Silvermines Hydroelectric Energy Storage Project versus batteries

Pumped storage is cool. We have too much energy at night and not enough at peak times. So saving some electricity up is a good idea. 

One such scheme is €650m hydroelectric energy storage which will be able to store as much as 296 Megawatts (MW), with a daily storage capacity up to 2,175MWh of electricity. And employee 50 people long term.

It is just in the process of getting planning permission now. So it probably wont we operating for 7 years based on experiences elsewhere. 

Pumped storage has advantages of batteries. It doesn't go on fire. And the turbines last about 50 years not the 15-20 that batteries last. The initial infrastructure costs are high but once built it is cheap.

But just on the face of it how much would a battery version of the Silvermines project cost?

Technology	€/kW (power)	€/kWh (energy)	Notes
Pumped storage hydro (PSH)	~2,000–3,000 €/kW	~100–200 €/kWh	Civil-heavy, very site-dependent; long life (80–100y). Costs stable for decades.
Lithium-ion (utility scale, LFP)	~400–600 €/kW	~80–120 €/kWh	Costs have fallen ~90% since 2010; China auctions hit <€50/kWh module-only. Life ~15–20y, ~6,000 cycles.
Iron-air (Form Energy target)	~1,700–2,400 €/kW	~20–30 €/kWh	Still pre-commercial; very cheap energy, but low efficiency (~60%) and expensive per kW install (slower response). Life ~30y.

Iron-air batteries are inefficient and not widely used yet but they do get around the fire issue that worries people with lithium ion batteries. Lithium batteries have had a long term trend of more than halving in price every 5 years. 

It looks to me that at the moment pumped storage and batteries are about equal. Given how batteries keep getting cheaper though it is probably the case that by the time the Silvermines project completes they will seem to be the better option.

The best Worlde Words for the Lazy

 If you pick early words in wordle that have a lot of the commonly used letters you are likely to get to the correct word guess faster.

But say you were lazy and want to use the same 2 or 3 words all the time and then look at what letters hit or nearly hit to find the next word to guess. 

the best pair of words is 'raise' and 'clout' which leaves an expected remaining 5.1 words that could be the answer given what letters hit and near hit.
And the best 3 words are raise clout nymph which leaves 1.75 words on average that could still match the patters you will have seen.

These won't be as good as Crane followed by optimal picking of the next word given pattersnt hat were hit. But it will be pretty close and good for the lazy.

Grid Batteries could pay for themselves in 18 months in Ireland

I think grid batteries could pay for themselves in 18 months in Ireland. In January I calculated this as taking 3 years. 

Solar in May and June were enough here that it caused a bigger drop in wholesale price than usual during the day. You can see this as electricity prices drop below night time prices during the afternoons now.

This means that if you have a cheap enough battery it is economically feasible to buy at night and sell at 7am. And buy again at 2pm and sell at 8pm.

The recently set record-low tender price of €44 per kWh of battery storage, a one-kilowatt-hour battery following the May–June 2025 Irish spot-price spread would recoup its capital cost in  about 16 months on a gross basis, or  about 18 months after allowing for 90% round-trip efficiency. 

This is buying every night at 3am. Selling at 7am.
Buying again at 2pm and selling at 8pm. Losing 10% each time.
If you were clever and you could predict the best time that day to buy and sell for that day. Not just a do this everyday at this time strategy. These correct predictions would increase this profit. and reduces the payback time to 13 months including round trip losses. 

This wrongly assumes the all months are sunny like May and June were so spread persists year-round and excludes maintenance, inverter, and degradation costs. But also there is a lot of free electricity you would not have to buy at the wholesale price. ''2024's wind dispatch down rate is 14%'' means 14% of the time (usually winter nights) the electricity has no price and is not put onto the grid. Storing that, at your wind farm, and selling it in the morning is higher profit than our May/June calculations. Which would offset some of the lower profit from the lower solar then.

This is a rough calculation using Chinese battery prices but still it looks like a battery asset with a long lifespan is paid off in 2-3 years.

Code for this analysis is here

Solar has been doubling every 3 years for a long time. This graph might give some idea of what 2026 and 2027 will look like. The higher the peaks and troughs the higher the profit in storing the power.

An analysis of the last 365 days assuming knowing the perfect time to buy and sell electricity gives enough profit to pay for the battery at the Chinese tender prices. 

