The resulting Battle of Granikos was not only the first that Alexander the Great fought
against the Persians, it was also the one in which he came the closest to being killed in.
While the various accounts of the battle agree with each other very well in some respects,
in others respects there are remarkable, and indeed, perhaps irreconcilable differences.
All the accounts agree that the battle was opened by the horse of each side, and that Alexander was nearly killed in a furious cavalry melee. Most sources have the battle fought in the late afternoon, directly across the flow of the Granikos river, with the Persian cavalry defending the river bank, while their infantry were stationed to the rear. Diodoros however tells a very different story about the role of the river - in his version the battle takes place only after the Macedonians have crossed the river, at dawn, before the Persians were able to respond to his move move.
Traditionally, most recreations of the battle have followed the majority of the sources,
despite the seeming inherent military unlikelyness of the accounts presented. Why defend
a river bank with stationary cavalry (a force needing space to manoeuvre in), when you have
a perfectly competent infantry force (Memnon's Greek mercenaries) far more suited to the task
at your disposal? Why indeed - and this is a question that many have laboured (unsuccessfully)
to answer. The Persians of course successfully used Greek mercenaries to defend a (lesser) river
bank at Issos against the Macedonian phalanx just one year later, so saying it was a dangerous
thing to do, as Hammond would have us believe, is nonsense, and any battle reconstruction should
account for why the Persians didn't defend the banks with their infantry here, but did so at Issos.
(It has been argued that the Persians had defended a river like this before, at Centrites as described by Xenophon, but in fact at Centrites, what was defended was the entrance to mountain defile that just happened to have a river running in front of it. The Persian cavalry had nowhere else to go but between the hills and the river.)
However, if we look at Diodoros' account, the Persian dispositions are perfectly reasonable - their cavalry is now stationed at the front because the battle is contested in the open plain, rather than directly across the slippery river banks, and so the infantry are more sensibly deployed to the rear on higher ground.
Therefore some scholars such as Beloch, have taken Diodoros' account of the crossing at face value, rejecting the testimony of Arrian et al. The reconstruction presenetd below on this web-page will do so likewise. For the other version of this famous battle, I have prepraed another scenario, which can be accessed here. One of the most interesting theories about the discrepant accounts has been advanced by Peter Green, who hypothosises that there was an initial late afternoon attack across the river led by Alexander (which Arrian's story describes), which was rebuffed, and that the Macedonians then waited until dawn before crossing the river downstream, before engaging the Persians with their full forces. Unfortunately, Green then goes and argues for a battle at right angles to the river line, despite Diodoros' statement (17.23.2) that Alexander fought the battle with the river to his rear.
Opponents of Diodoros' version of course ask how then why do most of the sources all agree in having Alexander rashly charging across the river into ill-deployed Persian forces, and this is a serious question. Green argues for a cover up by Alexander and his officers, such as Ptolemy, Arrian's main source, since among other things the battle's execution reflected badly on Alexander and much better on Parmenio, whom Alexander later had murdered...
However, such speculation isn't really neccesary to arrive at a plausible battle scenario, so I will leave this question open (though I will talk about if more in my other scenario). From the military perspective, if one source appears militarily plausible, and the others wildly improbable, a war*gamer* might do better to plump for the plausible one, even if it looks less likely from an historiographical point of view.
Plutarch (Alex., 15 and also Moralia 327D-E) records that ancient estimates (Aristobulus, Ptolemy, Anaximenes) of Alexander's forces ranged from 30000 to 43000 foot and 4000 to 5500 horse; Justin (11.6.2) records 32000 foot and 4500 horse; Polybios (12.19.1) has Kallisthenes recording 40000 foot and 4500 horse; Diodoros, the only source to give a force composition (17.17), gives 30000 foot and 4500 horse (though his figures actually total 32000 foot and 5100 horse). Some time ago Brunt proposed that the two main groups of figures (ca. 32000 foot and 4500 horse, and ca. 43000 foot and 5500 horse, can be accounted for by adding in the advance force Philip had already sent to Asia (which would therefore be about, or a bit over 10000 men in very round terms), and indeed, Diodorus states that the numbers he quotes are for those that crossed over to Asia with Alexander, rather than those with Alexander at the battle itself. Similarly, Arrian gives Alexander over 5000 horse, and a little over 30000 foot before crossing the Hellespont (1.11.3) rather than at the battle itself.
