were already ideas that the evolution to land dwelling was associated with tidal pools but I’m not sure anyone’s suggested that the beating pattern in the tidal heights and the narrowing of the ocean channel between the Devonian continents could have played a role. I also don’t know much about this stuff, so it may well not really be anything new.

63. EFS_Junior says:

PP,

Well, oops, there I go again M2/O2 should have been M2/S2 (just a “bit” rusty, don’t you know).

It’s usually best to get some actual tide data, subtract the known tidal components from that time series and look at the residuals (SLR, seasonal variations (fairly strong (?, define strong) tropical year annual variations), storm surges, etceteras). Do this for many distinct locations, tide ranges, etceteras.

However, IMHO/AFAIK the M2/S2 would still be the largest contributors for semi-diurnal shallow water coastal locations (and IMHO/AFAIK would be (much?) larger in amplitude then for diurnal tidal areas).

The whole coastal bathymetry/topography thing can really be rather messy at times. Abysmal deep ocean tides, not so much.

64. EFS_Junior says:

ATTP,

It is probably a newer idea in the published literature for all I (don’t) know. But we do know current tidal patterns fairly well. Tidal patterns that, a priori, would have existed since the beginnings of the Sun-Earth-Moon system and continents-erosion-continental drift (creating shallow water coastal areas of various bathymetries/topographies).

At the end of the day, it would appear that some empirical evidence is necessary to promote various hypotheses?

65. EFS_Junior says:

This paper would appear to somewhat support the Balbus hypothesis from an empirical POV:

http://www.geology.cz/bulletin/contents/art1460

“The invertebrate trace fossil assemblage, tetrapod tracks and associated sedimentological features point to deposition in a marginal-marine, mostly peritidal and lagoonal environment with minor terrestrial influences.”

YMMV

66. Maybe we really are alone.

Not a chance. Probability of that is indeed zero.

67. TLE,
Really? Do you mean other life in the galaxy, other intelligent life in the galaxy, other intelligent technologically advanced life in the galaxy, or something else altogether?

68. The decay pathways of the primordial energy are diverse.The isotopic nuclide spectrum is pre-emplaced by nucleosynthesis and is indeed engaged in rapid decay at geological timescales this stuff is inevitable with the kind of setup we are seeing not even considering exotic cosmology.

It is demonstrated on an energy cascade tree analysis alone. This is a good place to start.

http://sandwalk.blogspot.com/2014/10/metabolism-first-and-origin-of-life.html

There is a very good polymerization dynamics theory out there too.

69. Neil White says:

Hi

Following on (mainly) from Tom Curtis’ comments. The gory detail on the relative influence of the Sun and the Moon is here:

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm

– scroll down about half way to the paragraph starting “Clearly, the calculation of tides is…” and equations 17.12 to 17.14. The influence of the Moon is approximately double that of the Sun, and this is not related to angular size. If you go down to table 17.2 the amplitude of the main lunar constituent is roughly twice that of the main solar constituent – S1.

Typical tidal analyses of tide gauge records have a similar ratio between the amplitudes of these constituents.

Neil

70. Andrew Dodds says:

TLE –

Yes, I’ve looked at the metabolism-first stuff before, it’s far more convincing than other hypotheses I’ve seen.

One of the interesting consequences is that if true, it implies that life will arise wherever we have an ocean forming on a silicate planet large enough to hold it, and that the origin of life is geologically instant. These black smokers are geologically transient features (<10^6 years, IIRC), so life would have to form and become free-living in a very short timescale. This does fit with the essentially-instant origin of life on earth.

As far as the progression of life goes.. This vertebrate-on-land stuff is not at all convincing. We have examples of fish coming out of water right now, the reason they don't evolve into frogs (or neo-amphibians of any sort) is because the niche is already filled by better-adapted creatures, with very well-adapted predators. There are plenty of seasonal biomes where the evolution of features useful on land would be promoted, even without tides. Plus..

http://en.wikipedia.org/wiki/Mudskipper

For me, the more interesting thing is the chemical evolution of the planet, and very specifically the time taken to shift the redox state of the upper mantle such that CO2 became the dominant volcanic carbon species. Very boring, but until such a shift happens, life is basically stuck in anerobic metabolism. That shift took something like 3 billion years – a large chunk of the time that Earth is expected to spend in the habitable zone. Whereas it only took half a billion years, give or take, to get from the very first Chordates to The Kardashians. Indeed, the prerequisites for intelligent life – land dwellers with constant internal temperature – have only been around for perhaps 200 million years maximum. All this suggests that the hard step isn't the origin of life, and it probably isn't even the evolution of intelligence, it's going from the anerobic, single-celled biosphere to the aerobic, muticellular biosphere.

