Percy Ludgate: Early Computer Pioneer and his Irish Logarithms

 

Irish Logarithms are a multiplication method invented by Irishman Percy Ludgate in 1909. 

1. Why use Logarithms

a logarithm transforms multiplication into addition:
logb(x⋅y)=logb(x)+logb(y)

By storing precomputed “log” values and then adding them, we reduce the hard part of multiplication to a single addition followed by a lookup (the inverse logarithm).

Classical log-based multiplication steps:

1. Log lookup: retrieve and from a table.

2. Add: compute .

3. Anti-log lookup: retrieve from another table.
   
   
   

2. What Irish Logarithms involve 

To multiply two one digit numbers

table1 = [50, 0, 1, 7, 2, 23, 8, 33, 3, 14]

table2 = [ 1,  2,  4,  8, 16, 32, 64,  3,  6, 12, 
          24, 48,  0,  0,  9, 18, 36, 72,  0,  0, 
           0, 27, 54,  5, 10, 20, 40,  0, 81,  0, 
          15, 30,  0,  7, 14, 28, 56, 45,  0,  0, 
          21, 42,  0,  0,  0,  0, 25, 63,  0,  0, 
           0,  0,  0,  0,  0,  0, 35,  0,  0,  0, 
           0,  0,  0,  0,  0,  0, 49,  0,  0,  0, 
           0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
           0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 
           0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 
           0]

Lets say 4*5. Look up the 4th position in table 1. That is 2 (table starts at 0). and the 5th is 23. Add these together to get 25.
Now look up the 25th position in table 2 (the anti-log table) is 20. the right answer.

To do multi digit multiplication you do the multiplication of individual digits and then add them like in school. 

Ludgate worked out this logarithm and anti-logarithm mapping himself which in a pre computer time was a huge amount of effort.  As he wrote 'the result of about six years' work, undertaken . . . with the object of designing machinery capable of performing calculations, however, intricate or laborious, without the immediate guidance of the human intellect'

3. Who was Percy Ludgate

He was an Irish accountant and computer pioneer who invented the second ever design for a Turing complete computer. and one that was much more practical than Babbage's. But he never got the money needed to construct it.

Brian Coghlan has done a huge amount of research on Ludgate's computer. There is a popular press  article on Ludgate here

Ludgate's original article describing his computer is here. The Irish logarithms were only one of his inventions needed to make a practical computer. I think his story should be better known. 

4. Hex Irish Logarithms


Here is the python code to work out what the base 16 hex Irish logarithm would be. For no reason other then no one else seems to have worked it out before. 

#!/usr/bin/env python3

# Requires: pip install z3-solver

from z3 import *

# 1. Variables Z0…Z15, plus M

Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14, Z15 = \

Ints('Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z13 Z14 Z15')

Z = [Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14, Z15]

M = Int('M')

opt = Optimize()

# 2. Symmetry-breaking: log(1)=0, log(2)=1

opt.add(Z1 == 0, Z2 == 1)

# 3. Bounds on Z1…Z15 in [0..M], and send Z0 out-of-range

for i in range(1, 16):

opt.add(Z[i] >= 0, Z[i] <= M)

opt.add(Z0 == M + 1)

# 4. Force worst-case = sum of two largest primes 13+13

opt.add(M == Z13 + Z13)

# 5. Prime-ordering to break permutations

opt.add(Z2 < Z3, Z3 < Z5, Z5 < Z7, Z7 < Z11, Z11 < Z13)

# 6. Collision-avoidance for all non-zero digit-pairs

pairs = [(a, b) for a in range(1, 16) for b in range(a, 16)]

S = {(a, b): Z[a] + Z[b] for (a, b) in pairs}

for i, (a, b) in enumerate(pairs):

for (c, d) in pairs[i+1:]:

if a*b == c*d:

opt.add(S[(a, b)] == S[(c, d)])

else:

opt.add(S[(a, b)] != S[(c, d)])

# 7. Ensure every valid sum ≤ M

for (a, b) in pairs:

opt.add(S[(a, b)] <= M)

# 8. Minimize M

opt.minimize(M)

# 9. Solve & report

if opt.check().r == 1: # sat

model = opt.model()

# Convert each Z[i] (an IntNumRef) into a plain Python int

table1 = [model[Z[i]].as_long() for i in range(16)]

M_val = model[M].as_long()

print("Minimum max-sum M =", M_val)

print("Table1 (Z0…Z15) =", table1)

max_sum = max(table1) + max(table1)

print("Verified max_sum =", max_sum)

else:

print("No solution found")

Minimum max-sum M = 178 Table1 (Z0…Z15) = [179, 0, 1, 21, 2, 51, 22, 77, 3, 42, 52, 85, 23, 89, 78, 72] Verified max_sum = 358

Visiting Santa's Grave

I found out recently that Santa is buried in Ireland. No really he is and you can go visit his grave. Though a bonus, I didn't go to avoid having to get the sprog Christmas presents, I'm pretending to be Buddhist to do that.