Period analysed: 2024-07-03 → 2025-07-03 (365 complete days)

Total profit: €45.01 per 1 kWh

Lido in the micro nation of Pimlico

I watched passport to Pimlico. A 1949 fantasy about the ability to buy fruit, clothes etc without rationing.

The post war labor government that introduced the NHS kept strict reasons and export controls. The film is effectively wish fulfilment about these being removed.

The 19 families in the besieged nation, in the bombers out ruins off Post WW2 London, build an outdoor swimming pool. Something Dublin can't do now

Euclid, Fermat, and the 65537 Reasons We Have Never Drawn Their Last Shape

 1. Straight Edge and Compass Euclidean Constructions

From the time of ancient Greece, geometers have been fascinated by what can be built using only two tools: a compass and a straightedge. These "Euclidean constructions" formed the foundation of classical geometry. You can copy a line segment, bisect an angle, draw perpendiculars Euclid's Elements are full of constructions and theorems that are built from these two tools.

But some polygons cannot be drawn this way. A regular 7-gon is impossible. Why? Because the set of constructible polygons is tied deeply to number theory, to Fermat primes.

2. Fermat Primes and Drawing Them

A Fermat prime is a prime number of the form

Only five such primes are known: 3, 5, 17, 257, 65537

Carl Friedrich Gauss at age 19 by proved that a regular polygon with sides is constructible if and only if is a product of a power of 2 and distinct Fermat primes. This means a regular 65537-gon is theoretically constructible.

One mathematician actually attempted to do it. Johann Gustav Hermes spent over a decade and 200 pages , detailing how to construct a 65537-gon using Euclidean methods in Ueber die Teilung des Kreises in 65537 gleiche Teile  in 1894. 

3. The 65537-gon

If you tried to actually draw a 65537-gon on a circle the size of the Earth (with of 6,371 km), each side would be approximately 611 meters long. Which means on a flat lake one side of the 65537-gon would not follow the earth's curvature by 3cm. A 65537-gon would be 3cm per 611 meter side off being a perfect circle. 

No one has ever made a by hand 65537-gon because it would just be too involved. though Hermes did spend ten years working out how it could be done in principle.

A 65537-gon (not a circle)

4. A Machine to Draw It for Us?

Could we build a machine that uses only a compass and a straightedge, like Euclid himself? Plotters could draw the 65537-gon by calculating angles and coordinates, but Euclid has famously tough lawyers and anyone making his shape not using his methods is likely to be mired in law suits

Such a Euclid Geometry machine would have to:

• Set distances using a mechanical compass

• Draw arcs

• Align a straightedge through marked points

• Draw straight lines with a pen

• Combine these steps tens of thousands of times

It would follow the ancient Greek rules of construction.

This would be rock hard to make and not practically useful. It would involve, aligning a  ruler through two points. Resetting a compass to exactly the distance between two previous marks, which is mechanically fiddly. Detecting intersections and points on paper. All of this is simple for Ancient Greek humans but not for machines.

And yet, it would be beautiful. It would make visible not just the result of geometric thinking, but the process. A Euclid-bot wouldn’t just draw geometry it would demonstrate it.

There are cool online geometry tools but something about plotters and physical drawing things still appeals. Maybe it would be possible to make a ruler and compass wielding machine that could finally draw the 65537 sides of the last Polygon.

Shock as Ireland goes mainly solar

 

In the Summer of 2026 there will be shock reported when solar energy supplies the majority of the power to the grid. 

When utility-scale solar reached a record output of 719MW during the early afternoon on August 31, rooftop solar is also estimated to have reached a record high output of 399MW. 

Demand at that time was 4300MW.

This won't happen this year. but I think it will in 2026 and when it does people will 
1. Claim this is a surprise
2. Ask about what happens at night
3. Ask about what happens in winter (which is actually a reasonable question)

38% annual growth rates of solar means that it will go from 50% at noon on the sunniest day of the year to near 100% at 4pm on a good day in May in a few years.

Drawing the US flag

 

 What happens to the US Flag they add more States

They have always added more stars sincde the original 13 up to the current 50.
There has been talk of Puerto Rico and Washington DC being added for some time. And recently Trump has been talking about adding Panama Canadian and Greenland.

Python Code Works

Here is some code to make a flag. 
The line to change the number of stars on each line is

layout = [10, 10, 10, 10, 10, 10, 10, 10] #60

the code is here and it is based on this original article.

