Astronomy

Estimating Sun luminosity from first principles

Estimating Sun luminosity from first principles


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In a lecture, it was claimed that luminosity can be estimated by dividing how much energy there is in the Sun with the typical time it takes for a photon to get out from the centre of the Sun to its surface. I don't see how that argument holds. Why would that give me luminosity?


The thermal energy of the Sun is something like $$E sim left(frac{3k_BT}{2} ight)(N_i + N_e) , $$ where $N_i$ is the number of ions and $N_e$ is the number of electrons and the interior temperature $T sim 10^7$ K.

To first order we can consider the Sun to be made of hydrogen, so $N_e = N_i sim M/m_p$, where $m_p$ is the mass of a proton.

Putting in the numbers gives $E sim 5 imes 10^{41}$ J.

The typical mean free path of a photon in the solar interior is $lsim 10^{-3}$ m. The solar radius is $Rsim 7 imes 10^{8}$ m. Since the photons get out by a "random-walk" diffusion process, then it takes about $(R/l)^2$ steps, each of which takes a time $l/c$. Thus the diffusion timescale $$ au sim left(frac{R}{l} ight)^2 left(frac{l}{c} ight) = frac{R^2}{lc} = 1.6 imes 10^{12} { m s}$$.

The ratio of these two numbers gives $3 imes 10^{29} { m W}$, so about 3 orders of magnitude larger than the solar luminosity.

This ratio does not give the solar luminosity.


Understanding the Luminosity of Radiative Stars

If you would touch the mirror, you could convince yourself that its temperature is defined.

GMm/R. That is a first principle. It doesn't apply to your case (1) because it neglects radiation pressure, and it doesn't apply to case (3) because it associates kT with the average kinetic energy per particle, but degeneracy reduces T way below that.

M 3 scaling we find in the mass-luminosity relationship

It is the mass-luminosity relationship (essentially the same derivation as the one on Wikipedia page). And it is not really surprising that the luminosity is basically only determined by the mass (after all, the mass of the primordial cloud is the only parameter that can possibly make any difference for the star formation (assuming identical chemical composition)).

It is not further surprising that fusion didn't come into it, as the assumption of 'blackbody' radiation doesn't have to care about the details of the processes by means of which radiation is created and destroyed. It is a 'black box' model based on the assumption of an equilibrium between emission and absorption processes (whatever they may be).

In any case, you can calculate the luminosity from the surface temperature (as determined from the spectrum), and I bet you will get a far more accurate value for it than from your mass-luminosity relationship (where, as you seem to realize yourself, you have to make certain assumptions about the stellar structure and other parameters determining the diffusion process if you want to arrive at an absolute numerical value for the luminosity).

That would contradict your derivation above: the time t increases with increasing radius and thus with increasing mass. So a more massive star should take longer to emit a certain percentage of the radiative energy it contains.

It is extremely surprising that it depends only on the mass, in the sense that it is surprising it does not depend on either R or the fusion physics.

The lack of dependence on R means that if you have a radiating star that is gradually contracting (prior to reaching the main sequence), its luminosity should not change! That would be true even if the star contracted by a factor of 10, if the opacity did not change, and the internal physics did not shift from convection to radiation. But contracting stars do tend to start out highly convective, so do make that transition, and that's why we generally have not noticed this remarkable absence of a dependence on R.

The lack of dependence on fusion physics means that when a star initiates fusion, nothing really happens to the star except it stops contracting. That's not necessarily what must happen, for example when later in the star's life it begins to fuse hydrogen, it will undergo a radical change in structure, and change luminosity drastically. But the onset of hydrogen fusion does not come with any such drastic restructuring of the star, because it started out with a fairly simple, mostly radiative structure, and when fusion begins, it just maintains that same structure because all the fusion does is replace the heat that is leaking out.

Thank you for bringing that up, it's an important part of the mistake that many people make. You will see a lot of places that say words to the effect that "because fusion depends so sensitively on temperature, the fusion rate controls the luminosity". That's exactly backward. Because the fusion rate depends so sensitively on temperature, tiny changes in T affect the fusion rate a lot, so the fusion rate has no power to affect the star at all. After all, the thermodynamic properties of the star are not nearly as sensitive to T, so we just need a basic idea of what T is to get a basic idea of what the star is doing. But since fusion needs a very precise idea of what T is, we can always get the fusion to fall in line with minor T modifications. That's why fusion acts like a thermostat on the T, but it has little power to alter the stellar characteristics other than establishing at what central T the star will stop contracting.

If you don't see that, look at it this way. Imagine you are trying to iterate a model of the Sun to get its luminosity right. You give it an M and a R, and you start playing with T. You can get the T basically right just from the gravitational physics (the force balance), and you see that it is in the ballpark of where fusion can happen. You also get L in the right ballpark, before you say anything about fusion (as I showed). But now you want to bring in fusion, so you tinker with T. Let's say originally your T was too high, so the fusion rate was too fast and was way more than L. So you lower T just a little, and poof, the fusion rate responds mightily (this is especially true of CNO cycle fusion, moreso than p-p chain, so it works even better for stars a bit more massive than the Sun). So you don't need to change T much at all, so you don't need to update the rest of your calculation much, so you end up not changing L to reach a self-consistent solution! So we see, it is precisely the T-sensitivity of fusion that has made it not affect L much, though many places you will see that logic exactly reversed.

Yes, it is the contribution of degeneracy pressure.
Now imagine a shrinking ball of gas, and make the assumption that its radial distribution of temperature and density remains unchanged, that it obeys ideal gas laws, and also that its heat capacity is constant (this last is least likely).
If the radius shrinks twice
then the density increases 8 times
the surface gravity increases 4 times
the pressure of a column of fixed depth thus increases 32 times
since the column of gas from surface to centre gets 2 times shorter, the central pressure grows 16 times
but since the central density grew just 8 times, the central temperature must have doubled.

Now, think what degeneracy pressure does.
If you heat water at 1 atmospheres from 273 K to 277 K, it does NOT expand 1,5 % like an ideal gas would - it actually shrinks.
When you heat water from 277 K to 373 K, it does expand - but not 35 % like ideal gas, only 1,5 %
Then, when you heat water from 373,14 to 373,16 K, it expands over 1000 times!

If you heat water at higher pressures, you will find:
that it is slightly denser, because very slightly compressed, at any equal temperature below boiling point
that the boiling point rises with pressure
that water expands on heating near the boiling point at all pressures over about 0,01 atm
that the density of water at boiling point decreases with higher temperature and pressure
that steam, like ideal gas, expands on heating at each single pressure
that steam, like ideal gas, is compressed by pressure at each single temperature
that the density of steam at boiling point increases with pressure and temperature
that the contrast between boiling water and boiling steam densities decreases with temperature and pressure.

At about 220 atmosphere pressure, the contrast disappears.
Now, if you heat water at slightly over 220 bar then the thermal expansion still starts very slight at low temperatures but increases and is, though continuous, very rapid around the critical point (a bit over 374 Celsius).

But when you increase pressure further, you would find that the increase of water thermal expansion from the low temperature liquid-like minimal expansion to the ideal gas expansion proportional to temperature would take place at increasing temperatures and also become monotonous, no longer having a maximum near the critical point.

And interiors of planets and stars typically have much higher pressures than critical pressure. The transition between liquidlike behaviour of little thermal expansion and mainly degeneracy pressure at low temperature, and ideal-gas-like behaviour of volume or pressure proportional to temperature and mainly thermal particle pressure, would be continuous and monotonous.

They do.
Now, excluding general relativistic effects but also heat production, and assuming only one radial distribution of temperature and density for each radius:

when a shrinking ball of gas is large and tenuous, its pressure is dominated by thermal pressure and therefore its internal temperature is proportional to the inverse of its radius, as demonstrated before
whereas when the ball is dense and cool, its pressure is dominated by degeneracy pressure and therefore it has minimal thermal expansion - its radius is near a finite minimum and increases very slightly with temperature.
This is a continuous transition. The temperature of a shrinking ball of gas goes through a smooth maximum - first the temperature increases with inverse of radius, then the temperature increase slows below that rate, the temperature reaches a certain maximum, then the temperature falls while still being high and accompanied by significant further shrinking, finally the temperature falls to low levels with very little further shrinking near the minimum size.

If there is no heat production then this is what happens to the shrinking ball of gas. The speed of evolution varies with heat loss rate, which gets slow at the low temperatures, so the ball would spend most of its evolution with temperature slowly falling towards zero and radius slowly shrinking towards nonzero minimum value. But the maximum of internal temperature would happen just the same.

Now what happens if there IS heat production through fusion?
Thermonuclear fusion is strongly dependent on temperature - but the dependence is still continuous. So the heat production rate goes through a continuous maximum roughly where temperature goes through its continuous maximum.
The rate of heat loss via radiation and convection is also dependent on temperature. But it also depends on the temperature gradient and area for the same temperature but different radius, opacity, thermal expansivity, viscosity. all of which change with density around the continuous maximum of temperature.

Therefore, the ratio of heat production rate through fusion to heat loss rate goes through a continuous maximum which is generally somewhere else than the continuous maximum of temperature (in which direction?), but since the heat production rate through fusion is strongly dependent on temperature, the maximum of heat production/heat loss rate is somewhere quite near the maximum of temperature.

Now, if a shrinking ball of gas near the maximum of temperature, at which point it is significantly degenerate and nonideal gas (otherwise it would be nowhere near maximum!) reaches a maximum of heat production/heat loss rate which is close to one but does not reach it then it never reaches thermal equilibrium - the brown dwarf goes on to cool, whereupon the heat generation decreases. Note that there WAS significant amount of fusion - since the heat generation rate through fusion did approach the heat loss rate near the maximum temperature, it significantly slowed down shrinking in that period. So fusion was significant but not sustained.