Thomastown in Kilkenny is a funny town. It is beautiful looking and full of hippys but also has a rough edge to it. There are all sorts of art workshops and tea shops that the posh people run during the day and at night there is an air of menace and divilment about some of the pubs there.

John Martyn the towns most famous resident seems to also traverse these two characteristics. He has the hippy spirituality of his friend Nick Drake but also looked and acted like he was well up for a row.

It turns out that Thomastown may have always had the strange mixture of spiritual and hedonistic. Just outside the town is the famous Jerpoint Abbey and close to there is the newly rediscovered and Newtown.

The story of Newtown is that some Norman knights from Kilkenny headed off on the crusades in the 12 century. Taking religious relics was one of the major hobbies of the time like pokemon but with dead people. These two took back to Newtown what they claimed were Santa's bones and relics of St Nicholas. The story goes they got these in modern day Turkey. The aim of collecting these was possibly to create a tourist attraction to compete with other relics in Ireland. There is no way of telling at this remove that they were but contemporary accounts at least reveal that the people of the time believed they were.

The town thrived with these relics used as a draw for tourists and pilgrims. A three story church of St Nicholas was built.

A town developed around it including three mills. Eight pubs and a whore house the remains of which still exist. This was out of a total of 13 houses so pubs played a big role in the town. This shows religious pilgrimage may not have been so holy.

The town is at the last navigable point on the Nore, where it meets the Arygle.

These rivers powered the mills and allowed fish farming in the floodplain. Fish farming still takes place in the next door Goatsbridge farm which shows how little changes over time.

On the grave of Santa himself is the famous symbol of St Nicolas, the three figures.

These represent the three bags of gold Santa put down the chimney to pay the dowry of a poor mans three daughters. This both explains Santas chimney shimmying antics and the Pawn shop symbol. St Nicholas is the patron saint of pawn shops.

The guide explained the three heads on the gravestone as representing St Nicholas and the two crusaders who took his bones back to Ireland. The three figures symbol was generally thought to represent Jesus and Mary in medieval symbols.

The town was abandoned when the plague struck around 1346. Mills were havens for rats and towns were decimated while the more Gaelic countryside was much less effected. Monk John Clyn in nearby Kilkenny as the plague descended wrote the chilling 'so that the writing does not perish with the writer, or the work fail with the workman, I leave parchment for continuing the work, in case anyone should still be alive in the future and any son of Adam can escape this pestilence and continue the work thus begun'. The bridge over the river collapsed though the remains can still be seen. And the very existence of the town faded from memory to only recently be rediscovered. The stones from the houses were used in the railway bridge you can see form the ruins of Newtown.

The grave of St Nicholas is well worth a visit. The tour is informative and entertaining. The site is not over developed like some Irish tourist destinations. And the trip ends on the brilliant Father Ted touch of watching a sheep dog herd geese. Next time you are in Kilkenny head to Thomastown and Jerpoint and take the right lane up by the fish farm, it will at least save you money on Christmas presents.

How byzantine was the Byzantine civil service?

Byzantine is a descriptive adjective for a very complicated bureaucracy

Byzantine: Highly complicated; intricate and involved: a bill to simplify the byzantine tax structure.

Byzantine: (of a system or situation) Excessively complicated, typically involving a great deal of administrative detail - Byzantine insurance regulations

John D Cook talks here about how the Roman bureaucracy was less than the size of Heuston's. How does the Roman Empire figure compare to a famously bureaucratic empire?

According to recent historians the Byzantine empire did not have that many beaueacrats '‘In terms of staff numbers the Byzantine bureaucracy was relatively small: a recent estimate for the ninth century central civil service places the number of core staff at five to six hundred men, split between thirteen different bureaux or departments of state’'

This was in an empire of around 7 million people. France has about 90 civil servants to 1000 people. Which by the per capita numbers in more than 1000 times the dictionary definition of bureaucratic.