Diodoros gives the breakdown of the 32000 foot and 5100 horse he mentions as:
The advance force is said to have been composed of Macedonians and mercenaries (Diodurus17.7.10). Diodorus (16.89) hints that allies (i.e. Greeks coerced into fighting by the League of Corinth) could have been sent, but actually goes on to say that Philip sent a portion of his 'own' forces, discounting their presence (16.91). I assume mercenaries were more numerous than Macedonians: Philip had the money to pay for mercenaries at the time, and Macedonians were more likely needed at home. I think we can assume that Hypaspists (Philip's foot guardsmen, as the Pezetairoi had been named at some unknown time before the battle) were unlikely to have been sent in the advance force as Philip's domestic situation was far from secure, so the troops that could have been sent might be supposed to be mainly Greek and Thracian mercenaries (Illyria having not been subjugated in quite the same way then as it was by the time Alexander left for Asia), and non-guard Macedonians. Companions, the elite Macedonian heavy cavalry, might possibly be less likely to be present than other troops, given their noble origins, but shouldn't be discounted - a Macedonian force lacking the favoured heavy-strike force provided by the Companions would seem to run counter to Philip's practice of using balanced combined arms forces whenever possible.
While we can reasonably assume that the whole of the advance force was present for the battle, since Alexander had yet to capture any significant strong-points that would require him to detach men for garrison duties and the like, they are also likely to have suffered some losses over the campaign against Memnon. These are hard to quantify - the campaign started out well, but Memnon was getting the upper hand towards the end. However, the initial numbers of men are not our present concern, but rather the number of men after they had joined Alexander. Polyainos (5.44.4) records Parmenio and Attalos having 10000 men when attacked by Memnon, but it seems that this might not have been the entire force sent by Philip, since we learn of Kalas leading another force of Macedonians (Diodorus 17.7.10, called Kallas, Polyainos 5.44.5, also called Khalkos in his Excerpts, 28.3). Thus equating the 11000-plus men difference betwen the high and low estimates for Alexander's force to the Asian force seems entirely reasonable.
Duncan Head has suggested to me that it is possible that some local Asiatic Greeks may have joined Parmenio's advanced force - it is certainly possible, although not attested in any source, and the Asiatic Greeks (or, at least, their ruling classes which made up their military strength) generally seemed to have preferred the Persian cause rather than the Macedonian one. In any case, they are unlikely to have differed too much from the other Greeks in the Macedonian army, so we need not be too concerned about them.
Let's assume they came to the following when they joined Alexander:
The Greek horse were probably those mercenaries from which 200 were later detailed off to guard Karia (Arrian 1.23.6, the text is actually 'open to interpretation' as to their mercenary status, but mercenaries horse were certainy present much later, and would likely have been present from the outset). Macedonian archers were not in the main force (these archers being listed in the 'non-Macedonian' section of Diodoros' troop list, no doubt in part being the Kretans mentioned in 17.57.4), but are later mentioned by Arrian (3.12.2) so had either arrived later as (unremarked) reinforcements, or they were part of the advance force. I prefer the advance force option, since archers are so handy in seiges, and the advance force had to do a lot of city-taking. The 2000 other Macedonian foot would have been phalangites - see my notes on Macedonian numbers and unit organisations for these, and the Macedonian horse.
The Persian numbers are even harder to estimate. Arrian (1.14.4) gives 'about' 20000 horse and somewhat fewer foot, Justin (11.6.11) a wildly exaggerated all-in total of 600000 (!); Diodoros (17.19.5) gives 'over' 10000 horse, and an improbable 100000 foot - improbable not least because Arrian says the Persian infantry was outnumbered (1.13.3), but also Memnon's advised scorched-earth policy would make no sense if the Persians had far more men than the Macedonians to feed. Diodoros, the only source to give a Persian order of battle, lists the following horse:
Let us strike a mid-point somewhere between Diodoros and Arrian and plump for 16000. We can assume that Memnon's contingent would be very small compared to the others - probably no more than 500 strong, even including any retainers from his own Persian estates. Paphlagonians ought to have been well represented, since Paphlagonians were noted horsemen and the battle was fought in Paphlagonia (also known as Hellespontine Phrygia). Spithridates also ought to have had a large contingent if he was leading Hyrkanians in addition to cavalry from his own satrap of Lydia and Ionia (perhaps counted in the 'other national contingents' next to the Hyrkanians), although these Hyrkanians might have been colonist soldiers rather than contingents that had recently arrived from the East. Arsames' contingent would likely have been smaller - Kilikia was further away from the battlefield than Lydia, and again, unlike Lydia, was not a place noted for its horsemen. Arsames is named as satrap of Kilikia in both Arrian and Curtius; presumably Diodoros has confused him with Orontobates of Karia (Arrian 1.23.8), who is somewhat surprisingly absent (Karia is between Kilikia and Ionia). Casualty estimates of the Persian horse range from 1000 (Arrian - although he may here be referring to Iranian horsemen only) to 2500 (Plutarch); not particularly high losses for the losers of an ancient battle.