If, however, the maximum of heat production/heat loss ratio is slightly over one then it is never reached. The star will stop shrinking when the heat production/heat loss ratio equals one, so it will not reach the target maximum temperature, nor the maximum (over one) ratio of heat production to heat loss.

But as shown above, it has a very significant contribution of degeneracy pressure (otherwise it would have been nowhere near the maximum temperature, and the maximum heat production/heat loss ratio would have been far over one, not slightly over one).

And such a stable star IS, by definition, a main sequence star. Most main sequence stars are red dwarfs. and have a significant contribution of degeneracy pressure/nonideal behaviour.

@snorkack, your analysis essentially begins from the perspective of a star that does not have enough mass to ever reach the main sequence, and then you gradually increase the mass and ask what happens when you get to stars that barely reach the main sequence. These types of stars tend to have two physical effects that are not in my derivation: degeneracy and convection. So your point is well taken that this is a kind of "forgotten population", because no one ever sees any of these stars when they look up in the night sky, yet they are extremely numerous and no doubt play some important role in the grand scheme that those who research them must keep reminding others of. That must be a frustrating position, so when you see people refer to "main sequence stars" in a way that omits this population, you want to comment. I get that, point taken-- but I am still not talking about that type of star, whether we want to call them "main sequence stars" or not. (Personally, I would tend to define a main-sequence star as one that has a protium fusion rate that is comparable to the stellar luminosity, so if it has more deuterium fusion, or if it is mostly just radiating its gravitational energy, then it is not a main-sequence star. The question is then, just how important is degeneracy when you get to the "bottom of the main sequence," and I don't know if it gets really important even in stars that conform to this definition, or if it only gets really important for stars that do not conform, but either way, it is clearly a transitional population, no matter how numerous, between the standard "main sequence" and the brown dwarfs.)

Anyway, you make interesting points about the different physics in stars that are kind of like main-sequence stars, but have important degeneracy effects, in that transitional population that does include a lot of stars by number. The standard simplifications are to either treat the fusion physics in an ideal gas (the standard main-sequence star), or the degeneracy physics in the absence of fusion (a white dwarf), but this leaves out the transitional population that you are discussing. Your remarks are an effort to fill in that missing territory, but are a bit of a sidelight to this thread.

Still, I take your point that if we hold to some formal meaning of a "main-sequence star", and we look at the number of these things, a lot of them are going to be red dwarfs, and the lower mass versions of those are in a transitional domain where degeneracy is becoming more important, and thermal non-equilibrium also raises its head. My purpose here is simply to understand the stars with higher masses than that, say primarily in the realm from 0.5 to 50 solar masses, which are typically ideal gases with a lot of energy transport by radiative diffusion. The interesting conclusions I reach are that not only is the surface temperature of no particular interest in deriving these mass-luminosity relationships, neither is the presence or absence of fusion, in stark refutation of all the places that say you need to understand the fusion rate if you want to derive the luminosity.


Estimating Sun luminosity from first principles - Astronomy

My field of research is theoretical high-energy astrophysics.

I investigate the origin of non-thermal emission from Pulsar Wind Nebulae (PWNe), AGN jets, fast radio bursts (FRBs), gamma-ray bursts (GRBs), supernovae, galaxy clusters, and low-luminosity accretion flows like Sgr A* around the supermassive black hole at the center of our Galaxy.

It i s still a mystery how these objects can accelerate particles up to the highly non-thermal energies required to explain the observed emission, that typically extends from the radio up to the gamma-ray band.

By means of ab initio large-scale plasma simulations, I investigate particle acceleration in shocks, turbulence and magnetic reconnection from first principles, with the aim of using the simulations to interpret the observations, and ultimately unveil the nature of astrophysical non-thermal sources.


Thread: Deriving and checking mass-luminosity relation

Yes, we are indeed off the main sequence at that point.

Now, continue with derivation.
A star with 2 times the radius has 4 times the area of any corresponding surface to leak energy.
At equal temperature, suppose that the conductivity is inversely proportional to density. Which is 1/4 that of Sun.
The radius is 2 times bigger. Therefore, the star should be 2 times worse insulator than Sun (1/4 times the density, but 2 times the thickness of insulating layer).
With 4 times the area and 2 times poorer insulation, the star should be emitting 8 times the luminosity of Sun.
Correct?

Next, how much energy should the star produce?
At equal temperature, a nucleus should have equal probability of fusing when it collides.
But at 1/4 the density, a nucleus will collide 4 times less often.
There are 2 times as many nuclei. So the star should produce 1/2 the energy Sun does, while losing 8 times as much.
It should be losing energy and contracting, as a protostar on a Henyey track.

Now have a look at the other end.
Suppose a star has 2 times the mass of Sun, and exact same radius, and mass distribution - 2 times the density at each depth.
Then the star has 2 times the gravitational acceleration at each depth, 4 times the weight of each gas column, and 4 times the pressure at each depth.
Correct?
Sticking to the assumptions that contribution of radiation pressure to total pressure is negligible and that additional ionization of inner electrons of heavy ions also is negligible, it can be said that ideal gas should have about 2 times the temperature in order to have 4 times the pressure at 2 times the density.

What should the luminosity be?
The radiating area is the same.
Radiating area is the same.
Radiation density at any depth is 16 times bigger.
The amount of matter in the way of radiation is 2 times bigger.
Therefore the luminosity should be 8 times bigger.

Note the matching conclusions!
Whether it is the same temperature and different radius or the same radius and different temperature, the total escaping luminosity ought to be 8 times that of Sun.
Actually, it can be derived that the luminosity also ought to be 8 times that of Sun for any radius and temperature in between. Omitting the derivation now.
Correct?


Here I am collecting a list the problems with Electric Universe (EU) claims that EU supporters persistently ignore. Currently, it will expand as I use it to index much of my existing material. I hope to maintain this as a 'master list' of EU problems and it should be regarded as the first place to check for a EU topics on this site.

What does EU provide that is not already provided by mainstream astronomy and geophysics?
General Physics
Every book on how to write applications & interpret the signals from GPS satellites emphasizes the importance of relativity in converting these signals into a high-precision receiver position (see Scott Rebuttal. I. GPS & Relativity). Yet EU supporters deny the importance of relativity in this application.

Has any EU supporter designed and built a working high-precision (< 1 meter accuracy) GPS receiver that can be certified as free of relativistic corrections?
General Plasma Physics
If EU claims that we should only rely on laboratory observations of plasmas and that our mathematical models are worthless, then where does that leave magnetohydrodynamics (MHD) (wikipedia)?

Is MHD valid in its domain of applicability? If MHD is invalid and it is not possible to use it for building mathematical models of plasmas, aren't EU supporters saying that Alfven didn't deserve a Nobel prize for MHD?
Astronomers have studied the effects of free charges and electric fields in space as far back as 1922 (1922BAN. 1..107P) and 1924 (1924MNRAS..84..720R). Note that this work predates Langmuir coining the term 'plasma' for an ionized gas (1928, 1928PNAS. 14..627L). Rosseland and Pannekoek's work is still cited today since gravitational stratification is one of the easiest ways to generate and sustain an electric field in space. George Ellery Hale was looking for electric fields on the Sun back in 1915 (1915PNAS. 1..123H). Electric fields are long acknowledged as important in the solar atmosphere (see Electric fields in the solar atmosphere - A review, The REAL Electric Universe, Charge Separation in Space, 365 Days of Astronomy: The Electric Universe). Some EU supporters go so far as to claim that cosmic electric fields were only considered after Immanuel Velikovsky invoked them, contrary to the historical record (The Real Electric Universe: Inspired by Velikovsky?).

Why do EU supporters continue to claim that astronomers ignore electric fields and free charges in space in spite of all the evidence to the contrary?
Hannes Alfven received his Nobel prize (Nobelprize.org) for the accomplishment of making certain types of plasmas mathematically tractable. Langmuir (1913PhRv. 2..450L, 1924PhRv. 24. 49L) and others developed other mathematical models of discharge plasmas, predating Alfven. REAL plasma physicists continue to revise the mathematical models and these models have improved significantly. Even the classic discharge graphic in Cobine's “Gaseous Conductors” (pg 213, figure 8.4) has been modeled with Particle-In-Cell (PIC) plasma modeling software (see Studies of Electrical Plasma Discharges, figure 10.1). Plasma models, some sold as commercial software, are also used to understand the plasma environment in a number of research, space, and industrial environments (see VORPAL). See also: Electric Universe: Real Plasma Physicists BUILD Mathematical Models, Electric Universe: Plasma Physics for Fun AND Profit!, Electric Universe: Plasma Modeling vs. 'Mystic Plasma'

  • If mainstream models of the solar interior are so wrong, why does this technique work at all?
  • All of the solar data for this capability are PUBLIC (see MDI Data Services & Information) and the software runs on desktop-class computers you can buy at almost any computer store. So when will EU demonstrate that their Electric Sun model can generate equivalent or better results?
  • predicts magnetic fields for the surface of the Sun and at the orbit of the Earth, 1000 to 1,000,000 times larger than measured.
  • ignores that free current streams of ions and electrons are subject to numerous instabilities which make them break up in short timescales.