(*Note, n=1, other planets may differ)

71. Neil,

The influence of the Moon is approximately double that of the Sun, and this is not related to angular size.

Maybe I’m missing your point, but if you were to multiply the equations in your link by $(4/3 \pi r^3)/(4/3 \pi r^3)$, where $r$ is either the radius of the Sun of the Moon, you could rewrite the tidal effect of each body as being proportional to $\rho \theta^3$, where $\rho$ is the average density and $\theta$ is the angular size. Therefore the relative tidal effect approximately depends on the ratio of the densities and the ratio of the cube of the angular sizes.

72. EFS_Junior says:

ATTP,

Agreed, conservation of mass (for small theta).
= constant
Changing theta requires rho to change in direct (inverse) proportion

It works because as long as theta (in radians) << 1 then tan(theta) ~ theta
My definition of theta is the half angle ~ 0.00465 (Sun radius/Earth distance to Sun) and 0.00453 (Moon radius/Moon distance to Earth)

And I only varied the Sun by making it smaller, not larger.

If one were to make the body large than one would need the correct tan(theta) and not theta itself (now I need to go through that spreadsheet one more time).

73. EFS_Junior,
Yes, good point. I apply the small angle formula without thinking these days 🙂

74. EFS_Junior says:

Well I don’t know how to embed an image!

Also, I’m thinking it should be sin(theta) not tan (theta), but in either case for theta << 1 then tan(theta) ~ sin(theta) ~ theta. Anyways, I need to draw up the geometry for an observer on Earth.

75. EFS_Junior,
I’m not 100% sure myself, but I think the html embed command works if you’re embedding a link to a figure.

76. izen says:

The coincidence of lots of tidal pools and the evolution of one aquatic tetrapod into a terrestrial form may not indicate that tidal pools are necessary for such a transition to occur.
That only one form made the transition may be explained by the first arrivals rapidly evolving to occupy the available niches blocking new entrants.
But that does imply that the terrestrial environment had few, or difficult niches for aquatic vertebrates forms to exploit.

Here is an oldie but goodie on the life as metabolism idea-

http://www.gla.ac.uk/projects/originoflife/html/2001/critical_aspects.htm

And a reminder that Frank Drake of ‘equation fame did not consider that life could only evolve on gy=c planets. Or that intelligencemust be land-based –

http://www.daviddarling.info/encyclopedia/N/neutronstarlife.html

77. Andrew Dodds says:

izen –

The interesting thing is the configuration of the continents at the time – it looks like we have a single shallow-sea zone at the time, with no geographical separation, just at the time when it’s becoming possible for fish to evolve into amphibians. So as soon as it happens, the resultant animals have no geographic boundaries. This would also tend to crowd out other attempts to evolve land-dwelling.

It’s also possible that there have been several ‘attempts’ to evolve onto land but one branch ‘won’. Just as marsupials look to be progressively losing out to placentals amongst the mammals, we could have branches of land dwellers that have been wiped out without leaving much trace; the fossil record for these things is sparse.

78. EFS_Junior,
Okay, I fixed your comment. One way to do it is to do open triangle bracket img src = ” ” close triangle bracket.

79. izen says:

@-Andrew Dodds
Not sure there would not have been climate boundaries, despite the single continent – single shallow sea set up.
It is easy to slip up by 100million years that far back, but ‘shortly’ after the emergence of vertebrates on land, plants started using lignin for structural growth, generating most of the coal we now risk burning. But then it reduced CO2 causing cooling until fungi evolved decomposition chemistry.
I do miss the old PALEOS site when wanting to check the timeline on this sort of thing…

‘-“It’s also possible that there have been several ‘attempts’ to evolve onto land but one branch ‘won’.”

The five-toes?!

80. Rachel M says:

To embed an image: copy the URL for the image and paste it into the comment box on a line by itself. You don’t need to use HTML.

81. Rachel,
Thanks. I thought that was possible but maybe EFS_Junior’s URL wasn’t on a line by itself.

82. Rachel M says:

I can’t see his comment with the image but I haven’t been paying close attention to this thread. My eyes glaze over when it gets too sciency 🙂

83. It’s the one at 11.46am. It had “= constant” after the URL which probably messed it up.

84. Rachel M says:

Ah, I see. Yes, that would be why.

For anyone interested, you can also type Latex into the comment box –

$\rho\theta^3$

Instructions at http://en.support.wordpress.com/latex/

85. afeman says:

One good (to me) summary of the abundant life/rare intelligence thesis is Ward & Brownlee’s Rare Earth.

