The article is based on a
graduate thesis by Martin Marek Mileiko delivered at the department
of physics of the University of Tartu in 1994 (Mileiko 1994). The
thesis aims to shed light on the application of physics to the areas
commonly considered as very remote from physics. Mileiko's thesis
received wide attention among scientists and was assigned the highest
grade. As the results of the work have attracted further attention
(see, e.g., Voolaid & Mileiko 1996, Voolaid 1998), the
topic has been elaborated on even more. The following is but a fancy,
a mind game which has nothing to do with reality, or folklore, for
that matter. But why not play the game?
Kalevipoeg, in
some regions also known as Sohn (Kreutzwald 1975: 28), the youngest
son of Kalev and Linda, is the best known Old Estonian epic hero.
Various natural monuments like furrows, beds, stones he arguably
threw, etc. still bear witness to Kalevipoeg's adventures (Laugaste,
et al. 1959). As compared to humans, all these monuments are
extremely large. The furrows are tens of metres deep and tens of
kilometres long, the thrown stones weigh hundreds of tons. Judging by
that Kalevipoeg must have been very large indeed. Could someone of
that size be human? The national epic offers no explicit answer to
that question. The only indication to his human origin is his
intimate relations with mortal Saarepiiga [The Isle Maiden]
(Kreutzwald 1975: 54). The present work will make an attempt to find
out whether Kalevipoeg could have been human, on the presumption that
Kalevipoeg did really exist and that the aforementioned natural
monuments are connected to him. We will pose a hypothesis that
Kalevipoeg was an extremely large and strong person and will put the
hypothesis to test.
The method
Firstly,
let us determine Kalevipoeg's height. For that we simply consider the
length of his beds, as a bed is generally as long as the person who
sleeps in it. There are several natural monuments in Estonia, called
the beds of Kalevipoeg, which length is e.g. 85 m at Alatskivi, or 40
m near Lake Saadjärv (Kirt 1988). The length of other similar
monuments is approximately the same. In order to simplify the
estimation we will consider the length of a bed 100 metres and equal
it with the height, L_{K},
of Kalevipoeg.
Could a man of this stature have
performed all the feats commonly attributed to Kalevipoeg?
To solve this problem we have to examine the feats of Kalevipoeg (the
casting of huge rocks and carrying a load of boards from Pskov), as
there are quite a few references to that in legends. On the basis of
the estimated height of Kalevipoeg we should be able to determine
whether a 100 metres tall human could have performed such deeds. If
he could, we have reason to believe that Kalevipoeg was human, if
not, he must have been of non-human origin.
Our
estimation is based on a method called scaling (Marion 1996).
Namely, the qualities of a body, like muscular strength, are related
to the so-called characteristic dimension. The dimension of a body
can be called characteristic, if it functions as a means for
describing the body as a whole. For example, the characteristic
dimension of a cube is the length of its side, the characteristic
dimension of a circle is its radius, etc. The characteristic
dimension of an ordinary human is therefore its height, L_{I},
and the characteristic dimension of Kalevipoeg is his height,
L_{K}.
The larger a person's characteristic dimension, the stronger he is, as
muscular strength depends on the cross section area of a muscle. The
larger the area, the more myofibrils the muscle contains. A taller
man with proportionally developed body has thicker arms with stronger
muscles.
We will come to the value to be determined (the
distance of the stone's cast or the weight of the carried load) by
comparing the abilities of a normal human to these of Kalevipoeg.
Disregarding the physical and mathematical details of the problem, we
will hereby apply the terms derived in the graduation paper (Mileiko
1994), which allow us estimate the distance, x_{K},
of Kalevipoeg's stone's throw:
L^{3}_{K} mx_{K} =___.___.x_{I} (1),
L^{3}_{I} M
where
m is the mass of the body thrown by an ordinary man, M
is the mass of a body cast by Kalevipoeg and x_{I} is the distance of a body thrown by an ordinary man.
The
stone-throwing hypothesis
The estimation of the
distance of a stone cast by Kalevipoeg is based on one of his longest
known stone throws, described in the legend about the stone of
Painuva (Laugaste et al 1959):
Once again Kalevipoeg
visited Finland. The Evil One had come to Viru [Estonia] to
spite him and throw stones in front of the seagoing ships. Kalevipoeg
had seen Old Nick from Cape Porkkala in Finland and thrown a huge
rock at him, which had landed near Mohn, the tip of Cape Turbuneem,
right under the Evil One's nose without actually hitting
him.