Solar Capacitor model (Don Scott, The Electric Sky)
An alternative solar model, radically different from the Thornhill model above, is a spherical capacitor model with the heliopause as the cathode (source of electrons) and the solar photosphere as the source of ions & protons (anode). I call this the solar capacitor model. This spherical current configuration has been studied heavily in theory and experiment since the 1920s.
Electric Cosmos: The Solar Capacitor Model. I. II. III.

  • predicts a solar proton wind speed 200 times faster than observed.
  • predicts energetic particle fluxes far in excess of what we observe. (proton fluxes a billion times larger). These fluxes are also far higher than the most deadly regions of the Earth radiation belts, meaning that interplanetary travel would be sure death for astronauts.
  • in situ measurements do not show a high-energy stream of electrons heading towards the Sun.
  • Without an external EMF maintaining the potential between the photosphere and heliopause, the Electric Sun will shut down due to charge neutralization in a very tiny fraction of a second.
    . Don Scott concocts a revised electron density measurement to lower his Electric Sun voltage requirements. It doesn't help much.
  • Electric Universe Fantasies & Heliopause Electrons. II. Just where did Don Scott get his electron density revision, because it certainly did not come from the measurements made by Voyager 1. If the electron density in interplanetary space is too high, radio waves can't propagate

Contents

Illuminance Edit

Illuminance is a measure of how much luminous flux is spread over a given area. One can think of luminous flux (measured in lumens) as a measure of the total "amount" of visible light present, and the illuminance as a measure of the intensity of illumination on a surface. A given amount of light will illuminate a surface more dimly if it is spread over a larger area, so illuminance is inversely proportional to area when the luminous flux is held constant.

One lux is equal to one lumen per square metre:

A flux of 1000 lumens, spread uniformly over an area of 1 square metre, lights up that square metre with an illuminance of 1000 lux. However, the same 1000 lumens spread out over 10 square metres produces a dimmer illuminance of only 100 lux.

Achieving an illuminance of 500 lux might be possible in a home kitchen with a single fluorescent light fixture with an output of 12 000 lumens . To light a factory floor with dozens of times the area of the kitchen would require dozens of such fixtures. Thus, lighting a larger area to the same level of lux requires a greater number of lumens.

As with other SI units, SI prefixes can be used, for example a kilolux (klx) is 1000 lux.

Here are some examples of the illuminance provided under various conditions:

Illuminance (lux) Surfaces illuminated by
0.0001 Moonless, overcast night sky (starlight) [4]
0.002 Moonless clear night sky with airglow [4]
0.05–0.3 Full moon on a clear night [5]
3.4 Dark limit of civil twilight under a clear sky [6]
20–50 Public areas with dark surroundings [7]
50 Family living room lights (Australia, 1998) [8]
80 Office building hallway/toilet lighting [9] [10]
100 Very dark overcast day [4]
150 Train station platforms [11]
320–500 Office lighting [8] [12] [13] [14]
400 Sunrise or sunset on a clear day.
1000 Overcast day [4] typical TV studio lighting
10,000–25,000 Full daylight (not direct sun) [4]
32,000–100,000 Direct sunlight

The illuminance provided by a light source on a surface perpendicular to the direction to the source is a measure of the strength of that source as perceived from that location. For instance, a star of apparent magnitude 0 provides 2.08 microlux (μlx) at the Earth's surface. [15] A barely perceptible magnitude 6 star provides 8 nanolux (nlx). [16] The unobscured Sun provides an illumination of up to 100 kilolux (klx) on the Earth's surface, the exact value depending on time of year and atmospheric conditions. This direct normal illuminance is related to the solar illuminance constant Esc, equal to 128 000 lux (see Sunlight and Solar constant).

The illuminance on a surface depends on how the surface is tilted with respect to the source. For example, a pocket flashlight aimed at a wall will produce a given level of illumination if aimed perpendicular to the wall, but if the flashlight is aimed at increasing angles to the perpendicular (maintaining the same distance), the illuminated spot becomes larger and so is less highly illuminated. When a surface is tilted at an angle to a source, the illumination provided on the surface is reduced because the tilted surface subtends a smaller solid angle from the source, and therefore it receives less light. For a point source, the illumination on the tilted surface is reduced by a factor equal to the cosine of the angle between a ray coming from the source and the normal to the surface. [17] In practical lighting problems, given information on the way light is emitted from each source and the distance and geometry of the lighted area, a numerical calculation can be made of the illumination on a surface by adding the contributions of every point on every light source.

Relationship between illuminance and irradiance Edit

Like all photometric units, the lux has a corresponding "radiometric" unit. The difference between any photometric unit and its corresponding radiometric unit is that radiometric units are based on physical power, with all wavelengths being weighted equally, while photometric units take into account the fact that the human eye's image-forming visual system is more sensitive to some wavelengths than others, and accordingly every wavelength is given a different weight. The weighting factor is known as the luminosity function.

The lux is one lumen per square metre (lm/m 2 ), and the corresponding radiometric unit, which measures irradiance, is the watt per square metre (W/m 2 ). There is no single conversion factor between lux and W/m 2 there is a different conversion factor for every wavelength, and it is not possible to make a conversion unless one knows the spectral composition of the light.

The peak of the luminosity function is at 555 nm (green) the eye's image-forming visual system is more sensitive to light of this wavelength than any other. For monochromatic light of this wavelength, the amount of illuminance for a given amount of irradiance is maximum: 683.002 lux per 1 W/m 2 the irradiance needed to make 1 lux at this wavelength is about 1.464 mW/m 2 . Other wavelengths of visible light produce fewer lux per watt-per-meter-squared. The luminosity function falls to zero for wavelengths outside the visible spectrum.

For a light source with mixed wavelengths, the number of lumens per watt can be calculated by means of the luminosity function. In order to appear reasonably "white", a light source cannot consist solely of the green light to which the eye's image-forming visual photoreceptors are most sensitive, but must include a generous mixture of red and blue wavelengths, to which they are much less sensitive.

This means that white (or whitish) light sources produce far fewer lumens per watt than the theoretical maximum of 683.002 lm/W. The ratio between the actual number of lumens per watt and the theoretical maximum is expressed as a percentage known as the luminous efficiency. For example, a typical incandescent light bulb has a luminous efficiency of only about 2%.

In reality, individual eyes vary slightly in their luminosity functions. However, photometric units are precisely defined and precisely measurable. They are based on an agreed-upon standard luminosity function based on measurements of the spectral characteristics of image-forming visual photoreception in many individual human eyes.

Specifications for video cameras such as camcorders and surveillance cameras often include a minimal illuminance level in lux at which the camera will record a satisfactory image. [ citation needed ] A camera with good low-light capability will have a lower lux rating. Still cameras do not use such a specification, since longer exposure times can generally be used to make pictures at very low illuminance levels, as opposed to the case in video cameras, where a maximal exposure time is generally set by the frame rate.

The corresponding unit in English and American traditional units is the foot-candle. One foot candle is about 10.764 lux. Since one foot-candle is the illuminance cast on a surface by a one-candela source one foot away, a lux could be thought of as a "metre-candle", although this term is discouraged because it does not conform to SI standards for unit names.

One phot (ph) equals 10 kilolux (10 klx).

One nox (nx) equals 1 millilux (1 mlx).

In astronomy, apparent magnitude is a measure of the illuminance of a star on the Earth's atmosphere. A star with apparent magnitude 0 is 2.54 microlux outside the earth's atmosphere, and 82% of that (2.08 microlux) under clear skies. [15] A magnitude 6 star (just barely visible under good conditions) would be 8.3 nanolux. A standard candle (one candela) a kilometre away would provide an illuminance of 1 microlux—about the same as a magnitude 1 star.

Unicode has a symbol for "lx": (㏓). It is a legacy code to accommodate old code pages in some Asian languages. Use of this code is not recommended.


Variational Principles for Irreversible Hyperbolic Transport

2 Restricted variational principles and EIT

Restricted variational principles for irreversible processes are useful for calculation and they provide physical insight into various phenomena. One of the first of them was proposed by Onsager that is known as the principle of the least dissipation of energy. For a review and generalizations see Ref. [28] .

In this section the variational approach to hyperbolic phenomena on the basis of restricted principles is described. The first to propose a variational formulation of this kind for heat transfer in processes near equilibrium were Onsager and Machlup [9] . This allowed them to describe the behavior of fluctuations near equilibrium giving the first statistically supported formalism on this topic. Much later, Gyarmati [29] introduced the concept of dissipative potential to deal with hyperbolic transport equations.

The variational formulation in the restricted form of extended irreversible thermodynamics (EIT) began with our own 1990 paper [16] . We describe in this section that work and show how it is possible to consider nonanalytic expressions for generalized equations of state. We also show one of the main results of restricted variational principles, namely, the derivation of generalized time-evolution equations for the dissipative fluxes [21–24] . These equations are then not only thermodynamically supported but they are also consistent with the variational approach.