Theatre Riots In Irish History

We detail the events that marked a new low in Ireland’s relationship with drink, drugs and casual violence

Were the events at the Phoenix Park last weekend uniquely bad in Irish history? I am not arguing here that they were acceptable, I just want to see if they were a uniquely low level? Ireland was fairly well known in the past of excessive drinking, fighting and sex at festivals. The sedate suburb of Donnybrook and its poshest shop gave English eponymous nouns for excess

Donnybrook: an inordinately wild fight or contentious dispute; brawl; free-for-all.

Donnybrook Fair: a fair which until 1855 was held annually at Donnybrook, County Dublin, Ireland, and which was famous for rioting and dissipation.

If the original Donnybrook fair rave can give rise to the fancy shop of the same name maybe in 2200 Ikea will be called the Swedish House Mafia. But an Oxegen squared in the 1800's doesn't prove much. Were Irish concerts generally well behaved?

THE BEST PLACE for a good riot is a theatre. The left likes to imagine rioting as the oppressed rising up against the oppressors, and the right sees it as evidence of the moral decay of society. But there’s a long history, in Dublin and London, of theatrical rioting. Indeed, to my knowledge, the longest and most sustained riots in both cities in the past three centuries happened in and around theatres. This surely says something about the nature of both theatre and riots.

According to the history of Irish theatre the Smock alley riot of 1747 suggests not. Just down from the Phoenix Park Smock Alley was where Trinity Toffs seemed to go to feel superior. Edmund Kelly a student went backstage told an actress Mrs Dyer that he would 'do what her husband Mr Dyer, had done to her', using the obscene expression. Another young Trinity student of the time, Edmund Burke, saw Kelly put his hands 'under the actress's petticoats'. Edmund Burke the intellectual founder of conservatism is now considered venerable enough to have a statue outside Trinity. The manager Sheriden kicked Kelly out but because he was not a 'gentleman' Kelly demanded an apology. Rioting shut the theatre and spread to the streets. Days of riots followed over whether a theatre owner stopping a girl getting raped could say "I am as good a gentleman as you are” about a would be rapist.

In 1821 the Bottle Riots also started in a theatre. 'Orange sentiment which, in the heated condition of public opinion, had become dangerous, and he prohibited the dressing of the statue of William III. on College Green on July 12, then regarded as an annual demonstration. This was followed by a riot, afterwards known as "the bottle riot," when an organized body of Orangemen packed the pit and gallery of the Dublin theatre when the Marquess was present and with cries of, "Down with the Popish Lord-Lieutenent" they flung missiles, one of which was a large whiskey-bottle, at the royal box'

Next up in the entirely 21st century phenomena of fights at concerts is the 1851 riot in the Mechanics theatre

The Beatles song "Being for the benefit of Mr Kite" was inspired by one of the posters of Pablo Fanque the proprietor the night of the riot. 'playgoers threatened to riot and destroy the theatre in protest to the winner of a "conundrum" contest' which puts loud words at someone using a mobile during the pub table quiz into perspective.

Synge’s The Playboy of the Western World and O’Casey’s The Plough and the Stars also incited riots. The Playboy riots were incited by Arthur Griffith the President of Dáil Éireann. He described the play as "a vile and inhuman story told in the foulest language we have ever listened to from a public platform". O'Casey's riot was seen by Yeats as again showing how uncouth Irish concert goers were "You have disgraced yourself again, is this to be the recurring celebration of the arrival of Irish genius? Wilde's Salome caused a bit of a ruck as well but does not seem to have descended into open fighting.

There is a long history of people having fights at concerts. History seems to better remember those with political roots unlike what happened in Phoenix Park. To decide this is a particularly bad incident requires us to at least look at the history of these riots.

That's no way to kill an elephant

It seemed dreadful to see the great beast Lying there, powerless to move and yet powerless to die, and not even to be able to finish him. I sent back for my small rifle and poured shot after shot into his heart and down his throat. They seemed to make no impression.

wrote George Orwell in Shooting an Elephant

I read Orwell's essay ages ago and figured it pretty much had the elephant execution story covered. Looking back I was amazingly naive about quite how many bizarre possibilities for dispatching pachyderms existed.

1. Hanging. Erwin, Tennessee thought it was a good idea to hang Mary the elephant.

2. Electrocution. In order to show that his DC current was a great idea Edison decided to show AC was really dangerous. So he got Topsy the elephant and electrocuted her. Which is a massively dick move anyway you cut it. He also invented and sold the electric chair to execute criminals as a similar negative publicity campaign against AC current. The video he produced is here

3. Shooting. Tyke (elephant) Police fired 86 shots at Tyke, who eventually collapsed from the wounds onto a blue car and died. This video is of Tyke's attack and later shooting. I am not going to embed it as it is frankly horrifying.