51 stars is a hot mess

I cant work out how to make this nice. Maye a circle layout can do it. 

52 Stars looks better 

60 stars

Let's make Bee honeycomb more natural

Honeycombs in nature are not entirely regular. In a 2016 study, Nazzi found that cell size variation in honeycomb averaged just 2.1%, with standard deviation across samples of ±0.6%. This highlights how remarkably consistent bees are — yet not perfectly so.

A little irregularity might actually help bees, by making the environment less predictable for their enemies

• Mites might find entirely regular honeycombs easier to deal with
• Entirely regular honeycombs might produce bees with less variety in sizes
• This might make it easier for predators and parasites to specialise given less variance in the bees
• It might slightly reduce the variety of foods bees eat
  

When we manage hives, we often insert wax foundation sheets embossed with perfect hexagons to guide the bees' construction. But maybe we shouldn’t.
Maybe our foundation should closely match the natural variation bees already produce. It might be a small change — but one that works with evolution, not against it.

Here’s the code I used to simulate a naturally varied honeycomb layout.

import numpy as np

import matplotlib.pyplot as plt

from scipy.spatial import Voronoi

from shapely.geometry import Polygon, Point

def generate_jittered_hex_points(rows, cols, spacing=1.0, jitter=0.05):

"""Generate a grid of points in a hexagonal layout with jitter applied."""

points = []

h = np.sqrt(3) * spacing / 2 # vertical distance between rows

for row in range(rows):

for col in range(cols):

x = col * 1.5 * spacing

y = row * h * 2 + (h if col % 2 else 0)

# Add jitter

x += np.random.uniform(-jitter, jitter) * spacing

y += np.random.uniform(-jitter, jitter) * spacing

points.append((x, y))

return np.array(points)

def filtered_voronoi_polygons(vor, points, margin):

"""Return only Voronoi regions that are within the central margin area."""

regions = []

valid_polygon_centers = []

center_x = (np.max(points[:, 0]) + np.min(points[:, 0])) / 2

center_y = (np.max(points[:, 1]) + np.min(points[:, 1])) / 2

width = np.max(points[:, 0]) - np.min(points[:, 0])

height = np.max(points[:, 1]) - np.min(points[:, 1])

allowed_box = Polygon([

(center_x - width/2 + margin, center_y - height/2 + margin),

(center_x - width/2 + margin, center_y + height/2 - margin),

(center_x + width/2 - margin, center_y + height/2 - margin),

(center_x + width/2 - margin, center_y - height/2 + margin),

])

for point_idx, region_index in enumerate(vor.point_region):

region = vor.regions[region_index]

if not region or -1 in region:

continue

polygon = Polygon([vor.vertices[i] for i in region])

if allowed_box.contains(Point(points[point_idx])):

regions.append(polygon)

valid_polygon_centers.append(points[point_idx])

return regions

# Parameters

rows, cols = 20, 20

spacing = 1.0

jitter = 0.042 # to get an average of 2.1% jitter

points = generate_jittered_hex_points(rows, cols, spacing, jitter)

# Voronoi diagram

vor = Voronoi(points)

# Margin (in same units as spacing)

margin = spacing * 1.0 # Leave one cell of wax space around

# Get filtered polygons

filtered_polygons = filtered_voronoi_polygons(vor, points, margin)

# Plotting

fig, ax = plt.subplots(figsize=(10, 10))

ax.set_aspect('equal')

ax.axis('off')

for poly in filtered_polygons:

x, y = poly.exterior.xy

ax.plot(x, y, color='black', linewidth=0.5)

plt.savefig("jittered_voronoi_clean_edges.png", dpi=300, bbox_inches='tight', pad_inches=0)

plt.close()

As well as encouraging natural variation in cell size, I would also like to see foundation sheets reflect the natural tilt of honeycomb cells.
Bees build each cell with a slight upward slope, typically between 9 and 13 degrees, averaging around 9°. 

While bees in managed hives do seem to recreate this slope reliably on their own, adding a subtly varied tilt to the foundation embossing rather than a perfectly uniform angle. Mind you, since bees usually reproduce this slope, sloped embossing is likely less useful than capturing variation in cell size.