We begin with the axiomatic form of EITs within the framework of a restricted variational principle. The existence of a nonequilibrium entropy potential Sne [30] satisfying a balance equation is assumed. This function must be continuous and differentiable and depends on the thermodynamic variables space that is enlarged with nonconserved variables. So, the system is described with the usual balance equations for the conserved densities and the time-evolution equations for the nonconserved variables. Consider now the functional L given by

where d/dt is the material derivative and JS and σS are the generalized flux and the source terms associated with Sne, respectively. The axiomatic form of the variational version of EIT may be stated in terms of the existence of the thermodynamic potential Sne and a variational principle of the restricted type

The variation δ is taken only over the nonconserved part of the thermodynamic variables space, while the conserved part and the tangent thermodynamic space remain constant. The balance equations of the conserved properties of the system act as subsidiary conditions of Eq. (2) and the other quantities in this same equation are generated as the most general scalars, vectors, tensors within the extended thermodynamic space. Eq. (2) gives, as an extreme condition, the time-evolution equations for the fast variables closing the set of equations describing the system. We now illustrate this framework with the case of the isothermal transport of a fluid through a porous medium [17] . The thermodynamic state of the water–soil system may be specified with two variables. On the one hand, the water matric potential Ψ, on the other, the volumetric water flux density Jw. The enlarged thermodynamic space is constructed with these properties of the system <Ψ, Jw>. The nonequilibrium entropy Sne depends on this space

This functional dependence leads to a generalized Gibbs equation that is written as follows:

where the differential operator with respect to time defined as d/dt = (/∂t) + θ ‒1 Jw·∇, is the usual material derivative with θ(Ψ) the water content and

As mentioned above, the extremum condition (2) gives the time-evolution equation for the fast variable that in this case is the volumetric water flux density Jw. We show in some detail how the restricted variation works in Eq. (2) . First, we express any scalar e and vector V as e = e(Ψ, I) and V = e(Ψ, I)Jw, respectively, where I = Jw·Jw is the only invariant of the system. As is usual in EITs [36] , the αi0(i = 2, 3) are the scalars introduced in the construction of α2 and Jw through the representation theorems

We now introduce expressions (4) and (6) in Eq. (2) . It is a direct task to calculate the restricted variation in Eq. (2) to obtain the time-evolution equation for the fast variable of the system, namely, the volumetric water flux density Jw. One just considers all the derivatives and the slow variable Ψ as constants under the derivation process. The equation reads as follows

Note that in Eq. (7) the coefficient of the material derivative of Jw is not independent of the anisotropy introduced by the flux in the system and it is a tensor of second rank. In order to exhibit the thermodynamic origin of nonlinear effects up to second order in Jw as well as to fulfill the required compatibility with linear irreversible thermodynamics (LIT) [17] we assume that

where τw is the relaxation time of the water flux and the functions f(Ψ) and g(Ψ) are parameters that we interpret later. With this selection we can recover Darcy’s Law assuring the compatibility with LIT. By substituting Eq. (8) into Eq. (7) we get

Eq. (9) is a generalization of the corresponding constitutive relation in LIT, namely, Darcy’s law, which reads

In the case of unsaturated porous media, this equation combined with an energy-balance equation gives a parabolic equation called the Richards equation [31] , all this in the framework of LIT. Darcy’s law and the Richards equation, like other constitutive equations in LIT, have certain limitations that have motivated heuristic corrections such as, for instance, the so-called Brinkman’s and Forchheimer’s corrections to incorporate viscous and nonlinear effects. Eq. (9) implies a finite velocity of transmission of water-potential perturbations in the porous medium and the third and fourth terms on the r.h.s. resemble somewhat the Forchheimer’s correction. The choice made for the scalars in Eq. (8) is not unique. The selection made allows us to exhibit the Forchheimer’s correction. It also involves other nonlinear terms that should be taken into account in the description of the nonlinear behavior of the transport of the fluid. In particular, a simplified version of Eq. (9) has provided an alternative description for the water flux in unsaturated porous media [32] generalizing the Richards equation. Recently, the Richards equation has been found to be inappropriate to describe the gravity-driven fingers in unsaturated porous media [33] . On the other hand, using ideas based on the generalized Richards equation it has been possible to describe the nonmonotonicity of the density in gravity fingers in unsaturated porous media [34] .

The restricted variational principle summarized in this section gave us the opportunity to look for a Hamiltonian formalism able to lead to a hyperbolic transport equation. In the next section we review an effort in this direction.


Properties and impact of defects in semiconductors.

‘First-principles' calculations for a wide range of defects an impurities, mostly in crystalline Si. Ongoing work deals with the possibility of using defects to control heat flow in semiconductors. Ab-initio molecular-dynamics simulations have shown that defects do not ‘scatter' thermal phonons but interact with heat flow via their own, localized, vibrational modes. The behavior of a heat front encountering a defect depends on the temperature and can be predicted. Ongoing calculations deal with designing a simple (theoretical) ‘thermal circuit' that would remove some of the heat generated by a CPU or laser pulse.


Science and Astronomy Questions

Question about the little ice age- is it possible there was some sort of connection between volcanic eruptions and changes in the solar cycle? This also happened around the time the dinosaurs died out (and of course the big asteroid impact.)

Also, since we are in the process of switching magnetic poles, how will this impact the aurora?

Science and Astronomy Questions

Science and Astronomy Questions

Isn't auroral activity caused by magnetic processes that occur far higher then the stratosphere, in the magnetosphere with the excited protons and electrons precipitating into the thermo/exosphere? Wouldn't this place it beyond atmospheric temperature influences? While I'd agree that there is a connection between solar-activity and global temperatures (there is a lot of evidence for this), it would be considered a parallel affect to our particular greenhouse effect, which is of course caused by multiple sources of industrialization and agriculture. As midtskogen stated, attributing all the causes for something as complex as GLOBAL weather is very messy business. I'm honestly surprised meteorology can be presented on the morning news - even if that is just local weather.

Erm, no. Solar activity like sun-spots or even solar-flares could not influence volcanism on Earth. While there are SOME tentative conclusions as to their connection, it generally doubted, or could have some coincidental cause, or might be a bit more complicated then just solar minimum=volcanic activity. An interesting question of course, since both phenomena, including earth-quakes, can influence the ionosphere in many ways.

Science and Astronomy Questions

That's right, but as I explained, the greenhouse effect also cools the upper atmosphere, including at the altitudes where the aurora occur. It even affects the decay of orbital debris, by reducing the atmospheric drag on them. This isn't very obvious or well known -- there is more to the greenhouse effect than just "trapping heat" and warming the surface as it is commonly described.

The key insight to why it works this way is that a good absorber of radiation is also a good emitter. The greenhouse effect warms the surface by absorbing the heat it radiates, and re-emitting some of it back downward. So for the lower altitudes the greenhouse effect is just like adding an insulating blanket. But at higher altitudes, increasing the concentration of greenhouse gases allows those layers to radiate more efficiently to space, cooling them.

The aurora are produced by charged particles (mostly electrons) being accelerated by magnetic fields and slamming into the upper atmosphere, exciting the atoms or molecules there. When those excited atoms relax back down, they re-emit that energy as light, some in the visible spectrum which we see as aurora. But that emission doesn't happen instantly -- it takes different amounts of time for the different colors. A competing effect is that collisions of the atoms with one another can transfer that excess energy away, preventing the aurora from being emitted. Aurora colors that take a long time to be emitted cannot occur at low altitudes, because the collisions with other atoms are too frequent. That's why the base of the aurora happens at a specific altitude, like

100km for the green aurora.

So, with a warming world, the conditions for which the aurora can glow should be met at lower altitudes, because the upper atmosphere is cooling and collapsing downward, giving excited atoms at a given altitude more time to emit that glow.


Contents

The dates of Thales' life are not exactly known, but are roughly established by a few datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. [9] Diogenes Laërtius quotes the chronicle of Apollodorus of Athens as saying that Thales died at the age of 78 during the 58th Olympiad (548–545 BC) and attributes his death to heat stroke while watching the games. [10]

Thales was probably born in the city of Miletus around the mid-620s BC. The ancient writer Apollodorus of Athens [11] writing during the 2nd century BC, [4] thought Thales was born about the year 625 BC. [11] Herodotus, writing in the fifth century BC, described Thales as "a Phoenician by remote descent". [12] Tim Whitmarsh noted that Thales regarded water as the primal matter, and because thal is the Phoenician word for moisture, his name may have derived from this circumstance. [13]

According to the later historian Diogenes Laërtius, in his third century AD Lives of the Philosophers, references Herodotus, Duris, and Democritus, who all agree "that Thales was the son of Examyas and Cleobulina, and belonged to the Thelidae who are Phoenicians." [14] [15] Their names are indigenous Carian and Greek, respectively. [12] Diogenes then states that "Most writers, however, represent him as a native of Miletus and of a distinguished family." [14] [15] However, his supposed mother Cleobulina has also been described as his companion instead of his mother. [16] Diogenes then delivers more conflicting reports: one that Thales married and either fathered a son (Cybisthus or Cybisthon) or adopted his nephew of the same name the second that he never married, telling his mother as a young man that it was too early to marry, and as an older man that it was too late. Plutarch had earlier told this version: Solon visited Thales and asked him why he remained single Thales answered that he did not like the idea of having to worry about children. Nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. [17]

It has been claimed that he was roughly the professional equivalent of a contemporary option trader. [18]

It is assumed that Thales at one point in his life visited Egypt, where he learned about geometry. [19] Diogenes Laërtius wrote that Thales identifies the Milesians as Athenian colonists. [20]

Thales (who died around 30 years before the time of Pythagoras and 300 years before Euclid, Eudoxus of Cnidus, and Eudemus of Rhodes) is often hailed as "the first Greek mathematician". [21] While some historians, such as Colin R. Fletcher, point out that there could have been a predecessor to Thales who would have been named in Eudemus' lost book History of Geometry, it is admitted that without the work "the question becomes mere speculation." [21] Fletcher holds that as there is no viable predecessor to the title of first Greek mathematician, the only question is whether Thales qualifies as a practitioner in that field he holds that "Thales had at his command the techniques of observation, experimentation, superposition and deduction…he has proved himself mathematician." [21]

Aristotle wrote in Metaphysics, "Thales, the founder of this school of philosophy, says the permanent entity is water (which is why he also propounded that the earth floats on water). Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption from this and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things." [7]

Activities Edit

Thales involved himself in many activities, including engineering. [22] Some say that he left no writings. Others say that he wrote On the Solstice and On the Equinox. The Nautical Star-guide has been attributed to him, but this was disputed in ancient times. [23] No writing attributed to him has survived. Diogenes Laërtius quotes two letters from Thales: one to Pherecydes of Syros, offering to review his book on religion, and one to Solon, offering to keep him company on his sojourn from Athens. [ clarification needed ]

A story, with different versions, recounts how Thales achieved riches from an olive harvest by prediction of the weather. In one version, he bought all the olive presses in Miletus after predicting the weather and a good harvest for a particular year. Another version of the story has Aristotle explain that Thales had reserved presses in advance, at a discount, and could rent them out at a high price when demand peaked, following his prediction of a particularly good harvest. This first version of the story would constitute the first historically known creation and use of futures, whereas the second version would be the first historically known creation and use of options. [24]

Aristotle explains that Thales' objective in doing this was not to enrich himself but to prove to his fellow Milesians that philosophy could be useful, contrary to what they thought, [25] or alternatively, Thales had made his foray into enterprise because of a personal challenge put to him by an individual who had asked why, if Thales was an intelligent famous philosopher, he had yet to attain wealth.