For the Persian infantry we can reject figures in the 100000 plus range - such an immense horde would have been impossible to gather in the time required (Persian defences had been stood down after Philip's assassination, let alone supply. Arrian's figure of around 20000 is certainly plausible enough so we shall stick to it. However, there is no way that they could have all been Greek mercenaries as he implies (he actually calls them 'foreign', by which he means Greek when used in a Persian context, but references to their Greekness may apply to only part of the mercenary body, not the whole) - according to Polyainos (5.44.4) Memnon had only 4000 at the start of his command, while Diodoros records 5000 mercenaries (17.7.3) and it is hard to see how he could have come by many more in the meantime. Even if we settle for 6000 we may be allowing him too many. Plutarch (Alex, 16.6) and Diodoros (17.21.5) both record heavy Persian casualties amongst the Persian foot. The composition of these remaining Persian infantrymen must remain an educated guess at best. Karians are likely to be included (e.g. Arrian 1.29.1).
Turning to commanders, the Persians certainly had several satraps (provincial govorners) present: Arsites of Paphlagonia (Arrian 1.16.3, Pausanias gives him as satrap, 1.29.10), Spithridates of Lydia and Ionia (Arrian, 1.16.3; Diodoros 17.20.2), Arsames of Kilikia (Arrian 1.12.8), Atizyes of Phrygia (Diodoros 17.21.3, Arrian 1.25.3, 2.11.8); it is possible that Orontobates of Karia (Arrian 1.23.8) was also present, but his absence could be explained by any number of reasons.
Arrian however lists the Persian commanders as Arsames, Rheomithres, Petenes and Niphates, plus Spithridates and Arsites (1.12.8, where is is referred to as a 'hyparch'). In addition to these should also be added the Greek general Memnon, whose advice was rejected before the battle, but was soon to be made supreme commander of the war against Alexander. Arrian also says that the mercenaries were lead by one Omares (1.16.3), and that other commanders included Mithrobuzanes the hyparch of Kappadokia, Mithridates, Arbupales and Pharnaces, who all died in the battle (Arrian, 1.16.3).
Less than half these leaders are Satraps, which would seem to give some support to Xenophon's statement about civil and military commands being kept separate (in his Oeconomicus). Hyparch is usually translated as a subordinate of a satrap, but sometimes it is hard to see why, when many men named as hyparchs seem to just as influential with the King as satraps; hyparch may be an indication of (purely) military high command (although not excluding the possibility of other civil appointemenst as well). Cf. Xenophon on Tiribazus (Anabasis 4.4.4), who was according to Diodoros also a satrap, and various other instances, especially Arrian 3.16.9 with Diodoros 17.64.5 where Menes the hyparch is given command of military forces in Syrian, Cilicia and Phoenicia. Arsites' suicide after the battle would seem to indicate he felt (or that Darius would feel him to be) responsible for the battle's loss (Arrian 1.16.3) so he would appear to have been the chief commander.
Arsames seems not to have taken any prominent part in the battle in any case, and the entire Persian right flank's horse was entrusted to Rheomithres. Possibly Petenes and Niphates commanded the Persian foot that composed the rear line (Diodoros 17.19.5) since they are not recorded leading any horse. In any case, the plethora of commanders did the Persians little good in the event of the battle.