4. Harpooning. Chunee "Kneeling down to the command of his trusted keeper, Chunee was hit by 152 musket balls, but refused to die. Chunee was finished off by a keeper with a harpoon or sword". Having to harpoon an elephant has to be the definition of a hard day at work.

Not execution but still weird

5. Lethal Injection of LSD. Tusko was a 14 year old who weighed 32000kg. Some scientists decided to give him enough LSD to get 3000 people off their mash. This mammoth dose killed him under two hours later. The scientific paper that came out of this mess is "Lysergic Acid Diethylamide: Its effect on a Male Asiatic Elephant."

6. Lightening "Norma Jean, struck by lightning, c. 1972, during a circus parade in Oquawka, Illinois. She was buried where she died, and a marker now lies on this spot."

7. Drowning (ish). Dan Rice was a sort of PT Barnum character. He ran loads of stunts to advertise his various travelling circus events. One of these for one poor elephant was "In August 1860, Rice had Lallah Rookh swim across the Ohio River in Cincinnati, Ohio to drum up publicity for his new "Monster Show." It took her 45 minutes to swim across the river. A month later, Lallah died of a fever brought about by her swim".

While on this elephantine swimming subject my favourite theory about the Loch Ness Monster is that it was a swimming circus elephant. And once the mistake was made the circus owner used the publicity to drum up business 'In 1933 a circus promoter in the area—acting perhaps on inside information that the monster was really a big top beast—offered a rich reward for Nessie's capture'

8. Burning. In 1681 an elephant was burned to death in Dublin. How the poor creature got to Dublin at that time is difficult to imagine. But then to have your crate set on fire is just tragic. The autopsy revealed information that later helped show elephants had evolved from an aquatic animal. "An anatomical account of the elephant accidentally burnt in Dublin on Fryday, June 17 in the year 1681" is Allen Mullen's description of the autopsy

And the weirdest one, and I realise that is saying something, is not an execution of elephants but by elephants. Most of the elephants killed listed above had killed a person. But elephants were once a really common. Apparently death by Nelly was wildly popular from prehistoric times up until the late 1800s. Execution by elephant is an incredible wikipedia page, hard to extract from but worth reading through.

Because elephants are so easy to train and because an elephant standing on your head was such a gruesome way to die most south Asian countries seemed to practice it.

I do not know what the wide an varied history of death of and by elephant tells us. They are all pretty tragic tales. Recently an elephant escaped in Cork . Then later crushed one of the circus workers. It seems the same sort of issues that killed Chunee, Mary, Tyke and many people who have been killed by performing elephants still exist and that more than these historic stories is a tragedy.

Predictions for 2030

I have no idea what will happen to the euro in the next month. And whatever happens will have big consequences. Yet I was willing to make predictions for 2030 about lbr, driverless cars, solar power and education in my last post.

The thing is I think I am cheating with technology predictions. Theres a wildly unpopular branch of Marxism that argues for technological determinism. Marx can be interpreted as saying that our technology is inevitable and will change us in unavoidable ways. "The windmill gives you society with the feudal lord: the steam-mill, society with the industrial capitalist"

After reading "What technology wants" by Kevin Kelly I am a convinced technological determinist. There is a podcast from Kelly on technology at econtalk

The book makes a compelling case that

1. You cannot shut yourself off form technological change. The Japanese tried it and failed. The Amish dont try it, they stay about 50 years behind on average but they do not avoid new technology forever.

2. No technology ever dies out.

3. Each new technology is an inevitable consequence of the last. No one person of country can cause or prevent a new technology, though they can shape its exact form.

Almost all patents of significant technologies have multiple very similar independant patents lodged at nearly the same time. Airplanes, radio, transisters, computers, television whatever you can think of about three guys thought of it and implemented it independantly within a few months of each other. This suggests that once the right prior technologies exist the next one is inevitable.

Kevin Kelly: What Technology Wants

Keynes wrote about 2030 in 1930 in the article “The Economic Possibilities for Our Grandchildren.” which has been surprisingly on accurate for the last eight decades. So I am betting it will continue to be for the next two. He made brought claims about future growth rates that have been accurate. I will make similar claims now. Given that I dont think non technological predictions can be made I am going to try anyway
1. Grinding poverty will be gone. This is a low bar of 365 dollars a year in 1990 dollars. Thats really bad. Much worse than medieval England but it is one I think we can reach.

2. Polio and guinea worm will be eradicated.

3. World population will be slightly lower than the medium UN estimate of 8321380. The high is 8776486 and the low is 7867332. So I will guess 8250000.