Diogenes Laërtius tells us that Thales gained fame as a counselor when he advised the Milesians not to engage in a symmachia, a "fighting together", with the Lydians. This has sometimes been interpreted as an alliance. [26] [ failed verification ] Another story by Herodotus is that Croesus sent his army to the Persian territory. He was stopped by the river Halys, then unbridged. Thales then got the army across the river by digging a diversion upstream so as to reduce the flow, making it possible to cross the river. [27] While Herodotus reported that most of his fellow Greeks believe that Thales did divert the river Halys to assist King Croesus' military endeavors, he himself finds it doubtful. [28]

Croesus was defeated before the city of Sardis by Cyrus, who subsequently spared Miletus because it had taken no action. Cyrus was so impressed by Croesus’ wisdom and his connection with the sages that he spared him and took his advice on various matters. [ citation needed ] The Ionian cities should be demoi, or "districts".

He counselled them to establish a single seat of government, and pointed out Teos as the fittest place for it "for that," he said, "was the centre of Ionia. Their other cities might still continue to enjoy their own laws, just as if they were independent states." [29]

Miletus, however, received favorable terms from Cyrus. The others remained in an Ionian League of twelve cities (excluding Miletus), and were subjugated by the Persians. [ citation needed ]

Astronomy Edit

According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. [9] Thales also described the position of Ursa Minor, and he thought the constellation might be useful as a guide for navigation at sea. He calculated the duration of the year and the timings of the equinoxes and solstices. He is additionally attributed with the first observation of the Hyades and with calculating the position of the Pleiades. [30] Plutarch indicates that in his day (c. AD 100) there was an extant work, the Astronomy, composed in verse and attributed to Thales. [31]

Herodotus writes that in the sixth year of the war, the Lydians under King Alyattes and the Medes under Cyaxares were engaged in an indecisive battle when suddenly day turned into night, leading to both parties halting the fighting and negotiating a peace agreement. Herodotus also mentions that the loss of daylight had been predicted by Thales. He does not, however, mention the location of the battle. [32]

Afterwards, on the refusal of Alyattes to give up his suppliants when Cyaxares sent to demand them of him, war broke out between the Lydians and the Medes, and continued for five years, with various success. In the course of it the Medes gained many victories over the Lydians, and the Lydians also gained many victories over the Medes. Among their other battles there was one night engagement. As, however, the balance had not inclined in favour of either nation, another combat took place in the sixth year, in the course of which, just as the battle was growing warm, day was on a sudden changed into night. This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it actually took place. The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on. [29]

However, based on the list of Median kings and the duration of their reign reported elsewhere by Herodotus, Cyaxares died 10 years before the eclipse. [33] [34]

Sagacity Edit

Diogenes Laërtius [35] tells us that the Seven Sages were created in the archonship of Damasius at Athens about 582 BC and that Thales was the first sage. The same story, however, asserts that Thales emigrated to Miletus. There is also a report that he did not become a student of nature until after his political career. Much as we would like to have a date on the seven sages, we must reject these stories and the tempting date if we are to believe that Thales was a native of Miletus, predicted the eclipse, and was with Croesus in the campaign against Cyrus.

Thales received instruction from an Egyptian priest [ citation needed ] and was told to have had close contacts along with the priests of Thebes and their linear geometry. [36]

It was fairly certain that he came from a wealthy, established family, in a class which customarily provided higher education for their children. [ citation needed ] Moreover, the ordinary citizen, unless he was a seafaring man or a merchant, could not afford the grand tour in Egypt, and did not consort with noble lawmakers such as Solon. [ citation needed ]

In Diogenes Laërtius' Lives of Eminent Philosophers Chapter 1.39, Laërtius relates several stories of an expensive object that is to go to the most wise. In one version (that Laërtius credits to Callimachus in his Iambics) Bathycles of Arcadia states in his will that an expensive bowl "'should be given to him who had done most good by his wisdom.' So it was given to Thales, went the round of all the sages, and came back to Thales again. And he sent it to Apollo at Didyma, with this dedication. 'Thales the Milesian, son of Examyas [dedicates this] to Delphinian Apollo after twice winning the prize from all the Greeks.'" [37]

Early Greeks, and other civilizations before them, often invoked idiosyncratic explanations of natural phenomena with reference to the will of anthropomorphic gods and heroes. Instead, Thales aimed to explain natural phenomena via rational hypotheses that referenced natural processes themselves. For example, rather than assuming that earthquakes were the result of supernatural whims, Thales explained them by hypothesizing that the Earth floats on water and that earthquakes occur when the Earth is rocked by waves. [38] [39]

Thales was a hylozoist (one who thinks that matter is alive, [40] i.e. containing soul(s)). Aristotle wrote (De Anima 411 a7-8) of Thales: . Thales thought all things are full of gods. Aristotle posits the origin of Thales thought on matter generally containing souls, to Thales thinking initially on the fact of, because magnets move iron, the presence of movement of matter indicated this matter contained life. [41] [42]

Thales, according to Aristotle, asked what was the nature (Greek arche) of the object so that it would behave in its characteristic way. Physis ( φύσις ) comes from phyein ( φύειν ), "to grow", related to our word "be". [43] [44] (G)natura is the way a thing is "born", [45] again with the stamp of what it is in itself.

Aristotle characterizes most of the philosophers "at first" ( πρῶτον ) as thinking that the "principles in the form of matter were the only principles of all things", where "principle" is arche, "matter" is hyle ("wood" or "matter", "material") and "form" is eidos. [46]

Arche is translated as "principle", but the two words do not have precisely the same meaning. A principle of something is merely prior (related to pro-) to it either chronologically or logically. An arche (from ἄρχειν , "to rule") dominates an object in some way. If the arche is taken to be an origin, then specific causality is implied that is, B is supposed to be characteristically B just because it comes from A, which dominates it.

The archai that Aristotle had in mind in his well-known passage on the first Greek scientists are not necessarily chronologically prior to their objects, but are constituents of it. For example, in pluralism objects are composed of earth, air, fire and water, but those elements do not disappear with the production of the object. They remain as archai within it, as do the atoms of the atomists.

What Aristotle is really saying is that the first philosophers were trying to define the substance(s) of which all material objects are composed. As a matter of fact, that is exactly what modern scientists are attempting to accomplish in nuclear physics, which is a second reason why Thales is described as the first western scientist, [ citation needed ] but some contemporary scholars reject this interpretation. [47]

Geometry Edit

Thales was known for his innovative use of geometry. His understanding was theoretical as well as practical. For example, he said:

Megiston topos: apanta gar chorei ( Μέγιστον τόπος· ἄπαντα γὰρ χωρεῖ. )

The greatest is space, for it holds all things. [48]

Topos is in Newtonian-style space, since the verb, chorei, has the connotation of yielding before things, or spreading out to make room for them, which is extension. Within this extension, things have a position. Points, lines, planes and solids related by distances and angles follow from this presumption.

Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in Diogenes Laërtius (loc. cit.) that he measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the pyramid's shadow measured from the center of the pyramid at that moment must have been equal to its height.

This story indicates that he was familiar with the Egyptian seked, or seqed, the ratio of the run to the rise of a slope (cotangent). [ citation needed ] The seked is at the base of problems 56, 57, 58, 59 and 60 of the Rhind papyrus — an ancient Egyptian mathematical document.

More practically Thales used the same method to measure the distances of ships at sea, said Eudemus as reported by Proclus ("in Euclidem"). According to Kirk & Raven (reference cited below), all you need for this feat is three straight sticks pinned at one end and knowledge of your altitude. One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate the seked from the height of the stick and its distance from the point of insertion to the line of sight (Proclus, In Euclidem, 352).

Thales' theorems Edit

There are two theorems of Thales in elementary geometry, one known as Thales' theorem having to do with a triangle inscribed in a circle and having the circle's diameter as one leg, the other theorem being also called the intercept theorem. In addition Eudemus attributed to him the discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. According to a historical Note, [49] when Thales visited Egypt, [19] he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.