We may therefore conjecture the Persian order of battle, at 250 men per element as:
1 x Reg Kn (I) Sub-general - Memnon, his household troops, and Greek mercenaries
1 x Reg Kn (I) - Greek mercenaries
24 x Reg Sp (O) - Greek mercenaries under Omares
1 x Irr Cv (O) - Arsames, satrap of Kilikia and his household troops
1 x Irr Cv (O) - Orontobates and his household troops
4 x Irr Cv (I) - Other Karians and Kilikians
1 x Reg Cv (O) CinC - Arsites and his household troops
7 x Irr Cv (I) - Paphlagonian colonists
8 x Reg Sp (I) - Karians
20 x Irr Ax (O) - Takabara and various Paphlagonian hillmen under Niphates
8 x Irr Ps (O) - Mixed archers
8 x Irr Bg (I) - Immobile Baggage
1 x Reg Cv (O) Sub-general - Spithridates, satrap of Lydia and Ionia
1 x Reg Cv (O) - Persian 'Kinsmen' under Mithridates (Diodoros, 17.20.2)
6 x Irr Cv (O) - Other Persians
4 x Irr Cv (S) - Hyrcanian and other armoured cavalry
2 x Irr Cv (O) - Kappadocian cavalry under the hyparch Mithrobuzanes
4 x Irr Cv (I) - Lydians
2 x Irr Cv (I) - Ionians
8 x Reg Sp (I) - Ionians
4 x Reg Ax (O) - Court takabara from Sardis under Petenes
8 x Irr Ax (O) - Other Lydian takabara
1 x Irr Cv (O) - Atizyes, satrap of Phrygia and his household troops
3 x Irr Cv (I) - Other Phrygians, etc.
5 x Irr LH (O) - Medians
1 x Reg Cv (O) Sub-general - Rheomithres
8 x Irr LH (O) - Paphlagonians, Kappadokians, etc.
8 x Irr Cv (O) - Bactrians
4 x Irr LH (F) - Armenians, etc.
774 AP, 26/46/40/30 ee, 142 ee total
In the field, the Macedonian army was divided into two halves, the left being commanded by Parmenio, the right by Alexander. Each appear to have controlled their cavalry more closely than their infantry, so in DBM terms we will assume that their respective phalanx brigades were 'commanded' by another subordinate general. This will then give the Macedonians 4 tabletop generals like the Persians (it seems scarcely credible that the DBM Persian army lists allows them a better command and control ability than the Macedonians). Such a command structure was in place at Issos and Granikos, so was likely put into in place when the advance force joined the main body before the battle.
The Macedonians, again at 250 men per element, can be conjectured as:
1 x Reg Kn (F) CinC - Alexander
7 x Reg Kn (F) - Companions
4 x Reg LH (O) - Macedonian prodromoi
1 x Irr LH (O) - Paeonian prodromoi
2 x Reg Ps (S) - Agrianians
2 x Irr Ps (S) - Illyrians
2 x Reg Ps (O) - Macedonian archers
8 x Reg Pk (S) - Hypaspists
2 x Reg Kn (I) - Mercenary Greek horse
6 x Reg Sp (O) - Greek mercenary hoplites
12 x Reg Ax (X) - Other Greek mercenaries
1 x Reg Pk (O) Sub-general - Coenus
23 x Reg Pk (O) - Phalanx
28 x Irr Sp (I) - Allied infantry
1 x Reg Pk (O) Sub-general - Craterus
23 x Reg Pk (O) - Phalanx
26 x Irr Ax (O) - Thracians
8 x Irr Bg (I) - Mobile Bg
1 x Reg Kn (F) Sub-general - Parmenio
6 x Reg Kn (F) - Thessalians
2 x Reg Kn (I) - Allied Greek horse
2 x Irr LH (O) - Thracians
8 x Irr Ax (S) - Illyrians
2 x Reg Ps (O) - Cretan archers
4 x Irr Ps (S) - Thracians
24 x Reg Ax (X) - Other Greek mercenaries
956 AP, 46/52/50/46 ee, 194 ee total
Although I would classify the Greek mercenaries mostly as Sp (I): "Iphikratid peltasts", DBM makes this somewhat too effective versus horsemen, especially horsemen with missile weapons, and so for this refight probably need them to be classified as Ax (X). (Otherwise the Macedonians will just extend their frontage and push the the Persian horse off the playing table).