I believe SJ Gould thought the evolution of intelligence was very contingent, noting that sophisticated terrestrial life had been around in various dominant forms for a couple hundred million years before we popped up not too long ago.

86. You can get this

ρθ³

also using only html:

<i>&rho;&theta;&sup3;</i>

87. I think the biggest thing to remember about this is that by the Devonian the Earth was populated with complex multicellular mobile articulating organismal animalia with nervous systems and brains and indeed primitive minds, and so yes, having a super moon near the double planet border and a super giant continental Bay of Fundy would certainly help things along for the proto amphibians it is just another fortuitous event that eventually led us to paradise planet. Of course there are many such events, we would not be here if it was otherwise as there are many dead ends too.

People need to understand that we are indeed biological organisms with the greatest energy requirements delivered by consuming other high protein biological creatures, as such, we are predators. The only thing stopping us from consuming each other are the minds that live in our brains. The carbon crisis is just the reason for life to develop another more efficient energy pathway, and certainly quantum physics and solar energy is that critical energy pathway.

I personally think this can be done. As such I am proposing a ‘Quantum Initiative’.

88. Andrew Dodds says:

afeman –

The issue is, 200 million years is not that long, geologically speaking. Even in terms of evolution it’s not a huge span of time; one of the problems for evolution is that for long stretches of time you don’t actually get any; if the climate and continental configuration don’t change significantly for 5 million years, you won’t see much evolution happening. You might see an increase in specialists, but specialists are not generally important. Much of the Jurassic and Cretaceous might fall into this category.

Try using ‘percent of the age of the earth’ as the measurement unit..

Abiotic->Biotic : Some ocean oxygeneation : ~30% AoE
Some oxygen->Full oxygenation : ~45% AoE
First Metazoans -> Fish : 3% AoE (~150 ma)
Fish -> Full Land animals : 3% AoE (~150ma)
Full Land Animals -> Humans : 4% AoE (~200ma)

Perhaps 80% of the story of our planet is one of single celled life and very slow geochemical change. Once the chemistry was right, life seems to have gone very quickly and in a pretty straight line towards humans. (For a geologist’s definition of ‘straight’, ignoring anything that takes <10ma)

The conclusion I take from this is that what people think are the hurdles – Abiogenesis and Intelligence – are probably not. The hurdle is evolving the hydrosphere to the point where macroscopic life can evolve. At which point we are looking at the whole 'rare earth' problem. Because if Earth was significantly bigger (Hence more volcanic activity, faster processing of the oceans through the lithosphere), the timescale to transform the hydrosphere and allow oxygen might grow, and possibly grow exponentially – you might be waiting longer the the current age of the universe to get an oxygen atmosphere. And if it's a lot smaller you lose the stabilizing/fertilizing effect of plate tectonics.

Note that if the Archean and Proterozoic had combined to be 30% longer than they were, we would never exist, because the increasing heat of the sun would have put us into runaway greenhouse territory, as I understand it.

89. Tom Curtis says:

Anders, I will take the wikipedia article on Tidal Force as my guide to the mathematics. Doing so, we can see that the tidal force, ie, the difference in the force between components the first body due to their different distances from a second body exerting the gravitational force can be represented as

-\$rcirc;GMm/R^2 x (-2r/R+3r^2/R^2-4r^3/R^3…)
where &rcirc; is the unit vector, G is the gravitational constant, M is the mass of the second body, m is the mass of the component of the first body, R is the radial distance between the center of mass of the second body and the center of mass of the first body, and r is the difference in radial distance between the center of mass of the second body and that of the component of the first body and R.

The terms in brackets are just the expansion of the Mclaurin series with x =r/R and the first term deleted as representing the common force (and hence not the tidal force).

With this formula in mind, it is evident that Balbus has approximated this expansion by deleting all but the first term, which allows him to cancel out G, m and 2r, leaving him with M/R^3. Had he retained more than one term, however, he would not have been able to cancel out r, which would block his derivation of the relationship between angular size and tidal force. That simplification seems justified with the Earth Moon system as it only makes a difference of about 0.1% in the ratio of lunar to solar tidal forces.

My point was that it is not evident that it is justified across the full range of plausible lunar densities, and Earth-Moon vs Earth-Sun distances compatible with life. Having seen the actual formula for this, I am not so certain it is the case. I still suspect you could find conditions compatible with life where tidal force differs by an order of magnitude despite the moon having the same angular size as the Sun, and certainly were relative tidal force does not scale with relative angular size; but also suspect those conditions will be relatively rare.