The evidence for the primacy of Thales comes to us from a book by Proclus who wrote a thousand years after Thales but is believed to have had a copy of Eudemus' book. Proclus wrote "Thales was the first to go to Egypt and bring back to Greece this study." [21] He goes on to tell us that in addition to applying the knowledge he gained in Egypt "He himself discovered many propositions and disclosed the underlying principles of many others to his successors, in some case his method being more general, in others more empirical." [21]

Other quotes from Proclus list more of Thales' mathematical achievements:

They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre. [21]

[Thales] is said to have been the first to have known and to have enunciated [the theorem] that the angles at the base of any isosceles triangle are equal, though in the more archaic manner he described the equal angles as similar. [21]

This theorem, that when two straight lines cut one another, the vertical and opposite angles are equal, was first discovered, as Eudemus says, by Thales, though the scientific demonstration was improved by the writer of Elements. [21]

Eudemus in his History of Geometry attributes this theorem [the equality of triangles having two angles and one side equal] to Thales. For he says that the method by which Thales showed how to find the distance of ships at sea necessarily involves this method. [21]

Pamphila says that, having learnt geometry from the Egyptians, he [Thales] was the first to inscribe in a circle a right-angled triangle, whereupon he sacrificed an ox. [21]

In addition to Proclus, Hieronymus of Rhodes also cites Thales as the first Greek mathematician. Hieronymus held that Thales was able to measure the height of the pyramids by using a theorem of geometry now known as the intercept theorem, (after gathering data by using his walking-stick and comparing its shadow to those cast by the pyramids). We receive variations of Hieronymus' story through Diogenes Laërtius, [50] Pliny the Elder, and Plutarch. [21] [51] According to Hieronymus, historically quoted by Diogenes Laërtius, Thales found the height of pyramids by comparison between the lengths of the shadows cast by a person and by the pyramids. [52]

Due to the variations among testimonies, such as the "story of the sacrifice of an ox on the occasion of the discovery that the angle on a diameter of a circle is a right angle" in the version told by Diogenes Laërtius being accredited to Pythagoras rather than Thales, some historians (such as D. R. Dicks) question whether such anecdotes have any historical worth whatsoever. [28]

Water as a first principle Edit

Thales' most famous philosophical position was his cosmological thesis, which comes down to us through a passage from Aristotle's Metaphysics. [53] In the work Aristotle unequivocally reported Thales' hypothesis about the nature of all matter – that the originating principle of nature was a single material substance: water. Aristotle then proceeded to proffer a number of conjectures based on his own observations to lend some credence to why Thales may have advanced this idea (though Aristotle did not hold it himself).

Aristotle laid out his own thinking about matter and form which may shed some light on the ideas of Thales, in Metaphysics 983 b6 8–11, 17–21. (The passage contains words that were later adopted by science with quite different meanings.)

That from which is everything that exists and from which it first becomes and into which it is rendered at last, its substance remaining under it, but transforming in qualities, that they say is the element and principle of things that are. …For it is necessary that there be some nature ( φύσις ), either one or more than one, from which become the other things of the object being saved. Thales the founder of this type of philosophy says that it is water.

In this quote we see Aristotle's depiction of the problem of change and the definition of substance. He asked if an object changes, is it the same or different? In either case how can there be a change from one to the other? The answer is that the substance "is saved", but acquires or loses different qualities ( πάθη , the things you "experience").

Aristotle conjectured that Thales reached his conclusion by contemplating that the "nourishment of all things is moist and that even the hot is created from the wet and lives by it." While Aristotle's conjecture on why Thales held water as the originating principle of matter is his own thinking, his statement that Thales held it as water is generally accepted as genuinely originating with Thales and he is seen as an incipient matter-and-formist. [ citation needed ]

Thales thought the Earth must be a flat disk which is floating in an expanse of water. [54]

Heraclitus Homericus states that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems likely that Thales viewed the Earth as solidifying from the water on which it floated and the oceans that surround it.

Writing centuries later, Diogenes Laërtius also states that Thales taught "Water constituted ( ὑπεστήσατο , 'stood under') the principle of all things." [55]

Aristotle considered Thales’ position to be roughly the equivalent to the later ideas of Anaximenes, who held that everything was composed of air. [56] The 1870 book Dictionary of Greek and Roman Biography and Mythology noted: [2]

In his dogma that water is the origin of things, that is, that it is that out of which every thing arises, and into which every thing resolves itself, Thales may have followed Orphic cosmogonies, while, unlike them, he sought to establish the truth of the assertion. Hence, Aristotle, immediately after he has called him the originator of philosophy brings forward the reasons which Thales was believed to have adduced in confirmation of that assertion for that no written development of it, or indeed any book by Thales, was extant, is proved by the expressions which Aristotle uses when he brings forward the doctrines and proofs of the Milesian. (p. 1016)

Beliefs in divinity Edit

According to Aristotle, Thales thought lodestones had souls, because iron is attracted to them (by the force of magnetism). [57]

Aristotle defined the soul as the principle of life, that which imbues the matter and makes it live, giving it the animation, or power to act. The idea did not originate with him, as the Greeks in general believed in the distinction between mind and matter, which was ultimately to lead to a distinction not only between body and soul but also between matter and energy. [ citation needed ] If things were alive, they must have souls. This belief was no innovation, as the ordinary ancient populations of the Mediterranean did believe that natural actions were caused by divinities. Accordingly, Aristotle and other ancient writers state that Thales believed that "all things were full of gods." [58] [59] In their zeal to make him the first in everything some said he was the first to hold the belief, which must have been widely known to be false. [ citation needed ] However, Thales was looking for something more general, a universal substance of mind. [ citation needed ] That also was in the polytheism of the times. Zeus was the very personification of supreme mind, dominating all the subordinate manifestations. From Thales on, however, philosophers had a tendency to depersonify or objectify mind, as though it were the substance of animation per se and not actually a god like the other gods. The end result was a total removal of mind from substance, opening the door to a non-divine principle of action. [ citation needed ]

Classical thought, however, had proceeded only a little way along that path. Instead of referring to the person, Zeus, they talked about the great mind:

"Thales", says Cicero, [60] "assures that water is the principle of all things and that God is that Mind which shaped and created all things from water."

The universal mind appears as a Roman belief in Virgil as well:

In the beginning, SPIRIT within (spiritus intus) strengthens Heaven and Earth,
The watery fields, and the lucid globe of Luna, and then –
Titan stars and mind (mens) infused through the limbs
Agitates the whole mass, and mixes itself with GREAT MATTER (magno corpore) [61]

According to Henry Fielding (1775), Diogenes Laërtius (1.35) affirmed that Thales posed "the independent pre-existence of God from all eternity, stating "that God was the oldest of all beings, for he existed without a previous cause even in the way of generation that the world was the most beautiful of all things for it was created by God." [62]

Due to the scarcity of sources concerning Thales and the discrepancies between the accounts given in the sources that have survived, there is a scholarly debate over possible influences on Thales and the Greek mathematicians that came after him. Historian Roger L. Cooke points out that Proclus does not make any mention of Mesopotamian influence on Thales or Greek geometry, but "is shown clearly in Greek astronomy, in the use of sexagesimal system of measuring angles and in Ptolemy's explicit use of Mesopotamian astronomical observations." [63] Cooke notes that it may possibly also appear in the second book of Euclid's Elements, "which contains geometric constructions equivalent to certain algebraic relations that are frequently encountered in the cuneiform tablets." Cooke notes "This relation, however, is controversial." [63]

Historian B.L. Van der Waerden is among those advocating the idea of Mesopotamian influence, writing "It follows that we have to abandon the traditional belief that the oldest Greek mathematicians discovered geometry entirely by themselves…a belief that was tenable only as long as nothing was known about Babylonian mathematics. This in no way diminishes the stature of Thales on the contrary, his genius receives only now the honour that is due to it, the honour of having developed a logical structure for geometry, of having introduced proof into geometry." [21]

Some historians, such as D. R. Dicks takes issue with the idea that we can determine from the questionable sources we have, just how influenced Thales was by Babylonian sources. He points out that while Thales is held to have been able to calculate an eclipse using a cycle called the "Saros" held to have been "borrowed from the Babylonians", "The Babylonians, however, did not use cycles to predict solar eclipses, but computed them from observations of the latitude of the moon made shortly before the expected syzygy." [28] Dicks cites historian O. Neugebauer who relates that "No Babylonian theory for predicting solar eclipse existed at 600 B.C., as one can see from the very unsatisfactory situation 400 years later nor did the Babylonians ever develop any theory which took the influence of geographical latitude into account." Dicks examines the cycle referred to as 'Saros' – which Thales is held to have used and which is believed to stem from the Babylonians. He points out that Ptolemy makes use of this and another cycle in his book Mathematical Syntaxis but attributes it to Greek astronomers earlier than Hipparchus and not to Babylonians. [28] Dicks notes Herodotus does relate that Thales made use of a cycle to predict the eclipse, but maintains that "if so, the fulfillment of the 'prediction' was a stroke of pure luck not science". [28] He goes further joining with other historians (F. Martini, J.L. E. Dreyer, O. Neugebauer) in rejecting the historicity of the eclipse story altogether. [28] Dicks links the story of Thales discovering the cause for a solar eclipse with Herodotus' claim that Thales discovered the cycle of the sun with relation to the solstices, and concludes "he could not possibly have possessed this knowledge which neither the Egyptians nor the Babylonians nor his immediate successors possessed." [28] Josephus is the only ancient historian that claims Thales visited Babylonia.