This is just a few predictions based on the world continuing to go the way it has for the last two hundred years. But like I said I cannot predict what will happen to the cash in my pocket over the next two months so two decades away is being ambitious. If you have any predictions for 2030 please put them in the comments. It might be fun for the floating brains in a jar to laugh at them at the time.

The Dead Zoo Dodo

I have mentioned before my weird obsessions with taxidermy, weird tourist destinations and tall dwarfs but I have not mentioned here my first scientific obsession: Dodos

Adam Savage the Mythbuster talks here about the same obsession he has


Like Möbius strips, Dinosaurs and Steve Reich, Dodos are like flypaper for nerds. There is just something about these things that seem to spark off nine year olds and set them off on a lifetime being the makers and doers of nerdy things. It was the dodo in the natural history museum of Ireland, known locally as "the dead zoo" that set me off at this age.

Unfortunately this dodo is no longer viewable to the public. I was in the museum last week, admiring the cool steampunk Victoriana makes the museum as interesting for what it says about the 1800's when it was created as about the animals in it. For example the polar bear still has an obvious bullet mark in its head, you would not see that in a modern museum.

The museum was bigger but large areas are no longer open
Exhibition space does a dodo and vanishes

The museum shut on July 5, 2007, when a flight of the main staircase collapsed. The Department of Arts originally decided to take the opportunity to carry out a €15m renovation and extension, but that was cancelled last year due to the state of the public finances.

Instead the staircase was reinstated and other minor repair works carried out, but two large balconies on the second floor have been shut off from the public due to health and safety concerns. The museum’s biggest attraction, a skeleton of a dodo, is on one of these balconies and, unless it is moved, will no longer be viewable by visitors.

Cuts keep half of 'Dead Zoo' exhibits out of public view

However, some of its best known exhibits, including a dodo skeleton and a piece of moon rock given to the State by the US, will not be on public view for the foreseeable future.

This glass box in the top floor bottom middle holds the Dodo skeleton.

The Dodo is one of the most iconic images of environmentalism before Stuart Brand persuaded Nasa to take a release of the earth the phrase "as dead as a dodo" was one of the best metaphors for the fragility of nature that we had. This sight of these bones is an important warning for us and we should make every effort that nine year olds now get to see them. For this reason I want to see the Dublin NHM Dodo moved down to a floor that is open to the public. Moving a glass box is not going to make a massive improvement to the world, but it should also not be a huge difficulty. A full restoration of the museum would be vastly preferable to this but this would be a relatively simple change to make in the meantime. This dodo is important the Natural History Museum badge has a dodo on it which says to me it is one of the most important and interesting items in the museum.

Here is my favorite song sung by an extinct flightless bird The Mountain Goats- Deuteronomy 2:10

I'm all alone here as I try my tiny song
Claim my place beneath the sky but i won't be here for long
I sang all night the moon shone on me through the trees
No brothers left and there'll be no more after me

The Bayeux Tapestry is a Swashbuckling Adventure

I went to see the Bayeux tapestry a few days ago. If you are ever in Northern France go see it. It is an amazing experience to see a thousand year old hand made item, particularly one that tells a story. Seeing the individual threads and mistakes of something that old is just breathtaking.



But one thing that struck me about it is how fun the story is. I imagined it either as a dry scolarly repetition of the story or an ancient piece of propaganda. Instead it is more of a swashbuckling adventure. Compare one swashbuckling film 'The Princess Bride' with the tapestry and see the similarity. They both have

Kidnapping
Harold gets kidnapped when he lands in France




Quicksand
Harold rescues two men from Quicksand



I really miss quicksand it used to be everywhere "nearly 3 percent of the films in that era (the 60s) showed someone sinking in mud or sand or oozing clay". But you just don't see it anymore. It has sadly gone the way of grappling hooks and that using a knife to slide down a sail trick.


Abseiling
A guy they are trying to catch uses a rope to escape.




Forced Marriage
Williams daughter is married by herself with a priest slapping her.


The princess bride marriage is also forced

God's Hand
Monty Python style God's hand comes from the clouds.


Which is a bit like having a miracle man around

Sword Fights




And the tapestry has all sorts of other stuff you see in matinee adventures like horse chases, giant animals, oaths, dragons and divine heavenly light


In Table form you can see the genre cliches


Obviously the Bayeux Tapestry served many purposes at the time. But I think we might underestimate one of those was entertainment. You could remake this story now as 'Indian Jones and the Norman Conquests', it is already in comic book form.