There's also a theory that a small number of undersized cells in the comb may help control Varroa mites. The idea is that bees raised in smaller cells hatch slightly earlier, disrupting the mites' reproductive cycle. While results from studies are mixed to negative, it's another reason to consider embracing natural variation, rather than enforcing a rigid cell size across the hive.

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

We have a 'Can I get a Loan?' Problem

I made a chatbot for a bank a decade ago and one answer was getting terrible ratings from users. I looked up the questions being asked that lead to the answer and they should have gone to that answer. I checked the answer in case it was rude, unclear or missing details and it was not.

The 'bad' answer was not wrong it was just what people did not want to hear. It was telling people they were not qualified for an immediate loan and giving details of how they could try a slower method to get a loan. The answer was not wrong just not what people wanted to hear. 

LLMs have gotten so good at telling us what we want now that they just make stuff up more than they used to. There is a great article here on the increasing misalignment. Hee hallucination growing is an indication the LLM is making stuff up to make us happier.

We should reward correctness (including in the steps getting to the answer) than people liking the answer. But the incentives of the testing mechanism and more seriously the companies making LLMs do not do this. If users prefer LLMs that tell them they are great and give plausible sounding reasons why they should do what they want to do these will be more popular. 

Dirk Gently's Holistic Detective Agency by Douglas Adams has a program called REASON that LLMs are turning into. It which would take any conclusion you gave it and construct a plausible series of logical steps to get there.

They will give us a series of plausible sounding steps that will make us happy. It is us who are misaligned not just the LLMs

Doctor Deaths in the Famine

During the famine doctors cared that many of their number were dying. the collected data and wrote up their findings in the The Dublin quarterly journal of medical science Volume 5, 1848. in the section Art. VII. — On the Mortality of Medical Practitioners in Ireland. Second Article. By James William Cusack, M. D. President of the Royal College of Surgeons, and William Stokes, M. D., Regius Professor of Physic in the University of Dublin.

These data tables seem never to have been graphed before. But now using OCR it is really easy to extract the data. Here for the first time ever is graphs of what doctors recorded as killing them

A python notebook to make these is here and data here.

Football ball improvement is back

There is a trade off between how fast a football goes and how much control you have on it. And football designers are always trying to get a ball that goes faster and that has great control. The trade off involves seams (panels) big bumps. The texture of the ball (tiny bumps). This is a graph to tell the story of how theyre has been back and forth over time as technology tries to get us to 1 panel but also sometimes we go to far and step back.

Bray's prediction of one panel by 2022 and why 

Nature paper on football shape 

The drag crises, spin and how the 2024 football works 

I talked before about how we should be playing with 1 panel balls by 2022 here 

Code and data for this graph is here 

Grid Battery Payback Time

Grid batteries, at current Irish wholesale prices, would pay for themselves in 2 years with a optimal strategy and 3 with a simple one. 

This latest auction for supplying batteries to the Chinese grid had a lowest bid at CNY 0.458/Wh ($63/kWh) That is 61 euro. Times a thousand for MWh of storage is 61,000 euro.

Irish wholesale electricity prices per hour are here.

If we take the price at the cheapest hour that day and say we fill the battery at that time. And add 20% to the cost to account for round trip losses. And then the price at the most expensive hour that day for the discharge the profit made is shown below.

A simple strategy of buy at 3am and sell at 5pm takes 3 years to pay off. So the practical optimum is somewhere in between.
The 20% round trip losses means it only occasionally makes sense in 2024 to top up at night, sell in the morning peak time. Top up at noon using solar and sell at 5pm peak again. But Solar has been increasing 38% year on year for decades so this strategy would work a lot better in future. Twice the usage would result in faster payback times.

A fair amount of Irelands wind energy is just lost. This could be bought very cheap near where it is made and later fed back into the system. Wind Energy Ireland said that over 3% was lost last year as due to wind farms being shut down because the electricity grid is not strong enough. Local buying and storage of that excess 3% would be very cheap as at the moment it is wasted. And this locally cheaper price is not reflected in all Ireland wholesale prices used in the calculation.

Business people do not miss opportunities to get the price of a 20 year long asset like grid batteries paid off in 2-3 years. So something must be stopping them adding these batteries at the moment. But knowing what could be achieved now without constraints is still an interesting exercise if we want to work out what constraints need to be reduced.

The code for this analysis is here and i can update it with more realistic assumptions as I learn them.