Herodotus wrote that the Greeks learnt the practice of dividing the day into 12 parts, about the polos, and the gnomon from the Babylonians. (The exact meaning of his use of the word polos is unknown, current theories include: "the heavenly dome", "the tip of the axis of the celestial sphere", or a spherical concave sundial.) Yet even Herodotus' claims on Babylonian influence are contested by some modern historians, such as L. Zhmud, who points out that the division of the day into twelve parts (and by analogy the year) was known to the Egyptians already in the second millennium, the gnomon was known to both Egyptians and Babylonians, and the idea of the "heavenly sphere" was not used outside of Greece at this time. [64]

Less controversial than the position that Thales learnt Babylonian mathematics is the claim he was influenced by Egyptians. Pointedly historian S. N. Bychkov holds that the idea that the base angles of an isosceles triangle are equal likely came from Egypt. This is because, when building a roof for a home – having a cross section be exactly an isosceles triangle isn't crucial (as it's the ridge of the roof that must fit precisely), in contrast a symmetric square pyramid cannot have errors in the base angles of the faces or they will not fit together tightly. [63] Historian D.R. Dicks agrees that compared to the Greeks in the era of Thales, there was a more advanced state of mathematics among the Babylonians and especially the Egyptians – "both cultures knew the correct formulae for determining the areas and volumes of simple geometrical figures such as triangles, rectangles, trapezoids, etc. the Egyptians could also calculate correctly the volume of the frustum of a pyramid with a square base (the Babylonians used an incorrect formula for this), and used a formula for the area of a circle. which gives a value for π of 3.1605—a good approximation." [28] Dicks also agrees that this would have had an effect on Thales (whom the most ancient sources agree was interested in mathematics and astronomy) but he holds that tales of Thales' travels in these lands are pure myth.

The ancient civilization and massive monuments of Egypt had "a profound and ineradicable impression on the Greeks". They attributed to Egyptians "an immemorial knowledge of certain subjects" (including geometry) and would claim Egyptian origin for some of their own ideas to try and lend them "a respectable antiquity" (such as the "Hermetic" literature of the Alexandrian period). [28]

Dicks holds that since Thales was a prominent figure in Greek history by the time of Eudemus but "nothing certain was known except that he lived in Miletus". [28] A tradition developed that as "Milesians were in a position to be able to travel widely" Thales must have gone to Egypt. [28] As Herodotus says Egypt was the birthplace of geometry he must have learnt that while there. Since he had to have been there, surely one of the theories on Nile Flooding laid out by Herodotus must have come from Thales. Likewise as he must have been in Egypt he had to have done something with the Pyramids – thus the tale of measuring them. Similar apocryphal stories exist of Pythagoras and Plato traveling to Egypt with no corroborating evidence.

As the Egyptian and Babylonian geometry at the time was "essentially arithmetical", they used actual numbers and "the procedure is then described with explicit instructions as to what to do with these numbers" there was no mention of how the rules of procedure were made, and nothing toward a logically arranged corpus of generalized geometrical knowledge with analytical 'proofs' such as we find in the words of Euclid, Archimedes, and Apollonius." [28] So even had Thales traveled there he could not have learnt anything about the theorems he is held to have picked up there (especially because there is no evidence that any Greeks of this age could use Egyptian hieroglyphics). [28]

Likewise until around the second century BC and the time of Hipparchus (c. 190–120 BC) the Babylonian general division of the circle into 360 degrees and their sexagesimal system was unknown. [28] Herodotus says almost nothing about Babylonian literature and science, and very little about their history. Some historians, like P. Schnabel, hold that the Greeks only learned more about Babylonian culture from Berossus, a Babylonian priest who is said to have set up a school in Cos around 270 BC (but to what extent this had in the field of geometry is contested).

Dicks points out that the primitive state of Greek mathematics and astronomical ideas exhibited by the peculiar notions of Thales' successors (such as Anaximander, Anaximenes, Xenophanes, and Heraclitus), which historian J. L. Heiberg calls "a mixture of brilliant intuition and childlike analogies", [65] argues against the assertions from writers in late antiquity that Thales discovered and taught advanced concepts in these fields.

Lastly, we have one admitted instance of a philosophic guild, that of the Pythagoreans. And it will be found that the hypothesis, if it is to be called by that name, of a regular organisation of scientific activity will alone explain all the facts. The development of doctrine in the hands of Thales, Anaximander, and Anaximenes, for instance, can only be understood as the elaboration of a single idea in a school with a continuous tradition.

According to the 10-th century Byzantine encyclopdia Suda, Thales had been the "teacher and kineman" of Anaximander. [67]

Nicholas Molinari has recently argued for an important Greek influence on Thales' idea of the archai, namely, the archaic water deity Acheloios, who was equated with water and worshipped in Miletos during Thales' life. He argues that Thales, as a sage and world traveler, was exposed to many mythologies and religions, and while they all had some influence, his hometown Acheloios was the most essential. For evidence, he points to the fact that hydor meant specifically "fresh water," and that Acheloios was seen as a shape-shifter in myth and art, so able to become anything. He also points out that the rivers of the world were seen as the "sinews of Acheloios" in antiquity, and this multiplicity of deities is reflected in Thales' idea that "all things are full of gods." [68]

In the long sojourn of philosophy, there has existed hardly a philosopher or historian of philosophy who did not mention Thales and try to characterize him in some way. He is generally recognized as having brought something new to human thought. Mathematics, astronomy, and medicine already existed. Thales added something to these different collections of knowledge to produce a universality, which, as far as writing tells us, was not in tradition before, but resulted in a new field.

Ever since, interested persons have been asking what that new something is. Answers fall into (at least) two categories, the theory and the method. Once an answer has been arrived at, the next logical step is to ask how Thales compares to other philosophers, which leads to his classification (rightly or wrongly).

Theory Edit

The most natural epithets of Thales are "materialist" and "naturalist", which are based on ousia and physis. The Catholic Encyclopedia notes that Aristotle called him a physiologist, with the meaning "student of nature." [69] On the other hand, he would have qualified as an early physicist, as did Aristotle. They studied corpora, "bodies", the medieval descendants of substances.

Most agree that Thales' stamp on thought is the unity of substance, hence Bertrand Russell: [70]

The view that all matter is one is quite a reputable scientific hypothesis. . But it is still a handsome feat to have discovered that a substance remains the same in different states of aggregation.

Russell was only reflecting an established tradition for example: Nietzsche, in his Philosophy in the Tragic Age of the Greeks, wrote: [71]

Greek philosophy seems to begin with an absurd notion, with the proposition that water is the primal origin and the womb of all things. Is it really necessary for us to take serious notice of this proposition? It is, and for three reasons. First, because it tells us something about the primal origin of all things second, because it does so in language devoid of image or fable, and finally, because contained in it, if only embryonically, is the thought, "all things are one."

This sort of materialism, however, should not be confused with deterministic materialism. Thales was only trying to explain the unity observed in the free play of the qualities. The arrival of uncertainty in the modern world made possible a return to Thales for example, John Elof Boodin writes ("God and Creation"):

We cannot read the universe from the past.

Boodin defines an "emergent" materialism, in which the objects of sense emerge uncertainly from the substrate. Thales is the innovator of this sort of materialism.

Later scholastic thinkers would maintain that in his choice of water Thales was influenced by Babylonian or Chaldean religion, that held that a god had begun creation by acting upon the pre-existing water. Historian Abraham Feldman holds this does not stand up under closer examination. In Babylonian religion the water is lifeless and sterile until a god acts upon it, but for Thales water itself was divine and creative. He maintained that "All things are full of gods", and to understand the nature of things was to discover the secrets of the deities, and through this knowledge open the possibility that one could be greater than the grandest Olympian. [72]

Feldman points out that while other thinkers recognized the wetness of the world "none of them was inspired to conclude that everything was ultimately aquatic." [72] He further points out that Thales was "a wealthy citizen of the fabulously rich Oriental port of Miletus. a dealer in the staples of antiquity, wine and oil. He certainly handled the shell-fish of the Phoenicians that secreted the dye of imperial purple." [72] Feldman recalls the stories of Thales measuring the distance of boats in the harbor, creating mechanical improvements for ship navigation, giving an explanation for the flooding of the Nile (vital to Egyptian agriculture and Greek trade), and changing the course of the river Halys so an army could ford it. Rather than seeing water as a barrier Thales contemplated the Ionian yearly religious gathering for athletic ritual (held on the promontory of Mycale and believed to be ordained by the ancestral kindred of Poseidon, the god of the sea). He called for the Ionian mercantile states participating in this ritual to convert it into a democratic federation under the protection of Poseidon that would hold off the forces of pastoral Persia. Feldman concludes that Thales saw "that water was a revolutionary leveler and the elemental factor determining the subsistence and business of the world" [72] and "the common channel of states." [72]

Feldman considers Thales' environment and holds that Thales would have seen tears, sweat, and blood as granting value to a person's work and the means how life giving commodities travelled (whether on bodies of water or through the sweat of slaves and pack-animals). He would have seen that minerals could be processed from water such as life-sustaining salt and gold taken from rivers. He would’ve seen fish and other food stuffs gathered from it. Feldman points out that Thales held that the lodestone was alive as it drew metals to itself. He holds that Thales "living ever in sight of his beloved sea" would see water seem to draw all "traffic in wine and oil, milk and honey, juices and dyes" to itself, leading him to "a vision of the universe melting into a single substance that was valueless in itself and still the source of wealth." [72] Feldman concludes that for Thales ". water united all things. The social significance of water in the time of Thales induced him to discern through hardware and dry-goods, through soil and sperm, blood, sweat and tears, one fundamental fluid stuff. water, the most commonplace and powerful material known to him." [72] This combined with his contemporary's idea of "spontaneous generation" allow us to see how Thales could hold that water could be divine and creative.