The battle was fought in May/June, or Spring in DBM terms. The Granicus, flowing northeastwards towards the Black Sea, could well have still been swollen by snow-melt, although still crossable in many places. Its bank is recorded as being muddy and slippy, and we should probably accordingly grade its fordablity as 'tricky'. Hammond says however that the river is a narrow stream at this time of year (when he looked at it on June 15th, 1976), flowing between wider dry clay banks (although thousands of men and horse crossing it would probably have soon turned its banks wet and slippery), and in any case, hardly effects the classification in DBM terms, where the banks are what matters at least as much as the actual water content.
In any case, Hammond himself suspects that the ancient river held more water, due to modern irrigation works, and since the battle was probably fought earlier than the 15h of June, it would probably have been fuller in case becase of the earlier season. Howevere, playtesting has revealed that crossing a tricky river in DBM with more than one element is essentially impossible if the enemy moves to defend the bank, so it needs to be graded easy, but depicted just over 100 paces wide in compensation. The Persians must have blocked the normal route towards Dascylium (Plutarch, Alex. 16.1, talks of 'THE crossing of the Granikos'), so a road and ford would feature (no bridge is mentioned in any source) in the vicinity. Hammond's places the river in an older water course east of the present river, since the present river is 3 km from the low hills which played a part in the battle; the older course no more than half a kilometer distant, and often less.
Although Green's recreation of battle envisage's the Macedonians advancing towards the Persians with the river hard upon their right flank, this is contradicted by Diodoros, who describes Alexander fighting the battle with the river to his rear (17.23.2). It is hard to see how Alexander could have crossed unnoticed, even at dawn, without moving somewhat away from the area of the ford, despite the numerous trees to be found along the river banks, and so I assume that they crossed downstream of the Persians, and the Persian's ford would be to the south-western edge of the battlefield, possibly near the confluence with the Biga which would be a natural feature for the Persians to anchor their initial left flank on.
The other important battlefield feature was the low hill/ridge to the Persia rear upon which the Persians' Greek Mercenaries made their last stand. This should count as a gentle hill with smooth slopes. (The plain was ranged with low foothills to the east, though these would be too far away to depict on the tabletop). Plutarch (Alex. 16.3) describes the hill as a 'ridge', although Arrian (1.14.4) merely talks of 'high' or 'rising' ground. Diodoros (17.19.2) describes the hill as the 'last slope' which I believe accords with my battle plan with the battlefield to the north of this last slope better than Hammond's plan where rising ground is continuous all along the rear of the Persian line, and beyond.
Hammond's reconstruction of the battle (from the traditional perspective) is suspect in one great area: he positions the battlefield on the narrow strip of flat land to the west of the hill/ridge, saying that the Persians would only need a 100m for a cavalry charge. This is clearly ludicrous, and ignores Justin's refrence to the 'Adrasteian Plain'. To me, the battle was likely to have been fought in the plain more to the north of the hill/ridge. If the Biga ran in the same course as it did today, there would be a confluence with the Granikos near the hill.
The time is early morning, say 8 a.m., with fair weather. The Persians count as defending, and so deploy first, along the southern edge of the battlefield. The Macedonians deploy on the northern side of the battlefield - they may deploy elements of upto one command (but not Alexander's) on the north-western side of the river if they wish, to represent forces disguising their crossing (as at Hydaspes); all the other commands must be deployed across the river. Flank-marches are not permitted. Fight the battle until one side is broken. Hammond reports that trees grow abundantly along the banks of the river (though not thickly enough to count as DBM woods or orchards), and these would have provided some screen for Alexander's manoeuvers before crossing the river.
The odds of straight military victory are heavily weighed against the Persians. However, as the initial battle of a campaign, the Persians need not win the battle to score an important strategic victory - merely damaging the Macedonian army may be enough to win the war. To further spicen things up, we shall assume that Peter Green's hypothesis of an initial rash assault by Alexander the previous day has occurred, and that to recover his prestige, Alexander must personally lead his men to victory, or lose lasting influence with the Macedonain rank-and-file to Parmenio and the 'old-guard'. This will make the table-top battle more interesting, and less likely to result in an easy Macedonian victory.
Accordingly, to gain a complete victory, the Macedonians must break the Persian army without one of their own commands being broken, and Alexander's element must not only survive, but his element must destroy at least 15 AP worth of undemoralised elemnts in frontal combat (the historical outcome, with Spithridates' campanions going down to Alexanders').