Geologists have estimated the volume of Painuva
stone at 340 cubic metres. The density of the rock being 2.800 kg/m^{3}
(granite), we will find that its mass is M ~ 1.000 tons. We will
calculate the throwing potential of a human on the basis of grenade
throwing, which was a popular sports during the Soviet time and
resembles stone throwing. Stronger men used to throw grenade (m = 0.7
kg) to the distance of ca 80 metres. To simplify the calculation, we
will determine the distance of grenade throwing at x_{I}
= 100 m and the characteristic dimension of a human L_{I}
= 2 m. The characteristic dimension of Kalevipoeg L_{K}
= 100 m.
The estimated distance of stone's throw from
the formula (1) indicates that had Kalevipoeg been human he would
have cast the rock to the approximate distance of 10 m. Which is
considerably less than the geographical distance between Cape
Porkkala and Cape Turbuneem, which is approximately 80 km.
How
tall should have been a human Kalevipoeg to be able to throw a rock
so far? We will find this height also with the help of the formula
(1), assuming that x_{K}
= 80 km. The result is approximately 2 km. Consequently, the stone's
cast reveals that a man who slept in Kalevipoeg's bed could not have
been able to throw the rock as far as Kalevipoeg.
The
boards-bringing hypothesis
Secondly, we can test our
hypothesis on the basis of a legend describing how Kalevipoeg brought
boards from Pskov (Laugaste et al 1959):
Once
Kalevipoeg forded through Lake Peipus, carrying seven hundred boards
on his back, and cursed that the damned water wetted his
dick.
Again we will estimate the value of
Kalevipoeg's capacity on the basis of the formula derived in the
thesis (Mileiko 1994):
L^{2}_{K}x_{K} =___.m (2),
L^{2}_{I}
where
M is the mass of Kalevipoeg's load and m is the mass load of an
ordinary human.
We will equal the mass load of an
ordinary man with a mass of a larger backpack, as according to the
legend the load was not too heavy: The load of boards was not too
large/ Nor was it too small, /Just the size of a man's waist
(Kreutzwald 1975: 135). Thus, let us assume m = 30 kg, which is a
proper weight for a hiker's backpack. Calculations using the formula
(2) indicate that Kalevipoeg could carry approximate 75 tons of
boards across Lake Peipus.
However, according to the
legend (Laugaste et al 1959), his load consisted of 700 boards with
particular dimensions:
The boards were not thick
Somewhere over three inches,
Nor were they wide
Somewhere over two feet
Nor were they long
Somewhere over three fathoms (Kreutzwald 1975: 135).
Thus, a board was approx. 0.08 m thick, ca 0.6 m
wide and ca 21 m long. Considering the density of wood to be equal to
700 kg/m^{3}, the
load must have weighed ca 500 tons. But a load like that must have
been beyond the powers of a 100 m tall human Kalevipoeg. According to
the formula (2), Kalevipoeg should have been at least 300 metres tall
to be able to carry such a load. However, legends tell that
Kalevipoeg could carry even heavier loads: some ancient accounts
reveal that Kalevipoeg has carried a load of nearly 1700 boards.
Regretfully, the accounts mention nothing of the size of the boards
in the load, which makes it impossible for us to estimate the weight
of the load.
Why Kalevipoeg could not have been
human
The examples might suggest that the human
Kalevipoeg must have been much taller than 100 m. But a human body
can never reach the height of 100 metres, not to mention even taller
heights. There are at least two reasons for it:
Firstly,
the bones of a man of this height would crush under the weight of his
body, as the mass of body is proportional to the cube of the
characteristic length, L_{I},
while the strength of human bones is proportional to L_{I}^{0.66}
(Kane & Sternheim 1978). Calculation shows that the mass of a 100
m tall giant exerts nearly 200 times higher pressure on his bones
than in case of a man of 2 metres. Therefore, the bones of such a
tall man would collapse under his body weight and
splinter.
Secondly, a man of his stature would have
suffered under excessive heating, as his skin surface area would be
too small to remove the heat emitted from such a huge body. The
amount of heat produced by the body is proportional to the cube of
the characteristic length, while the amount of heat emitted through
the skin is proportional to the square of the characteristic length
(Marion 1996). Consequently, the body of a 100 metre tall giant emits
50 times less heat than an ordinary person, which leads to
overheating.
To sum up, we might claim that Kalevipoeg,
who might have slept in the natural beds, that can still be seen in
different parts of Estonia, could not have been of human origin. His
muscles and bones must have been made of altogether different
material than the muscles and bones of ordinary
humans.
Translated by Kait Realo
For exact view, here is a pdf version of this article,
human.pdf, size 156 kb.
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