Feldman points to the lasting association of the theory that "all whatness is wetness" with Thales himself, pointing out that Diogenes Laërtius speaks of a poem, probably a satire, where Thales is snatched to heaven by the sun. [72]

Rise of theoretical inquiry Edit

In the West, Thales represents a new kind of inquiring community as well. Edmund Husserl [73] attempts to capture the new movement as follows. Philosophical man is a "new cultural configuration" based in stepping back from "pregiven tradition" and taking up a rational "inquiry into what is true in itself" that is, an ideal of truth. It begins with isolated individuals such as Thales, but they are supported and cooperated with as time goes on. Finally the ideal transforms the norms of society, leaping across national borders.

Classification Edit

The term "Pre-Socratic" derives ultimately from the philosopher Aristotle, who distinguished the early philosophers as concerning themselves with substance.

Diogenes Laërtius on the other hand took a strictly geographic and ethnic approach. Philosophers were either Ionian or Italian. He used "Ionian" in a broader sense, including also the Athenian academics, who were not Pre-Socratics. From a philosophic point of view, any grouping at all would have been just as effective. There is no basis for an Ionian or Italian unity. Some scholars, however, concede to Diogenes' scheme as far as referring to an "Ionian" school. There was no such school in any sense.

The most popular approach refers to a Milesian school, which is more justifiable socially and philosophically. They sought for the substance of phenomena and may have studied with each other. Some ancient writers qualify them as Milesioi, "of Miletus."

Thales had a profound influence on other Greek thinkers and therefore on Western history. Some believe Anaximander was a pupil of Thales. Early sources report that one of Anaximander's more famous pupils, Pythagoras, visited Thales as a young man, and that Thales advised him to travel to Egypt to further his philosophical and mathematical studies.

Many philosophers followed Thales' lead in searching for explanations in nature rather than in the supernatural others returned to supernatural explanations, but couched them in the language of philosophy rather than of myth or of religion.

Looking specifically at Thales' influence during the pre-Socratic era, it is clear that he stood out as one of the first thinkers who thought more in the way of logos than mythos. The difference between these two more profound ways of seeing the world is that mythos is concentrated around the stories of holy origin, while logos is concentrated around the argumentation. When the mythical man wants to explain the world the way he sees it, he explains it based on gods and powers. Mythical thought does not differentiate between things and persons [ citation needed ] and furthermore it does not differentiate between nature and culture [ citation needed ] . The way a logos thinker would present a world view is radically different from the way of the mythical thinker. In its concrete form, logos is a way of thinking not only about individualism [ clarification needed ] , but also the abstract [ clarification needed ] . Furthermore, it focuses on sensible and continuous argumentation. This lays the foundation of philosophy and its way of explaining the world in terms of abstract argumentation, and not in the way of gods and mythical stories [ citation needed ] .

Because of Thales' elevated status in Greek culture an intense interest and admiration followed his reputation. Due to this following, the oral stories about his life were open to amplification and historical fabrication, even before they were written down generations later. Most modern dissension comes from trying to interpret what we know, in particular, distinguishing legend from fact.

Historian D.R. Dicks and other historians divide the ancient sources about Thales into those before 320 BC and those after that year (some such as Proclus writing in the 5th century C.E. and Simplicius of Cilicia in the 6th century C.E. writing nearly a millennium after his era). [28] The first category includes Herodotus, Plato, Aristotle, Aristophanes, and Theophrastus among others. The second category includes Plautus, Aetius, Eusebius, Plutarch, Josephus, Iamblichus, Diogenes Laërtius, Theon of Smyrna, Apuleius, Clement of Alexandria, Pliny the Elder, and John Tzetzes among others.

The earliest sources on Thales (living before 320 BC) are often the same for the other Milesian philosophers (Anaximander, and Anaximenes). These sources were either roughly contemporaneous (such as Herodotus) or lived within a few hundred years of his passing. Moreover, they were writing from an oral tradition that was widespread and well known in the Greece of their day.

The latter sources on Thales are several "ascriptions of commentators and compilers who lived anything from 700 to 1,000 years after his death" [28] which include "anecdotes of varying degrees of plausibility" [28] and in the opinion of some historians (such as D. R. Dicks) of "no historical worth whatsoever". [28] Dicks points out that there is no agreement "among the 'authorities' even on the most fundamental facts of his life—e.g. whether he was a Milesian or a Phoenician, whether he left any writings or not, whether he was married or single—much less on the actual ideas and achievements with which he is credited." [28]

Contrasting the work of the more ancient writers with those of the later, Dicks points out that in the works of the early writers Thales and the other men who would be hailed as "the Seven Sages of Greece" had a different reputation than that which would be assigned to them by later authors. Closer to their own era, Thales, Solon, Bias of Priene, Pittacus of Mytilene and others were hailed as "essentially practical men who played leading roles in the affairs of their respective states, and were far better known to the earlier Greeks as lawgivers and statesmen than as profound thinkers and philosophers." [28] For example, Plato praises him (coupled with Anacharsis) for being the originator of the potter's wheel and the anchor.

Only in the writings of the second group of writers (working after 320 BC) do "we obtain the picture of Thales as the pioneer in Greek scientific thinking, particularly in regard to mathematics and astronomy which he is supposed to have learnt about in Babylonia and Egypt." [28] Rather than "the earlier tradition [where] he is a favourite example of the intelligent man who possesses some technical 'know how'. the later doxographers [such as Dicaearchus in the latter half of the fourth century BC] foist on to him any number of discoveries and achievements, in order to build him up as a figure of superhuman wisdom." [28]

Dicks points out a further problem arises in the surviving information on Thales, for rather than using ancient sources closer to the era of Thales, the authors in later antiquity ("epitomators, excerptors, and compilers" [28] ) actually "preferred to use one or more intermediaries, so that what we actually read in them comes to us not even at second, but at third or fourth or fifth hand. . Obviously this use of intermediate sources, copied and recopied from century to century, with each writer adding additional pieces of information of greater or less plausibility from his own knowledge, provided a fertile field for errors in transmission, wrong ascriptions, and fictitious attributions". [28] Dicks points out that "certain doctrines that later commentators invented for Thales. were then accepted into the biographical tradition" being copied by subsequent writers who were then cited by those coming after them "and thus, because they may be repeated by different authors relying on different sources, may produce an illusory impression of genuineness." [28]

Doubts even exist when considering the philosophical positions held to originate in Thales "in reality these stem directly from Aristotle's own interpretations which then became incorporated in the doxographical tradition as erroneous ascriptions to Thales". [28] (The same treatment was given by Aristotle to Anaxagoras.)

Most philosophic analyses of the philosophy of Thales come from Aristotle, a professional philosopher, tutor of Alexander the Great, who wrote 200 years after Thales' death. Aristotle, judging from his surviving books, does not seem to have access to any works by Thales, although he probably had access to works of other authors about Thales, such as Herodotus, Hecataeus, Plato etc., as well as others whose work is now extinct. It was Aristotle's express goal to present Thales' work not because it was significant in itself, but as a prelude to his own work in natural philosophy. [74] Geoffrey Kirk and John Raven, English compilers of the fragments of the Pre-Socratics, assert that Aristotle's "judgments are often distorted by his view of earlier philosophy as a stumbling progress toward the truth that Aristotle himself revealed in his physical doctrines." [75] There was also an extensive oral tradition. Both the oral and the written were commonly read or known by all educated men in the region.

Aristotle's philosophy had a distinct stamp: it professed the theory of matter and form, which modern scholastics have dubbed hylomorphism. Though once very widespread, it was not generally adopted by rationalist and modern science, as it mainly is useful in metaphysical analyses, but does not lend itself to the detail that is of interest to modern science. It is not clear that the theory of matter and form existed as early as Thales, and if it did, whether Thales espoused it.

While some historians, like B. Snell, maintain that Aristotle was relying on a pre-Platonic written record by Hippias rather than oral tradition, this is a controversial position. Representing the scholarly consensus Dicks states that "the tradition about him even as early as the fifth century B.C., was evidently based entirely on hearsay. It would seem that already by Aristotle's time the early Ionians were largely names only to which popular tradition attached various ideas or achievements with greater or less plausibility". [28] He points out that works confirmed to have existed in the sixth century BC by Anaximander and Xenophanes had already disappeared by the fourth century BC, so the chances of Pre-Socratic material surviving to the age of Aristotle is almost nil (even less likely for Aristotle's pupils Theophrastus and Eudemus and less likely still for those following after them).

The main secondary source concerning the details of Thales' life and career is Diogenes Laërtius, "Lives of Eminent Philosophers". [76] This is primarily a biographical work, as the name indicates. Compared to Aristotle, Diogenes is not much of a philosopher. He is the one who, in the Prologue to that work, is responsible for the division of the early philosophers into "Ionian" and "Italian", but he places the Academics in the Ionian school and otherwise evidences considerable disarray and contradiction, especially in the long section on forerunners of the "Ionian School". Diogenes quotes two letters attributed to Thales, but Diogenes wrote some eight centuries after Thales' death and that his sources often contained "unreliable or even fabricated information", [77] hence the concern for separating fact from legend in accounts of Thales.

It is due to this use of hearsay and a lack of citing original sources that leads some historians, like Dicks and Werner Jaeger, to look at the late origin of the traditional picture of Pre-Socratic philosophy and view the whole idea as a construct from a later age, "the whole picture that has come down to us of the history of early philosophy was fashioned during the two or three generations from Plato to the immediate pupils of Aristotle". [78]