A marginal Macedonian victory will be achieved if the Macedonians break the Persian army without one of their own commands being broken, and Alexander's element survives, but doesn't destroy at least 15 AP worth of undemoralised elements in frontal combat (the Macedonians win, but Alexander doesn't have full control over the Macedonian army, and has to settle for conquering just Asia Minor).
The Persians gain a complete victory by breaking the Macedonian army, or if Alexander's element is destroyed (jn frontal combat only), or if the Macedonians lose all 8 Bg elements (the campaign won't get far without supplies or money).
The Persians gain a marginal victory if Memnon's element is not destroyed (Memnon was the only decent general the Persians had, without him, they have much reduced chances in the future), AND, in addition, the Persians either A, break a Macedonian command (damaging Macedonian morale, and encouraging uprisings at Greece by demonstrating the Macedonians can still be beaten), or B, destroy Parmenios's element in close combat and prevent Alexander's element from destroying at least 15 AP of undemoralised elemnts in frontal combat (Alexander fails to redeem himself, but Parmenio is killed depriving the army of dynamic leadership), or, C, destroy at least four Macedonian Bg elements (seriously hampering the Macedonian advance).
Any other result is a draw.
Persian Cv (S) may not receive rear support from Cv (O), as these represent separate national contingents. This also ensures the Thessalian cavalry, graded (O), will have a frontal combat factor at least as high as their best Persian rivals by fighting double-ranked.
As an alternative rule, a general such as Alexander or Memnon is not autmotically killed if destroyed in close combat, and not automatically safe otherwise. In the case of a general's element being destroyed; after taking the requisite PiP-checks next bound (the troops won't know immediately what happened) roll a die. Add 1 if the element was destroyed in close combat with (at least some) enemy mounted troops; deduct 2 if destroyed when not in close combat with enemy. On a 5 or more, the great man is killed outright. On a 2 or less, he escapes barely injured. Next bound, before PiPs are rolled, his general's function is transfered to any one friendly element of the same command within 200p (if none available, he has to hide until the battle is finished). If a C-in-C this will allow the army to swap PiP dice again; it won't return a demoralised command to undemoralised however. On a 3 or 4, he is severely wounded and manages to make it off-field. He is treated as lost for purposes of the game, but not for victory conditions.
I have graded some of the Greek mercenaries as hoplites. The present DBM Macedonian list grades them all as "peltasts", whereas the same type of men in the Persian list are almost all hoplites. It has been argued that Persians were more in need of heavy infantry than light, since they had more than enough lights of their own, but no quality foot, and while this seems reasonable, it must be pointed out that of course the Macedonians also had more than enough light troops of their own, just taking Thracians and what-not into account, let alone native Macedonians (the pikemen could fight as peltasts if need be, as recorded at the siege of Halikarnassos). There seems to me to be little to recommend making all Greek mercenaries serving with the Macedonians peltasts, even if the majority were. Given the position of the Achaian mercenaries in the front line at the battle of Gaugamela (Diodoros, 17.57.5), these at least are likely to have been hoplites.
See Macedonian numbers and unit organisations has become so long, I have had to put them elsewhere! Follow this link.... The alternative (Arrian, Plutarch te.) version of this scenario is here.
Alexander of Macedon, P. Green, Uni.Cal.Press, 1991
Diodorus Siculus, esp. book 17 (here is the text on-line)
Plutarch's Life of Alexander
Plutarch's On the Fortune or Virtue of Alexander (in 'Moralia')
Justin 's Epitome of the Philippic History of Pompeius Trogus. Translated by J.C.Yardley, American Philological Association, Classical Resources Series, Scholars Press, Atlanta GA, 1994, ISBN 1-55540-951-2. Introduction and Notes by R.Develin.
Arrian's History of Alexander
P.A. Brunt, Alexander's Macedonian Cavalry; Journal of Hellenic Studies, 83 (1963), 27
Polyainos' Strategems and Excerpts. Translated by Peter Krentz and Everett Wheeler, Ares Publishers, 1994, ISBN 0-89005-503-3
Quintus Curtius' History of Alexander
N.G.L.Hammond, The Battle of the Granicus River; Journal of Hellenic Studies, 100 (1980), 73
I would like to thank Duncan Head, Nik Fincher and Michael Anastasiadis for so many useful discussions and ideas.